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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↗

DOE OSTI2020

X-ray free-electron laser wavefront sensing using the fractional Talbot effect

Wavefront sensing at X-ray free-electron lasers is important for quantitatively understanding the fundamental properties of the laser, for aligning X-ray instruments and for conducting scientific experimental analysis. A fractional Talbot wavefront sensor has been developed. This wavefront sensor enables measurements over a wide range of energies, as is common on X-ray instruments, with simplified mechanical requirements and is compatible with the high average power pulses expected in upcoming X-ray free-electron laser upgrades. Single-shot measurements were performed at 500 eV, 1000 eV and 1500 eV at the Linac Coherent Light Source. These measurements were applied to study both mirror alignment and the effects of undulator tapering schemes on source properties. The beamline focal plane position was tracked to an uncertainty of 0.12 mm, and the source location for various undulator tapering schemes to an uncertainty of 1m, demonstrating excellent sensitivity. These findings pave the way to use the fractional Talbot wavefront sensor as a routine, robust and sensitive tool at X-ray free-electron lasers as well as other high-brightness X-ray sources.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Single-Grating Talbot Imaging for Wavefront Sensing and X-Ray Metrology

Single-grating Talbot imaging relies on high-spatial-resolution detectors to perform accurate measurements of X-ray beam wavefronts. The wavefront can be retrieved with a single image, and a typical measurement and data analysis can be performed in few seconds. These qualities make it an ideal tool for synchrotron beamline diagnostics and in-situ metrology. The wavefront measurement can be used both to obtain a phase contrast image of an object and to characterize an X-ray beam. In this work, we explore the concept in two cases: at-wavelength metrology of 2D parabolic beryllium lenses and a wavefront sensor using a diamond crystal beam splitter.

Grating Interferometry↗

DOE OSTI2021

Binary Amplitude Reflection Gratings for X-ray Shearing and Hartmann Wavefront Sensors

New, high-coherent-flux X-ray beamlines at synchrotron and free-electron laser light sources rely on wavefront sensors to achieve and maintain optimal alignment under dynamic operating conditions. This includes feedback to adaptive X-ray optics. We describe the design and modeling of a new class of binary-amplitude reflective gratings for shearing interferometry and Hartmann wavefront sensing. Compact arrays of deeply etched gratings illuminated at glancing incidence can withstand higher power densities than transmission membranes and can be designed to operate across a broad range of photon energies with a fixed grating-to-detector distance. Coherent wave-propagation is used to study the energy bandwidth of individual elements in an array and to set the design parameters. We observe that shearing operates well over a ±10% bandwidth, while Hartmann can be extended to ±30% or more, in our configuration. We apply this methodology to the design of a wavefront sensor for a soft X-ray beamline operating from 230 eV to 1400 eV and model shearing and Hartmann tests in the presence of varying wavefront aberration types and magnitudes.

47 OTHER INSTRUMENTATION↗

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↗

NASA NTRS2004

Phase Contrast Wavefront Sensing for Adaptive Optics

Most ground-based adaptive optics systems use one of a small number of wavefront sensor technologies, notably (for relatively high-order systems) the Shack-Hartmann sensor, which provides local measurements of the phase slope (first-derivative) at a number of regularly-spaced points across the telescope pupil. The curvature sensor, with response proportional to the second derivative of the phase, is also sometimes used, but has undesirable noise propagation properties during wavefront reconstruction as the number of actuators becomes large. It is interesting to consider the use for astronomical adaptive optics of the "phase contrast" technique, originally developed for microscopy by Zemike to allow convenient viewing of phase objects. In this technique, the wavefront sensor provides a direct measurement of the local value of phase in each sub-aperture of the pupil. This approach has some obvious disadvantages compared to Shack-Hartmann wavefront sensing, but has some less obvious but substantial advantages as well. Here we evaluate the relative merits in a practical ground-based adaptive optics system.

adaptive optics↗

NASA NTRS2012

A Phase-Shifting Zernike Wavefront Sensor for the Palomar P3K Adaptive Optics System

A phase-shifting Zernike wavefront sensor has distinct advantages over other types of wavefront sensors. Chief among them are: 1) improved sensitivity to low-order aberrations and 2) efficient use of photons (hence reduced sensitivity to photon noise). We are in the process of deploying a phase-shifting Zernike wavefront sensor to be used with the realtime adaptive optics system for Palomar. Here we present the current state of the Zernike wavefront sensor to be integrated into the high-order adaptive optics system at Mount Palomar's Hale Telescope.

adaptive optics↗

NASA NTRS2012

End-to-end Coronagraphic Modeling Including a Low-order Wavefront Sensor

To evaluate space-based coronagraphic techniques, end-to-end modeling is necessary to simulate realistic fields containing speckles caused by wavefront errors. Real systems will suffer from pointing errors and thermal and motioninduced mechanical stresses that introduce time-variable wavefront aberrations that can reduce the field contrast. A loworder wavefront sensor (LOWFS) is needed to measure these changes at a sufficiently high rate to maintain the contrast level during observations. We implement here a LOWFS and corresponding low-order wavefront control subsystem (LOWFCS) in end-to-end models of a space-based coronagraph. Our goal is to be able to accurately duplicate the effect of the LOWFS+LOWFCS without explicitly evaluating the end-to-end model at numerous time steps.

coronagraphs↗