Transparent element surface measurement using binary pattern in phase-measuring deflectometry

This paper presents a short review for phase measuring deflectometry (PMD). PMD is a phase calculation based technique for three-dimensional (3D) measurement of specular surfaces. PMD can achieve nano-scale form measurement accuracy with the advantages of high dynamic range, non-contact, full field measurement which makes it a competitive method for specular surface measurement. With the development of computer science, display and imaging technology, there has been an advancement in speed for PMD in recent years. This paper discusses PMD focusing on the difference on its system configuration. Measurement principles, progress, advantages and problems are discussed for each category. The challenges and future development of PMD are also discussed.

Phase measuring deflectometry (PMD) is a competitive method for specular surface measurement that offers the advantages of a high dynamic range, non-contact process, and full field measurement; furthermore, it can also achieve high accuracy. Camera calibration is a crucial step for PMD. As a result, a method based on the calibration of the entrance pupil center is introduced in this paper. Then, our proposed approach is compared with the most popular photogrammetric method based on Zhang’s technique (PM) and Huang’s modal phase measuring deflectometry (MPMD). The calibration procedures of these three methods are described, and the measurement errors introduced by the perturbations of degrees of freedom in the PMD system are analyzed using a ray tracing technique. In the experiment, a planar window glass and an optical planar element are separately measured, and the measurement results of the use of the three methods are compared. The experimental results for the optical planar element (removing the first 6 terms of the Zernike polynomial) show that our method’s measurement accuracy reached 13.71 nm RMS and 80.50 nm PV, which is comparable to accuracy values for the interferometer.

Phase measuring deflectometry (PMD) is a robust, noncoherent technique for the characterization of specular surface. For measuring high specular reflectivity surface, PMD can deliver micron radian range local gradient. However, when the measured surface has low specular reflectivity, the accuracy of the measured gradient is low since the captured fringe pattern shows low signal to noise ratio. The phase error characteristics in PMD system when testing low reflectivity surfaces are analyzed. The analysis illustrates that the random phase error increases rapidly while the nonlinear error drops slowly with the decreasing of the tested surface reflectivity. In order to attain high precision measurement of low reflectivity specular surface, a robust error reduction method based on wavelet de-noising is proposed to reduce the phase error. This error reduction method is compared with several other normally used methods in both simulation and experiment work. The method based on the wavelet de-noising shows better performance when measuring the low reflectivity specular surface.

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.

BackgroundThe accuracy of three-dimensional measurement of object surface is always affected by the nonlinear gamma of the projector. The defocusing binary projection can overcome the nonlinear gamma distortion of the projector and reduce the effect of high harmonics without gamma calibration. Although researches have already reduced the errors to get a clear sinusoidal curve, there still leave room for improvement, especially when wide stripes are applied during the measurement.MethodsThis paper presents a kind of ellipse binary pattern. By analyzing the property and spectrum, the binary pattern can produce high quality sinusoidal curve and produce smaller errors. It has a better effect to use an ellipse pattern to overcome the nonlinear gamma distortion of the projector and it is suit to be used as wide stripes.ResultsSimulation and comparison experiments plus three-step phase shifted method are conducted to verify feasibility and accuracy of this binary pattern. The experimental results have indicated that this binary pattern can increase the accuracy of 3D measurement and reduce phase errors caused by the nonlinear gamma of the projector. The defocusing ellipse pattern is superior to traditional methods. In addition, the defocusing binary stripe is robust and suit to measure object with large period.ConclusionsIn this paper, an binary ellipse pattern is proposed for high-accuracy 3D measurement profilometry. It is easy to generate high-quality sinusoidal fringe pattern. Experiment results have demonstrated the feasibility and accuracy of the improved binary pattern besides it proved that the period of fringe pattern has little impact on the accuracy of measurement.

Fringe projection profilometry (FPP) and phase measuring deflectometry (PMD) are the currently popular technologies for measuring diffuse and specular reflective surfaces respectively. Both methodologies demonstrate superior performance for single-type reflective surfaces. However, with the rapid development of advanced manufacturing and intelligent manufacturing technologies, products have seen significant improvements in complexity, diversity, and personalization, often exhibiting composite reflective characteristics on their surfaces. The aforementioned single technology cannot meet the measurement requirements for composite reflective surfaces. To address this challenge, this paper presents a composite reflective surfaces measurement method combining FPP with PMD techniques, and an optimized system calibration method based on binocular stereo vision is proposed to enhance the system's measurement accuracy. To improve the measurement efficiency, a strategy in which the LCD screen and projector project different colorful fringe patterns simultaneously is adopted. To mitigate stray light interference from the projector on specular surface profilometry, a partition projection method is presented. Instead of establishing the pixel mapping relationship between the projector and diffused surface aeras, the coordinate mapping relationship between the specular reflective region and the projector pixel is established according to the phase-height relationship to realize the accurate projection of the projector to the diffused surface. Experiments have been performed to validate the proposed method, and the results demonstrate that it can reconstruct the composite surfaces with higher accuracy. In particular, the reconstruction accuracy of specular surface can reach several tens of nanometres.

Phase measurement deflectometry (PMD) is an excellent method for high-precision optical surface measurement; through the simple system structure, accuracy comparable to that of interference methods can be realized. The key of PMD is to solve the ambiguity between the surface shape and normal vector. Considering all kinds of methods, the binocular PMD method is undoubtedly a method with a very simple system structure and can be easily applied to complex surfaces, such as free-form surfaces. However, this method relies on a large screen with high accuracy, which not only increases the weight of the system, but also reduces the flexibility of the system, and manufacturing errors in the large-size screen can easily become error sources. In this Letter, we have made some improvements based on the traditional binocular PMD. At first, we try to replace the large screen with two small screens to increase the flexibility and accuracy of the system. Further, we replace one small screen with a single point to simplify the system structure. Experiments show that the proposed methods not only improve the system flexibility and reduce the complexity, but can also achieve high measurement accuracy.

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.

Simultaneous measurement of 3D surface and thickness of large area and thickness transparent materials based on polarization model and TOF correction