Using 10AFC to further improve the efficiency of the quick CSF method

Abstract

The contrast sensitivity function (CSF) provides a fundamental characterization of spatial vision, important for basic and clinical applications, but its long testing times have prevented easy, widespread assessment. The original quick CSF method was developed using a two-alternative forced choice (2AFC) grating orientation identification task (Lesmes, Lu, Baek, & Albright, 2010), and obtained precise CSF assessments while reducing the testing burden to only 50 trials. In this study, we attempt to further improve the efficiency of the quick CSF method by exploiting the properties of psychometric functions in multiple-alternative forced choice (m-AFC) tasks. A simulation study evaluated the effect of the number of alternatives m on the efficiency of the sensitivity measurement by the quick CSF method, and a psychophysical study validated the quick CS method in a 10AFC task. We found that increasing the number of alternatives of the forced-choice task greatly improved the efficiency of CSF assessment in both simulation and psychophysical studies. The quick CSF method based on a 10-letter identification task can assess the CSF with an averaged standard deviation of 0.10 decimal log unit in less than 2 minutes.

Figure 1

Comparison between the quick CSF and convention methods. Conventional methods measure contrast sensitivity a few pre-defined spatial frequencies (a), select stimuli in contrast space (b) at each spatial frequency, and distribute trials evenly over spatial frequencies (c). In contradistinction, the quick CSF method adopts a four-parameter log parabolic functional form (d), selects stimuli in both contrast and frequency spaces (e), and allocates trials more efficiently over two-dimensional space (f). To achieve the same precision, the quick CSF method requires many fewer trials.

Figure 2

The probability correct psychometric functions for 2, 4, 8, 10, and 16 AFC tasks (b) with the same underlying d′ psychometric function (a). Different colors indicated different numbers of alternatives.

Figure 3

(a) Standard deviation of the CSFs obtained by the quick CSF method with m-AFC tasks as functions of trial number. (b) HWCI of the CSF obtained by the quick CSF method with m-AFC tasks as functions of trial number. (c) The ratios between HWCI and standard deviation for all m-AFC tasks as functions of trial number. (d) Bias of the CSFs obtained by the quick CSF method as functions of trial number. Different m-AFC tasks are represented by different colors.

Figure 4

The relative efficiencies of the quick CSF procedures with 4, 8, 10, and 16 AFC tasks as functions of trial number.

Figure 5

(a) Standard deviation, (b) half width of 68.2% credible interval, and (c) bias of the CSF measured by the 10AFC quick CSF procedure as functions of trial number. Red curves represent the result of an observer with a 0.04 lapse rate; green, blue, and cyan curves represent the results of an observer with 100% lapse in the first 1, 3, and 5 trials, respectively.

Figure 6

(a) Ten filtered letters. (b) Illustration of filtered letter “C” in different spatial frequency conditions.

Figure 7

CSFs obtained from different quick CSF runs are plotted along with that measured by the conventional method for all observers. HWCI of 68.2% is indicated by shaded region for the CSF measured in the third quick CSF run, and by error bars for the CSF measured by the conventional method.

Figure 8

CSFs measured by the quick CSF procedure with 10, 20, and 50 trials were compared against those measured by the conventional method. Pearson correlation coefficients and linear regression fits are shown.

Figure 9

(a) Standard deviation, (b) HWCI, and (c) bias of the CS from the quick CSF procedure with 10AFC and 2IFC tasks as functions of trial number. Blue and red curves represent the results from the 10AFC and 2IFC quick CSF procedures, respectively. Shaded regions represent ±1 SD.

Figure 10

Standard deviation, HWCI, and bias as function of trial number for the overall, low, medium, and high frequency AULCSF. Different colors represent results from different m-AFC quick CSF procedures.

Figure 11

The standard deviation and HWCI the CSF from a 2AFC quick CSF procedure (red) and a 4AFC procedure (green). The slope of the d′ psychometric function is ζ = 2.35 in the 2AFC procedure and 1.1 in the 4AFC procedure.

Figure A1

An illustration of the marginal distributions of the four parameters before (prior: red) and after (posterior: blue) measurement. The plot is based on the simulation of a single quick CSF run with 100 trials.