Current approaches for phasing of segmented space telescopes require complex dedicated optics and mechanisms, such as Dispersed Hartmann sensors or grisms. These methods do not scale well as the number of segments increases. The Broadband Phasing (BPH) approach used at the Keck Observatory does scale well and can work on space telescopes without the need for any additional hardware. We show that this method implemented as White Light Interferometry (WLI), using a standard imaging detector and filters, has a capture range limited only by the range of the segment actuators and can easily phase the mirrors to within the capture range of single wavelength phasing methods. An analysis of the Keck BPH performance is presented and used to develop a formula for implementation of WLI on other segmented telescopes. As an example, a WLI implementation for the NASA Habitable Worlds Observatory (HWO) telescope (Exploratory Analytic Case 1 (EAC1)) is developed and demonstrated via detailed wave-optics simulations. The implementation, performance and limitations of the proposed WLI method are discussed in detail in the paper.

Lentil is a Python package for developing high-performance diffraction simulations. Lentil provides an easy to use framework for modeling optical systems and simulating the wave propagation of light through them. Traditional Fourier optics-based approaches for numerically modeling diffraction rely on the Fast Fourier Transform (FFT) for simulating free space propagation. Despite computational efficiencies provided by the FFT, these simulations can be slow and memory-intensive due to very large array sizes needed to satisfy numerical sampling requirements imposed by the FFT algorithm. Modeling large apertures, highly aberrated or misaligned systems, or small features like primary mirror segment gaps demand even finer sampling, further degrading performance. Directly computing the discrete Fourier transform (DFT) in diffraction calculations provides greater flexibility and increased performance when compared with computing an equivalent FFT. Lentil offers generalized diffraction propagation routines using the DFT that improve simulation performance substantially, with additional optimizations for modeling segmented apertures. Lentil also implements a hybrid propagation algorithm blending physical and geometric optics to greatly improve performance in simulations where representing large tilts is required. Additionally, Lentil includes tools for modeling static and dynamic wavefront errors, radiometry, and focal plane arrays. The Lentil package and its accompanying documentation are freely available as open-source software.

The Habitable Worlds Observatory will have uniquely stringent wavefront stability requirements, in the single-digit picometers for observations lasting days, to preserve coronagraph contrast for imaging earth-like exoplanets. This need will be addressed using high-precision Wavefront Sensing and Control methods, including continuous picometerprecision metrology and control of the Optical Telescope Assembly (OTA). This paper reviews methods for initializing and maintaining the OTA wavefront, evolved from those used for the James Webb Space Telescope, but extended to much higher precision. It concludes by identifying performance targets for WFSC technology development, to help guide NASA technology investments.

Large aperture telescope commonly features segment mirrors and a coarse phasing step is needed to bring these individual segments into the fine phasing capture range. Dispersed Fringe Sensing (DFS) is a powerful coarse phasing technique and its alteration is currently being used for JWST. An Advanced Dispersed Fringe Sensing (ADFS) algorithm is recently developed to improve the performance and robustness of previous DFS algorithms with better accuracy and unique solution. The first part of the paper introduces the basic ideas and the essential features of the ADFS algorithm and presents the some algorithm sensitivity study results. The second part of the paper describes the full details of algorithm validation process through the advanced wavefront sensing and correction testbed (AWCT): first, the optimization of the DFS hardware of AWCT to ensure the data accuracy and reliability is illustrated. Then, a few carefully designed algorithm validation experiments are implemented, and the corresponding data analysis results are shown. Finally the fiducial calibration using Range-Gate-Metrology technique is carried out and a <10nm or <1% algorithm accuracy is demonstrated.

Dispersed Fringe Sensing (DFS) is a technique for measuring and phasing segmented telescope mirrors using a dispersed broadband light image. DFS is capable of breaking the monochromatic light ambiguity, measuring absolute piston errors between segments of large segmented primary mirrors to tens of nanometers accuracy over a range of 100 micrometers or more. The DFSA software tool analyzes DFS images to extract DFS encoded segment piston errors, which can be used to measure piston distances between primary mirror segments of ground and space telescopes. This information is necessary to control mirror segments to establish a smooth, continuous primary figure needed to achieve high optical quality. The DFSA tool is versatile, allowing precise piston measurements from a variety of different optical configurations. DFSA technology may be used for measuring wavefront pistons from sub-apertures defined by adjacent segments (such as Keck Telescope), or from separated sub-apertures used for testing large optical systems (such as sub-aperture wavefront testing for large primary mirrors using auto-collimating flats). An experimental demonstration of the coarse-phasing technology with verification of DFSA was performed at the Keck Telescope. DFSA includes image processing, wavelength and source spectral calibration, fringe extraction line determination, dispersed fringe analysis, and wavefront piston sign determination. The code is robust against internal optical system aberrations and against spectral variations of the source. In addition to the DFSA tool, the software package contains a simple but sophisticated MATLAB model to generate dispersed fringe images of optical system configurations in order to quickly estimate the coarse phasing performance given the optical and operational design requirements. Combining MATLAB (a high-level language and interactive environment developed by MathWorks), MACOS (JPL s software package for Modeling and Analysis for Controlled Optical Systems), and DFSA provides a unique optical development, modeling and analysis package to study current and future approaches to coarse phasing controlled segmented optical systems.

The Modified Gerchberg-Saxton (MGS) algorithm is an image-based wavefront-sensing method that can turn any science instrument focal plane into a wavefront sensor. MGS characterizes optical systems by estimating the wavefront errors in the exit pupil using only intensity images of a star or other point source of light. This innovative implementation of MGS significantly accelerates the MGS phase retrieval algorithm by using stream-processing hardware on conventional graphics cards. Stream processing is a relatively new, yet powerful, paradigm to allow parallel processing of certain applications that apply single instructions to multiple data (SIMD). These stream processors are designed specifically to support large-scale parallel computing on a single graphics chip. Computationally intensive algorithms, such as the Fast Fourier Transform (FFT), are particularly well suited for this computing environment. This high-speed version of MGS exploits commercially available hardware to accomplish the same objective in a fraction of the original time. The exploit involves performing matrix calculations in nVidia graphic cards. The graphical processor unit (GPU) is hardware that is specialized for computationally intensive, highly parallel computation. From the software perspective, a parallel programming model is used, called CUDA, to transparently scale multicore parallelism in hardware. This technology gives computationally intensive applications access to the processing power of the nVidia GPUs through a C/C++ programming interface. The AAMGS (Accelerated Adaptive MGS) software takes advantage of these advanced technologies, to accelerate the optical phase error characterization. With a single PC that contains four nVidia GTX-280 graphic cards, the new implementation can process four images simultaneously to produce a JWST (James Webb Space Telescope) wavefront measurement 60 times faster than the previous code.

Dispersed Fringe Sensing (DFS) is an elegant method of coarse phasing segmented mirrors. DFS performance accuracy is dependent upon careful calibration of the system as well as other factors such as internal optical alignment, system wavefront errors, and detector quality. Novel improvements to the algorithm have led to substantial enhancements in DFS performance. In this paper, we present Advanced DFS, an advancement of the DFS algorithm, which allows the overall method to be less sensitive to calibration errors. This is achieved by correcting for calibration errors, which appear in the fitting equations as a signal phase term. This paper will outline a brief analytical explanation of the improvements, results of advanced DFS processed simulations and experimental advanced DFS results.

We have successfully demonstrated significant improvements in the high contrast detection limit of the Well-Corrected Subaperture (WCS) using a number of steps aimed at reducing non-common path (NCP) wavefront errors, including the Autonomous Phase Retrieval Calibration (APRC)1 software package developed at the Jet Propulsion Laboratory (JPL) for the Palomar adaptive optics instrument (PALAO). APRC utilizes the Modified Gerchberg-Saxton (MGS) wavefront sensing algorithm, also developed at JPL2. The WCS delivers such excellent correction of the atmosphere that NCP wavefront errors not sensed by PALAO but present at the coronagraphic image plane begin to factor heavily as a limit to contrast. The APRC program was implemented to reduce these NCP wavefront errors from 110 nm to 35 nm (rms) in the lab, and now these exceptional results have been extended to targets on the sky for the first time, leading to a significant suppression of speckle noise. Consequently we now report a contrast level of very nearly 1×10-4 at separations of 2λ/D before the data is post processed, and 1×10-5 after post processing. We describe here the major components of our instrument, the work done to improve the NCP wavefront errors, and the ensuing excellent on sky results, including the detection of the three exoplanets orbiting the star HR8799.

Phase retrieval is an image-based wavefront sensing process, used to recover phase information from defocused stellar images. Phase retrieval has proven to be useful for diagnosis of optical aberrations in space telescopes, calibration of adaptive optics systems, and is intended for use in aligning and phasing the James Webb Space Telescope. This paper describes a robust and accurate phase retrieval algorithm for wavefront sensing, which has been successfully demonstrated on a variety of testbeds and telescopes. Key features, such as image preprocessing, diversity adaptation, and prior phase nulling, are described and compared to other methods. Results demonstrate high accuracy and high dynamic range wavefront sensing.

An autonomous wavefront sensing and control software suite (APRC) has been developed as a method to calibrate the internal static errors in the Palomar Adaptive Optics system. An image-based wavefront sensing algorithm, Adaptive Modified Gerchberg-Saxton Phase Retrieval (MGS), provides wavefront error knowledge upon which actuator command voltages are calculated for iterative wavefront control corrections. This automated, precise calibration eliminates non-common path error to significantly reduce AO system internal error to the controllable limit of existing hardware, or can be commanded to prescribed polynomials to facilitate high contrast astronomy. System diagnostics may be performed through analysis of the wavefront result generated by the phase retrieval software.

Image based wavefront sensing methods such as Adaptive Modified Gerchberg-Saxton Phase Retrieval(1) (MGS) require a matrix of a-priori phase knowledge to avoid high dynamic range "phase wrapping" during estimation. Previous unwrapping methods have met with limited success or have required some degree of expert intervention. We have succeeded in developing a method and algorithm for automatically unwrapping the phase estimate to generate "prior phase knowledge". By utilizing first-round wavefront sensing results and image processing techniques, the algorithm is able to create sufficient a-priori phase information to feed back to the phase retrieval software. The autonomous phase unwrapping algorithm utilizes edge detection, morphological processing, and spatial filtering, and is able to perform well on a variety of phase wrapping anomalies for both monolithic and segmented optical systems.

Adaptive MGS Phase Retrieval software uses the Modified Gerchberg-Saxton (MGS) algorithm, an image-based sensing method that can turn any focal plane science instrument into a wavefront sensor, avoiding the need to use external metrology equipment. Knowledge of the wavefront enables intelligent control of active optical systems.

We describe the current performance of an adaptive optics testbed for free space optical communication. This adaptive optics system allows for simulation of night and day-time observing on a 1 meter telescope with a 97 actuator deformable mirror. In lab-generated seeing of 2.1 arcseconds (at 0.5μm) the system achieves a Strehl of 21% at 1.064μm (210nm RMS wavefront). Predictions of the system's performance based on real-time wavefront sensor telemetry data and analytical equations are shown to agree with the observed image performance. We present experimentally measured gains in communications performance of 2-4dB in the received signal power when AO correction is applied in the presence of high background and turbulence at an uncoded bit error rate of 0.1. The data source was a 100Mbps on-offkeyed signal detected with an IR-enhanced avalanche photodiode detector as the receiver.