A method has been developed to increase the accuracy of estimates of phase differences attributable to the optical-path-length difference between the arms of a long-baseline, white-light interferometer. The method is intended for use in the Space Interferometer Mission (SIM), in which there are requirements to (1) keep the phase error averaged over a 30-second integration time low enough to correspond to a path-length error-30 pm and (2) estimate phase differences at a rate of 1 kHz for use in feedback control of the optical-path-length difference of the arms of the interferometer, even when the light is from a distant star or other source that is so dim that the amount of light received from the source amounts to as few as 240 photons per millisecond. The algorithms were developed for monochromatic light, since the combined light is sent through a prism so that light impinging on a single pixel of the detector is nearly monochromatic. Techniques are then used to combine several different monochromatic results into a single, more accurate phase estimate.

Histograms Were Generated In Monte Carlo Simulations of the error in phase estimates of an interferometer operating at a wavelength of 725 nm with a total actuator stroke of 900 nm. The estimates were made by use of (a) a prior non-bias correcting algorithm and (b) a bias correcting algorithm of the present method for integration times of 1 and 100 s. The simulations were repeated 1,000 times to obtain the histograms.

The method is also applicable to ground-based interferometers that are required to operate at low light levels. Most prior phase-estimation algorithms for optical interferometers would exhibit significant biases at the low light levels and short integration times like those required for the SIM. These biases are attributable to shot noise and readout noise of the detector. The noise propagation properties of the algorithms themselves are also of concern. Feedback control actuations and vibrations of the interferometer structures and the consequent changes of optical path lengths during sampling and computation periods also contribute to errors.

The present method involves the use of techniques and algorithms that reduce the error from all of these sources. In this technique, covariances of error sources are taken into account in estimating the desired phase differences by use of optimal nonlinear least-squares techniques. In addition to highly accurate estimates of the average phase difference for relatively long integration periods (e.g., 30 seconds), the method provides estimates of the phase at sub-sampling steps (e.g., 1 millisecond) for feedback control. A Kalman smoothing filter is used to reduce the error associated with temporal variations of phases. The advantage of this method over prior methods is that the phase is estimated more accurately (see figure). The disadvantage is that in comparison with prior methods, this method entails more computation.

This work was done by Scott Basinger and Mark Milman of Caltech for NASA's Jet Propulsion Laboratory.

This software is available for commercial licensing. Please contact Don Hart of the California Institute of Technology at (818) 393-3425. Refer to NPO-30337.

This Brief includes a Technical Support Package (TSP).
Estimating White-Light-Interferometer Phases in Dim Light

(reference NPO30337) is currently available for download from the TSP library.

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This article first appeared in the November, 2002 issue of Photonics Tech Briefs Magazine.

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