To solve this problem, we proposed placing the object far outside the two reference planes. We call this method extrapolation, while the conventional method is called interpolation (Fig. 6). Using extrapolation, we can measure larger and more distant objects than the reference planes. Fig. 7 shows an example of the extrapolation measurement of an aircraft's delta wing deformed by load. We believe that there is a large demand for plane-profile measurement, not only in outer space but also on the ground.
Instead of projecting the lattice onto the object and reference planes, we can attach or paint it on. Or have the object and planes themselves display the grating pattern. We are also trying to improve accuracy by integrating with stereo view. Fig. 8 shows measurement of the surface profile of a semi-transparent concave mirror by the interpolation method using two cameras. In this example, the light-and-dark stripe pattern was displayed by using a plane TV monitor as the reference panel.
Although the measured-object data required for profile calculation is a single image shot by a fixed-position camera, we can use multiple stripe images photographed from the same position in order to improve the determination accuracy of phase per sine-wave grating pixel. Fig. 5, 7 and 8 used the phase-determination technique by multiple stripe images. In Fig. 5, we use simultaneously the whole-space tabulation method to improve accuracy and shorten the measuring time. In Fig. 7, we combined extrapolation with the geometry-calculation method to calculate pixel position of the object and the calibration method to improve accuracy. As discussed above, various accuracy-improving techniques can be used in conjunction with the grating-projection method so we are now conducting further research.
Since it is possible to determine in principle the phase of the surface stripe pattern from a single image of the object, we can also deal with successive profile change - though this depends on deformation speed, surface optical profile and measurement accuracy. We believe that we can apply this method to profile measurement during deployment, for example, and surface dynamic profile measurement such as waving after deployment, crimp or sag motion, etc.
If we can maintain the positional relation between the reference planes and the camera/projector and take an image of the planes on the ground in advance, there is no need to carry the planes into orbit. In fact, in our experiments on the ground, we shot the reference planes in advance and then removed them and positioned the object for measurement. Although in the above experiments we used the commercially available, inexpensive liquid-crystal projector, in orbit it is better to use a projector composed of light source and slits, or to mark in advance the stripe pattern on the part to be measured. The grating-projection method is not limited to use in orbit, but can also be used on Earth, the Moon and other planets. We are sure that we can provide an inexpensive and simple technique for the pre-ground tests of space-deployable structures. With the continuing improvement in accuracy, it is expected that the all-in-one equipment for this method will be developed using its chief merit Esimple and compact setup.