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Albert J. Ahumada, Nancy J. Coletta; Neural transfer functions from interferometric measurements. Journal of Vision 2009;9(14):50. doi: https://doi.org/10.1167/9.14.50.
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Simplified models for the prediction of visual discriminations use a Contrast Sensitivity Function (CSF) to represent an observer's sensitivity as a function of spatial frequency (Watson and Ahumada, 2005). For these models to predict visual discrimination as a function of optical variables such as aberrations, the optical component of the CSF must be removed to obtain a Neural Transfer Function (NTF). Watson and Ahumada (2008) divided the CSF of their standard observer by an estimate of the optical transfer function of a typical observer to estimate an NTF. However, dividing the typical CSF by a typical OTF might not result in a typical NTF.
Contrast sensitivity can be measured with interference fringes that remove the effect of the OTF, thus providing a more direct measurement of the NTF. We analyzed the interferometric CSFs measured by Coletta and Sharma (JOSA A, 1995) for two observers at four light levels. They added varying proportions of incoherent light to the background and found that as the proportion p of coherent light decreased, the contrast sensitivity increased, due to the loss of masking by laser speckle.
We used an additive model to estimate from their data both the CSF in the absence of noise speckle (the NTF) and the spectrum of the noise. The model assumes that there are two sources of noise that mask the signal grating: the speckle noise S(f), a function of spatial frequency f, and the observer's internal noise referred to the signal domain (Ahumada & Watson, 1985), N(f,I) a function of frequency f and retinal illumination I. The contrast threshold T is assumed to depend on the sum of these,
T2 = k (p2 S(f) + N(f,I)).
The NTFs estimated by the model are essentially the average over p of the Coletta and Sharma CSFs for I=0.3 photopic trolands and the CSF for p=0.1 for I=3, 30, and 300 photopic trolands. The estimated speckle spectrum falls as spatial frequency increases as expected at low frequencies, but it rises again at high frequencies suggesting the intrusion of aliasing noise. Parametric estimates of these functions show the expected effects of illumination on the NTF. These functions should help predict the effects of optical variables on visual acuity and other measures of visual performance.
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