New phasor reconstruction for speckle imaging

¹ GCD Associates, 2100 Alvarado NE, Albuquerque, NM 87110, USA
² Boeing LTS, PO Box 5670, Kirtland AFB, NM 87185, USA
e-mail: Michael.Tilton@kirtland.af.mil

Received: 15 December 2010
Accepted: 2 March 2011

Abstract

We will develop and then compare object spectrum phasor reconstruction results for several speckle imaging approaches. Each phasor reconstruction algorithm results from minimizing a very naturally defined weighted-least-squares error function. Once we pick a phasor-based error function, the remaining steps in our algorithms are developed by setting the error function variation, with respect to each phasor element, to zero. The resulting coupled nonlinear equations for the minimum error phasor array are then solved iteratively. In the applications, we will specifically compare and contrast three implementations: 1) Knox-Thompson; 2) bispectrum, using only two bispectrum planes; 3) bispectrum, using four bispectrum planes. In each application of the three approaches, we first calculate the modulus of the object spectrum using a Wiener-Helstrom filter to remove the speckle transfer function. The methods then differ only in their object spectrum phasor reconstructions. In the simulations, we will implement all three methods on a simple object at low photon-per-frame light levels. Next, we will apply the methods to a complex extended object. Although we develop and minimize error functions for three specific speckle methods, the approach readily generalizes to other cases.