Introduction
This paper reports on the application of non-coherent speckle photography and coherent optical processing (Reference CloudCloud and others, 1980) to map small displacements on various rock, earth, and ice surfaces. Briefly, this optical technique requires a high-resolution double-exposed photographic image of the surface of interest: the first image is taken before displacement; the second after. The photographic image is then analyzed with coherent light as described below.
Since the method requires only optical access to the straining surface, other applications include volcanic rock stability, mine-wall strains, and perhaps tectonic plate strains.
Method
The experiments, conducted at Michigan State University and at the Nisqually Glacier site (Fig. 1) during September 1981, were organized in four phases:
Fig. 1. Nisqually Glacier, Rainier National Park, Washington.
First, speckle patterns were obtained using non-coherent light from a partially gravelled parking lot located near the Michigan State University Engineering Building. Although this surface seems quite different from that of an ice field, the variable roughness and random large-scale patterns (e.g. recent tire tracks) resulted in a fair approximation for technique development. The parking lot was photographed from a perch about 20 m above grade; the surface extending from 150 to 200 m horizontally from the camera location.
As noted, the surface in question must be moved or displaced slightly in order to produce Young’s fringe patterns during final processing of the double-exposure high-resolution photograph. The camera back was rotated a small amount, approximately 20 minutes of arc, between exposures in order to create an artificial field displacement.
During this phase trade-offs between experimental parameters were explored. Investigated factors include f-stop, shutter speed, resolution, film speed, focal length, developing technique, etc.
Phase two began with the determination of useful focal length, proper exposure, developing time, etc., for actual glacier conditions. During these tests the camera back was again rotated between exposures in order to create the required artificial field displacement.
Third, time-lapse, double-exposure photographs of the upper elevations of the Nisqually Glacier (Fig. 2) were taken from several viewpoints, each within one kilometer of the terminus. The time interval between exposures was 24 h. The 24 h tests were started in the morning since an oblique sun angle on the south-facing Nisqually Glacier helps to delineate surface roughness. A full 24 h between exposures results, in addition, in a nearly identical sun angle which increases precision. During this phase, the camera was first mounted on a tripod and then on a large rock in order to minimize camera movement.
Fig. 2. View of upper elevations of Nisqually Glacier.
Fourth, the data plates were analyzed in a coherent optical system at Michigan State University to obtain Young’s fringe patterns which are indicative of the flow vector field.
Extraction of surface displacements from the double-exposed photoplates was accomplished as follows:
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Spacing and orientation of Young’s fringes were measured relative to vertical. Corresponding points were then located on the glacier surface using topological maps.
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The ice surface normals were determined at these points.
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The magnitude and direction of any rigid body motion (i.e. camera movement) was detected through microscopic examination of the plate. (Fixed objects appearing on the horizon, such as large boulders resting on the bare rock surface, were useful for this.) The rigid-body reference point was then located on the topological map.
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A computing routine subtracted appropriately scaled rigid-body motion from each point on the plate where fringe patterns were logged, and then it projected the resulting displacement vector onto the glacier surface.
Results
During phase one it was found that small rotations of the camera back about the center of the film produced circular rings of classical speckle pairs which appear superimposed on the parking lot surface. When scanned by a narrow beam of coherent light, the resulting Young’s fringe patterns appeared to rotate and become more fine as the film was scanned from the center outward. This behavior was exactly as expected for rigid-body rotation.
A similar result was produced during the second phase by rotating the camera back with the glacier surface as the object.
The first 24 h double exposures of the glacier surface did not yield results because of apparent large camera movement. This problem was reduced by mounting the camera on a large rock. The desired speckle pairs were produced on large areas of the glacier surface image.
Typical Young’s fringes obtained from the glacier photoplate can be seen in Figure 3. These were obtained by illuminating small areas (nine in all) of the double-exposed glass-plate transparency reproduced by enlargement in Figure 4. These Young’s fringe patterns have not been retouched or subjected to any of the common speckle reduction procedures. They do appear to contain substantial “noise”, of course. Much of this optical noise can be eliminated by well-known methods.
Fig. 3. Young’s fringe patterns generated by passing laser light through two points on high-resolution double-exposure negatives of Nisqually Glacier.
Fig. 4. Englargement of high-resolution double-exposed speckle plate of Nisqually Glacier. Note/ne image structure which creates speckle data is not reproduced except in a few limited areas such as near point A.
Figure 5 is a plan view of the Nisqually Glacier surface showing the location, relative magnitude and direction of ice displacement S mag in meters/day for nine points on the glacier surface. Tabulated results are also shown for the three component directions.
Fig. 5. Surface displacement vector map, plan view. Note surface displacement vectors have length
It should be noted that since optical data-processing does not reveal a sign, assumptions were made regarding the direction of movement. First, it was assumed that ice flows downhill. The second assumption, that of rigid-body motion direction, is somewhat less clear intuitively. Two quite different plots such as shown in Figure 5 could be generated depending on the choice of direction for the rigid-body movement. We give Figure 5 as simply the most reasonable choice since the alternative computation gives displacements of 3 to 4 times greater magnitude. The simultaneous use of two cameras would eliminate this ambiguity.
Points 7 and 8 in Figure 5 roughly correspond to points tracked by conventional methods over a two-year period and reported by Reference HodgeHodge (1974). The 1973 report gives displacement in the range of 0.3 to 0.4 m/d and apparently increasing with time. Figure 5 shows a rate of 0.6 m/d for September 1981. At this early stage of the program such correspondence is highly satisfactory.
The following summary conclusions can be drawn:
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1. Motion of a natural surface illuminated by non-coherent light can be evaluated by Young’s fringe patterns produced from double-exposure high-resolution photoplates.
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2. Analysis of typical fringe patterns from the 24 h tests, such as shown in Figure 3, yields the displacement vector map (Fig. 5) for the glacier surface.
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3. The displacement vectors determined to date agree with the limited field data previously reported.
Acknowledgement
This research was supported by the National Science Foundation under grant No. CME-80-08273. The authors are grateful to Mr Eric Burgoon for his insight, patience and diligent efforts in field and laboratory. The staff persons at Mount Rainier National Park have been kind and helpful, and we are appreciative.
