Perturbation methods in optics: application to the interferometric measurement of surfaces

Garbusi, Eugenio

doi:10.1364/josaa.26.002538

Cited by 38 publications

(19 citation statements)

References 15 publications

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“…There are four types of interferometric measurements in the testing of freeform optics. 5,[18][19][20][21][22] As shown in Fig. [9][10][11] However, for each specific surface, a matching CGH has to be manufactured which makes it nonuniversal.…”

Section: Introductionmentioning

confidence: 99%

“…[9][10][11] However, for each specific surface, a matching CGH has to be manufactured which makes it nonuniversal. 22 But it would be a better method if we could directly calculate the shape error from the fringes, as with a common Fizeau interferometer, in contrast to getting the perturbation of the surface's description polynomial coefficients from the fringe, because some freeform optics cannot be represented by a polynomial with high precision. Third, for increasing the interferometric dynamic range, scanning or stitching interferometry methods have also been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm

et al. 2015

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Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 08/17/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm Abstract. As is well-known, optical testing has begun to emerge as a limiting factor in the application of freeform surfaces. In all kinds of published freeform optical metrology, the tilted-wave-interferometer (TWI) is the precise and flexible method for testing a freeform surface as it can compensate the local surface's deviation from its best fit sphere by using a set of tilted waves. In the process of measurement with TWI, accurate assessment of the test surface error from the fringes plays a key role. We present a method for evaluation and characterization of surface aberrations in TWI by combining computer-generated wave technology and a retrace errors elimination algorithm. The feasibility of the method is proved by the simulation and experimental results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm

et al. 2015

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“…The analysis has been applied to provide means to determine the effects of lens profile imperfection [7], misalignment of aspheric surfaces [8] and to study the economical fabrication problem [9]. However, none of the previous studies were devoted to the power against the LSM.…”

Section: Introductionmentioning

confidence: 99%

Illumination variation under a freeform lens and misalignment of light source

Lin

2011

2011 6th IEEE Conference on Industrial Electronics and Applications

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Use of an optical lens with a freeform surface is a popular and flexible approach in the LED applications for uniform illumination. The lens topologies are flexible for design to achieve a desired illumination pattern. However, different topologies may have different powers against the misalignment of the light source. The misalignment problem was studied based on the ray-tracing simulation that is inefficient on the computer time. In this study, the problem of misalignment along the lens optical axis is analyzed and formulated by applying the perturbation analysis. The formulations developed are applicable for the problems with small misalignment and large misalignment as well. The superiority of the proposed analytical approach over the ray-tracing simulation approach is highlighted. The adequacy of the proposed formulations is confirmed by cross validation. Good consistency between the analysis and the simulation is demonstrated by examples.

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Results of a Sensitivity Analysis for the Tilted-Wave Interferometer

et al. 2014

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IntroductionTilted-wave interferometry (TWI) is a novel measurement technique for the highly accurate optical measurement of aspheres and freeform surfaces [1][2][3][4][5][6][7]. It combines interferometric measurements with ray tracing and mathematical reconstruction procedures. The first results of a sensitivity analysis were given in [8]. The results support the feasibility of the basic TWI principle, and good reconstruction results were obtained for surfaces whose deviations from the design topography are described by Zernike polynomials. The TWI reconstruction procedure is divided into two parts. The first part reconstructs the long-wave deviation of the specimen from its design form. The second part aims at the reconstruction of high spatial frequencies [7]. This paper investigates the robustness of the long-wave TWI reconstruction method. Therefore, we extend the sensitivity analysis to surfaces whose deviation from their design topography no longer corresponds to a Zernike polynomial. We utilize a simulation environment that was developed at PTB for assessing optical measuring systems [8,9]. Reconstruction accuracies are then investigated in dependence on the variation of the specimen's topography and the measurement noise. Different variations of the specimen's topography with different spatial frequencies are studied. Furthermore, the influence of the deviation of the vertex radius of the design topography is investigated. Throughout all simulations no errors in the characterization of the TWI were assumed to be present which corresponds to a perfect calibration. Mathematical Reconstruction ProcedureThe TWI reconstruction principle for the basic form of the specimen utilizes measurements of the optical path length (OPL) in order to calculate the deviation of the surface under test from its design topography. The idea is that small changes of the surface topography lead to small changes in the OPLs. The long-wave

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Perturbation methods in optics: application to the interferometric measurement of surfaces

Cited by 38 publications

References 15 publications

Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm

Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm

Illumination variation under a freeform lens and misalignment of light source

Results of a Sensitivity Analysis for the Tilted-Wave Interferometer

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