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Theses
1982
Derivation of the Optimum Film Contrast Gradient in Photographic Tone-Reproduction Systems
William R. Dowling
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Recommended Citation Dowling, William R., "Derivation of the Optimum Film Contrast Gradient in Photographic Tone- Reproduction Systems" (1982). Thesis. Rochester Institute of Technology. Accessed from
This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. DERIVATION OF THE OPTIMUM FILM CONTRAST
GRADIENT IN PHOTOGRAPHIC TONE-REPRODUCTION SYSTEMS
by
William Race Dowling
A the~is submitted in partial fulfillment of the requirements for the degree of Bachelor of Science ln the School of Photographic Arts and Sciences in the College of Graphic Arts and Photography in the Rochester Institute of Technology April, 1982
Signature of the Author •• ...... ••...•... • •...... ~~~~/~~ Photographic Science and Instrumentation certified by ...... ~d.~~r? .G.r~~~e.r •.. , •.••...... Vl ~i~. 7 .. Thesis Advisor
Accepted by...... , ...... -...... Supervisor, Undergraduate Research ROCHESTER INSTITUTE OF TECHNOLOGY
COLLEGE OF GRAPHIC ARTS AND PHOTOGRAPHY
PERMISSION FORM
Title of Thesis: Derivation of the Optimum Film Contrast
Gradient in Photographic Tone-Reproduction Systems
I William Race Dowling hereby grant permission to the
Wallace Memorial Library, of R.I.T., to reproduce my thesis in whole or in part. Any reproduction will not be for commercial use or profit. I wish to be informed in writing after each reproduction reguest is granted, stating the party or parties requesting such reproduction. I can be reached at the following address:
2403 Penatiquit Avenue
Seaford, New York 11783
April 23, 1982
n . DERIVATION OF THE OPTIMUM FILM CONTRAST
GRADIENT IN PHOTOGRAPHIC TONE -REPRODUCTION SYSTEMS
by
William Race Dowling
Submitted to the Photographic Science and Instrumentation Division in partial fulfillment of the requirements for the Bachelor of Science degree at the Rochester Institute of Technology
ABSTRACT
The optimum tone-reproduction characteristics were determined for a high contrast, a low contrast and a controlled contrast scene, by subjective analysis of the resulting prints. From this, mathematical models of the optimum film characteristic curves and fractional gradients were derived. Optimal system gamma (filmT x paper 7 ) was determined to be between 1.2 and
1.4, however, the gradient contrast was determined for the film so that contrast is defined over the entire toe and straight line regions. Luther's equation and its derivitive were used as the models in this study, and it was found that these can be used to describe a given film's characteristics over a wide range of development times. ACKNOWLE DGEMENTS
The author wishes to express his gratitude to Dr. Edward
Granger of the Eastman Kodak Company, whose ideas and time
aided in the successful completion of this thesis.
Since I had not the means to fund this project, a
special salute of thanks is in order for the Central
Intelligence Agency for their generous funding.
Mel Simon of Mel Simon Inc. deserves a note of thanks
since it was his initial assignment given to me which led
to the main idea in this project.
The author's wife, Joyce, who held the homestead
together during the long hours and late nights, deserves
his highest praise as the most patient woman on Earth. It
is to her, that this thesis is dedicated.
111 . TABLE OF CONTENTS
List of Tables , v.
List of Figures vi .
List of Equations vii .
Introduction 1
Experimental 6
Sensitometry 6 Mathematical Modeling 8 Printing 10
Subjective Evaluation of Prints 11
Results 12
Discussion and Conclusion 15
Determining Optimum Contrast 15 Conclusion Summary 16
References 19
Appendices 20
Appendix A 21
Appendix B 26
Appendix C 29
Vita 32
iv. LIST OF TABLES
Table 1- The Range of Luther's Equation Parameters
Which Yield Optimal Results 13
Table 2- Output of Best-Fit Luther's Equations 30
Table 3- Output of Best-Fit Luther's Equations 31
v. LIST OF FIGURES
Figure la- A Typical Tone-Reproduction System 2
Figure lb- Known System Response 2
Figure 2- A Theoretical Film Response 2
Figure 3- Comparison of High and Low Contrast Scene Optimums 18
Figure 4- Optimum Curve for General Case 22
Figure 5- Optimum Curve for High Contrast Scene 23
Figure 6- Optimum Curve for Low Contrast Scene 24
Figure 7- Optimum Curve for Portrait 25
Figure 8- Graphical Explanation of Luther's Equation. 27
vi, LIST OF EQUATIONS
Equation 1 8 , 27
Equation 2 8
Equation 2a 9
Equation 3 28
Equation 4 28
Equation 5 28
vi 1. INTRODUCTION
The single most important part of photographic repro
duction is viewer satisfaction. Aesthetic considerations
aside, the viewer is most influenced by the quality of the
reproduction. This quality is not necessarily associated
with accurate tone reproduction, but rather, it is associated
with the way the viewer feels the scene should look.
In figure la, we see a graphical representation of a
tone reproduction system. The system response curve shows
how original scene luminances transform to resulting
densities in the print. In completely accurate tone repro
duction, this curve is a straight line, with the lowest
density representing the brightest specular highlight and
the highest density, the deepest shadow.
In simple systems, the response curve can be assumed to
be a straight line. For example, in copy work, we wish to
have an exact duplicate of an original. This necessitates a
straight tone-reproduction curve, since we want an exact
density-to-density match between original and copy. If the
"backwards" tone reproduction cycle is worked from this
assumption (see Fig. lb), a suitable copy film characteristic
curve can be determined, even if no such film exists (Fig. 2).
This theoretical characteristic curve can then be used as an
aim, where the photographic technician or photographer can
adjust the exposure and processing of a film to give the
closest match. Paper Response System Response Paper Response System Response
/ \ \
/
, / 1
Flare (system) Rim Response Flare (system) Rim Response
Figure la (left)- A typical tone-reproduction system where film, paper and flare characteristics are significant.
Figure lb (right)- If the needed system response is known, the necessary film characteristics can be derived and the results used to choose a film-development time-exposure
combination which yields optimum results.
Log Exposure
Figure 2- A theoretical copy film characteristic curve derived from the process described in figure lb. Note that no known film has the characteristic curve shown above. This is not such a simple task when the system involves
a natural scene. The viewer's eyes adapt to different lum
inance levels depending upon the object on which they are
fixed. When a viewer is asked to observe a print of any
given scene, he must make an evaluation based only on his memory and experience. For this reason, a system exhibiting
an exact reproduction of a scene will not necessarily be
judged the best in quality.
The study performed here has established the optimum
tone-reproduction range for three basic scenes encountered
in standard pictorial photography, by assessing subjective
evaluations of photographs processed to different specifi
cations. From these, the optimum film characteristic curves
have been determined. Since subjective testing of tone re
production is laborious and time consuming, extensive work
2 in this area has not been done.
The primary tone reproduction factor studied in this
experiment is contrast. Effects such as granularity and
viewing conditions, have been extensively investigated in the
literature, and have valid, well-established numerical
2 > 3 ' 4 ' 5 ' 6 characterizations. Contrast however, has had the
misfortune of being associated with a single number, ever
since the studies of Hurter and Driffield in 1890. Gamma,
the slope of the straight-line portion of the characteristic
curve, is not always an appropriate means of judging con-
trast. The questionable nature of gamma has been addres
sed by Niederpruem, Nelson and Yule of the Kodak Research 7 Laboratories. These researchers developed a better measure of contrast, the contrast index, which considers the toe region, as well as the straight-line portion of the curve.
While the advantages of having a single number associated with contrast, in most cases, outweighs the mathematical
rigor of defining contrast as a function of exposure, a
single number cannot adequately define the contrast over
the entire range of a sensitized material. For this reason,
the characteristic curves of the film for varied development
times have been well established, and the fractional
gradient of the material over the entire useable range has
7 ' R been determined. This is absolutely essential, since
. . 9 contrast is affected by both developer activity and exposure.
A film exposed on the straight-line portion will yield an
entirely different result than the same film exposed mainly
on the toe region. Since gamma is still the most widely
used method of determining contrast, all results in this
study have been left in a form where gamma is readily deter
mined from the gradient equation. Observations have been
made when scene contrast, development time, exposure and
paper grade are varied independently, in order to determine
the optimum combinations of these factors.
Knowing the results of this experiment, a photographer
or photographic technician will be able to determine the
correct combination of exposure, development time, paper
grade and film choice for any given scene without guesswork, and be assured of optimum results. The technician is also liberated from the drudgery of producing four-quadrant
tone-reproduction plots, a time-consuming process and cer
tainly too much to ask of a person with a busy schedule. EXPERIMENTAL
This study has shown that a range of optimum tone-repro duction curves exists for any given scene, and these curves can be explicitly defined. It has shown that an optimum set of parameters for contrast can be defined from the tone reproduction curve.
Clearly = four main steps had to be performed in this study: film and paper sensitometry, mathematical modeling, printing and subjective evaluation. These will be discussed
separately, although some overlap of topics is unavoidable.
1 . Sensitometry
In order to model the film curve. Its characteristics had to be defined over a given range of development times.
The film chosen for this experiment was Kodak Panatomic-X, since it had the longest toe region of all currently avail
' able films in 35mm. A long toe region was found necessary, since these are most affected by contrast changes due to exposure. Due to processing constraints, it was decided that the range of development time should be from
3h minutes to 25 minutes. This allowed a gamma from about
0.3 to 1.0 when processed on a reel in Kodak D-76 developer diluted 1:1. Five development times were chosen within this range so that their replicate 30 limits of density did not overlap. This resulted in development times of: 3^, 5%, 8,
14 and 25 minutes; which yielded gammas of, 0.36, 0.48, 0.65,
0.80 and 1.00 respectively. This gave the development times to be used in the photographs for subjective evaluations.
3 Frieser and Beidermann discussed the four basic scenes
encountered in standard pictorial photography. The cate gories they determined are as follows:
1. Distant objects without foreground (200+ ft.)
2. Scenes with objects in medium distance (60-300 ft.)
3. Groups of persons standing 10-15 ft. away
4. Portraits, subject about 5 ft. away.
While this researcher feels that the above categories are valid, it was felt that since this was a study of contrast,
scene contrast should also be taken into account. A com
promise was found necessary, since the number of original
scenes had to be kept to a minimum. Therefore, two outdoor
scenes with objects in medium distance were chosen, one in
bright sun, the other in -heavy overcast. A portrait scene
was chosen, where the photographer has full control over
lighting. A fourth scene (groups of persons) was photogra
phed but not used in this study. Each scene was photographed
on five rolls of film, corresponding to the five development
times discussed earlier. The scene exposure (using the
camera meter) was varied 5 stops, on each roll, in Jf-stop
increments. A step tablet exposure was included on each roll
so that the characteristics for that roll could be explicitly
defined. From these, the film curves for all five develop
ment times were produced.
Sensitometry of Kodak Polycontrast Rapid II RC paper
a 21 tablet was performed by projecting step through 8
Kodak Polycontrast Filters number 1, 2, 3, and 4. Since
the processing was performed in a Kodak Ektamatic Stabiliza
tion processor, the effects of development variability on
the paper were not pursued. This practice is not recommended
by the manufacturer, however this researcher did not detect
any ill effects by using this method.
2. Mathematical Modeling:
Luther's equation for the toe and straight-line portion
of the characteristic curve has been described by Nelson and
Q Simmonds. The use of Luther's equation for the purposes
of this experiment is discussed in Appendix B. There are
essentially two constants in the equation which control the
shape of the characteristic curve model. The equation as
given in Nelson and Simmonds is shown below:
(D = Jj D iog[l00'6*/w+l] . 0.6
Where 7 is the slope of the straight-line portion of the characteristic curve, is the log exposure, D is the density corresponding to the log exposure and w is the distance between the intersection of the slope of the straight-line portion with base + fog density and the intersection of the slope of the curve at that point with the base + fog density (see Appendix B).
if we let K=0.6/cj, then equation 1 reduces to:
(2) = _2_ D log[l0"*+l] .
Equation 1 or 2 is then used to model a given set of
densities. This modeling can be done easily, either graphically or by computer. In order to perform this graphically, equation 1 is the preferred form. It is done
in the following manner:
1. Plot the densities
2. Determine the value of gamma in the usual manner
3. Determine the value of omega by the procedure
described in Appendix B
4. Plot and adjust the value of omega until an accept
able match is made.
If many curves are to be tested it is best to use equation
2 and a computer. This was the method employed in this
study. Shift values were added to equation 2 as follows:
<2a> D = * -ilog[10K<*-f->+l] Vf .
Where e. is the amount the model must be shifted along the + abscissa and D, +f. is the base fog density.
The best fit model can then be determined by varying 7,
K and 6. independently, and summing the squared difference
in density of each step of the 21 step tablet. The process
is repeated until the best least-squares solution is found.
In this study, it was found that the last four steps of the
tablet had to be ignored, since in some cases, these lay on the shoulder region of the curve. Using this method, the
following sum-squares error resulted (see Appendix C for a complete description of the modeled curves). 10
3h min. , 0. 0007
5% min. , 0.0008
8 min., 0.0006
14 min. , 0.0006
25 min. , 0.0012
After the modeling was complete, the values of 1/K and 7 were plotted vs. development time. This allowed Luther's
equation and its derivitive to be found over the entire
range of development time, knowing only the gamma of the
film. Once the optimum gamma was found for each scene, all
that was necessary was to find that gamma on the graph, and
read the value of 7/k , which allowed Luther's equation for
that gamma to be produced.
3. Printing
In order to reduce the final number of prints used
in the subjective evaluations to a manageable size, certain
compromises had to be made. First, the scene exposure
increment had to be increased to one full stop, and the
range reduced to 3 stops. Even with this reduction, one
scene had to be eliminated (the group of persons). This
allowed an initial screening reduction, yielding a total of
201 prints, 67 for each scene.
Printing was performed on a condenser enlarger.
Contrast was varied for each frame by the use of Polycontrast
"Inbetween" filter numbers 1, 2, 3 and 4. contrast grades
were not used.
A system of four-space coordinates was set up in order
to identify the conditions which produced a given print. 11
The format of this system is as follows:
(4) (W,X,Y,Z)
Where W is the scene number (1,2,4), X is the development time number (1 to 5) corresponding to the five development times used, Y is the exposure difference in stops from normal (-3 to +3) and Z is the Polycontrast filter number.
Prints judged acceptable for the analysis were randomized and sequentially numbered. The individual judging the prints had no knowledge of the coordinates corresponding to the sequential numbers.
4. Subjective Evaluation of Prints
The evaluations were performed using fifteen analysts under the standard viewing conditions of: 5000K diffuse source illumination, with fixed viewing distance and angle.
Fifteen evaluations had been determined the minimum number necessary to produce acceptable results.
The method of categories was used, as this method has been known to produce the best results in the past.
The Discussion and Conclusion section of this thesis in cludes more information about how the prints were evaluated. 12
RESULTS
The results of this report take the form of a series
of equations which describe the optimal characteristic
curves for printing on a Polycontrast grade 2 or 3 paper.
The subsequent plots of these equations can be found in
Appendix A. Two equations are given so that one need only
match a set of densities to within the limits of the two.
The optimum system results will then be assured, while still
allowing sufficient flexibility in paper grade selection.
Equations for the gradient are also given both for com
pleteness and in the event one wishes to use these to
determine film parameters. The equations are given in
generalized form, that is, log exposure and density are
only relative quantities. It is the shape of the curve
which must be matched. The specific exposures and densities
of the film will vary depending on the film and developer
type. To use the curves, it is suggested that the tech
nician draw or trace them (Appendix A) onto a clear plastic
sheet, on the same scale which is normally used in the lab.
A plot of any film can be tested by placing the sheet over
the graph paper and shifting it vertically or horizontally until a match (if any) is made.
Four sets of curves are given. The first set is a
general case, which will yield good results if the scene contrast is not known, or if the technician wishes to sim plify matters. The next set is for use in high contrast 13
scenes. That is, bright sun/clear sky, or indoors with clear flash. The next is for low contrast scenes, specif
ically, heavy overcast. The fourth set is for a standard
studio portrait, where the photographer has full control
over the lighting. It should be noted that the character
istics of the latter scene type closely match the general
case. The sets of curves are in tabular form, listed
below.
Table 1- The Range of Luther's Equation Parameters Which Yield Optimal Results.
RANGE OF OPTIMUM FIL M QUALITY PARAMETERS
FROM TO
7* SCENE 7 K 7/K 7 K 7/K SYSTEM
GENERAL 0.775 1.947 0.398 0.665 1.939 0.343 1.33
HIGH CONTRAST 0.676 1.931 0.350 0.578 2.064 0.280 1.16
LOW CONTRAST 0.833 2.062 0.404 0.713 1.912 0.373 1.43
PORTRAIT 0.752 1.913 0.393 0.643 1.966 0.327 1.29 * FILM 7 X PAPER 7)
Values given in the above table are for Luther's equation in
the form of Equation 2, and its derivitive in the form of
note that represents the relative Equation 5 . Please fc
the- independent and D log exposure and is variable, rep
dependent variable. resents relative density and is the
For the gradient, G represents the absolute slope and is
the dependent variable. The gradient equation is in the
form of 7 x correction factor. Therefore, film gamma can
be read directly from this equation. The last column in
the above table represents the optimum film x paper gamma 14
determined in the subjective evaluation. It is included here for completeness. 15
DISCUSSION AND CONCLUSION
It was felt by the author, that a discussion of the treatment of subjective evaluations should be included here instead of in the experimental section, since it is im portant to know how the results were derived.
1 . Determining Optimum Contrast
Once the subjective evaluations were performed (using the method of categories), results were obtained by using the prints which scored the highest. Each analyst was told to rate the prints in terms of contrast quality using the
following categories. Each category was given a number.
7. Excellent 6. Very Good 5. Good 4. Satisfactory 3. Acceptable 2. Unsatisfactory 1. Poor 0. Unuseable
The analysts' responses were summed, normalized and ranked.
A print was included in the analysis if it met one of the following criteria: it appeared in the top one-third of all the prints or it appeared in the top one-third of its particular scene; for the general case and the individual
cases respectively.
System contrast was determined by multiplying the film gamma by the paper gamma. The X and Z coordinates were ranked in order of increasing system gamma. A histogram was made of the top one-third (67) prints. Three additional 16
histograms were made, one for each of the top one-third (20) prints for each scene. The mean of each histogram was calculated. This represented the best system gamma for the given scene conditions. The gamma of grade 2 paper was divided out of the mean, as was the gamma of grade 3 paper. This yielded two gammas of the optimum film curve for each scene and the combined scenes. These gammas were located on the graph described in the Experimental section, and the values for the optimal Luther's equation were
found. The same values were used in the derivitive to
determine an expression for the fractional gradient.
Please note that all of the data collected for this project is based on the use of a condenser enlarger (specif
ically an Omega D5V) with an excellent quality 50mm lens.
The use of a diffusion enlarqer will more than likely produce results which are drastically different than those
stated here.
2. Conclusion Summary
We see that the use of a full tone-reproduction plot
can be circumvented by the methods discussed, and a range
of acceptable film characteristics can be defined. Un
fortunately, there is no real optimum characteristic curve which can be used in every case, since the low and high
contrast scene optimums do not overlap (see figure 3).
This is not the case when the lighting can be artificially
controlled. In this case, the optimums have a mutual area;
the portrait and general scenes almost match. If the 17
photographer cannot control the lighting, he must adjust his development procedure. If the scenes on a particular
roll of film are a mixture, the general case will more than
likely yield good, if not optimum, results.
The establishment of aim values in photographic
technology is not new. However, things such as contrast
tend to be oversimplified (gamma). The use of mathematical
modeling, and specifically, the derivitive of Luther's
equation, gives us the ability to be more rigorous in our
approach. The form of the derivitive is exquisite, since it
factor" is in the form of gamma times a "correction which
varies with log exposure. This allows us to apply the in
formation about the toe region, if needed, without abandoning
the use of gamma.
Up to this point, the variation of contrast with res
pect to film exposure has not been mentioned. It was
determined that there is no significant contrast variation
with mild amounts of overexposure (up to one stop). As the
amount of overexposure exceeds two stops, or the amount of
underexposure exceeds one stop, this effect becomes more
significant. It is concluded that it seems to be better to
overexpose slightly, however the differences in metering
systems causes the author to advise caution about any
further conclusions or practices. 18
0.2 0.4 0.6 0.8 1.0 Rel. Log Exposure ()
Figure 3- Comparison of High and Low Contrast Scene Optimums Note that the two are mutually exclusive and therefore, an optimum curve range that works for every scene is unlikely. 19
REFERENCES
1. M. A. Bouman, "Peripheral Contrast Thresholds of the Human Eye," J. Opt. Soc. Am., 1950, pp. 825. 2. J. L. Simonds, "A Quantitative Study of the Influence of Quality," Tone-Reproduction Factors on Picture PS&E, ~5, 1961, pp. 270. 3. H. Frieser, K. Biedermann, "Experiments on Image Quality in Relation to Modulation-Transfer Function and Graininess Photographs," of PS&E, 7, 1963, pp. 28. 4. D. E. MacDonald, J. T. Watson, "Detection and Recognition Detail," of Photographic J. Opt. Soc. Am., 46, 1956, pp. 715. 5. L. D. Clark, C. N. Nelson, "The Effect of Granularity of the Negative on the Tone-Reproduction Characteristics of Print," the PS&E, 6, 1962, pp. 84. 6. G. C. Higgins, F. H. Perrin, "The Evaluation of Optical Images," PS&E, 2, 1958, pp. 66. 7. C. J. Niederpruem, C. N. Nelson, J. A. C. Yule, "Contrast Index," PS&E, 10, 1966, pp. 35. 8. C. N. Nelson, J. L. Simonds, "Simple Methods for Approx imating the Fractional Gradient Speeds of Photographic Materials," J. Opt. Soc. Am., 46, 1956, pp. 324. 9. C. N. Nelson, "Safety Factors in Camera Exposures," PS&E, 4, 1960, pp. 48. 0. Personal correspondence with Dr. Granger.
1. Kodak Professional Black and White Films, 2nd ed. , Eastman Kodak Company, 1976.
2. Kodak Black and White Photographic Papers, 1st ed. , Eastman Kodak Company, 1978. 3. S. J. Briggs, "Photometric Technique for Deriving a Gamma' Displays," 'Best for Opt. Eng., 20, 1981, pp. 651. Photography," 4. M. Levy, "Wide Latitude PS&E, 11, 1967, pp. 46 20
APPENDICES APPENDIX A
OPTIMUM CHARACTERISTIC CURVES MODELED BY LUTHER'S
EQUATION AND THEIR CORRESPONDING GRADIENT MODELS
The following are the optimum characteristics for the scenes
tested in this study. The characteristic and gradient
curves are plotted on the same graph. The characteristic
curve is, of course, the one possessing no shoulder region. 22
lueipejQ -sqv - Ansuoa '|8ti
Figure 4 23
jueipeJO -sqv - Ajisuaa 'Pd Fiqure 5 24
juejpejo 'SQV - Aijsuea *|9H
Ficrure 6 25
jjuajpBJO 'sqv - Ajjsuea M^U
Figure 7 26
APPENDIX B
LUTHER'S EQUATION AND ITS DERIVITIVE 27
-.4 -.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 . Rel. Log Exposure ()
Figure 8- Graphical Explanation of Luther's Equation
Recall Equation 1
log(100'6^ D = + (1) ^ l) , where the parameters are as shown above. The point b is known as the inertia point, and is equal to a log exposure of zero.
To determine the value of to , the author suggests the follow ing procedure:
1. Consider the conditions at b. equals zero and equation 1 reduces to
D = L log(2) 28
2. Let the density at point b minus the base + fog density (D,+f) equal AD, then the equation becomes (after some
algebra)
(06)AD .. (3) ro= 2AD 71og 2 7
Thus, we have an expression which will determine the parameter to, knowing only the 7 and the base + fog density. Both of these are easily determined.
this Using method will yield good results, however, a
slight adjustment of omega may be needed to bring the
curve within replicate error.
The derivitive of Luther's equation is used to define the
fractional gradient contrast over the toe and straight-line
regions of the characteristic curve. Taking the derivitive
with respect to log exposure yields equation 3:
~in(0.6 /w) ' l = (4) G ' (10(0.6^ + 1)
or, in the form of Equation 2:
ioKt J (5) G = 7 (10K*+1)
Use equations 2 and 5 when using the results table. 29
APPENDIX C
BEST-FIT LUTHER'S EQUATIONS USING ITERATIVE COMPUTER TECHNIQUE 30
ro cm ii -t o CM in rv i1 CO .-( ts ro i r -0 O CK 11 -0 CM 0- Cv 1 o ro . CM -H 1 - 1 . CM - 1 - H .-( |1
ro m i' CO h r> | (M r> * ii r I o * Ii - .4 -H 1
NN I n O <-< a in i
O-'O^Ith-ocD - -*. . COw 1.i ro. . ^ co co I o to ^r cm i cm m o- o ! 0"- CD O I *0 -<| 1-0 IO 1 O *- co oo i ro * o o 1 * - i * -^ - 1 i .H -H 1 >o rv i .-i ro in i rj t in i -h -o * (NN I O -H CM i1 -H "0 0- I i-i *0 ro o- o 1 *H ^ < n i ro * CO 0- 1 * * I * -rt 1 - I I 1 1 WO I ID C* mm i o os iv -h CJ :i ~ ck r ck i in -o rv ^ in in i ro * tv rv i1 O * * I * * w-A 1 i 1 1 cm i co is rj CM 1 CD ro *in i o in ok Cs CD 1 O th in in i ro mrvicoro*o vw i n fM ON I o m N N hh | o *H^-^-iro *-* *o o -h cm i o- r c* om i in c* co i ro r o-isirH <-t ro ro i o ro h c^ i o i * * * . i . i I rorsi rooirors in i in co i -c cj co is is i roroior-j* roroi . - i - * * i . > i i in rs | CM o- r co I CM rs 4>0 I O (SO in hpi | O n n I o h roroi * i * * i - li i) UJ ^03lrvC>-i-H X. CMCMI O T r I CM *H *-* *>0 CO CO i I CM CJ I iH ? CJ CJ I O * * . I * * I I ^ i r ro *o uj i in cm ro i o rv cm o in -o*o i o cm CM I O O CM CM I o . . . . . I . . I I II Z II CD -1 -V CO O I CM - 2 2 ! 2 -h cm i o ro -r * _ S ?, 2 CM CM I O CM CM 5 * I . I \ I I I ' I in N ro cm I -h rv rv DI-,2;S!S ooro-HTHiOrtin M t?J- E E 2 ~o cm cm i o o cm cm o . . . . . i o . i . i r> O I .. o I O CDhO a. CD T CM O -rr cm in o *>o ro ii ro * ro-H-r -* o i -h ooro o C i!1 5 ? CM rt -H u. CM ro ro o CM CM I O O CM CM 11 o _l i1 I UJ CC i Ci o t < o i t ro o cc *r ro i1 H i1 -h w I O O r cc ro ro 1 CM CM I O O UJ CM CM 1 o I r- i! *-* ;1 u. C3 UJ* c in _l tn _j cc c CC t- (_ T. CD II UJ D U. fl. r to 0. UJ -J o 3- to -C UJ LU C. 1- CC OX 01 s UI r u a r- cc r- o u cc UJ Table 2- Output of Best-Fit Luther's Equations 31 o- cm CM I 0- N in n rj i o- in o co i o i -H -H I m co o in i in ro co rv i o i -* t i rv rv ro o i ro rv o rv ro i -r -h ro ro o o i o I -4 .-t I ro in m in i o co rv ro cn I w CM CM in in i i . n i o- in rv in i cm o m HH | O I o I - *H T-l | cm o rv cm i in o rv rv o- o i o H o cm ro i o i T* t | | t rv o tv o ro i rv rv c> o- in oo CD 0> I O o- -< w 0~ 0- h .n i o rv I .H t | | co rv ro CM CM I r o- o CD CO I th CO CO -o O O I n o T O I ro o o C -0 I t oo m 0- O- I o in Of i c cm o o ro cm i .- t rv rv CO CD I O o o 0- O I ~l t CM CM ro c i o T4 -CO rv rv i i rv cm o in in i -. co o ro ro ro ro i CM C t< in in o in cm rv t t O I m in ^ ro ro ro i in in in i - i i CO o in i CO 0- c ro i ro ro v c i - i i o ci c-i t o in i cm ro ro o >o <> I ro ro ro ro ro i i i c m CM O I CD CD -i CM I cm n ro ro i rv cm (V CM I in in rv co i CM CM CM CM I UJ - I o ON I Ml co n O 00 00 in co i ro oo ro cm m v v \ o in CM CM in CM CM I O in . I . o I I OOO 0* in o co r oo o I t CM CJ CM ro r i o CM M CM CM I O I I I ro o w CM >o ro i ro CM ^ CM CM w r> cc ro ro i .-I D- CM CM o UJ CM CM I o I I _j -I cc UJ UJ UJ _j UJ -J o fl. Cu Dh CC o o o cj cc o u T. Table 3- Output of Best-Fit Luther's Equations 32 VITA Race Dowling was born and raised in Seaford, New York. He first attended College at the Fashion Institute of Technology in New York City, and received an associate's degree in Photography. He then worked as a photographer in New York until his acceptance into the Rochester Institute of Technology in September, 1978. He is cur Photographic rently an undergraduate student, majoring in Science and Instrumentation.