DOI: 10.17586/1023-5086-2023-90-12-96-110

УДК: 535.231.16

# Dependence of the signal magnitude on displacement of the point spread function relative to the center of the photosensitive matrix pixel

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Publication in Journal of Optical Technology

Знаменский И.В. Зависимость величины сигнала от смещения функции рассеяния точки относительно центра пиксела фоточувствительной матрицы // Оптический журнал. 2023. Т. 90. № 12. С. 96–110. http://doi.org/10.17586/1023-5086-202390-12-96-110

Znamenskiy I.V. Dependence of the signal magnitude on displacement of the point spread function relative to the center of the photosensitive matrix pixel [In Russian] // Opticheskii Zhurnal. 2023. V. 90. № 12. P. 96–110. http://doi.org/10.17586/1023-5086-2023-90-12-96-110

**The subject of study** is the change in the signal value of a matrix pixel, when the point spread function is shifted relative to the center of the matrix pixel. **The aim of the work** is to determine the dependence of the signal magnitude on the displacement of the point spread function relative to the center of the photosensitive matrix pixel for three cases of irradiance distribution: a function describing the distribution in the Airy circle, a Gaussoid of rotation and a uniform distribution. **Method.** The calculation is based on the method of dividing the scattering function of a point on the matrix pixel into separate areas, for which the signal is calculated. The displacement of the point scattering function by D*x* along the *X* axis and by D*y* 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 spread function along the *X*, *Y* axes, the displacement axis of the point spread function is introduced. The signal at the pixel input is presented in relative units and normalized to the maximum signal generated in the absence of the shift in the point spread function. The spectral sensitivity of the pixel is constant within the pixel area. **Main results. **An algorithm for calculating the changes in the signal level of the matrix pixel, when the point scattering function shifts relative to the matrix pixel, has been developed. The dependence of the normalized matrix pixel signal on the relative displacement of the point spread function at an angle of 45° has been plotted for the above cases of irradiation. When the point spread function is shifted at an angle of 45° by an amount of 1.41*R* relative to the pixel, the signal changes by 4 times for all 3 cases, and when the point spread function is shifted along one of the axes by an amount *R*, the signal changes by 2 times for the Gaussian and cylindrical function. **Practical significance.** When the point scattering function shifts relative to the center of the matrix pixel, the irradiance of the matrix decreases, 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 space objects. In energy calculations of optoelectronic systems the signal drop due to the shift of the point spread function by half a pixel allows to determine the minimum signal and, therefore, the minimum signal-tonoise ratio.

diffraction, matrix, pixel, Bessel function, Gaussian function, Airy disk, point spread function

Acknowledgements:the author thanks Tungushpaev A.T., Dr. Sci. (Engineering) for careful editing, during which he made a number of comments that were taken into account when compiling the final text. The author thanks the reviewers and the editorial board of the journal for their valuable comments, which made it possible to significantly improve the article.

OCIS codes: 260.1960, 260.2160.

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