Measurement Of Aspheric Surfaces Research Articles

Quantitative measurement of large-aperture aspheric surfaces by off-axis Ronchi test

An off-axis Ronchi test based on the phase-shifting technique is presented to measure the aspheric mirror quantitatively. In this paper, slopes of deviations from the mirror's ideal aspheric shape are derived when an off-axis point source is used. By integrating these slopes, the deviations of the shape are obtained and then the tested shape can be reconstructed. Compared with the coaxial Ronchi test, the measurement error caused by combination fringes can be avoided, and this system is more flexible. In the experiment, a marked point is used to guide the phase unwrapping procedure, which improves the accuracy of extracting corresponding phase points. In addition, the method has strong anti-noise ability. The validity of the method has been verified by both computer simulations and a preliminary experiment.

Solving the Two-Objective Shop Scheduling Problem in MTO Manufacturing Systems by a Novel Genetic Algorithm

With the characteristics of un-touching, high-automatic and high-speed, we measured 3D shape by digital moiré patterns. And it can measure 3D shape without compensator, auxiliary mirror, hologram and other assistant modules. So it is widely used in measurement of 3D shape. But with the negative effect of grating area and CCD resolution of the camera, it has some problems in large aperture, steep aspheric surface, even off-axis aspheric testing. Focus on these problems; this paper established a sub-region splicing measurement of aspheric surface by using the combination of digital moire patterns and digital phase shifting technology. This paper also illustrated the basic theory, and the mathematical implementation procedure. In all, sub-region splicing digital moiré patterns can be considered as another method, which beyond compensation tests to measurement of aspheric surface.

Nanometer profile measurement of large aspheric optical surface by scanning deflectometry with rotatable devices: Uncertainty propagation analysis and experiments

Abstract High-accuracy mirrors and lenses with large dimensions are widely used in huge telescopes and other industrial fields. Interferometers are widely used to measure near flat surfaces and spherical optical surfaces because of their high accuracy and high efficiency. Scanning deflectometry is also used for measuring optical near flat surfaces with sub-nanometer uncertainty. However, for measuring an aspheric surface with a large departure from a perfect spherical surface, both of these methods are difficult to use. The key problem for scanning deflectometry is that high-accuracy autocollimators usually have a limited measuring range less than 1000″, so it cannot be used for measuring surfaces having a large slope. We have proposed a new method for measuring large aspheric surfaces with large slopes based on a scanning deflectometry method in which rotatable devices are used to enlarge the measuring range of the autocollimator. We also proposed a method to connect the angle data which is cut by the rotation of the rotatable devices. An analysis of uncertainty propagation in our proposed method was done. The result showed that when measuring a large aspheric surface with a diameter over 300 mm and a slope of 10 arc-deg, the uncertainty was less than 10 nm. For the verification of our proposed method, experimental devices were set up. A spherical optical mirror with a diameter of 35 mm and curvature radius of 5000 mm was measured. The measuring range of the autocollimator was successfully enlarged by our proposed method. Experimental results showed that the average standard deviation of 10 times measurement was about 20 nm.

An improved phase retrieval algorithm for optical aspheric surface measurement

In order to overcome the measurement and calculation difficulty for aspheric surface with phase retrieval technology, an improved phase retrieval algorithm was proposed. Due to significant departure from sphere surface, reflected light from different part of the aspheric surface under test will overlap in some areas in the collected images by CCD with general phase retrieval measurement setup, which will lead to the failure to recover the surface phase. The proposed algorithm will only use those areas without light overlapping in each image in the iteration process and employ several defocused images to recover the whole surface. This algorithm can improve the measurement range for aspheric surface with phase retrieval technology. The experimental system was established and a 180 mm diameter, f/1.6 parabolic mirror and a 180 mm effective diameter, f/1.33 hyperboloid mirror were tested by the proposed method. The experimental results show that the retrieved surface errors are in good consistent with that obtained by interferometer, which confirms the validity of the proposed algorithm.

Profile Measurement of Large Aspheric Optical Surface by Scanning Deflectometry with Rotatable Optical Devices - Error Analysis and Pre-Experiment-

Large aspheric mirrors with diameter over 300 millimeters with high surface accuracy are wildly used in many areas such as astronomical telescopes. Interferometers are widely used in profile measurement of optical flat and sphere. However, standard reference aspheric surface which is necessary for this method is difficult to make. Scanning defletometry based on ESAD (Extended Shear Angle Difference) is used to measure ultra-precise large near-flat and slight curved optical surface with the accuracy of sub-nanometer. However, it is not possible for it to measure aspheric surface because of the limitation of the measuring range of autocollimators. We proposed a new measuring method to scan the surface of a large aspheric optical surface using autocollimator with rotatable optical devices fixed on linear motion stage. To eliminate the influence of the pitching error of the scanning stage, we use two mirrors reflecting laser comes from autocollimator, which have the same effect with a pentaprism used in ESAD. To enlarge the measuring range of the autocollimator, we use a rotatable mirror to fit the changes of the slope of the mirror surface under measurement. The error analysis of the method is done. Measurement of an optical flat mirror and a sphere mirror with diameter of 50 mm and biggest slope of 6000 arc-second are done. The rotatable optical devices that we designed are proved effective on eliminating the pitching error of the moving stage.

Nanometer Profile Measurement of Large Aspheric Optical Surface (2nd report)

Nanometer Profile Measurement of Large Aspheric Optical Surface (2nd report)

Analytical study of disturbing diffraction orders in in-line computer generated holograms for aspheric testing

The effect of spurious diffraction orders due to an in-line diffractive compensator for the measurement of aspheric surfaces is analytically studied. The use of a filtering aperture to isolate the measurement diffraction order from the stray orders introduces additional spurious fields that must be analyzed for a correct evaluation of surface defects. In this work the influence of the additional diffraction orders is studied and an analytical expression for the disturbing field on the detector is obtained.

非球面面形测量技术

非球面面形测量技术

非球面面形测量技术

非球面面形测量技术

Perturbation methods in optics: application to the interferometric measurement of surfaces

Manufacturing and misalignment errors are present in every optical system. Usually these errors lead to intolerable wavefront deviations and system inaccuracies if they are not characterized and taken into consideration. In the interferometric measurement of surfaces, the characterization of the interferometer aberrations plays a central role, since unknown phase contributions lead to an erroneous assessment of the test surface and therefore an incorrect estimation of the performance of an optical system. In this work, we present a method for the interferometric characterization of surfaces based on the principles of Hamilton's characteristic functions and perturbation theory. The application of the proposed method to an interferometer for the measurement of aspherical surfaces is shown.

龙基光栅在大口径非球面定量测量中的应用

龙基光栅在大口径非球面定量测量中的应用

非球面检测中计算全息片的制作问题研究

Interferometric optical testing using computer-generated hologram (CGH) can give highly accurate measurement of aspheric surfaces has been proved. After the system is designed, a phase function is obtained according to the CGH's surface plane. For the requirement of accuracy, an optimization algorithm that transfers the phase function into a certain mask pattern file is presented in this letter, based on the relationship between the pattern error of CGH and the output wavefront accuracy. Then the writing machine is able to fabricate such a mask with this kind of file. With that mask, an improved procedure on fabrication of phase type CGH is also presented. Interferometric test results of an aspheric surface show that the whole test system obtains the demanded accuracy.

Interferometer for precise and flexible asphere testing

A novel non-null interferometer for the precise measurement of aspheric surfaces is presented. In contrast to a classical interferometer, where only one test wavefront is used, the proposed system makes use of multiple test beams propagating under different angles through the interferometer. This allows the measurement of aspheric surfaces in a very short time, even for strong aspheres with deviations from the best-fit sphere of up to 900 microm. The non-null test configuration implies that any additional aberrations introduced by the interferometer have to be well characterized to precisely measure the asphere. Experimental measurements of a calibrated non-null interferometer on an aspheric element with 900 microm SAG deviation are presented.

Measurement of High-NA Axisymmetric Aspherical Surface with Continuous Interference Method

The measurement principle where in a high-NA (Numerical Aperture) surface, for which the degree of the angle of surface inclination exceeds π/3 radians, could be evaluated with high precision and high speed is proposed. This is based on the stitching method, where aspherical surface measurement becomes possible by dividing the surface of the sample into a range so that measurements can be made with an interferometer and finally combined. We examine the method of applying an interferometer to the condition in which the sample is rotated on an air spindle at a constant speed. It is not necessary in this method to make the sample static. Therefore, the vibration of the servo motor and any location errors can be eliminated. Moreover, the measurement time does not depend on the number of divided areas which are necessary for the stitching method, allowing for high-speed measurement. The principle behind this technique is expanded first, and an experiment system based on it was constructed. The principle proposed was evaluated, and its effectiveness was confirmed.

Measurement of steep aspheric surfaces using an anamorphic probe

Synthetic aperture interferometry has been previously proposed as a possible in-process method to measure aspheric form (R. Tomlinson, Appl. Opt.42, 701, 2003.). Preliminary demonstration utilized a scanning probe consisting of a pair of bare single mode fibers to perform source and receive functions. It was found that this probe did not have sufficient numerical aperture (NA) to measure steep surfaces and that simply increasing the NA decreases the light gathering efficiency substantially. In this paper, we introduce supplementary optics to increase the NA, and the light gathering efficiency has been increased by adopting an anamorphic design. A spherical test optic of known form is measured to demonstrate the capability of the new probe design.

Design of a novel hologram for full measurement of large and deep convex aspheric surfaces

We proposed a valid method with a novel computer-generated hologram (CGH) to test large-aperture convex aspheric. The CGH consisted of two zones with different amounts of power: the central zone has a larger amount of power than the marginal zone. Compared with other CGHs used for convex aspheric testing [SPIE.2576.258 (1995)], it could overcome the difficulty of measuring the central region of the convex surface under test, while relaxing the requirement for the illumination optics and CGH of the test system. We have designed an optical test system with the novel CGH to test a 150 mm-diameter convex surface with full aperture by using optical design software Zemax. The simulated result verified the efficiency of the novel CGH. It is believed that this kind of CGHs can be used to measure any large and deep convex surface with full aperture.

Testing of steep convex aspheric surface with a Hartmann sensor by using a CGH

Most aspheric surfaces have been tested by interferometer with some null correctors. This approach, however, often fails when there are many aspherical terms or test surface is very steep because it is not easy to design the conventional null lens or CGH (Computer Generated Hologram). On the other hand, 3-D profilometer can measure aspheric surfaces without any null correctors; however, it takes some time to measure, which makes it unsuitable for the production line in the factory. In this paper, we apply the Hartmann test to the measurement of steep convex aspheric surfaces of which diameter is about 16 mm. In order to increase the measurement accuracy, we calibrated the test setup using a CGH that simulates the ideal test surface. We demonstrated that the significant amount of error in the test setup could be removed by this calibration process. The test results showed only 2 nm rms WFE (wave front error) difference even though the WFE of test setup was worsened by more than 0.13 mum rms. Since this method makes it possible to measure highly aspheric surface quickly and accurately, it can be used in the production line.

An algorithm for stylus instruments to measure aspheric surfaces

A reliable algorithm is developed for the analysis of machined aspheric surfaces with a stylus instrument. This research has been done prior to the evaluation of uncertainties in the aspheric surface analysis. The algorithm considers two factors: the pickup configuration (pivoted arm) and the stylus radius. It also compensates for the sample tilt and the axis offset (the setup error) in the best-fit least-squares process. The algorithm consists of two parts for instrument calibration and aspheric surface analysis, and has been coded by means of C++ and MATLAB. Further it was also applied to the instrument calibration and the aspheric surface measurement, and the results were compared with the instrument-produced ones. The developed algorithm shows better performance over the commercial instrument in both the instrument calibration and the analysis of aspheric surfaces. Besides the uncertainty analysis, the developed algorithm will be a basis for the applications that the commercial instrument cannot provide with its own built-in code.

GS(2)-11(GSW0444) A New Method of Measuring Aspherical Optical Surface

Aspherical mirrors are being widely used in modern photoelectron instrument. Hence measurement of optical aspherical surface is necessary. At present, there are several methods to obtain the shape of an aspherical surfaces, such as phase shifting interference method, laser scanning method, three-coordination measurement method, etc. Phase shifting technique has many advantages but it is marred by a few inaccuracies due to the vibration and mechanical movement of the phase shifter itself. This paper presents a novel aspherical surface measurement technique based on the fringe projection. Sinusoidal fringes produced by a Michelson interferometer are captured by a camera and stored in a computer. The fringe patterns are project onto aspherical surface by a Liquid Crystal Display (LCD) Projection system, which takes the role of a piezo-electric transducer (PZT) phase shifter. The projected fringe patterns are captured by a CCD camera and stored in a digital frame buffer for subsequent analysis by a computer. In this system, phase shift is done electronically and thus errors due to the vibration and mechanical movement of the phase shifter itself and eliminated. The shifting operation is easy and rapid, and furthermore, the displacement can be done precisely. In contrast to the conventional phase shift method, this method is relatively simple and accurate, and is capable of conducting fully automatic measurement. A practical example confirms the predictions of the proposed method.

Separation of form from orientation in 3D measurements of aspheric surfaces with no datum

Measurement and characterisation of 3D form to maintain manufacturing quality has particular problems in cases such as lenses which do not generally have a clear measurement datum. A 3D-form measurement includes information about the form, the orientation and the position of the surface under test. Orientation and position can be design parameters or may result from misalignment of the test specimen on a measurement table. In either case, it is necessary to separate form from orientation and position if the data-set is to be fitted and compared with an “ideal” surface. In this paper two pre-processing algorithms are presented and examples given of the separation of form from orientation and position. The algorithm is applied to simulated data-sets consisting of up to 26,000 discrete points on a square grid, simulating the measurement of an aspheric lens in 3D. The rotationally symmetric data-set is translated for a distance x 0, y 0 and z 0 and rotated about two axes, x and y, to simulate misalignment. To simulate inaccuracies from a manufacturing process, normally distributed random noise is superimposed on the ideal surface. An application of pre-processing using a real data-set is also shown. Furthermore, form fitting is addressed and the interpretation of form by decomposition of the data into error types is discussed.