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NASA NTRS2017

Wavefront sensing for a future HabEx space telescope.

HabEx is a concept study for a next generation space telescope having a 4 to 6.5 m primary mirror diameter. Primarily designed for exoplanet science, but also carrying general astrophysics instruments, it will have stability requirements orders of magnitude more stringent than any previously flown space-based observatory. Wavefront control, including active sensing/control of wavefront jitter and drift, will be essential to achieving and maintaining coronagraph performance. There are currently two complementary techniques that can be used to sense the wavefront drift. An attractive method is to use starlight rejected from the coronagraph to sense changes in the wavefront incident on the coronagraph mask. This method suffers from photon noise especially when imaging dim stars. It is also unavailable during slews between target stars. Laser metrology is a complementary system in which a laser “truss” enables rigid body displacements of the optics to be measured from changes in the separation of pairs of optical fiducials which can be separated by many meters. In closed loop with actuated optics, laser metrology actively maintains rigid body alignment of the front-end optics, thereby eliminating the dominant source of wavefront drift. This method can maintain rigid body stability of the telescope optics and thereby wavefront control, even during slews between targets.

Martin, Stefan↗

NASA NTRS2004

Simple broadband implementation of a phase contrast wavefront sensor for adaptive optics

The most critical element of an adaptive optics system is its wavefront sensor, which must measure the closed-loop difference between the corrected wavefront and an ideal template at high speed, in real time, over a dense sampling of the pupil. Most high-order systems have used Shack-Hartmann wavefront sensors, but a novel approach based on Zernike's phase contrast principle appears promising. In this paper we discuss a simple way to achromatize such a phase contrast wavefront sensor, using the pi/2 phase difference between reflected and transmitted rays in a thin, symmetric beam splitter. We further model the response at a range of wavelengths to show that the required transverse dimension of the focal-plane phase-shifting spot, nominally lambda/D, may not be very sensitive to wavelength, and so in practice additional optics to introduce wavelength-dependent transverse magnification achromatizing this spot diameter may not be required. A very simple broadband implementation of the phase contrast wavefront sensor results.

wavefront sensors↗

NASA NTRS2002

Sparse matrix wavefront reconstruction: simulations and experiments

Adaptive optics systems with Shack-Hartmann wavefront sensors require reconstruction of the atmospheric phase error from slope measurements, with every sensor in the array being used in the computation of each actuator command. This fully populated reconstruction matrix can result in a significant computational burden for adaptive optics systems with large numbers of actuators. A method for generating sparse wavefront reconstruction matrices for adaptive optics isproposed. The method exploits the relevance of nearby slope measurements for control of an individual actuator, and relies upon the limited extent of the influence function for a zonal deformable mirror. Relying only on nearby sensor information can significantly reduce the calculation time for wavefront reconstruction. In addition, a hierarchic controller is proposed to recover some of the global wavefront information. The performance of these sparse wavefront reconstruction matrices was evaluated in simulation, and tested on the Palomar Adaptive Optics System. This paper will present some initial results from the simulations and experiments.

space↗

NASA NTRS1975

Wavefront-error evaluation by mathematical analysis of experimental Foucault-test data

The diffraction theory of the Foucault test provides an integral formula expressing the complex amplitude and irradiance distribution in the Foucault pattern of a test mirror (lens) as a function of wavefront error. Recent literature presents methods of inverting this formula to express wavefront error in terms of irradiance in the Foucault pattern. The present paper describes a study in which the inversion formulation was applied to photometric Foucault-test measurements on a nearly diffraction-limited mirror to determine wavefront errors for direct comparison with ones determined from scatter-plate interferometer measurements. The results affirm the practicability of the Foucault test for quantitative wavefront analysis of very small errors, and they reveal the fallacy of the prevalent belief that the test is limited to qualitative use only. Implications of the results with regard to optical testing and the potential use of the Foucault test for wavefront analysis in orbital space telescopes are discussed.

Wilson, R. G.↗

NASA NTRS1990

Wavefront control of large optical systems

Several levels of wavefront control are necessary for the optimum performance of very large telescopes, especially segmented ones like the Large Deployable Reflector. In general, the major contributors to wavefront error are the segments of the large primary mirror. Wavefront control at the largest optical surface may not be the optimum choice because of the mass and inaccessibility of the elements of this surface that require upgrading. The concept of two-stage optics was developed to permit a poor wavefront from the large optics to be upgraded by means of a wavefront corrector at a small exit pupil of the system.

Meinel, Aden B.↗

NASA NTRS1997

Adaptive Full Aperture Wavefront Sensor Study

This grant and the work described was in support of a Seven Segment Demonstrator (SSD) and review of wavefront sensing techniques proposed by the Government and Contractors for the Next Generation Space Telescope (NGST) Program. A team developed the SSD concept. For completeness, some of the information included in this report has also been included in the final report of a follow-on contract (H-27657D) entitled "Construction of Prototype Lightweight Mirrors". The original purpose of this GTRI study was to investigate how various wavefront sensing techniques might be most effectively employed with large (greater than 10 meter) aperture space based telescopes used for commercial and scientific purposes. However, due to changes in the scope of the work performed on this grant and in light of the initial studies completed for the NGST program, only a portion of this report addresses wavefront sensing techniques. The wavefront sensing techniques proposed by the Government and Contractors for the NGST were summarized in proposals and briefing materials developed by three study teams including NASA Goddard Space Flight Center, TRW, and Lockheed-Martin. In this report, GTRI reviews these approaches and makes recommendations concerning the approaches. The objectives of the SSD were to demonstrate functionality and performance of a seven segment prototype array of hexagonal mirrors and supporting electromechanical components which address design issues critical to space optics deployed in large space based telescopes for astronomy and for optics used in spaced based optical communications systems. The SSD was intended to demonstrate technologies which can support the following capabilities: Transportation in dense packaging to existing launcher payload envelopes, then deployable on orbit to form a space telescope with large aperture. Provide very large (greater than 10 meters) primary reflectors of low mass and cost. Demonstrate the capability to form a segmented primary or quaternary mirror into a quasi-continuous surface with individual subapertures phased so that near diffraction limited imaging in the visible wavelength region is achieved. Continuous compensation of optical wavefront due to perturbations caused by imperfections, natural disturbances, and equipment induced vibrations/deflections to provide near diffraction limited imaging performance in the visible wavelength region. Demonstrate the feasibility of fabricating such systems with reduced mass and cost compared to past approaches.

Robinson, William G.↗

NASA NTRS2004

Wavefront Sensing via High Speed DSP

Future light-weighted and segmented primary mirror systems require active optical control to maintain mirror positioning and figure to within nanometer tolerances. Current image-based wavefront sensing approaches rely on post-processing techniques to return an estimate of the aberrated optical wavefront with accuracies to the nanometer level. But the lag times between wavefront sensing, and then control, contributes to a significant latency in the wavefront sensing implementation. In this analysis we demonstrate accelerated image-based wavefront sensing performance using multiple digital signal processors (DSP's). The computational architecture is discussed as well as the heritage leading to the approach.

Smith, J. Scott↗

NASA NTRS2008

On-Orbit Multi-Field Wavefront Control with a Kalman Filter

A document describes a multi-field wavefront control (WFC) procedure for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil. The control is applied to JWST primary mirror (PM) segments and secondary mirror (SM) simultaneously with a carefully selected ordering. Through computer simulations, the multi-field WFC procedure shows that it can reduce the initial system wavefront error (WFE), as caused by random initial system misalignments within the JWST fine-phasing error budget, from a few dozen micrometers to below 50 nm across the entire NIRCam Field of View, and the WFC procedure is also computationally stable as the Monte-Carlo simulations indicate. With the incorporation of a Kalman Filter (KF) as an optical state estimator into the WFC process, the robustness of the JWST OTE alignment process can be further improved. In the presence of some large optical misalignments, the Kalman state estimator can provide a reasonable estimate of the optical state, especially for those degrees of freedom that have a significant impact on the system WFE. The state estimate allows for a few corrections to the optical state to push the system towards its nominal state, and the result is that a large part of the WFE can be eliminated in this step. When the multi-field WFC procedure is applied after Kalman state estimate and correction, the stability of fine-phasing control is much more certain. Kalman Filter has been successfully applied to diverse applications as a robust and optimal state estimator. In the context of space-based optical system alignment based on wavefront measurements, a KF state estimator can combine all available wavefront measurements, past and present, as well as measurement and actuation error statistics to generate a Maximum-Likelihood optimal state estimator. The strength and flexibility of the KF algorithm make it attractive for use in real-time optical system alignment when WFC alone cannot effectively align the system.

Lou, John↗

NASA NTRS2009

Direct-Solve Image-Based Wavefront Sensing

A method of wavefront sensing (more precisely characterized as a method of determining the deviation of a wavefront from a nominal figure) has been invented as an improved means of assessing the performance of an optical system as affected by such imperfections as misalignments, design errors, and fabrication errors. The method is implemented by software running on a single-processor computer that is connected, via a suitable interface, to the image sensor (typically, a charge-coupled device) in the system under test. The software collects a digitized single image from the image sensor. The image is displayed on a computer monitor. The software directly solves for the wavefront in a time interval of a fraction of a second. A picture of the wavefront is displayed. The solution process involves, among other things, fast Fourier transforms. It has been reported to the effect that some measure of the wavefront is decomposed into modes of the optical system under test, but it has not been reported whether this decomposition is postprocessing of the solution or part of the solution process.

Lyon, Richard G.↗

NASA NTRS2009

Guaranteeing Failsafe Operation of Extended-Scene Shack-Hartmann Wavefront Sensor Algorithm

A Shack-Hartmann sensor (SHS) is an optical instrument consisting of a lenslet array and a camera. It is widely used for wavefront sensing in optical testing and astronomical adaptive optics. The camera is placed at the focal point of the lenslet array and points at a star or any other point source. The image captured is an array of spot images. When the wavefront error at the lenslet array changes, the position of each spot measurably shifts from its original position. Determining the shifts of the spot images from their reference points shows the extent of the wavefront error. An adaptive cross-correlation (ACC) algorithm has been developed to use scenes as well as point sources for wavefront error detection. Qualifying an extended scene image is often not an easy task due to changing conditions in scene content, illumination level, background, Poisson noise, read-out noise, dark current, sampling format, and field of view. The proposed new technique based on ACC algorithm analyzes the effects of these conditions on the performance of the ACC algorithm and determines the viability of an extended scene image. If it is viable, then it can be used for error correction; if it is not, the image fails and will not be further processed. By potentially testing for a wide variety of conditions, the algorithm s accuracy can be virtually guaranteed. In a typical application, the ACC algorithm finds image shifts of more than 500 Shack-Hartmann camera sub-images relative to a reference sub -image or cell when performing one wavefront sensing iteration. In the proposed new technique, a pair of test and reference cells is selected from the same frame, preferably from two well-separated locations. The test cell is shifted by an integer number of pixels, say, for example, from m= -5 to 5 along the x-direction by choosing a different area on the same sub-image, and the shifts are estimated using the ACC algorithm. The same is done in the y-direction. If the resulting shift estimate errors are less than a pre-determined threshold (e.g., 0.03 pixel), the image is accepted. Otherwise, it is rejected.

Sidick, Erikin↗

NASA NTRS2007

Filter Function for Wavefront Sensing Over a Field of View

A filter function has been derived as a means of optimally weighting the wavefront estimates obtained in image-based phase retrieval performed at multiple points distributed over the field of view of a telescope or other optical system. When the data obtained in wavefront sensing and, more specifically, image-based phase retrieval, are used for controlling the shape of a deformable mirror or other optic used to correct the wavefront, the control law obtained by use of the filter function gives a more balanced optical performance over the field of view than does a wavefront-control law obtained by use of a wavefront estimate obtained from a single point in the field of view.

Dean, Bruce H.↗

NASA NTRS2007

Wavefront Sensing With Switched Lenses for Defocus Diversity

In an alternative hardware design for an apparatus used in image-based wavefront sensing, defocus diversity is introduced by means of fixed lenses that are mounted in a filter wheel (see figure) so that they can be alternately switched into a position in front of the focal plane of an electronic camera recording the image formed by the optical system under test. [The terms image-based, wavefront sensing, and defocus diversity are defined in the first of the three immediately preceding articles, Broadband Phase Retrieval for Image-Based Wavefront Sensing (GSC-14899-1).] Each lens in the filter wheel is designed so that the optical effect of placing it at the assigned position is equivalent to the optical effect of translating the camera a specified defocus distance along the optical axis. Heretofore, defocus diversity has been obtained by translating the imaging camera along the optical axis to various defocus positions. Because data must be taken at multiple, accurately measured defocus positions, it is necessary to mount the camera on a precise translation stage that must be calibrated for each defocus position and/or to use an optical encoder for measurement and feedback control of the defocus positions. Additional latency is introduced into the wavefront sensing process as the camera is translated to the various defocus positions. Moreover, if the optical system under test has a large focal length, the required defocus values are large, making it necessary to use a correspondingly bulky translation stage. By eliminating the need for translation of the camera, the alternative design simplifies and accelerates the wavefront-sensing process. This design is cost-effective in that the filterwheel/lens mechanism can be built from commercial catalog components. After initial calibration of the defocus value of each lens, a selected defocus value is introduced by simply rotating the filter wheel to place the corresponding lens in front of the camera. The rotation of the wheel can be automated by use of a motor drive, and further calibration is not necessary. Because a camera-translation stage is no longer needed, the size of the overall apparatus can be correspondingly reduced.

Dean, Bruce H.↗

NASA NTRS2010

Wavefront Control and Image Restoration with Less Computing

PseudoDiversity is a method of recovering the wavefront in a sparse- or segmented- aperture optical system typified by an interferometer or a telescope equipped with an adaptive primary mirror consisting of controllably slightly moveable segments. (PseudoDiversity should not be confused with a radio-antenna-arraying method called pseudodiversity.) As in the cases of other wavefront- recovery methods, the streams of wavefront data generated by means of PseudoDiversity are used as feedback signals for controlling electromechanical actuators of the various segments so as to correct wavefront errors and thereby, for example, obtain a clearer, steadier image of a distant object in the presence of atmospheric turbulence. There are numerous potential applications in astronomy, remote sensing from aircraft and spacecraft, targeting missiles, sighting military targets, and medical imaging (including microscopy) through such intervening media as cells or water. In comparison with prior wavefront-recovery methods used in adaptive optics, PseudoDiversity involves considerably simpler equipment and procedures and less computation. For PseudoDiversity, there is no need to install separate metrological equipment or to use any optomechanical components beyond those that are already parts of the optical system to which the method is applied. In Pseudo- Diversity, the actuators of a subset of the segments or subapertures are driven to make the segments dither in the piston, tilt, and tip degrees of freedom. Each aperture is dithered at a unique frequency at an amplitude of a half wavelength of light. During the dithering, images on the focal plane are detected and digitized at a rate of at least four samples per dither period. In the processing of the image samples, the use of different dither frequencies makes it possible to determine the separate effects of the various dithered segments or apertures. The digitized image-detector outputs are processed in the spatial-frequency (Fourier-transform) domain to obtain measures of the piston, tip, and tilt errors over each segment or subaperture. Once these measures are known, they are fed back to the actuators to correct the errors. In addition, measures of errors that remain after correction by use of the actuators are further utilized in an algorithm in which the image is phase-corrected in the spatial-frequency domain and then transformed back to the spatial domain at each time step and summed with the images from all previous time steps to obtain a final image having a greater signal-to-noise ratio (and, hence, a visual quality) higher than would otherwise be attainable.

Lyon, Richard G.↗

NASA NTRS2012

Wavefront Compensation Segmented Mirror Sensing and Control

The primary mirror of very large submillimeter-wave telescopes will necessarily be segmented into many separate mirror panels. These panels must be continuously co-phased to keep the telescope wavefront error less than a small fraction of a wavelength, to ten microns RMS (root mean square) or less. This performance must be maintained continuously across the full aperture of the telescope, in all pointing conditions, and in a variable thermal environment. A wavefront compensation segmented mirror sensing and control system, consisting of optical edge sensors, Wavefront Compensation Estimator/Controller Soft ware, and segment position actuators is proposed. Optical edge sensors are placed two per each segment-to-segment edge to continuously measure changes in segment state. Segment position actuators (three per segment) are used to move the panels. A computer control system uses the edge sensor measurements to estimate the state of all of the segments and to predict the wavefront error; segment actuator commands are computed that minimize the wavefront error. Translational or rotational motions of one segment relative to the other cause lateral displacement of the light beam, which is measured by the imaging sensor. For high accuracy, the collimator uses a shaped mask, such as one or more slits, so that the light beam forms a pattern on the sensor that permits sensing accuracy of better than 0.1 micron in two axes: in the z or local surface normal direction, and in the y direction parallel to the mirror surface and perpendicular to the beam direction. Using a co-aligned pair of sensors, with the location of the detector and collimated light source interchanged, four degrees of freedom can be sensed: transverse x and y displacements, as well as two bending angles (pitch and yaw). In this approach, each optical edge sensor head has a collimator and an imager, placing one sensor head on each side of a segment gap, with two parallel light beams crossing the gap. Two sets of optical edge sensors are used per segment-to-segment edge, separated by a finite distance along the segment edge, for four optical heads, each with an imager and a collimator. By orienting the beam direction of one edge sensor pair to be +45 away from the segment edge direction, and the other sensor pair to be oriented -45 away from the segment edge direction, all six degrees of freedom of relative motion between the segments can be measured with some redundancy. The software resides in a computer that receives each of the optical edge sensor signals, as well as telescope pointing commands. It feeds back the edge sensor signals to keep the primary mirror figure within specification. It uses a feed-forward control to compensate for global effects such as decollimation of the primary and secondary mirrors due to gravity sag as the telescope pointing changes to track science objects. Three segment position actuators will be provided per segment to enable controlled motions in the piston, tip, and tilt degrees of freedom. These actuators are driven by the software, providing the optical changes needed to keep the telescope phased.

Redding, David C.↗

NASA NTRS2010

The Gemini Planet Imager Calibration Wavefront Sensor Instrument

The Gemini Planet Imager is an extreme adaptive optics system that will employ an apodized-pupil coronagraph to make direct detections of faint companions of nearby stars to a contrast level of the 10(exp -7) within a few lambda/D of the parent star. Such high contrasts from the ground require exquisite wavefront sensing and control both for the AO system as well as for the coronagraph. Un-sensed non-common path phase and amplitude errors after the wavefront sensor dichroic but before the coronagraph would lead to speckles which would ultimately limit the contrast. The calibration wavefront system for GPI will measure the complex wavefront at the system pupil before the apodizer and provide slow phase corrections to the AO system to mitigate errors that would cause a loss in contrast. The calibration wavefront sensor instrument for GPI has been built. We will describe the instrument and its performance.

planet detection↗

NASA NTRS2008

An Improved Wavefront Control Algorithm for Large Space Telescopes

Wavefront sensing and control is required throughout the mission lifecycle of large space telescopes such as James Webb Space Telescope (JWST). When an optic of such a telescope is controlled with both surface-deforming and rigid-body actuators, the sensitivity-matrix obtained from the exit pupil wavefront vector divided by the corresponding actuator command value can sometimes become singular due to difference in actuator types and in actuator command values. In this paper, we propose a simple approach for preventing a sensitivity-matrix from singularity. We also introduce a new "minimum-wavefront and optimal control compensator". It uses an optimal control gain matrix obtained by feeding back the actuator commands along with the measured or estimated wavefront phase information to the estimator, thus eliminating the actuator modes that are not observable in the wavefront sensing process.

adaptive optics↗

NASA NTRS2023

High-Order Coronagraphic Wavefront Control With Algorithmic Differentiation: First Experimental Demonstration

Future space-based coronagraphs will rely critically on focal-plane wavefront sensing and control with deformable mirrors to reach deep contrast by mitigating optical aberrations in the primary beam path. Until now, most focal-plane wavefront control algorithms have been formulated in terms of Jacobian matrices, which encode the predicted effect of each deformable mirror actuator on the focal-plane electric field. A disadvantage of these methods is that Jacobian matrices can be cumbersome to compute and manipulate, particularly when the number of deformable mirror actuators is large. Recently, we proposed a new class of focal-plane wavefront control algorithms that utilize gradient-based optimization with algorithmic differentiation to compute wavefront control solutions while avoiding the explicit computation and manipulation of Jacobian matrices entirely. In simulations using a coronagraph design for the proposed Large UV/Optical/Infrared Surveyor (LUVOIR), we showed that our approach reduces overall CPU time and memory consumption compared to a Jacobian-based algorithm. Here, we expand on these results by implementing the proposed algorithm on the High Contrast Imager for Complex Aperture Telescopes (HiCAT) testbed at the Space Telescope Science Institute (STScI) and present initial experimental results, demonstrating contrast suppression capabilities equivalent to Jacobian-based methods.

wavefront control↗

NASA NTRS2006

Fundamental Limits to Wavefront Sensing in the Submillimeter

With the advent of large-format submillimeter wavelength detector arrays, and a new 25 m diameter submillimeter telescope under consideration, the question of optimal wavefront sensing methods is timely. Indeed, not only should bolometric array detectors allow the use of a variety of wavefront sensing techniques already in use in the optical/infrared, but in some cases it should actually be easier to apply these techniques because of the more benign temporal properties of the atmosphere at long wavelengths. This paper thus addresses the fundamental limits to wavefront sensing at submillimeter wavelengths, in order to determine how well a telescope surface can be measured in the submillimeter band. First several potential measurement approaches are discussed and compared. Next the theoretical accuracy of a fringe phase measurement in the submillimeter is discussed. It is concluded that with Mars as the source, wavefront sensing at the micron level should be achievable at submillimeter wavelengths in quite reasonable integration times.

wavefront sensing↗