Nonnegative Matrix Factorization for Efficient Hyperspectral Image Projection

Hyperspectral imaging for remote sensing has prompted development of hyperspectral image projectors that can be used to characterize hyperspectral imaging cameras and techniques in the lab. One such emerging astronomical hyperspectral imaging technique is wide-field double-Fourier interferometry. NASA's current, state-of-the-art, Wide-field Imaging Interferometry Testbed (WIIT) uses a Calibrated Hyperspectral Image Projector (CHIP) to generate test scenes and provide a more complete understanding of wide-field double-Fourier interferometry. Given enough time, the CHIP is capable of projecting scenes with astronomically realistic spatial and spectral complexity. However, this would require a very lengthy data collection process. For accurate but time-efficient projection of complicated hyperspectral images with the CHIP, the field must be decomposed both spectrally and spatially in a way that provides a favorable trade-off between accurately projecting the hyperspectral image and the time required for data collection. We apply nonnegative matrix factorization (NMF) to decompose hyperspectral astronomical datacubes into eigenspectra and eigenimages that allow time-efficient projection with the CHIP. Included is a brief analysis of NMF parameters that affect accuracy, including the number of eigenspectra and eigenimages used to approximate the hyperspectral image to be projected. For the chosen field, the normalized mean squared synthesis error is under 0.01 with just 8 eigenspectra. NMF of hyperspectral astronomical fields better utilizes the CHIP's capabilities, providing time-efficient and accurate representations of astronomical scenes to be imaged with the WIIT

Recent Experiments Conducted with the Wide-Field Imaging Interferometry Testbed (WIIT)

The Wide-field Imaging Interferometry Testbed (WIIT) was developed at NASA's Goddard Space Flight Center to demonstrate and explore the practical limitations inherent in wide field-of-view double Fourier (spatio-spectral) interferometry. The testbed delivers high-quality interferometric data and is capable of observing spatially and spectrally complex hyperspectral test scenes. Although WIIT operates at visible wavelengths, by design the data are representative of those from a space-based far-infrared observatory. We used WIIT to observe a calibrated, independently characterized test scene of modest spatial and spectral complexity, and an astronomically realistic test scene of much greater spatial and spectral complexity. This paper describes the experimental setup, summarizes the performance of the testbed, and presents representative data

Spatio-Spectral Interferometric Imaging and the Wide-Field Imaging Interferometry Testbed

The light collecting apertures of space telescopes are currently limited in part by the size and weight restrictions of launch vehicles, ultimately limiting the spatial resolution that can be achieved by the observatory. A technique that can overcome these limitations and provide superior spatial resolution is interferometric imaging, whereby multiple small telescopes can be combined to produce a spatial resolution comparable to a much larger monolithic telescope. In astronomy, the spectrum of the sources in the scene are crucial to understanding the material composition of the sources. So, the ultimate goal is to have high-spatial-resolution imagery and obtain sufficient spectral resolution for all points in the scene. This goal can be accomplished through spatio-spectral interferometric imaging, which combines the aperture synthesis aspects of a Michelson stellar interferometer with the spectral capabilities of Fourier transform spectroscopy. Spatio-spectral interferometric imaging can be extended to a wide-field imaging modality, which increases the collecting efficiency of the technique. This is the basis for NASA’s Wide-field Imaging Interferometry Testbed (WIIT). For such an interferometer, there are two light collecting apertures separated by a variable distance known as the baseline length. The optical path in one of the arms of the interferometer is variable, while the other path delay is fixed. The beams from both apertures are subsequently combined and imaged onto a detector. For a fixed baseline length, the result is many low-spatial-resolution images at a slew of optical path differences, and the process is repeated for many different baseline lengths and orientations. Image processing and synthesis techniques are required to reduce the large dataset into a single high-spatial-resolution hyperspectral image. Our contributions to spatio-spectral interferometry include various aspects of theory, simulation, image synthesis, and processing of experimental data, with the end goal of better understanding the nature of the technique. We present the theory behind the measurement model for spatio-spectral interferometry, as well as the direct approach to image synthesis. We have developed a pipeline to preprocess experimental data to remove unwanted signatures in the data and register all image measurements to a single orientation, which leverages information about the optical system’s point spread function. In an experimental setup, such as WIIT, the reference frame for the path difference measured for each baseline is unknown and must be accounted for. To overcome this obstacle, we created a phase referencing technique that leverages point sources within the scene of known separation in order to recover unknown information regarding the measurements in a laboratory setting. We also provide a method that allows for the measurement of spatially and spectrally complicated scenes with WIIT by decomposing them prior to scene projection

Spatio-spectral interferometric imaging and the wide-field imaging interferometry testbed

Thesis (Ph. D.)--University of Rochester. The Institute of Optics, 2018.The light collecting apertures of space telescopes are currently limited in part by the size and weight restrictions of launch vehicles, ultimately limiting the spatial resolution that can be achieved by the observatory. A technique that can overcome these limitations and provide superior spatial resolution is interferometric imaging, whereby multiple small telescopes can be combined to produce a spatial resolution comparable to a much larger monolithic telescope. In astronomy, the spectrum of the sources in the scene are crucial to understanding the material composition of the sources. So, the ultimate goal is to have high-spatial-resolution imagery and obtain sufficient spectral resolution for all points in the scene. This goal can be accomplished through spatiospectral interferometric imaging, which combines the aperture synthesis aspects of a Michelson stellar interferometer with the spectral capabilities of Fourier transform spectroscopy. Spatio-spectral interferometric imaging can be extended to a wide-field imaging modality, which increases the collecting efficiency of the technique. This is the basis for NASA’s Wide-field Imaging Interferometry Testbed (WIIT). For such an interferometer, there are two light collecting apertures separated by a variable distance known as the baseline length. The optical path in one of the arms of the interferometer is variable, while the other path delay is fixed. The beams from both apertures are subsequently combined and imaged onto a detector. For a fixed baseline length, the result is many low-spatial-resolution images at a slew of optical path differences, and the process is repeated for many different baseline lengths and orientations. Image processing and synthesis techniques are required to reduce the large dataset into a single high-spatial-resolution hyperspectral image. Our contributions to spatio-spectral interferometry include various aspects of theory, simulation, image synthesis, and processing of experimental data, with the end goal of better understanding the nature of the technique. We present the theory behind the measurement model for spatio-spectral interferometry, as well as the direct approach to image synthesis. We have developed a pipeline to preprocess experimental data to remove unwanted signatures in the data and register all image measurements to a single orientation, which leverages information about the optical system’s point spread function. In an experimental setup, such as WIIT, the reference frame for the path difference measured for each baseline is unknown and must be accounted for. To overcome this obstacle, we created a phase referencing technique that leverages point sources within the scene of known separation in order to recover unknown information regarding the measurements in a laboratory setting. We also provide a method that allows for the measurement of spatially and spectrally complicated scenes with WIIT by decomposing them prior to scene projection