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Hybrid ray-tracing/Fourier optics method to analyze multilayer diffractive optical elements.

The performance (paraxial phase delay) of conventional diffractive optical elements is generally analyzed using the analytical scalar theory of diffraction, based on thin-element approximation (TEA). However, the high thickness of multilayer diffractive optical elements (MLDOEs) means that TEA yields inaccurate results. To address this, we tested a method based on ray-tracing simulations in mid-wave and long-wave infrared wave bands and for multiple f-numbers, together with the effect of MLDOE phase delay on a collimated on-axis beam with an angular spectrum method. Thus, we accurately generate optical figures of merit (point spread function along the optical axis, Strehl ratio at the "best" focal plane, and chromatic focal shift) and, by using a finite-difference time-domain method as a reference solution, demonstrate it as a valuable tool to describe and quantify the longitudinal chromatic aberration of MLDOEs.