Aspheric optics: smoothing the ripples with semi-flexible tools

Tuell, Michael T.; Burge, James H.; Anderson, Bill

doi:10.1117/1.1481898

Cited by 37 publications

(23 citation statements)

References 4 publications

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“…In Section 3(1), it was explained that the final k is related to κ total , V, and K p . Applying (11) to the K p measured in Section 3(3) and the κ total calculated from the SF function, we can express the surface error as a function of the smoothing time t directly. An example having a 0.3-µm ε ini is shown in Fig.…”

Section: Smoothing Experiments and Resultsmentioning

confidence: 99%

“…Subsequently, Jones simulated MSF error evolution based on a simple linear parametric model [9], and Mehta and Reid later proposed the classic Bridging model to study the smoothing effect, which is based on the theory of elasticity [10]. Tuell et al then improved the Bridging model using the spatial Fourier decomposition method [11]. Later, Kim et al introduced a parametric smoothing model based on the simplified Bridging model to describe smoothing effects [12]; this parametric smoothing model was further verified by Shu et al using a correlation-based model [13].…”

Section: Introductionmentioning

confidence: 99%

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Improving smoothing efficiency of rigid conformal polishing tool using time-dependent smoothing evaluation model

Song

Zhang

et al. 2017

Photonic Sens

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Abstract:A rigid conformal (RC) lap can smooth mid-spatial-frequency (MSF) errors, which are naturally smaller than the tool size, while still removing large-scale errors in a short time. However, the RC-lap smoothing efficiency performance is poorer than expected, and existing smoothing models cannot explicitly specify the methods to improve this efficiency. We presented an explicit time-dependent smoothing evaluation model that contained specific smoothing parameters directly derived from the parametric smoothing model and the Preston equation. Based on the time-dependent model, we proposed a strategy to improve the RC-lap smoothing efficiency, which incorporated the theoretical model, tool optimization, and efficiency limit determination. Two sets of smoothing experiments were performed to demonstrate the smoothing efficiency achieved using the time-dependent smoothing model. A high, theory-like tool influence function and a limiting tool speed of 300 RPM were obtained.

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Section: Smoothing Experiments and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improving smoothing efficiency of rigid conformal polishing tool using time-dependent smoothing evaluation model

Song

Zhang

et al. 2017

Photonic Sens

View full text Add to dashboard Cite

show abstract

“…The sinusoidal surface error's pressure distribution was attained from a series of differential equations under the given boundary conditions, and it was supposed to be proportional to its amplitude. The bridging model was further applied to the aspheric surface polished by Burge et al [9] and Tuell et al [10]. Kim et al [11] developed the normalized smoothing factor based on the simplified bridging model and conducted a contrast experiment on pitch lap and rigid conformal lap, which is verified by Shu et al [12] with the help of a correlation-based smoothing model.…”

Section: Introductionmentioning

confidence: 93%

“…In the SP process shown in Fig. 11, the optical surface is smoothed by a Φ150 mm semi-flexible polishing lap [10,11] while the average applied pressure is 20 KPa. The pitch pad is also 4 mm.…”

Section: Applicationmentioning

confidence: 99%

Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors

Nie

Shi

et al. 2014

Appl. Opt.

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The smoothing effect of the rigid lap plays an important role in controlling midspatial frequency errors (MSFRs). At present, the pressure distribution between the polishing pad and processed surface is mainly calculated by Mehta's bridging model. However, this classic model does not work for the irregular MSFR. In this paper, a generalized numerical model based on the finite element method (FEM) is proposed to solve this problem. First, the smoothing polishing (SP) process is transformed to a 3D elastic structural FEM model, and the governing matrix equation is gained. By virtue of the boundary conditions applied to the governing matrix equation, the nodal displacement vector and nodal force vector of the pad can be attained, from which the pressure distribution can be extracted. In the partial contact condition, the iterative method is needed. The algorithmic routine is shown, and the applicability of the generalized numerical model is discussed. The detailed simulation is given when the lap is in contact with the irregular surface of different morphologies. A well-designed SP experiment is conducted in our lab to verify the model. A small difference between the experimental data and simulated result shows that the model is totally practicable. The generalized numerical model is applied on a Φ500 mm parabolic surface. The calculated result and measured data after the SP process have been compared, which indicates that the model established in this paper is an effective method to predict the SP process.

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“…Computer-controlled polishing machines and mathematical models to analyze material removal characteristics have been developed for polishing spherical, aspheric and free form surfaces, where small-size tools are employed [3][4][5][6] . We presented our efforts in developing a polishing process using a large size polishing lap, where a mathematical model was developed to estimate the residual surface errors under a given set of operating parameter and lap configurations 7,8 .…”

Section: Introductionmentioning

confidence: 99%

Computer-controlled cylindrical polishing process for development of grazing incidence optics for the hard x-ray region

et al. 2010

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The focusing performance of shell optics for the hard X-ray region strongly depends on their axial mid-spatialfrequency-range figure errors. This paper presents the development of a deterministic computer-controlled polishing process to minimize these axial figure errors on cylindrical shaped mandrels from which the mirror shells are replicated. A mathematical model has been developed to simulate the residual surface figure errors due to the polishing process parameters and the polishing tools used, along with their non-conformance to the mandrel. We present design considerations of a large-size polishing lap where the experimentally determined process variables have been used for optimizing the lap configuration and the machine operational parameters. Furthermore, the developed model is capable of generating a corrective polishing sequence for a known surface error profile. Practical polishing experiments have been performed to verify the model and to determine its ability to correct known axial figure errors through polishing machine control.

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Aspheric optics: smoothing the ripples with semi-flexible tools

Cited by 37 publications

References 4 publications

Improving smoothing efficiency of rigid conformal polishing tool using time-dependent smoothing evaluation model

Improving smoothing efficiency of rigid conformal polishing tool using time-dependent smoothing evaluation model

Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors

Computer-controlled cylindrical polishing process for development of grazing incidence optics for the hard x-ray region

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