Study of weighted space deconvolution algorithm in computer controlled optical surfacing formation

Li, Hongyu; Zhang, Wei; Yu, Guoyu

doi:10.3788/col20090707.0627

Cited by 22 publications

(5 citation statements)

References 4 publications

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“…where R is the aperture radius of optical workpiece. The first matrix on the left of equation is a 2D convolution kernel matrix with N 1 matrix columns and N 2 columns in each submatrix F(h 1 , N 2 ) which is constructed by 1D convolution kernel [11].…”

Section: Zernike Mapping Methodsmentioning

confidence: 99%

“…To remove residual form error, previous researches have proposed several methods to compute dwell time for CCOS methods. According to literature review, the most popular algorithms for solving the dwell time are the convolution iterative method and Fourier transform [11]. The convolution iterative method proposed by Jones et al [12] is based on the 2D convolution algorithm and a computation loop for updating dwell time.…”

Section: Introductionmentioning

confidence: 99%

“…Experience indicates that a small factor results in a small residual error in the central region while causing a remarkably large error at the edge, which leads to a smaller clear aperture for the produced optical components in practice. Considering this kind of edge problem is induced in optimization by conventional deconvolution algorithm, the inclusion of an extra marginal factor was attempted to control the edge accuracy [11]. Besides, with a small damping factor, serious oscillation is generated on the dwell time map, which poses a huge mechanical burden for the polishing machine and challenges the machine dynamics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics

Zhu

Beaucamp

2019

Opt. Express

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In optics fabrication technologies such as computer controlled optical surfacing (CCOS), accurate computation of the dwell time map plays an essential role in the deterministic performance of the fabrication process. However, it is still difficult for existing methods to derive smooth dwell time maps that reduce dynamic stressing on the machine especially at the aperture edge region, while retaining fine correction capability on freeform optics. To answer these challenges, we propose a new method based on Zernike decomposition and improved differential evolution optimization of the dwell time map, which can be applied to time-dependent optics fabrication processes such as fluid jet machining. Simulations and experiments based on a bisinusoidal freeform design were carried out to assess the feasibility of the proposed methodology. With appropriate fluid jet pressure, a bi-sinusoidal optical surface with demanding form error target of sub-100 nm in peak-to-valley was achieved, showing a remarkable improvement on the state-of-the-art, while keeping a good average surface roughness of 2.6 nm Ra on the optical glass.

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Section: Zernike Mapping Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics

Zhu

Beaucamp

2019

Opt. Express

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“…Although practical fluid jet polishing is hardly affected by the polishing edge effect [21], the edge-up phenomenon occurs when performing polishing removal simulations, which is a common problem that is difficult to avoid when solving the dwell time [22,23]. In this algorithm, to avoid the influence of this phenomenon on the solution in the region of interest, the polished surface and its form error will extend outward by a specified distance, and so does the planned polishing path, as shown in Figure 7b.…”

Section: Variable Pitch Spiral Path Planning Methodsmentioning

confidence: 99%

Theoretical Study of Path Adaptability Based on Surface Form Error Distribution in Fluid Jet Polishing

et al. 2018

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In the technology of computer-controlled optical surfacing (CCOS), the convergence of surface form error has a close relationship with the distribution of surface form error, the calculation of dwell time, tool influence function (TIF) and path planning. The distribution of surface form error directly reflects the difference in bulk material removal depth across a to-be-polished surface in subsequent corrective polishing. In this paper, the effect of path spacing and bulk material removal depth on the residual error have been deeply investigated based on basic simulation experiments excluding the interference factors in the actual polishing process. With the relationship among the critical evaluation parameters of the residual error (root-mean-square (RMS) and peak-to-valley (PV)), the path spacing and bulk material removal depth are mathematically characterized by the proposed RMS and PV maps, respectively. Moreover, a variable pitch path self-planning strategy based on the distribution of surface form error is proposed to optimize the residual error distribution. In the proposed strategy, the influence of different bulk material removal depths caused by the distribution of surface form error on residual error is compensated by fine adjustment of the path spacing according to the obtained path spacing optimization models. The simulated experimental results demonstrate that the residual error optimization strategy proposed in this paper can significantly optimize the overall residual error distribution without compromising the convergence speed. The optimized residual error distribution obtained in sub-regions of the polished surface is more uniform than that without optimization and is almost unaffected by the distribution of parent surface form error.

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“…In the sub-aperture polishing of optical components, the amount of material removed is equal to the convolution of the tool influence function (TIF) with the dwell time along a specified polishing path, which can be expressed as follows [29]:…”

Section: Analysis Of Msf Error Sourcementioning

confidence: 99%

Research on the Influence of the Material Removal Profile of a Spherical Polishing Tool on the Mid-Spatial Frequency Errors of Optical Surfaces

He,

Hai,

et al. 2024

Micromachines

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Elastic spherical polishing tools effectively conform to the polishing surface and exhibit high efficiency in the removal of materials, so they are extensively used in the sub-aperture polishing stages of optical components. However, their processing is often accompanied by significant mid-spatial frequency (MSF) errors, which critically degrade the performance of optical systems. To suppress the MSF errors generated during polishing with spherical tools, this study investigates the influence factor of MSF errors during the polishing process through an analysis of the convolution effect in material removal. A material removal profile model is established, and a uniform removal simulation is conducted to assess the influence of different shape material removal profiles on MSF errors. Simulation and experimental results show that a Gaussian-like shape material removal profile is more effective in suppressing the MSF errors during polishing compared to the “W” and trapezoidal shape material removal profiles. In addition, based on the characteristics of the RMS decreasing in a serrated trend with the decrease in path spacing, a path spacing optimization method considering the polishing efficiency is proposed to improve the polishing efficiency while controlling the MSF errors, and the effectiveness of the path spacing optimization method is verified by comparing the MSF error at the maximum theoretical path spacing and the path spacing that is less than this. Finally, the path spacing optimization method is used to polish single-crystal silicon to further illustrate its practicality.

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Study of weighted space deconvolution algorithm in computer controlled optical surfacing formation

Cited by 22 publications

References 4 publications

Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics

Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics

Theoretical Study of Path Adaptability Based on Surface Form Error Distribution in Fluid Jet Polishing

Research on the Influence of the Material Removal Profile of a Spherical Polishing Tool on the Mid-Spatial Frequency Errors of Optical Surfaces

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