Point-diffraction interferometry for wavefront sensing in adaptive optics

Abstract

The work presented in this thesis aims at the development and validation of a wavefront sensor concept for adaptive optics (AO) called the pupil-modulated Point-Diffraction Interferometer (m-PDI). The m-PDI belongs to a broader family of wavefront sensors called Point-Diffraction Interferometers (PDIs), which make use of a small pinhole to filter a portion of the incoming light, hence generating a reference beam. This allows them to perform wavefront sensing on temporally incoherent light, such as natural guide stars in the context of astronomical AO.

Due to their high sensitivity, PDIs are being developed to address several difficult problems in AO, namely measuring quasi-static aberrations to a high degree of accuracy, the cophasing of segmented apertures, and reaching a high correction regime known as extreme AO. But despite their advantages, they remain limited by their narrow chromatic range, around ∆λ = 2% relative to central bandwidth, and short dynamic range, generally of ±π/2. The purpose of developing the m-PDI is to explore whether this new concept has any ad- vantages regarding these limitations. Indeed, we find that the m-PDI has a maximum chromatic bandwidth of 66% relative to the central wavelength and a dynamic range at least 4 times larger than that of other PDIs.

Although the m-PDI concept had been proposed previously, it had not been explored to the extent reached in this manuscript. This thesis presents an initial investigation into the m-PDI, beginning with the development of the theory. Here the theoretical framework is laid out to explain how interference fringes are modulated by the wavefront, how to then demodulate the propa- gating electric field’s phase and then finally how to measure the signal-to-noise ratio (SNR).

After building analytical and numerical models, a prototype is designed, built and characterised using CHOUGH, a high-order AO testbed in the lab. This incarnation of the m-PDI is called the Calibration & Alignment Wavefront Sensor (CAWS). The characterisation of the CAWS shows two things. The first one is that the CAWS’ response is approximately flat across its spatial frequency domain. The second one is that its dynamic range decreases at higher frequencies, suggesting that it depends, amongst other things, on the wavefront’s slope.

In order to prove that m-PDIs can be used for AO, a control loop is closed using the CAWS and CHOUGH’s deformable mirror, with both monochromatic and broadband light. The results show that the final Strehl ratio increases from 0.2 to 0.66, at a wavelength of 633 nm. The difference in residual aberrations seen separately by the imaging camera and by the CAWS is about 20 nm RMS. This is explained by non-common path aberrations and low order aberrations which are invisible to the CAWS.

Finally, the instrument was tested on the CANARY AO bench at the William Herschel Telescope. The CAWS was successful at characterising the quasi- static aberrations of the system and at demodulating the phase of wavefronts produced with the deformable mirror. When demodulating on-sky residual aberrations at the back of CANARY’s single-conjugate AO loop, the SNR remained too low for effective wavefront demodulation, only sporadically in- creasing above 1. These results are not discouraging as the CAWS was only a first prototype and CANARY is not a high-order system, reaching a Strehl ratio of around 0.5% at 675 nm. The lessons and improvements for future de- signs are to increase the diameter of the instrument’s pinhole by at least twice, and deliver it a higher Strehl ratio by moving towards longer wavelengths and employing a higher order AO system.