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Characterization of Fresnel images of an elongated circular grating

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We characterize theoretically and experimentally Fresnel images (or self-images) of an elongated circular (EC) grating which could be employed for the visual measurement of linear displacements in Talbot moiré deflectometry. Based on a Fresnel diffraction integral, we estimate the shape of the Fresnel image formed at a specific distance from the EC grating in which both parallel lines and semicircles are illuminated by a coherent plane wave. For a square type transmittance of the grating, we also compare the theoretical estimates with its self-images captured by an array of charge-coupled devices (CCD). We show that self-images of the EC grating are substantially aberrated near the center of the interface between the linear and semicircular parts but not in its off-central region. Moiré patterns by two self-imaged EC gratings are found not much affected by the central aberration.

Keywords: Self-image; Talbot effect; elongated circular grating

Document Type: Original Article


Affiliations: 1: Department of Physics, Hannam University, 133 Ojungdong, Taejon 300-791, Korea 2: Department of Physics Education, Kongju National University, 182 Sinkwandong, Kongju, Korea

Publication date: September 1, 2002


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