Developing on-machine 3D profile measurement for deterministic fabrication of aspheric mirrors: erratum.

This erratum adds a reference to the published paper, Appl. Opt.53, 4997 (2014)APOPAI0003-693510.1364/AO.53.004997.

Study of a wheel-like electrorheological finishing tool and its applications to small parts.

A wheel-like electrorheological finishing (ERF) tool for small parts polishing is proposed and thoroughly studied. First, the electrorheological polishing fluid is tested, and its properties suggest usability for electrorheological fluid-assisted finishing. Then, the mathematical removal model of the ERF tool is built employing the conformal mapping method and high-order multipolar moment theory. Finally, a micropattern of trough is fabricated on a slide glass (7 mm wide and 1 mm thick). The trough is 70 nm deep, and its flat bottom is 1.5 m wide (peak to valley of 3.16 nm and root mean square of 1.27 nm); the surface roughness finally achieves 0.86 nm. The results demonstrate the stable machining capability of the ERF tool for miniature parts.

Design of compact LED free-form optical system for aeronautical illumination.

A type of runway centerline light is designed for the application of light-emitting diode (LED) aeronautical illumination. A total internal reflection collimating lens and an integrated prism are designed, respectively, to meet the intensity distribution of International Convention on Civil Aviation (ICAO) regulations. The principle of geometric optics is adopted to construct the free-form surfaces of a collimating lens, which is simple. Different variations are used in the process of free-form surface calculation. An integrated prism with a diffuser is used for uniformly diffusing rays and then decreasing the central maximum intensity to avoid glare. The structure of the optical system is compact. Computer simulation results show that an optical efficiency of 79.2% is achieved for a 1 mm×1 mm LED source. Tolerance analysis is carried out to determine tolerance limits of manufacture and installation errors. To verify the optical performance of the proposed runway centerline light, the practical illumination distribution is measured by using Cree XP-E2 LED, which can comply with ICAO regulations.

Robust linear equation dwell time model compatible with large scale discrete surface error matrix.

The linear equation dwell time model can translate the 2D convolution process of material removal during subaperture polishing into a more intuitional expression, and may provide relatively fast and reliable results. However, the accurate solution of this ill-posed equation is not so easy, and its practicability for a large scale surface error matrix is still limited. This study first solves this ill-posed equation by Tikhonov regularization and the least square QR decomposition (LSQR) method, and automatically determines an optional interval and a typical value for the damped factor of regularization, which are dependent on the peak removal rate of tool influence functions. Then, a constrained LSQR method is presented to increase the robustness of the damped factor, which can provide more consistent dwell time maps than traditional LSQR. Finally, a matrix segmentation and stitching method is used to cope with large scale surface error matrices. Using these proposed methods, the linear equation model becomes more reliable and efficient in practical engineering.

Compensating for velocity truncation during subaperture polishing by controllable and time-variant tool influence functions.

The velocity-varying regime used in deterministic subaperture polishing employs a time-invariant tool influence function (TIF) to figure localized surface errors by varying the transverse velocities of polishing tools. Desired transverse velocities have to be truncated if they exceed the maximal velocity of computer numerical control (CNC) machines, which induces excessive material removal and reduces figuring efficiency (FE). A time-variant (TV) TIF regime is presented, in which a TIF serves as a variable to compensate for excessive material removal when the transverse velocities are truncated. Compared with other methods, the TV-TIF regime exhibits better performance in terms of convergence rate, FE, and versatility; its operability can also be strengthened by a TIF library. Comparative experiments were conducted on a magnetorheological finishing machine to validate the effectiveness of the TV-TIF regime. Without a TV-TIF, the tool made an unwished dent (depth of 76 nm) at the center because of the velocity truncation problem. Through compensation with a TV-TIF, the dent was completely removed by the second figuring process, and a TV-TIF improved the FE from 0.029 to 0.066 mm(3)/h.

Calibrating system errors of large scale three-dimensional profile measurement instruments by subaperture stitching method.

This study presents a subaperture stitching method to calibrate system errors of several ∼2 m large scale 3D profile measurement instruments (PMIs). The calibration process was carried out by measuring a Φ460 mm standard flat sample multiple times at different sites of the PMI with a length gauge; then the subaperture data were stitched together using a sequential or simultaneous stitching algorithm that minimizes the inconsistency (i.e., difference) of the discrete data in the overlapped areas. The system error can be used to compensate the measurement results of not only large flats, but also spheres and aspheres. The feasibility of the calibration was validated by measuring a Φ1070 mm aspheric mirror, which can raise the measurement accuracy of PMIs and provide more reliable 3D surface profiles for guiding grinding, lapping, and even initial polishing processes.

Subsurface damages of fused silica developed during deterministic small tool polishing.

The subsurface damages (SSD) of fused silica developed during deterministic small tool polishing are experimentally investigated in this study. A leather pad (i.e., poromeric) is validated to be nearly SSD-free and superior to pitch and polyurethane. Rough abrasives are found to obviously increase SSD depth, and a leather pad can efficiently suppress the adverse effect of rough abrasives. The SSD depth induced by pitch and polyurethane pads (with rough abrasive) ranges from 0.77 to 1.49µm (~1/7-1/5 of abrasive size). High pressure, low velocity and slurry concentration can slightly increase SSD depth. Material removal rate of leather pad is also validated to be comparable with polyurethane and much higher than pitch tool; surface roughness polished by leather pad is Ra = 1.13nm, which is close to that of pitch but much better than polyurethane.

Subsurface damage of fused silica lapped by fixed-abrasive diamond pellets.

Minimizing subsurface damage (SSD) is in high demand for optics during grinding, lapping, and polishing. A fixed-abrasive diamond pellet (FADP) has been validated as a potential tool in fast lapping and polishing of hard optical materials. This study inspects and measures the SSD of fused silica developed in lapping and microlapping by FADPs tool through a taper polishing method, assisted with profile measurement and microexamination. A series of experiments is conducted to reveal the influence of lapping parameters on SSD depth and surface roughness, including diamond size, lapping pressure, and velocity, as well as rubber type. Results indicate that SSD depth and surface roughness are mostly sensitive to diamond size but are generally independent of lapping pressure and velocity. Softer rubber can reduce SSD depth and improve surface roughness. The ratio of SSD depth to surface roughness (peak to valley: Rt) is confirmed to be 7.4±1.3, which can predict the SSD depth of fused silica lapped by FADPs with a rapid roughness measurement.

Developing on-machine 3D profile measurement for deterministic fabrication of aspheric mirrors.

Three-dimensional profile measurement is perceived as an indispensable process for deterministic fabrication of aspheric mirrors. In this work, we develop on-machine 3D profile measurement on a subaperture polishing machine, namely, JR-1800. The influences of mechanical errors, misalignments, output stability, temperature variation, and natural vibration are investigated in detail by calibration, mechanical alignment, and finite-element analysis. Two quantitative methods are presented for aligning the turntable, length gauge, and workpiece into together. An error compensation model is also developed for further eliminating misalignments. For feasibility validation, two prototypical workpieces are measured by JR-1800 and an interferometer. The results indicate that JR-1800 has an RMS repeatability of ~λ/30 (λ=632.8 nm). The data provided by the two systems are highly coincident. Direct subtractions of the results from the two systems indicate that the RMS deviations for both segments are less than 0.07 µm.

Modified dwell time optimization model and its applications in subaperture polishing.

The optimization of dwell time is an important procedure in deterministic subaperture polishing. We present a modified optimization model of dwell time by iterative and numerical method, assisted by extended surface forms and tool paths for suppressing the edge effect. Compared with discrete convolution and linear equation models, the proposed model has essential compatibility with arbitrary tool paths, multiple tool influence functions (TIFs) in one optimization, and asymmetric TIFs. The emulational fabrication of a Φ200 mm workpiece by the proposed model yields a smooth, continuous, and non-negative dwell time map with a root-mean-square (RMS) convergence rate of 99.6%, and the optimization costs much less time. By the proposed model, influences of TIF size and path interval to convergence rate and polishing time are optimized, respectively, for typical low and middle spatial-frequency errors. Results show that (1) the TIF size is nonlinear inversely proportional to convergence rate and polishing time. A TIF size of ~1/7 workpiece size is preferred; (2) the polishing time is less sensitive to path interval, but increasing the interval markedly reduces the convergence rate. A path interval of ~1/8-1/10 of the TIF size is deemed to be appropriate. The proposed model is deployed on a JR-1800 and MRF-180 machine. Figuring results of Φ920 mm Zerodur paraboloid and Φ100 mm Zerodur plane by them yield RMS of 0.016λ and 0.013λ (λ=632.8 nm), respectively, and thereby validate the feasibility of proposed dwell time model used for subaperture polishing.

Modified subaperture tool influence functions of a flat-pitch polisher with reverse-calculated material removal rate.

Numerical simulation of subaperture tool influence functions (TIF) is widely known as a critical procedure in computer-controlled optical surfacing. However, it may lack practicability in engineering because the emulation TIF (e-TIF) has some discrepancy with the practical TIF (p-TIF), and the removal rate could not be predicted by simulations. Prior to the polishing of a formal workpiece, opticians have to conduct TIF spot experiments on another sample to confirm the p-TIF with a quantitative removal rate, which is difficult and time-consuming for sequential polishing runs with different tools. This work is dedicated to applying these e-TIFs into practical engineering by making improvements from two aspects: (1) modifies the pressure distribution model of a flat-pitch polisher by finite element analysis and least square fitting methods to make the removal shape of e-TIFs closer to p-TIFs (less than 5% relative deviation validated by experiments); (2) predicts the removal rate of e-TIFs by reverse calculating the material removal volume of a pre-polishing run to the formal workpiece (relative deviations of peak and volume removal rate were validated to be less than 5%). This can omit TIF spot experiments for the particular flat-pitch tool employed and promote the direct usage of e-TIFs in the optimization of a dwell time map, which can largely save on cost and increase fabrication efficiency.

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).

Optimal strategy for fabrication of large aperture aspheric surfaces.

Aspheric surfaces are widely used because of their desirable characteristics. Such a surface can obtain nearly perfect imaging quality with fewer optical elements and reduce the size and mass of optical systems. Various machine systems have been developed based on modern deterministic polishing technologies for large aperture aspheric surfaces. Several factors affect the final precision of large aperture aspheric surfaces, such as the velocity limit of the machine and the path design. Excess velocity, which will be truncated automatically by the computer numerical control system, may cause the dwell time to deviate from the desired time. When a path designed on a two-dimensional surface map with equidistant pitch is projected onto an aspheric surface, the pitch changes as a result of the varied curvature of the aspheric surface. This may affect the removal map and cause some ripple errors. A multiregion distribution strategy, which includes velocity checking, is proposed in this study to avoid exceeding the velocity limits. The strategy can be used to modify local errors and edge effects. A three-dimensional spiral path generation method is also presented using an iterative method to ensure uniformity in the space length of the adjacent circle of the spiral path. This process can reduce the ripple error caused by the overlapping of tool paths. A polishing experiment was conducted, and the results proved the validity of the proposed strategies.

Modified stitching algorithm for annular subaperture stitching interferometry for aspheric surfaces.

In this paper, a modified stitching algorithm for annular subaperture stitching interferometry (ASSI) for aspheric surfaces is proposed. The mathematical model of adjustment error is deduced based on the wavefront aberration theory and rigid body movement; meanwhile, its basic principle and theory are introduced. The modified stitching algorithm is established based on the mathematical model and the simultaneous least-squares method, which keeps the error from transmitting and accumulating. So the adjustment error can be compensated efficiently. In addition, the standard deviation (SD) in the overlapped regions is used as the figure of merit to determine the stitching accuracy. Finally, simulations and experiments are given to verify the validity and rationality of the proposed algorithm. The results show that the introduced method is quite efficient.

Peano-like paths for subaperture polishing of optical aspherical surfaces.

Polishing can be more uniform if the polishing path provides uniform coverage of the surface. It is known that Peano paths can provide uniform coverage of planar surfaces. Peano paths also contain short path segments and turns: (1) all path segments have the same length, (2) path segments are mutually orthogonal at the turns, and (3) path segments and turns are uniformity distributed over the domain surface. These make Peano paths an attractive candidate among polishing tool paths because they enhance multidirectional approaches of the tool to each surface location. A method for constructing Peano paths for uniform coverage of aspherical surfaces is proposed in this paper. When mapped to the aspherical surface, the path also contains short path segments and turns, and the above attributes are approximately preserved. Attention is paid so that the path segments are still well distributed near the vertex of the surface. The proposed tool path was used in the polishing of a number of parabolic BK7 specimens using magnetorheological finishing (MRF) and pitch with cerium oxide. The results were rather good for optical lenses and confirm that a Peano-like path was useful for polishing, for MRF, and for pitch polishing. In the latter case, the surface roughness achieved was 0.91 nm according to WYKO measurement.

Investigation on removal features of multidistribution fixed abrasive diamond pellets used in the polishing of SiC mirrors.

To obtain removal functions (RFs) with high removal rate and stability in the polishing of silicon carbide mirror, an optical fabrication technology based on fixed abrasive diamond pellets (FADPs) is adopted. In this paper, we focus on the removal characteristics of FADPs, including removal profile, removal rate, stability of RFs, and surface roughness. Diamond pellets polishing is analyzed theoretically with respect to removal rate and stability. A universal algorithm is proposed for computing theoretical removal profile of different distribution models. By evaluating the cutoff frequency of RFs, optimized parameters including speed ratio and eccentricity are confirmed. A series of experiments are conducted to verify the effectiveness of the algorithm; within 300 min (even more), the pellets could provide highly stable RFs with about 5 times removal rate than loose abrasives; the surface roughness 4.86 nm is obtained.

A Pocket-Textured Surface for Improving the Tribological Properties of Point Contact under Starved Lubrication.

This paper reports a novel pocket-textured surface for improving the tribological properties of point contact under starved lubrication by possibly storing and releasing oil, and homogenizing the surface contact pressure. The ball-on-disk experimental results confirmed the coefficient of friction (COF) and wear reduction effect of such pocket-texturing. The maximum reduction rate was 40% compared with a flat surface under the same operating conditions. Analyses on experimental results attributed the oil storage effect and enhanced the secondary lubrication effect within the starved lubrication state, to become the main mechanism. In addition, the plate elasticity and the Hertzian contact principles were employed to estimate the pressure and the load acting on the surface. The experimental results and numerical analysis substantiated the design of pocket-textured surface, making it likely to enlarge about 50% of contact surface and to reduce 90% of equivalent stress in comparison to those of conventional surfaces.