Numerical reconstruction of wavefront in phase‐shifting point diffraction interferometer by digital holography

Abstract

A phase-shifting point diffraction interferometer (PS/PDI) is applied for absolute surface figure measurement for large aperture optics. The intensity and phase distributions of measurement wavefront containing the surface figure profile are measured on the projection plane. The phase map gives the surface figure of the mirror. However, the wavefront reflected by the test mirror changes itself while propagating due to the surface figure of the mirror and the position of the point light source. The wavefront is different from the surface figure on the projection plane. For absolute surface profiling, the wavefront on the mirror has to be reconstructed from the measurement results. To reconstruct the wavefront digital holography has been studied. We have developed the numerical reconstruction method by using the Helmholtz-Kirchhoff formula. Spherical concave mirror measurements have been simulated to verify the availability. Ideal spherical mirror measurements, aspherical mirror measurements and a spherical mirror measurement in which the point light source was slightly displaced were simulated. As a result, the phase map on the projection plane did not fit the surface figure. It was also revealed that the light intensity distribution causes changes in the wavefront. In contrast, the reconstructed phase map on the mirror gave the real surface figure. For precise reconstruction the number of sampling on the projection plane must be increased.

Phase-Shifting Point Diffraction Interferometer Having Two Point Light Sources of Single-Mode Optical Fibers

“…In other words, the surface figure of the reflected wavefront depends on the observation or recording position, and the PS/PDI result with a glassless CCD camera will not agree with the exact surface figure of the test mirror. To obtain the actual mirror surface data, the reflected wavefront should be reconstructed on the test mirror surface using a digital holography technique with both phase and intensity maps computed from the CCD data (Yamaguchi et al, 2006;Matsuura et al, 2008). Fig.…”

Two-Step Converging Spherical Wave Diffracted at a Circular Aperture of Digital In-Line Holography

“…The point diffraction interferometer is well developed [20][21][22]. A near-ideal spherical wave produced by pinhole diffraction is employed as the reference wave surface [23][24][25][26].…”