Pacific University CommonKnowledge
College of Optometry Theses, Dissertations and Capstone Projects
3-1-1977
Ocular rotations and the Hirschberg test
A John Carter Pacific University
Recommended Citation Carter, A John, "Ocular rotations and the Hirschberg test" (1977). College of Optometry. 448. https://commons.pacificu.edu/opt/448
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Abstract The Hirschberg test is an objective means of determining the angle of strabismus by noting the distance the corneal reflex of a light source is from the center of the entrance pupil. A scale factor is used in converting the amount the reflex distance is in millimeters ot prism diopters. Recent studies have demonstrated this factor to be 22 prism diopters for each millimeter. This study notes how axial length would effect this scale factor. Using ultrasound axial lengths of thirty eyes were measured and compared to the results of a Hirschberg simulation. A small effect results from this comparison. The mean values of scale factor determination noted twenty-three prism diopters per millimeter.
Degree Type Thesis
Degree Name Master of Science in Vision Science
Committee Chair Niles Roth
Subject Categories Optometry
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artial fulfillment of
the Doctor cf Optomct:r.�'
degree
A. ,John Carter \\"'1! 31�r- .. -. 11 1 1, . .-·077. . ABSTRACT
The Hirschberc test is an objective means of determining the angle of strabismus oy noting the distance the corneal reflex Of a light �our6e· is 'ftom thb ·center pf.the entrance pupil. A scale factor is used in convertinc the amount the
reflex distance. is In miliimeters to prism diopters. Recent
studies have demonstrated this factor to be 22 pr.ism diopters
for each millimeter. This study note::; how axial length would
effect this scale ·factor. Using ultrasound axial lenr,ths .of
ts thirty eyes were. mea�-;ured and compared' to the re:::iul of a._
Hirschberg s:i.mulation. A small effect results from this.
comparison. 'I'he mean values of scale factor determination
noted. twenty-three prism diopters per. m111:1.met'er � I would like to 0,xtend an appreciation t() Dr§ Niles
Roth my a.dviser, for the many hours, thought, foresie.ht,
knowledge, and assistance he· has put in·this project�
1
' I I
1�•
i ! Te �:;t
t - �]e\rictt.. os
relative rOtational 11ostion of the eyi"!�
"" " i , , '- + . ,·· · ·n ' _ o u r e.... . _. + L •J • •• . .!p•1�- -� _ r;-,.-,··1..\ formGd .1"'�' ··;:1 .l' 1rld .J.� -i 'n'' b o, J. ·--GI l v ,:_, 1...... ,. J0"'i . .. ·f'rcr+>'- ' cf".. Ji-1·p ;,.,. ·1·, ct ..... ,.1 c., J. l t..o c . 1.u
having. him fixate the _The ·smooth corne� 0111 reflect
an image of the light visible to the �xaminor. The position
of the reflex relative to the entre:"3.nCt'� pup1l, cl�''pends OD
where the eye is fixa.tin.g. An eye wh�ch w.111 r5.x3.te the J.ic,ht
_._, source rl, ("",I l'D"� ; o" .•11 ...l.....,, \1 'I will have L·H8 reflex n•.?.ar the center .of the
cntra.nce pupil of tho eye or rnorr::� common:J.y :3.bout 0.25 mj_lli-
· �- -1,._,·}·1·-" •. __ ./ �-· n,e·l · ...... r�":!... .. -t...,. o','•'!O''-·' . -"..· · ·d �� · !"i . ',c-' ... 4 -... 0 ...... ) � ("',_,..... �,,. \.J -,,. J,.A.(1.."" '°'"'i::.' �·J.,. c.. 1 t • s:o_-,"'.l ]_- r.:: _ .1 t·1,:.>. . B1·,t· + ,_J.:.t.::, ": r··,�.:."j r1. f: ·t: t ·'• l point other than the.fixation target, as happens in strabisw1�, the corneal light reflex seE·n by t..:he examiner w j 11 be in "'·
• · •' .... •. .. .. - . "' �- ...... 1 , j .. . 1:'no� :.i.i·tJ"on c'1 ·e+ n vr�1" n p � . b/ "h c d 1;:;via.t ion accurate
·r ixat1onw.
. fi Julius H.i:rsc-hhrg - , who originated th.e mrothod, c.1. ted
relationships between ocular devia.tion and app:J.r<;:nt location
of the corneal reflex. Theso are, Page 2
1) Tf the corn0a1·1ight reflex is seen within the pupil-
lary ·area, the deviatio� can ranee from 0-20 decrees of a�c.
2) if thP reflex is seen within the interval �ounded by
the pupillary margin and th.e limbus of the cc.rnc;:1_, the dnviation
Ca.n ra.nge fr<:Hn 0-lJ_5 2 degree S, 3) sclerc-:.) L if the ref lex 1 ies outside the limbus (on the
·I then the deviation is greater than 45 dec,ree:3. l L Krims};:y9 notedthat the radius of curvature of the cornea
is about eight millimeters. He reasoned that each millimeter on
the corneal curvat.un� would correspond to ��even 8.1'.'C degrees.·
His reasoninc is that e�ch millimetbr the reflex deviates from
the �enter of the entrance pupil, or the apex a:f the cornea,
corresponds to seven a,�grees of arc, or o.bont tw1.;::lve prism
diopters deviatiori.
Other investigators have used similar scale factors :for . 1� angular deviation per millimeter. Among them are Scobee-�
who claims·t.11-t eight.degrees deviation ls noted for ·each milli-
...... � . meter. Burian and van Noorden� agree with the seven degrees
or t1..velve prism diopters quoted by Krimsky. Nore rccent1y
Optometric the Weekly18 in a series of articl��s a.bout strab-
L ismus for optometric assistants, .claim that the amount of s6ven Page _,1.
prism diortet�s degrees or tw.:'.)lve . for each milL�_mr-:te�::- :f:corn the center of the entrance pupil. is the scale factor to use.
Krims1cy9 noted. that the rotation of the eye was the crucial
factor, not the 6urvatur� of the cornea. 1\lth.0:1;.ri1._, the rotation.
isn • t directly me2wured. in th� Hirschber0 test, the amount of
the strabismic devis.tion of eye s.hould equal the amount of
rotation of a normal eye to that deviating position. He points
of the cornea o�t that th� curvature doesn·t .affect the rotation
the strabismus the or and that apex of the cornea would move
with the rest of the eye. This idea was further D.dvanced by
Jones a.nd Eskridge who noted that their recrnlts using J\rimsk.y's
conversion ratio crossly miscalcul ated actual d•2viations they
8 e measured. They theorized that th distance from the center
the of curvature of the cornea and center of thE� entrance
pupil was constaLLt at all rotations of the e-:,1E�. · And that· the
center of curvature of th8 cornea moved as well the various rotations of the eye. mathematical formula They der.ived a which rletermin(Jd the position of. the corneal reflex with a.ny rotation of the eye� between the reflex and . The distance the centtC)T of the entrance pupil they labelled lt. The distance between the corneal center 1�i ,- TA.BI.J E Center o:f' Rot3.tion Determined by ;_i;a:cl:i Ir-.vestiDa.ton_:; recorded in millimeters behind tho cornea f:rr;motropic E;ye AxiaJ_ 1,ength 2J • .53 25.55 22.10 Doncers 1. 3 ' _5.1+ 1q., 52 lJ.Ol lJ.?J .13.22 .·.1 :J. r' :)•-!l'.'f ! �- of curvatur8 and the entrance pup:il center, they labelled This distance (h) equalled the distance r times the sine of· two rotation of the (0) angJes 1 the 8.ngle of. eye {G) and anc,le Kappa ,y ' 1 6 or h= r sin (G+,0) • Using St ens t rom s - data for the eye, an average £ of 2.9J millimeters was introduced giving an average h of one millimeter equalling 12.2 degrees or 21.6 prism diopters • . They tested the ab6ve ratio (21.6 prism diopters/millimeter) in sulijects who were asked to fixate a t:.irr.et at various d i��ta.'11ces on either sid f� of the straightforward posit:i.on. By photo2,i:-a1-ih;y, 'they were able to determine how much the corneal light reflex deviated from the center of the entrance pupil of th(� eye (.!}.) and the relation of this deviation to known amounts the eye had rotated (G). Their averaged results clofJely resembled the scale factor �heir mathematici predicted. .::ic: .Griff.in and Poyer tested these results using a number of t'nown strabism:tc cases. They also photographed the posit ion of the corneal light r�flex from the center of the entrance pupil and compared th<�se -a.mounts to .the measured strabisrnus angle of the subject • . The amount was determined from the cover test. Their results exhibited a mean close to 22 prism diopters for each millimeter· the reflex was from the center of the cnt:cance pupil, The re�ults� however, showed � d e··l .l::i:I. :ion� . · Griffin 6 poin· t· �· t o ti ie wo r'k. ·he. 11-.1as done .-i.nc1. th2.t of �Tones. and Eskridge and the controversy that ss�ms .L�, Q 1···)rf >, " V·.1:.."'� ·-.l l ("'-'l jl the prope� scale factor (prism diopt�rs po� millim0ter) to use for • the Hirschberg i·,c:;s t , '1 I '""'.. expla.ins the irn·i::i-ort�1r1c_ a of lr..��eping up wi�h modern a eve�opmen., ·. t s, On�r:. -such develo.t·;iment has been · the realization that the ang 1 e 1r-.appo. :::n1d i' +, . s infliwnce 01�.. the · · · ..,, estimated. J.·S no t )'.,ero . 11'1 mos-t . peO')- l le- · r c• ....<) c>a:clvv inve8-t. i11.ators<� assumed in the il' wor1c with the Hirschbere, test. He expl<.'l.ins that it is impor·ta.nt to include angle Kappa :in nny rNaluation .. of the Hirschberg test.7 Hereafter, the d ista.nce from the center of the entrance pupil to th·;? reflex \'lill be :;Gferrcd to as the amount the reflex has "rnoved, ,.. There flex i tsolf doesn't r:iove but the pc>s i t:ion it taked would be exhibited when the eye moves. This includes the a.snumption that. angle th.::i.t l�appa is zero or its effect�$ have been a..ccountccl for, rna.t�ing it zero. The value of £. u;.31.::!d in the clata. by .Jone1-c� a:nd EskridGc was an average V8.lue of £) there are a variety of r v�?.lues as there are· a. variety· of eyes. 'It would seem then that tho ratio devised by Jones cind Es1.\.ridge would b·� influcnct")d b�/ a few uncon- ' t · . · · · · · mo:.:;t, obv Ile of r. trolled va.r iable:3'- .the jous be inc, the .val } ' ... ' . . - .. Another variable, the axial length ·of the eye might ho.ve an · - · . . · . � . Ci. cc:1tcr c•f the- 0"0 will Scrvr� �J.G the center o: rc.t:�tion,' ,- .:...- ..... · ... �J·m�1 • • - . . ' "· .• _ __ , 11:; i"J •• 1x...., o.l .:J.;:-.cd.\.. 1,.-·�' • l' 1.-· -·1 · 01, - • -�I..-1 �"...,·' -1-'' l) ,...;" r. 1r.J:. �· n� ;., ' ('t, , d -l ',;· _ .'�. ·c�1.1 . A larger . · . I .. - I � � w i <" ,, eye would rotate a certain dit:tance of arc 'to h.J.ve its corneal t . • - .�I /. r" .� - - ' • . . ' - . ' the f�ct th�t the rotational amount in decrees o� �re is the �ame - - J,, · the.distance travellnrJ is c1 iffercnt. PerJ�ins not::-d th ii:..; d iffcrcncc ------· . . 1 Ji. with steel balls of. Yar.1 ous curvatures and center�� of rotation. :...... 1.' -. ' I - Deterrninin; ·tho c1�nter of i·otc;i.tion har.m' t bcon too ea::;y. I .. " · Stcve.ns17 quotP.s. tv10 er-irly invcctic,a.tors who c](�tcrminncl the . � center of. rotation, These value.s arc noted in Tal,l.e on•2. La.ter · iriver:it:i.gato:rR claimed that these met.hods v1cre c.r\id e • . Dond ers method 1 · vrh i.ch involved tf]ometr�', v1as un�l r�J' t118. er) tic lsrn that the vel''"J' point he Wcl.3 try?,.r.g to determine Hor.; a.�.>::::urJc d in his calculation:.:� Hit. stci.tecJ corl:Lc1: o.f coL;::·l.ion fo:c- the .ernmctropic eye ha.s been 'lividely ,accEJpted, appl"OXirnation 'for the Center Of :t·ota.tion of the emrnetropic Sorne investigators have sho·:;n similar. amounts •13 -·--- -:----- . ·. . :.1 . . ' ' - 1 'J. ?a.gs 7 . . 1 J Park and Park- nc:>ted that there i�m· t one point acting as the center of rotation, but a. number of 1>oints which vary as the increase s. horiz.ontal gaze decreases or · They gav(�. 8.n averac,e �lalue, however, of 13. 8 millimeters behind the cornea, frnmcwhat similar to Dander's value. . 11� � P er·k. l.ns, hI 1 m mond, and Th · 11·1_ 1 rnn useo the aGsurnpt1on. t,11a \. · t the center of rotation will serve as the radius of the globe and that twice this rr::idius would give the ax:lal length. Their determination of the radius was derived from th<� formula ex (radius) = XY / 2 x sin Q / 2, ·wher� XY is the change in the corneal light reflex positiqn as the eye rotate::; thro1)gh anc,le G, consistt':int Their results for the axial length indicate a three millimeters greater than that obtained by x-ra�' The· teehniques. XY value resembles the refl(!X "rno1rernent" ... Tones' . h- value. Then if .the distance (h) were substitued for ·the XY value in the equation, and assign Q a constant, it is observed that th� value of h relies on the radius of the globe� · center Despite the problems involved with mi.:�a�;url.nc, the of rotation, axial length would irlfluence the position of the rotation center. It would be of benefit, then,·· to investic;at.e R.ny efft1cts the axial lengths of ::1 nu.1nber of subjects has on t!w) r responses to theHir�chberc test. --- Axial lene,ths were dGtermined with th0 (lse of 1ll trasona- graphic technicp.rns. In the time..;G.mplitud8 syGtem de�>cd.bed (") by Goldberc and Steinu, a transducer capa1)lc of ::;ending l and receiving th0 ul·�;ra.sound wa.vcs was p aeed on th2 corn0a. Sound wave::; ti�a.veJ_led throughthe eye beinr; ·reflected by the ·.; · �, " . . . various structures . "echoes" of the eye •. These were lJicked� tnJ� : . the by transduc0r and thcrt displayed on an or>cilJ.ouco1)c r;croen separated ·by. the ·l'ariablc t:lmo elements that the reflections occur. A }>olaroid photograph gave reproductions of. tht} oscilloscope screen. Measurements were ma.de of the separation ,, r ' distances of the cchor3's a.nd converted. to incorpo:r.ating a stand.:lrd conversion fa.ctor derived from a class and the speed of sound through t1w various med :i.a :hwolvccl. l To note the eye's rotationa affects on the corneal reflex a light source was placed in front of the subj·ect. ThG source was a. household 100 watt bulb, attached to a variable resis- tor to ad just the amount· of lig11t tha,t is ur3ed·. Alumh1urn foil wa.�3 wrapped around the bulb. to enable a. :C>rr1al1 ight1 to serve as the reflBi. A semi�reflecting glass was placed in ., . - .,- ..l. t frdnt of the·eye to allow t,ne i.ie,n., .o <.l°S a. photo&,raph of the eye to be ta.ken. To cacl1 sich� o:f t:ne �;ubj1-:'Ct a tare.et with five fixation mar}::s we.r:> plac1�n. Fo.r co1weienc·e of calculations and construction of the target, it was placed a total of one meter from the eye. The semi-reflectJng glass enabled the s0bj0ct to see the tareet. The subject was tlwn asked to first fixate the first ma.r1< and a: 1Jhotograp11 was taken. The subject was then asked to fixate the second target separated from the first by tv.. 'o clegroes and a second photograph was taken. • The process eontinued until all five fixation marks were viewed · b:'./ the subject. Both eyes of fifteen subjects were used in· the set-up, Each of the fifteen subjeets were determined not to have any eccentric fixation, using monocular l i.c,ht f ixa ti on technique. A Nikon camera was used with. tr i-X Pan film (ASA I.mo) 9 The camera was focused with the l�nses once and ar� further focusirig was done hy r.1ov:i.ng tllc ca.mer-a or the subject forward and bacJ(wa�cd to insure a constant magnification factor� A millimeter rule was also photo- L graphed to derive. a con\rersion f actor. for the photoc,1°aph measure s. Paee 10 RESULTS Table 'I'wo is a. re conl of the axial lensths notf}d for ea.ch ;:,;uh ject. rr hc ultrasound pie tu.res gav e four dist 3.nct echoes for each of the fou� parts of the ey e the cornea . the anterior ···. �- •. ·-- �'t ( ... � "" -i.:. Johe ,I. - c:· +cv . r .\.... "··· 1 e""l l ""....;i r.1·• I,.,tT·f · ...... j \J 1� (J � . ) .,.- .J0 - \,,:.._) � , le1... .. A. ;;:::i Gurface, and the back of the ey e or the aclera . The �is tanc e between these echoes represent 7-hl? various tnE�dia the :=:ound waves travell<�d throuf..h, th(-3 vit; re ous , and the aqueous •1 The conversion fa:ctor do't.errn:i.ned from the el ass standard involved two surfacc:s :s eparated by tJre c,lc:tsa me•:J ia � The dis ta.nee between the surfact,s . WEU1 known a::.; Hell n ;:; tlH� speed of sound c:onverwlon fa.cter through the glas:3 ma terial . In . measuring the distanc e shown on th(� photor;raph , ti-ds known conversion was appl ied to (l f?termine the· actual d ista.nc0 . The conv e1.. s ion factor�:; thus determined 'Na::J. equal to O ._53J iii:i.cro�Jecondf;,/rr.illimr:i;er.. For t:::acl1 of the nv�d ia·, a :furth er conversion involved t.h e usage of the speed of sotmd tin�ouc;h tlv? se various med ia; fo:r thr:� vit:ri�ous and the acq_ueouc , the conv er:3lon factor is 1.532 . Ar:d for the ler�s substar:.:: .o .t he r;criv ers j ':J n fact.or is t. 61-�o w Th� measure- ment of the y. hoto._:,:r:· ar;h w::1,:c. convertcc� to a measurement by multiply inc, it by the conv (:'!r·sion factor for each of' the med ia . TAB LE T Vi 0 Ax ial lencths determined by ul tr?t;-:;ound ,, it1 mill imeters S UB.TECT EYE B ,J • R • 0 .D . J.1J J . 83 6, If· 1. ..., ·1 · 9 D.S. _,."') ... · ...... J. 61. 7,09 ,.., ,.., ,.., r""J '"''I',) � � ....,, .• • ...., �SL� J.H. 0 .D . c, � f / J.; hl;. ( c.,.-:.. l _, If'·�/ £.� . 22 1 r:' ·P-/., 0.,S-1!1 J .06 4·ft J6 ?, LlJ h •.) !!I ( j · 2.J. l-.6 C.N. 0 ,D . 3,13 6.62 t 6, ?7 ,, ? r: o.s. ..) '�_,; 6,68 16.5G � ,, .... D.C. O.D. 2 �.50 3�93 l) e ..�� ) 2:1:.06 2 .93 J.99 U� • q1/ J_ 21.ho D.B. 0,D. J ,JJ. J,59 6 . Q?/ ..... o.s. J.�l B J.59 6 . 79 c.1. O .D . 2.)7 6.02 l5e61 21�63 411 ' 9·, 5 2 .o .s .2. 69 6 . 73 l · 21 .96 0.D. J.25 J.16 6.�·l 19.31 o.s. 3.69 J • QL� (...� ; � '7Jl 1?.52 D ,Jr • 0,D. J.J? 6.69 l?,li. P, 2h.17 0 .s. J.29 6.67 l 7. 514. 21+ '20 .• L.R O.D. 2.65 ·J•,, 5"'.) 6, 18 22.08 o.s. J.;2 J .38 6.69 22 .87 w.c. O.D. J,OL � 6.53 l).67 22·. 2t1. o.s4 J.lJ 6.77 15. 82 22 . 59. R.H. O.D . J • OL� J.66 6.70 th.JO 20.99 0 ,8' 2.90 3 .37 6.27 lL�.J5 20.62 ._T • I,.. . o,D. . J 8 7. 08 17.15 2!J-�2J J.70 J..., ·h .. o· � s, J . o4 .) • '-+"l, G&h5 1.7.21 2J e66 B.C. 0 .D � .)...., • Li.')y (.• 6�97 t6,.J} 2J �J9 J 0 '�)' .05 ..,t � _) 5 r' 16.36 2J .91 0,D , J.90 6 . 11... .!., , }.!re '"'.. �0 � 7 · J J 5 o � -s , l� . 2 6 6.60 1h.22 20'"82 -:>,· 11. - ".L· . h --::. !.,.r . O,D� � c� 3 , l:.Li 6.60 . _, 20.93 · 7 .02 .L 0 s. J . 1�. s · -1 . 5l� 15t' -::· -'1 ...- 22 .J5 As the repro::: entat ion is - of tin·12 ,_ however , to the .-:;tructuro and ba.cJ( , the ro oult needs to be divided b�r tV10 . Thir:; re sult � l I gives a. mc.3:surernent of the d.istanct:,;.; throi}gh the rno d ia . Tl1<� r d i::;t is labelled !); on the tabl e, throut:;h the lenr: � s J. abi:�llec! _B 1 . - - and throue;h the vitreous is labelled -c. meas1J.r inc; them :from the te mp oral . limbus . - Thi:: :t imb1J :::; W8.S ea�\'/ to see and insured an ear;ier i� eading as the P''-fd.l r:;i7.. P. var ied 1 s.nd find inc, 1 ts center vra·s _difficult. These rn<::a0ur1;ments _,i were convcrt0.d into actual me asure ments by ·J 0 ing the pho tognq>h � 1 I of the milliffieter rule and sometimes croas check inc by an actual measu1'cment ·of the co1�nea . The resnltG of the measurements <.1.re shovm in Table Three. Thi� cJ i s-t.ance s ·,.,'0re subtracted, f 01� each tw0 d cc,r1� 12 S0.grnent a mean \'; aG e l and avcrac,ed for dista.nc e whl. c h recordocl on th tab e. A .stand a.rel ei.""ror for · the two d r:.1 C,ree mcnx1 was aJ so.: cornputwJ and results a�pGor on the - table . ·Also included o� the tabl e 5.G a projeGtion of the arnc,unt the reflex woulcl "mov e" for twelve degr ees . This pro jection ic ·from simple mathemat ical calcula. - tions . data 6ollected from �hotoeraphs , recorded in mill imeters Ax ial Distance to position Stand ard " ".) f -· l Le ngth 0 1 __!:;_:__ J _,.._ Ave . Error 12° ,.., r' .....,. 0 ' · 0.038 c. ;i , � . . u 7,15 7.27 ? •. 3 f1,) ;:;-7( • 0 0. ..,( • (0q)) 0.19 L 11 o.s. ?5. l+ R 7.63 7.79 s.oo s.1 7 B.JJ 0.18 0.012 1. 0.5 J t r' T. • 0.D. 2J .66 8�h6 8.67 B.8 8 0.19· 0.021 1.13 o.s. .2 2.51 �, 7,55 7 •. 75 0�19 0.007 1.13 C.N.. 0 .D . 7�58 7.71 ?�92 8.08 B.25 0.17 0.028 1.0l 0 . s . s.oo s.21 s.41 s.56 s.75 0.19 0.;010 1.13 D.C. O.D. ?1..lG 6�38 6.58 6.71 6.79 6.92 0.11+ 0.022 o.84 ' 0.s. 21 .11-0 7 ,18 7.29 7�JG J O,1! -1- 0. OJJ o. Sl-1- '---- ?.S 7,75 . .• • • . .• • n.B. o.n. f.- L1� ,f .. (_·, _S l...,• C.I, .. O.D. 01f�.. . • (-..� ' .,,I ""). . (; . 1 7 6. 2 9 6. !�.?_ 6. 54 6 .6J 0 .12 0. 011:. o.69 o.s. (-.�?1. • os-� c 5.75 5.SJ 5. 92 6.o4 6.21 0.12 0.021. 0.69 K.D. 0- .D . s.67 5.75 S . 84 5,96 6.07 0,10 0.012 0.60 ofs, �.7� 6.92 � . 04 7.17 7.?5 0.11 0.014 o·. 69 n.F. O.D. 2 !1 • 11 5.83 6.oo 6.os 6.21 G.18 0,1lJ. 0.023 o. BJ 0.022 0.s. 21+.JO 6,GS ?.OO 7.17 7�31 7.JG 0.13 0 . 75 IJ . n.. . 0._f) • 22 .0R 6.21 6.JJ 6.46 6.58 6.79 0.15 0.021 o.87 o.s·.. 2·2 . 87 7.6 8 7.73 7.95 8.09 B.27 0.15 0.037 0.89 7 O? 0.021. W,C, 0 .1.) . 22 .25 7.29 7.5 8 7.71 . .' -- 0.16 0 .95 0 .s � 22 . . 59 7.79 8.08 8.17 8,Li 2· o.:6 o.o�J(, 0 . 95 0 • D • B.19 8. 26 B.JJ f1.h2 0.09 o.n10 0.52 o.s. 7•1+ 9 7 .58 7.,71 �' •. 79 7• • Cl?,,,· !. () .11 0.011 0. E1 5 ')..,£..,. ;;. • /...(.) (-,).. . .8 • . 1 3 8, 29 P1.Lt.(; ·C. i 6J p...J • . '7' -1 r: 0.16 0.012 0.93 . • . 50 0 ') 211 211 7 . 29 7 . 7.58 7.79 7 • / 1-...> 0 .16 0.031 0 . 95 n.c. o.D. 2.3 j 39 7.29 7.50 ?.67 ?.79 e.oo 0.18 0.021 1.07 0 ,s 41 2}. 91 7.79 7,95 8,08 8.25 ,8. 71 0 .23 0.077 1.30 0 �".l �. · , • 1 ?? p ..D. 0 D �' 0 . 7 5 7. 7 5 7. 92 8. l 7 I.) .) ..) s.r; 6 n. ?O 0.022 -- *' "'"' "-� ,.., ...... -;.. . b . �·.. 20 .02 6.,95 7.1J ?.25 7 . J.1-2 ( • D) 0.17 6.018 l.02 ,J .C . ·o .D . 20 • . 93 . 8.09 B.16-8�25 8.JJ 8.50 0.1.0 0,022 .o .s. 2.2 ,35 6.79 6.92 7.oh 7.16.-- 0.13 0.003 l The me�n for the two degr ee rotation is 0.1� mill imeters, with a stand ard deviation of 0,04 millimeters , ahd for the pro- jected twelve degrees rotation, the mean i:::; o. 87 m:i11imet1;rs with a standard deviat ion of 0.24 millimet�rs. Th� se results convert to a mean of 2}.JJ prism diopters for ea.ch millimeter of "movement" with a standard cl evia.t ioh of : :f our pr ism c1 iopters. Figure One is a 9-Cattergraph . of the two dr�gree rotat ion reflf;X d istance.s D. s compared with the axial length9 The lj.nc that is draw n in the fir.ure is an observed bes � fit line , disregarding the few rad ically differing points . The line shows a sJope of 1/10, or for each -l .O millimeter chance . is ax ial lenc, th, 1� 11 c:ff e is O.01 millime ter chi:i.nge in reflex . ·. . "movement ." The ch::.i.n.ge is in like directior\s , · suge,r.?sting that an increase In axial length will show a small increase in refl ex "rnovemEmt ." A stat is tical anal;y sis of the data using Pearson' s correlation coefficient show s a correlation of 0,27. CONCLUS ION The difference in the center of rotat ions of the various sized ey es was the ba sis for the que stion posed of th any effects of e ax ial 1engt1� on the Hirschberg tf;st . The F I C URE 0 N E j 0 I L- 0 . 2 • I � x ' I , I� · o . ti I\) · o 20.0G 21 .co 2? .00 23 .00 25 .00 26.00 c:,,.., 7 •.n 1 Axial lB neth , in mill imeters L mad e that the center assumption wa.s of . rotat ion was . in the I that the L geometr ic cent(�r of the ey e. But :t t \·1<1G ;p oint ed ou.t center ·of rotat ion i:-2 not in the center of the c,1ob1� , but varied . Dond ers eatly data "ind icates a differeri�e of 1.51 milli� meters betvn:en the small eyes ' a:nd large eyes ' center of rota- tion, a d iffererice in the reflex move me nt of O.05 millimeters. in the Errors note.a data may have come mostly fr om ob-. All servat ional errors . measurements wer�� f inc measi_irements using the travelling microscope . Inaccurac ies of � 0.015 millime ters were poss:lbl e in the read ings •. Us ing the conversions introduced for a.n 8.Ctual measure from the photogra.r)h; a possible 0.06 millimete�s is diff�rece of + present . Thj.s is a resemblance of the differences no ted in the reflex "movements" calculated from Donders data . . . • � f3 that This study , a.nd tw o others before itJ ' , ind icate the popular ized co.nversion factor of one millimeter of movement for twelve pr ism ioptc�rs of deviat ion is d a low estimate o The results in thid study ind i cate there is a mean of 1J .JJ degrees or twenty -three pr.ism d ioptcrs for each millimeter of "movement." Anothet· stud�/ a;:;pect of this emerges from the fact that the highly my opic ey es of subjects D.B. and K.D. show unex- pectedly small amounts of rnovemr:nt . Also ; the hy peropic eyes subject show an unexpect�dly great amount of : of P.D. .movement. The scattergram shows a wide vari ety of similar unexpected results , ind ic ating that other f8 ctors may be .involv ed in the · Hirschberg te st . Some of these factors may rely on the mu scle streneth of the ocular muscles, the ·who1e size of the eye (our concei1n was for the axial l.encth), the we ight o:f the ey e, any eccentric fixat ions , of the var iable physical size of the subjects involved . The fact that the center of r· otat ion varies with the horizontc:.1.l gaze may al::-:; o influence the results towards the unex1)ectcd . In this experiment, deviat ions from linearity of the i relat ion between corneal reflex displacement and. angular rota.t .on, as w ell a.s intersub ject var iations in scall� f?.1.c tor (prism d :i.opters per millimeter ) are so mu ch smaller than those to be r:;xpected when performing tlu:: custo mary Hirschberg test evaluat ion, that , fo� clinical pur�oses, they are insienificant. SUMMARY With the vary ine scale factors recomme nd ed for ob jectively estimat ing strab ism us ahgle th1? Hirschberg usine test, fm;ther L Page 15 . � Q study was ne ed.ed to Yerify find ings of recent investiGat ors-) ' •) . This study includ ed an imrestigation of the subjects ax ial i lengths and the ir possible effects on the Hirschbere, test . L Although an effect was shown, its resul ts are i. .ns 1gn1 . . f.ica n t , as ·� 11.trep resen t s a srna 11 a.mount . Results showc�d a �;cale factor of twenty -thr.·ee pr ism diopters per mi llimeter a isplac<-;ment of the corneal reflex from the entrance pupil cent er . .'rhis value is very close to those found · apd recommend ed by Eskrid ge and Jones8; and also by Griffin and Boy er5 L I_ L HEFEHENCES i. Boed er, P. , An a.r:nJ. y sis of the General Type of Un i ocular , L__ Rotat ions , .•\ ntCX' l C:J. n Mr'ciic a1 AsscciGtion Archives of O· h thalmolopy 57 :200-200, 1957 • 2. Barish, I.Wl . , Clinica.l Hefraction, 3rd ed . , (Chicago, Ill : Profissiorial Press. 1970). J. - Goldberg ·, •.Sa1 :·in, Ultra.s onic :-:; in Ophthalmol 4. R .E. and L.V · (p'11·1rj · . .., • -.· ·' ? . �'0 V . _, l .:.- �Lcl � eJ, "'.I. )} l.J·�C...,l. , Prc1• � 1'[{ B@I · c�) a· t-'-4..n .cl 1.;,·-,j,..� ..:Jc• , ·1 q I�.l') ri{/\ .fl l · I I 5. Gr iffin 1 .· ,J . TL and P.rn . Boy er, St.rabis mw:::: l".Te :=i t;11rc nH;nt with I • · "'" ·-�·c:t ·· or e: l '·· n .. .i .... r. ,r ...I +hv.1.1. e 1-r--1· . J. ..• h.l. l 1o -...... :- ,�, t·.,,1\_'.,;C)e+ v' · 0r1::.' tl-' )rn° +rv ·J· . c· '·" e (.1. . 1:·"11 � �r:(! _) . e6.),, - 866, )--r ,. \•�-:', np·..... t· fl! 12 , ·1974) � 6. Griff in , J ,R. , Cons id erations 'N ith Hi. rschberc, Tt"?sting , Opto metric WeekJ.y 67 :1046-1047 , (Sept. 2J , 1976). Griffin , LT .R �, Binoc<;lar Ano mal i e s -Pr o ce6ures. for Vision i__ · Therapy , (Chica.go , Ill : Prof e ssiona.l P1�es�:>, 1. 97bT:'" . l - J t,,. r....J J ·l. Ill' t_ · I. • I i... '• -•· "' ·- •" I� • .:,. �-• :;.. I.,� -,(• • \, � - 8. J·o1� �� . R· ana. J B �a�� Jr ridct.::• e. , T�' ne H� r �.)<, 'nb� r n -T��t '1 Re · 47:1: 0 5-11Lk, (1970). '.� L evaluat ion , _A merican. Journal of Optome try j TrJ\..r· ...1· n1 "'1nrt-..).1....u � "'�� , �, ,..,.., i ·:.1 :r) -1u .1. o-"'.1. -- .•...... o.. _ '-... c.. .J·�t'\.,.-ne- r {Philadelphia 9. �-1"1 .;l.'·" ffP '" Ct' 't 13 i 1101'.11.l�r.. Ir11b �· l•J 19Ii78'). - 1 . Pa. : Lea and Fe rbiger , pp . 19 2 � . _ lO. Krimsk:,r , E. , 'rhe Corneal Light Reflex : ! Gu:icJ e to Binocular Disoi.�d erz , (Springfield , Ill : Charkes Thomas , 1973). 11 . Mo��es , R.A. , Adl0r's Ph1 s i olo:'.v of thn E,ye , (St. Louis,, f•1o : . c.v. Mosby , .1.97.Q). PP •' 2-83� . 12 . My ers , P. Some Cons idera:t ions of Ocular Rotat ions , Ameri can ,Journal o:f Opto metr;v, 52 :106-- 118� (Feb, 1975) . 13 . Park , R.S� and Yark , G.E. , The Center of Ocular Rotation in · tho Hor.izontHl Plane , Ame1:.. ican Journal of Ph;;;:o iol(Jf'.Y 1 0 1-1- : 5lJ.5-552 , (19JJ ). 14. Perk ins , E.S., B. Hammond , and A.B. MillJken, Simp le Method of Determining the Axial Le ngth of the Ey e, Br itish Journal · of Ophthalmol·og;y , 60 : 266:-270, (April , 1976) � . 15. Scobee , R.G. , The OcuL1rotar;y f11uscle�o;� (St. Louis, Mo ; c.v. rtiosby , 1. 9t�7) , pp . 46- 50. 16. Stenstrom, S �, Invest igation of the Variat ion and · Correlation of Opt ic�l Elements of Human Ey es, pt . J, trans . by Daniel . VIoolf ; Ame rican .J ournal of Optornc�tr;v, 25 : Jl.�O-J50, (Jul;:/ , 191+8 ). 17. Steveris , G .F. I1'!otor 1\Trp;:.,ratu;-3 of the Eye ( PhiJ.ad elphia , Pa : F.A. Davis , 1906) , pp . 86-90 . 18, Strahisrnus , part 2 for Optometric Assist<:mts , Ontornetric 'ii 0okl:y, 67 1151 {July 1, 1976) . I L_, I I (_