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The modulation of a sinusoidal luminance pattern is defined by the amplitude of the sinusoidal variation divided by the average luminance. See Fig. 2.1. According to the generally used definition, the contrast sensitivity is the reciprocal of the threshold value of the modulation for the detection of the variation. Therefore, the modulation threshold plays an important role in the contrast sensitivity. In this chapter the concept of the modulation threshold will be treated as will the effects of noise on this threshold. In practice, it appears that there is not a fixed threshold below which a luminance variation is not observed and above which the luminance variation is always observed, but, instead, there is a gradual increasing probability for observing the variation. To avoid confusion, it is therefore necessary to define which modulation level is considered as threshold. A detection probability of 50% is generally used as threshold and the modulation with this detection probability is, therefore, defined as the modulation threshold. The function that describes the detection probability as a function of the signal strength is called psychometric function. This function is very useful to determine the modulation threshold in a well-defined way. The first part of this chapter will, therefore, be devoted to this function. The psychometric function also gives a good understanding of the underlying detection mechanism. The statistical factors that influence the shape of the psychometric function may be considered to be caused by noise. This noise partly consists of noise generated in the visual system, which is called internal noise, but can also partly consist of noise that is already present in the observed image, which is called external noise. The basic properties of the noise will be treated in this chapter and equations will be given for the calculation of the modulation threshold from the data of the noise. The given equations will further be used in the following chapters for the calculation of the contrast sensitivity.
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