Calculation of the higher-order axial spherical aberrations of a high-aperture focusing holographic optical element with the corrected third-order spherical aberration. Part 1

Results of calculating the radius of higher-order spherical aberrations (fifth, seventh and ninth orders) of a high-aperture focusing holographic optical element (HOE) with corrected third-order spherical aberration in the operating spectral range are discussed. As examples, high-aperture axial HOEs with relative apertures close to 1:1 in specified spectral ranges are considered. Coordinates of the point sources of a divergent deference wave and a convergent object wave of the HOE are given. It is shown that when imaging a point source emitting in the 0.250-0.281-$\mu$m and 0.500-0.563-$\mu$m spectral ranges, the use of an HOE in the first and second diffraction orders makes it is possible to correct the third-order spherical aberration on two wavelengths and the fifth- and seventh-order spherical aberrations on one wavelength. Note that these visible-spectrum wavelengths are different from the HOE's recording wavelength of 0.532$\mu$m.