Novel optical designs have been proposed for future space-based imaging systems, generally consisting of mirrors with lower areal densities and shorter fabrication times than their conventional counterparts. This may translate into significant cost savings. However, lightweight mirrors are less rigid and often exhibit aberrations in dynamic thermal and mechanical environments. Digital post-processing can compensate for the associated negative effects, but the net loss in image quality compared with unaberrated systems is difficult to quantify.
Image-quality metrics based solely on resolution are inadequate because they do not consider the impact of either noise or artifacts. The expected mean-squared error—compared to an ideal image—is not equivalent to perceived image quality. For our work, the quality of an image is specified in terms of the national imagery interpretability rating scale (NIIRS), which tracks the ability of image analysts to perform various object-recognition tasks.1 The general image-quality equation (GIQE) is used to compute the NIIRS level that one can expect from a particular system, but human-subject trials are needed to validate GIQE predictions. We have designed such trials to obtain accurate NIIRS ratings from untrained observers. We currently use a tumbling-E eye chart with various contrast ratios (see Figure 1) as test targets. We simulate aberrated images under various conditions. We then ask observers to select images of the same quality from a carefully calibrated set of reference images, basing their selections on their ability to recognize the orientation of the E at various scale sizes, as opposed to the specific object-recognition tasks from the NIIRS tables.1 There are many details regarding the generation of the calibrated image set and the display of images that must be addressed to obtain accurate results.2 Nevertheless, the NIIRS ratings we obtained in preliminary control studies with unaberrated imagery were of fairly good quality.2
Figure 1. Simulated images of this tumbling-E eye chart are used to evaluate the impact of aberrations on the ability of human observers to perform simple object-recognition tasks.
The GIQE is intended for use with well-corrected imaging systems and standard image-sharpening algorithms. It accounts for resolution, noise, and artifacts (see Figure 2). While the resolution terms are based on physics,2 those representing the impact of noise and artifacts on the human visual system are based on regression analysis of image-analyst evaluations. In general, more aggressive post-processing is needed to compensate for substantial aberrations, which leads to noise-texture patterns in the resulting images (see Figure 3). The human visual system responds differently to a given level of noise depending on this texture.3 Thus, we anticipate that the noise term in the GIQE will need to be modified to provide accurate NIIRS predictions for aberrated systems.
Figure 2. Image quality is affected by (left column) optical resolution, (center column) noise, and (right column) edge-overshoot artifacts. The influence of each factor increases from top to bottom.
We also need to worry about the amplification of artifacts during aberration compensation. We prefer the Wiener filter for aberration compensation because it is computationally efficient, yields results as good as or even better than more complex nonlinear algorithms,4 and provides valuable physical insights. We have reformulated the Wiener filter in the Fourier domain to explicitly account for aliasing artifacts and include parameters that provide tailored control over the tradeoffs between resolution, noise gain, and artifact suppression in post-processed imagery.5 Our analysis also yields a net system-transfer function that characterizes the combined effects of the optics, detector, and post-processing on all spatial scales, even at high spatial frequencies that may be undersampled by the system's focal-plane array. This enables us to compute the resolution terms in the GIQE for aliased imagery.
Figure 3. Unprocessed aberrated imagery (top row) with increasing high-spatial-frequency aberrations (left to right). As aberration strength increases, more aggressive post-processing is required to compensate for the loss in contrast, causing textured noise in post-processed imagery (bottom row).
It is difficult to quantify the impact of aberrations on the ability to perform various object-recognition tasks with post-processed imagery. We have formulated the analytic tools necessary for computing the image-quality tradeoffs associated with aberrations in the context of the GIQE. Our next step is to conduct human-subject trials with aberrated imagery. A regression analysis of the trial results will likely lead to a modified form of the GIQE for aberrated imagery.
This research has been performed in collaboration with James R. Fienup (University of Rochester). Robert D. Fiete, Jason R. Calus, and James A. Mooney (ITT Space Systems Division) provided invaluable advice.
Samuel T. Thurman
The Institute of Optics
University of Rochester