Calculation of RMS Radiuses of the Point Spread Function Using Zernike Fringe Coefficients
摘要
RMS-radiuses, calculated from the illumination distribution in the aberration image of a point, serve as parameters that characterizes the quality of the image formed by the optical system. To improve image quality, aberration images of points with minimum RMS-radiuses are sought. Computer programmers for optical system analysis recover the polar RMS—radius to images of the axial and peripheral points of the objects space. These programmers use spot diagrams to calculate RMS—radiuses, which cannot accurately represent the illumination distribution in aberration point images. When the image quality approaches diffraction-limited, the use of spot diagrams becomes incorrect. In this paper, we propose to use the wave aberration function approximated using Zernike polynomials rather than transverse ray aberrations to calculate the RMS radii of the aberration spot. In this paper, we propose to use the wave aberration function approximated using Zernike polynomials rather than transverse ray aberrations to calculate the RMS radii of the aberration spot. These new coefficients allow the calculation of all kinds of RMS-radiuses—polar, axial, centrifugal. Formulas for calculating the polar, axial, and centrifugal RMS-radii, including coefficients of the classical approximation of the wave aberration function by Zernike polynomials, are obtained. The correctness of the obtained formulas is confirmed by the results of direct integration of RMS-radii on the given wave aberration function. The practical value of such a method of RMS-radiuses calculations is demonstrated on the example of estimation of ametropia and astigmatism of the eye, when these parameters were reconstructed by two different methods. The first traditional method used values of only the amplitudes of aberration terms of defocus and primary astigmatism. In the second proposed method, the RMS radiuses values of polar, axial and centrifugal moments were used. T is revealed that the values of ametropia and astigmatism parameters reconstructed by these methods turned out to be somewhat different, because unlike the first method, the second method takes into account the influence of aberration terms of higher degree orders.