Phase Measuring Deflectometry Research Articles

Single-shot phase-measuring deflectometry for cornea measurement

Abstract Phase-measuring deflectometry (PMD) has become a standard tool to measure the topography of specular surfaces. We implemented PMD for the measurement of the human cornea topography, exploiting an earlier idea of Lingelbach et al. Two problems occur: a large angular dynamical range and a single-shot measurement are required. We solve these problems by an optimized geometry with minimal occlusion and by single sideband demodulation with a pre-distorted fringe pattern with optimal fringe period. An in vivo measurement of an astigmatic cornea displays a deviation from the medical diagnosis of only 0.15 D, which is within the medical quantization step of 0.25 D.

Four-step shear method for the absolute measurement of a flat surface based on phase measuring deflectometry.

This paper proposes a new shearing approach to eliminate the systematic errors in phase measuring deflectometry (PMD). Besides a normal measurement using PMD, another three measurements are taken when the test surfaces are translated and rotated with an amount of known magnitude in our proposed method. The four measurements give three sheared wavefronts, and then the difference Zernike polynomial fitting and a least squares algorithm are proposed to reconstruct the true test surface figure. The proposed method is demonstrated and verified through computer simulation and experimental results. The error propagation when the sheared wavefronts include random noise and the introduced errors due to the incorrect shearing values are both analyzed.

Novel method for high accuracy figure measurement of optical flat

Phase Measuring Deflectometry (PMD) is a non-contact, high dynamic-range and full-field metrology which becomes a serious competitor to interferometry. However, the accuracy of deflectometry metrology is strongly influenced by the level of the calibrations, including test geometry, imaging pin-hole camera and digital display. In this paper, we propose a novel method that can measure optical flat surface figure to a high accuracy. We first calibrate the camera using a checker pattern shown on a LCD display at six different orientations, and the last orientation is aligned at the same position as the test optical flat. By using this method, lens distortions and the mapping relationship between the CCD pixels and the subaperture coordinates on the test optical flat can be determined at the same time. To further reduce the influence of the calibration errors on measurements, a reference optical flat with a high quality surface is measured, and then the system errors in our PMD setup can be eliminated by subtracting the figure of the reference flat from the figure of the test flat. Although any expensive coordinates measuring machine, such as laser tracker and coordinates measuring machine are not applied in our measurement, our experimental results of optical flat figure from low to high order aberrations still show a good agreement with that from the Fizeau interferometer.

Improved phase-measuring deflectometry for aspheric surfaces test.

An improved phase-measuring deflectometry (PMD) is presented for the aspheric surfaces test. We explore this method from the Ronchi test in a reverse way. With this concept, a camera aperture is placed near the center of curvature of the test mirror, and fringes are displayed on a liquid crystal display screen. The fringes reflected off the test mirror are observed by the camera. By analyzing the captured fringes, the deviations of the test mirror from its ideal shape are obtained and the aspheric surface under test is reconstructed. Compared with traditional PMD, this method needs only to determine reflected rays and doesn't need to know the corresponding incident rays by calibrations, moving screen, or approximation. Both a computer simulation and preliminary experiment have been carried out to demonstrate the validity of the improved PMD. This improved PMD provides a new tool to measure aspheric surfaces quantitatively in full field for optical manufacturing.

Integrated Ray Tracing simulation of the SCOTS surface measurement test for the GMT Fast Steering Mirror Prototype

Software Configurable Optical Testing System (SCOTS) is one of relatively new optical testing methods for large optical surfaces and uses the principle of Phase Measuring Deflectometry (PMD). A camera captures images of the target surface illuminated by a light source screen with patterns. Then, the surface slope and height are obtained by camera image analysis. In the meantime, Integrated Ray Tracing (IRT) concept was developed for the simultaneous end-to-end imaging and radiometric performance simulation of space instruments. It incorporates a light source, medium, target and observing instrument into single computation environment for real scale ray tracing. In this study, we combined these two techniques for the development of an optical testing simulation model applicable to testing the secondary mirror (M2) of Giant Magellan Telescope (GMT). Using the IRT SCOTS model, we simulated SCOTS test runs and reconstructed its surface slopes and heights from the simulated image data. The result shows 1.05nmrms in difference between the input and reconstructed surface heights. It demonstrates the high fidelity of the suggested IRT approach showing nanometer level numerical accuracy and therefore it shows the potential applicability of the IRT simulation technique to SCOTS test method for large precision optical surfaces.

Phase error analysis and reduction in phase measuring deflectometry

In phase measuring deflectometry (PMD), the inspection accuracy of the defects and height of the specular surface are related to the level of phase errors. The usage of numeric integration in reconstructing the shape and the defocusing capture of the fringe pattern, which will amplify the phase errors, make error discussion more significant in PMD than other shape measurement techniques. Phase error analysis and reduction in PMD are presented. The random noises, nonlinear response function, the nontelecentric imaging of the charge-coupled device camera, and the nonlinear response function of the liquid crystal display screen are the main phase error sources in PMD. The analytical relation between the random phase error and its influence factors in PMD is deduced. From the relation formulation, the influence factors of random phase error are analyzed, and the results are proven by the simulation and experiment. A possible phase error-reduction method, which integrates several methods for congeneric errors in fringe projection profilometry, is investigated to reduce phase errors in PMD. This composite method is proven to have a good performance by a plane mirror experiment.

Machine Integrated Measurement of Ultra Precision Machined Specular Non-Rotational Symmetrical Surfaces

In this paper, current results of a research project combining ultra precision machining and optical measurement are presented. The goal is to improve the quality of specular freeform surfaces manufactured by ultra precision slow slide servo turning by running appropriate correction cycles on the basis of machine integrated measurements. These measurements are conducted using the principle of Phase Measuring Deflectometry (PMD) in order to optically acquire full-field 3D-height data. For this purpose, a special setup the so called Mini PMD that can be operated within the limited installation space of an ultra precision machine tool has been designed and implemented. Results of machine integrated measurements of a specular non-rotational symmetrical surface are presented. Furthermore, using Mini PMD and a rotationally symmetric test surface, a complete correction cycle is demonstrated without the necessity of taking the workpiece off the machine for measurement.

편향법을 이용한 웨이퍼 변형 측정

Phase-measuring deflectometry is a full-field gradient measuring technique that lends itself very well to testing specular optical surfaces. We have measured deformation of a large specular surface by deflectometry. In this work, we have used a Fourier-transform method to get the phase from a measured deformed fringe pattern, and we have used least squares method to obtain the height information of the specular surface from the calculated slope. Experimentally, we have confirmed that deflectometry can be used for deformation measurement of a specular surface like that of a wafer.

Deflectometric analysis of high volume injection molds for production of occupational eye wear

PurposeMost of the protective eye wear devices currently on the market are manufactured on simple polycarbonate shields, produced by injection molding techniques. Despite high importance of optical quality, injection molds are rarely inspected for surface quality before or during the manufacturing process. Quality degradation is mainly monitored by optical testing of the molded parts. The purpose of this work was to validate a non-contact deflectometric measurement technique for surface and shape analysis of injection molds to facilitate deterministic surface quality control and to monitor minor conformity of the injection mold with the design data. Material and MethodsThe system is based on phase-measuring deflectometry with a operating measurement field of 80×80 mm2 (±18° slope), a lateral resolution of 60μm and a local sensitivity of some nanometers. The calibration was tested with a calibration normal and a reference sphere. The results were crosschecked against a measurement of the same object with a tactile coordinate measuring machine.Eight injection molds for production of safety goggles with radii of +58mm (convex) and -60mm (concave) were measured in this study. The molds were separated into two groups (cavity 1 and 2 of the tool with different polishing techniques) and measured to test whether the measurement tool could extract differences. The analysis was performed on difference height between the measured surface and the spherical model. ResultsThe device could derive the surface change due to polishing and discriminate between both polishing techniques, on the basis of the measured data. The concave nozzle sides of the first group (cavity 1) showed good shape conformity. In comparison, the nozzle sides of the second group (cavity 2) showed local deviations from design data up to 14.4μm. Local form variations of about 5μm occurred in the field of view. All convex ejector sides of both groups (cavity 1 and 2) showed rotational symmetric errors and the molds were measured in general flatter than design data. ConclusionWe applied a deflectometric system for measuring and evaluating specular reflective injection molding tools to optimize the production process of occupational eye wear. The surface quality could be inline monitored in the production processes for actual spectacle models.

A carrier removal method in phase measuring deflectometry based on the analytical carrier phase description

In phase measuring deflectometry (PMD), a camera observes a sinusoidal fringe pattern via the surface of a specular object under test. Any slope variations of the surface lead to distortions of the observed pattern. Without height-angle ambiguity, carrier removal process is adopted to evaluate the variation of surface slope from phase distribution when a quasi-plane is measured. However, in the usual measurement system, the carrier phase will be nonlinear due to the restrictions of system geometries. In this paper, based on the analytical carrier phase description in PMD, a carrier removal method is proposed to remove the nonlinear carrier phase. Both the theoretical analysis and the experiment results are presented. By comparison with reference-subtraction method and series-expansion method, this proposed method can achieve carrier removal process with only the measurement of one single object, as well as high accuracy and time-saving.

Qualifying parabolic mirrors with deflectometry

Phase-measuring deflectometry is a full-field gradient technique that lends itself very well to testing reflective optical surfaces. In the past, the industry’s interest has been focussed mainly on the detection of defects and ripples, since it is easy to achieve sensitivity in the nm range. On the other hand, attempts to reconstruct the absolute surface shape from the gradient map have been plagued by systematic errors that accumulate to unacceptable uncertainties during data integration. Recently, thanks to improved measurement and evaluation techniques, the state of the art in absolute surface measurement has reached a level of maturity that allows its practical usage in precision optical manufacturing and qualification systems. We demonstrate the techniques, and the progress, by way of results from mirrors for telescopes, solar concentrators, and precision laboratory assemblies.

A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging

In phase measuring deflectometry (PMD), the fringe pattern deformed according to slope deviation of a specular surface is digitized employing a phase-shift technique. Without height-angle ambiguity, carrier-removal process is adopted to evaluate the variation of surface slope from phase distribution when a quasi-plane is measured. However, the difficulty lies in the fact that the nonlinearity is generally contained in the carrier frequency due to the restrictions of system geometries. This paper investigates nonlinear carrier components introduced by the generalized imaging process in PMD. Furthermore, the analytical expression of carrier components in PMD is presented for the first time. The presented analytical form of carrier components can be extended to analyze and describe various effects of system parameters on carrier distortion. Assuming a pinhole perspective model, carrier phase distribution of arbitrary geometric arrangement is modeled as a function of spatial variables by exploring ray tracing method. As shown by simulation and experimental results, the carrier distortion is greatly affected by non-telecentric camera operation. Experimental results on the basis of reference subtraction technique further demonstrate that restrictions on reflection system geometry can be eliminated when the carrier phase is removed elaborately.

High-accuracy measurement for small scale specular objects based on PMD with illuminated film

In this paper we describe an approach to measure small glossy objects by illuminated film based on Phase Measuring Deflectometry (PMD) system. In this setup, the standard sinusoidal fringe patterns are produced by the photographic film frame (135-film), which is illuminated from behind using LED and diffuser, instead of the well-known LCD monitor plane or digital projector. This setup can avoid the influence of electronic noise and screen refreshing, and fulfill the test of small objects in low cost. Moreover the system is easily calibrated with its vertical setup. With the experiments of measuring a plastic contactless smartcard and a metal plate, it is proven that the setup can reach sub-micrometer accuracy with respect to the data of the Wyko white light interferometer. This setup will be promising in the small scale measurement field.

3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry

An advanced Phase Measuring Deflectometry(PMD) is proposed to measure the three dimensional (3D) shape of the aspheric mirror. In the measurement process, a liquid crystal display(LCD)screen displaying sinusoidal fringe patterns and a camera observing the fringe patterns reflected via the tested mirror, are moved along the tested mirror optical axis, respectively. At each movement position, the camera records the fringe patterns of the screen located at two different positions. Using these fringe patterns, every camera pixels can find a corresponding point on the tested mirror and gets its coordinate and slope. By integrating, the 3D shape of the tested mirror can be reconstructed. Compared with the traditional PMD, this method doesn???t need complex calibration and can measure the absolute height of the aspheric mirror which has large range of surface geometries unambiguously. Furthermore, this method also has strong anti-noise ability. Computer simulations and preliminary experiment validate the feasibility of this method.