<p>In traditional phase measurement deflectometry (PMD), a number of sinusoidal fringe patterns are displayed on the screen in two orthogonal directions, which is time-consuming and not suitable for dynamic measurements. A phase-extraction algorithm based on the spatial-carrier phase-shifting technology for a single-shot spatial-carrier orthogonal fringe pattern is proposed. The phase increment of each pixel in two orthogonal directions is obtained by the least squares method and then the amount of spatial phase shift of all pixels relative to the probe pixel in the rectangular neighborhood centered on the probe pixel can be obtained. The number of fringe patterns required for the PMD is reduced to one by displaying a spatial-carrier orthogonal fringe pattern. Finally, the feasibility of the algorithm is verified by simulation and experiment.</p>
For on-line surface measurement of transparent optical elements, phase measuring deflectometry (PMD) is a very promising method. However, the parasitic reflection from the rear surface is an existing problem for PMD to measure transparent element. A parasitic reflection eliminating method using binary pattern is proposed, the principle of which is described in detail. And the proposed method is implemented on a transparent window glass with a thickness of about 10mm. The surface shape result shows a good agreement with the interferometer data with a sub-wavelength level accuracy.
In the phase measurement deflectometry, sinusoidal fringe patterns are separately projected on a specular test surface, and the distorted fringes reflected by the surface are recorded by a charge-coupled device (CCD) camera. The phase shift algorithm is used to find the position of the light source on the display corresponding to the pixel point on the CCD, thereby calculating the slope of each point on the element to be tested, and finally retrieving the surface shape of the test element by using the surface reconstruction algorithm. The phase information is usually obtained by traditional 16-step phase-shifting algorithm, which involves certain complicated and time-consuming procedures, for instance, fringe projection in the horizontal and vertical directions. Therefore, to avoid these procedures, a four-step phase shift algorithm based on crossed fringes is proposed. Based on Gram–Schmidt orthonormalization method, only four crossed fringe patterns are needed to determine the phase in both directions simultaneously. Both numerical simulation and experiment are conducted to verify the validity of the algorithm.
Phase measuring deflectometry (PMD) with structured light projection and phase-shifting technique is a highly accurate optical surface measuring method. For surface shape measurement of transparent planar elements, PMD suffers from parasitic reflection. To avoid the unwanted effect of parasitic reflection, a method based on fringe frequency tuning and Fourier-transform is introduced in this paper. Numerical simulations and experiments are both conducted to evaluate the performance of the proposed method. An optical planar element with a thickness of 24.5mm is measured, and measurement error is within 200nm PV.
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.
In phase measuring deflectometry, two orthogonal sinusoidal fringe patterns are separately projected on the test surface and the distorted fringes reflected by the surface are recorded, each with a sequential phase shift. Then the two components of the local surface gradients are obtained by triangulation. It usually involves some complicated and time-consuming procedures (fringe projection in the orthogonal directions, accurate phase shifting).To avoid the complex process, a novel phase extraction algorithm with crossed fringes is presented in this paper. It is based on a least-squares iterative process. Both a numerical simulation and a preliminary experiment are conducted to verify the validity and performance of this algorithm. Experimental results obtained by our method are shown, and comparisons between our experimental results and those obtained by the traditional phase-shifting algorithm and between our experimental results and those measured by the Fizeau interferometer are made.