Dual surface form measurement of optics using a contact profilometer

We present a rapid process for producing flat and smooth surfaces. In this technical note, a fabrication result of a carbon mirror is shown. Electrolytic in-process dressing (ELID) grinding with a metal bonded abrasive wheel, then a metal-resin bonded abrasive wheel, followed by a conductive rubber bonded abrasive wheel, and finally magnetorheological finishing (MRF) were performed as the first, second, third, and final steps, respectively in this process. Flatness over the whole surface was improved by performing the first and second steps. After the third step, peak to valley (PV) and root mean square (rms) values in an area of 0.72 x 0.54 mm2 on the surface were improved. These values were further improved after the final step, and a PV value of 10 nm and an rms value of 1 nm were obtained. Form errors and small surface irregularities such as surface waviness and micro roughness were efficiently reduced by performing ELID grinding using the above three kinds of abrasive wheels because of the high removal rate of ELID grinding, and residual small irregularities were reduced by short time MRF. This process makes it possible to produce flat and smooth surfaces in several hours.

In order to realize testing of a large aperture convex sphere, large aperture standard transmission spheres are designed and manufactured. The system focal length of 4400 mm, 350 mm aperture are required. The design and performance comparison, surface quality and radius of curvature testing, large aperture SiC convex sphere surface testing are complished. The simulation result analysis of optical design software shows that the wavefront performance of the system design is 0.0001 [peak to valley (PV), =632.8 nm], and it can offer a high-quality spherical wave and the reference spherical surface quality is up to 0.088 (PV, =632.8 nm), 0.006 [root mean square (RMS), =632.8 nm]. For a SiC convex sphere of 320 mm aperture and 4092 mm radius of curvature the manufactured results of the surface quality are up to 0.102 (PV, =632.8 nm), 0.011 (RMS, =632.8 nm). The results indicates that the large aperture standard transmission spheres are helpful for the testing large aperture convex sphere surface with large radius of curvature, the highly precision testing is complished only by standard sphere and non-null testing method based on digital mask, and the problems of large-aperture convex asphere or freeform mirror testing are solved.

The control of surface errors as a function of spatial frequency is critical during the fabrication of modern optical systems. A large-scale surface figure error is controlled by a guided removal process, such as computer-controlled optical surfacing. Smaller-scale surface errors are controlled by polishing process parameters. Surface errors of only a few millimeters may degrade the performance of an optical system, causing background noise from scattered light and reducing imaging contrast for large optical systems. Conventionally, the microsurface roughness is often given by the root mean square at a high spatial frequency range, with errors within a 0.5×0.5 mm local surface map with 500×500 pixels. This surface specification is not adequate to fully describe the characteristics for advanced optical systems. The process for controlling and minimizing mid- to high-spatial frequency surface errors with periods of up to ∼2-3 mm was investigated for many optical fabrication conditions using the measured surface power spectral density (PSD) of a finished Zerodur optical surface. Then, the surface PSD was systematically related to various fabrication process parameters, such as the grinding methods, polishing interface materials, and polishing compounds. The retraceable experimental polishing conditions and processes used to produce an optimal optical surface PSD are presented.

The complicated surface part generally possesses exceptional properties, then the developments of high-end equipment and the precision physics experiment are in pressing demand of it. To accurately manufacture the complicated surface part, this study presents a toolpath generation strategy for slow tool servo (STS) turning with position-velocity-time (PVT) interpolation under the constraint of the specified interpolation error. Based on the mathematical principle of PVT interpolation, the interpolation point is calculated. With the anticipant curve represented with a spatially circular arc, the cutter contact point (CCP) of the toolpath with PVT interpolation is derived under the constraint of the specified interpolation error by way of the presented bisection algorithm. Then the cutter location point (CLP) of the toolpath is calculated through the tool nose radius compensation for STS turning. The validated experiment shows that the workpiece machined with the toolpath with PVT interpolation generated through the proposed scheme satisfies the constraint of the specified interpolation error. The peak to valley (PV) value of the form error of the surface is 8.2 μm, besides the root mean square (RMS) value of the form error is 1.9 μm. The volume of CLPs of the toolpath is reduced by 51.7% compared with the toolpath discretized by an equal angle. The achievement of this study provides guidance for the STS precision turning with PVT interpolation for the complicated surface.

Due to its excellent optical performance, freeform optics has found extensive applications into sophisticated optical systems. Ultra-precision diamond milling (UPDM) offers an advanced solution for manufacturing high-quality freeform optics with sub-micrometric form error. However, its varying curvature characteristics would lead to uneven residual and inconsistent surface quality. Therefore, to improve the registration process accuracy, this study proposes a multi-technique based coarse to fine form registration for UPDM of freeform optics and it provides a benchmark for evaluating the form error of machined surfaces. Firstly, two-dimensional Fourier transform and Pearson correlation coefficient were used for area coarse registration. Next, singular value decomposition was utilized to transform the coordinate systems for fine registration. Then, simulations were performed to construct two representative freeform optics-light emitting diode lens and virtual reality lens-and their forms were registered. Finally, the form error between the designed and measured surfaces was discussed in UPDM experiments. The results revealed that the proposed form registration method demonstrated strong robustness and accuracy under various errors. After registering simulation, the peak to valley and root mean square deviations between the designed surface and the measured surface of the two types of freeform optics were both less than 10−7 μm. Significantly, this study applies advanced mathematical tools in the form registration and thus improves the precision and efficiency of form registration in freeform optics.

The in-situ measurement of complex optical surfaces is a challenging task in precision engineering. The phase measuring deflectometry is a powerful measuring method for complex specular surfaces, and it has higher measuring efficiency, stability and dynamic range compared to interferometry. Consequently it is promising to widespread applications in various fields. Deflectometry is essentially a calibration problem, and the measuring accuracy is directly determined by the quality of geometrical calibration. An in-situ deflectometric measuring system is designed based on the single point diamond turning machine. A self-calibration method is developed to specify the relative positions of the camera and screen. Ray tracing is conducted at two positions of an auxiliary reflecting mirror, which is mounted on an air bearing spindle. The accuracy of the geometrical positions can be improved by an order of magnitude by minimizing the deviations of the traced points with respect to the true correspondences. According to the statistical properties of the deviations in reverse ray tracing, the form errors and the position errors can be separated, and the positioning error of the workpiece can be corrected accordingly. Henceforth, the nominal shape of the fabricated workpiece can be fully utilized, and the conventional one-way position-form mapping can be converted into a two-way mapping problem. As for the complex shapes, the whole surface can be covered by sub-aperture measurement. Precise localization of a local region under test is achieved by multi-position imaging, so that correct convergence of the iterative reconstruction process can be guaranteed. Several typical optical surfaces including an off-axis paraboloid mirror are measured, and the measuring accuracy of the proposed method is proved better than 150 nm RMS.

As one of the coherent diffractive imaging (CDI) techniques, coherent modulation imaging (CMI) is a lensless phase imaging technology with diffraction limited resolution in theory. Unlike multiple measurement phase retrieval algorithms, the CMI can achieve fast convergence speed with single-shot measurement by introducing a pre-characterized random phase modulator. Besides, it has simple structure without reference wave based on iterative engine. Despite the fact that the matured phase imaging can be used to implement the on-line wave diagnostics of laser pulse, in this work we accurately measure the face-type of optical component with peak-to-valley value below 0.5<i>λ</i> (<i>λ</i> = 632.8 nm) by using the CMI for the first time. In order to verify its measurement capability, 10 quartz windows with a diameter of 80 mm and PV value between 0.1<i>λ</i> and 0.5<i>λ</i> are repeatedly measured. Compared with the results of commercial interferometer, the root mean square error (Root MSE) of the peak-to-valley (PV) ratio of the results of the CMI is 0.0305<i>λ</i>, and the Root MSE of the root mean square (RMS) is 0.00522<i>λ.</i> The measurement accuracy of PV ratio and RMS can reach 0.1<i>λ</i> and 0.01<i>λ</i> respectively. In addition, the parallel flat with PV ratio = <i>λ</i>/20 is measured and analyzed with CMI, and its noise level is also analyzed. Considering that the potential improvement of CMI is available in the future, the CMI is expected to become a new technique for optical metrology with high precision, which is different from interferometry.

The optical 3D surface measurement technique aligns the optical axis of the projector with that of the camera, enabling the measurement of objects with significant height variations, such as deep holes and grooves. This technique encodes the height of the object into the modulation of the fringe pattern, eliminating the requirement for phase unwrapping and avoiding issues such as shadow occlusion. To further enhance the noise reduction capability of fringe analysis and reconstruct objects with high-frequency detail, this paper introduces the two-dimensional generalized S-transform (2D-GST) method for modulation extraction. By incorporating two additional parameters px and py to adjust the resolution in the time domain/frequency domain, 2D-GST can provide higher reconstruction precision. The root mean square (RMS) for tested plane with 2D-GST is 4.35 μm, whereas for the traditional 1D S-transform (1D-ST), the RMS is 4.97 μm.

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.

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.

The Ritchey-Common test is widely adopted to measure large optical flats. The traditional Ritchey-Common test eliminates the defocus error with multiple tests by changing the position of the mirrors, which suffers from cumbersome steps, poor repeatability, coupled system error, extra mirror deformation, and potential overturning. The above problems increase the test time, decrease the reliability and accuracy, increase the test cost, and threaten manufacturing safety. We propose a single-test Ritchey-Common interferometry to avoid the obligatory position change in the traditional method. A sub-aperture of test flat is directly measured by a small-aperture interferometer before the test, which is easy to implement, to replace the extra system wavefront measurement in different positions. The defocus is calculated in sub-aperture at exactly the same position as the full-field measurement without the position change, then the surface form under test can be obtained with accurate optical path modeling. Measurement experiments for 100 mm and 2050 mm aperture flats were performed to demonstrate the feasibility of this method. Compared with a direct test in a standard Zygo interferometer, the peak to valley (PV) and root mean square (RMS) errors were 0.0889 λ and 0.0126 λ (λ=632.8 nm), respectively, which reaches the upper limit of accuracy of the interferometer. To the best of our knowledge, this is the first proposal of the Ritchey-Common test that can eliminate the defocus error and realize high accuracy measurement in a single test. Our work paves the way for reliable and practical optical metrology for large optical flats.

PurposeThis paper aims to investigate how form error of journal affects oil film characteristics, which are composed of several parameters including the maximum film pressure, film moment, frictional coefficient and carrying-load capacity.Design/methodology/approachA new generalized equation based on the small displacement torsor theory is derived, as well as its capability of representing types of form error on the journal, using four specified parameters in a three-dimensional (3D) state. Based on the new generalized equation of form errors, the Reynolds equation is represented and solved numerically using the Swift–Stieber boundary condition.FindingsThe results show that the form errors of journal have significant influence on all oil film characteristics. However, the film moment remains nearly unchanged as film characteristics, especially eccentricity ratio, become large. All film characteristics investigated vary periodically as the form error. More importantly, it is found that the film pressure distribution transforms to an asymmetric shape along the axial direction of the bearing, no longer a symmetric shape in the case of two-dimensional (2D) form errors. It is necessary to substitute the 3D form error model, which takes the variations of the film characteristics in axial direction into account, for the 2D model in the designing stage of journal bearings.Originality/valueFirst, the effect of the form error of the journal on the performance of hydrodynamic journal bearings is studied in the view of the film characteristics systematically. Secondly, the new generalized equation of form error, derived by SDT theory, is capable of representing any types of form error on the journal, not only representing one type of form error merely.

Irregularity of an optical surface is commonly characterized by peak-to-valley or root mean square error after subtraction of low order aberrations. It is sufficient if the surface is fabricated with the help of conventional techniques. Modern manufacturing methods employ undersized polishing tools generating irregularities on sub-aperture scales or mid-spatial frequencies. This is particularly important for the fabrication of aspheric or free-form surfaces. The smoothness of local polishing depends on how uniformly the influence of a tool is distributed and how well the dwell time is controlled over a part. Diamond turning is known for the variety of shapes, however, a single point tool tends to form surface features on the scale determined by the uniformity of feed rate. A deterministic way to quantify and specify mid-spatial irregularity is important for all areas of optical production. Interferometric map of an optical surface is usually obtained from original data by subtraction of the fit of 9 Zernike fringe polynomials corresponding to piston, tilt, focus and third order astigmatism, coma and spherical aberrations. This paper describes how to characterize the spectral content of residual surface height error, which depends on multiple factors during the fabrication. To quantify small scale irregularities, the residual error is regarded as a statistical process. The method of structure function is applied to the surface errors at different spatial scales yielding RMS height difference vs. physically measurable separation on an optical surface.

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