Revisiting the differential optical transfer function wavefront sensing technique for high-contrast imaging

Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, France

^★ Corresponding author: patrice.martinez@oca.eu

Received: 2 April 2025
Accepted: 7 July 2025

Abstract

Context. Wavefront sensors (WFSs) are widely used in optical measurements. Initially developed more than 40 years ago for adaptive optics (AO) systems in astronomy, they have become essential components in various stages of high dynamic range imaging systems.

Aims. The differential optical transfer function (dOTF) is a wavefront sensing technique that estimates the complex field of the pupil using differential intensities in the image plane. dOTF has a wide range of applications in astronomy, from optical shop testing to cophasing of segmented optics. This study aims to expand the application of dOTF from classical to high-contrast imaging.

Methods. Building on prior analyses in the literature, where the dOTF phase estimator was derived under the small-phase approximation and applied in classical imaging mode, we reformulated the phase estimator and extended it to include amplitude aberrations. This reformulation enabled the reconstruction of the complete electric field, allowing us to assess its applicability to dark hole digging, and to measure and correct non-common path aberrations (NCPAs) and cophasing misalignments, in coronagraphic imaging mode. Our findings are validated through comprehensive simulations, statistical analysis, and supported by preliminary experimental data.

Results. With a single-actuator probe, the dOTF demonstrates effective joint phase and amplitude wavefront sensing in coronagraphic imaging mode, without prior knowledge of the coronagraph type, a capability not previously documented. Beyond its capability to correct for NCPAs and cophasing misalignment, dOTF provides a simplified alternative to pair-wise probing (PWP) wavefront sensing.

Conclusions. The dOTF enables straightforward complex field measurement, with the deformable mirror (DM) actively participating in the process. By reducing imaging workload, it offers a promising alternative to other coronagraphic wavefront sensors. Its potential for high-contrast imaging has implications for current telescopes, upcoming missions like the Nancy Grace Roman Space Telescope, future large observatories, and laboratory conditions during instrument AIT phases.