Mid-spatial Frequency Errors Research Articles

Investigation of the influence of constant pressure oil source fluctuations on ultra-precision machining

The waviness errors on the machined surfaces have significant impact on the performance of optical components. Mid-spatial frequency errors (amplitude near 10 nm, wavelength about 1 mm) are found on the machined surfaces along feeding direction, and the oil pressure fluctuations of the hydrostatic slide are confirmed to be the main source which produces such waviness errors. In this article, the influence of oil pressure fluctuations on the machined surface is studied quantitatively for the first time, and the corresponding experiments are carried out. Besides, the three-dimensional surface profile simulations of workpieces considering the oil pressure fluctuations are achieved. The simulation results have been verified by the experiments on an ultra-precision flycutting machine.

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

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.

Further investigations on fixed abrasive diamond pellets used for diminishing mid-spatial frequency errors of optical mirrors

As further application investigations on fixed abrasive diamond pellets (FADPs), this work exhibits their potential capability for diminishing mid-spatial frequency errors (MSFEs, i.e., periodic small structure) of optical surfaces. Benefitting from its high surficial rigidness, the FADPs tool has a natural smoothing effect to periodic small errors. Compared with the previous design, this proposed new tool employs more compliance to aspherical surfaces due to the pellets being mutually separated and bonded on a steel plate with elastic back of silica rubber adhesive. Moreover, a unicursal Peano-like path is presented for improving MSFEs, which can enhance the multidirectionality and uniformity of the tool's motion. Experiments were conducted to validate the effectiveness of FADPs for diminishing MSFEs. In the lapping of a Φ=420 mm Zerodur paraboloid workpiece, the grinding ripples were quickly diminished (210 min) by both visual inspection and profile metrology, as well as the power spectrum density (PSD) analysis, RMS was reduced from 4.35 to 0.55 μm. In the smoothing of a Φ=101 mm fused silica workpiece, MSFEs were obviously improved from the inspection of surface form maps, interferometric fringe patterns, and PSD analysis. The mid-spatial frequency RMS was diminished from 0.017λ to 0.014λ (λ=632.8 nm).

基于经验模态分解-Wigner分布的光学元件中频误差识别

The mid-spatial frequency error of high precision optical surface is crucial to the performance of high-energy laser system. To assure the performance and stability of the system, the low frequency error and high frequency error of the optical lens surface must be strictly controlled, the mid-spatial frequency error must also be strictly limited. In this paper, the relationship between empirical mode decomposition-Wigner-Ville distribution (EMD-WVD) method and power spectrum density is analyzed, and EMD-WVD diagnosis method is applied to identifying and locating the mid-spatial frequency error of the precision optical surface. The experimental results show that, with EMD-WVD method, the mid-spatial frequency error distribution of optical surface can be located in 15-27 mm and the spatial frequency is 0.1 mm-1, the interference of cross-term caused by multi-component signal whose spatial frequency is about 1.0-1.5 mm-1 can also be reduced, which enhances the identification accuracy of mid-spatial frequency error.

Opto-thermal analysis of a lightweighted mirror for solar telescope

In this paper, an opto-thermal analysis of a moderately heated lightweighted solar telescope mirror is carried out using 3D finite element analysis (FEA). A physically realistic heat transfer model is developed to account for the radiative heating and energy exchange of the mirror with surroundings. The numerical simulations show the non-uniform temperature distribution and associated thermo-elastic distortions of the mirror blank clearly mimicking the underlying discrete geometry of the lightweighted substrate. The computed mechanical deformation data is analyzed with surface polynomials and the optical quality of the mirror is evaluated with the help of a ray-tracing software. The thermal print-through distortions are further shown to contribute to optical figure changes and mid-spatial frequency errors of the mirror surface. A comparative study presented for three commonly used substrate materials, namely, Zerodur, Pyrex and Silicon Carbide (SiC) is relevant to vast area of large optics requirements in ground and space applications.

400 mm口径平面窗口元件中频误差控制技术

For large optics of high-power laser facility, the controlling technology of mid-spatial frequency error is developed. Firstly, the CCOS convolution residual error caused by regular path is analyzed, and the residual error model is established. And then, the optimization parameters for controlling mid-spatial frequency error are achieved by this model. Finally, according to the optimization parameters, the mid-spatial frequency error of 400 mm aperture window is remarkably improved. After several CCOS iteration, the peak-to-valley(PV) is 170.856 nm, the root-mean-square(RMS) of PSD1 is 1.67 nm and no obvious mid-spatial frequency error is found. The result shows that the mid-spatial frequency error of 400 mm aperture window is under control, and the 400 mm aperture windows can be achieved and meet the requirement of mid-spatial frequency error in high-power laser facility.

Mid-spatial Frequency Error Identification of Precision Optical Surface Based on Empirical Mode Decomposition

Mid-spatial frequency surface error of optical lens is crucial to the performance of high-energy laser systems and high-resolution optical systems.Power spectrum density(PSD) is generally employed to evaluate mid-spatial frequency error of optical surface.PSD is based on Fourier transform which averages local characters to the whole space.And it gives a whole evaluation of mid-spatial frequency error of optical surface.It not only weakens characters but also loses location information of surface error.Abrasive processing,such as grinding and polishing,always introduces local waviness with time-varying frequency on optical lens surface,PSD fails for this situation.A new error separation method,which is based on empirical mode decomposition,is introduced in this paper in order to more accurately evaluate mid-spatial frequency error and guide compensation machining.Curve of optical surface is preliminary fitted and the difference between the origin data and the fitting curve is decomposed to a series of intrinsic mode functions(IMFs).Local waviness characters of optical lens surface and its frequency can be recognized from each IMF and the corresponding instantaneous frequency plot.All IMFs are divided into high-frequency group and mid-spatial frequency group by average of instantaneous frequency of each IMF considering with IMF characters.IMFs in the same group are added to acquire high-frequency error or mid-spatial frequency error of optical surface.The simulation and experimental results of optical surface with different machining methods are employed to validate the effectiveness and correctness of the method.

环形抛光中频误差的计算模拟

环形抛光中频误差的计算模拟

Mid-Spatial Frequency Error (PSD-2) of optics induced during CCOS and full-aperture polishing

Mid-Spatial Frequency (MSF) Wavefront Error of optics divided into the PSD-1 and PSD-2 ranges plays an important role in the performance of high power laser systems. The present work focuses on the PSD-2 range in terms of short ripples which haven’t been well studied in the literature. Characteristics and origins of these short ripples were detailed, whereafter small tool computer controlled polishing (CCP) and conventional full aperture polishing experiments were conducted on fused silica. It is revealed that PSD2 error is independent of the main process parameters including lap rotating rate and polishing pressure in continuous polishing and tool path pitch and crossfeed velocity in small tool CCP processes. Whereas the type of polishing lap has a decisive effect on PSD2 error of the optics. The pitch lap shows superiority in restraint of short ripples over polyurethane pad. By introducing diamond conditioner for dressing polyurethane pad, the PSD2 error has been greatly decreased.

Technology and Application of Ultra-precision Machining for Large Size Optic

The ultra-precision machining technology of large size optic is a comprehensive application of various sciences, which promotes the development for civil and national defense use. Under the processing of national optical project, our country makes great progress in this field. The development of ultra-precision machining technology for large size optic in micro/nano machining and measuring laboratory of Xiamen University is introduced, particularly in grinding equipment, grinding process, precise measuring, controlled bonnet polishing, environment monitoring, mid-spatial frequency error assessing and et al. From the requirement of the ultra-precision machining, the laboratory uses the experience of other countries for reference and integrates the above technology, then forms an intellectual property of grinding and polishing system independently for large size optic manufacture.

400 mm口径平面窗口元件中频误差控制技术

400 mm口径平面窗口元件中频误差控制技术

磁流变加工对中频误差的影响

Experiments on magnetorheological finishing (MRF) were carried out to remove the subsurface defect (SSD) layer left by conventional polishing. The simulation and experiment results show that, the scanning interval of MRF will lead to the mid-spatial frequency error of corresponding frequency, the instability of the polishing spot will leave the mid-spatial frequency error of uncertain frequency, and an approximately linear correlation is found between the depth of removal and the peak value of power spectral density (PSD) of processed components. With MRF as the method to remove the SSD layer, the quality of processed components concerning the mid-spatial frequency is greatly affected by the processing settings. If a thick SSD layer is left by an inappropriate prior polishing, the PSD after MRF will exceed the limit.

Wavelet methods for the representation, analysis and simulation of optical surfaces

In this paper, we introduce a wavelet method for the description, approximation, analysis and simulation of optical surfaces. We describe the new method and show results of several numerical experiments for relevant applications in optics. We focus on three main aspects. First, we describe a highly accurate representation of smooth optical surfaces in terms of a B-spline quasiinterpolant. This representation is used in a ray trace algorithm for the analysis of optical systems and is particularly suited for a wavelet decomposition. The fast wavelet transform gives access to the use of wavelets for the separation of low and mid spatial frequency errors modelled by Zernike polynomials and power spectral density functions as well as the localization and correction of errors. We compare our results with the classical representation in terms of Zernike polynomials.

Effects of structured mid-spatial frequency surface errors on image performance

Optical designers are encouraged to adopt aspheric and free-form surfaces into an increasing number of design spaces because of their improved performance. However, residual tooling marks from advanced aspheric fabrication techniques are difficult to remove. These marks, typically in the mid-spatial frequency (MSF) regime, give rise to structured image artifacts. Using a theory developed in previous publications, this paper applies the fundamentals of MSF modeling to demonstrate how MSF errors are evaluated and toleranced in an optical system. Examples of as-built components with MSF errors are analyzed using commercial optical design software.

Modeling of dynamic characteristic of the aerostatic bearing spindle in an ultra-precision fly cutting machine

Axis orientation stability of aerostatic bearing spindles has great influence on machining precision of ultra-precision fly cutting machines used for processing ultra-precision optical components of large diameter. Mid-spatial frequency errors (amplitude<0.1 μm, wavelength about 100 nm) always existed on the machined surfaces along feeding direction. Generally, the waviness errors on processed surfaces will impact the performance of workpiece used as optical components greatly, and the tilting motions of spindles were believed to be the main source which produced the waviness errors. In this paper, to study the tilting motions of spindles, the Euler dynamic equations of angular displacements of spindles were proposed, and analytic solutions of the equations were also presented. At the same time, the 3D surface profile simulations of workpieces based on analytic solutions of Euler equations were achieved. The simulation results have been verified by lots of experiments on an ultra-precision fly cutting machine. At last, the inertia tensor criterion which can decrease the waviness errors of machining surface was represented, and it can be applied to instruct the structure design of aerostatic bearing spindles.

Restraint of mid-spatial frequency error in magneto-rheological finishing (MRF) process by maximum entropy method

In order to restrain the mid-spatial frequency error in magnetorheological finishing (MRF) process, a novel part-random path is designed based on the theory of maximum entropy method (MEM). Using KDMRF-1000F polishing machine, one flat work piece (98 mm in diameter) is polished. The mid-spatial frequency error in the region using part-random path is much lower than that by using common raster path. After one MRF iteration (7.46 min), peak-to-valley (PV) is 0.062 wave (1 wave =632.8 nm), root-mean-square (RMS) is 0.010 wave and no obvious mid-spatial frequency error is found. The result shows that the part-random path is a novel path, which results in a high form accuracy and low mid-spatial frequency error in MRF process.

The Initial Sphere in the Fabrication of Conic Surfaces with Small Focal Ratio

The fabrication of a conic surface begins with the grinding of a best-fit sphere. The desired conic surface can then be obtained by further grinding with a subaperture tool. Finally, the surface is polished. Normally the best-fit sphere is chosen so as to minimize the second grinding step. However, this method tends to produce mid-spatial frequency errors near the edge of the surface and can cause errors in the paraxial radius of curvature. This paper presents an alternative method of calculating the initial sphere so as to avoid these errors. It requires more grinding time but far less time for polishing.

At-wavelength characterization of an extreme ultraviolet camera from low to mid-spatial frequencies with a compact laser plasma source

The final alignment and characterization of an extreme ultraviolet (EUV) lithographic projection optics system must be performed at the operating wavelength in order to account for errors associated with the combined effect of multilayer coating and substrate fabrication error. Two complementary metrology techniques have been developed which can operate on a compact laser plasma source: EUV lateral shear interferometry (LSI) and aerial image monitoring (AIM). LSI quantifies residual low spatial frequency wave front errors associated with the “figure” of each optical element. To characterize the effect of mid-spatial frequency errors that lead to scatter in the image plane, an EUV aerial image monitor was employed. EUV interferometry was compared to visible light interferometry measurements of the optical system and was found to be in reasonable agreement for low spatial frequency errors. The contrast as measured by AIM and photoresist exposures indicates an additional reduction of contrast associated with scatter due to large mid-spatial frequency errors.