Absolute testing of weakly aspheric surfaces with pixel-level resolution and subnanometer accuracy.

Most of the commercial available sub-aperture stitching interferometers measure the surface with a standard lens that produces a reference wavefront, and the precision of the interferometer is generally limited by the standard lens. The test accuracy can be achieved by removing the error of reference surface by the absolute testing method. When the testing accuracy (repeatability and reproducibility) is close to 1nm, in addition to the reference surface, other factors will also affect the measuring accuracy such as environment, zoom magnification, stitching precision, tooling and fixture, the characteristics of optical materials and so on. We establish a stitching system in the thousand level cleanroom. The stitching system is including the Zygo interferometer, the motion system with Bilz active isolation system at level VC-F. We review the traditional absolute flat testing methods and emphasize the method of rotation-shift functions. According to the rotation-shift method we get the profile of the reference lens and the testing lens. The problem of the rotation-shift method is the tilt error. In the motion system, we control the tilt error no more than 4 second to reduce the error. In order to obtain higher testing accuracy, we analyze the influence surface shape measurement accuracy by recording the environment error with the fluke testing equipment.

Abstract: By using a CGH test plate fabricated with our equipment and techniques, we measured a perfect sphere surface. The measurement result is quantified into four parts: the figure error from the spherical surface under test; the figure error from the spherical reference surface; the error from hologram and the adjustment error from misalignment. The measurement result removed from the later three errors, shown excellent agreemen t with Zygo test of the same sphere surface. This verified that the measurement accuracy by using this kind of CGH coul d be very high. Key words : computer-generated hologram; convex aspheric surface; test 1. Introduction It is well known that the use of large and deep convex aspheric surfaces in reflective optical system allows improved performance with fewer elements. However, it is difficult and expensive to measure them accurately with traditional me thods [1-4]. Recently, a valid met hod by using computer-generated hologram (CGH) test plat has been studied [5-8]. In this method, the CGH was constructed using thermally selective oxidization to transfer a CGH pattern onto a metallic film on a curved substrate. However, the resolution and linear profile of the gr atings that compose the CGH was of inferior quality in comparison with that produced by use of lithography. This may decrease significantly surface measurement accuracy. Our lab has he ld the technology to transfer a large CGH pattern onto a concave lens surface with precise alignment [9-12]. The technology combined laser direct writing and lithography. And we have successfu lly test a convex aspheric surface wi th a CGH test plat fabricated with this method [13-14]. However, the measurement error was not analyzed, and the measurement result was not verified by compared with that of other methods. In this paper, we built an optical test system to measure a perfect sphere surface with 100mm of diameter and 279mm of radius of curvature. The system had two illumination lenses and a test plate with a CGH fabricated by using our new technology. We analyzed the errors existing in this test. The measurement result was quantified into four parts. One is the figure error from the spherical surface under test, and it can be gotten with absolute test method by using Zygo interferometer. One is the figure error from the spherical reference surface, and it can also be gotten with absolute test method by using Zygo interferometer. One is the error from hologram, and it can be verified by confirming the ring positions. One is the adjustment error from misalignment, but it can be removed by using the method of Zernike polynomials fitting and measuring twice[15]. The measurement result removed from the later three errors, shown excellent agreemen t with Zygo test of the same sphere surface. 1. The Optical system design

Pentaprism scanning technology (PPS) is an absolute testing method that has the advantages of a simple structure and absolute testing without an extra reference flat, as well as being able to provide in situ surface measurements, and more. It plays an important role in the manufacturing process of large flat mirrors. For calibrating the PPS's uncertainty, this paper describes a multi-mode scanning method to implement the measurement of low-order aberrations and introduces the concept of an autocorrelation coefficient to evaluate the data processing progress. These improvements were applied to the measurement of a large flat mirror (1630mm in diameter), which demonstrates that the measuring uncertainty of PPS can be about 20nm rms. Furthermore, in regard to the special requirements of M3MP, the prototype mirror of M3M (the tertiary mirror) in the Thirty Meter Telescope project with a non-circular aperture, we analyzed the slope distribution of low-order aberrations, power, and astigmatism. The sample route lines of PPS are then reorganized and a new data process algorithm is implemented. This work was performed in order to improve the PPS's performance in measuring low-order aberrations of large flat mirrors.

We present an absolute measurement of flats in a Fizeau interferometer with the method of shift-rotation, which only requires rotational measurements and shift measurement with a translation. Experiments have been carried out to verify the validity of the absolute testing method, and the results show that the reference surface deviation measured with the shift-rotation method agrees well with that of another calibration result with traditional three-flat absolute procedure; the root-mean-square (RMS) of the residual figure between them is ∼0.4 nm.

Interferometry is a relative measurement method for optical surface testing, and thus its testing accuracy depends on the accuracy of the reference surface. Absolute measurement is one of the most effective methods to improve the testing accuracy in interferometry. We present an efficient absolute measurement method based on Zernike polynomial fitting algorithms. With our proposed method, the profiles of both the test surface and the reference surface can be calculated simultaneously. We further carried out simulation analysis to scientifically evaluate the test accuracy of the proposed method. Finally, we conducted actual experiments to demonstrate the feasibility and practicability of our method.

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that out-performs general purpose numerical solvers and is able to handle the large problem instances commonly occurring in structure from motion settings. The potential of this proposed method is demonstrated on a number of different problems, consisting of both synthetic and real-world data.

Today’s giant telescopes use mirrors that require new methods of optical testing. This paper summarizes developments at University of Arizona for measuring off-axis primary mirror segments, large convex aspheric secondary mirrors, and giant turning flats.

The measurement of aspheres and freeforms poses several challenges to interferometric and other optical testing methods which are well established for spherical surfaces. Accuracy, measurement time and flexibility are requirements encountered in a production environment. The approach of tilted-wave-interferometry is to illuminate the specimen with a whole ensemble of wavefronts. Each of these wavefronts has a different amount of tilt with respect to the optical axis. The surface under test is completely covered by interferogram patches where rays from one source hit the surface such that resolvable fringe densities result. Yet, one still deviates from the null setup which requires that the interferometer is calibrated precisely. This is obtained by recording interferograms of a known reference object placed in the test space. The aberrations of the interferometer are described within a black box model. A sophisticated set of algorithms is used to reconstruct these coefficients with high accuracy. The non-null configuration prohibits a direct evaluation of the measurement from the interferograms. Instead, the surface is reconstructed by the solution of an inverse problem. A second step gives access to the remaining high-frequency errors. The key ideas and implementations in the process of measurement and calibration are explained and the differences to other common concepts in optical testing are elaborated. As an example, results of a freeform measurement, including both form and high-frequent deviations from design, are discussed.

The reconstruction of the absolute conductivity distribution using electrical resistance tomography (ERT) is important, such as for the quantitative measurements of phase distribution in the fluidized bed. However, due to the nonlinearity in ERT, the accurate reconstruction of the absolute conductivity distribution is difficult to achieve using the common algorithms. In order to address this problem, the absolute conductivity distribution reconstruction method based on an explicit nonlinear model (ENM) is proposed. The explicit nonlinear relationship between the boundary currents and the conductivity distribution is first derived. Then, the explicit nonlinear relationship is transformed into a new form of system of linear equations. The common iterative algorithm is utilized to solve the system of linear equations and thus obtain the conductivity distribution. In addition, the substitution of the empty field data for background field data is implemented to make the ENM method applicable to the situation, where the background conductivity varies significantly. The reconstruction quality of the ENM method is significantly better than that of the traditional sensitivity-based linear algorithm and worse than that of the D-bar algorithm. The calculation time of the ENM method is close to that of the sensitivity-based linear algorithm, but much less than that of the D-bar algorithm.

Five interferometric tests were conducted at cryogenic temperatures on a lightweight, 50 cm diameter, hot isostatic pressed (HIP) beryllium mirror in the Ames Research Center (ARC) Cryogenic Optics Test Facility. The purpose of the tests was to determine the stability of the mirror's figure when cooled to cryogenic temperatures. Test temperatures ranged from room ambient to 8 K. One cycle to 8 K and five cycles to 80 K were performed. Optical and thermal test methods are described. Data is presented to show the amount of cryogenic distortion and hysteresis present in the mirror when measured with an earlier, Shack interferometer, and with a newly-acquired, phase-measuring interferometer.

Accurate cavity volume testing based on micropressure differential gas inflation and deflation

International audience

This chapter contains sections titled: Introduction Principles of Optical Nondestructive Testing Techniques (ONDTs) Optical Methods for NDT Conclusions and Perspectives Acknowledgments References

In every optical testing method, the time taken to process data, the precision of the results and the sensitivity are among the most relevant aspects to be taken into account when the viability of its implementation is been under consideration. An accuracy and sensitivity analysis of a topographer based on a conical null-screen with a semi-radial distribution of targets is presented. On the other hand, we proposed a custom evaluation algorithm in order to reduce the time in the calculation of the normal to the corneal surface. Finally, we perform some corneal topographical measurements.

Corundum-based abrasives are commonly used for cutting extremely hard materials like e.g. ceramics by means of abrasive waterjets. Due to a reduced lifetime of the used focusing tubes, this type of abrasive is only applied under special consideration of economic circumstances. The cutting centres which use this technology retain only a small amount of used abrasives because of the limited application of this grain type. Nevertheless, observing the disintegration of particles which have interacted with mostly advanced materials is of scientific interest. Garnet-based abrasives are commonly classified in different grain size classes after sieving to evaluate their recycling potential. Based on a feasibility study, this paper will present some results on achieved cutting data and also shows the geometrical change of the used focusing tubes which was realized by non-destructive examination. The mass loss factor of the used focusing tubes was calculated for different corundum materials and compared with the commonly used in AWJ machining abrasive, garnet. Additionally, cutting and recycling properties of the tested corundum-based abrasive was tested. The disintegration properties of the corundum-based abrasive were monitored by sieving and optical test methods. Particle identification after cutting process (grain or chip) was realized by energy-dispersive X-ray microanalysis (EDX). Finally, the results obtained were used to make a rough calculation for lifetime estimations of the focusing tubes related to the observed wear process.