Prediction of identification difficulty of sloan letters based on spatial frequency content

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Abstract

Purpose. Standardization of visual acuity optotypes is crucial to the accurate measurement of visual acuity. The currently used charts have been developed based on subjective measures and clinical calibration. Sloan (AJO 1959) observed that there is a difference in rate of identification of each letter at threshold visual acuity. We propose a set of quantitative measures to predict the identification difficulty of visual acuity optotypes based on their spatial frequency content that we expect to aid in the development of future optotypes to test for specific deficiencies. Methods. The magnitude of the two-dimensional Fourier transform of the Sloan letters (in order of ease of recognition) ZNHRVKDCOS was calculated. Each spectrum was integrated over 45 degree wedges oriented at 90, 45, 0 and -45 degrees between the spatial frequencies of 1.5 and 30 cycles/degree. The following quantitative measures were chosen: the ratio of the integrated volume under the Fourier transform in the 90 and 0 degree wedges (horizontal vs. vertical information); the ratio of the 45 to the -45 degree wedges (symmetry in the diagonal directions); the ratio of the sum of the 90 and 0 degree wedges to the sum of the 45 and -45 degree (vertical and horizontal vs. oblique information); and the circular symmetry of the transform (curves in the object). Results. Multiple linear regression on these 4 parameters yielded a prediction for the reported difficulty of identification with r2 = 0.91 and p = 0.008 and ease of detection order of ZNHVRDKSCO. Conclusions. Analysis of the spatial frequency content of optotypes is useful in predicting their detectability at visual acuity threshold.

Original languageEnglish (US)
JournalInvestigative Ophthalmology and Visual Science
Volume37
Issue number3
StatePublished - Feb 15 1996

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Visual Acuity
Fourier Analysis
Spatial Analysis
Calibration
Linear Models

ASJC Scopus subject areas

  • Ophthalmology

Cite this

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title = "Prediction of identification difficulty of sloan letters based on spatial frequency content",
abstract = "Purpose. Standardization of visual acuity optotypes is crucial to the accurate measurement of visual acuity. The currently used charts have been developed based on subjective measures and clinical calibration. Sloan (AJO 1959) observed that there is a difference in rate of identification of each letter at threshold visual acuity. We propose a set of quantitative measures to predict the identification difficulty of visual acuity optotypes based on their spatial frequency content that we expect to aid in the development of future optotypes to test for specific deficiencies. Methods. The magnitude of the two-dimensional Fourier transform of the Sloan letters (in order of ease of recognition) ZNHRVKDCOS was calculated. Each spectrum was integrated over 45 degree wedges oriented at 90, 45, 0 and -45 degrees between the spatial frequencies of 1.5 and 30 cycles/degree. The following quantitative measures were chosen: the ratio of the integrated volume under the Fourier transform in the 90 and 0 degree wedges (horizontal vs. vertical information); the ratio of the 45 to the -45 degree wedges (symmetry in the diagonal directions); the ratio of the sum of the 90 and 0 degree wedges to the sum of the 45 and -45 degree (vertical and horizontal vs. oblique information); and the circular symmetry of the transform (curves in the object). Results. Multiple linear regression on these 4 parameters yielded a prediction for the reported difficulty of identification with r2 = 0.91 and p = 0.008 and ease of detection order of ZNHVRDKSCO. Conclusions. Analysis of the spatial frequency content of optotypes is useful in predicting their detectability at visual acuity threshold.",
author = "Hall, {H. L.} and Miller, {Joseph M} and Greivenkamp, {John E} and Schwiegerling, {James T}",
year = "1996",
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N2 - Purpose. Standardization of visual acuity optotypes is crucial to the accurate measurement of visual acuity. The currently used charts have been developed based on subjective measures and clinical calibration. Sloan (AJO 1959) observed that there is a difference in rate of identification of each letter at threshold visual acuity. We propose a set of quantitative measures to predict the identification difficulty of visual acuity optotypes based on their spatial frequency content that we expect to aid in the development of future optotypes to test for specific deficiencies. Methods. The magnitude of the two-dimensional Fourier transform of the Sloan letters (in order of ease of recognition) ZNHRVKDCOS was calculated. Each spectrum was integrated over 45 degree wedges oriented at 90, 45, 0 and -45 degrees between the spatial frequencies of 1.5 and 30 cycles/degree. The following quantitative measures were chosen: the ratio of the integrated volume under the Fourier transform in the 90 and 0 degree wedges (horizontal vs. vertical information); the ratio of the 45 to the -45 degree wedges (symmetry in the diagonal directions); the ratio of the sum of the 90 and 0 degree wedges to the sum of the 45 and -45 degree (vertical and horizontal vs. oblique information); and the circular symmetry of the transform (curves in the object). Results. Multiple linear regression on these 4 parameters yielded a prediction for the reported difficulty of identification with r2 = 0.91 and p = 0.008 and ease of detection order of ZNHVRDKSCO. Conclusions. Analysis of the spatial frequency content of optotypes is useful in predicting their detectability at visual acuity threshold.

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