Shearography is an interferometric method that overcomes several limitations of holography by eliminating the reference beam. It greatly simplifies the optical setup and has much higher tolerance to environmental disturbances. Consequently, the technique has received considerable industrial acceptance, particularly for nondestructive testing. Shearography, however, is generally not applicable to the measurement of an obstructed area, as the area to be measured must be accessible to both illumination and imaging. We present an algorithm based on the principle of tomography that permits the reconstruction of the unavailable phase distribution in an obstructed area from the measured boundary phase distribution. In the process, a set of imaginary rays is projected from many different directions across the area. For each ray, integration of the phase directional derivative along the ray is equal to the phase difference between the boundary points intercepted by the ray. Therefore, a set of linear equations can be established by considering the multiple rays. Each equation expresses the unknown phase derivatives in the obstructed area in terms of the measured boundary phase. Solution of the set of simultaneous equations yields the unknown phase distribution in the blind area. While its applications to shearography are demonstrated, the technique is potentially applicable to all full-field optical measurement techniques such as holography, speckle interferometry, classical interferometry, thermography, moiré, photoelasticity, and speckle correlation techniques.
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