An innovative iterative search method called the synthetic phaseshifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.
We report laboratory results of a coronagraphic test bench to assess the intensity reduction differences between a "Gaussian" tapered focal plane coronagraphic mask and a classical hard-edged "top hat" function mask at extreme adaptive optics (ExAO) Strehl ratios of ∼94%. However, unlike a traditional coronagraph design, we insert a reflective focal plane mask at 45Њ to the optical axis. We also use an intermediate secondary mask (mask 2) before a final image in order to block additional mask-edge-diffracted light. The test bench simulates the optical train of ground-based telescopes (in particular, the 8.1 m Gemini North Telescope). It includes one spider vane, different mask radii (r p 1.9l /D, 3.7l /D, and 7.4l /D), and two types of reflective focal plane masks (hard-edged top-hat and Gaussian tapered profiles). In order to investigate the relative performance of these competing coronagraphic designs with regard to extrasolar planet detection sensitivity, we utilize the simulation of realistic extrasolar planet populations (Nielsen et al.). With an appropriate translation of our laboratory results to expected telescope performance, a Gaussian tapered mask radius of 3.7l /D with an additional mask (mask 2) performs best (highest planet detection sensitivity). For a full survey with this optimal design, the simulation predicts that ∼30% more planets would be detected than with a top-hat function mask of similar size with mask 2. Using the best design, the point contrast ratio between the stellar point-spread function (PSF) peak and the coronagraphic PSF at 10l /D (0Љ .4 in the H band if D p 8.1 m) is ∼10 times higher than a classical Lyot top-hat coronagraph. Hence, we find that a Gaussian apodized mask with an additional blocking mask is superior (∼10 times higher contrast) to the use of a classical Lyot coronagraph for ExAO-like Strehl ratios.
We have designed and are developing a novel proof-of-concept PET system called BazookaPET. In order to complete the PET configuration, at least two detector elements are required to detect positron-electron annihilation events. Each detector element of the BazookaPET has two independent data acquisition channels. One side of the scintillation crystal is optically coupled to a 4×4 silicon photomultiplier (SiPM) array and the other side is a CCD-based gamma camera. Using these two separate channels, we can obtain data with high energy, temporal and spatial resolution data by associating the data outputs via several maximum-likelihood estimation (MLE) steps. In this work, we present the concept of the system and the prototype detector element. We focus on characterizing individual detector channels, and initial experimental calibration results are shown along with preliminary performance-evaluation results. We measured energy resolution and the integrated traces of the slit-beam images from both detector channel outputs. A photo-peak energy resolution of ~5.3% FWHM was obtained from the SiPM and ~48% FWHM from the CCD at 662 keV. We assumed SiPM signals follow Gaussian statistics and estimated the 2D interaction position using MLE. Based on our the calibration experiments, we computed the Cramér-Rao bound (CRB) for the SiPM detector channel and found that the CRB resolution is better than 1 mm in the center of the crystal.
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