Measurement Of Aspheric Surfaces Research Articles

A profile measurement method of large aspheric optical surface based on optimal stitching planning

This paper proposes an optimal stitching planning for two-dimensional profile measurement of large aspheric surface by applying small range profiler as the measuring machine. The originality of this paper reflects on two aspects: (1) According to the applied range of probe, the amount of overlap region and the geometric characteristic of large aspheric surface, a segmentation planning algorithm is presented to determine the segment parameters during the measuring process. Considering the measurement efficiency and stitching accuracy synthetically, the applied range of probe with ±4mm and the amount of overlap region with 20% of segment length are regarded as the optimal parameters. (2) Based on the invariance of curvature radius of overlap region, a data matching algorithm is developed to match the adjacent segments. Through the simulation analysis, the deviation of adjacent segments is reduced to 0.03mm with the sampling interval of 0.01mm. Then on the basis of the simulation settings with the translation error of 1μm and the rotation error of 30′, the accumulative stitching errors of three different curves are predicted within sub-micron level. Finally the optimal stitching method is verified by experiments of two groups of 110-mm aspheric curves. The PV (Peak-to-valley) values of the stitching errors of the two curves are in the range of ±1μm and the standard deviations are less than 0.2μm.

Fabrication of Computer Generated Hologram for Aspheric Surface Measurement

High-precision aspheric surfaces are generally measured using interferometer with a computer-generated holograms (CGH), which has a wavy line pattern fabricated onto a glass substrate. CGH patterns are generally made using lithographic techniques that was developed for semiconductor industry. Patterns can be subsequently etched into glass substrate using reactive ion or chemical etching. The accuracy of the drawn pattern on a CGH decides the accuracy of the measurement. Draw pattern error mainly includes the line-width deviation and its position error. In this paper, the influences of defocus of drawing laser and the wet-etching processes on the line-width were firstly investigated. On the other hand, the position error under different line-width was obtained by analyzing the relationship of line-width error and the position error. Based on the above-obtained results, a CGH having a diameter of 80 mm and the minimum line-width of 1.8 μm was successfully fabricated. Testing results showed that the wavefront error was only 3.79 nm, significantly higher than the commercial-available ones. The fabricated CGH is expected to use in the high-precision measurement of asphercal surfaces.

Fabrication of Computer Generated Hologram for Aspheric Surface Measurement

High-precision aspheric surfaces are generally measured using interferometer with a computer-generated holograms (CGH), which has a wavy line pattern fabricated onto a glass substrate. CGH patterns are generally made using lithographic techniques that was developed for semiconductor industry. Patterns can be subsequently etched into glass substrate using reactive ion or chemical etching. The accuracy of the drawn pattern on a CGH decides the accuracy of the measurement. Draw pattern error mainly includes the line-width deviation and its position error. In this paper, the influences of defocus of drawing laser and the wet-etching processes on the line-width were firstly investigated. On the other hand, the position error under different line-width was obtained by analyzing the relationship of line-width error and the position error. Based on the above-obtained results, a CGH having a diameter of 80 mm and the minimum line-width of 1.8 μm was successfully fabricated. Testing results showed that the wavefront error was only 3.79 nm, significantly higher than the commercial-available ones. The fabricated CGH is expected to use in the high-precision measurement of asphercal surfaces.

Development of aspheric surface profilometry using curvature method

A curvature method is one promising possibility for the measurement of optical aspheric or freeform surface, which is the major part of an optical system, such as google glasses, and wearable devices. Increasing demand for highly accurate optical components requires accurate and efficient measurement techniques. In this paper, we have presented a method of aspheric surface reconstruction from curvature data by using white-light-interferometer as a curvature sensor. This sensor was found to be robust to mechanical position error and environmental noise via error diagnosis. The primary mirror of cassegrain type astronomical telescope was tested. The measurement results showed that white-light scanning interferomete was found to be suitable for measuring the aspheric surface profile as a curvature sensor.

Measurement for off-axis aspheric mirror using off-axis annular subaperture stitching interferometry: theory and applications

An off-axis annular subaperture stitching interferometry (OASSI) is presented to test off-axis aspheric surfaces. In view of this, the relationship between misalignment and wavefront aberration is deduced with a strict theoretical analysis. The analytic result shows that the relative misalignment errors between the interferometer and the off-axis mirror tested will lead to complex wavefront aberrations in the measurement result other than the ordinary terms of piston, tilts, and power. Based on the analytic result, a suitable off-axis stitching algorithm is developed for stitching the off-axis subaperture. Both the numerical simulations and preliminary experimental results prove the potential of the proposed approach for the measurement of off-axis aspheric surfaces. As far as we know, this is the first time that OASSI has been used to test the off-axis aspheric surface.

Measurement of aspheric surface combining point diffraction interferometry and annular subaperture stitching

Point diffraction interferometry (PDI) combined with annular subaperture stitching is proposed for ultrahigh-accuracy measurements of aspheric surfaces. By adding an axial movement to the test optics in the PDI system, aspheric surfaces with large departures can be measured with high accuracy by stitching the annular measurement data of different axial positions. We examine the principle of PDI-based annular subaperture stitching and the stitching algorithm. Simulations and experiments demonstrate the feasibility and effectiveness of our proposed method. Our method retains the ultra-high accuracy of PDI while extending the vertical dynamic range of the interferometer, enabling nanometer or even subnanometer accuracy measurements of large-departure rotationally symmetric aspheric surfaces.

Correction for mapping errors in non-null test of aspheric surface

The non-null testing methods have the potential to allow measurement of aspheric surfaces with large departures from a reference sphere. In a non-null configuration, the ray will return along a different path and interfere with a different reference ray. This difference in “mapping” between the test and reference rays creates an additional optical path difference (OPD) contribution, which causes test part errors to be mapped to the wrong location. To correct the mapping errors in non-null test of aspheric surface, correction method are proposed by ray trace and wave-front analysis. Experiments are carried out to illustrate the effectiveness of this approach. The methods can work well, despite large deviation between the theoretic value of the aspheric and the reference wave-front.

3D Measurement and Characterization of Ultra-precision Aspheric Surfaces

Aspheric surfaces have become widely used in various fields ranging from imaging systems to energy and biomedical applications. Although many research works have been conducted to address their manufacturing and measurement, there are still challenges in form characterization of aspheric surfaces considering a large number of data points. This paper presents a comparative study of 3D measurement and form characterization of an aspheric lens using tactile and optical single scanning probing systems. The design of the LNE high precision profilometer, traceable to standard references is presented. The measured surfaces are obtained from the aforementioned system. They are characterized with large number of data points for which a suitable process chain is deployed. The form characterization of the aspheric surfaces is based on surface fitting techniques by comparing the measured surface with the design surface. A comparative study of registration methods and non-linear Orthogonal Least-Squares fitting Methods is presented. Experimental results are analyzed and discussed to illustrate the effectiveness of the proposed approaches.

Calibration of a non-null test interferometer for the measurement of aspheres and free-form surfaces.

The measurement of aspheric and free-form surfaces in a non-null test configuration has the advantage that no compensation optics is required. However, if a surface is measured in a non-null test configuration, retrace errors are introduced to the measurement. We describe a method to calibrate the test space of an interferometer, enabling to compensate retrace errors. The method is effective even for strong deviations from null test configuration up to several 100 waves, enabling the fast and flexible measurement of aspheres and free-form surfaces. In this paper we present the application of the method to the calibration of the Tilted Wave Interferometer. Furthermore, the method can be generalized to the calibration of other setups.

Research on mechanism and application of effect of adjustment errors in aspheric surface stitching interferometry

Due to the existence of imprecise fitting of subapertures’ overlap zone, the accumulation of adjustment errors is significant during the measurement of aspheric surface by stitching interferometry. Theoretical analysis indicates that the effect and the appearance of three-direction adjustment errors accords with that of Seidel aberration, of which the axial error leads defocus, third-order spherical aberration and higher-order errors of wave front distribution. Based on the analysis we have made, a correction model has been established, and the estimated values of adjustment errors have been acquired. By correcting the higher-order aberration in the model, fitting precision of subapertures’ overlap zone can be improved. Experiment for comparison shows that, after fitting, the value of both residual error and uncertainty of measurement become smaller than those values obtained by traditional correction method of three-direction adjustment error, which proves that the stitching precision of proposed method is higher.

Analytical Jacobian and its application to tilted-wave interferometry.

Tilted-wave interferometry (TWI) is a novel optical measurement principle for the measurement of aspherical surfaces. For the reconstruction of the wavefront and the surface under test, respectively, perturbation methods are applied, which require the calculation of the Jacobian matrix. For the practical use of the instrument, a fast and exact calculation of the Jacobian matrices is crucial, since this strongly influences the calculation times of the TWI. By applying appropriate approaches in optical perturbation methods we are able to calculate the required Jacobian matrices analytically when the nominal optical path through the system is given. As a result, calculation times for the TWI can be considerably reduced. We finally illustrate the improved TWI procedure and apply methods of optimal design to determine optimal positions of the surface under test. For such applications the fast calculation of the Jacobian matrices is essential.

Measurement of aspheric surfaces using annular subaperture stitching interferometry based on an automatic positioning method: theory and application

A simple and effective automatic positioning method (APM) is proposed for the application of annular subaperture stitching interferometry in the stage of precision polishing. In the testing process, a series of optical path difference (OPD) data of subaperture are obtained since the interferometer is shifted relative to the tested aspheric surface. These OPD data are analyzed by the APM to get the key stitching parameters (e.g., aspheric departure) without a precision motion system. The basic principles of the APM are described. The performance of the method is simulated in some pertinent cases. Finally, we study the applicability of the proposed method to subaperture stitching tests of a hyperbolic mirror. The stitching results agree with the full-aperture test results. It demonstrates the validity and practicability of the proposed algorithm.

Profile measurement of aspheric surfaces using scanning deflectometry and rotating autocollimator with wide measuring range

High-accuracy aspherical mirrors and lenses with large dimensions are widely used in large telescopes and other industry fields. However, the measurement methods for large aspherical optical surfaces are not well established. Scanning deflectometry is used for measuring optical signals near flat surfaces with uncertainties on subnanometer scales. A critical issue regarding scanning deflectometry is that high-accuracy autocollimators (AC) have narrow angular measuring ranges and are not suitable for measuring surfaces with large slopes and angular changes. The goal of our study is to measure the profile of large aspherical optical surfaces with an accuracy of approximately 10 nm. We have proposed a new method to measure optical surfaces with large aspherical dimensions and large angular changes by using a scanning deflectometry method. A rotating AC was used to increase the allowable measuring range. Error analysis showed that the rotating AC reduces the accuracy of the measurements. In this study, we developed a new AC with complementary metal-oxide semiconductor (CMOS) as a light-receiving element (CMOS-type AC). The CMOS-type AC can measure wider ranges of angular changes, with a maximum range of 21 500 µrad (4500 arcsec) and a stability (standard deviation) of 0.1 µrad (0.02 arcsec). We conducted an experiment to verify the effectivity of the wide measuring range AC by the measurement of a spherical mirror with a curvature radius of 500 mm. Furthermore, we conducted an experiment to measure an aspherical optical surface (an off-axis parabolic mirror) and found an angular change of 0.07 rad (4 arcdegrees). The repeatability (average standard deviation) for ten measurements of the off-axis parabolic mirror was less than 4 nm.

Algorithms of wavefront generation for aspheric surface measurement

For aspheric surface measurement with wavefront sensing technology, after obtaining the slope or curvature as the measurement raw data, the data processing algorithm must be re-studied for high performance in practical application. This paper designs, analyzes and compares five different algorithms to generate wavefront for aspheric surface measurements, especially for practical measurements with noises and missing data. Simulation and experimental results show that in ideal condition without any noise in the system, direct fitting yields perfect results without error; the algorithms including Southwell reconstruction achieve better results under practical conditions, where there exist real issues such as noise and abnormal data. Reconstruction is therefore an essential step as it significantly improves the measurement stability and reliability, and enables the system feasible for practical applications. Furthermore, Southwell algorithm is extended for applications with missing data, which is most likely happen when the surfaces to be measured possess large dynamic range.

Discussions on on-machine measurement of aspheric lens-mold surface

At present, regarding to the machining of aspheric lens mold, there are two major methods to carry out the on-machine measurement (OMM) — contacting method (CM) and non-contacting method (NCM). Here such two methods are reviewed in detail. CM is mainly based on the contacting probe which is scratching aspheric surface of lens mold to achieve profile data. To be efficient, an idea with 45° tilt of probe is proposed for OMM of lens mold by Suzuki. But generally speaking, the contacting OMM is not so efficient and can only deal with axisymmetric aspheric lens mold. On the contrary, NCM mostly uses laser to achieve aspheric profile without any contact. On ultra-precision lathe, laser scanning system or laser interferometer is mounted on the frame of lathe and transfers measurement data to machining system efficiently. However, most NCMs need stable environment and low working noise except instantaneous phase-shifting shearing interferometry (IPSSI). Therefore, a new idea about IPSSI is proposed in this paper to realize OMM of lens molds. Unfortunately, it's also difficult to test the high numerical aperture aspheric or free-form lens molds. By comparison, the newly-developed fringe reflection (FR) method is becoming the promising method because it features the high efficiency and high accuracy. However, this method has not been used for OMM system yet. Much research should be conducted for FR OMM technology.

Random error analysis of profile measurement of large aspheric optical surface using scanning deflectometry with rotation stage

a b s t r a c t Scanning deflectometry method has been successfully employed for the measurements of large flat surfaces with sub-nanometer uncertainty. In this paper, we propose an alternative scanning deflectometry method for measuring large aspheric optical surfaces, wherein a rotation stage is incorporated to increase the measurement range of the high-accuracy autocollimators used to measure small angles. Further, the pitching error of the linear stage is compensated with offline measurement data. In this study, we conducted random error analysis to estimate the measurement repeatability. Our results show that for the measurements of large aspheric surfaces with large slope changes, 10-nm repeatability is achievable under the suitable conditions. To verify the random error analysis results, we also constructed an experimental setup for test the measurement repeatability. The repeatability distribution of the experimental results was in good agreement with the error analysis distribution. We have thus demonstrated the applicability of the random error analysis in the measurement of large aspheric surfaces with high accuracies.

三坐标轮廓测量仪测量离轴非球面的数据处理

In order to research the data processing of the off-axis aspheric surface measurement by coordinate contour measuring machine(CMM),the principle of the off-axis aspheric surface measurement by the CMM is introduced,the detailed analysis of the errors except the instrument itself errors is given,the off-axis aspheric surface data processing model for these error corrections is built on this basis.Matlab and C language are mixed programming in the model.After data simulation the actual off-axis aspheric surfaces are measured.In the data simulation,the surface error PV value is less than 0.001μm.For a practical application,the surface error PV value of an actual off-axis aspheric surface is about 0.245μm,and using the data processing model it can reach 1.2μm,close to the instrument itself measurement precision.The result indicates that the established model and the data processing software are correct.

Aspheric surface measurement based on sub-aperture stitching interferometry

In order to test convex aspheric surfaces without the aid of other null optics, a novel method combined sub-aperture stitching and interferometry called SSI (sub-aperture stitching interferometry) is introduced. In this letter, the theory, basic principle, and flow chart of SSI are researched. A synthetical optimization stitching mode and an effective stitching algorithm are established based on homogeneous coordinate's transformation and simultaneous least-squares fitting. The software of SSI is devised, and the prototype for testing of large aspheres by SSI is designed and developed. The experiment is carried out with five subapertures for a convex silicon carbide (SIC) aspheric mirror with a clear aperture of 130 mm. The peak-to-valley (PV) and root-mean-square (RMS) error are 0.186 \lambda and 0.019 \lambda, respectively. For the comparison and validation, the TMA system which contained the convex asphere is tested by interferometry. The wavefront error of the central field of the optical system is 0.068 \lambda RMS which approaches to diffraction limitation. The results conclude that this technique is feasible and accurate. It enables the non-null testing of aspheric surfaces especially for convex aspheres.

Calculation of aberration and direction of a normal to aspherical surface

The work deals with the problem of aspherical surfaces in optics. General relations for the calculation of wave aberration, ray aberrations and the influence of change of radius of the reference sphere on the wave aberration of a normal to aspherical surface are derived. Furthermore, general formulas are derived for the calculation of the direction of the normal to the aspherical surface in case that the directions of the incident and the reflected (or refracted) rays are known. These equations are of a high importance for the design and manufacturing process of aspherical surfaces, design and adjustment of compensation optics in interferometric measurements of aspherical surfaces, measurement of aspherical surfaces by deflectometry, etc.

激光跟踪仪检验非球面面形的方法

In order to test middle and low precision asphere and measurement of asphere during grinding and polishing,a new method by extending the ability of laser tracker is proposed.The testing principle is analyzed,and the testing procedure is devised.The coordinate of several points on the tested asphere can be measured by the laser tracker,and the figure error can be calculated by analyzing the testing data and CAD model of the asphere.An off-axial aspheric surface with the aperture of 420 mm×270 mm is measured by this method,the surface map by this method is consistent to the entire surface map from the null test,and the relative error of the PV and RMS error between null test and this method is 6.22% and 3.37%,respectively.The proposed method provides another quantitive measurement for testing large aperture aspheres without any assistant optics,and the data processing and testing operation are very convenient.