Dependence of the signal magnitude on the displacement of the scattering function of a point inscribed in four pixels of the matrix

An algorithm has been developed for calculating changes in the signal level of a matrix pixel when the point scattering function is shifted at an angle of 45º relative to the joining point of 4 matrix pixels. In the initial state of the point spread function, the point is inscribed in four pixels. The spectral sensitivity of a pixel is constant within the pixel area. The distribution of pixel irradiance in the point spread function in the form of uniform irradiance is considered. Method. The calculation is based on the method of dividing the point spread function on each pixel of the matrix into separate areas for which the signal is calculated. The displacement of the point scattering function by Δx along the X axis and by Δy along the Y axis is taken in a form normalized to the radius of the spot. To create a two-dimensional graph of the dependence of the pixel signal on the displacement of the point scattering function along the X, Y axes, we introduce the relative displacement of the point scattering function η. Main results. An algorithm has been developed for calculating changes in the signal level of a matrix pixel when the point scattering function is shifted relative to the matrix pixels for the case of pixel irradiation in the lens scattering circle in the form of uniform irradiance. The dependence of the normalized matrix pixel signal on the relative displacement of the point scattering function η at an angle of 45º has been plotted for the above case of irradiation. Practical significance. Matrix photodetectors are widely used in guidance and tracking systems for space objects and astronomical sensors. For a defocused optical system, uniform distribution is used. When the point scattering function shifts relative to the joining point of the four pixels of the matrix, the matrix signal drops, which, with a low signal-to-noise ratio, can lead to a breakdown in tracking or an increase in the error in measuring the angular coordinates of a space object. The results of these studies can be used to model a target guidance system and determine target coordinates.