Method for Pre-Conditioning a Measured Surface Height Map for Model Validation

This software allows one to up-sample or down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transform-based) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity. The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the "pre-conditioning" or pre-processing of the measured surface maps before using them in a model validation software tool. This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for re-sampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the "nearest," "linear," "cubic," and "spline" fitting in Matlab. The conventional, FFT-based spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects. During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map

Techniques for Down-Sampling a Measured Surface Height Map for Model Validation

This software allows one to down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. The software tool of the current two new techniques can be used in all optical model validation processes involving large space optical surface

Fast linearized coronagraph optimizer (FALCO) I: a software toolbox for rapid coronagraphic design and wavefront correction

The Fast Linearized Coronagraph Optimizer (FALCO) is an open-source toolbox of routines for coronagraphic focal plane wavefront correction. The goal of FALCO is to provide a free, modular framework for the simulation or testbed operation of several common types of coronagraphs. FALCO includes routines for pair-wise probing estimation of the complex electric field and Electric Field Conjugation (EFC) control, and we ask the community to contribute other wavefront correction algorithms. FALCO utilizes and builds upon PROPER, an established optical propagation library. The key innovation in FALCO is the rapid computation of the linearized response matrix for each deformable mirror (DM), which facilitates re-linearization after each control step for faster DM-integrated coronagraph design and wavefront correction experiments. FALCO is freely available as source code in MATLAB at github.com/ajeldorado/falco-matlab and will be available later this year in Python 3 at github.com/ajeldorado/falco-python

Fast linearized coronagraph optimizer (FALCO) III: optimization of key coronagraph design parameters

Deformable mirrors (DMs) are increasingly becoming part of nominal coronagraph designs, such as the hybrid Lyot coronagraph, in addition to their role counteracting optical aberrations. Previous studies have investigated the effects of the inter-DM Fresnel number on achievable contrast, throughput, and tip/tilt sensitivity for apodized coronagraphs augmented with DMs to suppress diffraction from struts and segment gaps. In this paper, we build upon that previous work by directly suppressing tip/tilt sensitivity with the controller, both for coronagraphs with and without apodizers. We also explore the effects of other important design parameters such as actuator density and tip/tilt controller weighting on performance. These comprehensive coronagraph design studies are enabled by the Fast Linearized Coronagraph Optimizer (FALCO) software toolbox, which provides rapid re-calculation of the DM response matrix for a variety of coronagraphs

New Variance-Reducing Methods for the PSD Analysis of Large Optical Surfaces

Edge data of a measured surface map of a circular optic result in large variance or "spectral leakage" behavior in the corresponding Power Spectral Density (PSD) data. In this paper we present two new, alternative methods for reducing such variance in the PSD data by replacing the zeros outside the circular area of a surface map by non-zero values either obtained from a PSD fit (method 1) or taken from the inside of the circular area (method 2)

Dependence of Adaptive Cross-Correlation Algorithm Performance on the Extended-Scene Image Quality

No abstract availabl

Power Spectral Density Specification and Analysis of Large Optical Surfaces

The 2-dimensional Power Spectral Density (PSD) can be used to characterize the mid- and the high-spatial frequency components of the surface height errors of an optical surface. We found it necessary to have a complete, easy-to-use approach for specifying and evaluating the PSD characteristics of large optical surfaces, an approach that allows one to specify the surface quality of a large optical surface based on simulated results using a PSD function and to evaluate the measured surface profile data of the same optic in comparison with those predicted by the simulations during the specification-derivation process. This paper provides a complete mathematical description of PSD error, and proposes a new approach in which a 2-dimentional (2D) PSD is converted into a 1-dimentional (1D) one by azimuthally averaging the 2D-PSD. The 1D-PSD calculated this way has the same unit and the same profile as the original PSD function, thus allows one to compare the two with each other directly

Extended Scene SH Wavefront Sensor Algorithm: Minimization of Scene Content Dependent Shift Estimation Errors

Adaptive Periodic-Correlation (APC) algorithm was developed for use in extended-scene Shack-Hartmann wavefront sensors. It provides high-accuracy even when the sub-images in a frame captured by a Shack-Hartmann camera are not only shifted but also distorted relative to each other. Recently we found that the shift-estimate error of the APC algorithm has a component that depends on the content of extended-scene. In this paper we assess the amount of that error and propose a method to minimize it

Adaptive Periodic-Correlation Algorithm for Extended Scene Shack-Hartmann Wavefront Sensing

We present an adaptive periodic-correlation algorithm for large dynamic range extended-scene Shack-Hartmann wavefront sensing. We show that it accurately measures very fine image shifts over many pixels under a variety of practical imaging conditions