Bisymmetric pupil modification deconvolution strategy for differential optical transfer function (dOTF) wavefront sensing

Abstract

Context. The differential optical transfer function (dOTF) is a model-independent image-based wavefront sensor for measuring the complex pupil field (phase and amplitude). This method is particularly suitable for compensating non-common path aberrations or for the phasing of segmented telescopes that often prevent the so-called diffraction-limit resolution from being achieved with real-world instruments. Aims. The main problem inherent to the dOTF approach is to address the effect of the convolution. The resolution of the recovered complex pupil field is impacted by the size of the pupil modification. The complex pupil field estimated by the dOTF is blurred by convolution with the complex conjugate of the pupil modification. If the pupil modification involves a non-negligible region of the pupil (actuator or segment poke), it causes significant blurring and resolution loss. Methods. We propose a bisymmetric pupil modification deconvolution strategy to solve this problem. We use two different dOTFs with the opposite-sign pupil modification to identify the pupil modification location and four dOTFs with a symmetric pupil modification to complete the knowledge of their impact on the complex pupil field prior to the deconvolution process in the Fourier domain. The proposed strategy solves the intrinsic limitation of a former deconvolution algorithm, namely the cross-iteration deconvolution algorithm, which is restricted to amplitude pupil modification and precludes its applicability to phase pupil modification. Results. The bissymetric pupil modification deconvolution strategy is a novel probing pattern that permits the extension of iterative cross-deconvolution to phase-only probes. The effectiveness of the proposed approach has been validated analytically and with numerical simulations. Conclusions. The bisymmetric pupil modification deconvolution strategy can improve the resolution and accuracy of dOTF wavefront sensing and contributes to efficient and precise image-based wavefront sensing techniques.