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Rigid body motion measurements with Fourier lensless holography.

A recently proposed1 holographic and moiré technique for in-plane motion measurements is generalized to certain cases of rigid body motion measurements. In this case, a three-recording-plates set, in a trihedral arrangement attached to an object, registers the interference between spherical and plañe coherent wave fronts. The in­ terference fringes are plañe sections of a paraboloid revolution family with a common axis parallel to the plañe wave propagation direction; it also contains the point source originating the spherical wave. If, between two such exposures, the arrangement is translated or rotated in the space, the two overlapping interference patterns registered will produce low frequency moiré patterns. If the movement is small (less than the innermost Fresnel ring), the moiré pattern consists of families of equally spaced straight lines, the spacing and orientation of which are related to the magnitude and orientation of the displacement or rotation. So, as in the case of inplane motions of the photographic píate, these moiré fringes can be used to determine the magnitude and direction of the displacement or the angles of rotation. In addition, each family of moiré fringes gives rise, in the Fourier plañe, to two bright spots separated by a distance proportional to the magnitude of the displacement or rotation. Also, a slanted image of the pupil limiting the plañe wave, reconstructed in the Fourier plañe, is njodulated by Young’s fringes, whose interfringe is also reciprocally proportional to the magnitude of the movement. First, let us consider the intensity moiré pattern produced by the overlapping of the two interference patterns in each of the three recording plates of the trihedral arrangement. In general, the transmittance of the developed plates will be