We analyze a Fourier-domain Wiener filter for the reconstruction of aliased imagery. The filter is designed to minimize the expected mean square error for the unaliased portion of the object Fourier transform. This analysis yields a net system transfer function, which characterizes the combined effects of the imaging system, sampling, and the reconstruction process, that is valid at both aliased and unaliased spatial frequencies. This transfer function provides insight into how aliasing artifacts are modified by the reconstruction process. Additionally, the net transfer function is useful for characterizing the combined performance of the imaging system and post processing. For example, the net system transfer function can be used to calculate the edge response for reconstructed imagery even in the presence of aliasing. Examples are used to illustrate these aspects of using the Wiener filter with aliased imagery.
The general image quality equation (GIQE) [Leachtenauer et al., Appl. Opt. 36, 8322-8328 (1997)] is an empirical
formula for predicting the quality of imagery from a given incoherent optical system in terms of the National Imagery
Interpretability Rating Scale (NIIRS). In some scenarios, the two versions of the GIQE (versions 3.0 and 4.0) yield
significantly different NIIRS predictions. We compare visual image quality assessments for simulated imagery with
GIQE predictions and analyze the physical basis for the GIQE terms in an effort to determine the proper coefficients for
use with Wiener-filtered reconstructions of Nyquist and oversampled imagery in the absence of aberrations. Results
indicate that GIQE 3.0 image quality predictions are more accurate than those from GIQE 4.0 in this scenario.
Fourier transform imaging spectroscopy (FTIS) can be performed with a Fizeau imaging interferometer by recording a series of images with various optical path differences (OPDs) between subapertures of the optical system and postprocessing. The quality of the spectral data is affected by misregistration of the raw image measurements. A Fizeau FTIS system possesses unique degrees of freedom that can be used to facilitate image registration without further complication of the system design. We describe a registration technique based on the fact that certain spatial frequencies of the raw imagery are independent of the OPDs introduced between subapertures. Operational and post-processing tradeoffs associated with this technique are described, and the technique is demonstrated using computer-simulated data with image shift misregistrations under realistic noise conditions.
Fourier transform imaging spectroscopy can be performed with a segmented-aperture telescope or a multiple-telescope array using the subaperture piston control mechanisms. Spectrum recovery from intensity measurements is analyzed for a general aperture configuration. The spatial transfer functions of the recovered spectral images are shown to vanish necessarily at the DC spatial frequency. This poses an interesting image reconstruction problem as the recovered spectral data is missing low spatial-frequency content. Results of a band-by-band reconstruction of simulated data are presented where the low spatial frequency data is reconstructed by maximizing a sharpness metric based on the spatial derivatives of the object estimate.