Shift invariant spaces are common in the study of analysis, appearing, for example, as cornerstones of the theories of wavelets and sampling. The interplay of these three notions is discussed at length over R, with the one-dimensional study providing motivation for later discussions of Rn, locally compact abelian groups, and some non-abelian groups. Two fundamental tools, the so-called bracket" as well as the Zak transform(s), are described, and their deep connections to the aforementioned areas of study are made explicit.
We describe the fringe-packet tracking software installed at the infrared optical telescope array (IOTA). Three independently developed fringe-packet tracking algorithms can be used to equalise the optical path lengths at the interferometer. We compare the performance of these three algorithms and show results obtained tracking fringes for three independent baselines on the sky.
An automatic fringe tracking system has been developed and implemented at the Infrared Optical Telescope Array (IOTA). In testing during May 2002, the system successfully minimized the optical path differences (OPDs) for all three baselines at IOTA. Based on sliding window discrete Fourier transform (DFT) calculations that were optimized for computational efficiency and robustness to atmospheric disturbances, the algorithm has also been tested extensively on off-line data. Implemented in ANSI C on the 266 MHz PowerPC processor running the VxWorks real-time operating system, the algorithm runs in approximately 2.0 milliseconds per scan (including all three interferograms), using the science camera and piezo scanners to measure and correct the OPDs. Preliminary analysis on an extension of this algorithm indicates a potential for predictive tracking, although at present, real-time implementation of this extension would require significantly more computational capacity.
The first tests of an infrared fringe-tracker prototype for the IOTA interferometer (Mount-Hopkins, Arizona) were carried out during 1999. The aim of this real-time system is to minimize the optical path difference (OPD) fluctuations between the two beams such that interference fringes (obtained in J, K, or L band) can always be observed within the `scan window' given by the instrument. After an introduction of the employed technology (hardware and software), we present results obtained from star observations. Finally, we discuss the possibility of improving the fringe-tracker by prediction of the OPD, using statistical properties of its fluctuations. The improvement of the fringe-tracker already existing for the FLUOR recombiner is discussed as well.
The Infrared/Optical Telescope Array (IOTA) is a multi- aperture Michelson interferometer located on Mt. Hopkins near Tucson, Arizona. To enable viewing of fainter targets, an on-line fringe tracking system is presently under development at NASA Ames Research Center. The system has been developed off-line using actual data from IOTA, and is presently undergoing on-line implementation at IOTA. The system has two parts: (1) a fringe tracking system that identifies the center of a fringe packet by fitting a parametric model to the data; and (2) a fringe packet motion prediction system that uses characteristics of past fringe packets to predict fringe packet motion. Combined, this information will be used to optimize on-line the scanning trajectory, resulting in improved visibility of faint targets. Fringe packet identification is highly accurate and robust (99% of the 4000 fringe packets were identified correctly, the remaining 1D were either out of the scan range or too noisy to be seen) and is performed in 30 - 90 milliseconds (depending on desired accuracy) on a Pentium II-based computer. Fringe packet prediction, currently performed using an adaptive linear predictor, delivers a 10% improvement over the baseline of predicting no motion.
NASA Kuiper telescope personnel identified computer-aided telescope balancing as a needed capability which will save significant amount of time and will improve SOFIA operational effectiveness. Automated telescope balancing is considered a 'critical technology need' for SOFIA. It is necessary to balance the telescope to accommodate the different science instruments. The telescope must be adequately balanced to enable the pointing and tracking system to operate properly. In-flight balancing may be necessary because the mass properties of the science instruments can change during its operation and because of disturbance torques. In the past, a trial and error procedure was used to balance the Kuiper telescope, which can take up to several hours and requires a highly skilled, experienced technician to perform the task. Various approaches for balancing the telescope are reported in this paper. Potential benefits are: 1) enable balance compensation to be performed quickly, thereby reducing operations costs, 2) enable a much wider range of balance compensation to be performed in-flight, which may increase science observation time and science return, 3) enable technicians of any skill level to balance the telescope with the aid of a computerized system, and 4) improve the performance of the telescope by increasing the precision of the balance, which may increase science return.