Efficient, nonlinear phase estimation with the nonmodulated pyramid wavefront sensor

Abstract

The sensitivity of the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems. The PyWFS is at its most sensitive when it is used without modulation of the input beam. In nonmodulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirable. This article argues that nonlinear estimation based on Newton's method for nonlinear optimization can be useful for mitigating the effects of nonlinearity in the nonmodulated PyWFS. The proposed approach requires all optical modeling to be pre-computed, which has the advantage of avoiding real-time simulations of beam propagation. Further, the required real-time calculations are amenable to massively parallel computation. Numerical experiments simulate a PyWFS with faces sloped 3.7° to the horizontal, operating at a wavelength of 0.85 μm, and with an index of refraction of 1.45. A singular value analysis shows that the common practice of calculating two "slope" images from the four PyWFS pupil images discards critical information and is unsuitable for the nonmodulated PyWFS simulated here. Instead, this article advocates estimators that use the raw pixel values not only from the four geometrical images of the pupil, but from surrounding pixels as well. The simulations indicate that nonlinear estimation can be effective when the Strehl ratio of the input beam is greater than 0.3, and the improvement relative to linear estimation tends to increase at larger Strehl ratios. At Strehl ratios less than about 0.5, the performances of both the nonlinear and linear estimators are relatively insensitive to noise since they are dominated by nonlinearity error.

Nonlinear wavefront reconstruction with convolutional neural networks for Fourier-based wavefront sensors

“…Instead of using a model based approach to nonlinear wavefront reconstruction, such as done by [20,21], it is also possible to use a data-driven approach. The advantages of a data-driven approach is that it is not necessary to know the exact details of the optical system and its environment.…”

Review on methods for wavefront reconstruction from pyramid wavefront sensor data

“…70,[81][82][83][84][85][86][87] Later, the development of fast model-based linear reconstructors 60,63,78,79,[88][89][90][91][92][93][94][95][96] began and experiments with nonlinear algorithms, including applications of learning approaches, were reported. 4,60,77,97,98 The algorithms reviewed in this section are split into several groups according to the common underlying model they invert or the common idea they employ for the reconstruction. Before describing the reconstruction methods, we start with one more feature that distinguishes various reconstruction approaches-the way the wavefront control is handled.…”

“…For instance, it was suggested to use the four intensity patterns directly or other combinations of them. 5,6,[75][76][77] An analytical comparison of the standard difference-like data definition [Eq. 7] with the usage of the four intensities directly showed that the former one provides an improved linearity with respect to the incoming wavefront.…”

Nonlinear wavefront reconstruction methods for pyramid sensors using Landweber and Landweber–Kaczmarz iterations

“…Non-linear wavefront reconstructors are considered as one possibility to handle the non-linearity effects of the pyramid sensor introduced by influences such as NCPAs. Currently, there still exist only a few attempts, e.g., [10,22,19,20,37,38,39,73] for handling the non-linearity of pyramid sensors with applications in astronomical AO. We introduce a new idea of non-linear wavefront reconstruction and propose to apply the non-linear Landweber/Landweber-Kaczmarz method.…”