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Register a new userTelescope interferometers: an alternative to classical wavefront sensors
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Authors
Francois Henault
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Several types of Wavefront Sensors (WFS) are nowadays available in the field of Adaptive Optics (AO). Generally speaking, their basic principle consists in measuring slopes or curvatures of Wavefront Errors (WFE) transmitted by a telescope, subsequently reconstructing WFEs digitally. Such process, however, does not seem to be well suited for evaluating co-phasing or piston errors of future large segmented telescopes in quasi real-time. This communication presents an original, recently proposed technique for direct WFE sensing. The principle of the device, which is named Telescope-Interferometer (TI), is based on the addition of a reference optical arm into the telescope pupil plane. Then incident WFEs are deduced from Point Spread Function (PSF) measurements at the telescope focal plane. Herein are described two different types of TIs, and their performance are discussed in terms of intrinsic measurement accuracy and spatial resolution. Various error sources are studied by means of numerical simulations, among which photon noise sounds the most critical. Those computations finally help to define the application range of the TI method in an AO regime, including main and auxiliary telescope diameters and magnitude of the guide star. Some practical examples of optical configurations are also described and commented.
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This paper is the third part of a trilogy dealing with the principles, performance and limitations of what I named Telescope-Interferometers (TIs). The basic idea consists in transforming one telescope into a Wavefront Error (WFE) sensing device. This can be achieved in two different ways, namely the off axis and phase-shifting TIs. In both cases the Point-Spread Function (PSF) measured in the focal plane of the telescope carries information about the transmitted WFE, which is retrieved by fast and simple algorithms suitable to an Adaptive Optics (AO) regime. Herein are evaluated the uncertainties of both types of TIs, in terms of noise and systematic errors. Numerical models are developed in order to establish the dependence of driving parameters such as useful spectral range, angular size of the observed star, or detector noise on the total WFE measurement error. The latter is found particularly sensitive to photon noise, which rapidly governs the achieved accuracy for telescope diameters higher than 10 m. We study a few practical examples, showing that TI method is applicable to AO systems on telescope diameters ranging from 10 to 50 m, depending on seeing conditions and magnitude of the observed stars. We also discuss the case of a space-borne coronagraph where TI technique provides high sampling of the input WFE map.
Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and Achromatic Phase Shifter (APS) subsystems, both required to achieve planet detection and characterization, can sensibly affect the nulling maps produced by a simple Bracewell interferometer. Analytical relationships involving cross correlation products are provided and numerical simulations are performed, demonstrating marked differences in the aspect of extinction maps and the values of attained fringes contrasts. It is concluded that depending on their basic principles and designs, FS and APS will result in variable capacities for serendipitous discoveries of planets orbiting around their parent star. The mathematical relationships presented in this paper are assumed to be general, i.e. they should apply to other types of multi-apertures nulling interferometers.
Fourier-based wavefront sensors, such as the Pyramid Wavefront Sensor (PWFS), are the current preference for high contrast imaging due to their high sensitivity. However, these wavefront sensors have intrinsic nonlinearities that constrain the range where conventional linear reconstruction methods can be used to accurately estimate the incoming wavefront aberrations. We propose to use Convolutional Neural Networks (CNNs) for the nonlinear reconstruction of the wavefront sensor measurements. It is demonstrated that a CNN can be used to accurately reconstruct the nonlinearities in both simulations and a lab implementation. We show that solely using a CNN for the reconstruction leads to suboptimal closed loop performance under simulated atmospheric turbulence. However, it is demonstrated that using a CNN to estimate the nonlinear error term on top of a linear model results in an improved effective dynamic range of a simulated adaptive optics system. The larger effective dynamic range results in a higher Strehl ratio under conditions where the nonlinear error is relevant. This will allow the current and future generation of large astronomical telescopes to work in a wider range of atmospheric conditions and therefore reduce costly downtime of such facilities.
A new concept of using focus-diverse point spread functions (PSFs) for modal wavefront sensing (WFS) is explored. This is based on relatively straightforward image moment analysis of measured PSFs, which differentiates it from other focal-plane wavefront sensing techniques (FPWFS). The presented geometric analysis shows that the image moments are non-linear functions of wave aberration coefficients, but notes that focus-diversity (FD) essentially decouples the coefficients of interest from others, resulting in a set of linear equations whose solution corresponds to modal coefficient estimates. The presented proof-of-concept simulations suggest the potential of the concept in WFS with strongly aberrated high SNR objects in particular.
Increasing interest in astronomical applications of non-linear curvature wavefront sensors for turbulence detection and correction makes it important to understand how best to handle the data they produce, particularly at low light levels. Algorithms for wavefront phase-retrieval from a four-plane curvature wavefront sensor are developed and compared, with a view to their use for low order phase compensation in instruments combining adaptive optics and Lucky Imaging. The convergence speed and quality of iterative algorithms is compared to their step-size and techniques for phase retrieval at low photon counts are explored. Computer simulations show that at low light levels, preprocessing by convolution of the measured signal with a gaussian function can reduce by an order of magnitude the photon flux required for accurate phase retrieval of low-order errors. This facilitates wavefront correction on large telescopes with very faint reference stars.
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