We describe a slitless spectrograph designed for use in the IR region between 2.6 and 5.2 micrometers . The dispersing element is a grism fabricated in silicon by binary-optical techniques. This approach permits the incorporation of aberration correction into the grating element. When combined with simple, all-silicon field and camera optics, the grism forms zero-order images and 3.5 mm- long dispersed spectra on a 256 by 256 element array of 38 micrometers InSb detectors. Interchangeable field lenses provide for 8:1, 6:1, and 4:1 reduction to a final focal ratio of f/2.5.
We present an analysis and computational results relating to the regularized restoration of subpixel information from undersampled data. The method makes use of a small set of images in various stages of defocus. An iterative implementation permits the incorporation of a non- negativity constraint. The problem we consider is fundamentally under-determined, but useful results can be obtained in reasonably low noise conditions.
Image restoration procedures are commonly unstable in the presence of noise, and some technique for restoring stability becomes essential. The methods of regularization theory are particularly appropriate for this purpose. A specific type of regularized solution is introduced in the general context of image reconstruction. A super-resolution problem is then considered from the point of view of the computational tasks involved, with particular reference to the estimation of certain key parameters and to implementations which increase the efficiency of the calculations. Parameter estimation is performed by weighted cross-validation. The improvement in efficiency is achieved through the exploitation of symmetries or cyclic properties inherent in the reconstruction operator. The concept of displacement rank is introduced and estimates made of the computational burden associated with various classes of regularized reconstruction matrices.