THE
INFLUENCE UPON
OF RAPID PRISM ADAPTATION FIXATION DISPARITY CLIFTON M. SCHOR
University of California. School of Optometry. Berkeley. California 94720. U.S.A. (Rucritrd 19 Junr 1978; in rerisedfornl
28 Nocc~hrr 1978)
Abstract-Small errors of fusional vergence (fixation disparity) were examined as a function of the magnitude of horizontal prism stimulating convergence or divergence for a short (30sec) duration. Marked differences were observed between the amplitude of fixation disparity resulting from convergent and divergent stimulus disparities. In another experiment. subjects wore a horizontal prism for 30~ after which time one eye was occluded for 40sec. Measurements of vergence eye movements revealed an incomplete relaxation of fusional vergence (prism adaptation) after 4Osec of occlusion. Marked differences were observed between the amplitude of prism adaptation resulting from convergent and divergent stimuli. Maximum prism adaptation and minimum fixation disparity occurred with the same direction of prism. suggesting that a slow fusional vergemx mechanism minimizes errors of binocular
vergence.
Kr_r Words-Fixation
disparity: prism adaptation:
fusional vergence:
tonic
convergence:
disjunctibe
eye movements.
INTRODL’CTION Small errors of binocular fixation can occur without disrupting binocular vision as long as the errors do not exceed panum’s fusional limits. Vergence errors. which are referred to as fixation disparity. vary in amplitude with the magnitude of the stimulus disparity to fusional vergence. Ogle and his co-workers
(1967) have quantified various relationships between fixation disparity and the amplitude of convergent and divergent fusional vergence stimuli. They have observed that fusional vergence responses are slightly less than their stimuli and that this lag increased with the amplitude of the fusional vergence stimulus. The lag of convergence and divergence responses are termed exo and eso fixation disparity respectively. Ogle has classified fixation disparity plotted as a function of prism vergence stimulus as Type I when the amplitude of fixation disparity increases in response to both divergent and convergent stimuli about equally. Prism-induced fixation disparity curves are classified as Type II when errors of convergence are smaller than errors of divergence. Type 111.describes fixation disparity that is greater with convergent than divergent stimuli. Errors of fixation associated with prism vergence stimuli appear to become smaller as the duration of binocular fixation increases. Ogle and Prangen (1953) observed a reduction in vertical fixation disparity after subjects wore a vertical prism for 2 hr. After adapting to the prism. vertical fixation disparity had the same amplitude that was measured before the prism was worn. Mitchell and Ellerbrock (1955) and Carter (1965) observed a reduction in horizontal fixation disparity after wearing a lateral prism for 15-30 min. Mitchell and Ellerbrock (1955) observed marked reductions in oso fixation disparity that occurred after prolonged wearing of a base-in prism: 757
however. they were unable to find adaptation of fixation disparity to small amounts of base-out prism. Subsequently. Carter (1965) and Ogle (1967) observed a reduction of e.~o fixation disparity with long-term wearing of a base-out prism. The time course for the reduction of fixation disparity is approx I5 min for a 2” vertical prism (Ogle and Prangen. 1953) and 15 min for 32& horizontal prism or any horizontal prism amplitude within the range of horizontal fusional vergence (Ogle et al., 1967; Carter. 1965). Ogle and Prangen (1953) suggested that the reduction of fixation disparity with prolonged binocular fixation was due to a slow fusional process. They maintained that slow fusional vergence responded to stress on a faster form of fusional vergence. The sum of the fast and slow fusional vergence mechanisms equalled the total disparity-induced vergence response such that when slow fusional vergence increased there was an equal reduction of fast fusional vergence. This reduction would occur as a result of the negative feedback loop of the fusional vergence system. Thus the output of the slow fusional mechanism reEeved the stress upon the fast fusional mechanism. making it possible for fast fusional vergence to respond to subsequent stimulus disparities. Assuming that fixation disparity results from stress on fast fusional vergence. Ellerbrock (1955) and Carter (1965) proposed that a mechanism similar to slow fusional vergence could account for the reduction of horizontal fixation disparity following prolonged wearing of a lateral prism. Slow fusional vergence can be demonstrated after stimulating fusional vergence with a prism by occluding one eye and observing an incomplete relaxation of the fusional vergence response to the prism (Hoffmann and Bielschowsky, 1900). The unrelaxed portion of the fusional vergence response is identified as slow fusional vergence or prism adaptation. The
amplitude of this prism adaptation depends upon the duration that the prism is worn. If. prior to occlusion. the prism is worn for a short duration (5 set). total relaxation of the fusional vergence response will occur within 15 set (Ludvigh er ill.. 196J1. The temporal course of relaxation is described as an exponentiJ decay with a time constant of IO set (Krishnan and Stark. 1977). Ellsrbrock (1950) demonstrated that when a verttcal prism was worn for prolonged periods (several hours) rekttion of vertical fusion was incomplete. The temporal decay function of vertical vergence had two components: a rapid decay which was interrupted after 10 min by a slower decay function that had a time constant of several hours. Prism .tdaptation to a horizontal prism has been demonstrated by Carter (1965). who observed that relaxation of fusional vergence was incomplete for several hours or until binocular fixation was reinstated. This incomplete relaxation of fusional vergence has been interpreted by Ogle and Prangen (1953) as a modification of tonic convergence (Maddox. 1893). Several issues concerning prism adaptation and its relationship to fixation disparity ha\e yet to be resolved. Given that tonic vergence can be modified by prolonged wearing of either a base-in or a base-out prism. why were Mitchell and Ellerbrock (1955) unable to find any adaptation of fixation disparity to a base-out prism‘? Inspection of their data reveals that most of the measurements of prism-induced fixation disparities could be classified as type II. Their subjects showed less fixation disparity resulting from a baseout than a base-in prism. After vvearing the prism for 30min. fixation disparity resulting from the base-in prism was reduced so that its amplitude equaled that of the fixation disparity induced by the base-out prism. It appears as though fixation dispartry adapted to the base-out prism so rapidly that it was complete at the time fixation disparity was first measured. If rapid adaptation of fixation disparity to the base-out prism did occur. this raises a second question. What is the influence of rapid prism adaptation on fixation disparity induced by short-term stimulus disparities for fusional vergence? Are Type II and III curves associated with rapid adaptation to base-out and base in prisms respectively? In the current study, slow fusional vergence was examined in a group of subjects with normal binocular vision by recording the decay of disparity-induced vergence following occlusion of one eye. Prior to monocular occlusion. binocular vergence eye movements were stimulated for a short duration (30sec) with convergent (base-out prism) and divergent (base-in prism) stimuli. Slow fusional vergence. as evidented by incomplete relaxation of fusional vergence upon monocular occlusion. occurred during the short period of binocular stimulation. The amplitude of slow fusional vergence was usually unequal in response to convergence and divergence stimuli. Fixation disparity resulting from the same convergence and divergence stimuli was examined in the same group of subjects. Most observers showed unequal amplitudes of fixation disparity with convergence and divergence stimuli. Comparisons of fixation disparity and slow fusional vergence in individual subjects revealed a high correlation between the direction of minimum fixation disparity and maximum slow
iustonal vergence. These results support the hjpothesis that slo\v fusional vitrgence relieves the stress on bmocular
vision
that
I. PRISWINDLCED
results
tn fixation
FIY4TIO\
disparity.
DISPARITI
Firatton disparity uas examrned in ct group of 11 sub;ec!s with normal binocular vision. Fktion disparity was induced with base-in (convergence) and base-out prism tdtternence) stimulus disparities of 1.5’. 3’. 4.SA, and 6l. worn-for 30sec each C’ergence stimuli progressed from the small I.? to the large 6) stimulus in 1.~’ steps. The directions of the prism (base in or base out) were presented slrzrn.ttely for each prtsm amplitude. Fixation dispartth inducrd by prism was plotted as a function of the prism amplitude. and the curves generated bk the data were clajsitisd using Ogle’s system (1967) as Types 1. II or 111. Disparity-induced vergence uas stimulated for 30 set tiith a bright luminous square frame subtending I.5 visual angle (Fig. I I, The square surrounded a vertical nonius test Itne that \vas centered in the upper half of the square bciors the right eke and the lower half of the square rie*ed by. :he leit eye. The left and rtght eyes‘ t.trgets. generated on !uo cathode ray oscilloscopes. were viewed haploscopiCJ!!:. it d distance of 5 ft through two front surface mirrors. one placed 91 an angle of 45 und the other at I35 before ths subjects’ eyes. The subjects’ combined percept of the haploscopic targets is illustrated in Fig. I. The horizontal position of the upper nonius line seen by the left eke \~as fixed in the center of its square. The horizontal position of :hs louer line was controlled by the subject. who adjusted its position on the CR0 with a potentiometer uniil the upper and lower nonius lines appeared to be in \srtxal alignment. Fixation disparity was indicated by an otTset of the lower line and was quantified by the examiner uith .I digital voltmeter to within 0.5’ arc. Two lens holders before the subject’s eyes were used to hold the refractive correction and prismatic stimuli for fusional vergence. ;ir the beginning of each session and before exposure to each prism stimulus, the examiner adjusted the horizontal position of the lower nonius line to the center of its square. and the subject adjusted the angle of the mirrors so that the nonius lines appeared to be aligned vertically. This procedure set the subject’s phoria to zero before vergence was stimulated with the prism. After the mirrors were adjusted, the examiner removed the lower nonius line by turning the potentiometer to an extreme position. The examiner placed a prism stimulus before the subject’s right eye and instructed the subject to make the square single and clear while looking through the prism. Using the
fusion
1.5’
Riqht
eye
Fig. I. Fusional vergence was stimulated with. a bright luminous square subtending 1.5’ visual angle. Nonius lines within the square were adjusted by the subject to appear in vertical alignment. Fixation disparity resulting from prism stimuli for fusional vergence was indicated by an offset of the nonius lines and was quantified to within 0.5’ arc
759
Influence of rapid prism adaptation upon fixation disparity
curves of Fig 2 resemble a rare prism-induced lixation disparity curve described by Ogle (1967) as Type IV, which has an incidence of less than 24; and is observed in persons with subnormal binocular vision. Ogle er al. (1949) reports that of the four classical types of fixation disparity curves. Type I has the highest incidence (80%) and Types II and III have a much lower incidence of approx loO/, each. The high incidence of Types II and III and the unusual Type I prism-induced fixation disparity curves observed in the current study appear to be the result of the size of the square in Fig. I. which provided a stimulus for binocular fusion. Ogle er al. (1949) demonstrated for one subject that central binocular fusion stimuli such as the 1.5’ square used in the current study resulted in a Type 11 fixation disparity curve. whereas
asymmetric convergence stimulus, the subject adjusted the potentiometer after 30 set of viewing SO that the two nonius lines appeared in vertical alignment. The adjustment procedure was completed in 5 set such that the total time elapsed from the initial stimulation of binocular vergence to the final setting of the nonius lines was 35sec. After each setting the prism was removed. and the subject viewed the target binocularly for 60~ to reduce any etkts of prism adaptation that might have persisted from the prior stimuli for fixation disparity. This 60-set period of binocular stimulation without the prism was found to be sufficient to return the eyes to their usual phoria, which had been set to zero at the beginning of the experiment. Complete elimination of the after effects of prism stimuli was noted by occluding one eye and recording no change in average position of the covered eye. After effects of wearing the prism were also minimized by presenting prism stimuli alternately base-in and base-out for each prism amplitude. Fixation disparity was measured four times for each stimulus and averaged measures of fixation disparity in ‘arc were plotted as a function of stimulus amplitude and direction in prism diopters. The subjects were 14 young adults who had normal binocular vision, corrected refractive errors. and no history of ocular discomfort or symptoms of any visual disorder other than refractive error. Lateral phorias ranged from 5 c.vo to 5 eso phoria. Corrections for refractive error were worn and lateral phorias were set to zero as described above by adjusting the mirrors of the haploscope.
Fixation disparity in minutes of arc is plotted as a function of the stimulus to fusional vergence in prism diopteis. The resulting prism-induced fixation disparity curves are classified into three groups: Types I, II and III, as described earlier. Curves for two subjects were classified as Type I (Fig 2). eight were classified as Type II (Fig 3). and four were classified as Type III curves (Fig 4). Most of the curves in groups II and III have a shape similar to the classical Type II and III curves described by Ogle YI (11.(1967). The curves in Fig 2 are classified as Type I on the basis of their symmetry and the excellent binocular vision of the subjects in this investigation. These Type I curves have much lower amplitudes of fixation disparity than the classical Type I curves described by Ogle rt ul. (1967). The Type I
TYPE
I
FIXATION
peripheral
binocular
fusion stimuli
2. PRISIM ADAPTATION-INCOMPLETE
6’ or
RELAXATION
OF FUSIONAL VERGENCE Methods
Slow fusional vergence was examined in the same group of subjects who participated in experiment I. The same target (Fig I) and prism amplitudes were used to stimulate fusional vergence eye movements in both experiments. Horizontal prisms were placed before the subject’s right
eye, starting with the smallest prism. 1.5’. and progressing to 6’ in 1.5’ steps. After binocular fixation had been maintained for 3Osec. an electronic shutter occluded the sub ject’s left eye and simultaneously triggered a 4kec recording period for a Data General micro computer which averaged five separate responses of relaxed vergence eye movements. Eye movements were monitored photoekctrically with the Biometrics SGVH infra-red monitor which has a resolution limit of lo’ arc. Vergence eye movements were obtained from the difference signal from each separate eye. Relaxation of vergence eye movements was recorded while the right eye fixated the lower nonius line in the center
DISPARITY
EASE
subtending
more resulted in a Type I curve. The use of the central 1.5” binocular fusion stimulus in the current investigation made it possible to observe the marked asymmetries ‘in fixation disparity resulting from convergent and divergent stimuli that might have gone unnoticed with peripheral fusional stimuli.
-OUT
iz
6 g w
‘5 t
Fig 2
20
760
C~rno~
TYPE
Ii
FlXATlON
54.
SCHOR
OtSPARffY
SN
IO 15
i
Fig. 3
20
761
Influence of rapid prism adaptation upon fixation disparity TYPE
III
FIXATION
DISPARITY
BASE-OUT
BASE-OUT
BASE-IN Iprism
diopkn)
s 1.) I
30 I
5
BASE-OUT 4.5 30 a I
1.5 60 4.s 30 BASE-IN (prism dioptwrl
3.0
BASE -OUT 4.5 60
1.S :
Fig. 4 Figs 2-4. Fixation disparity in min arc is plotted for individual subjects as a function of the amplitude of the stimulus to fusional vergence in prism diopters. Convergent stimuli (base-out prism) and divergent stimuli (base-in prism) are represented respectively to the right and left of the Y-axis on each graph. Convergent @so) fixation disparity and divergent (exo) fixation disparity are plotted respectively above and below the X-axis. Prism induced fixation disparity curves are grouped into Types I, II and III in Figs 2-4 respectively.
of the 1.5” square. As in experiment 1. prior to each run the subject’s phoria was set to zero by adjusting the mirrors before the subject’s eyes until the two nonius lines appeared to be aligned vertically. After each run. the prism was removed, and the shutter was opened allowing the subject to view the square targets binocularly for 6Osec to reduce any cumulative effects of prism adaptation that might have persisted from the prior run. Prism adaptation was quantified as the amount of fusional vergena that remained after 40 set of monocular occlusion. This value was obtained by subtracting the amount of vergena relaxed during monocular occlusion from the amount of fusional vergena stimulated prior to occlusion. The amount of fusional vergence stimulated equalled the stimulus disparity. since the subject’s hetero-
phoria had been set to zero by adjusting the haploscope mirrors. Subjects were classified into three categories. depending on the relative amplitudes of prism adaptation in response to convergent and divergent stimulus disparities. Those who had equal adaptations to convergent and divergent disparities were classified as Type A: those who adapted more to convergent than divergent stimuli were classified as Type B. and the reverse relationship was classified as Type C. RCWltS
Averaged records for individual subjects of ver-. gence eye posture following occlusion of one eye reveal marked prism adaptation after a brief (30 set)
CLIFTON M. SCHOR 0.
b.
3 : ;. ,'
2-
: z E t w >
f PHORIP
z " 0 0
IO
I 20
1 30
40 TiME
frtcondri
Fig. 5. Averaged records of relaxation of fusional vergence following occlusion of one eye: (31 demonstrates total adaptation to a convergence stimulus which persists 4Osec after disrupting binocular fixation. (b) demonstrates total relaxation of the fusional vergence response. The decay is exponential and has a time constant of IOsec.
period of binocular fixation. Typical responses are shown in Fig. 5, which illustrates unequal adaptation to base-in and base-out prism. Marked prism adap tation to 3’ convergent stimulus disparity is illustrated in Fig. 5a. There is no change in vergence posture after oneeye has been occluded for 40 sec. Figure 5b. illustrates an exponental decay of the fusional divergence response to a base-in prism for the same subject. The curve has a time constant of IOsec and becomes asymptotic at 15 set to a vergence angle equal to the subjects’ phoria, which had been set to zero prior to the experiment. Prism adaptation was quantified from these records as the difference between the prism stimulus to fusional vergence and the reduction or decay of the vergence response after 4Osec of monocular occlusion. The amplitude of prism adaptation for indiyidual subjects is plotted in Figs 6 and 7 as a function of the amplitude of the fusional vergence stimulus. The diagonal line in each graph represents total adaptation or no relaxation of fusional vergence, and points falling along the X axis represent an absence of prism adaptation or complete relaxation of fusional vergence. Every subject demonstrated unequal adaptation to base-in and base-out prisms and was classified according to the direction of maximum prism adaptation as Type B (Fig. 6) or Type C (Fig 7). Eight subjects showed marked adap tation to base-out prisms (Fig. 6) and the remaining six subjects had marked adaptation to base-in prisms (Fig. 7). Four of the subjects showed complete prism adaptation in one direction, and nine subjects showed a complete absence of prism adaptation in one direction. Three subjects showed complete adaptation in one direction and no adaptation in the opposite direction. Two of these subjects adapted to base-out prisms and one to base-in prisms. When prism adaptation was partial but incomplete, the amount of prism adaptation was either a constant or it increased proportionally with the stimulus amplitude for fusional vergence. Constant amounts of prism adaptation demonstrate a saturation limit to the slow fusional vergence mechanism. Ahernatively, the constant could indicate that prism adaptation occurs at a velocity that is independent of the
TYPE
8
PRISM
ADAPTATIONS
Patoa [pit‘“,
Fig. 6
diopttr$t
TO OCCtUSloW
InRumce of rapid prism adaptation
763
upon fixation disparity
(1900) and later refined by Ogle and Prangen (1953). Comparison of the results of experiments 1 and :! reveals a high correlation between the direction of minimum fixation disparity and the direction for maximum prism adaptation. All eight subjects whose prism-induced fixation disparity curves were classified as Type I1 demonstrated more adaptation to base-out than base-in prisms. Similarly. all four subjects whose fixation disparity curves were classified as Type III demonstrated more adaptation to base-in than baseout prisms. The two remaining subjects whose fixation disparity curves were Type I (equal amplitude of fixation disparity with base-m and base-out prisms) demonstrated marked adaptation to base-in prisms and little if any adaptation to base-out prisms. Bielschowsky
DISCL’SSION
Comparisons of prism-induced fixation disparity with prism adaptation measured by disruption of binocular fixation illustrate that fixation disparity is a strong indicator of rapid prism adaptation. Invariably, low values of fixation disparity in one direction were associated with high prism adaptation in the same direction. Occasionally. equally low values of TYPE
C
PRISM
ADAPTATION
83 CO*YLwcUCL 0
VEIGENCE
AYCLITUOL
PRlOR
70
OCCLUSION
($dm
OI”C”aE*Ct
d~t~ll)
Fig. 7 Figs 6. 7. The amplitude of prism adaptation is plotted as a function of the stimulus to convergence (A) and divergence (0). Data points along the diagonal line indicate total adaptation. Points along the X-axis indicate an absence of adaptation or total relaxation of fusional ver. gence. Points between these extremes demonstrate partial prism adaptation. Subjects demonstrating marked adag tation to base-out prisms or base-in prisms are grouped in Figs 6 and 7 respectively.
amplitude of the stimulus to fusional vergence, and that, given enough time, prism adaptation woufd increase with stimulus amplitude. Subjects demonstrating partial prism adaptation that increased in proportion with the amplitude of the fusional vergence stimulus demonstrated that the rate of prism adap tation was related to the amplitude of the fusional vergence stimulus. These results and observations of sustained vergence following occlusion of one eye suggest that the control mechanism for prism adaptation can be described as a leaky neural integrator with a very long time constant. The input to the slow neural integrator appears to be the output or effort of fast fusional vergence, since slow fusional vergence responds after fast fusional vergence has reduced prism-induced retinal image disparity to a few minutes of arc. The output of the slow neural integrator would allow for a reduction of the output of fast fusiona! vergence by means of the negative feedback loop of the binocular vergence servo mechanism. This dynamic interaction between fast and slow fusional vergena: was originally suggested by Hoffmann and
VERGENCL AMPLITUDE TO OGCLUSIOW tptmm
PRIOR &#%?a)
Fig. 8. Adaptation to base-in prisms by 3 subjects with occasional convergent strabismus.
764
CLIFTOK TYPE
II
FIXATION
DISPARITY
h,
0ASE -OUT 75 60 45 30 EASE-IN (prirm diaptwd
4S
60
I5
w 120 9 \
30
‘:
t 20
EASE-IN
IV. SCHOR
fivlttton disparity uould occur for both base-tn end base-out prisms. but the associated prism adaptation uould be unequal for base-in and base-out prisms. Thus. it was not aiwa)s possible to predict the shape pi the prism-induced fixation dispariri curves using observations ofrapid prism adaptation. Other factors In addition to prtsm adaptation must influence the amplitude of tixation disparit) resulting from forced vergence. High values of prism adaptation uxs never assoctated with high values for prism-induced fixation disparity in subjects with normal binocular vision. Houever. this combination was observed in three additional subjects with occasional convergent strabismus. All three subjects demonstrated nearly complete prism adaptation to base-in prisms (Fig. Sh and aii three subjects had large fixation disparities resulting from both base-out and base-in prisms (Fig. 9). Factors interferring with sensory fusion. such as interocular suppression, may have been responsible for the marked elevation of fixation disparity. The resuhs of the current study provide some insight into the functional organization of control mechanisms that underly fusional veqence. Ogle L~.‘I cti. I 19671 has proposed that separate control mechanisms. which are in opposition to one another, control fusional convergence and divergence, Ogle’s model is supported by observed differences in velocity (Rashbass and Westheimer. 1961) and latency (Krishnan ef LJ/.. 1973) for convergence and divergence responses to step inputs. Observations in the current stud:, of different rates of prism adaptation to base-in and base-out prisms suggest that separate mechanisms control the tonic levels of fusional convergence and divergence that help sustain fusional vergence responses over long periods of time. The importance of slow fusional vergence was recognized by Hoffman and Bielschowsky (1900). who at the rum of the centhe important factor concerning turn stated: ... fusional movements is not the movement that leads to sensory fusion per se but the prolonged tonic fundamental innervation of the eye muscles that is adapted for the conditions of single vision.” .~ci\,ru~~.~rdyr,,i~nrs-This project was supported by NEI Grant Number EY 02573 and Bio Medical Research Support Grant Number 77-39.
REFERENCES Carter D. B. (1965) Fixation disparity and heterophoria following prolonged wearing of prisms. An. J. Opturn. 42, 111-151. Ellerbrock V. J. (1950) Tonicity induced by fusional movements. Am. J. Oprom. 27. 8-20. Hoffmann F. B. and Bielschowsky A. (1900) Ubsr die der Willkue entzogenen Fusions-Bewegungen der -\ug2n. Arehs ges. Ph~~~~~.80. l-40.
Fig. 9.
Prism-induced fixation disparity curves for 3 subjects with occasional convergenr strabismus.
Krjshnan V. V. and Stark L. (1977) A heuristic model for the human vergence eye movement system. [FEE Trans. bio. med. Engng 18, 44-49. Krishnan V. V.. Farazian F. and Stark L. 11973)An anal!sis of latencies and prediction in the iusionat vergencc sysiem. .%m. &ad. Optorn. 50. 933-939. Ludvigh E.. McKinnon P. and Zaitzeff L. t 1964 Tsmpora! ceurse of the. relaxation of binocular duction (fusion) movements. .Archs Ophrhol. 71. 389-399.
Influence of rapid prism adaptation upon fixation disparity Maddox E. C. (1893) The Clinical Use of Prisms 2nd edn. p. 83. Wright. Bristol Mitchell A. M. and Ellerbrock V. J. (1955) Fixation disparity and the maintenance of fusion in the horizontal meridian. Am. J. Oprom. 32. 5X-534. Ogle K. N.. Mussey F. and Prangen A. de H. (1949) Fixation disparity and the fusional processes in binocular single vision. Am. J. Ophrh. 32. 1069-1087.
“.L
19p-c
765
Ogle K. N.. and Prangen A. (1953) Observations on vertical divergences and hyperphorias. Archs Ophrhal. 49, 313-334. Ogle K. N., Martens T. G. and Dyer A. J. (1967) Oculomct tor Imbalance in Binocular Vision and Fixation Dispariry. Lea & Febiger. Philadelphia.
Rashbass C. and Westheimer G. (1961) Disjunctive eye movements. J. Phyriol.. Lend. 159. 339-360.
INFLUENCE UPON
OF RAPID PRISM ADAPTATION FIXATION DISPARITY CLIFTON M. SCHOR
University of California. School of Optometry. Berkeley. California 94720. U.S.A. (Rucritrd 19 Junr 1978; in rerisedfornl
28 Nocc~hrr 1978)
Abstract-Small errors of fusional vergence (fixation disparity) were examined as a function of the magnitude of horizontal prism stimulating convergence or divergence for a short (30sec) duration. Marked differences were observed between the amplitude of fixation disparity resulting from convergent and divergent stimulus disparities. In another experiment. subjects wore a horizontal prism for 30~ after which time one eye was occluded for 40sec. Measurements of vergence eye movements revealed an incomplete relaxation of fusional vergence (prism adaptation) after 4Osec of occlusion. Marked differences were observed between the amplitude of prism adaptation resulting from convergent and divergent stimuli. Maximum prism adaptation and minimum fixation disparity occurred with the same direction of prism. suggesting that a slow fusional vergemx mechanism minimizes errors of binocular
vergence.
Kr_r Words-Fixation
disparity: prism adaptation:
fusional vergence:
tonic
convergence:
disjunctibe
eye movements.
INTRODL’CTION Small errors of binocular fixation can occur without disrupting binocular vision as long as the errors do not exceed panum’s fusional limits. Vergence errors. which are referred to as fixation disparity. vary in amplitude with the magnitude of the stimulus disparity to fusional vergence. Ogle and his co-workers
(1967) have quantified various relationships between fixation disparity and the amplitude of convergent and divergent fusional vergence stimuli. They have observed that fusional vergence responses are slightly less than their stimuli and that this lag increased with the amplitude of the fusional vergence stimulus. The lag of convergence and divergence responses are termed exo and eso fixation disparity respectively. Ogle has classified fixation disparity plotted as a function of prism vergence stimulus as Type I when the amplitude of fixation disparity increases in response to both divergent and convergent stimuli about equally. Prism-induced fixation disparity curves are classified as Type II when errors of convergence are smaller than errors of divergence. Type 111.describes fixation disparity that is greater with convergent than divergent stimuli. Errors of fixation associated with prism vergence stimuli appear to become smaller as the duration of binocular fixation increases. Ogle and Prangen (1953) observed a reduction in vertical fixation disparity after subjects wore a vertical prism for 2 hr. After adapting to the prism. vertical fixation disparity had the same amplitude that was measured before the prism was worn. Mitchell and Ellerbrock (1955) and Carter (1965) observed a reduction in horizontal fixation disparity after wearing a lateral prism for 15-30 min. Mitchell and Ellerbrock (1955) observed marked reductions in oso fixation disparity that occurred after prolonged wearing of a base-in prism: 757
however. they were unable to find adaptation of fixation disparity to small amounts of base-out prism. Subsequently. Carter (1965) and Ogle (1967) observed a reduction of e.~o fixation disparity with long-term wearing of a base-out prism. The time course for the reduction of fixation disparity is approx I5 min for a 2” vertical prism (Ogle and Prangen. 1953) and 15 min for 32& horizontal prism or any horizontal prism amplitude within the range of horizontal fusional vergence (Ogle et al., 1967; Carter. 1965). Ogle and Prangen (1953) suggested that the reduction of fixation disparity with prolonged binocular fixation was due to a slow fusional process. They maintained that slow fusional vergence responded to stress on a faster form of fusional vergence. The sum of the fast and slow fusional vergence mechanisms equalled the total disparity-induced vergence response such that when slow fusional vergence increased there was an equal reduction of fast fusional vergence. This reduction would occur as a result of the negative feedback loop of the fusional vergence system. Thus the output of the slow fusional mechanism reEeved the stress upon the fast fusional mechanism. making it possible for fast fusional vergence to respond to subsequent stimulus disparities. Assuming that fixation disparity results from stress on fast fusional vergence. Ellerbrock (1955) and Carter (1965) proposed that a mechanism similar to slow fusional vergence could account for the reduction of horizontal fixation disparity following prolonged wearing of a lateral prism. Slow fusional vergence can be demonstrated after stimulating fusional vergence with a prism by occluding one eye and observing an incomplete relaxation of the fusional vergence response to the prism (Hoffmann and Bielschowsky, 1900). The unrelaxed portion of the fusional vergence response is identified as slow fusional vergence or prism adaptation. The
amplitude of this prism adaptation depends upon the duration that the prism is worn. If. prior to occlusion. the prism is worn for a short duration (5 set). total relaxation of the fusional vergence response will occur within 15 set (Ludvigh er ill.. 196J1. The temporal course of relaxation is described as an exponentiJ decay with a time constant of IO set (Krishnan and Stark. 1977). Ellsrbrock (1950) demonstrated that when a verttcal prism was worn for prolonged periods (several hours) rekttion of vertical fusion was incomplete. The temporal decay function of vertical vergence had two components: a rapid decay which was interrupted after 10 min by a slower decay function that had a time constant of several hours. Prism .tdaptation to a horizontal prism has been demonstrated by Carter (1965). who observed that relaxation of fusional vergence was incomplete for several hours or until binocular fixation was reinstated. This incomplete relaxation of fusional vergence has been interpreted by Ogle and Prangen (1953) as a modification of tonic convergence (Maddox. 1893). Several issues concerning prism adaptation and its relationship to fixation disparity ha\e yet to be resolved. Given that tonic vergence can be modified by prolonged wearing of either a base-in or a base-out prism. why were Mitchell and Ellerbrock (1955) unable to find any adaptation of fixation disparity to a base-out prism‘? Inspection of their data reveals that most of the measurements of prism-induced fixation disparities could be classified as type II. Their subjects showed less fixation disparity resulting from a baseout than a base-in prism. After vvearing the prism for 30min. fixation disparity resulting from the base-in prism was reduced so that its amplitude equaled that of the fixation disparity induced by the base-out prism. It appears as though fixation dispartry adapted to the base-out prism so rapidly that it was complete at the time fixation disparity was first measured. If rapid adaptation of fixation disparity to the base-out prism did occur. this raises a second question. What is the influence of rapid prism adaptation on fixation disparity induced by short-term stimulus disparities for fusional vergence? Are Type II and III curves associated with rapid adaptation to base-out and base in prisms respectively? In the current study, slow fusional vergence was examined in a group of subjects with normal binocular vision by recording the decay of disparity-induced vergence following occlusion of one eye. Prior to monocular occlusion. binocular vergence eye movements were stimulated for a short duration (30sec) with convergent (base-out prism) and divergent (base-in prism) stimuli. Slow fusional vergence. as evidented by incomplete relaxation of fusional vergence upon monocular occlusion. occurred during the short period of binocular stimulation. The amplitude of slow fusional vergence was usually unequal in response to convergence and divergence stimuli. Fixation disparity resulting from the same convergence and divergence stimuli was examined in the same group of subjects. Most observers showed unequal amplitudes of fixation disparity with convergence and divergence stimuli. Comparisons of fixation disparity and slow fusional vergence in individual subjects revealed a high correlation between the direction of minimum fixation disparity and maximum slow
iustonal vergence. These results support the hjpothesis that slo\v fusional vitrgence relieves the stress on bmocular
vision
that
I. PRISWINDLCED
results
tn fixation
FIY4TIO\
disparity.
DISPARITI
Firatton disparity uas examrned in ct group of 11 sub;ec!s with normal binocular vision. Fktion disparity was induced with base-in (convergence) and base-out prism tdtternence) stimulus disparities of 1.5’. 3’. 4.SA, and 6l. worn-for 30sec each C’ergence stimuli progressed from the small I.? to the large 6) stimulus in 1.~’ steps. The directions of the prism (base in or base out) were presented slrzrn.ttely for each prtsm amplitude. Fixation dispartth inducrd by prism was plotted as a function of the prism amplitude. and the curves generated bk the data were clajsitisd using Ogle’s system (1967) as Types 1. II or 111. Disparity-induced vergence uas stimulated for 30 set tiith a bright luminous square frame subtending I.5 visual angle (Fig. I I, The square surrounded a vertical nonius test Itne that \vas centered in the upper half of the square bciors the right eke and the lower half of the square rie*ed by. :he leit eye. The left and rtght eyes‘ t.trgets. generated on !uo cathode ray oscilloscopes. were viewed haploscopiCJ!!:. it d distance of 5 ft through two front surface mirrors. one placed 91 an angle of 45 und the other at I35 before ths subjects’ eyes. The subjects’ combined percept of the haploscopic targets is illustrated in Fig. I. The horizontal position of the upper nonius line seen by the left eke \~as fixed in the center of its square. The horizontal position of :hs louer line was controlled by the subject. who adjusted its position on the CR0 with a potentiometer uniil the upper and lower nonius lines appeared to be in \srtxal alignment. Fixation disparity was indicated by an otTset of the lower line and was quantified by the examiner uith .I digital voltmeter to within 0.5’ arc. Two lens holders before the subject’s eyes were used to hold the refractive correction and prismatic stimuli for fusional vergence. ;ir the beginning of each session and before exposure to each prism stimulus, the examiner adjusted the horizontal position of the lower nonius line to the center of its square. and the subject adjusted the angle of the mirrors so that the nonius lines appeared to be aligned vertically. This procedure set the subject’s phoria to zero before vergence was stimulated with the prism. After the mirrors were adjusted, the examiner removed the lower nonius line by turning the potentiometer to an extreme position. The examiner placed a prism stimulus before the subject’s right eye and instructed the subject to make the square single and clear while looking through the prism. Using the
fusion
1.5’
Riqht
eye
Fig. I. Fusional vergence was stimulated with. a bright luminous square subtending 1.5’ visual angle. Nonius lines within the square were adjusted by the subject to appear in vertical alignment. Fixation disparity resulting from prism stimuli for fusional vergence was indicated by an offset of the nonius lines and was quantified to within 0.5’ arc
759
Influence of rapid prism adaptation upon fixation disparity
curves of Fig 2 resemble a rare prism-induced lixation disparity curve described by Ogle (1967) as Type IV, which has an incidence of less than 24; and is observed in persons with subnormal binocular vision. Ogle er al. (1949) reports that of the four classical types of fixation disparity curves. Type I has the highest incidence (80%) and Types II and III have a much lower incidence of approx loO/, each. The high incidence of Types II and III and the unusual Type I prism-induced fixation disparity curves observed in the current study appear to be the result of the size of the square in Fig. I. which provided a stimulus for binocular fusion. Ogle er al. (1949) demonstrated for one subject that central binocular fusion stimuli such as the 1.5’ square used in the current study resulted in a Type 11 fixation disparity curve. whereas
asymmetric convergence stimulus, the subject adjusted the potentiometer after 30 set of viewing SO that the two nonius lines appeared in vertical alignment. The adjustment procedure was completed in 5 set such that the total time elapsed from the initial stimulation of binocular vergence to the final setting of the nonius lines was 35sec. After each setting the prism was removed. and the subject viewed the target binocularly for 60~ to reduce any etkts of prism adaptation that might have persisted from the prior stimuli for fixation disparity. This 60-set period of binocular stimulation without the prism was found to be sufficient to return the eyes to their usual phoria, which had been set to zero at the beginning of the experiment. Complete elimination of the after effects of prism stimuli was noted by occluding one eye and recording no change in average position of the covered eye. After effects of wearing the prism were also minimized by presenting prism stimuli alternately base-in and base-out for each prism amplitude. Fixation disparity was measured four times for each stimulus and averaged measures of fixation disparity in ‘arc were plotted as a function of stimulus amplitude and direction in prism diopters. The subjects were 14 young adults who had normal binocular vision, corrected refractive errors. and no history of ocular discomfort or symptoms of any visual disorder other than refractive error. Lateral phorias ranged from 5 c.vo to 5 eso phoria. Corrections for refractive error were worn and lateral phorias were set to zero as described above by adjusting the mirrors of the haploscope.
Fixation disparity in minutes of arc is plotted as a function of the stimulus to fusional vergence in prism diopteis. The resulting prism-induced fixation disparity curves are classified into three groups: Types I, II and III, as described earlier. Curves for two subjects were classified as Type I (Fig 2). eight were classified as Type II (Fig 3). and four were classified as Type III curves (Fig 4). Most of the curves in groups II and III have a shape similar to the classical Type II and III curves described by Ogle YI (11.(1967). The curves in Fig 2 are classified as Type I on the basis of their symmetry and the excellent binocular vision of the subjects in this investigation. These Type I curves have much lower amplitudes of fixation disparity than the classical Type I curves described by Ogle rt ul. (1967). The Type I
TYPE
I
FIXATION
peripheral
binocular
fusion stimuli
2. PRISIM ADAPTATION-INCOMPLETE
6’ or
RELAXATION
OF FUSIONAL VERGENCE Methods
Slow fusional vergence was examined in the same group of subjects who participated in experiment I. The same target (Fig I) and prism amplitudes were used to stimulate fusional vergence eye movements in both experiments. Horizontal prisms were placed before the subject’s right
eye, starting with the smallest prism. 1.5’. and progressing to 6’ in 1.5’ steps. After binocular fixation had been maintained for 3Osec. an electronic shutter occluded the sub ject’s left eye and simultaneously triggered a 4kec recording period for a Data General micro computer which averaged five separate responses of relaxed vergence eye movements. Eye movements were monitored photoekctrically with the Biometrics SGVH infra-red monitor which has a resolution limit of lo’ arc. Vergence eye movements were obtained from the difference signal from each separate eye. Relaxation of vergence eye movements was recorded while the right eye fixated the lower nonius line in the center
DISPARITY
EASE
subtending
more resulted in a Type I curve. The use of the central 1.5” binocular fusion stimulus in the current investigation made it possible to observe the marked asymmetries ‘in fixation disparity resulting from convergent and divergent stimuli that might have gone unnoticed with peripheral fusional stimuli.
-OUT
iz
6 g w
‘5 t
Fig 2
20
760
C~rno~
TYPE
Ii
FlXATlON
54.
SCHOR
OtSPARffY
SN
IO 15
i
Fig. 3
20
761
Influence of rapid prism adaptation upon fixation disparity TYPE
III
FIXATION
DISPARITY
BASE-OUT
BASE-OUT
BASE-IN Iprism
diopkn)
s 1.) I
30 I
5
BASE-OUT 4.5 30 a I
1.5 60 4.s 30 BASE-IN (prism dioptwrl
3.0
BASE -OUT 4.5 60
1.S :
Fig. 4 Figs 2-4. Fixation disparity in min arc is plotted for individual subjects as a function of the amplitude of the stimulus to fusional vergence in prism diopters. Convergent stimuli (base-out prism) and divergent stimuli (base-in prism) are represented respectively to the right and left of the Y-axis on each graph. Convergent @so) fixation disparity and divergent (exo) fixation disparity are plotted respectively above and below the X-axis. Prism induced fixation disparity curves are grouped into Types I, II and III in Figs 2-4 respectively.
of the 1.5” square. As in experiment 1. prior to each run the subject’s phoria was set to zero by adjusting the mirrors before the subject’s eyes until the two nonius lines appeared to be aligned vertically. After each run. the prism was removed, and the shutter was opened allowing the subject to view the square targets binocularly for 6Osec to reduce any cumulative effects of prism adaptation that might have persisted from the prior run. Prism adaptation was quantified as the amount of fusional vergena that remained after 40 set of monocular occlusion. This value was obtained by subtracting the amount of vergena relaxed during monocular occlusion from the amount of fusional vergena stimulated prior to occlusion. The amount of fusional vergence stimulated equalled the stimulus disparity. since the subject’s hetero-
phoria had been set to zero by adjusting the haploscope mirrors. Subjects were classified into three categories. depending on the relative amplitudes of prism adaptation in response to convergent and divergent stimulus disparities. Those who had equal adaptations to convergent and divergent disparities were classified as Type A: those who adapted more to convergent than divergent stimuli were classified as Type B. and the reverse relationship was classified as Type C. RCWltS
Averaged records for individual subjects of ver-. gence eye posture following occlusion of one eye reveal marked prism adaptation after a brief (30 set)
CLIFTON M. SCHOR 0.
b.
3 : ;. ,'
2-
: z E t w >
f PHORIP
z " 0 0
IO
I 20
1 30
40 TiME
frtcondri
Fig. 5. Averaged records of relaxation of fusional vergence following occlusion of one eye: (31 demonstrates total adaptation to a convergence stimulus which persists 4Osec after disrupting binocular fixation. (b) demonstrates total relaxation of the fusional vergence response. The decay is exponential and has a time constant of IOsec.
period of binocular fixation. Typical responses are shown in Fig. 5, which illustrates unequal adaptation to base-in and base-out prism. Marked prism adap tation to 3’ convergent stimulus disparity is illustrated in Fig. 5a. There is no change in vergence posture after oneeye has been occluded for 40 sec. Figure 5b. illustrates an exponental decay of the fusional divergence response to a base-in prism for the same subject. The curve has a time constant of IOsec and becomes asymptotic at 15 set to a vergence angle equal to the subjects’ phoria, which had been set to zero prior to the experiment. Prism adaptation was quantified from these records as the difference between the prism stimulus to fusional vergence and the reduction or decay of the vergence response after 4Osec of monocular occlusion. The amplitude of prism adaptation for indiyidual subjects is plotted in Figs 6 and 7 as a function of the amplitude of the fusional vergence stimulus. The diagonal line in each graph represents total adaptation or no relaxation of fusional vergence, and points falling along the X axis represent an absence of prism adaptation or complete relaxation of fusional vergence. Every subject demonstrated unequal adaptation to base-in and base-out prisms and was classified according to the direction of maximum prism adaptation as Type B (Fig. 6) or Type C (Fig 7). Eight subjects showed marked adap tation to base-out prisms (Fig. 6) and the remaining six subjects had marked adaptation to base-in prisms (Fig. 7). Four of the subjects showed complete prism adaptation in one direction, and nine subjects showed a complete absence of prism adaptation in one direction. Three subjects showed complete adaptation in one direction and no adaptation in the opposite direction. Two of these subjects adapted to base-out prisms and one to base-in prisms. When prism adaptation was partial but incomplete, the amount of prism adaptation was either a constant or it increased proportionally with the stimulus amplitude for fusional vergence. Constant amounts of prism adaptation demonstrate a saturation limit to the slow fusional vergence mechanism. Ahernatively, the constant could indicate that prism adaptation occurs at a velocity that is independent of the
TYPE
8
PRISM
ADAPTATIONS
Patoa [pit‘“,
Fig. 6
diopttr$t
TO OCCtUSloW
InRumce of rapid prism adaptation
763
upon fixation disparity
(1900) and later refined by Ogle and Prangen (1953). Comparison of the results of experiments 1 and :! reveals a high correlation between the direction of minimum fixation disparity and the direction for maximum prism adaptation. All eight subjects whose prism-induced fixation disparity curves were classified as Type I1 demonstrated more adaptation to base-out than base-in prisms. Similarly. all four subjects whose fixation disparity curves were classified as Type III demonstrated more adaptation to base-in than baseout prisms. The two remaining subjects whose fixation disparity curves were Type I (equal amplitude of fixation disparity with base-m and base-out prisms) demonstrated marked adaptation to base-in prisms and little if any adaptation to base-out prisms. Bielschowsky
DISCL’SSION
Comparisons of prism-induced fixation disparity with prism adaptation measured by disruption of binocular fixation illustrate that fixation disparity is a strong indicator of rapid prism adaptation. Invariably, low values of fixation disparity in one direction were associated with high prism adaptation in the same direction. Occasionally. equally low values of TYPE
C
PRISM
ADAPTATION
83 CO*YLwcUCL 0
VEIGENCE
AYCLITUOL
PRlOR
70
OCCLUSION
($dm
OI”C”aE*Ct
d~t~ll)
Fig. 7 Figs 6. 7. The amplitude of prism adaptation is plotted as a function of the stimulus to convergence (A) and divergence (0). Data points along the diagonal line indicate total adaptation. Points along the X-axis indicate an absence of adaptation or total relaxation of fusional ver. gence. Points between these extremes demonstrate partial prism adaptation. Subjects demonstrating marked adag tation to base-out prisms or base-in prisms are grouped in Figs 6 and 7 respectively.
amplitude of the stimulus to fusional vergence, and that, given enough time, prism adaptation woufd increase with stimulus amplitude. Subjects demonstrating partial prism adaptation that increased in proportion with the amplitude of the fusional vergence stimulus demonstrated that the rate of prism adap tation was related to the amplitude of the fusional vergence stimulus. These results and observations of sustained vergence following occlusion of one eye suggest that the control mechanism for prism adaptation can be described as a leaky neural integrator with a very long time constant. The input to the slow neural integrator appears to be the output or effort of fast fusional vergence, since slow fusional vergence responds after fast fusional vergence has reduced prism-induced retinal image disparity to a few minutes of arc. The output of the slow neural integrator would allow for a reduction of the output of fast fusiona! vergence by means of the negative feedback loop of the binocular vergence servo mechanism. This dynamic interaction between fast and slow fusional vergena: was originally suggested by Hoffmann and
VERGENCL AMPLITUDE TO OGCLUSIOW tptmm
PRIOR &#%?a)
Fig. 8. Adaptation to base-in prisms by 3 subjects with occasional convergent strabismus.
764
CLIFTOK TYPE
II
FIXATION
DISPARITY
h,
0ASE -OUT 75 60 45 30 EASE-IN (prirm diaptwd
4S
60
I5
w 120 9 \
30
‘:
t 20
EASE-IN
IV. SCHOR
fivlttton disparity uould occur for both base-tn end base-out prisms. but the associated prism adaptation uould be unequal for base-in and base-out prisms. Thus. it was not aiwa)s possible to predict the shape pi the prism-induced fixation dispariri curves using observations ofrapid prism adaptation. Other factors In addition to prtsm adaptation must influence the amplitude of tixation disparit) resulting from forced vergence. High values of prism adaptation uxs never assoctated with high values for prism-induced fixation disparity in subjects with normal binocular vision. Houever. this combination was observed in three additional subjects with occasional convergent strabismus. All three subjects demonstrated nearly complete prism adaptation to base-in prisms (Fig. Sh and aii three subjects had large fixation disparities resulting from both base-out and base-in prisms (Fig. 9). Factors interferring with sensory fusion. such as interocular suppression, may have been responsible for the marked elevation of fixation disparity. The resuhs of the current study provide some insight into the functional organization of control mechanisms that underly fusional veqence. Ogle L~.‘I cti. I 19671 has proposed that separate control mechanisms. which are in opposition to one another, control fusional convergence and divergence, Ogle’s model is supported by observed differences in velocity (Rashbass and Westheimer. 1961) and latency (Krishnan ef LJ/.. 1973) for convergence and divergence responses to step inputs. Observations in the current stud:, of different rates of prism adaptation to base-in and base-out prisms suggest that separate mechanisms control the tonic levels of fusional convergence and divergence that help sustain fusional vergence responses over long periods of time. The importance of slow fusional vergence was recognized by Hoffman and Bielschowsky (1900). who at the rum of the centhe important factor concerning turn stated: ... fusional movements is not the movement that leads to sensory fusion per se but the prolonged tonic fundamental innervation of the eye muscles that is adapted for the conditions of single vision.” .~ci\,ru~~.~rdyr,,i~nrs-This project was supported by NEI Grant Number EY 02573 and Bio Medical Research Support Grant Number 77-39.
REFERENCES Carter D. B. (1965) Fixation disparity and heterophoria following prolonged wearing of prisms. An. J. Opturn. 42, 111-151. Ellerbrock V. J. (1950) Tonicity induced by fusional movements. Am. J. Oprom. 27. 8-20. Hoffmann F. B. and Bielschowsky A. (1900) Ubsr die der Willkue entzogenen Fusions-Bewegungen der -\ug2n. Arehs ges. Ph~~~~~.80. l-40.
Fig. 9.
Prism-induced fixation disparity curves for 3 subjects with occasional convergenr strabismus.
Krjshnan V. V. and Stark L. (1977) A heuristic model for the human vergence eye movement system. [FEE Trans. bio. med. Engng 18, 44-49. Krishnan V. V.. Farazian F. and Stark L. 11973)An anal!sis of latencies and prediction in the iusionat vergencc sysiem. .%m. &ad. Optorn. 50. 933-939. Ludvigh E.. McKinnon P. and Zaitzeff L. t 1964 Tsmpora! ceurse of the. relaxation of binocular duction (fusion) movements. .Archs Ophrhol. 71. 389-399.
Influence of rapid prism adaptation upon fixation disparity Maddox E. C. (1893) The Clinical Use of Prisms 2nd edn. p. 83. Wright. Bristol Mitchell A. M. and Ellerbrock V. J. (1955) Fixation disparity and the maintenance of fusion in the horizontal meridian. Am. J. Oprom. 32. 5X-534. Ogle K. N.. Mussey F. and Prangen A. de H. (1949) Fixation disparity and the fusional processes in binocular single vision. Am. J. Ophrh. 32. 1069-1087.
“.L
19p-c
765
Ogle K. N.. and Prangen A. (1953) Observations on vertical divergences and hyperphorias. Archs Ophrhal. 49, 313-334. Ogle K. N., Martens T. G. and Dyer A. J. (1967) Oculomct tor Imbalance in Binocular Vision and Fixation Dispariry. Lea & Febiger. Philadelphia.
Rashbass C. and Westheimer G. (1961) Disjunctive eye movements. J. Phyriol.. Lend. 159. 339-360.
