Higher-moment and diffraction-order computation for deformation measurement

• Published in: Optics and lasers in engineering 2000-02, Vol.33 (2), p.165-175
• Main Author: Kokaj, J
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Image forming and processing; Imaging and optical processing; Measurements common to several branches of physics and astronomy; Metrology, measurements and laboratory procedures; Optics; Physics; Spatial dimensions (e.g.: position, lengths, volume, angles, displacements, including nanometer-scale displacements); Spatial dimensions (eg, position, lengths, volume, angles, displacements, including nanometer-scale displacements)
• ISSN: 0143-8166; 1873-0302
• DOI: 10.1016/S0143-8166(00)00031-2

Higher moment and diffraction orders are computed and used for deformation measurement. For a given two-dimenstional function lower-order moments are calculated. It is shown that simplified results can be obtained if an appropriate pattern is used for the calculation. The obtained results are employed for calculation of higher-order mements. Optical implementation and their use for deformation measurement is shown. High diffraction orders are introduced by using a projected grill-pattern on the model surface. This is performed by selecting higher frequency spots in the Fourier-Transform plane. Selection of the high-frequency diffraction orders and calculation of high-order moments are two image processing approaches useful for deformation measurement. Accuracy of the measurement for in-plane deformation and out-of-plane rotation is calculated. It is shown that accuracy of measurement is increased when higher orders are used.