Singular value decomposition approach to coherent averaging in digital holography.

We present a new approach to coherent averaging in digital holography using singular value decomposition (SVD). Digital holography enables the extraction of phase information from intensity measurements. For this reason, SVD can be used to statistically determine the orthogonal vectors that align the complex-valued measurements from multiple frames and group common modes accounting for constant phase shift terms. The SVD approach enables the separation of multiple signals, which can be applied to remove undesired artifacts such as scatter in retrieved images. The advantages of the SVD approach are demonstrated here in experiments through fog-degraded holograms with spatially incoherent and coherent scatter.

Phase-error correction in digital holography using single-shot data.

In remote-sensing applications, digital holography data often includes both phase errors from atmospheric turbulence and fully developed laser speckle from rough objects. When processing single-shot data, i.e., data from a single hologram, the high speckle contrast makes it more difficult to correct for atmospheric phase errors compared to scenarios where multiple speckle realizations are available for processing. A Bayesian phase-error correction algorithm [J. Opt. Soc. Am. A34, 1659 (2017)JOAOD60740-323210.1364/JOSAA.34.001659] was recently developed for use with single-shot data. The features of this approach are discussed and used to implement an alternative algorithm based on image-sharpness maximization. Algorithm performance is tested using simulated data for a range of signal-to-noise ratios (SNRs) and turbulence conditions. Using a combination of appropriate parameterization of the phase-error estimates and spatial binning for speckle-contrast reduction, the image-sharpness algorithm achieves performance comparable (better in the high-SNR regime but worse in the low-SNR regime) to the Bayesian approach. Limited experimental results are also presented.

Interferometric imaging using Si3N4 photonic integrated circuits for a SPIDER imager.

This paper reports design, fabrication, and experimental demonstration of a silicon nitride photonic integrated circuit (PIC). The PIC is capable of conducting one-dimensional interferometric imaging with twelve baselines near λ = 1100-1600 nm. The PIC consists of twelve waveguide pairs, each leading to a multi-mode interferometer (MMI) that forms broadband interference fringes or each corresponding pair of the waveguides. Then an 18 channel arrayed waveguide grating (AWG) separates the combined signal into 18 signals of different wavelengths. A total of 103 sets of fringes are collected by the detector array at the output of the PIC. We keep the optical path difference (OPD) of each interferometer baseline to within 1 µm to maximize the visibility of the interference measurement. We also constructed a testbed to utilize the PIC for two-dimension complex visibility measurement with various targets. The experiment shows reconstructed images in good agreement with theoretical predictions.

Self-plagiarism and conference papers: editorial.

Editor-in-Chief P. Scott Carney and Topical Editor Samuel T. Thurman discuss self-plagiarism and conference papers.

Experimental demonstration of interferometric imaging using photonic integrated circuits.

This paper reports design, fabrication, and demonstration of a silica photonic integrated circuit (PIC) capable of conducting interferometric imaging with multiple baselines around λ = 1550 nm. The PIC consists of four sets of five waveguides (total of twenty waveguides), each leading to a three-band spectrometer (total of sixty waveguides), after which a tunable Mach-Zehnder interferometer (MZI) constructs interferograms from each pair of the waveguides. A total of thirty sets of interferograms (ten pairs of three spectral bands) is collected by the detector array at the output of the PIC. The optical path difference (OPD) of each interferometer baseline is kept to within 1 µm to maximize the visibility of the interference measurement. We constructed an experiment to utilize the two baselines for complex visibility measurement on a point source and a variable width slit. We used the point source to demonstrate near unity value of the PIC instrumental visibility, and used the variable slit to demonstrate visibility measurement for a simple extended object. The experimental result demonstrates the visibility of baseline 5 and 20 mm for a slit width of 0 to 500 µm in good agreement with theoretical predictions.

Method of obtaining wavefront slope data from through-focus point spread function measurements.

A method is described for analyzing point source imagery collected with various amounts of defocus to obtain wavefront slope data at the exit pupil of an imaging system. Integration of this slope data yields the system wavefront aberration function. The method is based on a geometric optics interpretation of intensity point spread function measurements in the caustic region near focus. Algorithm performance is examined through Monte Carlo simulations. Application of the method to segmented-aperture systems is also explored. The proposed method is used to generate initial wavefront estimates for an iterative phase retrieval algorithm, significantly improving the capture range over a blind phase retrieval approach when segment tilt errors are large.

Application of the general image-quality equation to aberrated imagery.

The regression analysis for the general image-quality equation (GIQE) [Appl. Opt. 36, 8322-8328 (1997)] was performed using image data from well-corrected optical systems. We conducted human-subject experiments to examine the use of the GIQE with aberrated imagery. A modified image-quality equation for aberrated imagery is presented based on analysis of the experimental results.

Complex pupil retrieval with undersampled data.

The ability to retrieve the complex-valued, generalized pupil function of an imaging system from undersampled measurements of the defocused system point spread function (PSF) is examined through numerical simulations. The ability to do so degrades as the detector pixel pitch increases when using a fixed number of PSF measurements. Two strategies for obtaining better results with undersampled data are demonstrated using additional PSF measurements with (i) random shifts due to system pointing fluctuations and (ii) intermediate amounts of defocus.

Fizeau Fourier transform imaging spectroscopy: missing data reconstruction.

Fizeau Fourier transform imaging spectroscopy yields both spatial and spectral information about an object. Spectral information, however, is not obtained for a finite area of low spatial frequencies. A nonlinear reconstruction algorithm based on a gray-world approximation is presented. Reconstruction results from simulated data agree well with ideal Michelson interferometer-based spectral imagery. This result implies that segmented-aperture telescopes and multiple telescope arrays designed for conventional imaging can be used to gather useful spectral data through Fizeau FTIS without the need for additional hardware.

Wiener reconstruction of undersampled imagery.

We derive a Fourier-domain Wiener filter for the reconstruction of undersampled imagery. The filter differs from previous implementations in that it permits adjustment of the trade-offs between sharpness of the reconstruction, noise amplification, and aliasing artifact suppression. Additionally, a net transfer function that characterizes the combined effects of the imaging system and the reconstruction process is derived. This net transfer function is valid for both unaliased and aliased spatial frequencies. The expression for the net transfer function is applicable to more general linear image sharpening algorithms.

Phase retrieval with signal bias.

The effect of a uniform measurement bias, due to background light, stray light, detector dark current, or detector offset, on phase retrieval wavefront sensing algorithms is analyzed. Simulation results indicate that the root-mean-square error of the retrieved phase can be more sensitive to an unaccounted-for signal bias than to random noise in practical scenarios. Three methods for reducing the impact of signal bias are presented.

Amplitude metrics for field retrieval with hard-edged and uniformly illuminated apertures.

In field retrieval, the amplitude and phase of the generalized pupil function for an optical system are estimated from multiple defocused measurements of the system point-spread function. A baseline field reconstruction algorithm optimizing a data consistency metric is described. Additionally, two metrics specifically designed to incorporate a priori knowledge about pupil amplitude for hard-edged and uniformly illuminated aperture systems are given. Experimental results demonstrate the benefit of using these amplitude metrics in addition to the baseline metric.

Phase-error correction in digital holography.

The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than lambda/50 root-mean-square (RMS) were obtained. Corrections better than lambda/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.

Correction of anisoplanatic phase errors in digital holography.

The quality of coherent images computed from digital holography or heterodyne array data is sensitive to phase errors of the reference and/or object beams. A number of algorithms exist for correcting phase errors in or very near the hologram plane. In the case of phase errors introduced a nonnegligible distance away from hologram plane, the resulting imagery exhibits anisoplanatism. A feature of coherent imaging is that such phase errors may be corrected by simply propagating the aberrated fields (from the object) from the hologram plane to the plane where the phase errors were introduced and applying the phase-error correction algorithms to the fields in that plane. We present experimental results that demonstrate correction of such anisoplanatic phase errors.

Efficient subpixel image registration algorithms.

Three new algorithms for 2D translation image registration to within a small fraction of a pixel that use nonlinear optimization and matrix-multiply discrete Fourier transforms are compared. These algorithms can achieve registration with an accuracy equivalent to that of the conventional fast Fourier transform upsampling approach in a small fraction of the computation time and with greatly reduced memory requirements. Their accuracy and computation time are compared for the purpose of evaluating a translation-invariant error metric.

Noise histogram regularization for iterative image reconstruction algorithms.

We derive a regularization term for iterative image reconstruction algorithms based on the histogram of the residual difference between a forward-model image of a given object estimate and noisy image data. The term can be used to constrain this residual histogram to be statistically equivalent to the expected noise histogram, preventing overfitting of noise in a reconstruction. Reconstruction results from simulated imagery are presented for the cases of Gaussian and quantization noise.

Dealiased spectral images from aliased Fizeau Fourier transform spectroscopy measurements.

Fizeau Fourier transform imaging spectroscopy (FTIS) is a technique for collecting both spatial and spectral information about an object with a Fizeau imaging interferometer and postprocessing. The technique possesses unconventional imaging properties due to the fact that the system transfer functions, including the imaging and spectral postprocessing operations, are given by cross correlations between subapertures of the optical system, in comparison with the conventional optical transfer function, which is given by the autocorrelation of the entire aperture of the system. The unconventional imaging properties of Fizeau FTIS can be exploited to form spatially dealiased spectral images from undersampled intensity measurements (obtain superresolution relative to the detector pixel spacing). We demonstrate this dealiasing technique through computer simulations and discuss the associated design and operational trade-offs.

Signal-to-noise ratio trade-offs associated with coarsely sampled Fourier transform spectroscopy.

We derive the spectral signal-to-noise ratio (SNR) trade-offs associated with coarsely sampled Fourier transform spectroscopy using a step-and-integrate measurement scheme. We show that there is no SNR penalty in the shot noise limit and a slight SNR benefit in the detector noise limit for the case of coarse sampling to achieve the same spectral resolution as a baseline Nyquist sampling scenario, where the total detector integration time is the same for both sampling cases.

Controlling the spectral response in guided-mode resonance filter design.

Techniques for controlling spectral width are used in conjunction with thin-film techniques in the design of guided-mode resonance (GMR) filters to provide simultaneous control over line-shape symmetry, sideband levels, and spectral width. Several factors that could limit the minimum spectral width are discussed. We used interference effects for passband shaping by stacking multiple GMR filters on top of one another. A design is presented for a 200-GHz telecommunications filter along with a tolerance analysis. Compared with a conventional thin-film filter, the GMR filter has fewer layers and looser thickness tolerances. Grating fabrication tolerances are also discussed.