Liqun Xiang

Application of modulation measurement profilometry to objects with surface holes

We present a detailed discussion of how modulation measurement profilometry (MMP) is applied to measuring an object that has holes on its surface. MMP is not based on the conventional three-dimensional profilometry method with structured light triangulation but on modulation measurements; it has the advantage of measuring the surface of a test object by perpendicular projection, that is, the direction of the CCD camera is the same as that of the projecting light, and the wrapped phases need not be calculated. Thus the difficulties from shadows and spatial discontinuities in phase measurement profilometry and Fourier transform profilometry methods do not exist in MMP. Here we measure a wheellike object that is 31.5 mm thick with an outer diameter of 80 mm and an inner diameter of 20 mm. All the object seen with the CCD camera can be measured including the hole. Experimental results prove that this method is useful for three-dimensional profilometry measurement, especially for objects with discontinuous height steps and spatial isolation.

Using concentric circles and wedge grating for camera calibration.

This paper presents a method for camera calibration based on the orthogonal vanishing point calibration using concentric circles grating and wedge grating. This method, which we believe is new, uses the high-precision characteristics of phase extraction to obtain the feature points, thus decreasing the calibration errors caused by the traditional marker extraction errors of gray pattern. According to the simulation experiment analysis results, the concentric circles grating was designed with seven periods and the wedge grating was designed with four periods. In the real measuring experiment, the grating target and the similar gray concentric circles target were used to calibrate the camera, respectively. Through comparing the reprojective errors of the two methods, the method proposed is proven to improve the calibration accuracy and robustness for the vanishing point calibration algorithm.

Fourier transform profilometry based on a fringe pattern with two frequency components

A modified Fourier transform profilomtry (FTP) based on a fringe pattern with two frequency components is proposed. We discuss its principle, analyze the maximum measuring range and give an expression to describe the measurable slope of the height variation limitation of this method. The modified FTP provides us another approach to eliminate frequency overlapping. When the spectra distribution of a measured object is not spherical symmetry, we can avoid the frequency aliasing through projecting a fringe pattern with two frequency components, instead of increasing the density of the projected fringe and the resolution of CCD camera. The theoretical analysis and primary experiments verified the method.

Whole-field vibration analysis of a woofer's cone using a high-speed camera

In this paper we presented a method for whole-field three-dimensional (3D) shape measurement and vibration analysis of a vibrating woofers cone based on Fourier transform profilometry (FTP). A sequence of dynamic deformed fringe images can be grabbed by high-speed CCD camera and saved on disk rapidly. By Fourier transform, filtering, inverse Fourier transform and unwrapping these phase maps in 3D phase space, we can obtain the shape of the rapid vibrating woofers cone at different time. The results of our experiment indicate that the method, presented in this paper, can efficiently deal with the surface shape measurement for rapid motion object and will be a promising one with the development of high-speed frame grabber.

Both phase-height mapping and coordinates calibration in PMP

A new method for the system calibration in phase-measuring profilometry (PMP) is presented. A new calibration gauge containing four virtual calibration planes is designed. With this calibration gauge, both the phase-height mapping and 3D coordinates calibration could be done simultaneously through only one measurement. Additionally, to recover continuous phase distribution of all steps with same height, an iterative procedure is proposed. The effectiveness of the proposed method is demonstrated by experimental results. (Summary only available)

Intensity transfer function of DMD and its application in PMP

Phase measuring profilometry using structured illumination with a digital micro-mirror device(DMD) has been extensively studied because of its advantage of the programmable projection. In this paper we discussed the effect of intensity transfer function of the commercial projector with DMD, analyzed the influence of the intensity transfer function and the nonlinear of detector on the quantity of projected sinusoidal fringe and the accuracy of phase measurement, and proposed the correction method for intensity transfer function of DMD. A DMD based phase measuring profilometry system includes a commercial projector with DMD, a CCD camera and a fringe pattern analysis and processing unit. The experiments show that with the correction of the intensity transfer function of the projector the phase measurement accuracy has been improved obviously.

Study on Fourier transforms profilometry based on bi-color projecting

We propose an improved FTP based on bi-color grating projecting. Two individual sinusoidal fringe patterns with π phase difference can be decoded from the deformed bi-color sinusoidal fringe pattern captured by color digital camera. Accessing the two fringe patterns, we can not only eliminate zero order spectra but also automatically build a binary mask at the same time to mark the valid measurement area easily, by which unwrapping phase time is shorten as well as phase error from invalid area is not transferred into valid area; Furthermore, we can easily expand the captured non-full-field deformed fringe pattern to form full field fringe pattern to guarantee frequency resolution.

Time-average fringe method for vibration mode analysis

A new optical method of vibration mode analysis using time-average fringe is presented in this paper. A sequence of the deformed and partly blurred sinusoidal fringe images on the surface of a vibrating membrane are grabbed by a low sampling rate commercial CCD camera. By Fourier transform, filtering, inverse Fourier transform, the vibration mode is obtained from the fundamental component of the Fourier spectrum. The theoretical analysis of this approach is given. Computer simulations and experiments have proved to verify its validity. Under different excited vibration frequencies, the vibration modes of a vibrating surface can be qualitatively analyzed. In the experiment, when the excited vibration frequency changes continuously, the changing process of the vibration modes of membrane is observed clearly. Experimental results show that this approach as the features of rapid speed, high accuracy, and simple experimental set-up.

Wave front reconstruction based on phase-shift fringe analysis

In this paper, a simple and practical method is proposed. The fringe patterns are generated on a computer display (for example, a LCD or TFT monitor) and the images refracted via the tested optical component are recorded by a CCD camera. The intensity patterns in these images are distorted because of the tested object. Using the well-known phase-shifting algorithms, the alterant phase caused by the tested object can be precisely obtained. And the aberration of each refracted ray with the reference sphere can be obtained by use of geometry principle. Then the wave front aberration is restored with Zernike polynomial fitting algorithm according to the relation between wave aberration and ray aberration. The technique allows the measurement for high aberrated wave fronts, owing to its ability to measure large ray slope changes, and the use of a computer display generation leads flexible adjustment of period and direction of patterns and accurate phase shift. Compared with other techniques, this technique is simpler, cheaper and more flexible.

Simultaneous calibration algorithm of phase-shifting based on FFT

In phase-measuring profilometry, the accuracy of the phase- shifting is very important. In this paper, a new simultaneous calibration algorithm of phase-shifting based on fast Fourier transform (FFT) is presented. The current phase shifting is calculated with the help of the information of an additional fringe pattern and a FFT modulation mask. With this algorithm, we can accurately control the moving of the project grating simultaneous, the accuracy and the automation of the measuring system are improved greatly.