Direct, object brightness estimation from atmospheric turbulence degraded images using a new high-speed, modified phase diversity method

Wavefront sensorless adaptive optics system for extended objects based on linear phase diversity technique

Phase diversity experimental results: deconvolution of ν Scorpii

In this chapter, we consider the imaging properties of a system with a circular exit pupil by applying the general formulas derived in Chapter 1. We derive expressions for its point-spread function (PSF), optical transfer function (OTF), and encircled, ensquared, and excluded powers. The effect of aberrations on a PSF is first studied in terms of its central value, i.e., its Strehl ratio. An exact expression is obtained for the Strehl ratio and the results for primary aberrations are compared with those obtained from the approximate expressions based on the phase variance of the aberration across the pupil derived in Chapter 1. The tolerances for primary aberrations are given for a certain value of the Strehl ratio. Balanced primary aberrations are also discussed and they are identified with the Zernike circle polynomials. A defocused PSF is considered next, and it is shown that systems with large Fresnel numbers, such as photographic systems, have a very small depth of focus. However, systems with small Fresnel numbers, e.g., a laser transmitter, have a large depth of focus. Focused and collimated beams are discussed, and the concept of near- and far-field distances is introduced. It is shown that if the Fresnel number of the beam focused on a target is small, the axial irradiance is maximum at a point that is closer to the focusing optics. However, maximum central irradiance on a target at a given distance is obtained when a beam is focused on it, even though a larger irradiance is obtained at a closer point. Aberrated PSFs for rotationally symmetric aberrations are considered, and numerical results are obtained that show that the size of their central spot is practically independent of the aberration. Symmetry properties of the aberrated PSFs are considered next. Full PSFs for primary aberrations are shown graphically and pictorially. A brief comparison of the diffraction and geometrical PSFs is also given. The line of sight of an optical system is identified with the centroid of its PSF and discussed for aberrated systems. It is shown that only coma-type aberrations change the line of sight. The OTFs for primary aberrations are discussed, and the concept of contrast reversal is described. The OTF aberrated by coma is complex, and we give its real and imaginary parts as well as its modulus and phase. Aberration tolerances are given for a certain value of the Hopkins ratio. The geometrical OTF is also discussed and approximate expressions for it are obtained for the primary aberrations. It gives reasonably accurate results in the region of very low spatial frequencies, a region of practical interest when the MTF of an aberrated system at high frequencies is practically negligible. It is shown that the MTF averaged over all angular orientations of a spatial frequency vector is maximum when the standard deviation of the ray aberration [i.e., the root mean square (rms) radius of the spot diagram with respect to its centroid] is minimum. The diffraction OTF is shown to approach the geometrical OTF in the limit of zero wavelength. The differences between the diffraction and geometrical OTFs are summarized. The incoherent line- and edge-spread functions are discussed, and numerical results for both the aberration-free and the aberrated systems are given. The aberration tolerances for a certain value of the Struve ratio are also given.

There is high demand for deploying real-time or near real-time implementation of image reconstruction techniques for intelligence, surveillance, and reconnaissance (ISR) systems, as well as biomedical systems, and border applications. While many image restoration techniques have been implemented, their computational complexity makes them unsuitable for real-time systems. This work presents massively parallelized algorithms for two and three-dimensional image reconstruction of objects using deconvolution and bispectrum techniques. Speckle imaging (SI) techniques are more preferred for phase reconstruction because of its high restoration quality at the lower values of signal-to-noise ratio (SNR), especially for smaller targets, and its shift-invariant property which makes it insensitive to random motion of an object. This work proposes, a novel strategy for parallelization of recursive bispectrum algorithm. Furthermore, parallel bispectrum speckle imaging technique is used as an initial step for parallelized multi-frame blind deconvolution (MFBD) image restoration algorithm in order to speed-up the reconstruction process for anisoplanatic, long horizontal path imaging. The parallel hybrid Bispectrum- MFBD (B-MFBD) technique, through massive parallelization, provides significantly large improvement to both bispectrum SI and MFBD parts of the hybrid algorithm. The work also investigates phase diversity (PD) technique as the special case of MFBD algorithm, where the object is observed with a stack of intentionally defocused images. The known defocused information between phases is used to estimate the object and aberration function. The multi-plane PD was implemented for wide field fluorescence microscopy imaging of three-dimensional objects. The PD algorithm was subsequently used to generate 3D point cloud data for the image from its single view.

The joint impact of atmospheric refraction and turbulence effects on the modulation transfer function (MTF) of an incoherent imaging system is analyzed using numerical simulations based on the brightness function technique. Atmospheric refractivity is described by a combination of the standard MUSA76 and inverse temperature layer (ITL) models, and atmospheric turbulence effects are accounted for using the classical Kolmogorov turbulence framework. We show that ITL-induced refractivity located in the vicinity of an air volume essential for image formation can create strongly spatially anisotropic phase aberrations, which may significantly impact imaging system performance. Numerical analysis demonstrates that these phase aberrations may change the image size, and cause spatial frequency shifts in observed images of horizontally oriented sine-patterns. Numerical simulations show the that combined effects of atmospheric turbulence and ITL-induced refractivity cause the MTF to be a nonlinear function that is dependent on the imaging system characteristics, propagation path geometry, and atmospheric turbulence and ITL-induced refractivity parameters.

We propose an adaptive optics system for a lightweight remote sensing sensor. The phase diversity (PD) technique, in which known wavefronts (Phase Diversity) are applied to the optics and the inherent aberrations are estimated using the acquired images without a priori information, is a key to realizing the system. For the reduction of computing cost and the enhancement of the estimation accuracy of aberration, a spatial light modulator (SLM) is adopted not only for wavefront compensator but also for PD generator. The SLM produces arbitrary "aberration modes" that are each represented by a Zernike polynomial. Therefore, optimal phase diversities are applied to the optical system and particular modes are effectively obtained, which makes it possible to overcome the conventional PD generated by defocusing that describes only quadratic form and lacks information of a particular mode. In order to solve the complex inverse problem of phase diversity with low computing cost, a general regression neural network (GRNN) is used. Moreover, principal component analysis compresses the input data for GRNN by extracting information from collected images in Fourier space, and reduces computation cost considerably. The performance is validated by numerical simulation, and the result of experiment using SLM is described.

Optical transfer function (OTF) and the integral resolution of the optical system "turbulent atmosphere - telescope" are treated theoretically by different methods of posteriory processing of incoherently illuminated objects observed through the turbulent atmosphere. The following processing methods are examined: the averaged image recording ("very long" averaging times) and short-exposure images ("very short" averaging times), namely, Labeyrie, Knox-Thompson, and triple correlation of image intensity methods. The influence of the finite value of the turbulent atmosphere outer and inner scales on the OTF's under consideration is also estimated.

The misalignment between recorded in-focus and out-of-focus images using the Phase Diversity (PD) algorithm leads to a dramatic decline in wavefront detection accuracy and image recovery quality for segmented active optics systems. This paper demonstrates the theoretical relationship between the image misalignment and tip-tilt terms in Zernike polynomials of the wavefront phase for the first time, and an efficient two-step alignment correction algorithm is proposed to eliminate these misalignment effects. This algorithm processes a spatial 2-D cross-correlation of the misaligned images, revising the offset to 1 or 2 pixels and narrowing the search range for alignment. Then, it eliminates the need for subpixel fine alignment to achieve adaptive correction by adding additional tip-tilt terms to the Optical Transfer Function (OTF) of the out-of-focus channel. The experimental results demonstrate the feasibility and validity of the proposed correction algorithm to improve the measurement accuracy during the co-phasing of segmented mirrors. With this alignment correction, the reconstructed wavefront is more accurate, and the recovered image is of higher quality.

: The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence, and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time averaged Strehl ratio and the time averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few per cent for a range of representative residual wave-front errors. In these calculations, we have combined static optical system aberrations and time-varying residual phase distortion characteristic of deformable mirror (DM) fitting error, wave-front sensor (WFS) noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini beta-meter Telescopes project. The overall Strehl ratios and OTF's due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio due to both errors is greater than about 0.1. For lower Strehl ratios the products provide lower bounds on the actual values of the Strehl ratio and OTF. The speckle transfer function (STF) is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.

The phase diversity technique is studied as a wave-front sensor to be implemented with widely extended sources. The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images (in focus and out of focus) by use of a maximum-likelihood approach. The propagation of the photon noise in the images on the estimated phase is derived from a theoretical analysis. The covariance matrix of the phase estimator is calculated, and the optimal distance between the observation planes that minimizes the noise propagation is determined. The phase error is inversely proportional to the number of photons in the images. The noise variance on the Zernike polynomials increases with the order of the polynomial. These results are confirmed with both numerical and experimental validations. The influence of the spectral bandwidth on the phase estimator is also studied with simulations.

Exoplanet direct imaging with a ground-based telescope needs a very high performance adaptive optics (AO) system, so-called eXtreme AO (XAO), a coronagraph device, and a smart imaging process. One limitation of AO system in operation remains the Non Common Path Aberrations (NCPA). To achieve the ultimate XAO performance, these aberrations have to be measured with a dedicated wavefront sensor placed in the imaging camera focal plane, and then pre-compensated using the AO closed loop process. In any events, the pre-compensation should minimize the aberrations at the coronagraph focal plane mask. An efficient way for the NCPA measurement is the phase diversity technique. A pixel-wise approach is well-suited to estimate NCPA on large pupils and subsequent projection on the deformable mirror with Cartesian geometry. However it calls for a careful regularization for optimal results. The weight of the regularization is written in close-form for un-supervised tuning. The accuracy of NCPA pre-compensation is below 8 nm for a wide range of conditions. Point-by-point phase estimation improves the accuracy of the Phase Diversity method. The algorithm is validated in simulation and experimentally. It will be implemented in SAXO, the XAO system of the second generation VLT instrument: SPHERE.

Orbital angular momentum (OAM) of vortex beams can extend the capacity and spectral efficiency of free-space optical (FSO) communication for its orthogonality provide an extra dimension. However, atmospheric turbulence (AT) will lead to wave-front distortion, crosstalk between OAM modes and eventually reduce the communication system performance. This paper uses a Phase Diversity (PD)-based adaptive optics (AO) schema to compensate the OAM beam. With the General Regression Neural Network (GRNN), the relationship between the intensity distribution and the wave-front distortion of propagation in AT channel is established, and the wave-front aberration is retrieved. This method is simple in structure without phase sensor and probe beam, and reduces computation compared with the common phase retrieval algorithms. Therefore, it can compensate OAM beam in a second and ensure the similar retrieve effect.

The Optical Transfer Function (OTF) and its modulus the Modulation Transfer Function (MTF) are metrics of optical system performance. However in system optimization, calculation times for the OTF are often substantially longer than more traditional optimization targets such as wavefront error or transverse ray error. The OTF is typically calculated as either the autocorrelation of the complex pupil function or as the Fourier transform of the Point Spread Function. We recently demonstrated that the on-axis OTF can be represented as a linear combination of analytical functions where the weighting terms are directly related to the wavefront error coefficients and apodization of the complex pupil function. Here, we extend this technique to the off-axis case. The expansion technique offers a potential for accelerating OTF optimization in lens design, as well as insight into the interaction of aberrations with components of the OTF.

For the image quality analysis of photogrammetrical systems using the Modulation Transfer Function (MTF), the edge gradient analysis (EGA), using a Hanning function, and the grating pattern method are compared. Artificial edge and grating patterns were photographed from an airplane and were analyzed to determine the quality of the photogrammetric system. The pictures were scanned with a microdensitometer. For comparison with the artificial patterns, a natural roof edge was examined. Good agreement of all MTF measurements was found. Furthermore, the resolution found from MTF curves agreed well with the resolution obtained from three-bar targets. Generally, the MTF curves obtained from patterns in the flight direction were lower than the MTF's perpendicular to the flight direction due to airplane movement. The influence of linear image motion and its compensation was examined and is discussed. N PHOTOGRAMMETRY the image quality of photographs is of great importance. With digital image processing the image quality can be improved under certain conditions. Flight con­ ditions usually lead to reduced image quality (Holdermann, 1976). The optical transfer function (OTF) and especially the modula­ tion transfer function (MTF) are useful techniques for measuring the image quality of photographs. The MTF is the result of -the contributions of the links in the image transfer forming chain, namely, the camera, the film, image motion (in systems without forward motion compensation, FMC), vibrations, and the at­ mosphere (Tiziani, 1977). Artificial or natural edges are used for the edge gradient analysis (EGA), and varying spatial frequency patterns are used for the grating pattern technique. The aim of this paper is to compare both methods and to test their reliability. Results are shown and discussed. Furthermore, the influence of linear image mo­ tion on image quality is examined.

The effects of atmospheric turbulence on imaging systems, and beam projection systemssuch as laser designators, can be evaluated and the performance predicted in terms of aproperly path- weighted value of the turbulence structure constant, C,4. An operating sys-tem for direct field determination of this weighted value with a portable slit scanningtelescope and on -line data reduction minicomputer system will be described. This systemutilizes a point laser source located in the vicinity of the target and scans the image ofthat source from the opposite end of the optical path. The on -line computer system com-bines data, for the system on test, with the data taken on the atmosphere at the instant oftest firing, utilizing Fourier and Abel transform techniques, to provide a prediction ofbehavior of the system on test, or an evaluation of the effects of the atmosphere on that test. The results can be presented in a variety of forms, including immediate hard copyplots of the MTF of the atmosphere, of the overall system being tested, or plots of pre-dicted radial distribution of intensity on target for the system on test. The slit scan-ning telescope can track a slowly moving target, with internal optical tracking. A gyroplatform is under development which can provide operation from shipboard or other unstableplatform.The degradation of resolution of an imaging system, or the spot broadening for a beamprojection system such as a laser designator, for transmission through the turbulent atmos-phere, can be expressed in terms of the short -term and long -term atmospheric optical trans-fer functions (OTF), or the equivalent mutual coherence functions (MCF). The short -termand long -term modulation transfer functions (MTF) are also often used and are nearly equiva-