Parametric definition for the CGH patterns and error analysis in interferometric measurements

Zhou, Ping; Cai, Wenrui; Zhao, Chunyu; Burge, James H.

doi:10.1117/12.2010725

Cited by 8 publications

(7 citation statements)

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“…Given a 2 m diameter F ∕2 aspheric surface with the fourth-order coefficient A −1.220 × 10 −13 mm −3 , B −1.691 × 10 −20 mm −5 is under test, setting h 500 mm, p 450 mm, and L 0 0.5 mm, the needed t is 11.9 mm according to Eqs. (14), (16), and (17). Actually, t 11.7 mm (approximate error ∼1.7%) is chosen to design the CGH with Zemax.…”

Section: Cgh Design Example For a Concave Weak Aspheric Surface Wimentioning

confidence: 99%

“…Setting the filter plane 455.44 450 5.44 mm away from the CGH plane, while still treating p 450 mm, and assuming the required minimum separated distance L 0 0.5 mm, the needed t is 9.5 mm according to Eq. (14). Actually, t 9.5 mm is chosen.…”

Section: B Cgh Design Examples For Conic Surfacesmentioning

confidence: 99%

“…But the double-pass undesired orders were not considered. Zhou et al [14] proposed a paraxial solution for the amount of the needed power carrier frequency, but the CGH with tilt carriers was not discussed.…”

Section: Introductionmentioning

confidence: 99%

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Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

et al. 2015

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Computer-generated holograms (CGHs) are commonly used to test aspheric surfaces. In order to eliminate the influence of spurious diffraction orders, adequate carrier frequency is applied to CGHs to separate the overlapping orders. This paper describes a paraxial parametric model for separating the parasitic diffraction orders of a tilt carrier frequency CGH placed outside the interferometer focus. The approximate analytical expression for the disturbing field on the filter plane is derived using the paraxial model. This expression provides a recipe for determining the amount of tilt carrier frequency needed to eliminate the disturbing orders, and is applicable to concave weak aspheric surfaces with large f-numbers of the best-fit spheres, where paraxial approximation is valid. CGH design examples are provided.

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Section: Cgh Design Example For a Concave Weak Aspheric Surface Wimentioning

confidence: 99%

Section: B Cgh Design Examples For Conic Surfacesmentioning

confidence: 99%

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Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

et al. 2015

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“…Different with compensator, CGH is a diffraction optical element, shown in Fig.1 Aspheric surface under test r J circular, and the wanted diffraction order is (+1,+1) [4] . When the spherical wavefront from interferometer passes through CGH, the +1 diffraction order wavefront changes into aspherical wavefront, which is match with the aspheric surface under test.…”

Section: Cgh Test Technologymentioning

confidence: 99%

Experiment and analysis of computer generated hologram for testing aspheric surface

Chen

2014

SPIE Proceedings

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When testing aspheric surface by computer generated hologram (CGH), there are some engineering problems in experiments. Within a lot of experiments, some unknown conditions appeared, and we analyzed two of them in detail and simulated them in Zemax. The unwanted diffraction orders maybe bring ghost image, and ring source is a simple method to eliminate it. The parallelism error of CGH substrate will bring a non-rotational symmetric error in test result, which is shown as coma. The size of the coma is related by parallelism error and the degree of the coma is related by the angle compared with the origin position. And a rotation method was presented to know the influence of parallelism error. After that, the projection distortion is expounded in detail and distortion calibration is successful to guide to enhance the precision of aspheric surface. These analysis results are very useful in practical engineering applications.

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“…They argued the SDO (−1, 3) and (3, −1) has the most significant effect on measurement accuracy and calculated the minimum amount of power carrier frequency to separate SDO. In 2012, P. Zhou et al [7] developed the parameter model to describe the CGH null system in power carrier frequency and calculated the distance from the pinhole to its paraxial image. This distance was used to evaluate the separation of SDO.…”

Section: Introductionmentioning

confidence: 99%

Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology

He¹,

Hou²,

Wu³

et al. 2017

Opt. Express

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Abstract:Computer-generated hologram (CGH) has been widely used as a wavefront compensator in symmetric aspheric metrology. As a diffractive element, it generates different diffraction orders, but only the 1st-order diffraction is used to test aspheric surface. The light from spurious diffraction orders (SDO) will produce many high-frequency fringes in interferogram and reduce measurement accuracy. In this paper, we regard the CGH null system as an imaging system and develop an aberration model in Seidel formalism to analyze the SDO. This model has the advantage to address the difference between the SDO (k 1 , k 2 ) and (k 2 , k 1 ). We consider the effect of the pupil distortion so that our model can analyze the SDO with a large pupil distortion. We derive the condition to ensure the 2 nd -order and 4 th -order aberrations have the same sign and calculate the minimum defocused distance (power carrier frequency) of CGH. According to the marginal-ray heights ( 1 h and 3 h ) on the CGH in the first and second passes, we determine the condition that the SDO covers the whole CGH in the second pass. We analyze the SDO of 4 CGH designs and compare the results from our aberration model with these from real ray trace. These results validate that our aberration model is feasible whether the aspheric part is convex or concave and whether CGH is inside or outside the focus of the transmission sphere.

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Parametric definition for the CGH patterns and error analysis in interferometric measurements

Cited by 8 publications

References 0 publications

Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

Experiment and analysis of computer generated hologram for testing aspheric surface

Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology

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