Calculation of higher-order axial spherical aberrations of a high-aperture focusing holographic optical element with the corrected third-order spherical aberration. Part 2

The paper presents and discusses the results of calculations of the radii of transverse fifth-, seventh- and ninth-order spherical aberrations in a multi-order on-axis HOE (holographic optical element), recorded using two divergent spherical waves. As examples, focusing transmission and reflection on-axis HOEs with relative apertures close to 1:1 in given infrared spectral ranges are considered. Analytical expressions are presented for calculating the minimum distance from the HOE to a polychromatic point source and to its image. We study in which way these distances change with increasing operating wavelength in the spectral range of interest. Examples of two different transmission HOEs with identical chromatic aberrations are presented in the atmospheric infrared windows in the ranges of 2.15 – 2.50 $\mu m$ and 4.3 – 5.0 $\mu m$. It is pointed out that on the basis of these two HOEs, a dual-band holographic lens with working spectral ranges of 2.15 – 2.50 $\mu m$ and 4.3 – 5.0 $\mu m$ can be developed.