Engineering topics

Dean, Bruce H.

Publications and source records attributed to Dean, Bruce H..

At least 19 records

NASA NTRS2015

Discrete Fourier Transform in a Complex Vector Space

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Dean, Bruce H.↗

NASA NTRS2013

System and method for phase retrieval for radio telescope and antenna control

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for radio phase retrieval. A system practicing the method gathers first data from radio waves associated with an object observed via a first aperture, gathers second data from radio waves associated with the object observed via an introduced second aperture associated with the first aperture, generates reduced noise data by incoherently subtracting the second data from the first data, and performs phase retrieval for the radio waves by modeling the reduced noise data using a single Fourier transform. The first and second apertures are at different positions, such as side by side. This approach can include determining a value Q which represents a ratio of wavelength times a focal ratio divided by pixel spacing. This information can be used to accurately measure and correct alignment errors or other optical system flaws in the apertures.

Dean, Bruce H.↗

NASA NTRS2012

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Dean, Bruce H.↗

NASA NTRS2012

Method for utilizing properties of the sinc(x) function for phase retrieval on nyquist-under-sampled data

Disclosed herein are systems, methods, and non-transitory computer-readable storage media for simulating propagation of an electromagnetic field, performing phase retrieval, or sampling a band-limited function. A system practicing the method generates transformed data using a discrete Fourier transform which samples a band-limited function f(x) without interpolating or modifying received data associated with the function f(x), wherein an interval between repeated copies in a periodic extension of the function f(x) obtained from the discrete Fourier transform is associated with a sampling ratio Q, defined as a ratio of a sampling frequency to a band-limited frequency, and wherein Q is assigned a value between 1 and 2 such that substantially no aliasing occurs in the transformed data, and retrieves a phase in the received data based on the transformed data, wherein the phase is used as feedback to an optical system.

Dean, Bruce H.↗

NASA NTRS2012

Variable Sampling Mapping

The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.

Smith, Jeffrey, S.↗

NASA NTRS2011

Hybrid architecture active wavefront sensing and control system, and method

According to various embodiments, provided herein is an optical system and method that can be configured to perform image analysis. The optical system can comprise a telescope assembly and one or more hybrid instruments. The one or more hybrid instruments can be configured to receive image data from the telescope assembly and perform a fine guidance operation and a wavefront sensing operation, simultaneously, on the image data received from the telescope assembly.

Feinberg, Lee D.↗

NASA NTRS2011

Sampling Theorem in Terms of the Bandwidth and Sampling Interval

An approach has been developed for interpolating non-uniformly sampled data, with applications in signal and image reconstruction. This innovation generalizes the Whittaker-Shannon sampling theorem by emphasizing two assumptions explicitly (definition of a band-limited function and construction by periodic extension). The Whittaker- Shannon sampling theorem is thus expressed in terms of two fundamental length scales that are derived from these assumptions. The result is more general than what is usually reported, and contains the Whittaker- Shannon form as a special case corresponding to Nyquist-sampled data. The approach also shows that the preferred basis set for interpolation is found by varying the frequency component of the basis functions in an optimal way.

Dean, Bruce H.↗

NASA NTRS2011

Optimal Padding for the Two-Dimensional Fast Fourier Transform

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

Dean, Bruce H.↗

NASA NTRS2010

ATLAST-9.2m: a Large-Aperture Deployable Space Telescope

We present results of a study of a deployable version of the Advanced Technology Large-Aperture Space Telescope (ATLAST), designed to operate in a Sun-Earth L2 orbit. The primary mirror of the segmented 9.2-meter aperture has 36 hexagonal 1.315 m (flat to flat) glass mirrors. The architecture and folding of the telescope is similar to JWST, allowing it to fit into the 6.5 m fairing of a modest upgrade to the Delta-IV Heavy version of the Evolved Expendable Launch Vehicle (EELV). We discuss the overall observatory design, optical design, instruments, stray light, wavefront sensing and control, pointing and thermal control, and in-space servicing options.

Oergerle, William↗

NASA NTRS2010

Coronagraphic Wavefront Control for the ATLAST-9.2m Telescope

The Advanced Technology for Large Aperture Space Telescope (ATLAST) concept was assessed as one of the NASA Astrophysics Strategic Mission Concepts (ASMC) studies. Herein we discuss the 9.2-meter diameter segmented aperture version and its wavefront sensing and control (WFSC) with regards to coronagraphic detection and spectroscopic characterization of exoplanets. The WFSC would consist of at least two levels of sensing and control: (i) an outer coarser level of sensing and control to phase and control the segments and secondary mirror in a manner similar to the James Webb Space Telescope but operating at higher temporal bandwidth, and (ii) an inner, coronagraphic instrument based, fine level of sensing and control for both amplitude and wavefront errors operating at higher temporal bandwidths. The outer loop would control rigid-body actuators on the primary and secondary mirrors while the inner loop would control one or more segmented deformable mirror to suppress the starlight within the coronagraphic field-of view. Herein we discuss the visible nulling coronagraph (VNC) and the requirements it levies on wavefront sensing and control and show the results of closed-loop simulations to assess performance and evaluate the trade space of system level stability versus control bandwidth.

Lyon, RIchard G.↗

NASA NTRS2009

Hybrid diversity method utilizing adaptive diversity function for recovering unknown aberrations in an optical system

A method of recovering unknown aberrations in an optical system includes collecting intensity data produced by the optical system, generating an initial estimate of a phase of the optical system, iteratively performing a phase retrieval on the intensity data to generate a phase estimate using an initial diversity function corresponding to the intensity data, generating a phase map from the phase retrieval phase estimate, decomposing the phase map to generate a decomposition vector, generating an updated diversity function by combining the initial diversity function with the decomposition vector, generating an updated estimate of the phase of the optical system by removing the initial diversity function from the phase map. The method may further include repeating the process beginning with iteratively performing a phase retrieval on the intensity data using the updated estimate of the phase of the optical system in place of the initial estimate of the phase of the optical system, and using the updated diversity function in place of the initial diversity function, until a predetermined convergence is achieved.

Dean, Bruce H.↗

NASA NTRS2009

Discrete Fourier Transform Analysis in a Complex Vector Space

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Dean, Bruce H.↗

NASA NTRS2008

Wavefront Sensing with the Fine Guidance Sensor for James Webb Space Telescope

An analysis is presented that utilizes the Fine Guidance Sensor (FGS) for focal-plane wavefront sensing (WFS) for the James Webb Space Telescope (JWST). WFS with FGS increases the number of wavefront measurements taken in field of the telescope, but has many challenges over the other JWST instruments that make it unique, such as; less sampling of the Point Spread Function (PSF), a smaller diversity-defocus range, a smaller image detector size, and a polychromatic object or source. Additionally, presented is an analysis of sampling for wavefront sensing. Results are shown based on simulations of flight and the cryogenic optical testing at NASA Johnson Space Center.

Smith, J. Scott↗

NASA NTRS2007

Wavefront Control Toolbox for James Webb Space Telescope Testbed

We have developed a Matlab toolbox for wavefront control of optical systems. We have applied this toolbox to the optical models of James Webb Space Telescope (JWST) in general and to the JWST Testbed Telescope (TBT) in particular, implementing both unconstrained and constrained wavefront optimization to correct for possible misalignments present on the segmented primary mirror or the monolithic secondary mirror. The optical models implemented in Zemax optical design program and information is exchanged between Matlab and Zemax via the Dynamic Data Exchange (DDE) interface. The model configuration is managed using the XML protocol. The optimization algorithm uses influence functions for each adjustable degree of freedom of the optical mode. The iterative and non-iterative algorithms have been developed to converge to a local minimum of the root-mean-square (rms) of wavefront error using singular value decomposition technique of the control matrix of influence functions. The toolkit is highly modular and allows the user to choose control strategies for the degrees of freedom to be adjusted on a given iteration and wavefront convergence criterion. As the influence functions are nonlinear over the control parameter space, the toolkit also allows for trade-offs between frequency of updating the local influence functions and execution speed. The functionality of the toolbox and the validity of the underlying algorithms have been verified through extensive simulations.

Shiri, Ron↗

NASA NTRS2007

Zernike-like Orthogonal Basis Functions for Wavefront Characterization over Sampled, Irregular Apertures

For optical systems with circular apertures, wavefronts are often analyzed using Zernike polynomials, and individual Zernike functions are associated with familiar optical aberrations. For systems with noncircular apertures, or in practical situations in which wavefronts are measured at a limited number of points in the aperture, the Zernike polynomials are no longer an orthogonal basis for the measured data. Although there are an endless number of ways to create a basis for such measured data, a "Zernike-like" basis is useful to connect with our experience with the usual optical aberrations. In this paper, the steps required to identify a Zernike-like basis for wavefronts over sampled, irregular apertures are presented, based on the Gram-Schmidt orthogonalization technique. The benefits of analyzing optical wavefronts using an orthogonal basis specific to an optical system's aperture shape and wavefront sampling, instead of using the traditional Zernike polynomials, are detailed in two examples, from image-based wavefront sensing on a segmented-aperture telescope (the James Webb Space Telescope Testbed Telescope at Ball Aerospace) and from interferometer characterization for surface metrology of a hexagonal mirror segment.

Aronstein, David L.↗

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

Broadband Phase Retrieval for Image-Based Wavefront Sensing

A focus-diverse phase-retrieval algorithm has been shown to perform adequately for the purpose of image-based wavefront sensing when (1) broadband light (typically spanning the visible spectrum) is used in forming the images by use of an optical system under test and (2) the assumption of monochromaticity is applied to the broadband image data. Heretofore, it had been assumed that in order to obtain adequate performance, it is necessary to use narrowband or monochromatic light. Some background information, including definitions of terms and a brief description of pertinent aspects of image-based phase retrieval, is prerequisite to a meaningful summary of the present development. Phase retrieval is a general term used in optics to denote estimation of optical imperfections or aberrations of an optical system under test. The term image-based wavefront sensing refers to a general class of algorithms that recover optical phase information, and phase-retrieval algorithms constitute a subset of this class. In phase retrieval, one utilizes the measured response of the optical system under test to produce a phase estimate. The optical response of the system is defined as the image of a point-source object, which could be a star or a laboratory point source. The phase-retrieval problem is characterized as image-based in the sense that a charge-coupled-device camera, preferably of scientific imaging quality, is used to collect image data where the optical system would normally form an image. In a variant of phase retrieval, denoted phase-diverse phase retrieval [which can include focus-diverse phase retrieval (in which various defocus planes are used)], an additional known aberration (or an equivalent diversity function) is superimposed as an aid in estimating unknown aberrations by use of an image-based wavefront-sensing algorithm. Image-based phase-retrieval differs from such other wavefront-sensing methods, such as interferometry, shearing interferometry, curvature wavefront sensing, and Shack-Hartmann sensing, all of which entail disadvantages in comparison with image-based methods. The main disadvantages of these non-image based methods are complexity of test equipment and the need for a wavefront reference.

Dean, Bruce H.↗

NASA NTRS2007

Iterative-Transform Phase Retrieval Using Adaptive Diversity

A phase-diverse iterative-transform phase-retrieval algorithm enables high spatial-frequency, high-dynamic-range, image-based wavefront sensing. [The terms phase-diverse, phase retrieval, image-based, and wavefront sensing are defined in the first of the two immediately preceding articles, Broadband Phase Retrieval for Image-Based Wavefront Sensing (GSC-14899-1).] As described below, no prior phase-retrieval algorithm has offered both high dynamic range and the capability to recover high spatial-frequency components. Each of the previously developed image-based phase-retrieval techniques can be classified into one of two categories: iterative transform or parametric. Among the modifications of the original iterative-transform approach has been the introduction of a defocus diversity function (also defined in the cited companion article). Modifications of the original parametric approach have included minimizing alternative objective functions as well as implementing a variety of nonlinear optimization methods. The iterative-transform approach offers the advantage of ability to recover low, middle, and high spatial frequencies, but has disadvantage of having a limited dynamic range to one wavelength or less. In contrast, parametric phase retrieval offers the advantage of high dynamic range, but is poorly suited for recovering higher spatial frequency aberrations. The present phase-diverse iterative transform phase-retrieval algorithm offers both the high-spatial-frequency capability of the iterative-transform approach and the high dynamic range of parametric phase-recovery techniques. In implementation, this is a focus-diverse iterative-transform phaseretrieval algorithm that incorporates an adaptive diversity function, which makes it possible to avoid phase unwrapping while preserving high-spatial-frequency recovery. The algorithm includes an inner and an outer loop (see figure). An initial estimate of phase is used to start the algorithm on the inner loop, wherein multiple intensity images are processed, each using a different defocus value. The processing is done by an iterative-transform method, yielding individual phase estimates corresponding to each image of the defocus-diversity data set. These individual phase estimates are combined in a weighted average to form a new phase estimate, which serves as the initial phase estimate for either the next iteration of the iterative-transform method or, if the maximum number of iterations has been reached, for the next several steps, which constitute the outerloop portion of the algorithm. The details of the next several steps must be omitted here for the sake of brevity. The overall effect of these steps is to adaptively update the diversity defocus values according to recovery of global defocus in the phase estimate. Aberration recovery varies with differing amounts as the amount of diversity defocus is updated in each image; thus, feedback is incorporated into the recovery process. This process is iterated until the global defocus error is driven to zero during the recovery process. The amplitude of aberration may far exceed one wavelength after completion of the inner-loop portion of the algorithm, and the classical iterative transform method does not, by itself, enable recovery of multi-wavelength aberrations. Hence, in the absence of a means of off-loading the multi-wavelength portion of the aberration, the algorithm would produce a wrapped phase map. However, a special aberration-fitting procedure can be applied to the wrapped phase data to transfer at least some portion of the multi-wavelength aberration to the diversity function, wherein the data are treated as known phase values. In this way, a multiwavelength aberration can be recovered incrementally by successively applying the aberration-fitting procedure to intermediate wrapped phase maps. During recovery, as more of the aberration is transferred to the diversity function following successive iterations around the ter loop, the estimated phase ceases to wrap in places where the aberration values become incorporated as part of the diversity function. As a result, as the aberration content is transferred to the diversity function, the phase estimate resembles that of a reference flat.

Dean, Bruce H.↗