New three-dimensional displacement measurement system: modified four-beam moire´ interferometer–Twyman/Green

Abstract

An MMI-T/G system composed of a modified four-beam moire interferometer (MMI) and a Twyman/Green (T/G) interferometer is developed. The MMI-T/G can measure 3-D displacement fringe patterns with a single loading on the specimen. In the MMI-T/G system, one incident laser beam is diffracted into multiple beams by the cross-line grating on the specimen, where the ±1 order diffractive beams are redirected back to the specimen by flat mirrors, then rediffracted by the specimen grating onto the CCD, generating the in-plane displacement fringe pattern; the zero-order diffractive beam interferes with a reference beam of the T/G, generating the out-of-plane displacement fringe pattern. Details of the derivation of the fringe-governing equations are given based on the wavefront interference theory. The fringe-governing equations so obtained are comparable with those derived previously based the Doppler frequency shift theory and conventional moire interferometry. The in-plane displacement sensitivity of the new system can be shown to be twice of that of a normal moire interferometer. The optical setup has the advantages of structure novelty, flexibility, and high fringe contrast. Experiments are carried out to validate the derived governing equations, and clear thermodeformation fringe patterns of an electronic package are shown.