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To obtain a hollow variable biconical laser beam (HVBLB), a CO2 laser having a hollow circular-truncated cone resonator (HCTCR) is presented. This HCTCR comprises a rotationally symmetric total-reflecting concave mirror at the bottom, a rotationally symmetric part-reflecting convex mirror at the top, and a hollow circular-truncated cone discharge tube at the middle. The cross section of this generated biconical laser beam changes from annulus to circular to annulus and the size of this cross section from big to small to large as the propagation distance increases. So, a kind of laser beam with variable center intensity from zero to peak value to zero is obtained and is known as HVBLB. Due to the inclusion of part of the hollow laser beam (HLB) and solid laser beam, this HVBLB requires no additional beam-shaping element and has broad applications such as optical trapping and commercial manufacturing. [ABSTRACT FROM AUTHOR]

Phase measuring deflectometry (PMD) with structured light projection and phase-shifting technique is a highly accurate optical surface measuring method based on the law of reflection. Generally, for surface shape measurement of transparent planar elements, PMD suffers from parasitic reflection. To avoid the unexpected effect of parasitic reflection, a method based on fringe frequency tuning and Fourier-transform is introduced. Numerical simulations and experiments are both conducted to evaluate the performance of the proposed method. Experiment results are shown. Surface figures measured using the proposed method are compared with those measured using traditional phase-shifting algorithm and Fizeau interferometer. Both an optical planar element with a thickness of 24.5 mm and a planar window glass with a thickness of 10 mm are measured. For the optical element, the proposed method is accurate and the measurement error is within 200-nm PV. For window glass, the proposed method yields a better surface figure than the traditional phase-shifting algorithm does. [ABSTRACT FROM AUTHOR]