title: Multi-spatial-frequency and phase-shifting profilometry using a liquid crystal                 phase modulator.
abstract: Optical profilometry is widely applied for measuring the morphology of objects                 by projecting predetermined patterns on them. In this technique, the compact size is                 one of the interesting issues for practical applications. The generation of pattern                 by the interference of coherent light sources has a potential to reduce the                 dimension of the illumination part. Moreover, this method can make fine patterns                 without projection optics, and the illumination part is free of restriction from the                 numerical aperture of the projection optics. In this paper, a phase-shifting                 profilometry is implemented by using a single liquid crystal (LC) cell. The LC phase                 modulator is designed to generate the interference patterns with several different                 spatial frequencies by changing selection of the spacing between the micro-pinholes.                 We manufactured the LC phase modulator and calibrated it by measuring the phase                 modulation amount depending on an applied voltage. Our optical profilometry using                 the single LC cell can generate multi-spatial frequency patterns as well as four                 steps of the phase-shifted patterns. This method can be implemented compactly, and                 the reconstructed depth profile is obtained without a phase-unwrapping                 algorithm.
authors.affiliation: School of Electrical Engineering and Computer Science, Kyungpook National University, Buk-gu, Daegu, Korea.
authors.forename: Kyung-Il
authors.initials: KI
authors.lastname: Joo
authors.forename: Chang-Sub
authors.initials: CS
authors.lastname: Park
authors.forename: Min-Kyu
authors.initials: MK
authors.lastname: Park
authors.forename: Kyung-Woo
authors.initials: KW
authors.lastname: Park
authors.forename: Ji-Sub
authors.initials: JS
authors.lastname: Park
authors.forename: Youngmin
authors.initials: Y
authors.lastname: Seo
authors.forename: Joonku
authors.initials: J
authors.lastname: Hahn
authors.forename: Hak-Rin
authors.initials: HR
authors.lastname: Kim