David C. Hyland

Exo-planet detection via stellar intensity correlation interferometry

This paper considers the Hanbury Brown-Twiss effect and its application to astrometry in the service of extra-solar planet detection, particularly terrestrial planets at a range of 15 pc or less. The system considered comprises several modest-sized telescopes (light collectors) each equipped with photodetection apparatus and the means to record the photodetector signal time-history. At some convenient location, the cross-correlations of the individual light collector photodetection histories is computed to yield, in turn, a collection of values for the magnitudes of the mutual coherence of the target scene at various measurement baselines. With this type of observation system, we show that if there are known guide stars within the picture frame, the computed coherence magnitudes may be used to infer the apparent motion of the target star. Provided sufficiently large measurement baselines, the resolution of the target star motion can be very fine. We first compute the signal-to-noise (SNR) ratio of a single coherence magnitude measurement and then, using simple models of the telescope array and the target star gravitational perturbation due to a terrestrial planet, we compute the SNR for determination of the planet orbit parameters, up to the determinacy afforded by astrometric measurements. We have provided expressions for the region in the (planetary mass-orbital semi-major axis) plane for which SNR is above a desired value. With these results, we can determine the sensitivity and range of the overall instrument for astrometry in planet detection. Moreover, one can assess the relative advantages of this technique in comparison with amplitude interferometry.

Mitigating the effect of noise in the hybrid input–output method of phase retrieval

Here a modification to the hybrid input-output (HIO) method of phase retrieval is presented which aides in mitigating the negative effects of low signal-to-noise ratios (SNRs). Various type of interferometers measure diffraction patterns which are used to determine the Fourier transform modulus of an objective. Interferometry often suffers from very low SNRs making phase retrieval difficult because of the sensitivity of most phase retrieval algorithms to local minima. Here we analyze the effect of noise on the HIO method. The result is used as a rationale for the proposed modification to the HIO method. The algorithm presented here introduces a filtering scheme which removes much of the Fourier modulus noise. Examples are shown and the results are compared to the HIO method with and without the proposed modification. Comparisons are also made to other methods of filtering the Fourier modulus noise.

Calculation of signal-to-noise ratio for image formation using multispectral intensity correlation

In previous work, we explored the possibility of using intensity correlation techniques, based upon the Hanbury Brown-Twiss effect to perform fine resolution imaging in the service of exoplanet astronomy. Here we consider a multi-spectral variant of the Hanbury Brown-Twiss technique. At each of a number of independent, light-gathering telescopes photodetection data encompassing each of a set of frequency channels are obtained and then are communicated to some convenient computational station. At the computational station, the correlations among the photodetections in each of the frequency bands are time averaged and then further averaged over the various frequency channels to arrive at measurements of the mutual coherence magnitude for each pair of telescopes. From these statistics, imaging data are, in turn, computed via phase retrieval techniques. Here, within a modern quantum optics framework, we examine the signal-to-noise characteristics of the coherence estimates obtained in this way under a variety of non-ideal conditions. We provide step-by-step derivations of the statistical quantities needed in a largely self-contained treatment. In particular, we examine the effects of partial coherence on a scene typical of exoplanet imaging and show how partial coherence can be used to greatly attenuate the parent star. We find that the multispectral version of intensity interferometry greatly improves the signal-to-noise ratio in general and dramatically so for exoplanet detection. The results also extend the analysis of signal-to-noise to a wider variety of practical conditions and provide the basis for multispectral intensity correlation imaging system design.

Analysis and parameter selection for an adaptive random search algorithm

This paper presents an analysis of an adaptive random search (ARS) algorithm, a global minimization method. A probability model is introduced to characterize the statistical properties of the number of iterations required to find an acceptable solution. Moreover, based on this probability model, a new stopping criterion is introduced to predict the maximum number of iterations required to find an acceptable solution with a pre-specified level of confidence. This leads to the Monte Carlo version of the algorithm. Finally, this paper presents a systematic procedure for choosing the user-specified parameters in the ARS algorithm for fastest convergence. The results, which are valid for search spaces of arbitrary dimensions, are illustrated on a simple 3-dimensional example.

Analysis of noise-reducing phase retrieval

Previous work described a phase retrieval algorithm that accepts highly noisy Fourier modulus data and uses the numerous constraints on the coherence data, the image, and their interrelations to obtain high-quality images. In the context of intensity correlation imaging, computational results have shown that the technique is able to reduce the necessary imaging time by many orders of magnitude. The present paper is a theoretical examination of the algorithm, including the issues of convergence, the properties of the convergent image, and the relation between invariance of the image to random initial conditions and the accuracy of the foreground specification.

Noise reducing phase retrieval.

In the context of imaging using the Hanbury Brown-Twiss effect, this paper describes a phase retrieval algorithm capable of producing high-quality images despite large amounts of noise in the coherence magnitude measurement data. Previously the problem was conceived as two distinct steps: coherence magnitude estimation, followed by image construction. The present unified formulation accepts highly noisy data and estimates both the measurement noise and the image using the numerous constraints on the coherence data, the image, and their interrelations. The technique is shown to reduce the necessary imaging time by many orders of magnitude.

Phase retrieval of images using Gaussian radial bases

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction patterns frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transforms modulus, without background constraints. A practical example is shown.

Mitigating the Effect of Noise in Iterative Projection Phase Retrieval

Here the effect of noisy measurement data is explored within the traditional phase retrieval problem with the goal of filtering the noise to obtain an estimate of the true data. The method proposed can be applied to most existing phase retrieval methods.

Phase retrieval applied to stellar occultation for asteroid silhouette characterization

Here we expand on the current methods of characterizing small astronomical bodies, particularly asteroids, by viewing stellar occultation events. Stellar occultation has proven to be a viable method for determining the size of moons and asteroids; however, it comes with some limitations. In general the method does not consider or use all of the known diffraction effects that occur and thus provides a nominal radius--not a shape--of the occluder. We show that most stellar occultation events involving small near-Earth asteroids occur with low Fresnel numbers. This in effect renders the traditional methods useless to characterize the shape, because no sharp shadow exists. We show that using similar data collection to that of the traditional occultation method and inverting a Fresnel diffraction equation by a phase retrieval process can yield a complete reconstruction of the silhouette of the occluder. The effect of noise in the measurements is also discussed. A practical example applied to the asteroid 25143 Itokawa is shown.

Uni-Directional Motion Stability of Spatial Resolution Coverage Discs

A brief account of image synthesis via interferometry using collected light beams from selected pairs of telescopes that constitute a formation of free-flying telescopes is presented. A measure of image quality is adopted that accounts for the optical performance and geometry of the telescopes. Acceptable image quality is achieved when the MTF assumes sufficient magnitudes everywhere within the resolution disc in the spatial resolution plane of the equivalent optical system. The problem is thus a coverage problem where we formulate and find the necessary conditions for optimality and specialize them to distinct cases relevant to the multi-spacecraft imaging situation.