Measurement range of phase retrieval in optical surface and wavefront metrology

Abstract

Phase retrieval employs very simple data collection hardware and iterative algorithms to determine the phase of an optical field. We have derived limitations on phase retrieval, as applied to optical surface and wavefront metrology, in terms of the speed of beam (i.e., f -number or numerical aperture) and amount of aberration using arguments based on sampling theory and geometrical optics. These limitations suggest methodologies for expanding these ranges by increasing the complexity of the measurement arrangement, the phase-retrieval algorithm, or both. We have simulated one of these methods where a surface is measured at unusual conjugates.

Phase diversity with undersampled systems via superresolution preprocessing

“…Traditional phase diversity algorithms can then be applied. The potential feasibility of this approach has been mentioned [11]. Here I demonstrate this approach experimentally for PDPR.…”

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

“…[ 156 ] Such limitations were quantified by Brady and Fienup. [ 165 ] The conclusion is that the speed of the test beam is primarily limited by the pixel pitch of the detector array, e.g., the f /number of test beam must be greater than f /5.5 for 3.5 µm pixel pitch. In addition, the maximum wavefront slope is principally limited by the size of the detector array, e.g., the vertical range is 256 waves of SA for 1024 × 1024 pixels.…”

Calibrating a high-resolution wavefront corrector with a static focal-plane camera

“…Obviously, a successful use of the dOTF method requires that the detector array is at least Nyquist sampled (two pixels per diffraction-limited PSF core) -a limitation when compared to general phase-retrieval methods based on error metric minimization [9]. If the sampling was smaller (w < 2), aliasing would occur.…”