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Human visual CSF

A simple and widely used psychophysical test is the measurement of the contrast threshold of sine-wave gratings that is just detectable against a uniform background.  A grating can be described by the formula

L(x) = L0[1 + m cos(2p sf x) cos(2p tf t)],

where L0 is the mean luminance, m the contrast, sf the spatial frequency, and tf the temporal frequency of the grating.   When the reciprocal of the contrast threshold value is expressed as a function of spatial frequency, the resulting function is referred to as the CSF. Under normal viewing conditions (i.e., photopic illumination level and slow temporal variations), the CSF has a band-pass shape, displaying attenuation at both low and high spatial frequencies. To some extent, the CSF is similar to the MTF in optics, characterizing a system's response to different spatial frequencies. The behavior of the CSF is, however, much more complicated; it varies with the mean luminance, the temporal frequency, and the field size of the grating pattern.                   
       Why does CSF behaves differently in different conditions? One popular explanation of the CSF shape relies on retinal lateral inhibition. In this theory, the visual responses are determined by retinal ganglion cells, which take light inputs from limited retinal areas. These areas are called receptive fields. They are circular in shape and each of them contains two distinct function zones: the center and surround. The inputs to the two zones tend to cancel each other, the so-called center-surround antagonism. Such spatial antagonism attenuates uniform signals, as well as low frequency signals. This might explain why the system as a whole is insensitive to low frequencies, but it is difficult to offer a coherent description of all CSF behaviors based on this theory.

Explanation based on Implicit Masking:
In the effort to model the CSF, Yang and Makous suggested that the DC component, that is, a component at 0 cycle per degree (cpd) and 0 Hz, in any visual stimulus has all the masking properties of any other Fourier component. The associated effect of the DC component in visual detection was called implicit masking. The basic assumption here is that the energy of the DC component can spread to its neighboring frequencies, because of spatial inhomogeneities of the visual system. When a target is superimposed on a background field of similar features, the required stimulus strength for detection, i.e., threshold strength, is generally increased. This is a nonlinear interaction. It follows that the DC component can reduce the visibility of the targets at low spatial frequencies as a consequence of the energy overlap, given such nonlinear interactions. This concept simplifies the explanation of CSF behavior considerably, as discussed in the following.
      First, let us explore the roll-off of the CSF at the low spatial frequencies. Each of the frequency components spreads to a limited extent. The interaction between the target and the DC components should disappear when the spatial frequency of the stimulus is high enough. In this case, there is no effect of implicit masking. Therefore, the drop of contrast sensitivity because of implicit masking is restricted to low spatial frequencies.
     Second, this assumption offers an explanation of the effect of luminance on the contrast sensitivity at low spatial frequencies: as mean luminance decreases, the component at zero frequency decreases too. When this happens, other factors such as noise can dominate, and thus the relative attenuation at low frequencies decreases.
     Third, this assumption also offers an explanation of the dependence of the attenuation on temporal frequency. The DC component of a grating is at zero temporal frequency and zero spatial frequency in a 2-D spatiotemporal frequency domain, so the effects of implicit masking apply only to very low temporal and spatial frequencies. Test gratings that are modulated at high temporal frequencies would be exempt from the effect of implicit masking, no matter what the spatial frequency of the grating is.
      Finally, the effect of field size on contrast sensitivity can be explained by the breadth of implicit masking. The extent of implicit masking is determined by the spread of the DC energy in the frequency domain. The larger the viewing field, the less the spread. This explains why the peak sensitivity shifts to lower spatial frequency as field size increases, owing to the decreasing breadth of implicit masking. The exact amount of spread depends also on retinal inhomogeneities.

Calculating CSF values
       The descriptive model based on implicit masking has several model parameters, the value of which can be optimized based on particular experimental data sets.  One problem here is that the published data in one experiment can deviate significantly from those in other experiments due to some not well-know causes, which can be experimental settings, test procedures, and individual differences etc.
       In the calculation, you have the options to choose which data set to use as the baseline. The data sets include:
  • Kelly (1972) data,
  • Van Nes and Bouman (1967) data, and
  • a combination of   multiple data sets.

Go to the calculation page