December 1980. LOCAL INSTANCES OF GOOD SEEING ... correct for the image wandering using multiple frame image sequences. The average of many short ...
Volume 35, number 3
OPTICS COMMUNICATIONS
December 1980
LOCAL INSTANCES OF GOOD SEEING H.H. SZU, J.A. BLODGETT and L. SICA Applied Optics Branch, Optical Sciences Division, Naval Research Laboratory, Washington, D.C. 20735, USA Received 28 May 1980 Revised manuscript received 29 July 1980
One of the major causes of image degradation in imaging through an inhomogeneous medium with small aperture optics, or through an uneven boundary layer, is a local tilt term in the expression for the incoming wavefront. This manifests itself as a local or space variant distortion of the image. When a temporal sequence of such images is examined, there is wandering of the image both locally and as a whole. In this paper we describe a time selection technique which has been employed to correct for the image wandering using multiple frame image sequences. The average of many short exposures, the equivalent of one long exposure, is computed in a first pass through the images. Then in a second pass, the local image regions which are shifted too far from the long term average are deleted, while the centroids of those remaining are reregistered with respect to the equivalent long exposure. Such a two pass technique is mathematically analyzed and demonstrated experimentally with a sequence of images of an underwater bar.
1. Multiple-frame image sequence Numerous papers have been written about singleimage processing during the last two decades [ 1]. Many techniques have been developed for image acquisition [2], data reduction and transmission [3], edge detection [4], the trade-off of local resolution for noise suppression [5,6], the incorporation of a priori information into image restoration [7], and the development o f nonlinear and recursive image processing [8]. Nearly all, however, are concerned with an individual image I(x, y ) . This may be simultaneously recorded in multiple spectral regions [9] and, in the case of certain satellite imagery, transmitted blockwise every tenth o f a minute. These manipulations may suffer from instrumental noise and distortion, but they are particularly differentiated from the situation treated herein by the fact that the~e is little if any time correlation between successive images. Thus, many laboratories equipped with modern instruments work on single image processing with application to electron microscopy [10], computer vision [11], pattern analysis [12] and the fulfillment o f various goals o f the space program [13].
In the last few years, the utility of processing multiple samples of an image in the Fourier plane has been demonstrated by the success of stellar speckle interferometry. However, this technique assumes space-invariance of the point-spread function of the imaging system. When an unknown object is imaged over a horizontal path near the ground, object identification is complicated by space-variant image wandering over the image area. The utility of image space processing o f multiple samples in an image sequence has not been fully studied under this condition. The processing of multiple frame image sequences may prove very useful for distant surveillance. The important conceptual difference between single frame and multiple frame image processing will become clear in section 4.
2. Instances of good seeing Image degradation may be characterized by (a) shift as a whole, (b) space variant distortion, and (c) overall degeneration due to point spread function enlargement when the disturbance correlation length is small317
Volume 35, number 3
OPTICS COMMUNICATIONS
er than the receiving aperture. Thus, a long time exposure (LE) suffers from edge blurring and loss of fine detail. However, the location of a given feature in a LE image is correct with respect to other features in the sense that the image has been formed by a LE PSF which is spatially stationary. The study of image wandering [14] in astronomy has a long history. A brief survey of techniques in this field will make the need for mathematical analysis clear. The central idea in treating image wandering comes from the fact that a human observer, the astronomer, is frequently able to see more with "'live" imaging than from an image recorded on photographic film. Two reasons for this may be especially singled out, a priori knowledge in memory, and visual tracking in time. Both may be usefully implemented in image processing techniques for image sequences in time. A priori knowledge may be implemented in numerous time-selection schemes utilizing (i) postselection or (ii) pre-selection. The first may be carried out by simply throwing away bad frames taken with various exposure times at different time points based on some predetermined selection criteria. The second implies real-time sampling techniques. The visual tracking idea may be implemented with adaptive optics which can be traced back to Babcock's idea [15] of applying a modulated electric charge to the surface of the oil film covering the Eidopher mirror. Subsequently, extensive mathematical analyses [ 16, 18] have been devoted to adaptive optical systems. Many image stabilization devices have been developed to counter image wander. Leighton [19] invented a 2-Hz bandwidth mechanical device in 1956 to move the film plate to produce pictures of Saturn and Mars using the 60-inch reflecting telescope on Mount Wilson. Itek [20] developed an electronic image motion stabilization device ElMS which used feedback to lock on to the centroid of a 4.6 mm bar target vibrating at about 100 Hz for a 1 s exposure using the Cloudcroft telescope. Russian astronomers [21 ] used the time-selection technique of Platt [22] to study short exposure. In the Gregory [23] real-time sampling technique, a long exposure master negative, the a priori information, is inserted in the image plane. A short exposure (SE) is made [24] with a shutter and beamsplitter arrangement whenever the light in the instantaneous 318
December 1980
image is blocked sufficiently well by the negative as determined by a photomultiplier. Thus, instances of good seeing are preselected. These instances correspond to those moments when the PSF is relatively stationary and correct and thus are infrequent with an extended scene. In contrast, tire technique utilized here accepts a major portion of each image and performs a local correction, if required, which makes the imagery nearly spatially stationary.
3. Experiment In the present work, the image of an "unknown" bar object put at an arbitrary angle at the bottom of a water tank is degraded by surface waves created by tilting the tank along one edge of the tank shown in fig. 1. In different individual frames, the bar image moves from one side to the other (see figs. 2a and 2b). Variation of the image width along the bar clearly indicates the space-variant nature of the image wandering (see fig. 2c). The simulated long exposure time (1 s), resulting from the addition of 60 TV fields of short exposure time (1/60 s) information has not only e soft edge but also a nonuniform width in fig. 2d, i.e., the PSF is not yet spatially stationary along the v direction.
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