This dissertation has been 64-9559 microfilmed exactly as received
ESKRIDGE, Jess Boyd, 1 9 2 8 - INVESTIGATION OF THE HOROPTER AND THE APPARENT FRONTAL PLANE.
The Ohio State University, Ph.D., 1964 Physiology
University Microfilms, Inc., Ann Arbor, Michigan
INVESTIGATION OP THE HOROPTER AND THE APPARENT FRONTAL PLANE
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By JESS BOYD ESKRIDGE, B.Se., M. Opt., M.Sc.
******
The Ohio State University 1964
Approved by:
ISLXJKAAA/\ v/\ • rv Ad vise i* School of Optometry ACKNOWLEDGMENTS
A list of those individuals who have aided me in the attainment of this goal would indeed be long, and the acknowledgment of each would be impractical. I would be amiss, however, if I did not give special recognition and express my sincere appreciation to these few. I am grateful to Dr. Fred Hebbard for his interest and for the incentive that he gave me to begin graduate study, to the members of the American Optometric Foundation for the Research Fellowship awarded me made it possible for me to pursue this program, and to Dickson Call and the staff at the Ohio State University Numerical Computation Laboratory for their assistance in programming and operating the 1620 IBM computer. Only those who have "trod this path" can fully appre ciate the encouragement, guidance, and help given by my adviser, Dr. Glenn A. Fry. His devotion and the unselfish giving of his time, effort, and knowledge have been and will always be a stimulating example to those that know him. In an undertaking such as this, the support and interest of wife and family are invaluable, and I want to gratefully acknowledge the constant encouragement and assistance given by my wonderful wife, Beth, and my children, Chris and Cheryl. ii CONTENTS Page
INTRODUCTION...... 1 APPARATUS ...... 9
METHOD OF ANALYZING D A T A ...... 30 EFFECT OF CHANGE IN FIXATION DISTANCE ON THE HOROPTER AND THE APPARENT FRONTAL PL A N E ...... 35 EFFECT OF PROLONGED WEARING OF MERIDIONAL MAGNIFIERS ON THE HOROPTER AND THE APPARENT FRONTAL PLANE . . . 88
EFFECT OF ASYMMETRICAL CONVERGENCE ON THE HOROPTER, THE APPARENT FRONTAL PLANE, AND THE APPARENT NORMAL PLANE ...... 108 SUMMARY AND C O N C L U S I O N S ...... 128
BIBLIOGRAPHY...... 133 AUTOBIOGRAPHY ...... 135
111 FIGURES Figure Page 1. Hie horopter according to Aguilonis...... 3 2. The horopter according to Vieth and Mfiller . . . 4 3. Apparatus used to determine the horopter . . . . 10 Diagram of the apparatus vised to determine the horopter ...... 11 5* Diagram of the slides used to determine the horopter and the apparent frontal plane . . . . 15 6. Apparatus used to determine the apparent frontal plane and apparent normal plane . . . . 17 7. Diagram of the apparatus used to determine the apparent frontal plane and apparent normal plane...... 18 8. Diagram showing relation between size of the target and the apparent angular displacement of the target at the entrance pupil of the eye. 21 9. Apparatus used to calibrate separation of lenses and the apparent angular displacement of the target at the entrance pupil of the eye. 22 10. Ratio of the apparent angular displacement of the target to the linear dimension of the target as a function of the lens separation . . 24 11. Apparatus used to calibrate the target-prism separation and the displacement of the eccentrically located fixation line ...... 25 12. Apparent separation of target elements as a function of target-prism separation ...... 28 13. Diagram showing Vleth-Mttller Circle, objective frontal plane, and angles used in analyzing d a t a ...... 31 iv FIGURES— Continued Figure Page 14. Horopter apparatus of Ames et al ...... 36 15. Screens used In grid-nonius method of Ames et a l ...... 37 16. Binocular appearance of wires In grld-nonius m e t h o d ...... 3d 17. Horopter data of Ames et al. with fixation distance of 75-6 c m ...... 40 18. Horopter data of Ames et al. with fixation distance of 40.4 cm ...... 41 1 9. Horopter data of Ames et al. with fixation distance of 20.2 c m ...... 42 20. Analytical graph of horopter data of Ames et al. with fixation distance of 75*6 c m ...... 43 21. Analytical graph of horopter data of Ames et al. with fixation distance of 40.4 c m ...... 44 22. Analytical graph of horopter data of Ames et al. with fixation distance of 20.2 c m ...... 43 2 3. Hering-Hlllebrand deviation of the horopter data of Ames et a l . as a function of the fixation distance ...... 46
24. Horopter data with parallel lines of sight . . . 51 25. Horopter data with fixation distance of 100 cm . 52
26. Horopter data with fixation distance of 5 0 cm . . 53 2 7. Horopter data with fixation distance of 25 cm . . 54 28. Horopter data with fixation distance of 16.66 c m ...... 55 29. Horopter data for all fixation distances .... 5 6 v FIGURES— Continued Figure Page 30. Number of retinal elements per unit length as a function of linear distance from the fovea determined from Osterberg*s d a t a ...... 53
31. Analytical graph of horopter d a t a ...... 61 32. Hering-Hillebrand deviation of the apparent frontal plane as a function of the fixation distance for data of Zajaczkowska, Helmholtz, and Ames et al...... 65 33- Apparent frontal plane data with parallel lines of s i g h t ...... 69 34. Apparent frontal plane data with fixation distance of 100 c m ...... 70 35* Apparent frontal plane data with fixation distance of 50 c m ...... 71 3 6. Apparent frontal plane data with fixation distance of 25 c m ...... 72 3 7. Apparent frontal plane data with fixation distance of 16.66 c m ...... 73 3 8. Analytical graphs of apparent frontal plane data for fixation distances of infinity, 100 cm, 50 cm, and 25 c m ...... 75 39. Analytical graphs of apparent frontal plane data for fixation distance of 16.66 cm .... 76 40. Analytical graph of apparent frontal plane data for all fixation distances...... 77 41. Hering-Hillebrand deviation of the apparent frontal plane as a function of fixation d i s t a n c e ...... 78
vi FIGURES— Continued Figure Page 42. Apparent frontal plane data with fixation distance of 40 cm using horopter apparatus . . 79 43. Analytical graph of apparent frontal plane data using horopter apparatus with fixation distance of 40 cm ...... 80 44. Hering-Hillebrand deviation of the apparent frontal plane and the horopter as a fvinetion of fixation for data of Ames et al ...... 83 45. Diagram to explain Fry's concept of the relation of the horopter to perceived object position ...... 85 46. Percent magnification needed f W apparent frontal plane determinations using the horopter apparatus during the prolonged wearing of a meridional magnifier. From B u r l a n ...... 90 47. Percent image size difference measured with the ophthalmoeikonometer and space elkonometer during the prolonged wearing of a meridional magnifier. From M i l e s ...... 92
48. Percent difference in magnification needed for apparent frontal plane determination during the prolonged wearing of a meridional m a g n i f i e r ...... 102 4 9. Percent difference in magnification needed for horopter determinations during the prolonged wearing of a meridional magnifier ...... 104 50. Reference planes during asymmetrical convergence. F ... F' frontal plane, N ... N* normal p l a n e ...... 109 51. Horopter and apparent normal plane data with symmetrical and asymmetrical convergence. From Herzau and O g l e ...... 113 vli FIGURES— Continued Figure Page 52. Spatial plot of horopter and apparent normal plane data with symmetrical and asymmetrical convergence. From Herzau and O g l e ...... 116 53. Horopter data with symmetrical and asymmetrical convergence ...... 118 54. Apparent frontal plane and apparent normal plane data with symmetrical convergence and 4° of asymmetrical convergence...... 120 55. Apparent frontal plane and apparent normal plane data with symmetrical convergence and 10° of asymmetrical convergence ...... 121 5 6. Analytical graphs of apparent normal plane data with symmetrical convergence and 4° and 10° of asyranetrical convergence...... 123 57. Spatial plot of apparent normal plane and apparent frontal plane data with sym metrical and 10° asymmetrical convergence . . . 126
viil INTRODUCTION
When an object Is placed in the visual field, the observer Is aware that it has a brightness, a color, a shape, and a specific direction in space. The directional attribute of this visual percept Is presumably due to the fact that each retinal area Is connected to a specific cortical area and that this retinal-cortical unit gives rise to a specific subjective visual direction relative to the direction in which the observer perceives himself to be fixating. Any given object normally forms an image on each retina, and If the object Is to be perceived single, in only one direction, using the two eyes, the stimulated retinal-cortical unit of one eye must give rise to the same subjective viBual direc tion as the stimulated retinal-cortical unit of the other eye. Any two retinal-cortical units which give rise to the same subjective visual direction are said to be corresponding. The retinal elements involved in the retinal-cortical units are said to be corresponding retinal elements or correspond ing retinal points. For any given fixation position, the plane of regard Is that imaginary plane containing the object of regard and the centers of the entrance pupils of the two eyes. If the eyes are rotated around their lines of sight so that there is no 1 cyclophoria for the plane of regard, It Is possible to locate objects in the plane of regard so that the retinal images of these objects fall on corresponding retinal elements. Those objects whoBe images fall on corresponding retinal elements are said to be located on the horopter. The horopter then is an imaginary curve, located in the plane of regard, whose shape and orientation is determined by the positions of the corresponding retinal elements in the two eyes. The term horopter was first proposed by Aguilonis (1) in 1613 to represent an imaginary plane passing through the fixation point to which the perceived images of objects in the visual field were mentally projected (Figure 1). Vieth and Mflller (1) used a different concept in defining the horopter. They believed that corresponding retinal elements were equally displaced from their respective foveas and in the same direction. Lines from the corresponding retinal elements in the plane of regard passing through the centers of the two eyes would intersect in space. ®ie intersections of these corresponding lines coincide with points on a circle passing through the point of fixation and the centers of the two eyes. This circle constitutes the original Vieth-Muller horopter (Figure 2). Tlie present concept of the Vieth-M&Ller circle, and the one used in this study, is that it is the circle passing through the object of regard and the centers of the entrance pupils of the eyes (Figure 13). It has been well established that this circle Is not the horopter, based 2 Aguilonis's Horopter
Pig. 1.— The horopter according to Agullonls
3 Vieth- Muller Horopter
Pig. 2.— The horopter according to Vieth and Muller on the definition discussed on page 2, but it still serves as a standard reference curve to which other reference curves in the plane of regard can be compared. Some authors have considered the horopter to be a sur face and have designated the trace of this surface in the plane of regard as the longitudinal horopter since it depends on longitudinal sections of the retinas. The horopter cannot be a surface for all fixation distances and directions of gaze. Theoretically, it would be possible for a given fixation distance, for all corresponding lines of sight in the two eyes to intersect in space, thereby forming a surface horopter based on the above definition. With a change in distance or lateral displacement of the fixation point, however, there would be secondary lines of sight of the two eyes which correspond but which would not intersect in space, and thus the horopter would not exist as a surface. 'Hie lines of sight in the plane of regard would still inter sect, however, and these crossing points can be used to study and measure the organization and characteristics of the cor responding retinal-cortical units. For the purpose of this paper then, the term horopter will be used to designate that curve in the plane of regard formed by objects which are imaged on corresponding retinal elements. Hie experimental measurements and investigations of the horopter have been attempted with several different procedures and consequently some confusion exists. Tschermak (2) indicated that four methods or criteria could be used to locate points on the horopter, and that different results could be obtained using the same criterion but different viewing or testing conditions. Shipley (3) indicates that when different methods are used to investigate binocular space perception different results should be expected and therefore each method, or the results of each method, should be classified as a particular reference curve in space and studied in its own right. One such reference curve is that determined by locating objects in the plane of regard so that the perceived visual directions of the various objects by the two eyes are the same. This criterion is called the criterion of common visual direction and it is the only one that really measures the horopter since it adheres strictly to the definition of the horopter. Another reference curve that is often used in the study of visual space perception is that based on the criterion of the apparent frontal plane. The apparent frontal plane is the reference surface which is determined by locating objects in space so that they appear to occupy a plane parallel to the face plane. It has been proposed that the trace of this surface in the plane of regard conforms to the horopter on the basis that when objects are arranged in a plane parallel to the face plane their relative stereoscopic depth perception is zero. Therefore, there is no retinal disparity and consequently the images of the objects should fall on corresponding retinal points. If the apparent frontal plane conforms to the horopter, then the results obtained using the two criteria should be identical. The early investigators of space perception, Helmholtz, Hering and others (1), found that the reference curve determined using the criterion of the apparent frontal plane did not coincide with the Vleth-Miiller circle. This deviation was studied by Hillebrand (4), who indicated that it could be
explained by assuming that corresponding retinal elements are not located at equal distances from their respective foveas.
The deviation in the curvature of the experimentally deter mined reference curves from that of the Vieth-Mdller circle is now called the Hering-Hillebrand deviation.
The purpose of this investigation is to study these two criteria, the criterion of common visual direction (horopter) and the criterion of the apparent frontal plane, using similar apparatus, to determine their relationship and to investigate the organization and characteristics of the cor responding retinal-cortical units. The following questions will be considered: 1. What Is the plan of retinal-cortical unit d Is t rlbut ion ?
2. Is there a constantcy of the correspondence between the retinal-cortical units of the two eyes?
7 3. Is there any fundamental relationship between the apparent frontal plane and the horopter which makes it possible to use the apparent frontal plane to locate the points on the horopter? 4. To what extent do the horopter and the apparent frontal plane depend on past experience?
8 APPARATUS
A. Design. The basic apparatus used in this study was a modified haploscope. This apparatus was selected because it could be used to locate points on both the horopter and the apparent frontal plane. Since a relationship is to be determined, it is important that both reference curves be located using essentially the same instrumentation. The modified haploscope is also compact and versatile. It pro vides independent targets for the two eyes, allows symmetri cal and asymmetrical viewing conditions, and provides an easy way for changing the accommodative stimuli. Photographs of the haploscope arranged to locate points on the horopter are illustrated In Figure 3 and a schematic diagram Is illustrated in Figure 4. The light sources (L) consist of 15 watt incandescent
lamps mounted in boxes (A,B). These boxes are light tight except for the openings which emit light to illuminate the targets (C,E). Diffusing plates (T) and Kodak red filters #2408 (F) are located between the light sources (L) and the targets (C,E). The intensity of the light sources can be varied by means of a variac. Two Identical Y shaped shutters
(H,I) are placed between the filters (F) and the targets (C,E). The shape of these shutters is illustrated in Figure 4.
9 A
Fig. 3.— Apparatus used to determine the horopter.
10 L_n_j H & I
Pig. 4.— Diagram of the apparatus used to determine the horopter The shutters were designed with the central area of each shutter cut out so that the central parts of the targets (the fixation points) are always visible, but the peripheral or measuring parts of the targets are only visible when the shutters are lifted. The positions of the shutters are controlled by solenoids which are energized simultaneously by means of a microswitch which the subject holds in one of his hands. The solenoids were originally connected to an automatic alternate flashing device utilizing two micro- switches and a rotating cam to control the microswitches. Six different cams producing six different types of alternate flashing were investigated, but it was concluded that the hand-held microswitch was subjectively easier to use and objectively produced the more reliable data. The optical system consist of two matched telescopes (1,2-5,6) and two first surface mirrors (3,4). The convex- plano lenses (1,6) have front vertex powers of +6.66 diopters. The piano concave lenses (2,5) have back vertex powers of
-3*75 diopters. The lenses in front of the right eye are permanently mounted with the convex-plano lens (6) located 30.0 cm from the target (E) and the plano-concave lens (5) located so that parallel rays of light are emitted from the system. The plano-concave lens (2) in front of the left eye is located in a position corresponding to that of the plano concave lens (5) in front of the right eye. The convex-plano
12 lens (1) In front of the left eye is mounted to a rack and pinion so that the separation between the convex-plano lens (1) and the plano-coneave lens (2) is adjustable. Wie plano concave lens (2) is mounted so that the distance from the target to the primary focal point of the plano-concave lens is four times the focal length of the convex-plano lens (1). Consequently, when the convex-plano lens is in its basic position or displaced a few cm in either direction from this position, the image of the target produced by the convex- plano lens will be formed at the primary focal point of the plano-concave lens. Therefore, as the separation of the lenses is varied the angular magnification is varied but bundles of parallel rays are still emitted from the system. The separation of the lenses is indicated by a scale (s). The light sources, targets, and optical elements are all centered on a common axis. The displacement of the center of rotation of the right haploscope arm from that of the left haploscope arm is adjustable and can be set to correspond to the interpupillary distance of the observer. The bite bar (M) is adjustable so that the centers of rotation of the two eyes can be located on the axes of the elements on the haploscope arras at the centers of rotation of the haploscope arms (R). This condition is assumed to be filled when the anterior surfaces of the corneas are located 14 mm in front of the centers of rotation of the haploscope arms (R). This
13 assumption agrees well with the results found by Pry and Hill (5) for horizontal movements of the eyes. Several different target types were investigated to determine which target type was subjectively the easiest to use and objectively produced the most reliable data. The targets that were used for this study are illustrated in Figure 5A. They are photographic transparent duplicates, the left target being the same as the right target except that it is mounted upside down. Using photographic dupli cates produced targets of exactly equal dimensions. A peripheral spur was added to the central ring to serve as a check on fixation disparity. Hie photographic transparencies were carefully cut with the uBe of a brass template and scapel and mounted between two glass slides which had one comer of exactly ninety degrees. The slides are held in place in front of the light sources (L) by L shaped frames (N) which had been previously positioned with the use of the brass template. The L shaped frames (N) are mounted to plates (0) which can be rotated around the lines of sight so that an existing cyc^-o deviation can be corrected. Hie first- surface mirrors (3*4) can also be rotated around the lines of sight and can therefore be used to correct for any existing vertical deviation. Lens holders (U,V) are mounted on the arms of the haploscope so that the lenses used to produce the accommoda tive stimulus will be properly positioned in front of the eyes and centered with respect to the optical system. 14 A
C E
B
X Y
Pig. 5.— A- Diagram, of the slides used to determine the horopter. B. Diagram of the slides used to determine the apparent frontal plane.
15 Photographs of the haploscope modified to measure the apparent frontal plane are illustrated in Figure 6. *nie same apparatus is used with the exceptions of new targets, elim ination of the shutters, and the addition of a prism to measure the curvature of the apparent frontal plane. A schematic diagram of the apparatus arranged to measure the apparent frontal plane is illustrated in Figure 7. The targets (X,Y) are illustrated in Figure 5B. They are also photographic duplicates of the same drawing. Ihe drawing was made with a central fixation line, three evenly spaced lines on each side of the fixation line, and an eccentrically located fixation line. For the target that is placed in front of the left eye (X), the eccentrically located fixation line was painted out. For the target that is placed in front of the right eye (Y), the central fixation line was painted out. A narrow rectangular prism (P) is located in a plane parallel to the target (Y) between the target and the convex- plano lens (6), and positioned so that it only covers the eccentrically located fixation line of the target (Figure 11). The prism is mounted to a rack and pinion so that the separ ation between the target (Y) and the prism (P) can be varied. The separation of the target and the prism is indicated by a scale (d). B. Calibration of adjustable lens. The adjustable lens needs to be calibrated in terns of the magnification produced 16 A
Fig. 6.— Apparatus used to determine the apparent frontal plane and apparent normal plane.
17 1 2 5 6 ' X / i 4 / N H - — - f - « - o f - P i . H s U / d ^ GO R R m 1/1 y M
Fig. 7.— Diagram of the apparatus used to determine the apparent frontal plane and apparent normal plane. by the optical system. The lateral physical displacements of the target elements (W) from the centers of the targets were measured with a travelling microscope and are given in Table 1. The apparent singular displacement of each target element from the center of the target measured at the entrance pupil of the eye (#) is a function of the lateral physical displacement of the target element (W) and the magnification produced by the optical system (Figure 8). The targets were designed so that the target elements would have an apparent angular displacement of six degrees right and left, four degrees right and left, and two degrees right and left. Although the final measurements are not exactly these amounts, they have been used for convenience in designating the various target elements. The relationship between the separation of the left convex-plano and plano-concave lenses (s) and the apparent angular displacement (y) was determined from direct measure ments. A frosted glass was placed perpendicular to the axis of the optical system and 200 cm behind the position of the entrance pupil of the left eye. A + 0.50 diopter lens was placed at the position of the entrance pupil of the eye so that an image of the target was sharply focused on the frosted glass (Figure 9)• With this arrangement, the angle e repre sents the apparent angular displacement of the target elements at the eye. Tlie separation of the lenses (s) was varied and the corresponding image element separation (W*) on the frosted
19 TABLE 1
HOROPTER APPARENT FRONTAL PLANE POSITION W W 6°R 2.7952 cm 2 .8 0 6 7 cm
4°R 1.8626 cm 1.8707 cm 2°R 0 .9 2 6 8 cm 0.9267 cm
2°L 0.9203 cm 0.9225 cm
H° L 1.8662 cm 1.8694 cm
6°L 2.8033 cm 2.7987 cm
20 %
Pig. 8.— -Diagram showing relation between size of the target and the apparent angular displacement of the target at the entrance pupil of the eye. 3 0 .0 cm
2 0 0 c m
F rosted Glass
W' — *!
Fig. 9.— Apparatus used to calibrate separation of lenses and the apparent angular displacement of the target at the entrance pupil of the eye.
22 glass was measured. The ratio of the apparent angular dis placement (y) to the linear physical displacement of the target (W) was then calculated and plotted as a function of the lens separation (s). See Figure 10. The data have been fitted with a straight line and the relationship between the apparent angular displacement (yQ.S.)* the lateral physical displacement of the target (W), and the lens separation (s) for the left eye can be expressed as follows:
y0.S. = (*°76 s + .9 0 6) arctan (1)
The separation of the lenses for the right eye is fixed. The relationship between the apparent angular displacement (y0.D.)» the lateral physical displacements of the target (W) for the right eye was found to be:
e0.D. = 1 *133 arctan (2)
C. Calibration of the adjustable prism. The adjustable prism was measured and found to have a power of 6.52 It needed to be calibrated in terms of the apparent displace ments of the central line of the target which it produces with various target-prism separations. The calibration of the adjustable prism was also accomplished by using the arrangement with the frosted glass and making direct measure ments (Figure 11). When the prism is positioned so that the apparent displacement of the eccentrically located fixation line is such that a = O .9 2 6 7 cm in Figure 11, the prism is 1.100
I. coo
MOO
1.000
0.0 0 0
Lena Separation, a (cm)
Fig. 10.— Ratio of the apparent angular displacement of the target to the linear dimension of the target as a function of the lens separation.
2 4 » - f i r i
Frosted Glass
b*
Fig* 11•— Apparatus used to calibrate the target-prism separation and the displacement of the eccentrically located fixation line.
25 in the zero or neutral position and is producing the target displacement (O.3638 cm) necessary to make the right target appear exactly equal to the left target. The apparent dis placement of the central target element (DX) from this equivalent position can be calculated from the following:
DX » % § § (y - d) (3)
Where DX equals the apparent target element displacement in cm, y equals the zero or neutral position of prism, and d equals the target-prism separation in cm. The target-prism separation (d) was varied and the cor responding separations of the image elements (a*, b 1) were measured. The apparent separation of the target elements (a) was then determined using the formula:
The apparent separation of the target elements (a) was then plotted as a function of the target-prism separation (d) (Figure 12). The zero or neutral position of the prism (y) equals the target-prism separation (d) when the apparent target displacement is such that the distance a is 0.9267 cm. From Figure 12 it is found that a = 0.9267 cm when d is 5 .5 8 cm, and therefore the zero or neutral position of the prism (y) is 5*58 cm. Using the calibrated value, equation (3) can be rewritten:
DX = .0652 (5.58 - d) (5) 26 Pig. 12.— Apparent separation of target elements as a function of target-prism separation.
27 Target-Prism Separation, d(cm) 8.00 . 0 S.0 6.00 S.OO 7.00 1.00 9.00 9.00 ' 9.00 paet eaain f re Elme s a (cm) a ts, en lem E arget T of Separation Apparent 70 .90 1.0 1.1 1.8 With the prism in place, the relationship between the apparent angular displacement (0^ ^ ), the apparent target u • u • element displacement (DX), and the lateral physical displace ment of the target (W), for the right eye can be expressed as follows:
W — TiY y0.D. = 1 ,1 3 3 arctan ( -^ 5--- ) (6 )
D. Sensltivlty. The scales for reading the lens separ ation (a) and the target-prism separation (d) can be approxi mated to a tenth of a millimeter. The sensitivity of the lens separation measurement in terras of the angular subtense at the eye (angle 0 ) is about 10" of arc when 0 = 4.5°. This possible error increases in direct proportion as 0 increases. The sensitivity of the target-prism separation measurement in terms of the angular subtense at the eye (angle 0 ) is about 4" of arc and is independent of which target element is used in conjunction with the central target element.
29 METHOD OF ANALYZING DATA
The method used to analyze the data Is that proposed by Fry (6). It is a modification of the analytical method used by Ogle (7). Ogle found that conic sections can be used to fit horopter and apparent frontal plane data when the resulting curves are symmetrical with respect to the median plane, and has derived the following analytical expression for these reference curves.
H = tan *1 " tan «2 ^
H is a constant and 0^ and «2 are the angles shown in Figure 13. The constant H, referred to as the Hering-Hiliebrand deviation, expresses the curvature of the reference curve in terms of its relationship with the Vieth-Muller circle. When H equals zero, the reference curve conforms to the Vieth- Mviller circle. This expression can be reduced to the following approx imate formula with the angles expressed in radians.
“ ^1 H = (8)
It is assumed in this equation that the tangents of the angles are equal to the angles expressed in radians and that
4> is equal to the average of and #2 * 30 Objective Frontal Plane Median Plane
Subjective Reference Curve
Vieth-M illie r C ir c le
2 A
Fig. 13.— Diagram showing Vieth-Milller Circle, objective frontal plane, and angles used in analyzing data.
31 £ (9) Prom Figure 13, the following relationship can be obtained:
■ yi = v ■ y (10) Combining equations (8) and (10) we obtain an equivalent but different equation for the reference curves.
(11)
This formula can be modified to yield an equation that will apply to unsymmetrical as well as symmetrical reference curves as follows: S 7 - 7 H0 = — 4— (12) 100 “ The modification involves the addition of the term S/100, which is used to express the relative sizes of the two cortical images, the aniseikonic deviation. When no anisei konia is present, the reference curves will be symmetrical, S will equal zero, and equations (11) and (12) will be equal.
In analyzing the data, the values of y and
Figure 13) and using instead the interpolated value of y when
involved can be determined from these scales. Since the center elements of the targets used to determine the horopter
are centered on the axes of the two haploscope arms, the
33 angle of convergence determined from the scales represents the angle of convergence (y) of the primary lines of sight of the two eyes when they are directed toward the center elements. In the case of the apparent frontal plane experi ment, the center element of the target of the right eye is not precisely on the axis of the arm of the haploscope except when the prism is located at its zero position, but in analyzing the data it has been assumed that the angle of convergence (y ) corresponds to the angle of convergence of the two haploscope arms. The experimental measurements of both the horopter and the apparent frontal plane yield values for 0]_, and y.
Values for y are then computed using equation (10), and values for
(Figure 13). In this case values of y may be computed by the following equation:
r - <13) This method of analyzing the horopter and the apparent frontal plane data involves numerous and tedious calculations. In order to reduce the calculation time and improve the accuracy an IBM 1620 Computer was programmed to accomplish the calculations.
34 EFFECT OF CHANGES IN FIXATION DISTANCE ON THE HOROPTER AND THE APPARENT FRONTAL PLANE
I. Horopter A. History. Measurements of the horopter as a function of testing distance have been made by Ames and his associ ates (8,9). They used the grid-nonius method. Their apparatus, called the horopter apparatus, consisted of thirteen channels mounted so that they converge to a point halfway between the mean nodal points of the observer's eyes (Figure 14). Vertical black steel wires were mounted to supports that could be moved freely along the channels. The positions of these wires were measured by a movable telescope. The black steel wires were viewed through a rectangular aperture and two unique screens against a uniform white background (Figure 15)• The binocular appearance of the wires is illustrated in Figure 16. The subject was properly positioned in the apparatus and instructed to fixate the central wire. The black steel wires were then moved along the channels until each wire appeared to be vertically aligned, as shown in Figure 16. When the wires had this appearance, they were located on the horopter. The positions of the wires when they were located on the horopter were measured with fixation
35 \
H i r e S u p p o r t* Ad j u s t in g an Fe l e s c o p e
S c r e e n H* t h S l i t
C y c l o p e a n P r o j e c t i o n Cc n t c r P l a n O r A p p a r a t u s Fig. 14.— Horopter apparatus of Ames et al. Fig. 15.— Screens used in grid-nonius method of Ames et al.
37 OS. 0. D
oo oo O.D O.S,
Pig. 16.— Binocular appearance of wires in grid-nonius method. distances of 20.2 cm, 40.4 cm, and 75*6 cm. TSie data of one subject, KNO, have been analyzed by the method which will be used In this study so that a better comparison of the results can be made. Only the data taken with peripheral targets of two, four, and eight degrees were analyzed.
These data are representative of their results. The experi mental values in terms of y and 4> are plotted In Figures 17 * 18, and 19. The data have been fitted with smooth curves that conform to equation (12). The smooth curves were used to determine the analytical graphs shown in Figures 20, 21, and 22. The slopes of the curves in Figures 20, 21, and 22 were calculated and plotted as a function of fixation distance expressed in diopters (Figure 23). TJiis curve indicates that the Hering-Hillebrand deviation is not a con stant, but changes with variation in fixation distance. Ihe change of the Hering-Hillebrand deviation with variations in fixation distance implies that the subjective visual direc tion associated with corresponding retinal-cortical units also changes as the fixation distance varies. Ogle (4) states that this change in the Hering-Hillebrand deviation does not necessarily prove the instability of the directional attributes of corresponding retinal-cortical units, since optical distortion and modification in the anatomical distri bution of the rods and cones due to choroid movement may occur during variations in accommodation and convergence, and thus account for the change.
39 5.12 B = 75. 6 cm
Xs O 5.00
8 7 6 5 4 3 2 0 2 3 4 b 6 7 8 L R 4> (Degrees)
Pig. 17.--Horopter data of Ames et al. with fixation distance of 75*6 cm. V V (Degrees) 9.40 9.44 9.48 9.56 9.60 8 Fig. 18.— Horopter data of Ames et al. with fixation distance of 40.4 cm.40.4 of distance fixation with al. et Ames of data Horopter 18.— Fig. 7 6 5 4 2 <(> (Degrees) 0 2 3 4 4.4 cm 4 40. =B 5 E 7 8 Y (D egrees 19.00 I9J04 18.92 18.96 8 i. 9—Horopterdata of Ames etal.Fig. with 19.— fixation distanceof20.2 cm. 7 6 5 5 4 3 2 <|> (Degrees) 0 2 3 4 = 0 cm 2 20. = B 6 7 8 .02
.01
Y .00 H = 0.087 B = 75. 6 cm
-.01
-.02
e 6 4 2 0 2 4 e e L R
Pig. 20.— Analytical graph of horopter data of Ames et al. with fixation distance of 75*6 cm. .OS
Of
oo 1 H = 08100 4> B = 40. 4 cm
8 6 4 2 O £ 4 6 8 4> (Degrees)
Pig. 21.— Analytical graph of horopter data of Ames et al. with fixation distance of 40.4 cm. .00
Y H = (~p|)(57. 2958)= 0. 186
-.01 B = 20. 2 cm
-.03
8 4 2 06 2 4 6 8
Pig. 22.— Analytical graph of horopter data of Ames et al. with fixation distance of 20.2 cm. distance. ofdata Amesal. et asafunction ofthe fixation
Hering-Hillebrand Deviation (H) .2 .04 joa .16 i.2. Hering-Hillebrand deviation ofFig.the 23.— horopter
0 - 0 cprcl f sig sa e n tr (lB) l/B ( eters M in ce istan D esting T of rocal ecip R B 4 5 I 2
Since the conclusions of this experiment are so impor tant in the study of ocular correspondence, it was decided to continue this study and to Investigate the horopter over the entire range of accommodation and to use a viewing system that would eliminate all visual stimulation except the fixation point and the measuring target. The apparatus discussed previously was developed with this in mind. B. Procedure. The subject was carefully positioned in the instrument in the following manner. Two small circular apertures were placed in the lens cells of the haploscope arms. Hie haploscope arms were set for parallelism and the head was then adjusted by moving the position of the bite bar (translational movements in the horizontal and vertical, and rotational movements around an anterior posterior axis) and the right haploscope arm (translational movement in the horizontal) until the fixation portions of the right and left targets appeared to be centered in the small circular apertures. A final adjustment of the head was then made by moving the position of the bite bar (translational movement in the anterior-posterior direction, and rotational movement around the vertical axis) until the anterior surfaces of the
corneas were located 14 mm from the centers of rotation of the haploscope arms. This was accomplished by aligning the front surfaces of the corneas with sights which had been
previously measured and positioned on the instrument. When the adjustment was completed, the approximate centers of
47 rotation of the eyes of the subject for horizontal rotations were located at the centers of rotation of the haploscope arras and the face plane was perpendicular to the floor. Considerable care was taken in the positioning of the subject since slight displacements of the head or rotations around the vertical axis will produce an asymmetrical convergence viewing condition which could change the results. To eliminate the possibility of various head positions affecting the results, all data were taken without changing or removing the bite bar. When the subject was properly positioned in the instru ment, the arms of the haploscope were diverged until binocular fusion was lost. Any vertical phoria or cyclo- phoria that was present was corrected by rotating the mirrors and/or targets. All of the measuring lines of the two tar gets except the six degree lines to the right in both targets were then occluded by placing small strips of black electri cal tape on the cover glass. The arms of the haploscope were set for parallelism and the subject was instructed to observe the central portion of the target and to notice the upper and lower spurs on the central ring of the target. The subject was then instructed to fixate the central cross of the tar get as steadily as possible but also to be aware of the position of the upper and lower spurs. When the spurs appeared to be in vertical alignment with the central cross and when the subject felt physically and mentally prepared to
48 make a measurement, he was to engage the hand-held micro-
switch, which would lift the shutters and expose the six degree measuring targets to the right of the fixation point, and assess the relative positions of the two peripheral
measuring lines while constantly maintaining central fixa tion. After the assessment was made, the shutters were closed and the separation of the lenses in front of the left eye was changed by the subject. The shutters were then lifted and an assessment of the relative positions of the
two peripheral measuring lines, while constantly maintaining central fixation, was again determined. This procedure was repeated until the measuring lines appeared to be in vertical alignment when the targets were exposed. When this was accomplished, the lens separation was recorded. In arriving at this end point, the subject was given complete freedom regarding the use of the shutters. Several exposures ranging from 1 sec to 4 sec duration were generally made before a satisfactory vertical alignment was achieved. Eight measurements were taken for each experimental position. Measurements were generally made in the order, six degrees right, six degrees left, four degrees right, four degrees left, two degrees right, and two degrees left, but the sequence appeared to make little difference in the measurements.
The above procedure was repeated using the minus lenses
and convergence of the haploscope arms necessary to simulate
49 fixation distances of 100 cm, 50 cm, 25 cm, and 1 6 .6 6 cm. Some measurements were alBo taken at a simulated fixation distance of 12.5 cm, but since prolonged fixation was neces sary, considerable ocular discomfort was present and the data were unreliable due to the inability to maintain fixation. Considerable practice was necessary before reliable results could be obtained. The author, who served as the subject, practiced making measurements for three weeks before the actual data were collected. Due to this necessary lengthy practice period, only one subject was used in the study.
C. Results. The data, plotted in terms of y as a function of
U1
-.12
-.16
L R
Pig. 24.— Horopter data with parallel lines of sight. y (Degrees) 3.80 9.84 3.68 3.64 6 7 3 3.72 i.2. Horopter data withfixation distanceFig.25.— of100 cm. 6 3 4 5 R L 2 I <)> (Degrees) O 2 5 3 m 100= c B 4 6 I
B = 50 cm 7.60
7.56
7.52
Q 748
7.44
7 4 0
LR «j> (Degrees)
Pig, 26.— Horopter data with fixation distance of 50 cm. Y (Degrees) 15.20 15.12 15.16 i . 7—HoropterFig. 27-— data with fixation distanceof 25cm. L
near the fovea may be the same, the spacing and arrangement of the retinal elements may differ. Osterberg arrived at his results by determining the density of the retinal
elements in different meridians at various distances from the fovea. He made several measurements on the temporal hemiretina in the zero degree meridian, but very few on the nasal hemiretina, so that the change in distribution of the retinal elements in the two hemiretinas cannot be compared. The number of retinal elements per unit length for various distances from the fovea in the temporal hemiretina in the zero degree meridian was determined from his drawings and Is shown in Figure 30. This Illustrates that the distribution of retinal elements In the zero degree meridian of the temporal hemiretina is uneven and unless this distribution is duplicated in the zero degree meridian of the nasal hemi retina of the opposite eye, the horopter will be an uneven
curve.
57 function oflinear distancefrom thefovea determinedfrom Osterberg!sdata. Elements Per 20n Distance 2 8 7 3 6 9 4 5 Fig. 30.--Number ofretinal elements per unit length as a 10 0 400 300 0 0 2 100 0 Linear Distance from the Fovea the Fovea from Linear Distance (|i)
Polyak (11) has also pointed out that the distribution of the retinal elements is not uniform but that the retinal elements are arranged in fields and that these fields are irregularly oriented in straight, arched, or curved rows. If the irregularity in the nasal hemiretina of one eye is not the same as the irregularity in the temporal hemiretina of the other eye, an uneven horopter could result. The various neural connections from the retinal elements to the visual cortex could also produce or contribute to the uneveness of the horopter. The second Important aspect of the horpter that is obtained from these results is that the shapes of the curves connecting the experimental points are essentially the same for the various fixation distances (Figure 29)• The differ ences between the curves becomes greater as
.0 0 H = 0.2126 V
-.01
-.02
6 e 4 8 £ o 2 8 4 5 L R
of research in this area. Shipley (3) has presented an excellent historical review of the reported investigations of the changes in curvature of the apparent frontal plane with changes in fixation distance. Two types of targets have been utilized in apparent frontal plane measurements, verti cal lines and small spots. The results using the two methods have been comparable. Helmholtz (1) was one of the first to make measurements of the apparent frontal plane using lines, and Zajaczkowska (15) was one of the first to make measure ments using spots. The results of these two studies along
with those of Ames, Ogle, and Gliddon (9) have been analyzed by the analytical method utilized in this study so that better comparisons can be made with the results of the present study. Helmholtz (l) used three fine black silk threads sus pended in front of a uniform background as a target. The threads were fastened to the ceiling and stretched by weights. The three threads were placed in space so that they were part
of an Imaginary cylindrical surface which was physically
concave to the observer. T h e measurements were made by having the observer m 63 threads until the threads appeared to be in a frontoparallel plane. The results of the analysis of Helmholtz's data are illustrated in Figure 32. Zajaczkowska (15) used three spots of light, in an otherwise darkroom, as a target. The spots of light were arranged in the horizontal meridian at eye level. The two outside lights were symmetrically fixed on either side of the central light and were approximately parallel to the face plane. The central light was adjustable so that it could be moved closer to or farther from the observer in the plane perpendicular to the face plane. The observer's head was placed in a headrest with the median sagittal plane of the head in line with the central target. Tlie two outside lights were placed at a given fixation distance and the observer was then asked to "place the central light exactly on a straight line between the two fixed lights." The sub jects were encouraged to move their eyes and fixate each spot while making the measurements. The results of the data analysis of one of Zajaczkowska's subjects (TK) are illus trated in Figure 32. The data of Ames, Ogle, and Gliddon (9) have also been analyzed by the method used in this study since more attention was given to fixing the head, which reduces the problem of asymmetrical convergence, and since this is the only study that measured both the horopter and the apparent frontal plane using essentially the same instrumentation. The 64 data of Zajaczkowska, Helmholtz, and Ames Ames and Helmholtz, Zajaczkowska, of data rna pae s ucino h fxto itne for distance fixation the of function a as plane frontal Hering-Hillebrand Deviation (H) • o 06 24 28 20 i. 2—Hrn-ilbaddvaino te apparent the of deviation Hering-Hillebrand 32.— Fig. 0 eirclo i of Reciprocal 2 sii it i ■ (1 /B) csti-i)it i ■ 3 65 4 o- etal. apparatus that they used was the same as that used for the horopter measurements except the "grid-nonius11 screens were eliminated. The subjects were carefully positioned in the instrument so that symmetrical convergence on the fixation wire was obtained. IJie subject was asked to maintain fixa tion on the central wire and to move the other wires so that they appeared to be located in a frontoparallel plane. The results of the data analysis of one of their subjects (KNO) are illustrated in Figure 32. Though different testing methods and conditions were used in these studies— lines and spots, fixed head and moving head, adjusting the central part of the target and adjusting the peripheral parts of the target, steady fixation and mov ing eyes, dark surround and bright surround— there is good agreement between the results (Figure 32). The results of these studies indicate that there is a consistent change in the Hering-Hillebrand deviation of the apparent frontal plane with a change in fixation distance. The shorter the fixation distance, the greater the Hering-Hillebrand deviation. The previously discussed apparatus was developed to gather information regarding the curvature of the apparent frontal plane for various testing conditions. The first procedure was to determine the Hering-Hillebrand deviation of the apparent frontal plane with changes in fixation distance. 66 B. Procedure. The mouth bite had already been posi tioned for the horopter measurements, and it was only necessary to check the position of the subject in the instrument. When the subject was properly positioned, the vertical phoria and/or cyclophoria were corrected and the arms of the haploscope set for parallelism. The two and four degree lines to the right and left of the central line were then occluded by placing small strips of black electri cal tape on the cover glass. The subject then "moved" the central line, by adjusting the prism, so that it appeared to be behind the six degree peripheral lines. Following this, the subject "adjusted" the two six degree peripheral lines, by changing the lens separation of the lenses in front of the left eye, until the lines appeared to be in an apparent frontoparallel plane. The subject then moved the central line until it appeared to be in the same frontoparallel plane as the peripheral lines. The subject then made some final adjustments of both the peripheral and central lines, and when he felt that he had all three lines in an apparent frontoparallel plane, the lens-separation and the prism- target separation were recorded. For the next measurement, the prism was moved so that the central line appeared to be in front of the six degree peripheral lines, and then the above procedure was repeated. Five such measurements were made. TSiis measuring procedure was also used for the four degree and the two degree 67 peripheral targets. Although the target was examined and the curvature assessed with fixed and moving eyes, the measure ments were made with the subject fixating the central element of the target. Shipley (16) has indicated that there is a slight difference between results obtained with moving and fixed eyes in measurements of the apparent frontal plane. With moving eyes the measured apparent frontal plane had a slightly greater negative curvature, i.e., more concave curva ture toward the observer, than did the measured apparent frontal plane with fixed eyes, and the difference was about the same for all observation distances. The above routine was repeated using the minus lenses and convergence of the haploscope arms necessary to simulate fixation distances of 100 cm, 50 cm, 25 cm, and 1 6 .6 6 cm. Practice measurements were made for several weeks before the actual data were collected. Two complete sets of data for each simulated fixation distance were collected, averaged, and analyzed. C. Results. The data are presented in Figures 33 to 37 where y is platted as a function of 4> for the various fixa tion distances. The change in curvature of the apparent frontal plane with changes in fixation distance is evident from these results. As indicated previously, the smooth curves were drawn guided by the experimental data points but adjusted so that the analytical graph would plot as a straight line. Although 68 Y Y (Degrees) +.04 +02 -.06 + -.04 -.02 0.0 Pig* 33*— Apparent frontal plane data with parallel lines of sight. of lines parallel with data plane frontal Apparent 33*— Pig* (D+ egrees) y (D egrees) 3.77 .5 - 3.75 385 i- 4—Apparentfrontal plane data Pig- with 34-— fixation distanceof100 cm. L 21 9C 21 84 21 82 • 2! 80 2170 21 76 21 74 21 70 6 3 a 3 2 r o 2 3 4 5 6 o (Jegree») Fig. 37.— Apparent frontal plane data with fixation distance of 1 6 .6 6 cm. 73 there is not exact agreement between the smooth curves and the experimental points, the agreement appears good enough to Justify the use of this method of analysis. The analytical graphs are illustrated in Figures 38 and 39, and in composite form in Figure 40. The failure of the data lines in Figure 40 to intersect the zero ordinate at the same point indicates an apparent increase in aniseikonia as the fixation distance decreases. The aniseikonia increases from 0.6# with infinite fixation to 1.3# with fixation at 16.66 cm. The aniseikonia measured in the horopter experi ment indicates no change with changes in fixation distance. This implies that the change in aniseikonia measured with the apparent frontal plane criterion is not due to changes brought about by accommodation and convergence or to instru ment error. This aniseikonia change may be due to an error in curve fitting. It may also be due to an error in judgment on the part of the subject as to what constitutes an apparent frontal plane. The Hering-Hillebrand deviations determined from the analytical graphs and plotted as a function of fixation distance are illustrated in Figure 41. To determine if these measurements were peculiar to the type of instrument used, a measurement of the apparent frontal planewas made with an apparatus similar to that used by Ames et al. (9). The analysis of this "free space" apparent frontal plane data is illustrated in Figures 42 and 43, 74 ♦ .006 oo (a) ♦ 004 ♦ 01 H = 0o0344 (b) B = 100 c .02 H = 0 „ 0716 30 cm 03 .02 H = (d) Lb c - 01 4 2 O 2 - 6 L R (J e g re e s ) Fig* 38*— Analytical graphs of apparent frontal plane data for fixation distances of Infinity, 100 cm, 5 0 cm, and 25 cm. 75 .09 JO 8 H = 0. 2063 JOI B = 16 0 66 c m Y 4> .oo e 4 o 2 4 e c|> (Degrees) Pig. 39*— Analytical graphs of apparent frontal plane data for fixation distance of 1 6 .6 6 cm. .04 B.66 cm .03 28 cm .02 X co cm -.01 -02 6 4 L 2 0 2 R '4 6 <}> (Degrees) Pig. 40.— Analytical graph of apparent frontal plane data for all fixation diatances. frontalplane as afunction offixation distance. Hering-Hillebrand Deviation (H) .0 .0 .08 i. 1—Hering-Hillebrand deviation ofPig.the 41.— apparent J .20 .16 4 0 2 0 cprcl f sig sa e n tr (/ ) (l/B eters M in ce istan D esting T of rocal ecip R I 2 78 8 Haploscope H O A A 4 Apparatus Horopter 8 6 .168 B = 40 cm n .167 .166 .160 L R .00 S = 0. 0046 H = 0.0922 -.01 B = 40 cm <|> (Degrees) Pig* 43•— Analytical graph of apparent frontal plane data using horopter apparatus with fixation distance of 40 cm. and the Hering-Hillebrand deviation is plotted as a triangle in Figure 41. It is apparent that the measurements of the Hering-Hillebrand deviation made using the different appar atuses are in good agreement. The relationship between the Hering-Hillebrand deviation (H) and the fixation distance (B), illustrated in Figure 41, is a linear function of the first degree and can be expressed by the following: H = ^ ( M ) The results of measurement of the Hering-Hillebrand deviation using the criterion of the apparent frontal plane in this study agree with the results of the previously mentioned investigations, i.e., there is a consistent change in the Hering-Hillebrand deviation with a change in fixation distance. Ihe basis for this change is unknown. It could be due to a change In the directional characteristic of cor responding retinal-cortical units, a change in the relative location of the retinal elements due to a stretching of the retinas, disfiguration of the eyeballs, or changes in re fracting surfaces associated with accommodation and converg ence, or it could be due to a learning process, which would indicate that the apparent frontal plane Is a product of experience as well as the physiological processes of vision. •Hie results of the horopter measurements in this study indicate that the first two possibilities mentioned above are unlikely, and therefore imply that the change in the 81 Hering-Hillebrand deviation with variations in fixation distance as measured with the apparent frontal plane cri terion is associated with a learning process. The results of the horopter measurements in the present study differ from those found by Ames et al. Their results indicate that the horopter can be represented by a smooth curve and that the Hering-Hillebrand deviation of the horopter changes with variations in fixation distance. They have attributed the change in the Hering-Hillebrand devia tion of the horopter with variations in fixation distance to the optical and mechanical changes accompanying accommodation and convergence, and have therefore maintained the concept that the directional attribute of the retinal-cortical units is innate. However, the very close agreement in their results between the Hering-Hillebrand deviation of the horopter and that of the apparent frontal plane for the various fixation distances (Figure 44) suggests that stereo cues may have been present in their horopter experiments. In their study, the screen with the horizontal aperture, the grid-nonius screens, the fixation target, and all of the measuring targets were always visible and may have given the field of view a three dimensional character. It is conceiv able that stereopsis could give a cue of relative distance in spite of the fact that only the upper half of a given wire was seen with one eye and the lower half with the other. Variations in the apparent size of the wires with changes in 82 and the horopter as a function of fixation for data of Ames et al. et Ames of data for fixation of function a as horopter the and Fig. 44.--Hering-Hillebrand deviation of the apparent frontal plane frontal apparent theof deviation 44.--Hering-Hillebrand Fig. Hering-Hillebrand Deviation (H) o.o .20 •»6h eircl f etn Dsac i Mtr (l/B) Meters in Distance Testing of Reciprocal 0 2 3 —oAFP O— A— -dHor opter 5 4 distance could also give additional information regarding the distance and alignment of the wires. In the present study, the stereo and other depth cues were minimized since the only objects that were visible during the measurements of the horopter were the fixation target and, when the shutters were raised, the involved measuring target. Pry (17) has proposed a theory of the perception of object location with the horopter as the physiological basis. Objects that are located on the horopter have zero lateral disparity whereas objects located in front of the horopter give rise to crossed lateral disparity and those located behind the horopter give rise to uncrossed lateral disparity. The perceived location of an object that is not on the horopter depends on the relation of the object to the horopter and the point of fixation. The perceived location of point P in Figure 45, is dependent upon the determination of the perceived location of the fixation point ("P), then the perceived location of point P-^ relative to P, and then the perceived location of point P relative to point P-j^ based on the amount of disparity involved for P(7^ “ y )• The relationship between the perceived fixation distance Cp1) of the fixation point ("F) and the actual physical distance (fT) of the fixation point can be expressed by: Pig. 45-— Diagram to explain Fry *s concept of the relation of the horopter to perceived object position. e 85 The relationship between the perceived distance and the physical distance is learned through the association of visual, tactual, and kinesthetic responses. Consequently, the value of k is a function of the environment and the clues present and will vary accordingly. With the distances expressed in meters, the range of k would probably vary from zero to about 0.1. Gilinsky (l8) determined the value of k for one subject in an open environment to be 0 .0 3 5• Although the perceived location of point P does not . necessarily coincide with the physical location of "F, it is assumed that the perceived direction of "P, or for that matter any other object,will coincide with its physical direction. As the fixation distance changes, the perceived location of the fixation point changes as indicated by equation (15)* For each perceived fixation distance (p^1) and for each value of , the observer learns through experience to associate a given position of P£ with zero disparity. The relationship between p^ and p’1 is as follows: - M (16) p1 For each value of 86 can be expressed by: fr - f* “ Yj - Y (17) It follows from this theory that the equation for the apparent frontal plane is as indicated below. (18) p* ♦ Combining equations (11), (15) j and (18) yields: H = ~ =- + A* (19) P The experimental results with the criterion of the apparent frontal plane (Figure 41) indicate that when "p (b) equals 1 meter, H equals 0.0345. With these values and the interpupillary distance of the subject (O.O67 meters), a value for k of 0.0299 Is obtained. This k value Is in the expected range of the k values and close to that obtained by Gilinsky. It appears that this experiment corroborates Fry*s theory and Indicates that the curvature of the apparent frontal plane is a function of a learning process. 87 EFFECT OF PROLONGED WEARING OF MERIDIONAL MAGNIFIERS ON THE HOROPTER AND THE APPARENT FRONTAL PLANE A. History. Burlan (19) Investigated the effects of the prolonged wearing of an afocal magnifier at axis 90° in front of one eye on the subjective reactions and on the determina tion of the apparent frontal plane. He used three subjects; they wore the lenses constantly for periods of eight to fif teen days. The subjective reactions and the changes in the apparent frontal plane were essentially the same for all observers. When the afocal magnifiers were first placed in front of the eyes, the typical spatial distortion associated with meridional magnifiers at axis 90 degrees was experienced and subjective symptoms of eyestrain, slight headache, nervous tension, and even some gastric distress were present. The spatial distortion was more noticeable with near than with distance fixation, and more noticeable when movements of the eyes were avoided. The subjective symptoms decreased as the magnifiers were worn. The spatial distortion also decreased with wearing of the magnifiers so that after wearing the meridional magnifiers for three or four days no spatial dis tortion was present when the observer was in surroundings 88 which contained several empirical depth clues. However, even at the end of the experiment, when the observers were placed in an environment which contained few empirical clues for depth perception, the spatial distortion became apparent. When the meridional magnifiers were removed, a spatial dis tortion opposite to that which was present when the meridional magnifiers were first put on was evident and was present for from one to three days. The adaptation to the spatial dis tortion that occurred following the wearing of the meridional magnifiers was faster than the adaptation to the spatial distortion that was present when the meridional magnifiers were first put on. The effect of the meridional magnifier on the apparent frontal plane determined with the horopter apparatus for one subject (REB) is shown in Figure 46. The curve Indicates that following the application of the meridional magnifier in front of the right eye, shown by A in Figure 46, there was a corresponding change in the magnification needed in the image of the left eye in order for the target to appear in a frontal plane. 'Eiis was followed by a gradual reduction of the needed magnification, so that after wearing the meridional magnifier for nine days only two-thirds of the initial magnification was needed in the image of the left eye in order that the target appear in a frontal plane. When the meridional magnifier was removed, shown by B in Figure 46, the image of the right eye had to be magnified greater than 89 I Size Lens On T» u rty rt»4 Size Lens Off •H Cb 2 vo to £ o nJ 3 st; +■ ^ o PM o<3 r)^ 4 o H © AM 0) V 5 & ri &• 20 Time (Days) Pig. 46.— Percent magnification needed for apparent frontal plane determinations using the horopter apparatus during the prolonged wearing of a meridional magnifier. Prom Burian. that needed before the meridional magnifier was worn in order that the target appear in a frontal plane, but the needed magnification quickly reduced to that required before the meridional magnifier was worn. Miles (20) studied the effects of prolonged wearing of meridional magnifiers at axis 180 degrees on subjective reactions and space perception. The subjective responses of discomfort to the wearing of the lenses were essentially the same as those indicated by Burian. When the meridional magnifier was first put on, the typical spatial distortion associated with afocal magnifiers at axis 1 80 degrees was present but disappeared in about five days except when the observer was in an environment devoid of empirical depth clues. Measurements made with the space eikonometer showed a corresponding change in measured aniseikonia when the meridional magnifier was first put on, and then a gradual reduction in the measured aniseikonia during the wearing of the magnifier so that after 24 days only about two-thirds of the initially measured aniseikonia was present (Figure 47). Measurement of the image size differences with the opthalmoelkonometer, while quite erratic, did not indicate the complete image size difference produced by the meridional magnifier and indicated little or no change in the measured aniseikonia during the wearing of the magnifier (Figure 47). Miles (20) also investigated the subjective reactions and 91 Prom Miles. andspace eikonometer duringtheprolonged wearingof a meridional magnifier. i. 7—PercentImage size differences Pig. 47.— measured withthe opthalmoeikonometer Image Size Difference (percent) 2 O Time (Days) Time —o Eikonometer Space O— —• Ophthalmoeikonometer °— 26 28 the spatial distortions during the prolonged wearing of meridional magnifiers at oblique axes. He found that although there was some subjective adaptation to the spatial distortion, even after wearing the meridional magnifiers for 2 8 days, most of the spatial distortion was subjectively still present. Hie subjective symptoms of eyestrain, head ache, etc., were also present during the entire period that the meridional magnifiers were worn. Measurements with the space eikonometer, however, indicated a gradual reduction in the measured declination error during the wearing of the meridional magnifiers at oblique axes. The reduction in the declination error leveled off in about five days to a value of about one-half that of the original measurement. These experiments indicate that with the prolonged wearing of meridional magnifiers at axis 9 0 degrees or at axis 1 80 degrees in front of one eye, there was a gradual reduction in the apparent spatial distortion and the subjec tive responses of discomfort so that after about five days of wearing the magnifiers, no spatial distortion or subjective discomfort was present. With the prolonged wearing of merid ional magnifiers at oblique axes, hcwever, there was only a slight reduction in the apparent spatial distortion and the subjective discomfort. Ogle (4) has stated that subjective adaptation is a learning process and is derived from the empirical factors that are involved in the perception of space. 93 If there is a conflict from the various visual clues regarding the orientation of objects in space, the subject can learn to ignore that visual Information which is not compatible with what he encounters when he attempts to manipu late himself and other objects in space or with what he has learned from past experience. ©ie question arises, however, why is the learning process effective for one type of spatial distortion and much less effective for another? There are probably several fac tors involved in this differential adaptation process, but the information from other sensory and servomechanism systems, kinesthesis, proprioception, touch, etc., is undoubtedly a most significant factor. With the wearing of meridional magnifiers at axis 180 degrees or 90 degrees, there is a sloping of the floor, desk, or table surfaces to one side or another and normally hori zontal contour is no longer horizontal but slopes either up or down. We are nearly always in contact with the floor or desk or table surfaces through our feet and hands. This nearly constant information from proprioception from kinesthetic and tactual receptors and the knowledge from our previous experience that horizontal contours are not sloped, gradually dominates the conflicting information received from vision and the spatial distortion decreases. With the wearing of meridional magnifiers at oblique axes the essen tial spatial distortion is that the walls are tilted toward 94 or away from the observer. The floor and table surfaces will also slant toward or away from the observer but normally horizontal contours will remain horizontal, and for any given position, proprioception information does not conflict with visual information. The tactual and kinesthetic information from hands and arms would conflict with visual information and this would encourage adaptation. The ocular symptoms of discomfort associated with the wearing of meridional magnifiers at oblique axes could result from the presence of the apparent tilting of vertical con tours which are produced by the magnifiers. Hie apparent tilting of vertical contours serves as a stimulus for cyclo- fusional eye movements. The neuromuscular activity associ ated with the cyclofusional eye movements would contribute to the ocular discomfort and would probably remain as long as the apparent tilted vertical contours were present. No corresponding stimulus is present with the wearing of meridional magnifiers at axis 9 0 degrees or at axis 180 degrees. These experiments indicate that measurements of refer ence curves using certain techniques show a gradual change or compensation with the prolonged wearing of meridional magni fiers . This implies that there is either an instability in the subjective visual direction associated with corresponding retinal-cortical units or that the reference curves showing 95 the change or compensation are subject to change through learning. Burian did not accept the theory of unstable cor responding elements and indicated that the compensation was probably due to the influence of empirical factors which were not completely eliminated from the measuring instrument. This concept seems to be somewhat substantiated by the fact that the longer the subject viewed the testing target, which was designed to minimize or eliminate empirical clues for depth perception, the less the amount of measured compensation. An evaluation of the results reveals that measurements of the image size differences made with the space eikonometer or the horopter apparatus using the criterion of the appar ent frontal plane indicate a measured compensation, whereas measurements of the image size differences using the opthalmoeikonometer showed less or no measured compensation. Measurements with the space eikonometer depend on stereopsis and utilize the criterion of the apparent frontal plane. Pre vious measurements of the apparent frontal plane in the pres ent study have indicated that it is a function of the visual environment and therefore the compensation measured with the space eikonometer and the horopter apparatus using the criterion of the apparent frontal plane does not necessarily imply an instability of corresponding retinal-cortical units. Measurements with the ophthalmoeikonometer, however, do not depend on stereopsis and will yield measurements of the true horopter. The fact that the measurements with this instru- ment showed little or no compensation supports the concept of stability of corresponding retinal-cortical units. Burian indicated that he had made some preliminary measurements with the "grid-nonius" horopter and although the results were quite variable they showed that less compensation occurred. It was decided to repeat this experiment measuring the effect of the unilaterally worn meridional magnifier with the criterion of the apparent frontal plane and the criterion of identical subjective visual direction, the horopter, using the previously described Instrument, and to determine the effect of the meridional magnifier over a longer period of time. B. Procedure. The subject (JBE) was not accustomed to wearing frames and lenses, so for six weeks preceding any measurement in this experiment his refractive correction of -0.50 D. each eye was worn continually. Following this, several determinations of the horopter and the apparent frontal plane were made over a period of two weeks with the apparatus set for symmetrical convergence on a fixation distance of 100 cm. Hiis was done to determine the initial configuration and orientation of the reference curves. A meridional magnifier which was calculated to produce 2.22# magnification was then placed before the right eye with the axis 9 0 degrees and worn continually every waking moment during which binocular vision was used for MM days. Hie 97 meridional magnifier was mounted in a comfortably fitting opthalmic frame. Several determinations of the horopter and the apparent frontal plane were made during the 44 day period, with most of them being made when the magnifier was first put on. Ihe meridional magnifier was then removed and determinations of the horopter and apparent frontal plane were again made for 12 days. Measurements were generally taken about the same time of day so as to avoid the diurnal variations found by Burian (19). A diary was kept during this period of time and the subjective symptoms and evalu ations of the spatial distortion in the usual environment and in a fullsized leaf room were recorded. The measurements taken before the wearing of the meridional magnifier were averaged and the apparent angular displacements of the target elements at the left eye (e^ in Figure 13) for the six measuring elements of the tar get were determined. TSie apparent angular displacements of the target elements at the left eye were then determined for the measurements taken during and following the wearing of the meridional magnifier and compared to the initial value by the following formula: £ « 100 D - — ___ *______(20) 6 The angle, TOS2* equals the apparent angular displacement of a given target element at the left eye during or after the wearing of the meridional magnifier, and the angle, TOSp 98 equals the apparent angular displacement of the same target element at the left eye before the wearing of the meridional magnifier. This formula actually yields the average difference in percent angular magnification between the two testing condi tions. Tbis can be shown as follows: T0S2 - (TOS1)(M) 4> ^ TOSx (T0S2 - TOSx) 100 _ [(TOSiXM) - (TOS^ ] 100 4> T0S1 [TQSl (M - 1).]10 0 _ (M , 1)100. M T0Sl There are six measuring conditions so that the sum of the 6 angular magnification changes divided by six yields the average percent angular magnification. C. Results. When the meridional magnifier was placed in front of the right eye with the axis at 9 0 degrees, the typical distortion of objects in visual space became appar ent in about one minute. T5ie desk top appeared to have the form of an isoseafes trapezold and slope down to the right. The floor also appeared to slope down to the right. The tops of doors, windows, pictures, etc., appeared to tilt uo to the right, whereas the bottoms of doors, pictures, etc., appeared to tilt down to the right. The distortion was more apparent with near fixation distances and with restricted 99 movements of the eyes. This agrees with the results of Burian. The distortion was particularly evident in a small elevator that was frequently used. A mild headache and pain in the right eye was experienced but no nausea or real dis comfort was present. In walking there was a tendency to drift slightly to the right but no difficulty of manipulation of objects in space was experienced. By the third day the subjective symptoms had almost disappeared. In the elevator, in the leaf room, or at the desk, the spatial distortion was still evident. No visual discomfort was present on the fourth day and only a slight amount of spatial distortion was evident. On the sixth day no spatial distortion in usual surroundings was present. The comment was made in the diary on the sixth day, " I ^ quite use to the lens now and sometimes forget that I have it on." On the eighteenth day the observer was in a small forest area and observed the weird sensation of a small stream of water apparently moving uphill. The leaf room was observed almost every day during and immediately after the wearing of the meridional magnifier. The distortion was strikingly evident at first but seemed to decrease after about the twentieth day, and on the forty- fourth day, the floor of the leaf room seemed almost level, the back wall was almost in an apparent frontal plane, but the ceiling slopped up to the right. 100 When the lens was removed on the forty-fourth day, a spatial distortion just opposite to that associated with a meridional magnifier placed axis 90 degrees In front of the right eye was apparent. The leaf room, the elevator, the desk, and all objects in visual space were distorted as if a meridional magnifier had been placed at axis 90 degrees in front of the left eye. This spatial distortion decreased rapidly and was gone on the third This difference was present for several days but disappeared by the twelfth day. 101 determination duringtheprolorged wearingof a meridional magnifier. OS>OD O D > O S +2.5 + 3.0 + + + + + 1.5 .5 + .5 - - 0.0 2.0 1.0 2.0 i. 8—Percent differenceIn magnification Pig. 48.— needed for apparentfrontal plane 4 1 2 2 24 28 3 3 40 4 4 5 56 52 48 44 0 4 3S 32 8 2 4 2 20 26 12 8 4 0 T i m e (Days) e m i T = A Afocal B =B Afocal C = End of =C End Spatial Introduced Magnifier Distortion eoved e v Remo Magnifier The results of the measurement of the horopter are Illustrated In Figure 49* When the meridional magnifier was introduced (A) a magnification difference with the right image larger than the left of about 2.6# was measured. Sub sequent measurements were quite variable but it appears that no significant reduction in the magnification difference between the two eyes occurred during the time that the magni fier was worn. Tlie measurement on the forty-fourth day still indicated a magnification difference of 2.4#. When the meridional magnifier was removed, on the forty-fourth day (B), the magnification difference between the two eyes changed to nearly that found before the magnifier was worn. D. Discussion. The change In the orientation of the apparent frontal plane during the wearing of the meridional magnifier, exhibited by the change in the measured magnifica tion difference between the two eyes, corroborates the results of Burian and again illustrates the instability of this reference curve. There appears to be a correlation between the subjective adaptation and the measured compensation since the time required for the complete subjective adaptation to the spatial distortion to occur, both during the wearing of the meridional magnifier and after its removal, coincides well with the time period during which the measured compensation takes place. An important point to consider, however, is the difference 103 + 3.0 Meridional Magnifier +2.5 Intr oduced Meridional ♦ 2.0 Magnifier R e m o v e d ♦ 1.5 D 0.0 - .5 - 1.0 20 24 28 32 36 40 44 48 52 56 T i m e (Days) Fig. 4 9.— Percent difference in magnification needed for horopter determinations during the prolonged wearing of a meridional magnifier. between the amount of measured compensation and the extent of the subjective adaptation. The subjective adaptation to the spatial distortion is complete whereas the measured com pensation only amounts to about one-third of the meridional magnifier being worn. Why this difference should exist is a problem that will require further study and research. Another problem to consider is the change in the appear ance of the leaf room that occurs after wearing the meridional magnifier for twenty days without any corresponding change in the measured magnification difference between the two eyes using the criterion of the apparent frontal plane. Ihe leaf room and the apparent frontal plane both depend on stereopsis for their spatial perception, yet different results are obtained with different procedures. Tttie absence of distor tion of the leaf room after wearing the magnifier for 20 days could have been due to the fact that not enough time was spent viewing the leaf room at the time of assessment, for it has been pointed out by Miles (20) that prolonged viewing is sometimes necessary before the spatial distortion produced by magnification differences between the two eyes will become manifest. This factor was considered in the present study and prolonged viewing of the leaf room was utilized. Another aspect to be considered is that some empirical factors which are not too prominent could still be present in the leaf room and could have been utilized by the perceptual mechanism, through repeated observations of the leaf room, to 105 minimize the distortion. This is somewhat confirmed by the fact that the floor and walls of the leaf room appeared un distorted while the roof still appeared distorted. In the usual environment, empirical clues and other sensory informa tion are utilized by the perceptual mechanism so that after prolonged viewing through meridional magnifiers, the more frequently encountered surfaces appear normal. If the leaf room inadvertently contained any existing empirical clues for depth perception, they could be utilized by the perceptual mechanism and the normally encountered surfaces, the walls and floor of the leaf room, would appear undistorted. Hie roof, however, is not a normally encountered surface so that any existing empirical clues would be of little consequence and therefore the roof would appear distorted in the leaf room. Although the horopter data are quite variable, after the initial change, the wearing of the meridional magnifier does not appear to produce any consistent change in the orientation of the horopter. This result illustrates the stability of this reference curve. Another characteristic difference between these two reference curves, which again points out their basic differ ence, is the difference in the effects that occur when the meridional magnifier was removed. The measurements with the horopter returned very close to those found before the meridional magnifier was worn, whereas the measurements with 106 the appearent frontal plane Indicated a magnification dif ference of the opposite nature from that found during the time that the meridional magnifier was worn. It appears from the change in the apparent frontal plane during the wearing of the meridional magnifier, that the perceptual mechanism, through learning and past experience, Is able to modify the information received from the retinal-cortical system so that the final visual percept conforms to the empirical knowledge of space. If the information from the retInal-cortical system is suddenly changed, by removing the meridional magnifier, the immediate visual percept will be erroneous since the perceptual mechanism has "learned" to evaluate visual information with the meridional magnifier before one eye. Through this regulating system, however, the visual percept will once again be modified so as to conform to the empirical knowledge of visual space. The relative stability of the horopter during and following the wearing of the meridional magnifier indicates that this reference curve is not a function of this modifying mechanism and is therefore not dependent on an experiential knowledge of visual space. 107 EFFECT OF ASYMMETRICAL CONVERGENCE ON THE HOROPTER, THE APPARENT FRONTAL PLANE, AND THE APPARENT NORMAL PLANE A. History. The orientation and configuration of the reference curves obtained with asymmetrical convergence as compared to the results obtained with symmetrical convergence yield important information about the nature of these curves. The horopter concept applies in asymmetrical convergence as well as in symmetrical convergence and if there is a stabil ity of corresponding retinal-cortical units, the relation between the angles 7, 7, and Pig. 50.— Reference planes during asymmetrical conver gence. F ... F* frontal plane, N ... N* normal plane. 109 plane. In symmetrical convergence these two planes become coincident. Previous investigators have analyzed the horopter and the apparent normal plane in asymmetrical convergence. Herzau (21) first investigated this problem and found that the difference in orientation between the nonius horopter and the apparent normal plane determined with symmetrical con vergence was not the same as that obtained with asymmetrical convergence. He proposed that the orientation of the appar ent normal plane in asymmetrical convergence was not dependent solely on ocular correspondence but was also a function of the rayosensory influence from the extraocular muscles. Ames et al. (9) measured the horopter in asymmetrical convergence using the "grid-nonius11 technique. Their results showed that the Hering-Hillebrand deviation determined with asymmetrical convergence was lower than that determined with symmetrical convergence. They concluded that this change did not indicate unstable corresponding retinal elements but demonstrated variations in the dioptric system through deformation of the eyeball and a rearrangement of the internal « parts of the eyeball (tilting of the lens, stretching of the retina). Herzau and Ogle (22) investigated the horopter with ten degrees of asymmetrical convergence to the right and ten degrees of asymmetrical convergence to the left. They only used two measuring points, one located four degrees to the 110 right and the other located four degrees to the left of the fixation point. Their results have been analyzed by the method used in this study and are illustrated in Figure 51A. The results of measurement of the horopter with the two asymmetrical viewing conditions are in close agreement, and Ogle and Herzau state that this result shows that there is no significant change in the effective functional patterns of corresponding points with asymmetrical convergence. Figure 51A also shows the results of measurement of the horopter with symmetrical convergence, and indicates a dis agreement between the horopter measured with symmetrical con vergence and the horopter measured with asymmetrical converg ence. Uiis discrepancy was not discussed, but it could well be due to changes in fixation disparity. Herzau and Ogle (22) also investigated the apparent normal plane in symmetrical and asymmetrical convergence. Their results have been analyzed by the method used in this study and are Illustrated in Figure £1B. There is a consid erable disagreement between the apparent normal plane measured with asymmetrical convergence and that measured with symmetrical convergences, and between the results obtained with right and left asymmetrical convergence. These results indicate that when objects are positioned in space so they appear to be located in a normal plane, the Images of these objects will fall on different parts of the retina depending on the type of convergence. Uierefore, the apparent normal 111 Fig. 51•— A. Horopter data with symmetric1 and asymmetrical convergence. B. Apparent normal plane data with symmetrical and asymmetrical convergence. From Herzau and Ogle. 112 Y (Degrees) Y (Degrees) IOO 9 .8 9 10 o 6 9 9.7 9 3 9 9.4 9 9 9.2 9.9 4 ' O 6 8 3 2 4 t ■•AsyTT^. • £ o o 2 -- 4>(Degrees) $(Degrees) o. (right) Con. . m y s ^ A A B O y. Con. Sym. O O y. Con. ■O Sym. 113 o. (left) Con. . m y s A (right) Con. . m y s A 2 Con,, (left) •2 4 3 8 6 4 plane is not directly associated with corresponding retinal elements. An evaluation of the data reveals that in asymmetrical convergence to the right the apparent normal plane rotates counterclockwise with respect to the physical normal (7 L > 7 R), and in asymmetrical convergence to the left the apparent normal plane rotates clockwise with respect to the physical normal (7 R > 7 L). This is better illustrated in Pigurjg 52 which is taken from Herzau and Ogle (22). Ogle (23) has indicated that the rotation of the apparent normal plane in asymmetrical convergence is produced by the differ ence that exists in the vertical dimensions of the two retinal images due to the fact that the distance of the object from one eye is greater than that from the other eye. He states that this rotation of perceptual space around the fixation point is a necessary part of vision and must occur if correct stereoscopic localization is to be maintained. Such a rota tion can be produced in symmetrical convergence if a meridional magnifier is placed in front of one eye with the axis at 180 degrees. Ogle (24) has called this peculiar spatial distortion phenomenon the induced effect. The determination of the reference curves with asym metrical convergence was undertaken in this study so as to acquire data on the apparent frontal plane as well as the apparent normal plane, to determine the horopter using more measuring points, and to determine the relationships of these three reference curves. 114 Fig. 52.— Spatial plot of horopter and apparent normal plane data with symmetrical and asymmetrical convergence. From Herzau and Ogle. 115 asymmetrische Konvergenz symmetrische Konvergenz asymmetrische Konvergenz Nonius■ Nonius — NE VO cm StE B. Procedure. The position of the subject in the instrument was as previously described. Measurements were taken for the three reference curves with an asymmetrical convergence to the right of four degrees and ten degrees using a fixation distance of 50 cm. The determination of the horopter was made as described previously. For the determin ation of the apparent normal plane, the targets were posi tioned so that they appeared to lie in space in a normal plane, and, for the determination of the apparent frontal plane, the targets were positioned so that they appeared to lie in space in a frontal plane. Although the settings for the apparent frontal plane were more difficult to make than those of the apparent normal plane, due to the difficulty of judging what constituted a frontoparallel plane, reliable measurements of both reference curves could be made. The data were collected, averaged, and analyzed by the method previously discussed. C. Horopter results. The results of the horopter measured with four degrees and ten degrees of asymmetrical convergence are shown along with the results with symmetrical convergence in Figure 53- 'Ehe shape and orientation of the horopter are essentially the same with both asymmetrical con vergence viewing conditions and with symmetrical convergence. This shows that the visual directions associated with cor responding retinal-cortical units are the same with various degrees of asymmetrical convergence as they are with 117 7.64 O O Sym . Con. » --- Asym . Con. (4 R) 7.60 ^ A.Asym. Con.(10° R) X 7.56 W> 0> Q 7.52 7.48 7.44 6 5 4 3 2 0 2 3 4 5 6 4> (Degrees) Pig* 53*— Horopter data with symmetrical and asymmetrical convergence. symmetrical convergence and further affirms the concept of the stability of corresponding retinal-cortical units. D. Apparent frontal plane and apparent normal plane results. The results of the apparent frontal plane and apparent normal plane measurements with four degrees and ten degrees of asymmetrical convergence along with the results with symmetrical convergence are illustrated in Figure 54 and Figure 55* The analytical graphs are shown in Figure 56. These data show that the results obtained by the two criteria with asymmetrical convergence differ from one another and differ from the results obtained with symmetrical converg ence . The curvature of the apparent frontal plane remains essentially the same with symmetrical and asymmetrical con vergence, but the curvature of the apparent normal plane is slightly less in asymmetrical convergence. The change in the curvature of the apparent normal plane could be due to a change in the perceived distance for it has been previously shown that the curvature of the apparent normal plane changes with changes in perceived distance. The most significant finding is the change in the orientation of the apparent frontal plane as the fixation condition changes from symmetrical to asymmetrical converg ence, and the lack of change in orientation of the apparent normal plane as indicated by the anlselkonlc deviation. TCils finding can also be illustrated by showing a plot of the spatial locations of the targets when they satisfy the two 119 metrical convergence. plane data with symmetricalconvergence and 4° of asym y (Degree*) 7 7 3 7 7.48 7.70 778 7.74 90 9 i. 4—Apparentfrontal planeand apparent Fig. 54.— normal * * . (AC) P F A 120 4> (Degrees) 4° Asymmetrical Convergenc 4° Asymmetrical =B 50 cm (AC) P N A &ANP(SC) P N & A P F A ercl convergence. metrical plane data with symmetrical convergence and 10° of asym of 10° and convergence symmetrical with data plane y (Degrees) 7 7 7 7 7 7 88 6 56 4 7 70 78 * i- 5—Aprn rna ln ad paet normal apparent and plane frontal Apparent 55-— Pig- 5 R L 3 _ o . 2 < > ( D e g r e e s ) 121 O (AC) P N A z 3 4 to Fig. 56.— Analytical graphs of apparent normal plane data with symmetrical convergence and 4° and 10° of asymmetrical convergence. 122 .Ol A N P St A F P Symmetrical Convergence H = 0. 072 0. 010 .oo- .Ol A N P 4 & Asymmetrical Convergence H = 0. 052 S = 0. 009 oo AFP 4 Asymmetrical Convergence H = 0.074 S = 0. 022 04 AFP 10 Asymmetrical Conver genee H = 0. 074 S = 0. 038 S o t 4 L R 4> (Degrees) 123 criteria. Such a plot for ten degrees of asymmetrical con vergence along with the theoretical VIeth-Muller circle is shown in Figure 57* These results indicate that with a ten degree asymmetrical convergence to the right, the apparent normal plane has rotated 1.5° in a clockwise direction and the apparent frontal plane has rotated 12° in a counterclock wise direction. If the apparent frontal plane and the appar ent normal plane are associated with the same corresponding retinal-cortical units in asymmetrical convergence as they are in symmetrical convergence, the orientation of these reference curves with respect to the Vieth-Mflller circle should be the same in the two viewing conditions. If, however, the apparent frontal plane and the apparent normal plane are dependent on the environment, we would expect, for a ten degree asymmetrical convergence to the right, a ten degree counterclockwise rotation of the apparent normal plane and a 20° counterclockwise rotation of the apparent frontal plane with respect to their orientation In symmetrical con vergence. We can conclude from this data that there was no effective rotation of the apparent normal plane and that the rotation of the apparent frontal plane was about half of that expected. This conclusion confirms Ogle's theory that the rotation of perceptual space around the point of fixation In asym metrical convergence is due to the difference in the vertical dimensions of the two retinal Images— the induced size effect. 124 Pig* 57 •— Spatial plot of apparent normal plane and apparent frontal plane data with symmetrical and 10° asymmetrical convergence. 125 Median! Plane ANP gence) • Circl In this experiment the centers of rotation of the haploscope arms were located at the approximate centers of rotation of the eye and, therefore, In asymmetrical as well as symmetri cal convergence, the targets would subtend equal angles at the eyes. With this arrangement no difference in the vertical dimensions of the two retinal Images would exist and, according to Ogle, no rotation of perceptual space should occur. Uiis was the result obtained. 127 SUMMARY AND CONCLUSIONS These experiments were designed to study the nature of ocular correspondence by investigation of the horopter, the apparent normal plane, and the apparent frontal plane. An instrument was designed which could be used to measure these reference curves for various fixation distances with symmet rical and asymmetrical convergence. The instrument was de signed so that there weie no objects in the visual field except those objects necessary for measurement. These reference curves were determined with various fixation distances, with i symmetrical and asymmetrical convergence, and before, during and after the prolonged wearing of a meridional magnifier in front of one eye. The results of the horopter measurements with various fixation distances in symmetrical convergence indicate that the locations of objects in space that are imaged on corres ponding retinal elements do not form a smooth curve in space, but that the 7 - 7 values for the different values of (Figure 13) are essentially unchanged for the various fixa tion distances. 15ie results of the apparent frontal plane and the apparent normal plane measurements with various fix ation distances in symmetrical convergence indicate that the positions of objects that appear to lie in a fronto-parallel 128 plane form a smooth curve which conforms to equation (12)* and that the Hering-Hillebrand deviation coefficient is directly proportional to the fixation distance expressed in diopters. This conclusion supports Fry*s theory concerning the perceived position of objects in space. The results of the horopter measurements with the wear ing of a meridional magnifier indicate that the locations of objects in space that are imaged on corresponding retinal points are changed in accordance with the power of the meridional magnifier, and do not undergo any consistent change during the wearing of the meridional magnifier. When the meridional magnifier is removed, the locations of objects in space that are imaged on corresponding retinal points are the same as they were before the lens was worn. The results of the apparent frontal plane and the apparent normal plane measurements with the wearing of a meridional magnifier indi cate that the locations of objects in space that appear to lie in a fronto-parallel plane are at first changed in accordance with the power of the meridional magnifier, but undergo a consistent change during the wearing of the magnifier so that after about one week the change in the locations of the objects in space are such that they reflect only 70 percent of the power of the meridional magnifier. When the magnifier is removed, the positions of objects in space that appear to lie in a plane parallel to the face plane are not the same as the premagnifier positions, but are changed to positions that 129 they would have if a meridional magnifier were placed before the opposite eye. The change corresponds to about 38 percent of the meridional magnifier, which approximately agrees with 30 percent change that occurred with adaptation. This effect quickly subsides and may be followed by apparent frontal plane measurements that indicate a small change of the same type as that produced by the previously worn meridional magnifier. The orientation of the apparent frontal plane then gradually returns to its pre-magnifier position. The results of the horopter measurements with asymmetri cal convergence indicate that the y - y values for various values of are essentially the same as those for symmetrical convergence. .The results of the apparent normal plane measurements with the described instrument in asymmetrical convergence indicate that objects that are arranged in space so that they appear to be perpendicular to the bisector of the lines of sight have essentially the same relative loca tions in symmetrical and asymmetrical convergence. Ihe results of the apparent frontal plane measurements in asym metrical convergence indicate that the locations of objects in space that appear to lie in a plane parallel to the face plane are rotated with respect to the Vieth-Mflller circle in the expected direction but only half of the amount expected. Since the apparatus used in this experiment produced no dif ference in the vertical dimensions of the retinal images with asymmetrical convergence, the lack of rotation of the apparent 130 normal plane and the 50 percent reduction in the expected rotation of the apparent frontal plane with asymmetrical convergence, support Ogle's theory that the rotation of per ceptual space in normal surroundings is brought about by the differences in the vertical dimensions of the two retinal images through a learning process. It appears from these experiments that the retinal- cortical unit distribution does not vary uniformly across the visual field but has areas of varying density. The subjec tive visual direction associated with each retinal-cortical unit, however, is constant and not a function of viewing condition or environment. The horopter is the direct spatial representation of these subjective visual directions and involves the same pairs of retinal-cortical units of the two eyes regardless of the testing or viewing condition. It would appear that the horopter involves an Innate arrangement of corresponding retinal-cortical units since the subjective visual directions associated with the retinal-cortical units are not subject to change or modification. Experiments with the apparent frontal plane and the apparent normal plane have Indicated that the shape and orien tation of these reference curves are associated with learning and environmental conditions and are therefore not entirely based on ocular correspondence. The horopter and the apparent frontal plane are thus different reference curves based on different processes of 131 vision. There appears to be no fundamental relationship between them which would allow the determination of one by the measurement of the other. 'Hie horopter is undoubtedly the standard or basic reference curve on which all judgments of stereoscopic distance are based and from which all other reference curves are formulated by the experiential processes of perception. 132 BIBLIOGRAPHY 1. von Helmholtz, H.: Treatise on Physiological Optica, Vol. Ill, translated and edited by J. P. C. Southall, The Optical Society of America (1925). 2. von Tscherraak-Seysenegg, A.: Introduction to Physiologi- cal Optics. Charles C. Thomas, Springfield, Illinois m 5ST:— 3. Shipley, T.: The frontal references surfaces of visual space, Docum. Ophthal., 13. 487 (1959)- 4. Ogle, K . : Binocular Vision, W. B. Saunders Co., Philadelphia (1950). 5. Fry, G. A., Hill, W. W.: The center of rotation of the eye, Am. J. of Optom. and Arch. Am. Acad. Optora., 32* 58J (1962). 6. Fry, G. A.: Visual perception of space, Am. J. of Optom. & Arch. Am. Acad. Optom., 2 7 , 531 (1950). 7. Ogle, K.: An analytical treatment of the longitudinal horopter; its measurement and application to related phenomena, especially to the relative size and shape of the ocular images, J.O.S.A., 22, 665 (1932). 8. Ames, A., Ogle, K., and Gliddon, G.: Corresponding retinal points, the horopter and size and shape of ocular images, Part I, J.O.S.A., 22, 538 (1932). 9. Ames, A., Ogle, K., and Gliddon, G . : Corresponding retinal points, the horopter and size and shape of ocular images, Part II, J.O.S.A., 22, 575 (1932). 10. Osterberg, G.: Topography of the layer of rods and cones in the human retina, Acta Ophthalamologlca, Supple ment VI (1935). 11. Polyak, S. L. : The Vertebrate Visual System, University of Chicago Press (1957)* 12. Ditchburn, R. W.: Eye-movements in relation to retinal action, Optica Acta, _1, 171 (1955)* 133 13* Hebbard, F. W.: Eye Movements during Fixation and Fusion, Ph.D. dissertation, University of California (1957)* 14. Riggs, L. A., Ratliff, F., Comsweet, J. C., and Corn- sweet, T. N.: The disappearance of steadily fixated visual test objects, J.O.S.A., 43, 495 (1953). 15- Zajaczkowska, A.: Experimental tests of Luneburg's theory. Horopter and alley experiments., J.O.S.A., 46, 514 (1 9 5 6). 16. Shipley, T.: An experimental study of the frontal refer ence curves of binocular visual space, Docum. Ophthal., 1 3, 321 (1 9 6 1). 17« Fry, G. A.: The discrepancy between physical and per ceived curvature, Am. J. of Optom. and Arch. Am. Acad. Optom., 3 3, 147 (1956). 18. Gilinsky, A. S.: Perceived size and distance in visual space. Psychol. Review, £8, 460 (1951). 19* Burian, H. M.: Influence of prolonged wearing of merid ional size lenses on spatial localization, Arch. Ophth., 3 0 , 645 (1943). 20. Miles, P. W.: A comparison of aniseikonic test instru ments and prolonged induction of artificial aniseikonia, Am. J. ephth., 3JL, 687 (1948). 11 21. Herzau, W.: Uber den Horopter bei scheifer Betrachtung, Arch. f. Ophth., 121, 75 6 (1928-29). 22. Herzau, W. and Ogle, K. N.: Uber den Grtfssenunterscheid der Bilder beider Augen bei asymmetrischer Konvergenz und seine Bedeutung ftlr das zweiaugige Sehen, Arch. f. ophth., 131, 327 (1937). 23. Ogle, K. N.: Induced size effect with the eyes in asym metric convergence, Arch, of Ophth., 23, 1023 (1940). 24. Ogle, K. N.: Induced size effect. I. A new phenomenon in binocular space perception associated with the relative sizes of the images of the two eyes, Arch, of Ophth., 20, 604 (1938). 134 AUTOBIOGRAPHY I, Jess Boyd Eskridge, was born on June 29, 1928 in Green River, Wyoming. I received my elementary and secondary education In the public schools of that city. My under graduate training consisted of one-half year at Ventura Junior College, one year at the University of California at Los Angeles, and three years at the University of California at Berkeley, from which I received the degree Bachelor of Science in 1953• I entered the Graduate School at the Uni versity of California at Berkeley and received the degree Master of Optometry, In 1954- I held the position of Instructor in Optometry from 1954 to 1956, and the position of Assistant Professor of Optometry from 1956 to 1958 at the University of Houston. I entered the Graduate School of The Ohio State University In 1958 and received the degree Master of Science in 1959* I was a recipient of an American Optometric Foundation Research Fellowship from 1958 to 1 9 6 1. I also held an appointment as a Research Assistant at The Ohio State University during the same period of time. Since 1 9 6 1, I have held an appointment as an Instructor In Optometry and Physiological Optics at The Ohio State University. 135