Mathematical properties of the encircled and ensquared energy functions for the diffraction-limited point-spread function (PSF) are presented. These include power series and a set of linear differential equations that facilitate the accurate calculation of these functions. Asymptotic expressions are derived that provide very accurate estimates for the relative amount of energy in the diffraction PSF that fall outside a square or rectangular large detector. Tables with accurate values of the encircled and ensquared energy functions are also presented.
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| http://dx.doi.org/10.1364/AO.54.007525 | DOI Listing |
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Mathematical properties of the encircled and ensquared energy functions for the diffraction-limited point-spread function (PSF) are presented. These include power series and a set of linear differential equations that facilitate the accurate calculation of these functions. Asymptotic expressions are derived that provide very accurate estimates for the relative amount of energy in the diffraction PSF that fall outside a square or rectangular large detector.
View Article and Find Full Text PDFPower contained in a square area of an image formed by a diffraction-limited imaging system with a centrally obscured circular pupil is calculated and compared with the power contained in a circular area. It is shown that, regardless of the amount of obscuration, the difference between the corresponding ensquared and encircled powers is less than 9% of the total image power. Approximate expressions are obtained for the power lying outside a large square or a circular area.
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