Shot noise limits to sensitivity of optical interferometry

By arguing that the limiting noise is the photoelectron shot noise, we show that the sensitivity of image synthesis by an ideal optical interferometer is independent of the details of beam-splitting and recombination. The signal-to-noise ratio of the synthesized image is proportional to the square root of the total number of photoelectrons detected by the entire array. For non-ideal interferometers, which are forced to employ a closure-phase method of indirect inference of the visibility data, essentially the same result holds for strong sources, but at weak light levels beam-splitting degrades sensitivity

Noise in optical synthesis images. I. Ideal Michelson interferometer

We study the distribution of noise in optical images produced by the aperture synthesis technique, in which the principal source of noise is the intrinsic shot noise of photoelectric detection. The results of our analysis are directly applicable to any space-based optical interferometer. We show that the signal-to-noise ratio of images synthesized by such an ideal interferometric array is essentially independent of the details of the beam-combination geometry, the degree of array redundancy, and whether zero-spatial-frequency components are included in image synthesis. However, the distribution of noise does depend on the beam-combination geometry. A highly desirable distribution, one of uniform noise across the entire image, is obtained only when the beams from the n primary apertures are subdivided and combined pairwise on n(n - 1)/2 detectors

Quantum Limits on Localizing Point Objects against a Uniformly Bright Disk

We calculate the quantum Fisher information (QFI) for estimating, using a circular imaging aperture, the two-dimensional location of a point source against a uniformly bright disk of known center and radius in the ideal photon-counting limit. We present both a perturbative calculation of the QFI in powers of the background-to-source brightness ratio and a numerically exact calculation of the QFI in the eigen-basis of the one-photon density operator. A related problem of the quantum limit on estimating the location of a small-area brightness hole in an otherwise uniformly bright disk, a problem of potential interest to the extrasolar planet detection community, is also treated perturbatively in powers of the ratio of the areas of the hole and the background disk. We then numerically evaluate the Cramer-Rao lower bound (CRB) for wavefront projections in three separate bases, those comprised of Zernike, Fourier-Bessel and localized point-source modes, for unbiased estimation of the two position coordinates of the point source and of the brightness hole center, respectively, for the two problems. By comparing these CRBs with the corresponding quantum-limited minimum error variances, given by inverting the QFI matrix, and with the CRBs associated with direct imaging, we assess the maximum efficiency of these wavefront projections in performing such estimations.Comment: Accepted for publication in Physical Review

Noise in optical synthesis images. II. Sensitivity of an ^nC_2 interferometer with bispectrum imaging

We study the imaging sensitivity of a ground-based optical array of n apertures in which the beams are combined pairwise, as in radio-interferometric arrays, onto n(n - 1)/2 detectors, the so-called ^nC_2 interferometer. Groundbased operation forces the use of the fringe power and the bispectrum phasor as the primary observables rather than the simpler and superior observable, the Michelson fringe phasor. At high photon rates we find that bispectral imaging suffers no loss of sensitivity compared with an ideal array (space based) that directly uses the Michelson fringe phasor. In the opposite limit, when the number of photons per spatial coherence area per coherence time drops below unity, the sensitivity of the array drops rapidly relative to an ideal array. In this regime the sensitivity is independent of n, and hence it may be efficient to have many smaller arrays, each operating separately and simultaneously