Determination of the signal for a shift of the point spread function in the form of a Gaussian rotation inscribed in four pixels of a matrix photodetector and comparison with the signal for a cylindrical point spread function

Subject of the study. Change in the signal level of a matrix pixel with a shift in the point spread function in the form of a Gaussoid of rotation relative to the junction point of four pixels of the photosensitive matrix. Purpose of the work. Determination of the dependence of the signal value on the shift of the point spread function inscribed in four pixels of the photosensitive matrix for the irradiance distribution in the form of a Gaussian and comparison with the signal for a cylindrical point spread function. 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 signal calculations are made. The shift of the point spread function by Δx along the X axis and by Δy along the Y axis is taken in a form normalized to the spot radius. The spectral sensitivity of a pixel is constant within the pixel area and for different pixels. To plot a graph of the pixel signal dependence on the shift of the point spread function, the shift axis η is introduced. Main results. An algorithm has been developed for calculating the change in the signal level of a matrix pixel when the point spread function in the form of a Gaussian is shifted relative to the junction of four pixels of the photosensitive matrix. The dependence of the normalized signal of a matrix pixel on the relative shift of the point spread function η at an angle of 45° and 0° (90°) for the above-mentioned case of irradiance has been constructed. The dependence of the total normalized signal for a Gaussian is plotted when the PSF is shifted at an angle of 45°: a) when binning pixels, b) when the sum of five pixels is in the form of a cross. A comparative assessment of signals for two types of point spread function is carried out: a Gaussian of rotation and a cylinder. Practical significance. When the point spread function shifts relative to the junction of four matrix pixels, the signal taken from these pixels drops, which, given a low signal-to-noise ratio, can lead to a breakdown in tracking or an increase in the measurement error of the angular coordinates of space objects. In the energy calculation of optical-electronic systems, a signal drop due to a shift in the point spread function by η will allow us to determine the minimum signal and, consequently, the minimum signal-to-noise ratio. An analytical expression for signals from pixels will be useful in modeling the reception of a signal and noise mixture.