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The Effect of Orientation on the Three-Dot Alignment Test
T H E E F F E C T O F O R I E N T A T I O N ON T H E T H R E E - D O T ALIGNMENT T E S T E L E K LUDVIGH, P H . D . , AND PAULINE M C K I N N O N , P H M . B .
Detroit, Michigan
The small displacements which can be perceived when the direction sense* (Bour don) of the eye is tested have long been of interest.1 The contour break test, the vernier alignment test and certain tests of the preci sion of stereopsis all show that displace ments subtending approximately two sec onds of arc at the nodal point of the eye can be detected.2"4 Since an average foveal cone subtends 30 seconds of arc at the nodal point of the eye, and even the smallest cones subtend about 12 seconds,5 it appears that displacements of the retinal image much smaller than the width of a cone may reli ably be detected. Numerous theories have been advanced to account for this paradox. Efforts have been made by Bourdon,1 Cowan8 and Hering 2 among others to explain perception accurate to fractional cone widths. However, none of these explanations has taken into account the fact that the accuracy of these tests is substantially independent of slight varia tions in orientation from the vertical, that diffraction and aberration produce a blur disc which subtends the order of two min utes of arc on the retina,7 and that the eye is in a constant state of tremor.8 ' 9 The problem seemed unresolved until An derson and Weymouth showed that stereo scopic accuracy was dependent upon the length of line presented.4 If the lines were so short as to be dots, then the resolution would be about 40 seconds of arc. But if the lines were long, then resolution of about two seconds of arc could be obtained. Thus the stereoscopic accuracy increased with length From the Kresge Eye Institute of Wayne State University. This investigation was supported in part by research grant B-3934 from the Na tional Institute of Neurological Diseases and Blindness of the National Institutes of Health, United States Public Health Service. * The tests of this so-called sense are, in fact, tests of the perception of relative direction.
of line. Anderson and Weymouth explained this observation in statistical terms. 4 They argued that with increased length of line more retinal elements would be stimulated, and that the accuracy of the perception of the mean position of the lines would in crease with longer lines. This hypothesis is very attractive, but un fortunately it is not consistent with recent experimental results. Ludvigh has shown that if two dots of light, one vertically above the other are presented to one eye, a third dot may be located to the right or to the left of the imaginary line drawn between the two reference dots. The accuracy with which this middle dot is located varies with the an gular separation of the outer dots, and is maximal when the outer dots are separated by 10 to 20 minutes of arc.10 This accuracy, of approximately two seconds of arc, cannot be accounted for in terms of averaging the mean position of a statistically large number of cones. Ludvigh concluded : If an hypothesis can be found to explain the high degree of accuracy of this three-dot align ment test, as well as its improvement with in creasing separation of the reference dots, then such an hypothesis would presumably also be ade quate to account for the improvement of the con tour break, vernier and depth perception test with increasing height of line. . . . It is difficult to see how the data here presented can be accounted for other than in terms of a field theory of some type.10
Recent investigations in lower mammals suggest a field theory capable of accounting for the accuracy of the three-dot alignment test. Hubel and Wiesel demonstrated that the stimulation of a linear region of the cat's retina could result in the excitation or inhibition of a single cortical cell.11 Con cerning the orientation of the linear region, Hubel and Wiesel state that :
261
This orientation is a characteristic of each cor tical cell, and may be vertical, horizontal, or oblique. There was no indication that any one or ientation was more common than the others."
262
AMERICAN JOURNAL OF OPHTHALMOLOGY
In anatomic studies of cortical cells of the cat, rat and monkey, Colonnier found a sta tistically significant excess number of cells with vertical orientations, and a nonrandom distribution of obliquely or horizontally ori ented cells.12 However, Colonnier does state : Hubel and Wiesel (1962) have found no clear preferential orientation of the visual fields of their "columns" of cells in any axis. In the pres ent studies the dendritic fields of the stellate cells, however, tend to be orientated towards the verti cal although admittedly this is not yet adequately proven in the cat."
If in man an orientation of the linear re gion is characteristic of each cortical cell, then the three-dot test may give some indi cation of the distribution of the linear re gions characteristic of each cortical cell. The purpose of this investigation is to ascertain whether the three-dot alignment test varies in accuracy with the obliquity of the imag inary line joining the outer dots. APPARATUS
The apparatus used in this study presents three dots of light against a black back ground. The outer dots are stationary, while the middle dot is movable to the right or left of the imaginary line through the centers of the outer reference dots. The dots are formed by drilling three holes in three brass plates. At the observa tion distance of 12 meters, the diameters of these holes subtend seven seconds of arc at the nodal point of the eye. The middle plate is displaced by means of a spring-loaded lead screw. One revolution of the screw displaces the middle dot by a distance subtending 18.2 seconds of arc at the nodal point of the eye. The apparatus is painted matte black. Linear contours are masked with irregularly cut black, dull paper. The dots are revealed or obscured by a black board with irregular contours. This board is moved manually in a slot. When the dots are presented in the verti cal plane, the apparatus rests upright on a
AUGUST, 1967
table. Three wedges are inserted under the apparatus so that the dots may be viewed either 15, 30 or 45 degrees from the vertical in a clockwise direction. One of three colored lamps behind the brass plates illuminates the holes. The lamps are so enclosed that light is seen only through the three holes. The white lamp, with power supplied through a 60-watt voltage regulator, is a G.E. L40/IF Lumiline lamp. The green lamp, used in conjunction with a Wratten neutral density filter, is a G.E. F15-T8-G6 fluorescent lamp with a dominant wave length of 528 πιμ and 72% purity. The blue lamp is an F15 T8-B Sylvania fluorescent lamp with a dominant wavelength of 481 ιημ and 67% purity. There is less than 20% difference in brightness among the three sources as measured by a Weston photovol taic cell fitted with a Viscor filter. The distance of separation between the outer two reference dots is 15 minutes of arc. The center dot is placed midway be tween the other two. PROCEDURE
All observations are taken on one naive subject whose Snellen visual acuity is 20/13. The subject is seated and his head is ad justed in a headrest so that his eye is at the same height as the central dot, and directly in front of it. Tilting of the head is avoided by the use of two adjustable side screws. The subject is instructed to state that the middle dot is to the right or to the left of the outer two dots. The dots are obscured while the experi menter moves the central dot. When the dots are revealed, the subject has five sec onds in which to make his decision, after which time the dots are again obscured. All observations are taken monocularly. The ambient illumination at eye level is 0.64 foot-candles as measured with a Macbeth Illuminometer. The central dot is moved four or eight
VOL. 64, NO. 2
THREE-DOT ALIGNMENT TEST
seconds of arc either to the right or to the left of the stationary dots. These displace ments are given in a random fashion. The orientation of the dots is also randomly cho sen. A series of eight observations is taken at any one of the predetermined orientations. The subject is given a minimum rest of five minutes between each series. ANALYSIS OF DATA
The difference limen is found by the method of right and wrong cases.13 Ninetysix observations are taken at each of the four displacements of the central dot, and for each color. A chi-square test indicates that there is no significant difference between the results ob tained with the different colored lights.14 The data for the different colors are grouped, resulting in a total of 288 observa tions at each offset. For each orientation, the data are fitted
Fig. 1 (Ludvigh and McKinnon). Relationship between the proportion of judgements called to the right and the position of the central dot. On the x-axis positive numbers indicate the middle dot was to the right of the reference dots while negative numbers indi cate the middle dot was to the left. The circled symbols represent the experimental data while the smooth curves represent the phi-gamma function fitted by the method of least squares.
263
by the method of least squares to the phigamma function.13 The experimental data and the phi-gamma functions are shown in Figure 1. The difference limen is found by computing the probable error of this func tion. RESULTS
Figure 2 shows the difference limen as a function of orientation. When the dots are oriented vertically, the threshold displace ment of the central dot is less than four sec onds of arc although the outer reference dots are separated by 15 minutes of arc. In fact, by the use of the fitted phi-gamma function and the application of the binomial theorem, the number of computed correct judgements with a displacement of less than one second of arc would be such that the odds would be 100 to one against this num ber of correct judgements occurring by chance.
264
AMERICAN JOURNAL OF OPHTHALMOLOGY
AUGUST, 1967
Fig. 2 (Ludvigh and McKinnon). Relationship between the dif ference limen and the orientation of the stimulus. The O degree ori entation is vertical, while the IS, 30 and 45 degree orientations are in a clockwise direction from the vertical. The height between each pair of bars represents two stan dard errors of the associated mean.
ORIENTATION IN DEGREES
As the orientation of the dots departs from the vertical, the difference limen in creases. DISCUSSION
The resolution of various stimuli has been found to be superior when the main axes of the patterns have been oriented vertically or horizontally than when they have been ori ented obliquely. Shlaer found that a just re solved grating could be rotated so that it was unresolvable at certain angles.15 Leibowitz,16 using vernier acuity and grating reso lution tests, and Ogilvie and Taylor,17 in vestigating the visibility of fine wires, found the vertical and horizontal meridians to be superior. In discussing the Poggendorf and Zollner illusion among others, Colonnier states: These phenomena are perhaps related to the greater number of coding units, in the form of elongated cells and fibres oriented in the vertical axis of vision.12
The results on the three-dot alignment test suggest that in man the fields of the cortical cells may tend to be oriented to ward the vertical as suggested by Colonnier for the rat, cat and monkey.12 SUMMARY
A significantly lower limen for the three-
dot alignment test has been found when the dots are presented in a vertical orientation than when they are presented 30 or 45 de grees from the vertical. In all orientations tested, the threshold displacement subtends a small fraction of a cone width. A field theory, to account for the super iority of the discrimination in the vertical meridian, is suggested. 690 Mullett Street (48226) REFERENCES
1. Bourdon, B. : La Perception Visuelle de L'Espace. Paris, Schleicher Frères, 1902, p. 136. 2. Hering: Ueber die Grenzen der Sehschärfe. Bericht d. math.-phys. Klasse d.k. sächs. Gesellsch. d. Wissenschaften, 1889 Bd. 51 (3), p. 16. 3. Bourdon, B. : Ibid, p. 145. 4. Anderson, E. and Weymouth, F. : Visual per ception and the retinal mosaic: 1. Retinal mean local sign—an explanation of the fineness of binoc ular perception of distance. Am. J. Physiol. 64:561, 1923. 5. Polyak, S. L. : The Retina. Chicago, Univ. Chicago Press, 1941, p. 201. 6. Cowan, A. : Variations in normal visual acu ity in relation to the retinal cones. Am. J. Ophth. 6 :676, 1923. 7. Ames, A. Jr. and Proctor, C. A. : Dioptrics of the eye. J. Opt. Soc. Am. 5 :22, 1921. 8. Adler, F. H. and Fliegelman, M. : Influence of fixation on the visual acuity. Arch. Ophth. 12:475, 1934. 9. Riggs, L. A. and Ratliff, F.: The steadiness of the eye. J. Opt. Soc. Am. 39:630, 1949. 10. Ludvigh, E. : Direction sense of the eye. Am. J. Ophth. 36:139 (June Pt II) 1953.
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THREE-DOT ALIGNMENT TEST
11. Hubel, D. H. and Wiesel, T. N.: Receptive fields, binocular interaction and functional archi tecture in the cat's visual cortex. J. Physiol. 160:106,1962. 12. Colonnier, M. : The tangential organization of the visual cortex. J. Anat. 98:327, 1964. 13. Guilford, J. P. : Psychometric Methods. New York, McGraw-Hill, 1936, ed. 1, pp. 166-200. 14. Guilford, J. P. : Fundamental Statistics in Psychology and Education. New York, McGraw-
265
Hill, 1950, ed. 2, pp. 273-287. 15. Shlaer, S. : The relation between visual acu ity and illumination. J. Gen. Physiol. 21:165, 1937-38. 16. Leibowitz, H. : Some observations and theo ry on the variation of visual acuity with the or ientation of the test object, J. Opt. Soc. Am. 43:902, 1953.. 17. Ogilvie, J. C. and Taylor, M. M. : Effect of orientation on the visibility of fine wires, J. Opt. Soc. Am. 48:628, 1958.
MONOCULAR VERTICAL DISPLACEMENT O F T H E HORIZONTAL RECTUS MUSCLES IN T H E A AND V P A T T E R N S JOSEPH H. GOLDSTEIN,
M.D.
Brooklyn, New York
The characteristics and various surgical approaches to the A and V patterns have been presented in several excellent review articles.1"4 It was the concensus of the panelists in a recent symposium that in cases in which there is obvious oblique mus cle dysfunction, the appropriate strengthen ing or weaking procedure on these muscles is the procedure of choice, but where no such dysfunction is found, symmetrical ver tical displacement of the horizontal rectus muscles should be performed.5 This ap proach necessitates symmetrical surgery on either both medial rectus or both lateral rec tus muscles. There are, however, cases with an A or V pattern in which one would ordi narily choose to do monocular surgery, such as those in which the near and distance deviations are equal or in which there is a strong monocular fixation pattern. One is then faced with choice of doing symmetrical surgery in order to be in a position to treat the A or V pattern, or of doing monocular surgery and either ignoring the pattern or operating on another set of muscles. It is the purpose of this report to present the results of cases with the A and V pattern treated by monocular surgery of the horizontal rec tus muscles together with their appropriate vertical displacement. The first case perFrom the Division of Ophthalmology, State University of New York Downstate Medical Center.
formed in this manner was done at New York University-Bellevue Hospital Center. MATERIAL
A total of 18 operations on 17 patients were performed. These patients ranged in age from two to 74 years. All patients demonstrated 25 Δ or more of V pattern or 15 Δ or more of A pattern. The deviation was measured with prism and cover test on an accommodative target where possible. The prism and light reflex was used when eccentric fixation was present. Where mea sured, the same vertical incomitance was present for distance but slightly less in amount. Most cases showed either a marked monocular fixation pattern secondary to amblyopia with or without organic disease or presented with the near and distance devia tion fairly close. The amount of displace ment ranged from 4.0 mm to 8.0 mm. The technique of reattachment was con sistent with the recommendations of Dunlap6 who advised maintaining the original relationship of the muscle to the limbus. In resections, the muscle was vertically dis placed and inserted at a distance from the limbus equal to the original insertion-limbus distance. On recessions, the muscle was ver tically displaced and inserted at a distance from the limbus equal to the sum of the recession plus the original insertion-limbus distance. The direction of displacement was
Detroit, Michigan
The small displacements which can be perceived when the direction sense* (Bour don) of the eye is tested have long been of interest.1 The contour break test, the vernier alignment test and certain tests of the preci sion of stereopsis all show that displace ments subtending approximately two sec onds of arc at the nodal point of the eye can be detected.2"4 Since an average foveal cone subtends 30 seconds of arc at the nodal point of the eye, and even the smallest cones subtend about 12 seconds,5 it appears that displacements of the retinal image much smaller than the width of a cone may reli ably be detected. Numerous theories have been advanced to account for this paradox. Efforts have been made by Bourdon,1 Cowan8 and Hering 2 among others to explain perception accurate to fractional cone widths. However, none of these explanations has taken into account the fact that the accuracy of these tests is substantially independent of slight varia tions in orientation from the vertical, that diffraction and aberration produce a blur disc which subtends the order of two min utes of arc on the retina,7 and that the eye is in a constant state of tremor.8 ' 9 The problem seemed unresolved until An derson and Weymouth showed that stereo scopic accuracy was dependent upon the length of line presented.4 If the lines were so short as to be dots, then the resolution would be about 40 seconds of arc. But if the lines were long, then resolution of about two seconds of arc could be obtained. Thus the stereoscopic accuracy increased with length From the Kresge Eye Institute of Wayne State University. This investigation was supported in part by research grant B-3934 from the Na tional Institute of Neurological Diseases and Blindness of the National Institutes of Health, United States Public Health Service. * The tests of this so-called sense are, in fact, tests of the perception of relative direction.
of line. Anderson and Weymouth explained this observation in statistical terms. 4 They argued that with increased length of line more retinal elements would be stimulated, and that the accuracy of the perception of the mean position of the lines would in crease with longer lines. This hypothesis is very attractive, but un fortunately it is not consistent with recent experimental results. Ludvigh has shown that if two dots of light, one vertically above the other are presented to one eye, a third dot may be located to the right or to the left of the imaginary line drawn between the two reference dots. The accuracy with which this middle dot is located varies with the an gular separation of the outer dots, and is maximal when the outer dots are separated by 10 to 20 minutes of arc.10 This accuracy, of approximately two seconds of arc, cannot be accounted for in terms of averaging the mean position of a statistically large number of cones. Ludvigh concluded : If an hypothesis can be found to explain the high degree of accuracy of this three-dot align ment test, as well as its improvement with in creasing separation of the reference dots, then such an hypothesis would presumably also be ade quate to account for the improvement of the con tour break, vernier and depth perception test with increasing height of line. . . . It is difficult to see how the data here presented can be accounted for other than in terms of a field theory of some type.10
Recent investigations in lower mammals suggest a field theory capable of accounting for the accuracy of the three-dot alignment test. Hubel and Wiesel demonstrated that the stimulation of a linear region of the cat's retina could result in the excitation or inhibition of a single cortical cell.11 Con cerning the orientation of the linear region, Hubel and Wiesel state that :
261
This orientation is a characteristic of each cor tical cell, and may be vertical, horizontal, or oblique. There was no indication that any one or ientation was more common than the others."
262
AMERICAN JOURNAL OF OPHTHALMOLOGY
In anatomic studies of cortical cells of the cat, rat and monkey, Colonnier found a sta tistically significant excess number of cells with vertical orientations, and a nonrandom distribution of obliquely or horizontally ori ented cells.12 However, Colonnier does state : Hubel and Wiesel (1962) have found no clear preferential orientation of the visual fields of their "columns" of cells in any axis. In the pres ent studies the dendritic fields of the stellate cells, however, tend to be orientated towards the verti cal although admittedly this is not yet adequately proven in the cat."
If in man an orientation of the linear re gion is characteristic of each cortical cell, then the three-dot test may give some indi cation of the distribution of the linear re gions characteristic of each cortical cell. The purpose of this investigation is to ascertain whether the three-dot alignment test varies in accuracy with the obliquity of the imag inary line joining the outer dots. APPARATUS
The apparatus used in this study presents three dots of light against a black back ground. The outer dots are stationary, while the middle dot is movable to the right or left of the imaginary line through the centers of the outer reference dots. The dots are formed by drilling three holes in three brass plates. At the observa tion distance of 12 meters, the diameters of these holes subtend seven seconds of arc at the nodal point of the eye. The middle plate is displaced by means of a spring-loaded lead screw. One revolution of the screw displaces the middle dot by a distance subtending 18.2 seconds of arc at the nodal point of the eye. The apparatus is painted matte black. Linear contours are masked with irregularly cut black, dull paper. The dots are revealed or obscured by a black board with irregular contours. This board is moved manually in a slot. When the dots are presented in the verti cal plane, the apparatus rests upright on a
AUGUST, 1967
table. Three wedges are inserted under the apparatus so that the dots may be viewed either 15, 30 or 45 degrees from the vertical in a clockwise direction. One of three colored lamps behind the brass plates illuminates the holes. The lamps are so enclosed that light is seen only through the three holes. The white lamp, with power supplied through a 60-watt voltage regulator, is a G.E. L40/IF Lumiline lamp. The green lamp, used in conjunction with a Wratten neutral density filter, is a G.E. F15-T8-G6 fluorescent lamp with a dominant wave length of 528 πιμ and 72% purity. The blue lamp is an F15 T8-B Sylvania fluorescent lamp with a dominant wavelength of 481 ιημ and 67% purity. There is less than 20% difference in brightness among the three sources as measured by a Weston photovol taic cell fitted with a Viscor filter. The distance of separation between the outer two reference dots is 15 minutes of arc. The center dot is placed midway be tween the other two. PROCEDURE
All observations are taken on one naive subject whose Snellen visual acuity is 20/13. The subject is seated and his head is ad justed in a headrest so that his eye is at the same height as the central dot, and directly in front of it. Tilting of the head is avoided by the use of two adjustable side screws. The subject is instructed to state that the middle dot is to the right or to the left of the outer two dots. The dots are obscured while the experi menter moves the central dot. When the dots are revealed, the subject has five sec onds in which to make his decision, after which time the dots are again obscured. All observations are taken monocularly. The ambient illumination at eye level is 0.64 foot-candles as measured with a Macbeth Illuminometer. The central dot is moved four or eight
VOL. 64, NO. 2
THREE-DOT ALIGNMENT TEST
seconds of arc either to the right or to the left of the stationary dots. These displace ments are given in a random fashion. The orientation of the dots is also randomly cho sen. A series of eight observations is taken at any one of the predetermined orientations. The subject is given a minimum rest of five minutes between each series. ANALYSIS OF DATA
The difference limen is found by the method of right and wrong cases.13 Ninetysix observations are taken at each of the four displacements of the central dot, and for each color. A chi-square test indicates that there is no significant difference between the results ob tained with the different colored lights.14 The data for the different colors are grouped, resulting in a total of 288 observa tions at each offset. For each orientation, the data are fitted
Fig. 1 (Ludvigh and McKinnon). Relationship between the proportion of judgements called to the right and the position of the central dot. On the x-axis positive numbers indicate the middle dot was to the right of the reference dots while negative numbers indi cate the middle dot was to the left. The circled symbols represent the experimental data while the smooth curves represent the phi-gamma function fitted by the method of least squares.
263
by the method of least squares to the phigamma function.13 The experimental data and the phi-gamma functions are shown in Figure 1. The difference limen is found by computing the probable error of this func tion. RESULTS
Figure 2 shows the difference limen as a function of orientation. When the dots are oriented vertically, the threshold displace ment of the central dot is less than four sec onds of arc although the outer reference dots are separated by 15 minutes of arc. In fact, by the use of the fitted phi-gamma function and the application of the binomial theorem, the number of computed correct judgements with a displacement of less than one second of arc would be such that the odds would be 100 to one against this num ber of correct judgements occurring by chance.
264
AMERICAN JOURNAL OF OPHTHALMOLOGY
AUGUST, 1967
Fig. 2 (Ludvigh and McKinnon). Relationship between the dif ference limen and the orientation of the stimulus. The O degree ori entation is vertical, while the IS, 30 and 45 degree orientations are in a clockwise direction from the vertical. The height between each pair of bars represents two stan dard errors of the associated mean.
ORIENTATION IN DEGREES
As the orientation of the dots departs from the vertical, the difference limen in creases. DISCUSSION
The resolution of various stimuli has been found to be superior when the main axes of the patterns have been oriented vertically or horizontally than when they have been ori ented obliquely. Shlaer found that a just re solved grating could be rotated so that it was unresolvable at certain angles.15 Leibowitz,16 using vernier acuity and grating reso lution tests, and Ogilvie and Taylor,17 in vestigating the visibility of fine wires, found the vertical and horizontal meridians to be superior. In discussing the Poggendorf and Zollner illusion among others, Colonnier states: These phenomena are perhaps related to the greater number of coding units, in the form of elongated cells and fibres oriented in the vertical axis of vision.12
The results on the three-dot alignment test suggest that in man the fields of the cortical cells may tend to be oriented to ward the vertical as suggested by Colonnier for the rat, cat and monkey.12 SUMMARY
A significantly lower limen for the three-
dot alignment test has been found when the dots are presented in a vertical orientation than when they are presented 30 or 45 de grees from the vertical. In all orientations tested, the threshold displacement subtends a small fraction of a cone width. A field theory, to account for the super iority of the discrimination in the vertical meridian, is suggested. 690 Mullett Street (48226) REFERENCES
1. Bourdon, B. : La Perception Visuelle de L'Espace. Paris, Schleicher Frères, 1902, p. 136. 2. Hering: Ueber die Grenzen der Sehschärfe. Bericht d. math.-phys. Klasse d.k. sächs. Gesellsch. d. Wissenschaften, 1889 Bd. 51 (3), p. 16. 3. Bourdon, B. : Ibid, p. 145. 4. Anderson, E. and Weymouth, F. : Visual per ception and the retinal mosaic: 1. Retinal mean local sign—an explanation of the fineness of binoc ular perception of distance. Am. J. Physiol. 64:561, 1923. 5. Polyak, S. L. : The Retina. Chicago, Univ. Chicago Press, 1941, p. 201. 6. Cowan, A. : Variations in normal visual acu ity in relation to the retinal cones. Am. J. Ophth. 6 :676, 1923. 7. Ames, A. Jr. and Proctor, C. A. : Dioptrics of the eye. J. Opt. Soc. Am. 5 :22, 1921. 8. Adler, F. H. and Fliegelman, M. : Influence of fixation on the visual acuity. Arch. Ophth. 12:475, 1934. 9. Riggs, L. A. and Ratliff, F.: The steadiness of the eye. J. Opt. Soc. Am. 39:630, 1949. 10. Ludvigh, E. : Direction sense of the eye. Am. J. Ophth. 36:139 (June Pt II) 1953.
VOL. 64, NO. 2
THREE-DOT ALIGNMENT TEST
11. Hubel, D. H. and Wiesel, T. N.: Receptive fields, binocular interaction and functional archi tecture in the cat's visual cortex. J. Physiol. 160:106,1962. 12. Colonnier, M. : The tangential organization of the visual cortex. J. Anat. 98:327, 1964. 13. Guilford, J. P. : Psychometric Methods. New York, McGraw-Hill, 1936, ed. 1, pp. 166-200. 14. Guilford, J. P. : Fundamental Statistics in Psychology and Education. New York, McGraw-
265
Hill, 1950, ed. 2, pp. 273-287. 15. Shlaer, S. : The relation between visual acu ity and illumination. J. Gen. Physiol. 21:165, 1937-38. 16. Leibowitz, H. : Some observations and theo ry on the variation of visual acuity with the or ientation of the test object, J. Opt. Soc. Am. 43:902, 1953.. 17. Ogilvie, J. C. and Taylor, M. M. : Effect of orientation on the visibility of fine wires, J. Opt. Soc. Am. 48:628, 1958.
MONOCULAR VERTICAL DISPLACEMENT O F T H E HORIZONTAL RECTUS MUSCLES IN T H E A AND V P A T T E R N S JOSEPH H. GOLDSTEIN,
M.D.
Brooklyn, New York
The characteristics and various surgical approaches to the A and V patterns have been presented in several excellent review articles.1"4 It was the concensus of the panelists in a recent symposium that in cases in which there is obvious oblique mus cle dysfunction, the appropriate strengthen ing or weaking procedure on these muscles is the procedure of choice, but where no such dysfunction is found, symmetrical ver tical displacement of the horizontal rectus muscles should be performed.5 This ap proach necessitates symmetrical surgery on either both medial rectus or both lateral rec tus muscles. There are, however, cases with an A or V pattern in which one would ordi narily choose to do monocular surgery, such as those in which the near and distance deviations are equal or in which there is a strong monocular fixation pattern. One is then faced with choice of doing symmetrical surgery in order to be in a position to treat the A or V pattern, or of doing monocular surgery and either ignoring the pattern or operating on another set of muscles. It is the purpose of this report to present the results of cases with the A and V pattern treated by monocular surgery of the horizontal rec tus muscles together with their appropriate vertical displacement. The first case perFrom the Division of Ophthalmology, State University of New York Downstate Medical Center.
formed in this manner was done at New York University-Bellevue Hospital Center. MATERIAL
A total of 18 operations on 17 patients were performed. These patients ranged in age from two to 74 years. All patients demonstrated 25 Δ or more of V pattern or 15 Δ or more of A pattern. The deviation was measured with prism and cover test on an accommodative target where possible. The prism and light reflex was used when eccentric fixation was present. Where mea sured, the same vertical incomitance was present for distance but slightly less in amount. Most cases showed either a marked monocular fixation pattern secondary to amblyopia with or without organic disease or presented with the near and distance devia tion fairly close. The amount of displace ment ranged from 4.0 mm to 8.0 mm. The technique of reattachment was con sistent with the recommendations of Dunlap6 who advised maintaining the original relationship of the muscle to the limbus. In resections, the muscle was vertically dis placed and inserted at a distance from the limbus equal to the original insertion-limbus distance. On recessions, the muscle was ver tically displaced and inserted at a distance from the limbus equal to the sum of the recession plus the original insertion-limbus distance. The direction of displacement was