Image Reconstruction with Analytical Point Spread Functions

The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems. These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computationally burden. To this aim, we generalize the recently developed extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function in case the wavefront is described using Zernike functions. We present a linear expansion of the point spread function in terms of analytic functions which, additionally, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique which is demonstrated through some applications. This suggest that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use presently and based on blind deconvolution.Comment: 10 pages, 4 figures, accepted for publication in Astronomy & Astrophysic

Automatic Estimation of Modulation Transfer Functions

The modulation transfer function (MTF) is widely used to characterise the performance of optical systems. Measuring it is costly and it is thus rarely available for a given lens specimen. Instead, MTFs based on simulations or, at best, MTFs measured on other specimens of the same lens are used. Fortunately, images recorded through an optical system contain ample information about its MTF, only that it is confounded with the statistics of the images. This work presents a method to estimate the MTF of camera lens systems directly from photographs, without the need for expensive equipment. We use a custom grid display to accurately measure the point response of lenses to acquire ground truth training data. We then use the same lenses to record natural images and employ a data-driven supervised learning approach using a convolutional neural network to estimate the MTF on small image patches, aggregating the information into MTF charts over the entire field of view. It generalises to unseen lenses and can be applied for single photographs, with the performance improving if multiple photographs are available

Is the sky the limit? Performance of the revamped Swedish 1-m Solar Telescope and its blue- and red-beam re-imaging systems

We demonstrate that for data recorded with a solar telescope that uses adaptive optics and/or post-processing to compensate for many low- and high-order aberrations, the RMS granulation contrast is directly proportional to the Strehl ratio calculated from the residual (small-scale) wavefront error. We demonstrate that the wings of the high-order compensated PSF for SST are likely to extend to a radius of not more than about 2 arcsec, consistent with earlier conclusions drawn from straylight compensation of sunspot images. We report on simultaneous measurements of seeing and solar granulation contrast averaged over 2 sec time intervals at several wavelengths from 525 nm to 853.6 nm on the red-beam (CRISP beam) and wavelengths from 395 nm to 484 nm on the blue-beam (CHROMIS beam). These data were recorded with the Swedish 1-m Solar Telescope (SST) that has been revamped with an 85-electrode adaptive mirror and a new tip-tilt mirror, both of which were polished to exceptionally high optical quality. The highest 2-sec average image contrast measured in April 2015 through 0.3-0.9 nm interference filters at 525 nm, 557 nm, 630 nm and 853.5 nm with compensation only for the diffraction limited point spread function of SST is 11.8%, 11.8%, 10.2% and 7.2% respectively. Similarly, the highest 2-sec contrast measured at 395 nm, 400 nm and 484 nm in May 2016 through 0.37-1.3 nm filters is 16%, 16% and 12.5% respectively. The granulation contrast observed with SST compares favorably with that of other telescopes. Simultaneously with the above wideband red-beam data, we also recorded narrow-band continuum images with the CRISP imaging spectropolarimeter. We find that contrasts measured with CRISP are entirely consistent with the corresponding wide-band contrasts, demonstrating that any additional image degradation by the CRISP etalons and telecentric optical system is marginal or even insignificant.Comment: In press in Astronomy & Astrophysic

An Analysis of Optical Contributions to a Photo-Sensor's Ballistic Fingerprints

Lens aberrations have previously been used to determine the provenance of an image. However, this is not necessarily unique to an image sensor, as lens systems are often interchanged. Photo-response non-uniformity noise was proposed in 2005 by Luk\'a\v{s}, Goljan and Fridrich as a stochastic signal which describes a sensor uniquely, akin to a "ballistic" fingerprint. This method, however, did not account for additional sources of bias such as lens artefacts and temperature. In this paper, we propose a new additive signal model to account for artefacts previously thought to have been isolated from the ballistic fingerprint. Our proposed model separates sensor level artefacts from the lens optical system and thus accounts for lens aberrations previously thought to be filtered out. Specifically, we apply standard image processing theory, an understanding of frequency properties relating to the physics of light and temperature response of sensor dark current to classify artefacts. This model enables us to isolate and account for bias from the lens optical system and temperature within the current model.Comment: 16 pages, 9 figures, preprint for journal submission, paper is based on a thesis chapte

Convolutional Deblurring for Natural Imaging

In this paper, we propose a novel design of image deblurring in the form of one-shot convolution filtering that can directly convolve with naturally blurred images for restoration. The problem of optical blurring is a common disadvantage to many imaging applications that suffer from optical imperfections. Despite numerous deconvolution methods that blindly estimate blurring in either inclusive or exclusive forms, they are practically challenging due to high computational cost and low image reconstruction quality. Both conditions of high accuracy and high speed are prerequisites for high-throughput imaging platforms in digital archiving. In such platforms, deblurring is required after image acquisition before being stored, previewed, or processed for high-level interpretation. Therefore, on-the-fly correction of such images is important to avoid possible time delays, mitigate computational expenses, and increase image perception quality. We bridge this gap by synthesizing a deconvolution kernel as a linear combination of Finite Impulse Response (FIR) even-derivative filters that can be directly convolved with blurry input images to boost the frequency fall-off of the Point Spread Function (PSF) associated with the optical blur. We employ a Gaussian low-pass filter to decouple the image denoising problem for image edge deblurring. Furthermore, we propose a blind approach to estimate the PSF statistics for two Gaussian and Laplacian models that are common in many imaging pipelines. Thorough experiments are designed to test and validate the efficiency of the proposed method using 2054 naturally blurred images across six imaging applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin

SLM-based Digital Adaptive Coronagraphy: Current Status and Capabilities

Active coronagraphy is deemed to play a key role for the next generation of high-contrast instruments, notably in order to deal with large segmented mirrors that might exhibit time-dependent pupil merit function, caused by missing or defective segments. To this purpose, we recently introduced a new technological framework called digital adaptive coronagraphy (DAC), making use of liquid-crystal spatial light modulators (SLMs) display panels operating as active focal-plane phase mask coronagraphs. Here, we first review the latest contrast performance, measured in laboratory conditions with monochromatic visible light, and describe a few potential pathways to improve SLM coronagraphic nulling in the future. We then unveil a few unique capabilities of SLM-based DAC that were recently, or are currently in the process of being, demonstrated in our laboratory, including NCPA wavefront sensing, aperture-matched adaptive phase masks, coronagraphic nulling of multiple star systems, and coherent differential imaging (CDI).Comment: 14 pages, 9 figures, to appear in Proceedings of the SPIE, paper 10706-9

Imaging through turbulence with a quadrature-phase optical interferometer

We present an improved technique for imaging through turbulence at visible wavelengths using a rotation shearing pupil-plane interferometer, intended for astronomical and terrestrial imaging applications. While previous astronomical rotation shearing interferometers have made only visibility modulus measurements, this interferometer makes four simultaneous measurements on each interferometric baseline, with phase differences of π/2 between each measurement, allowing complex visibility measurements (modulus and phase) across the entire input pupil in a single exposure. This technique offers excellent wavefront resolution, allowing operation at visible wavelengths on large apertures, is potentially immune to amplitude fluctuations (scintillation), and may offer superior calibration capabilities to other imaging techniques. The interferometer has been tested in the laboratory under weakly aberrating conditions and at Palomar Observatory under ordinary astronomical observing conditions. This research is based partly on observations obtained at the Hale Telescope