Zernike Integrated Partial Phase Error Reduction Algorithm

A modification to the error reduction algorithm is reported in this paper for determining the prescription of an imaging system in terms of Zernike polynomials. The technique estimates the Zernike coefficients of the optical prescription as part of a modified Gerchberg-Saxton iteration combined with a new gradient-based phase unwrapping algorithm. Zernike coefficients are updated gradually as the error reduction algorithm converges by recovering the partial pupil phase that differed from the last known pupil phase estimate. In this way the wrapped phase emerging during each iteration of the error reduction algorithm does not represent the entire wrapped phase of the pupil electric field and can be unwrapped with greater ease. The algorithm is tested in conjunction with a blind deconvolution algorithm using measured laboratory data with a known optical prescription and is compared to a baseline approach utilizing a combination of the error reduction algorithm and a least-squares phase unwrapper previously reported in the literature. The combination of the modified error reduction algorithm and the new least-squares Zernike phase unwrapper is shown to produce superior performance for an application where it is desirable that Zernike coefficients be estimated during each iteration of the blind deconvolution procedure

Fourier Propagation Tool for Aberration Analysis and a Point Spread Function Calculation of Systems with Curved Focal Planes

This paper describes a new Fourier propagator for computing the impulse response of an optical system with a curved focal plane array, while including terms ignored in Fresnel and Fraunhofer calculations. The propagator includes a Rayleigh-Sommerfeld diffraction formula calculation from a distant point through the optical system to its image point predicted by geometric optics on a spherical surface. The propagator then approximates the neighboring field points via the traditional binomial approximation of the Taylor series expansion around that field point. This technique results in a propagator that combines the speed of a Fourier transform operation with the accuracy of the Rayleigh-Sommerfeld diffraction formula calculation and extends Fourier optics to cases where the receiver plane is a curved surface. Bounds on the phase error introduced by the approximations are derived, which show it should be more widely applicable than traditional Fresnel propagators. Guidance on how to sample the pupil and detector planes of a simulated imaging system is provided. This report concludes by showing examples of the diffraction patterns computed by the new technique compared to those computed using the Rayleigh-Sommerfeld technique in order to demonstrate the utility of the propagator

Projection-based image registration in the presence of fixed-pattern noise

A computationally efficient method for image registration is investigated that can achieve an improved performance over the traditional two-dimensional (2-D) cross-correlation-based techniques in the presence of both fixed-pattern and temporal noise. The method relies on transforming each image in the sequence of frames into two vector projections formed by accumulating pixel values along the rows and columns of the image. The vector projections corresponding to successive frames are in turn used to estimate the individual horizontal and vertical components of the shift by means of a one-dimensional (1-D) cross-correlation-based estimator. While gradient-based shift estimation techniques are computationally efficient, they often exhibit degraded performance under noisy conditions in comparison to cross-correlators due to the fact that the gradient operation amplifies noise. The projection-based estimator, on the other hand, significantly reduces the computational complexity associated with the 2-D operations involved in traditional correlation-based shift estimators while improving the performance in the presence of temporal and spatial noise. To show the noise rejection capability of the projection-based shift estimator relative to the 2-D cross correlator, a figure-of-merit is developed and computed reflecting the signal-to-noise ratio (SNR) associated with each estimator. The two methods are also compared by means of computer simulation and tests using real image sequences

Statistical algorithm for nonuniformity correction in focal-plane arrays

A statistical algorithm has been developed to compensate for the fixed-pattern noise associated with spatial nonuniformity and temporal drift in the response of focal-plane array infrared imaging systems. The algorithm uses initial scene data to generate initial estimates of the gain, the offset, and the variance of the additive electronic noise of each detector element. The algorithm then updates these parameters by use of subsequent frames and uses the updated parameters to restore the true image by use of a least-mean-square error finite-impulse-response filter. The algorithm is applied to infrared data, and the restored images compare favorably with those restored by use of a multiple-point calibration technique

Near Earth Space Object Detection Using Parallax as Multi-hypothesis Test Criterion

The US Strategic Command (USSTRATCOM) operated Space Surveillance Network (SSN) is tasked with Space Situational Awareness (SSA) for the U.S. military. This system is made up of Electro-Optic sensors, such as the Ground-based Electro-Optical Deep Space Surveillance (GEODSS) and RADAR based sensors, such as the Space Fence Gaps. They remain in the tracking of Resident Space Objects (RSO’s) in Geosynchronous Orbits (GEO), due to limitations of SST and GEODSS system implementation. This research explores a reliable, ground-based technique used to quickly determine an RSO’s altitude from a single or limited set of observations. Implementation of such sensors into the SSN would mitigate GEO SSA performance gaps. The research entails a method used to distinguish between the point spread function (PSF) observed by a star and the PSF observed from an RSO by using Multi-Hypothesis Testing with parallax as a test criterion. Parallax is the effect that an observed object will appear to shift when viewed from different positions. This effect is explored by generating PSFs from telescope observations of space objects at different baselines. The research has shown the PSF of an RSO can be distinguished from that of a star using single, simultaneous observations from reference and parallax sensing telescopes. This report validates these techniques with both simulations and experimental data from the SST and Naval Observatory sensors

Statistical Photocalibration of Photodetectors for Radiometry without Calibrated Light Sources

Calibration of CCD arrays for identifying bad pixels and achieving nonuniformity correction is commonly accomplished using dark frames. This kind of calibration technique does not achieve radiometric calibration of the array since only the relative response of the detectors is computed. For this, a second calibration is sometimes utilized by looking at sources with known radiances. This process can be used to calibrate photodetectors as long as a calibration source is available and is well-characterized. A previous attempt at creating a procedure for calibrating a photodetector using the underlying Poisson nature of the photodetection required calculations of the skewness of the photodetector measurements. Reliance on the third moment of measurement meant that thousands of samples would be required in some cases to compute that moment. A photocalibration procedure is defined that requires only first and second moments of the measurements. The technique is applied to image data containing a known light source so that the accuracy of the technique can be surmised. It is shown that the algorithm can achieve accuracy of nearly 2.7% of the predicted number of photons using only 100 frames of image data

Unequal a priori Probability Multiple Hypothesis Testing in Space Domain Awareness with the Space Surveillance Telescope

This paper investigates the ability to improve Space Domain Awareness (SDA) by increasing the number of detectable Resident Space Objects (RSOs) from space surveillance sensors. With matched filter based techniques, the expected impulse response, or Point Spread Function (PSF), is compared against the received data. In the situation where the images are spatially undersampled, the modeled PSF may not match the received data if the RSO does not fall in the center of the pixel. This aliasing can be accounted for with a Multiple Hypothesis Test (MHT). Previously, proposed MHTs have implemented a test with an equal a priori prior probability assumption. This paper investigates using an unequal a priori probability MHT. To determine accurate a priori probabilities, three metrics are computed; they are correlation, physical distance, and empirical. Using the calculated a priori probabilities, a new algorithm is developed, and images from the Space Surveillance Telescope (SST) are analyzed. The number of detected objects by both an equal and unequal prior probabilities are compared while keeping the false alarm rate constant. Any additional number of detected objects will help improve SDA capabilities. Abstract © 2016 Optical Society of Americ

Image Deblurring and Near-real-time Atmospheric Seeing Estimation through the Employment of Convergence of Variance

A new image reconstruction algorithm is presented that will remove the effect of atmospheric turbulence on motion compensated frame average images. The primary focus of this research was to develop a blind deconvolution technique that could be employed in a tactical military environment where both time and computational power are limited. Additionally, this technique can be employed to measure atmospheric seeing conditions. In a blind deconvolution fashion, the algorithm simultaneously computes a high resolution image and an average model for the atmospheric blur parameterized by Fried’s seeing parameter. The difference in this approach is that it does not assume a prior distribution for the seeing parameter, rather it assesses the convergence of the image’s variance as the stopping criteria and identification of the proper seeing parameter from a range of candidate values. Experimental results show that the convergence of variance technique allows for estimation of the seeing parameter accurate to within 0.5 cm and often even better depending on the signal to noise ratio