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.
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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Overview
The document presents a technical support package from NASA detailing a novel method for estimating phase differences in long-baseline white-light interferometers, particularly under dim light conditions. Developed by Scott Basinger and Mark Milman at Caltech for NASA’s Jet Propulsion Laboratory, this method addresses the challenges faced by the Space Interferometer Mission (SIM), which requires precise phase measurements from very faint light sources, such as distant stars.
The primary goal of the method is to maintain a low phase error, corresponding to a path-length error of less than 30 picometers, averaged over a 30-second integration time. Additionally, it aims to provide phase difference estimates at a rate of 1 kHz for feedback control, even when the light received is as low as 240 photons per millisecond. Traditional phase estimation algorithms struggle with significant biases at these low light levels due to shot noise and readout noise, which can lead to inaccuracies in phase measurements.
The innovative approach utilizes optimal nonlinear least-squares techniques to account for covariances of error sources, thereby improving the accuracy of phase estimates. A Kalman smoothing filter is employed to mitigate errors associated with temporal variations in phase, allowing for more reliable data even amidst vibrational disturbances that the interferometer may experience. The method also enables phase estimation at sub-sampling intervals, which is crucial for real-time feedback mechanisms.
While the new technique offers enhanced accuracy over conventional methods, it does come with increased computational demands. The document highlights the advantages of this method, particularly its ability to correct for biases that conventional algorithms do not address, making it suitable for the specific requirements of the SIM and other low-light applications.
The software developed from this research is available for commercial licensing, and interested parties are directed to contact Don Hart at Caltech for further information. Overall, this work represents a significant advancement in optical phase measurement technology, with implications for both space-based and ground-based interferometry.
