Phase diversity for segmented and multi-aperture systems (2009)

As telescopes become larger, segmented and multi-aperture designs are being implemented to meet cost, size and weight constraints. These systems require alignment of the segments or sub-apertures to within fractions of a wavelength. We investigate the performance of phase diversity, a technique of image-based wavefront sensing, for characterizing and aligning segmented and multi-aperture systems. Supporting work developing the core phase-diversity algorithm is also presented. The modification of phase diversity to incorporate a broadband object model is discussed. Through digital simulation, we show a benefit to using a broadband, gray-world algorithm, as opposed to the conventional monochromatic algorithm, when bandwidths greater than 20% are used for imaging. We further demonstrate that knowledge of the gray-world object spectrum is not required to achieve improved performance. Using digital simulation, three regularization techniques for phase diversity metrics are compared to the conventional phase diversity algorithm. For low signal-to-noise ratio (SNR), we demonstrate an improvement in both the phase estimation accuracy and convergence properties of the algorithm when a regularization based on the object and noise power spectra is used. We present a novel implementation of phase diversity unique to segmented and multi-aperture systems that utilizes individual sub-aperture piston phases in the pupil. Through digital simulation, we compare sub-aperture piston phase diversity to conventional focus diversity and show that, for high SNR and optimal values of diversity, sub-aperture piston phase diversity yields higher phase estimation accuracy and comparable image reconstructions. Using large amounts of sub-aperture piston phase diversity we derive a modified phase-diversity metric and gradients that enable estimation of the average object spectral coefficients, in addition to the unknown phase and object. We successfully demonstrate the algorithm through digital simulation and explore limitations on spectral resolution and sampling. An experimental setup is described and used to demonstrate monochromatic and broadband versions of focus diversity and sub-aperture piston phase diversity. A hexagonally segmented MEMs deformable mirror is used as the system under test and a modified digital projector is used to provide an extended object source. Phase-shifting interferometry is used to corroborate phase estimates from the phase-diversity algorithm. Agreement between the estimated phase and measured phase to 0.06 λ RMS is achieved. Images are also reconstructed using the estimated phases. A new method of performing multi-field wavefront sensing that directly estimates a field-dependent model of the wavefront using phase-diverse phase retrieval is presented. Using digital simulations and information-theoretic Cramer-Rao bounds, we show an advantage to using the new method over a conventional technique in which the field-dependent wavefront is extrapolated or interpolated from a series of wavefronts across samples of the field of view. This work demonstrates that phase diversity is a useful method of aligning segmented and multi-aperture systems. Furthermore, the architecture of such systems offer unique opportunities for the implementation of phase diversity and for recovering the system phase, an image of the object and the average spectrum of the object.