Evaluating the goodness of various equations to model the contrast sensitivity function of the human eye

Abstract

Purpose : To evaluate the accuracy of different fitting functions for measured contrast sensitivity assessed with the psychophysical method PSI (Ψ).

Methods : Contrast sensitivity was assessed in 7 cyclopleged, full-corrected participants using an adaptive staircase procedure called PSI (Ψ) method. Sinusoidal grayscale patterns (Gabor patches) were generated for different spatial frequencies SF (from 0.5 to 60 cycle/deg (cdp) in 14 log steps) and the smallest visible contrast (contrast threshold CT) was found within 50 trials for each SF from 0.5 to 60 cpd in a measuring distance of 5 m under monocular viewing conditions, while the fellow eye was patched. A 5^th order polynom (Eq. 1), a double exponential (Eq. 2) and a square rooted double exponential function (Eq. 3) with each three degrees of freedom were fitted to the obtained contrast sensitivity (CS) data (CS = 1/CT). Accuracy of the different fit functions was compared by calculation of the root mean square error (RMSE) between the fitted values for each function and the original data set.

Results : In untrained participants, the measurement of 14 SF took around 15 minutes. The 95% confidence interval for repeated measurements (n = 3) at a spatial frequency of 1 cpd was 0.122 logCS and increase to 0.680 logCS for an SF of 7 cpd. The contrast sensitivity, when fitted with a polynomial function had a mean RMSE of 32.25 ± 33.93. Significant lower RMSE of 11.64 ± 12.11 (F(2,18) = 16.5, p < 0.01, ANOVA) and 12.21 ± 13.30 (F(2,18) = 16.5, p < 0.01, ANOVA) were found for the fits of Eq. 2 and Eq. 3, respectively. Post hoc analysis with SF as the group variable gave significant difference between the two double exponential functions for SF of 13 and 15 cpd, while lower errors were found for the double exponential function (Eq. 2).

Conclusions : Adaptive staircase procedures like the PSI method can provide a fast and repeatable estimation of individual contrast sensitivity measures. To minimize internal noise of individual measurements, the three-parameter double exponential function showed lowest errors for all spatial frequencies. Individual assessed CSF can lead to better predictions of image quality.

This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.

 

Equation 1 to 3 to model the contrast sensitivity function. CS = Contrast Sensitivity, SF = Spatial Frequency and parameter a to f represents degrees of freedom for each equation.