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Large Amplitude Tip/Tilt Estimation by Geometric Diversity for Multiple-Aperture Telescopes S

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Large Amplitude Tip/Tilt Estimation by Geometric Diversity for Multiple-Aperture Telescopes S Large amplitude tip/tilt estimation by geometric diversity for multiple-aperture telescopes S. Vievard, F. Cassaing, L. Mugnier To cite this version: S. Vievard, F. Cassaing, L. Mugnier. Large amplitude tip/tilt estimation by geometric diversity for multiple-aperture telescopes. Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2017, 34 (8), pp.1272-1284. 10.1364/JOSAA.34.001272. hal-01712191 HAL Id: hal-01712191 https://hal.archives-ouvertes.fr/hal-01712191 Submitted on 19 Feb 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1 INTRODUCTION Large amplitude tip/tilt estimation by geometric diversity for multiple-aperture telescopes S. VIEVARD1, F. CASSAING1,*, AND L. M. MUGNIER1 1Onera – The French Aerospace Lab, F-92322, Châtillon, France *Corresponding author: [email protected] Compiled July 10, 2017 A novel method nicknamed ELASTIC is proposed for the alignment of multiple-aperture telescopes, in particular segmented telescopes. It only needs the acquisition of two diversity images of an unresolved source, and is based on the computation of a modified, frequency-shifted, cross-spectrum. It provides a polychromatic large range tip/tilt estimation with the existing hardware and an inexpensive noniterative unsupervised algorithm. Its performance is studied and optimized by means of simulations. They show that with 5000 photo-electrons/sub-aperture/frame and 1024ˆ1024 pixel images, residues are within the capture range of interferometric phasing algorithms such as phase diversity. The closed-loop alignment of a 6 sub-aperture mirror provides an experimental demonstration of the effectiveness of the method. © 2017 OCIS codes: (070.0070) Fourier optics and signal processing, (220.1080) Active or adaptive optics, (010.7350) Wave-front sensing, (100.5070) Phase retrieval, (110.5100) Phased-array imaging systems, (220.1140) Alignment. http://dx.doi.org/10.1364/ao.XX.XXXXXX 1. INTRODUCTION sure the wavefront degradation. Since the near-focal images of any source taken by a 2D camera show distortions when the The resolution of a telescope is ultimately limited by its aperture telescope is not aligned (Fig. 1), these misalignments can be re- diameter, but the size of mirrors is bounded by current technol- trieved by solving the associated inverse problem. The phase ogy to about 10 m on the ground and to a few meters in space. retrieval technique, based on the analysis of the sole focal-plane To overcome this limitation, interferometry consists in making image, is generally not sufficient to retrieve piston and tip/tilt an array of sub-apertures interfere; the resulting instrument is without ambiguity except in specific cases [16]. The phase diver- called an interferometer or a multi-aperture telescope. sity technique [17, 18], typically based on a focal and a slightly The sub-apertures can either be telescopes per se, as in cur- defocused images, removes all ambiguities and operates even rent ground-based interferometers [1–3], or segments of a com- on unknown extended sources. mon primary mirror, such as in the Keck telescopes, the fu- The fact that phase diversity can be used as a CS on a seg- ture extremely large telescopes [4–7]) or large ground collectors mented aperture telescope was recognized very early [19], and (Cherenkov Telescope Array [8]). extensively studied for the JWST [20–23], for Darwin [24], and So far, this technique has been operational only on ground- for the European Extremely Large Telescope (E-ELT) [25] in par- based telescopes, but interferometers have long been forecast ticular. Additionally, in contrast with most pupil-plane-based for high-resolution spaceborne astronomy, for the soon-to-be- devices, phase diversity enjoys three appealing characteristics: launched James Webb Space Telescope (JWST) [9] or other firstly, it is appropriate for a large number of sub-apertures, be- projects [10–13], and for Earth observation [14, 15]. cause the hardware complexity remains essentially independent To reach the diffraction limit, all the sub-apertures of such of the number of sub-apertures. Secondly, the CS is included a telescope must be phased to within a small fraction of the in the main imaging detector, simplifying the hardware and wavelength. A critical sub-system of interferometers is thus minimizing differential paths. Thirdly, it can be used on very the Cophasing Sensor (CS), whose goal is to measure with this extended objects. These properties are strong motivations for kind of precision the relative positioning errors between the sub- the choice of phase diversity as a CS, even when looking at an apertures (differential piston and tip/tilt), which are the specific unresolved source. low-order aberrations of an interferometer and the main sources The measurement and correction described above of piston- of wave-front degradation (Fig. 1). tip-tilt by means of a CS to within a small fraction of l is hereafter Focal-plane wavefront sensing is an elegant solution to mea- called the fine phasing mode. This mode assumes that the tip/tilts 1 2 CLOSED-FORM MODEL FOR THE MULTI-APERTURE OTF WITH GEOMETRIC DIVERSITY are smaller than typically l{8 (see Eq.A36) and the differential these additional shifts is given by the defocus, and is different for pistons are within the coherence length (cf [16]). However, dur- each sub-aperture. Using these two images jointly, our method ing the first alignment steps (after integration or deployment), extracts the position and identifies the sub-aperture sub-PSF, the disturbances are much larger than a few micrometers. thanks to a modified cross-correlation. Based on geometrical A preliminary geometrical alignment mode is thus mandatory, optics similarly to GPR, it thus only needs two images of an to efficiently drive the telescope into the reduced capture range unresolved source and a simple data processing. Additionally, of an interferometric CS. This mode consists in an incoherent su- its capture range is only limited by the imaging sensor field of perimposition of the focal plane images from each sub-aperture. view. Only then can the relative piston errors between sub-apertures In Section2, a closed-form model of the multi-aperture Op- be measured and corrected for the fine phasing to operate. Using tical Transfer Function (OTF) is derived. Section3 provides a only one image, such as the common focal image of an unre- solution for large amplitude tip/tilt measurement from a mod- solved source, the geometrical alignment is impossible at least ified cross-spectrum of two diversity images. The method is when all sub-apertures are identical since their Point Spread then validated and optimized by simulation in Section4. Fi- Functions (or sub-PSFs) all have the same shape. Even if these nally, in Section5, an experimental validation is performed on a sub-PSFs are well separated in the field with clearly identifiable segmented mirror. positions, it is impossible to associate them with their respective sub-apertures. 2. CLOSED-FORM MODEL FOR THE MULTI-APERTURE The solution selected by JWST to identify the sub-PSFs is tem- OTF WITH GEOMETRIC DIVERSITY poral modulation [26], but the measurement time scales with the number of sub-apertures. A method called Geometrical Throughout this paper, the considered multiple-aperture tele- Phase Retrieval (GPR), with the ability to increase the JWST fine scope is based either on a segmented telescope or on a telescope algorithm capture range, was developed [27], refined [28], exper- array, all feeding a common focal-plane image detector and imentally demonstrated [29] and should be implemented in the operates at a central wavelength l with a focal length F. We JWST [30]. Based on geometrical optics, it uses typically four to assume the object is a point source at infinity. In this section, the six defocused images per segment. The JWST geometrical align- telescope’s pupil, its disturbances and its OTF are successively ment mode, called image-stacking operation [31], was originally introduced. forecast to last around 1 week of commissioning time, but the A. Model of the multiple aperture GPR should provide substantial time savings [29]. In this paper, a novel method for the geometrical alignment The pupil of the telescope is assumed for simplicity to be made of the subapertures is proposed. The alignment error is encoded of a set of Na circular sub-apertures (of index n ranging from 1 to by each sub-PSF’s shift in the focal plane image. As can be seen Na) with identical radius R. In the following we use the reduced on Figure1, a defocus induces an additional shift of the sub-PSFs coordinate u, defined as the usual coordinate r in the pupil plane in the diversity plane with respect to the focal plane. Each of divided by R (u “ r{R). Similarly we define cn as the reduced coordinates of the center of each sub-aperture. In each of the two so-called diversity planes (of index d P t1, 2u), each sub-aperture is characterized by its complex amplitude transmittance pn,d whose shape is described by the disk function P, 1 for |u| ¤ 1, Ppuq “ (1) $ 0 elsewhere, & and the pupil transmission% is constant over each sub-aperture, equal to rn. The phase of pn,d is the sum of unknown (and seeked) phases plus known diversity phases Yn,dpuq, and is ex- panded on a local orthonormal basis of Zernike polynomials [32].
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