Some Observations and Theory on the Variation of Visual Acuity with the Orientation of the Test Object*

Herschel Leibowitz

doi:10.1364/JOSA.43.000902

Journal of the Optical Society of America
Vol. 43,
Issue 10,
pp. 902-905
(1953)
•https://doi.org/10.1364/JOSA.43.000902

Some Observations and Theory on the Variation of Visual Acuity with the Orientation of the Test Object

Herschel Leibowitz

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Herschel Leibowitz, "Some Observations and Theory on the Variation of Visual Acuity with the Orientation of the Test Object*," J. Opt. Soc. Am. 43, 902-905 (1953)

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Abstract

The superiority of visual acuity obtained with a grating test object oriented vertically or horizontally over values obtained with oblique orientations is demonstrated for various combinations of pupil diameter and retinal illuminance level. This superiority, which has an average value of 7 percent of the mean threshold angle of resolution for all meridians, increases with pupil diameter but is not affected systematically by illuminance level.

The data are discussed with reference to the assumptions that meridional differences in acuity are a result of dioptric or of retinal factors. The systematic effect of pupil diameter points to the dioptric origin of some of the observed meridional differences. The influence of retinal or post-retinal factors as well is suggested by the persistence of the effect at a high illuminance level and with large pupil diameters, a condition where a slight decrease in retinal image contrast is shown not to lower acuity.

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Threshold angle of resolution (seconds of arc)
Subject	Reference Luminance (ml)	Orientation	Pupil diameter (mm)
Subject	Reference Luminance (ml)	Orientation	1.0	1.4	1.6	2.0	2.77	3.86	4.75
L	100	H	65.6	43.4	38.2	33.6	29.8	27.1	27.7
		V	61.6	45.1	39.0	33.1	29.2	29.0	29.6
		R	64.1	47.0	40.7	34.5	32.4	31.9	32.4
		L	65.6	45.5	40.9	34.2	31.9	33.1	31.6
	10	H	66.5	46.8	41.4	34.6	29.8	29.2	31.5
		V	66.2	51.5	42.7	34.7	30.9	30.7	31.7
		R	67.5	48.5	43.9	37.3	33.5	34.5	36.1
		L	66.5	51.1	43.6	37.1	33.4	33.4	34.9
	1.0	H	74.2	54.7	45.1	39.3	38.0	39.1	42.4
		V	71.8	55.2	49.7	41.2	39.1	39.1	41.2
		R	77.6	58.1	50.3	43.4	40.9	41.6	43.8
		L	71.6	57.1	49.4	40.7	40.9	40.7	44.6
	0.1	H	81.3	59.1	54.0	49.7	51.0	51.0	55.7
		V	79.8	61.4	56.1	49.2	50.9	53.9	57.4
		R	93.6	61.9	65.7	57.9	52.8	57.8	59.2
		L	79.6	65.8	57.8	52.2	50.6	53.9	58.4
	0.01	H	113.8	99.8	91.0	92.1	83.8	88.7	101.4
		V	108.2	98.0	83.8	82.4	87.1	92.3	96.0
		R	119.7	108.7	94.7	99.8	92.3	104.0	109.4
		L	111.2	101.0	85.9	95.3	85.9	92.1	97.3
S	100	H	65.6	45.0	39.0	35.5	30.7	28.7	⋯
		V	63.0	45.5	40.2	34.0	29.7	27.7	⋯
		R	65.0	46.5	42.1	37.4	34.5	30.5	⋯
		L	67.9	45.3	41.0	36.8	33.8	33.3	⋯
	10	H	66.2	45.6	40.5	33.9	29.9	29.0	29.8
		V	63.2	46.4	41.9	34.1	30.6	29.4	31.4
		R	63.8	48.6	42.8	37.6	35.3	34.7	36.5
		L	66.2	47.5	43.7	36.4	33.7	33.1	34.4
	0.1	H	83.4	60.5	55.6	49.2	49.0	51.3	52.6
		V	78.4	63.7	57.9	53.3	48.9	53.5	49.0
		R	84.8	68.3	62.5	58.6	56.1	61.4	62.8
		L	83.4	64.6	62.2	57.3	55.1	58.0	60.6

Threshold angle of resolution(seconds of arc)
		Pupil diameter (mm)
Subject	Grating	1.0	1.4	1.6	2.0	2.77	3.86	4.75
L	$\frac{1}{2}$	65.2	47.6	41.4	34.3	31.5	30.4	30.5
	$\frac{1}{4}$	67.1	49.3	43.5	35.7	32.1	30.7	30.3
	$\frac{1}{8}$	69.3	51.5	44.8	37.5	33.1	32.4	33.1
S	$\frac{1}{2}$	⋯	45.7	39.4	33.2	29.9	29.0	⋯
	$\frac{1}{4}$	⋯	46.8	40.5	33.7	30.4	28.8	⋯
	$\frac{1}{8}$	⋯	50.0	42.7	35.7	32.8	32.0	⋯

Orientation of grating test object	Threshold angle of resolution (seconds of arc)	Standard deviation (seconds of arc)
Degrees from vertical Counterclockwise
90 (H)	30.1	1.1
67.5	31.8	1.0
45 (L)	35.4	0.7
22.5	34.4	0.9
0 (V)	32.4	0.5
Vertical-clockwise
22.5	33.3	0.8
45.0 (R)	34.2	0.9
67.5	32.8	1.3
90 (H)	30.1	1.1

Threshold angle of resolution (seconds of arc)
Subject	Reference Luminance (ml)	Orientation	Pupil diameter (mm)
Subject	Reference Luminance (ml)	Orientation	1.0	1.4	1.6	2.0	2.77	3.86	4.75
L	100	H	65.6	43.4	38.2	33.6	29.8	27.1	27.7
		V	61.6	45.1	39.0	33.1	29.2	29.0	29.6
		R	64.1	47.0	40.7	34.5	32.4	31.9	32.4
		L	65.6	45.5	40.9	34.2	31.9	33.1	31.6
	10	H	66.5	46.8	41.4	34.6	29.8	29.2	31.5
		V	66.2	51.5	42.7	34.7	30.9	30.7	31.7
		R	67.5	48.5	43.9	37.3	33.5	34.5	36.1
		L	66.5	51.1	43.6	37.1	33.4	33.4	34.9
	1.0	H	74.2	54.7	45.1	39.3	38.0	39.1	42.4
		V	71.8	55.2	49.7	41.2	39.1	39.1	41.2
		R	77.6	58.1	50.3	43.4	40.9	41.6	43.8
		L	71.6	57.1	49.4	40.7	40.9	40.7	44.6
	0.1	H	81.3	59.1	54.0	49.7	51.0	51.0	55.7
		V	79.8	61.4	56.1	49.2	50.9	53.9	57.4
		R	93.6	61.9	65.7	57.9	52.8	57.8	59.2
		L	79.6	65.8	57.8	52.2	50.6	53.9	58.4
	0.01	H	113.8	99.8	91.0	92.1	83.8	88.7	101.4
		V	108.2	98.0	83.8	82.4	87.1	92.3	96.0
		R	119.7	108.7	94.7	99.8	92.3	104.0	109.4
		L	111.2	101.0	85.9	95.3	85.9	92.1	97.3
S	100	H	65.6	45.0	39.0	35.5	30.7	28.7	⋯
		V	63.0	45.5	40.2	34.0	29.7	27.7	⋯
		R	65.0	46.5	42.1	37.4	34.5	30.5	⋯
		L	67.9	45.3	41.0	36.8	33.8	33.3	⋯
	10	H	66.2	45.6	40.5	33.9	29.9	29.0	29.8
		V	63.2	46.4	41.9	34.1	30.6	29.4	31.4
		R	63.8	48.6	42.8	37.6	35.3	34.7	36.5
		L	66.2	47.5	43.7	36.4	33.7	33.1	34.4
	0.1	H	83.4	60.5	55.6	49.2	49.0	51.3	52.6
		V	78.4	63.7	57.9	53.3	48.9	53.5	49.0
		R	84.8	68.3	62.5	58.6	56.1	61.4	62.8
		L	83.4	64.6	62.2	57.3	55.1	58.0	60.6

Threshold angle of resolution(seconds of arc)
		Pupil diameter (mm)
Subject	Grating	1.0	1.4	1.6	2.0	2.77	3.86	4.75
L	$\frac{1}{2}$	65.2	47.6	41.4	34.3	31.5	30.4	30.5
	$\frac{1}{4}$	67.1	49.3	43.5	35.7	32.1	30.7	30.3
	$\frac{1}{8}$	69.3	51.5	44.8	37.5	33.1	32.4	33.1
S	$\frac{1}{2}$	⋯	45.7	39.4	33.2	29.9	29.0	⋯
	$\frac{1}{4}$	⋯	46.8	40.5	33.7	30.4	28.8	⋯
	$\frac{1}{8}$	⋯	50.0	42.7	35.7	32.8	32.0	⋯

Abstract

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Tables (3)

Journal of the Optical Society of America