bluuebunny/crossref_metadata_2025 huggingface dataset:
Soft X-Ray Images of the Solar Corona With a Normal-Incidence Cassegrain Multilayer Telescope
Authors: Walker A.B.C. , Barbee T.W. , Hoover R.B. , Lindblom J. F.
Published: February 2023

High resolution images of the sun in the soft x-ray/extreme ultraviolet (XUV) regime have been obtainec with normal-incidence Cassegrain multilayer telescopes for the first time. The inherent energy selective property of multilayer-coated optics allowed distinct groups of emission lines to be isolated in the solar corona and the transition region. The sounding rocket borne soft x-ray telescopes [1] were launched on October 23, 1987. In addition to the Cassegrain telescopes, which provided images in bands centered at 173 Å and 256 Å, the payload contained concave spherical mirror multilayer telescopes operating at 44 Å and 256 Å, and convex multilayer mirrors which magnified and spectroscopically analyzed the image produced by a grazing-incidence primary mirror. The images obtained with the Cassegrain telescope operated in the bandpass centered at 173 Å, which is dominated by emission from the ions Fe IX and Fe X, are presented here. This emission is from coronal plasma in the temperature range 0.8 x 106 to 1.3 x 106 K. The images have angular resolution of ~1.0 to 1.5 arc seconds, and show no degradation due to x-ray scattering. Many features of coronal structure, including magnetically confined loops of hot plasma, coronal plumes, polar coronal holes, faint structures on the size scale of supergranulation and smaller, and features due to overlying cool prominences are visible in the images. The density structure of polar plumes has been derived from the observations. The images were recorded on a new type of XUV sensitive film. Our 64 second exposure of the sun in the bandpass 171 - 175 Å is shown below.
An Array of Large Deployable Reflectors on the Moon
Authors: Scholl Marija S. , Breckinridge James B. , Scholl James W.
Published: February 2023

Exploration of planets both inside and outside the Solar System requires continued improvements in optical systems used to collect the light from the planet. Recently, the large deployable reflector1 (LDR) has been proposed as a novel telescope for infrared exploration. Thus, it is particularly suitable for the search for planets outside the Solar System or for more detailed remote exploration of the planets inside the Solar System. Infrared astronomy is more appropriately performed in space because the atmosphere attenuates IR radiation. The Space Station has been considered a suitable site for a single telescope. However, for an array of telescopes, a lunar site is preferable; it offers a rigid base, required either for interferometry or for phasing of individual telescopes.
On-Orbit Performance of the HST Optical Telescope Assembly
Authors: Facey T. A. , Krim M. H. , Ftaclas C. , Cernoch L. J. , Ruthven G. P. , Stoll R.
Published: February 2023

In evaluating the performance of the Hubble Space Telescope, much attention has been directed to the source of spherical aberration in the primary mirror and its impact on mission performance. However, other characteristics of both the primary and secondary mirrors, such as other low-order Zemike aberrations, mid-spatial frequency ripple, and micro-roughness merit examination since they too are crucial to image quality and straylight performance. Performance predictions using ground metrology data agree with an assessment of the on-orbit image quality based on phase retrieval results using Wide Field/Planetary Camera (WF/PC) and Faint Object Camera (FOC) images together with Wavefront Sensor (WFS) and Fine Guidance Sensor (FGS) data.
HST Aberrations and Alignment Determined by Phase Retrieval Algorithms
Authors: Fienup J.R.
Published: February 2023

It is important to determine very precisely the aberrations of the Hubble Space Telescope (HST) in order to (1) design correction optics to be included in replacement instruments, (2) align the secondary mirror of the HST’s Optical Telescope Assembly (OTA) and (3) form an analytic model of the system point-spread function (PSF) that can be used for image deblurring until the telescope is repaired.
Least Squares Image Inversion Applied to WF/PC II
Authors: Shao M.
Published: February 2023

Ours is one of several teams that independently worked on image inversion of HST wf/pc pictures to determine the spherical aberration error on the HST primary. The technique we chose to persue was based on a non-linear least squares solution for zeroike coefîcients of the aberrations of the optics. The code for modeling the optical system evolved from a relatively simple single Fourier tranform of the exit pupil to a complete multiplane diffraction propagation model with telescope jitter included.
Theoretical Analysis of Two Off-Axis Parabolic Mirrors for Solar Physics Applications
Authors: Saha Timo T. , Leviton Douglas B.
Published: February 2023

The SUMER - Solar Ultraviolet Measurements of Emitted Radiation - instrument will be flown on the SOHO mission. The instrument will study the upper atmosphere of the sun in the 600 Å -1600 Å wavelength region. The SUMER instrument consists of an off-axis paraboloid followed by a slit, off-axis collimating paraboloid, scan mirror, grating, and a detector. The design parameters for the rectangular SUMER telescope mirror are listed in Table I.
Hubble Space Telescope Prescription Retrieval
Authors: Redding D. , Dumont P. , Yu J.
Published: February 2023

Image inversion is a technique whereby computer-generated images based on an optical system model are compared with images from the real system in a nonlinear least squares estimation procedure. The differences are used to change model parameters until the model-based images match the actual images. Image inversion can be used with a simple exit-pupil optical model, using a single Fourier transform to generate point-source images. This “phase retrieval” approach is effective for determining overall wavefront aberrations, but not for directly determining individual optical element alignments or surface aberrations.
Aspheric Mirror Metrology for the HST Reflective Correctors
Authors: Kumler James J. , Gunnarsson Gunnar H. , Hull-Allen C. Gregory
Published: February 2023

With the advent of advanced, automated fabrication techniques, the limiting factor in the production of complex aspheric space optics is increasing the ability to accurately measure and characterize optical surface parameters. In addition to increased accuracy, the metrology is required to keep pace with the shorter fabrication cycles of advanced figuring techniques such as computer-controlled polishing. As a result, there is an emphasis on:

1) Integrated testing approaches. Instruments such as interferometers must be interfaced with the polishing machine and the performance prediction software in order to minimize the time required to perform a full metrology cycle.

2) Redundancy in testing. Each surface parameter is measured in two independent, complementary test methods using unique test equipment. This minimizes the risk of systematic errors and reduces measurement uncertainty.

3) Overlapping measurement bandwidths. Test methods used to evaluate the surface errors are selected to ensure all spatial periods are adequately sampled and a complete characterization of the mirror surface is obtained.
Vacuum ultraviolet performance of an off-axis parabolic mirror: evaluation, metrology, and analysis
Authors: Leviton Douglas B. , Saha Timo T. , Wright Geraldine A. , Keski-Kuha Ritva , Boucarut Rene A.
Published: February 2023

The normal incidence, off-axis parabolic, SERTS-D telescope mirror is an alternative technology to the glancing incidence Wolter Type II SERTS-A and -C rocket telescopes flown previously. The image quality and scattered light performance of this mirror uncoated have been measured at 124 nm in the GSFC Diffraction Grating Evaluation Facility (DGEF)1 using image dissection techniques. The results are compared with those from an analytical model of the experiment3 based on interferometry and optical surface profilometry.
Space Infrared Telescope Facility
Authors: Norris David , Bothwell Mary , Plamondon Joseph
Published: February 2023

The Space Infrared Telescope Facility (SIRTF) is the fourth and last Great Observatory of the NASA Astrophysics Program. The challenges in providing this Observatory range from new cryogenic optical and sensing technology to operating in a fixed price research environment.
USNO/RL Optical Interferometer Project
Authors: Johnson Kenneth J.
Published: February 2023

The U.S. Naval Research Laboratory and U.S. Naval Observatory are engaged in fabricating optical interferometers for imaging and astrometry. This presentation will summarize the progress in these programs accomplished to date.
Correction of Complex Figure Errors on Mirror Surfaces by Ion Figuring
Authors: Keim Robert E.
Published: February 2023

Until recently the correction of surface figure errors on optical surfaces (lenses, mirrors) by the use of inert ion beams has been limited to small area optics with relatively minor error profiles. Two techniques have been documented; the use of masks to define the removal pattern generated with the use of a large area ion beam and the use of scanning motions applied to small size ion beams. For the former operation, the masks may be rotated (1) to correct axisymmetric errors or remain stationery to provide discrete area removal. (The use of successive masks of various shapes produces an integrated pattern of any configuration.)
Silicon Carbide Telescope Mirrors
Authors: Arnold J. F. , Laughlin M. J.
Published: February 2023

The increasing demand for "exotic" telescope mirrors for space applications has prompted the examination of alternate materials and fabrication approaches. These mirrors must not only have the finely finished, precise, and stable optical surfaces generally characteristic of telescope mirrors, but they must also possess high stiffness and natural frequency and low mass or areal density. A highly efficient substrate structure is, therefore, an implicit requirement. Traditionally, mirrors have been made from glassy materials that are easily figured and polished, are thermally stable, have poor structural properties and are not amenable to fabrication into efficient structural configurations. Clearly, improved material properties and structural configurations could both reduce the mass and improve the structural characteristics of mirror substrates. A unique precision forming process developed by United Technologies Optical Systems can produce precise, complex, thin-section, monolithic formations of silicon carbide (SiC) that combine excellent material properties and highly efficient structural characteristics and offers the potential to achieve the lightweight, high performance telescope mirrors required for space. An example of this technology is shown by the inset photograph.
Optical Systems for Polarization Remote Sensing from Satellites
Authors: Egan Walter G.
Published: February 2023

Polarization remote sensing provides significant optical information not available from photometry, but system optical and data handling becomes exacting, particularly when multi-wavelength requirements are imposed.
Optical Design of a Zero Power Corrector for HST Simulators
Authors: Davila Pam , Hannan Paul G.
Published: February 2023

Images from the Hubble Space Telescope (HST) suffer from overcorrected spherical aberration1. The optical designs of the second generation instruments, such as the Wide Field/Planetary Camera (WFPC-2), the Space Telescope Imaging Spectrograph (STIS), and the Near Infrared Camera (NIC), are being modified to correct or compensate the spherical aberration of the HST.
The Role of Abrasion in the Optical Polishing of Metals and Glass
Authors: Brown Norman J. , Cook Lee M.
Published: February 2023

Reviews an abrasive technique for polishing diamond turned optics, a mathematical theory to provide necessary quantified information, and attempts to bridge from metal to glass.
Two-dimensional Reconstructions from One-dimensional Data by Maximum Entropy
Authors: Sibisi Sibusiso
Published: February 2023

The Maximum Entropy Method (MEM) is a powerful information-theoretic approach to the inversion of many types of data in science and engineering. It has been used for reconstructing positive images in such areas as radio astronomy [1,2], medical tomography [3], plasma diagnostics [4] and crystallography [5]. Practical data are always corrupted by noise and are usually incomplete: for example, there may be missing projections or missing Fourier components. Also the instrumental response function may be incompletely known [6]. These factors can lead to severely ill-posed inversion problems.
A Phase-retrieval Technique in Pupil Synthesis
Authors: Kiedron Piotr
Published: February 2023

The pupil function of an incoherent system is not defined uniquely by the incoherent transfer function [1]. This fact creates a phase-retrieval problem when the aberration function has to be determined from an intensity measurement. The phase and amplitude of the pupil function can be found from the point spread function only if additional information about the optical system is available. The information has a mathematical character if some constraints upon the class of admissible solutions are imposed. (See [2] and [3] where the class of phase functions is reduced to finite polynomials.) Another method assuring the uniqueness of the solution requires additional information of physical characteristics. (See [4], [5], [6], and [7] where the second measurement is postulated.)
Reconstruction in Electron Microscopy
Authors: Saxton W. O.
Published: February 2023

Summary not available
Partial Shape Recognition using Fourier-Mellin Transform Methods
Authors: Grogan Timothy A. , Mitchell O. Robert
Published: February 2023

In recognizing shapes automatically by computer, a problem often arises when the unknown object is partially obscured or poorly segmented. Most algorithms described in the literature use syntactic methods. A major problem is describing a proper grammar for several objects. This problem is even further complicated when each object may be imaged from many possible aspect angles. The algorithm in this paper avoids this problem. It uses a global method to normalize scale and starting point, even when part of the contour is missing or incorrect.
Phase Retrieval from Intensity Data degraded by Shot-Noise
Authors: Slump C.H. , Ferwerda H.A.
Published: February 2023

In the paper by one of us (H.A.F.) [1], the phase problem was reviewed for circumstances under which the stochastic character of the image could be ignored. A statistical description becomes imperative for images obtained under low-intensity illumination as occurs e.g. in low-dose electron microscopy. Under these circumstances the images are heavily degraded by shot-noise. Often(e.g. [2,3])images are described as a signal plus signal-independent noise. Such a treatment does not apply to shot-noise, the quanta arriving in non-overlapping image cells are statistically independent Poisson-distributed random variables [4]. The variances of the data-counts also contain information about the signal. In this contribution we discuss the retrieval of the object wave function (w.f.) from shot-noise degraded images. Due to the stochastic imaging process, the reconstructed object w.f. is also stochastic. The purpose of this contribution is to establish the statistical characterization of the object w.f. We assume axial coherent quasi-monochromatic illumination. The analysis is presented for one lateral dimension only, the extension to two dimensions is obvious.
Phase Retrieval for Functions with Sufficiently Disconnected Support
Authors: Crimmins T.R. , Fienup J.R.
Published: February 2023

The problem of phase retrieval is to reconstruct a function, f(x),from the modulus, |F(u)|, of its Fourier transform, This is equivalent to reconstructing the phase of F(u) from |F(u)| or to reconstructing f(x) from its autocorrelation function, which is given by the in verse Fourier transform of |F(u)|2. This problem arises in many fields, including astronomy, x-ray crystallography, wavefront sensing, pupil function determination, electron microscopy, and particle scattering. In this paper the function, f, is assumed to be a square-integrable, one-dimensional, complex-valued function. If f has disconnected compact support contained in the union of a sequence of intervals satisfying a certain separation condition, then it can be shown that f is almost always essentially the only solution with support contained in the union of those intervals. This holds no matter how many non-real zeroes F has.
Phase Retrieval in Astronomy
Authors: Fienup J.R.
Published: February 2023

Atmospheric turbulence severely limits the resolution of images from large earth-bound optical telescopes to about one second of arc or worse, as compared with the theoretical diffraction-limited resolution of 0.02 seconds of arc for a 5-meter diameter telescope.
Frequency Sampling of the Short-Time Fourier Transform Magnitude*
Authors: Quatieri Thomas F. , Nawab S. Hamid , Lim Jae S.
Published: February 2023

Under mild restrictions, a sequence x(n) is uniquely specified by its short-time Fourier transform magnitude at one or two frequencies for each n.
On an iterative algorithm for stabilised object restoration from limited spectral data
Authors: Abbiss J. B. , De Mol C. , Dhadwal H. S.
Published: February 2023

We analyse the problem of object restoration in the presence of noise, when the coherent image is formed by a space-invariant system consisting of a one-dimensional clear pupil extending over (−Ω, Ω). If the object distribution f(x) lies between −X and +X, the noiseless image
g¯(y) formed by such a system would be given by the equation (1) In Fourier space, the solution to this equation is equivalent to infinite extrapolation of the truncated spectrum.
A Novel Hankel Approximation Method for Arma Pole-Zero Estimation from Noisy Covariance Data*
Authors: Kung S.Y. , Arun K.S.
Published: February 2023

Model based methods have been gaining popularity in high resolution spectral estimation, and have recently demonstrated a great deal of success. Such methods allow us to parameterize the spectrum in terms of a relatively small number of unknown parameters, and thus reduce the spectral estimation problem to that of first, selecting the appropriate model, and second, estimating its parameters. The most popular models used today, are

1) Autoregressive model (AR),

2) Sinusoids plus noise model (S+N) and

3) Autoregressive moving average model (ARMA)
Four Models for the Band-Limited Signal Extrapolation Problem
Authors: Huang Thomas S. , Sanz Jorge L. C.
Published: February 2023

In refs. 2, 4, and 5, two algorithms for solving the continuous band-limited extrapolation problem were developed. However, in practical implementation of these algorithms, discretization is unavoidable. The relationships between the discrete and the continuous algorithms have never been adequately clarified in the literature. In the present paper, we attempt to shed some light on this question.
Some Signal Processing Issues in Radar Target Identification
Authors: Miller E. K.
Published: February 2023

When an object (target) is illuminated by an electromagnetic field, the energy it scatters to a given observation point depends upon its geometry and material characteristics, the conditions of illumination (angle of incidence, polarization, frequency(ies), etc.) and the medium through which the field propagates. It is intuitively obvious, and demonstrated by analysis and measurement, that the scattered field (which will also contain, in general, interference and/or noise energy) has impressed or encoded on it information about the target which might somehow be extracted for purposes of: 1) detection (i.e., is there a target?); 2) classification (determine whether the target belongs to a class of interest); 3) recognition (if in the class of interest, which one of that class is it?) and 4) imaging or inversion (reconstruct the target's geometry and/or material properties).*
Iterative Image Restoration From Data Available In Multiple Restricted Regions
Authors: Yamakoshi Yoshiki , Sato Takuso
Published: February 2023

Restoration of the original image from data available in restricted regions has been the subject of many studies in the field of optical, X-ray and acoustical imagings. Several concrete means for extrapolating of the observed data beyond the observed region have been proposed.1-5 Among them, iterative means for the image restoration is considered as one of the most effective methods, because of its stability even under faily noisy observed data.
ILL-Posedness and Precision in Object Field Reconstruction Problems
Authors: Root William L.
Published: February 2023

We suppose σ(x), called the object field, is an unknown real or
complex-valued function on a set E. Our knowledge of σ is given by
observation, with some (small) error, of a real or complex-valued
function s(ξ) given by

s(ξ)=[Bσ](ξ)=∫
E
b(ξ,x)σ(x)dx,     σ ε F

The sets E,F are subsets of Rn,
where normally n=1,2,3. It is desired to determine σ(x) as well as
possible; the result of this determination is denoted
σ^(x)
(in ideal circumstances σ^(x)=σ(x))
and is called an estimate of σ (the word estimate may or may not have
a statistical implication). An inversion problem is determined when
the following are specified: (1) the kernel b(ξ,x) of the integral
operator; (2) the region E on which σ(x) is defined; (3) the region F
over which the observation is made; (4) the set ∑ of functions σ that
are allowed. It is assumed that the situation is such that σ ε
L2 (E) (the space of square-integrable functions on E) and
s ε L2 (F). If ∑ is all of L2 (E), the problem
is an unconstrained linear inversion; if ∑ is not all of L2
(E) (∑ may be linear or nonlinear) it is a constrained linear
inversion.
Reconstruction of Multidimensional Signals from Zero Crossings*
Authors: Curtis Susan R. , Oppenheim Alan V.
Published: February 2023

We present theoretical and experimental results showing that it is possible to reconstruct a broad class of multidimensional signals from only zero crossing information.
A Cellular Automata Method for Phase Unwrapping
Authors: Ghiglia Dennis C. , Mastin Gary A.
Published: February 2023

Cellular automata are simple, discrete mathematical systems that can exhibit complex behavior resulting from collective effects of a large number of cells, each of which evolve in discrete time steps according to rather simple local neighborhood rules.
Computational vision as inverse optics: reconstructing spectral reflectances and illuminant
Authors: Poggio T. , Hurlbert A.
Published: February 2023

The standard definition of computational vision is that it is inverse optics. The direct problem - the problem of classical optics - or computer graphics - is to determine the images of three-dimensional objects. Computational vision is confronted with the inverse and ill-posed problems of recovering surface properties from the partial information contained in images. As a consequence, vision must rely on natural constraints, that is, general assumptions about the physical world to derive an ambiguous output.
Cramer-Rao Lower Bound for Fourier Modulus Wavefront Sensor
Authors: Cederquist J.N. , Robinson S.R. , Kryskowski D. , Fienup J.R. , Wackerman C.C.
Published: February 2023

A wavefront sensor receives the field from an object after it has acquired a phase aberration due to atmospheric turbulence. The Fourier modulus wavefront sensor operates by using a lens or mirror to Fourier transform the field in the sensor aperture to a measurement plane where the modulus squared (intensity) of the Fourier transform is detected. Motivation to study this sensor is given by the success of several iterative Fourier transform algorithms in making phase estimates from measured data of this type [1,2]. It is also known that, in most cases of practical interest, the atmospheric phase is uniquely related to Fourier (focal) plane intensity measurements [3].
A New Algorithm for Closed Form Image Reconstruction from Fourier Transform Magnitude1
Authors: Izraelevitz D. , Lim J. S.
Published: February 2023

Signal reconstruction from Fourier transform magnitude (FTM) has been the topic of much interest in the literature [1,2,3,4]. It has been recently shown that if the support of the image is known, then most images can be reconstructed from knowledge of only its FTM modulo a rotation by 180 degrees and a sign change [2].
Reconstruction of continuous object distributions from Fourier magnitude
Authors: Byrne C.L. , Fiddy M.A.
Published: February 2023

The phase retrieval from Fourier magnitude problem has traditionally been considered from the viewpoint of the analytic properties of Fourier transforms of finite support object distributions, [1]. It is well known that intrinsic phase ambiguities arise if the product representation of the Fourier transform has one or more non-self conjugate factors. In one dimension there can be an infinity of such factors but in two or more the exact number is difficult to ascertain. Recently there has been a trend towards considering object distributions comprising a set of discrete points,[2]. For several applications, e.g. astronomy, this is not unreasonable. This model has the great advantage that one can adopt a discrete Fourier transform representation for the Fourier data or, equivalently, a z-transform representation leading to a finite degree polynomial model. Such a model can be generally assumed to lead to a unique relationship between Fourier magnitude and phase [3] and has given confidence to the use of iterative methods which had been observed to succeed in the recovering Fourier phase from magnitude or vice-versa,[4].
Sufficient Support Information to Ensure a Unique Solution to the Phase Problem
Authors: Brames B.J.
Published: February 2023

It is evident that the support of a function can have a strong influence upon one’s ability to uniquely reconstruct that function from its autocorrelation, both in terms of solution multiplicity, and in the convergence of certain reconstruction algorithms. Greenaway [1] first demonstrated that the number of solutions to the one—dimensional phase problem is reduced if an internal region of the function in question is known to be zero. This is a strong statement, because generally the one-dimensional phase problem is intractable due to large numbers of non-equivalent solutions. More recently Sault [2] has shown that one can always ensure solution uniqueness for discrete functions if the internal zero region is specified and somewhat more complex.
Phase Retrieval for Discrete Functions with Support Constraints: Summary
Authors: Crimmins Thomas R.
Published: February 2023

The phase retrieval problem, i.e., the problem of reconstructing a function from its Fourier modulus or, equivalently, from its autocorrelation function, arises in many fields, e.g., astronomy, wave-front sensing, X-ray crystallography, electron microscopy, particle scattering and pupil-function determination. Here we consider the case in which the object function is assumed to be defined on a two-dimensional discrete grid of sample points.
Reconstruction of Axisymmetric Objects from One Silhouette
Authors: Van Hove Patrick
Published: February 2023

Silhouettes of opaque convex objects in orthographic projections were studied in an earlier paper, using a representation on the Gaussian Sphere [1]. A similar argument is applied here to solve for the direct and inverse relations between axisymmetric objects and their silhouettes. Furthermore, a new method for determining object orientation in three dimensions is proposed for such objects, using our analysis of silhouette curvature [1]. Axisymmetric objects are completely determined by a section through their axis of symmetry, which we refer to as the object generator; their silhouettes are symmetric curves in the projection plane. The projection of the object into its silhouette reduces to a transformation between the object generator and the silhouette, which are both planar curves. This paper investigates the conditions under which inversion of this transformation is possible; see Fig. 1. Two cases arise, depending on whether or not the tilt is known between the axis of the object and the projection plane. The derivations summarized here apply to a large class of axisymmetric objects, including non-convex objects. The presentation will be accompanied by a large number of computer generated examples which illustrate various aspects of the theories we developed.
Reconstructing a Vector Current Distribution from its Magnetic Field Using Linear Estimation Theory
Authors: Smith Warren E. , Dallas William J. , Schlitt Heidi A. , Kullmann Walter
Published: February 2023

Several methods currently exist for exploring the three-dimensional structure of the organs of the human body. They include x-ray computed tomography (CT),1 magnetic resonance imaging (MRI),2 and emission computed tomography (ECT).3,4 These techniques provide spatial information about an organ's attenuation coefficient, proton density, or the ability of the organ to take up a radioactive pharmaceutical, respectively.
A New Technique for Constrained Image Restoration by Compensating the PSF
Authors: Malaret Erick , McGillem Clare D.
Published: February 2023

The idea behind the method of constrained image restoration by compensating the point spread function (PSF) is to obtain a restoration filter such that when it is convolved with the PSF the resulting function, called the composite point spread function (CPSF), satisfies appropriate optimization criteria. Ideally it would be desirable to obtain a CPSF that is a delta function; i.e., the restoration filter would be the inverse filter. However this is not possible due to the instability and serious noise amplification of such filters. Stable filters using this approach can be obtained by minimizing an appropriate width measure while constraining the output noise power [1-3]. There are significant advantages in using this method for image (or signal) restoration over other commonly employed procedures. First, the restoration operator can be constrained to a specific size, thereby controlling the duration of transients due to edge effects and reducing the computational burden. Second, the procedure is not dependent on statistics of the image but only on the sensor PSF, the noise, and the sampling grid. Third, for image enhancement it is possible to combine the interpolation and deconvolution procedures into a single operation, thereby increasing the speed and efficiency of the processing.
Numerical Investigation of Phase Retrieval Uniqueness
Authors: Seldin J.H. , Fienup J.R.
Published: February 2023

The uniqueness of phase retrieval has been explored from a theoretical standpoint via the factorability of polynomials. The Fourier transform of a function (an image), f, sampled on a regular grid is a polynomial, F. Bruck and Sodin [1] have shown that if f can be written as the convolution of K non-Hermitian functions (equivalent to K irreducible polynomial factors in Fourier space), then there exist 2K-1 ambiguous solutions to the phase retrieval problem of reconstructing f from IFI. It is well known for the two-dimensional case that polynomials of two complex variables have probability zero of being factorable [1-3]. It has also been shown from a theoretical standpoint that the uniqueness condition is not sensitive to noise [4]. However, this does not answer the practical question: what is the likelihood of significant ambiguity when IFI is corrupted by a given level of noise? We approached this question by trying to determine, given an arbitrary image and its Fourier polynomial, how close is the nearest factorable polynomial, and does it have an ambiguous solution that is significantly different from the given polynomial? This paper explores this question for the case of images defined within a 3x2 support. A derivation of object-domain conditions for factorability provides a means for finding nearest factorable polynomials through a constrained minimization search over the space of 3x2 ambiguous images. These searches are implemented with different object-domain constraints in a Monte Carlo simulation to estimate the probability that the nearest factorable polynomial, with an ambiguous solution that is significantly different from a given image, is within some distance of the given polynomial.
Object reconstruction from experimental far-field data using phase retrieval algorithms
Authors: Nieto-Vesperinas M. , Pérez-Ilzarbe M.J. , Navarro R.
Published: February 2023

Recently a Simulated Annealing (S.A.) algorithm has been put forward [1] for phase retrieval from the power spectrum of a real and positive object. This method has been succesfully used in computer simulations, of object reconstruction, with different signal to noise ratios [2] and also of photon-limited stellar speckle interferometry [3]. The algorithm is flexible and permits an easy introduction of additional constraints. Its performance is uniformly high. However, it requires a rather lengthy computing time. In some cases, it can be accelerated by using first the hybrid input-output version of the iterative Fourier trasform (I.F.T.) algorithm [4-6].
Coherent Image Synthesis from Wavefront-Slope Measurements of a Nonimaged Laser-Speckle Field
Authors: Idell Paul S. , Gonglewski John D.
Published: February 2023

We demonstrate that images of coherently illuminated objects can be formed from measurements of the wavefront slope (gradient) associated with a backscattcred laser field. The theoretical basis for this imaging technique is outlined, and we present the results of computer experiments in which we construct coherent images from digitally simulated laser-speckle measurements. We investigate the effect that measurement noise has on the quality of the reconstructed imagery.
Component Pattern Separation of Completely Unknown Fluorescent Images by Double Eigenvector Analysis
Authors: Kawata Satoshi , Sasaki Keiji
Published: February 2023

We have proposed a new pattern recognition method, for interpreting image data from fluorescence microscopes. In this method, component patterns included in multispectral images of completely unknown mixture samples can be evaluated, without knowing the spectra or spatial patterns of the components [1,2]. Principal component analysis and optimization theory are used with nonnegativity constraints and entropy minimization. This method discovers unpredicted or unknown components in various microscopic environments. Even completely new material to the human beings could be found by this method. However, the method does not guarantee to give the true solution of component patterns, but instead an optimal one under the criterion of entropy minimization.
Iterative Design of Holographic Elements*
Authors: Sweeney D. W. , Schils G. F. , Gallagher N. C.
Published: February 2023

Iterative synthesis is a powerful technique for designing certain types of diffractive holographic elements. The designs especially amenable to iterative methods are characterized by nonlinear partial constraints in two domains that are related through a transformation. This paper reviews three iterative design projects of this type. In the first example, holographic concepts are used to design a microwave mirror that modifies the phase of a reflected wavefront.1,2 Second, holographic correlation filters are designed that recognize a three-dimensional object viewed from any direction.3,4 Third, an iterative design for computer generated holograms makes optimum use of the recording device resolution.5,6
Complex submicrometric object retrieval in partially coherent microscopy
Authors: Lantz E. , Duvemoy J.
Published: February 2023

This paper deals with the retrieval of an 1-d, space limited submicrometric complex object, from partially coherent images obtained by optical microscopy.
Experimental confirmation of superresolution in incoherent confocal scanning microscopy using a singular system inversion
Authors: Young M.R. , Davies R.E. , Pike E.R. , Walker J. G.
Published: February 2023

Singular system inversion techniques provide the basis for processing data obtained from an array of N detectors in the image plane of a confocal scanning microscope system as proposed by Bertero and Pike [1]. For an infinite number of detectors, the theory (see companion paper) predicts a transfer function of the form Experimental confirmation is presented here for the case of a 1-D low-numerical-aperture incoherent system, an important result being that with as few as five detectors, spaced at half the (coherent-case) Rayleigh distance, R, a notable improvement over the conventional confocal scanning microscope system is achieved.
Linear reconstruction of compensated images: theory and experimental results
Authors: Roggemann Michael C. , Tyler David W. , Bilmont Marsha F.
Published: February 2023

Linear image reconstruction techniques have been proposed for post-processing astronomical images measured with commpensated imaging systems. Linear techniques use averaging to overcome the effects of randomness and deconvolution to remove system effects. In this paper we report the first experimental results from compensated image measurements of single and binary stars at visible wavelengths, and verify the previously derived analytic expression relating the statistics of the compensated optical transfer function to the compensated image spectrum SNR.
Electromagnetic Inverse Scattering In Remote Sensing
Authors: Xia Jake J. , Kong Jin A.
Published: February 2023

Inverting the physical parameters which usually appear as inhomogeneous profiles from measurements has been a challenging task for the remote sensing community. Due to complexity of the media, the forward problem in remote sensing of forest, vegetation and sea ice, typically in random media, has attracted researchers’ efforts in the past two decades. Techniques which serve the ultimate goal of solving the inverse problem have also evolved and entered into a practical stage.
Super-Resolution
Authors: Fried David L.
Published: February 2023

We may define super-resolution as the ability to form an image with meaningful spatial frequency content at spatial frequencies for which the optical instrument has an optical transfer function (OTF) equal to zero. The 1964 paper by J. Harris1 showing that no two distinct, finite sized objects could result in the same (ordinary) focal plane image, no matter how slight the differences between the two objects, established a basis for believing that super-resolution was possible—that a signal processing algorithm could be found which could start with the ordinary focal plane image and, building on the details of that image, form a image of the object that clearly manifested all the fine details of that object. After some period of effort aimed at the development of a computationally tractable signal processing algorithm that would allow super-resolution to be achieved,2,3,4 it was concluded that a prohibitively large signal-to-noise ratio would be required,5 and interest in the subject waned.
Non-iterative Phase Recovery from Two Diffraction Plane Intensities
Authors: Maleki Mohammad H. , Devaney Anthony J.
Published: February 2023

Most algorithms for phase retrieval from two intensities are based on the iterative method first introduced by Gerchberg and Saxton [1] for recovering the phase of a field from aperture and diffraction plane intensities. Misell [2] generalized this algorithm to be used with intensities on any two planes related by a unitary operator, and later Wang et. al. [3] extended the iterative algorithm to the case of non-unitary operators. Non-iterative methods based on zero-location in the complex plane [4] and use of an exponential filter [5] as well as “tree pruning” methods [6] have also been proposed.
Fast Positron Emission Tomography and Techniques for Noise Amelioration and Resolution Enhancement
Authors: Yang Danping , Stark Henry , Galatsanos Nikolas P. , Wernick Miles N. , Chen Chin-Tu
Published: February 2023

Positron Emission tomography (PET) is a method for imaging the concentration of positron-emitting radioisotopes introduced into the body of a patient. Unfortunately, like other forms of emission computed tomography (ECT), PET is plagued by serious technical problems that have severely restricted its potential in unlocking the answers to difficult questions in brain research. In particular, two problems inherent to ECT methods have hampered progress in PET: 1) Patient safety considerations and detector response characteristics impose limits on the permissible radiation dose, therefore PET images are invariably severely quantum-noise-limited; and 2) The resolution of PET images is extremely poor owing primarily to the size of the scintillation detectors used in the data-acquisition step.
Imaging in the presence of temporal distortions
Authors: Landesman Barbara T. , Olson David F.
Published: February 2023

The imaging of a moving target by a typical CCD or CID camera with a finite integration time and finite-sized detectors presents a challenging problem in modeling and analysis. This problem is further complicated if the target is illuminated with a pulsed laser with a nonuniform temporal profile. However, a robust model of the imaging process can prove invaluable in the definition of system requirements, performance predictions, and in the development of post-detection correction algorithms.
Phase Diversity: Experimental Results from the Lick Observatory
Authors: Kendrick Richard L.
Published: February 2023

In the past, fixed aberrations in large astronomical telescopes were not considered to be a problem as long as the errors were no worse than the seeing at the telescope sight. Adaptive optics are now allowing researchers to correct for local seeing errors as well as fixed aberrations. In order to better understand the correction capabilities it is important to separate the fixed aberration errors from the seeing errors. The Lockheed Palo Alto Research labs ongoing phase diversity program has addressed this problem by using phase diversity techniques to estimate the fixed aberrations in the 1 meter and 3 meter telescopes at the Lick Observatory. The phase information extracted from the focused and defocused images is also used to enhance images of extended objects such as Jupiter, Saturn and the Earth’s moon.
Diagnostic Imaging with Light and Beyond
Authors: Barbour Randall
Published: February 2023

Optical tomography is rapidly evolving into a primary tool to investigate the physiological properties of tissues. Its application to studies of fluorescence for diagnostic and therapeutic uses are discussed.
Superresolution of MR images
Authors: Bones P.J. , Alwesh N. , Connolly T.J.
Published: February 2023

In magnetic resonance (MR) imaging, the resolution obtainable is related to the time available for data acquisition, yet this must be minimised to utilise an expensive MR scanner effectively (and to minimise the time a patient must remain immobile). In addition, a SNR penalty is incurred in acquiring images at higher resolution [1]. Therefore computational methods to superresolve MR images are keenly sought. The application of MR imaging for medical purposes clearly demands that any superresolution scheme does not introduce artefacts.
Inversion of Frequency-Resolved Optical Gating (FROG) Spectrograms in Real-Time: A Femtosecond Oscilloscope
Authors: Kane Daniel J.
Published: February 2023

Frequency-resolved optical gating (FROG) is a technique used to measure the intensity and phase of ultrashort laser pulses. The pulse to be measured is split into probe and gate pulses. The gate and probe pulses are combined in a non-linear optical medium to temporally select portions of the probe. The resulting signal is spectrally resolved at various time delays to produce a spectrogram of the probe.1-3 All the time and frequency information about the pulse (probe) is contained in its spectrogram (“FROG trace”). An iterative 2-dimensional phase retrieval algorithm is used to determine the phase of the FROG trace, and hence, the intensity and phase of the pulse.1,2
Psf calibration in astronomical imaging - physical constraints for a noisy problem
Authors: Hege E. Keith
Published: February 2023

Physically constrained iterative deconvolution attempts to realize the solution of an ill-posed problem, the iterative estimation of both the object function and the corresponding set of image point- spread-functions given a set of noisy realizations of images obtained with less than perfect optical imaging systems. Conjugate gradient-driven iterative estimation is used with physical constraints to guide the result to a physically consistent solution. The Art of using physically constrained iterative deconvolution in astronomical imaging, with and without adaptive optics, is discussed.
Multiframe iterative blind deconvolution using only a positivity constraint
Authors: Biggs David S. C. , Andrews Mark
Published: February 2023

The problem of blind deconvolution, extracting both the original image and point spread function (PSF) from only the measurement of their convolution, may at first seem a futile task. However Lane and Bates [1] have shown via separation of zero sheets that blind deconvolution is theoretically possible for dimensions of two or greater when very little noise is present. In practice noise is a significant problem that limits the ability to perform successful deconvolution. Many researchers have also found that the only way of achieving blind deconvolution is to impose spatial and spectral constraints on the solution, derived from a priori information about the imaging system, and to eliminate the trivial solution of the image or PSF being a delta function. This becomes less useful in situations where very little else is known except the measured data.
Direct Method for Phase Retrieval from the Intensity of Cylindrical Wavefronts
Authors: Larkin K. G. , Sheppard C.J.R.
Published: February 2023

Recently there has been some interest shown in the non-interferometric reconstruction of complex wavefields from intensity measurements [1,2]. At the same time it has been shown that for partially coherent systems this is not, in general, possible because different wavefields can exhibit identical intensity distributions [3]. The more restricted problem of finding the complex wave-field corresponding to the three dimensional intensity in a coherent system may be soluble by iterative phase retrieval techniques, but is not directly soluble. We consider a particular subset of the general problem which is demonstrably soluble by a direct method. The particular subset considered is essentially an optical wavefield propagating in a plane. This reduces the problem from three to two dimensions, resulting in a well-posed inverse problem. Initially we assume the system to be coherent, but we note that there are indications that the partially coherent case is also soluble. The solution presented is not just a theoretical curiosity because systems with the required geometry occur in slab waveguides and slit illumination systems.
3D reconstruction problems for cryo electron microscopy of viruses
Authors: Gao Wen , Doerschuk Peter C.
Published: February 2023

In this paper we describe several signal reconstruction problems that arise during the determination of the 3D structure of so-called spherical viruses. Spherical viruses are viruses with a shell of protein (the capsid) surrounding an inner core of nucleic acid. The capsid is “crystalline” in the sense that it is constructed from many repetitions of the same polypeptides and the entire capsid is invariant under some rotational symmetry, often the rotational symmetry of the icosahedron which is the case we focus on. The icosahedron is constructed from 20 equilateral triangles and has 60 rotational symmetries: a 5-fold axis where 5 triangles meet, a 3-fold axis through the center of each triangle, and a 2-fold axis at the midpoint of each edge between two triangles. A typical outer radius of the capsid is in the range 102-103Å.