Cophasing a wide field multi-aperture array by phase-diversity: influence of aperture redundancy and dilution

Abstract

Future high-resolution space telescopes will use discontinuous apertures, either primary segments ("Fizeau" case) or sub-telescopes (" Michelson" case) . One of the most critical points in the operation of such instruments will be the cophasing of the sub-apertures. Cophasing sensors are available on ground interferometers, allowing sub-aperture piston/tip/tilt measurement on unresolved or slightly resolved stars. But when observing a very extended object, such as the Earth as seen from space, no reference star can be found in the field. In this case, the cophasing measurement must be derived from the observed object itself, which is a major issue for extended objects.Phase diversity is one of the very few solutions to this problem. Phase diversity consists in the joint estimation of the object and the instrument aberrations from the analysis of several images obtained with different but perfectly known aberrations, for example the focal image and a slightly defocused image. Theoretical analysis and numerical simulations were carried out to investigate how our phase diversity algorithm behaves when estimating sub-aperture piston and tip/tilt in various conditions. Our study shows that the aperture configuration has a major impact on performance. For diluted apertures, when the optical transfer function has zeros within the frequency domain of interest, it can be shown that at least two possible solutions can be derived by phase diversity. For redundant apertures, when several pairs of subaperture contribute to the same spatial frequency, the piston or tip/tilt estimation is degraded for sub-apertures contributing to redundant frequencies.

Optical design of a Michelson wide-field multiple-aperture telescope

“…Using a relevant aperture configuration including optical design constraints [8,9], an efficient cophasing strategy [5][6][7]11], an optimized image processing [35] and a wide-field design such as presented here, Michelson MAOTs are thus a solution to be considered for high resolution wide-field imaging, from space or ground.…”

“…Cophasing non-adjacent sub-apertures requires a real-time piston sensor. Such components are now used on stars by stellar interferometers and more complex devices required for very extended objects have been validated recently [10,11].…”

Multiple aperture optical telescopes: some key issues for earth observation from a GEO orbit

“…We have shown that when used for phase measurement, the object can be integrated out of the problem and that this "marginal" PD is more efficient on monolithic telescopes than the classical joint PD methods [23,24]. Simulations show that marginal PD is also a good solution for MAOT cophasing [25]. An important feature of PD is that complexity is reported on the software: a simple optical hardware theoretically allows the simultaneous measurement of many Zernike modes on a large number of sub-apertures.…”

High resolution earth observation from geostationary orbit by optical aperture synthesys

“…Pursuit: This mode is activated to maintain the alignment within the required precision for the observation. This is done by the use of phase diversity method [9]. This method, presented in Fig.…”