Introduction

Image restoration is the process of removing artifacts caused by telescope imperfections from images. A good understanding of these imperfections is essential to the process. As part of the ST ScI Image Restoration Project, and continuing under new NASA funding, we are exploring improved ways for determining telescope imperfections, and for using that information to compute accurate point spread functions (PSFs) for restoration. We will be making the products of our work available to the community.

The core of our approach is a sophisticated optical modeling code that generates accurate PSFs directly from telescope optical prescription data. The prescription specifies the physical state of the telescope, namely the location, orientation and figure of the lenses, mirrors, obscurations, and detectors that comprise its optics. Our code utilizes a hybrid geometric and physical optics approach to generate PSFs from this information. It captures the essential physics of the image formation process, including the effects of induced aberrations and diffraction from multiple obscuring surfaces. It provides a rigorous basis for accurately predicting PSFs over widely varying field angles and focus settings without the need for data matching at each point of interest.

The accuracy of this approach is limited by the accuracy of the prescription information. A good starting-point prescription is usually available from the telescope design specifications and from post-fabrication optical test. Changes to the telescope due to environmental effects (or manufacturing errors) can occur, however. In this event, an improved estimate of the prescription data can be obtained using a technique termed ``prescription retrieval.''

Prescription retrieval ``inverts'' image data to determine the prescription of the telescope that made the images. It is a nonlinear parameter estimation technique, which works by varying prescription parameters so as to match diagnostic images with simulated images. It is capable of identifying optical element parameters that affect image location and quality, subject to limitations that we discuss below. Prescription retrieval works best with deliberately defocused, off-axis diagnostic images. We successfully developed prescription retrieval as a tool for determining the conic constant of the HST primary mirror (Redding, Dumont, and Yu 1993).

For image restoration purposes, prescription retrieval to determine a large number of telescope parameters will be required once following a major configuration change of a telescope. For HST, this means post-launch, post refit, and possibly following resetting of the secondary mirror decenter. Parameters to be identified include camera/telescope alignments and camera and OTA mirror figure parameters.

During normal operations of the telescope, minor prescription retrieval, probably to identify a single time-varying parameter such as telescope focus, may be desirable. For HST, this would provide a means of handling the effects of OTA ``breathing.'' This could be performed using the science images - diagnostic images are not required. Once prescriptions are determined for the telescope at a particular time, they can be archived and should be useful for restoring images taken at about that time.

Tracking the telescope prescription over a period of time should also help identify the root causes of changes, such as thermal cycling. It may then be possible to implement corrections to the prescriptions to be used in restoration based on the telemetry stream. For instance, temperature measurements could be used to adjust assumed secondary mirror position, yielding improved PSFs without retrieval.

The immediate product of our work will be a computer program for generating PSFs for each of the HST cameras, both pre and post-refit. This program will use the best current prescription data, and will incorporate retrieved prescriptions as they become available. It will be available from ST ScI early in 1994.

Our ultimate objective, which we will pursue over the next three years jointly with the ST ScI, is to provide a high-performance integrated prescription-based image restoration application. This application will provide functions and features such as PSF generation, prescription retrieval, prescription archiving, and restoration using spatially-variant PSFs. The application will be portable to different platforms and different architectures, including desk-top workstations and massively parallel supercomputers. When completed the application will support distributed processing across heterogeneous computing environments, allowing efficient utilization of networked workstations and supercomputers. We hope it will provide a flexible tool for rapid, high-accuracy restoration of images from HST and other instruments.