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.
This paper reports the results of a design study for an exoplanet imaging system. The design team consisted of
the students in the "Electromagnetic Sensing for Space-Bourne Imaging" class taught by the principal author in the
Spring, 2005 semester. The design challenge was to devise a space system capable of forming 10X10 pixel images of
terrestrial-class planets out to 10 parsecs, observing in the 9.0 to 17.0 microns range. It was presumed that this system
would operate after the Terrestrial Planet Finder had been deployed and had identified a number of planetary systems for
more detailed imaging.
The design team evaluated a large number of tradeoffs, starting with the use of a single monolithic telescope,
versus a truss-mounted sparse aperture, versus a formation of free-flying telescopes. Having selected the free-flyer
option, the team studied a variety of sensing technologies, including amplitude interferometry, intensity correlation
imaging (ICI, based on the Brown-Twiss effect and phase retrieval), heterodyne interferometry and direct electric field
reconstruction. Intensity correlation imaging was found to have several advantages. It does not require combiner
spacecraft, nor nanometer-level control of the relative positions, nor diffraction-limited optics. Orbit design, telescope
design, spacecraft structural design, thermal management and communications architecture trades were also addressed.
A six spacecraft design involving non-repeating baselines was selected. By varying the overall scale of the baselines it
was found possible to unambiguously characterize an entire multi-planet system, to image the parent star and, for the
largest base scales, to determine 10X10 pixel images of individual planets.
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.
In contrast to standard Michelson interferometry, the idea of entry pupil processing is to somehow convert light gathered at each telescope (of a multi-spacecraft array) into data, then process the data from several telescopes to compute the mutual coherence values needed for image reconstruction. Some advantages are that weak beams of collected light do not have to be propagated to combiners, extreme precision relative path length control among widely separated spacecraft is unnecessary, losses from beam splitting are eliminated, etc. This paper reports our study of several entry pupil processing approaches, including direct electric field reconstruction, optical heterodyne systems and intensity correlation interferometry using the Hanbury Brown-Twiss effect. For all these cases and for amplitude
interferometry, we present image plane signal-to-noise (SNR) results for exo-planet imaging, both in the case of planet emissions and for imaging the limb of planets executing a transit across their stars. We particularly consider terrestrial-class planets at a range of 15 pc or less. Using the SNR and related models, we assess the relative advantages and drawbacks of all methods with respect to necessary aperture sizes, imager sensitivity, performance trends with increasing
number of measurement baselines, relative performance in visible and in IR, relative positioning and path length control requirements and metrology requirements. The resulting comparisons present a picture of the performance and complexity tradeoffs among several imaging system architectures. The positive conclusion of this work is that, thanks to advances in optoelectronics and signal processing, there exist a number of promising system design alternatives for exo-
In this paper, we consider the design of minimum time maneuvers for multi-spacecraft interferometric imaging systems. We show that the process of image formation in a multi-spacecraft interferometric imaging system is analogous to painting a "large disk" with smaller "paintbrushes", while maintaining a minimum thickness of paint. We show that spiral maneuvers form the dominant set for the painting problem. Further, we frame the minimum time problem in the space of spiral maneuvers and obtain the Double Pantograph Problem. We show that the solution of the Double Pantograph Problem is given by the solution to two associated linear programming problems. We illustrate our results through an imaging example where the image of a fictitious exo-solar planet is formed using the maneuver prescribed by the Double Pantograph Problem.
The problem of quantifying minimum acceptable performance of multi-spacecraft interferometric imaging systems is considered. The noise corrupting the measurements is critical in the design of these systems and is dependent on the motion of the constituent spacecrafts.
Minimum acceptable performance is defined in terms of the misclassification error of an image given that the set of images has been partitioned into two distinct classes. Two measures of the noise corrupting the measurements are considered: mean squared error(MSE) and the worst case error(WCE). It is shown that these are consistent with the goal of image classification in the sense that as image estimates converge in the MSE/WCE sense, the probability
of misclassifying the image tends to zero. Error bounds are obtained on the MSE/WCE such that some minimum acceptable performance, in terms of the probability of correctly classifying an image, is acheived. An example is presented where the bandedness of the image of a planet is sought to be detected. Bounds on the noise corrupting the measurements are obtained such that a pre-specified level of performance is achieved for this case.
While significant theoretical and experimental progress has been made in the development of neural network-based systems for the autonomous identification and control of space platforms, there remain important unresolved issues associated with the reliable prediction of convergence speed and the avoidance of inordinately slow convergence. To speed convergence of neural identifiers, we introduce the preprocessing of identifier inputs using Principal Component Analysis (PCA) algorithms. Which automatically transform the neural identifier's external inputs so as to make the correlation matrix identity, resulting in enormous improvements in the convergence speed of the neural identifier. From a study of several such algorithms, we developed a new PCA approach which exhibits excellent convergence properties, insensitivity to noise and reliable accuracy.
Operation of sensitive equipment aboard multi-sensor platforms requires active vibration isolation technology. In response to these needs, the active isolation fitting (AIF) was developed to replace passive mechanical end fittings and joints in truss structures. The AIF combines intrastructural and inertial devices to cancel vibration transmission into a vibration-sensitive subsystem. This paper discusses the AIF principles of operation, details its robust performance characteristics and reviews the extensive experimental results that have been accumulated over the past several years. Test results show 20 to 30 dB of broadband isolation for both single AIF tests and six degree-of-freedom isolation systems demonstrated on two major, government- supplied testbeds.
This paper discusses the Adaptive Neural Control (ANC) Architecture for on-line system identification and adaptive control. After reviewing results to-date involving control of structural vibration, we describe extensions of the ANC architecture to handle adaptive control of smart structures involving large numbers of distributed actuators and sensors.
Many future space missions involving flexible structures for large optics may require active vibration control to satisfy mission objectives. Thus, it is important for active control of flexible structures to be practically demonstrated in ground based experiments. These experiments can validate (or invalidate) existing theories and technology and provide directions for future research. This paper discusses three experiments conducted by Harris which successfully demonstrate control of flexible structures. The paper concludes with some remarks on the lessons learned from conducting these experiments.