Experimental power spectral density analysis for mid- to high-spatial frequency surface error control.

Aims. The focusing performance of X-ray optics (conveniently expressed in terms of HEW, Half Energy Width) strongly depend on both mirrors deformations and photon scattering caused by the microroughness of reflecting surfaces. In particular, the contribution of X-ray Scattering (XRS) to the HEW of the optic is usually an increasing function H(E) of the photon energy E. Therefore, in future hard X-ray imaging telescopes of the future (SIMBOL-X, NeXT, Constellation-X, XEUS), the X-ray scattering could be the dominant problem since they will operate also in the hard X-ray band (i.e. beyond 10 keV). In order to ensure the imaging quality at all energies, clear requirements have to be established in terms of reflecting surfaces microroughness. Methods. Several methods were proposed in the past years to estimate the scattering contribution to the HEW, dealing with the surface microroughness expressed in terms of its Power Spectral Density (PSD), on the basis of the well-established theory of X-ray scattering from rough surfaces. We faced that problem on the basis on the same theory, but we tried a new approach: the direct, analytical translation of a given surface roughness PSD into a H(E) trend, and – vice versa – the direct translation of a H(E) requirement into a surface PSD. This PSD represents the maximum tolerable microroughness level in order to meet the H(E) requirement in the energy band of a given X-ray telescope. Results. We have thereby found a new, analytical and widely applicable formalism to compute the XRS contribution to the HEW from the surface PSD, provided that the PSD had been measured in a wide range of spatial frequencies. The inverse problem was also solved, allowing the immediate evaluation of the mirror surface PSD from a measured function H(E). The same formalism allows establishing the maximum allowed PSD of the mirror in order to fulfill a given H(E) requirement. Practical equations are firstly developed for the case of a single-reflection optic with a single-layer reflective coating, and then extended to an optical system with N identical reflections. The results are approximately valid also for multilayer-coated mirrors to be adopted in hard X-rays. These results will be extremely useful in order to establish the surface finishing requirements for the optics of future X-ray telescopes.

In the process of computer-controlled optical surfacing (CCOS), the key of correcting the surface error of optical components is to ensure the consistency between the simulated tool influence function and the actual tool influence function (TIF). The existing removal model usually adopts the fixed-point TIF to remove the material with the planning path and velocity, and it considers that the polishing process is linear and time invariant. However, in the actual polishing process, the TIF is a function related to the feed speed. In this paper, the relationship between the actual TIF and the feed speed (i.e. the compensation relationship between static removal and dynamic removal) is determined by experimental method. Then, the existing removal model is modified based on the compensation relationship, to improve the conformity between simulated and actual processing. Finally, the surface error modification correction test are carried out. The results show that the fitting degree of the simulated surface and the experimental surface is better than 88%, and the surface correction accuracy can be better than 1/10 λ (Λ=632.8nm).

For the space solar extreme ultraviolet telescope, the star point test can not be performed in the x-ray band (19.5nm band) as there is not light source of bright enough. In this paper, the point spread function of the optical system is calculated to evaluate the imaging performance of the telescope system. Combined with the actual processing surface error, such as small grinding head processing and magnetorheological processing, the optical design software Zemax and data analysis software Matlab are used to directly calculate the system point spread function of the space solar extreme ultraviolet telescope. Matlab codes are programmed to generate the required surface error grid data. These surface error data is loaded to the specified surface of the telescope system by using the communication technique of DDE (Dynamic Data Exchange), which is used to connect Zemax and Matlab. As the different processing methods will lead to surface error with different size, distribution and spatial frequency, the impact of imaging is also different. Therefore, the characteristics of the surface error of different machining methods are studied. Combining with its position in the optical system and simulation its influence on the image quality, it is of great significance to reasonably choose the processing technology. Additionally, we have also analyzed the relationship between the surface error and the image quality evaluation. In order to ensure the final processing of the mirror to meet the requirements of the image quality, we should choose one or several methods to evaluate the surface error according to the different spatial frequency characteristics of the surface error.

The use of light scatter to determine flat surface statistical information, such as a bandwidth limited section of the surface power spectral density (PSD) function and the associated rms roughness and slope numbers, is well documented in the literature. Systems which mea-sure scatter as a function of angular position often make use of the fact that the surface power spectral density function is essentially produced in the scatter pattern. Low spatial frequencies scatter close to the direc-tion of specular reflection and higher frequencies scatter further out. The technique relies on the one-to-one relationship between spatial frequen-cy and scatter position in the far field. This relationship is exact to within dimensions corresponding to the diffraction limit (i.e., dimensions much smaller than the usual detector aperture). For a curved surface, this one-to-one relationship is destroyed as scatter from a single spatial frequency can spread out to dimensions far exceeding those of a diffraction limited spot. As the spread approaches detector aperture dimensions, the ability to extract useful surface information is impaired. The amount of spread is determined by the illuminated spot radius r, the radius of curvature of the surface R, and the angle of incidence 01(r) and is plotted, for constant 01, as a function of r/R. Analytical data show that by reducing r to 0.5 mm, reasonable results are obtainable with workable scatter system geometries for curved surfaces with R _> 5 cm.

Edge effect is regarded as one of the most difficult technical issues in a computer controlled optical surfacing (CCOS) process. Traditional opticians have to even up the consequences of the two following cases. Operating CCOS in a large overhang condition affects the accuracy of material removal, while in a small overhang condition, it achieves a more accurate performance, but leaves a narrow rolled-up edge, which takes time and effort to remove. In order to control the edge residuals in the latter case, we present a new concept of the 'heterocercal' tool influence function (TIF). Generated from compound motion equipment, this type of TIF can 'transfer' the material removal from the inner place to the edge, meanwhile maintaining the high accuracy and efficiency of CCOS. We call it the 'heterocercal' TIF, because of the inspiration from the heterocercal tails of sharks, whose upper lobe provides most of the explosive power. The heterocercal TIF was theoretically analyzed, and physically realized in CCOS facilities. Experimental and simulation results showed good agreement. It enables significant control of the edge effect and convergence of entire surface errors in large tool-to-mirror size-ratio conditions. This improvement will largely help manufacturing efficiency in some extremely large optical system projects, like the tertiary mirror of the Thirty Meter Telescope.

Itek has developed computer-controlled optical surfacing (CCOS) for fabricating aspheric optical surfaces. The smoothing process plays a key role in all CCOS operations. A computer simulation algorithm was created to provide information on the CCOS smoothing process. The reliability of the algorithm was confirmed with several verification cases. The effect of pertinent tool, lap and error parameters on smoothing was determined from a series of simulations. Also, the smoothing algorithm was applied to an operational case to provide real world credibility. The smoothing simulation algorithm appears accurate and useful. The parametric study results are available and the algorithm can be applied to specific cases for guidance in proper CCOS parameter selection.

Due to the different curvature everywhere, the aspheric surface is hard to achieve high-precision accuracy by the traditional polishing process. Controlling of the mid-spatial frequency errors (MSFR), in particular, is almost unapproachable. In this paper, the combined fabrication process based on the smoothing polishing (SP) and magnetorheological finishing (MRF) is proposed. The pressure distribution of the rigid polishing lap and semi-flexible polishing lap is calculated. The shape preserving capacity and smoothing effect are compared. The feasibility of smoothing aspheric surface with the semi-flexible polishing lap is verified, and the key technologies in the SP process are discussed. Then, A K4 parabolic surface with the diameter of 500mm is fabricated based on the combined fabrication process. A Φ150 mm semi-flexible lap is used in the SP process to control the MSFR, and the deterministic MRF process is applied to figure the surface error. The root mean square (RMS) error of the aspheric surface converges from 0.083λ (λ=632.8 nm) to 0.008λ. The power spectral density (PSD) result shows that the MSFR are well restrained while the surface error has a great convergence.

Manufacturing methods for diamond machined optical surfaces, for application at infrared wavelengths, require that a new set of criteria must be recognised for the specification of surface form. Appropriate surface form parameters are discussed with particular reference to an XY cartesian geometry CNC machine. Methods for reducing surface form errors in diamond machining are discussed for certain areas such as tool wear, tool centring, and the fixturing of the workpiece. Examples of achievable surface form accuracy are presented. Traditionally, optical surfaces have been produced by use of random polishing techniques using polishing compounds and lapping tools. For lens manufacture, the simplest surface which could be created corresponded to a sphere. The sphere is a natural outcome of a random grinding and polishing process. The measurement of the surface form accuracy would most commonly be performed using a contact test gauge plate, polished to a sphere of known radius of curvature. QA would simply be achieved using a diffuse monochromatic source and looking for residual deviations between the polished surface and the test plate. The specifications governing the manufacture of surfaces using these techniques would call for the accuracy to which the generated surface should match the test plate as defined by a spherical deviations from the required curvature and a non spherical astigmatic error. Consequently, optical design software has tolerancing routines which specifically allow the designer to assess the influence of spherical error and astigmatic error on the optical performance. The creation of general aspheric surfaces is not so straightforward using conventional polishing techniques since the surface profile is non spherical and a good approximation to a power series. For infra red applications (X = 8-12p,m) numerically controlled single point diamond turning is an alternative manufacturing technology capable of creating aspheric profiles as well as simple spheres. It is important however to realise that a diamond turning process will possess a new set of criteria which limit the accuracy of the surface profile created corresponding to a completely new set of specifications. The most important factors are:- tool centring accuracy, surface waviness, conical form error, and other rotationally symmetric non spherical errors. The fixturing of the workpiece is very different from that of a conventional lap, since in many cases the diamond machine resembles a conventional lathe geometry where the workpiece rotates at a few thousand R.P.M. Substrates must be held rigidly for rotation at such speeds as compared with more delicate mounting methods for conventional laps. Consequently the workpiece may suffer from other forms of deformation which are non-rotationally symmetric due to mounting stresses (static deformation) and stresses induced at the speed of rotation (dynamic deformation). The magnitude of each of these contributions to overall form error will be a function of the type of machine, the material, substrate, and testing design. The following sections describe each of these effects in more detail based on experience obtained on a Pneumo Precision MSG325 XY CNC machine. Certain in-process measurement techniques have been devised to minimise and quantify each contribution.

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability necessary to perform pre-cisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.

Metal mirrors for precise optical applications are commonly fabricated by coating of a metal base substrate with a nickel-phosphorus alloy (NiP). The NiP layer is then processed by precision diamond turning and polishing to obtain a high-quality mirror surface. In this work, Ti-6Al-4V samples that were made by additive manufacturing, also called 3D printing, were used as a base for the development of metal mirrors. The additively manufactured samples were electroplated with a NiP coating and machined using single-point diamond turning (SPDT) to obtain a flat mirror with optical quality and low form error surface. The periodic structure of the SPDT toolmark was then removed by polishing postprocessing. Polishing optimization was first performed on NiP-coated aluminum test samples to find an optimal polishing setup. Based on this optimization, postprocessing of titanium samples was carried out by pitch polishing in combination with 1, 0.25, and 0.1µm diamond slurries. Using this polishing processing, a scratch-free surface was attained with surface microroughness below 0.5 nm.

We develop a kind of magnetorheological (MR) polishing fluid for the fabrication of a silicon modification layer on a silicon carbide substrate based on chemical theory and actual polishing requirements. The effect of abrasive concentration in MR polishing fluid on material removal rate and removal function shape is investigated. We conclude that material removal rate will increase and tends to peak value as the abrasive concentration increases to 0.3 vol. %, and the removal function profile will become steep, which is a disadvantage to surface frequency error removal at the same time. The removal function stability is also studied and the results show that the prepared MR polishing fluid can satisfy actual fabrication requirements. An aspheric reflective mirror of silicon carbide modified by silicon is well polished by combining magnetorheological finishing (MRF) using two types of MR polishing fluid and computer controlled optical surfacing (CCOS) processes. The surface accuracy root mean square (RMS) is improved from 0.087λ(λ=632.8 nm) initially to 0.020λ(λ=632.8 nm) in 5.5 h total and the tool marks resulting from MRF are negligible. The PSD analysis results also shows that the final surface is uniformly polished.

This study aimed to compare ocular wavefront aberrations for pupil diameters of 4 mm and 6 mm, and contrast sensitivity, in eyes with AcrySof IQ and AcrySof Natural intraocular lenses (IOLs). Sixty eyes of 60 patients were enrolled in this prospective randomized study. After phacoemulsification the eyes received either AcrySof IQ SN60WF or AcrySof Natural SN60AT IOLs. One month after surgery, all patients underwent complete ophthalmological examination including corneal topography, wavefront analysis for pupil diameters of 4 mm and 6 mm, and contrast sensitivity measurements with the CSV 1000E instrument under photopic and mesopic conditions with and without glare. There was no statistically significant difference between groups in age, sex or other preoperative ocular characteristics (p > 0.05). Patients with AcrySof IQ IOLs had higher contrast sensitivity at 6 c.p.d. under photopic conditions, at 6 c.p.d. and 18 c.p.d. under mesopic conditions, and at 6 c.p.d., 12 c.p.d. and 18 c.p.d. under mesopic conditions with glare (p < 0.05). Corneal spherical aberration was 0.273 ± 0.074 μm in the AcrySof Natural group and 0.294 ± 0.086 μm in the AcrySof IQ group (p = 0489). Ocular spherical aberration was 0.362 ± 0.141 μm and 0.069 ± 0.043 μm (p < 0.001) for 6-mm diameter pupils and 0.143 ± 0.091 μm and 0.017 ± 0.016 μm (p < 0.001) for 4-mm diameter pupils, with AcrySof Natural and AcrySof IQ IOLs, respectively. There were no significant differences in other higher-order aberrations between the groups (p > 0.05). Aspherical AcrySof IQ IOLs significantly reduced spherical aberration for pupil diameters of both 4 mm and 6 mm and also improved contrast sensitivity more than spherical AcrySof Natural IOLs, especially in mesopic conditions.

The prevailing technique for assessing surface roughness and related parameters from engineering surfaces in industry is mechanical stylus profilometry. Though it is a conceptually direct method it suffers from several drawbacks; the measurement is not area-covering while many important features of engineering surfaces are related to 3D topography; the technique is slow; and, the technique involves contact with the surface, potentially damaging it. For surfaces of optical quality, elastic light scattering provides an efficient way of characterizing surfaces, and two ASTM standards exist pertaining to such measurements. However, the theoretical models based on first order perturbation theory break down when the rms roughness approaches one tenth of the incident wavelength. We have used infrared scattering at 10.6 micrometers wavelength to provide area-covering, non-contact surface characterization of engineering surfaces. The surface power spectral density is calculated from the scattering distribution by Rayleigh-Rice vector perturbation theory. Measurement of bandwidth limited surface roughness is demonstrated for ground and polished surfaces in the root mean square roughness range of 0.03 micrometers to 1.7 micrometers . Good correlation with contact stylus measurements is achieved for nearly 1D surfaces, anisotropic surfaces, and isotropic surfaces. Measurement of scratch and lay characteristics are also demonstrated.

1. The appearance of square gratings with some of their Fourier components missing has been investigated for both threshold and suprathreshold contrasts.2. If high frequency components are removed from a square grating there is only a very small effect on the detection threshold, or suprathreshold appearance, unless the components are visible by themselves.3. If the fundamental frequency is removed from a square-wave grating which has a spatial frequency lower than 1 cycle per degree (c/d) the contrast sensitivity is not altered. This is a generalisation of the Craik-Cornsweet illusion. If the contrast is raised above the detection threshold the grating is indistinguishable from a square grating, unless the contrast is high enough to see the fundamental when it is presented alone.4. If the fundamental is removed from a square grating which has a spatial frequency higher than 1 c/d the contrast threshold and the appearance at all contrasts are changed. At threshold it appears as a sinusoidal grating of three times the fundamental frequency. The threshold is dictated solely by the amplitude of the third harmonic. If the contrast is further raised, so that the fifth harmonic also reaches threshold, the periodictiy of the fundamental is seen.5. Therefore, gratings of many different luminance profiles (including the Craik-Cornsweet profile) all produce the perception of a square grating simply because those missing components which would be required in each case to produce a perfect square are by themselves undetectable. The visual system responds as though hardwired to detect square gratings and edges by means of quasi-Fourier analysis.6. These results are analagous to the missing fundamental, or residue, effect in hearing.

Nowadays, large-aperture optical components are increasingly used in high-power laser systems, remote-sensing satellites, and space-based astronomical telescopes. Fabricating these surfaces with submicron-scale shape accuracy and a nanoscale surface finish has been a great challenge for the optical industry, especially for hard and difficult-to-machine materials. Thus, to achieve the high-efficiency and high-precision polishing of large-aperture aspherical optical parts, this study combined robotic machining technology with computer-controlled optical surfacing (CCOS) technology and investigated the effect of robot motion accuracy on the surface topography of workpieces during polishing. First, a material removal model considering the normal error of the polishing tool was developed based on contact mechanics, kinematic theory, and the abrasion mechanism. Next, in combination with the polishing trajectory, the surface morphology and form accuracy after polishing were predicted under different normal-error conditions. Then, preliminary experiments were conducted to verify the model. The experimental data agreed with the simulation results, showing that as the normal error increased from 0° to 0.5° and 1°, the peak-to-valley (PV) values of the surface profile of the optical element decreased from 5.42, 5.28, and 4.68 μm to 3.97, 4.09, and 4.43 μm, respectively. The corresponding convergence rates were 26.8%, 22.5%, and 5.3%. The root mean square (RMS) values decreased from 0.754, 0.895, and 0.678 μm to 0.593, 0.620, and 0.583 μm, with corresponding convergence rates of 21.4%, 30.7% and 14.0%, respectively. Moreover, a higher motion accuracy enabled the polishing robot to reduce the mid- and high-frequency errors of the optical element.