Diffraction efficiency and aberrations of diffractive elements obtained from orthogonal expansion of the point spread function

The Point Spread Function (PSF) indirectly encodes the wavefront aberrations of an optical system and therefore is a metric of the system performance. Analysis of the PSF properties is useful in the case of diffractive optics where the wavefront emerging from the exit pupil is not necessarily continuous and consequently not well represented by traditional wavefront error descriptors such as Zernike polynomials. The discontinuities in the wavefront from diffractive optics occur in cases where step heights in the element are not multiples of the illumination wavelength. Examples include binary or N-step structures, multifocal elements where two or more foci are intentionally created or cases where other wavelengths besides the design wavelength are used. Here, a technique for expanding the electric field amplitude of the PSF into a series of orthogonal functions is explored. The expansion coefficients provide insight into the diffraction efficiency and aberration content of diffractive optical elements. Furthermore, this technique is more broadly applicable to elements with a finite number of diffractive zones, as well as decentered patterns.