Transient full-field vibration measurement using spectroscopical stereo photogrammetry

Transient full-field vibration measurement using spectroscopical stereo photogrammetry

Kaiduan Yue,1 Zhongke Li,

2 Ming Zhang,

1,* and Shan Chen

1

1State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China 2The 401 Laboratory, The Second Artillery Engineering College, Xi’an 710025, China

*[email protected]

Abstract: Contrasted with other vibration measurement methods, a novel spectroscopical photogrammetric approach is proposed. Two colored light filters and a CCD color camera are used to achieve the function of two traditional cameras. Then a new calibration method is presented. It focuses on the vibrating object rather than the camera and has the advantage of more accuracy than traditional camera calibration. The test results have shown an accuracy of 0.02 mm.

©2010 Optical Society of America

OCIS codes: (110.5200) Photography; (120.2440) Filters; (120.6650) Surface measurement, figure; (120.7280) vibration analysis; (150.1488) calibration; (150.5670) Range finding.

Reference and links

1. B. J. Halkon, and S. J. Rothberg, “Vibration measurements using continuous scanning laser Doppler vibrometry: theoretical velocity sensitivity analysis with applications,” Meas. Sci. Technol. 14(3), 382–393 (2003).

2. Y. Y. Hung, “Shearography‒a new optical method for strain-measurement and non-destructive testing,” Opt. Eng. 21, 391–395 (1982).

3. S. Schedin, G. Pedrini, H. J. Tiziani, and F. M. Santoyo, “Simultaneous three-dimensional dynamic deformation measurements with pulsed digital holography,” Appl. Opt. 38(34), 7056–7062 (1999).

4. Y. Kaiduan, L. Zhongke, Y. Yaxing, and Z. Fei, “Full-field laser vibration measurement in NDT techniques,” Proc. SPIE 7160, 71600X (2008).

5. C. C. Chang, and Y. F. Ji, “Flexible videogrammetric technique for three-dimensional structural vibration measurement,” J. Eng. Mech. 133(6), 656–664 (2007).

6. C. Y. Chen, T. T. Yang, and W. S. Sun, “Optics system design applying a micro-prism array of a single lens stereo image pair,” Opt. Express 16(20), 15495–15505 (2008).

7. A. Benetazzo, “Measurements of short water waves using stereo matched image sequences,” Coast. Eng. 53(12), 1013–1032 (2006).

8. Q. Zhang, and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).

9. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).

10. P. I. Rockett, “Performance assessment of feature detection algorithms: a methodology and case study on corner detectors,” IEEE Trans. Image Process. 12(12), 1668–1676 (2003).

1. Introduction

Vibration measurement is critical for industrial production and scientific research, especially full-field surface vibration measurement of vibrating objects, the study of which is of great significance. For many years traditional non-contacting surface vibration measurements have been made by using scanning Doppler laser vibrometry [1], shearography [2], pulsed-laser interferometry [3], pulsed holography [3], and orvelectronic speckle pattern interferometer (ESPI) [4]. With the development of stereo vision technology, including the increase of acquisition speed and the improvement in resolution of CCD cameras, it is more frequently applied in the study of non-contacting surface vibration measurement.

Stereo vision is derived from the positioning of objects by the eyes. When people look at an object, two different images are formed on the retina, producing optical parallax due to the different perspective of two eyes. Stereo vision measurement developed more than 200 years ago, and many new methods based on it have emerged, especially stereo photogrammetry. The photogrammetric method, depending on the types of photographs used in the analysis, can be classified as aerial or terrestrial [5]. There are two methods of image acquisition for

#136477 - $15.00 USD Received 12 Oct 2010; revised 17 Nov 2010; accepted 18 Nov 2010; published 7 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 26866

stereo photogrammetry, one named one-lens-two-shots and the other two-lenses-single-shot [6]. The second one is used more commonly.

There are a few engineering applications using the two-lenses-single-shot technique. Alvise Benetazzo [7] proposed the two-lenses-single-shot technique to estimate the shape of water, which uses stereo vision based on two calibrated views to produce a time series of scattered 3-D points of the water’s surface from a sequence of synchronous, overlapping images. Qican Zhang and Xianyu Su [8] proposed an optical 3-D shape measurement of a vibrating drumhead based on Fourier Transform Profilometry (FTP). Vibration images are captured by using high-speed CCD cameras as sinusoidal patterns are projected onto the vibrating drumhead. Then, the vibration modes of the drumhead are reconstructed by digital image technology.

This paper presents a novel technique, named Spectroscopical Stereo Photogrammetry, to implement a full-field surface vibration measurement. A CCD color camera, colored light filters, a dispersion prism, and some plane mirrors are used in this technique. When the object is vibrating, the CCD color camera captures the vibration images. Then, these images are processed by digital image technology, and the vibration modes are obtained.

Compared with the full-field surface vibration measurement by the measurement range and environment of ESPI,ESPI is used in the precision measurement (nm), and it requires strict measuring environment. The method proposed in this paper is used under the condition of large amplitude vibration measurement (um) and has the advantage of simple experimental setup and convenient adjustment.

2. Principle of the stereo vision measuring system

The principle of spectroscopical stereo photogrammetry comes from binocular stereovision. This measuring system consists of a CCD color camera, which is a standard Bayer RGB sensor, an optical circuit, and a calibration board. Steps of measurement include adjustment of the optical circuit, camera calibration, stereo matching, and 3-D reconstruction of vibration modes. Details of these tasks are briefly discussed in the following section.

2.1 The Principle of spectroscopical stereo photogrammetry

The white light emitted by high-power LEDs fixed on the instrument irradiates the surface of the vibrating object to be measured, and the reflected light penetrates the instrument. In Fig. 1, the reflected light, irradiated by any arbitrary point on the object, passes through the red and blue filters and is separated into two beams, red ray and blue ray, and they have single spectrum. Then, it enters into an optical circuit, which consists of a dispersion prism and three plane mirrors. Finally, the color images, actually having only red and blue pixels, are produced by the red and blue rays projected on the CCD plane.

To any certain point on the object, the image points captured through the red and blue beams project on the CCD plane overlap. Then, the object is in standard position L shown in Fig. 1(a). When the displacement between the point and the instrument is bigger than the displacement between the point on Line L and the instrument, the displacement is formed between the two image points shown in Fig. 1(b). On the contrary, when the displacement between the point and the instrument is smaller than the displacement between the point on Line L and the instrument, the displacement formed between the two image points is in the opposite direction.

The spectroscopical stereo photogrammetic system replaces two cameras in binocular stereovision with a CCD color camera and two colored filters. In a specific time, t , a series

of color images are captured when photographing a vibrating object. These color images contain the temporal and spatial information of the vibrating object. The images at any moment are separated into two kinds of images (red and blue), the same as the two images captured by two cameras in binocular stereovision. This method is called the one-lens-single-shot method. It solves the problem of synchronizing the triggering in a binocular stereovision


system, because it cannot achieve complete synchronization or be used in the field of transient full-field vibration measurement using two cameras.

Fig. 1. Schema of the spectroscopic stereo photogrammetry.

2.2 Principle of calibration and measurement

Before calibrating the camera, it is necessary to adjust the optical circuit to make sure the displacement of two images in the Y-axis is correspondence, which makes it convenient for the following calibration. Common methods of camera calibration focus on the cameras, such as the method of Dr. Zhang et al. [9] Some parameters of the cameras are needed to calculate the space coordinates of objects, including intrinsic parameters, external parameters, and transformation of coordinates. After the 3-D reconstruction, the vibration modes are demonstrated.

A new calibration method used in this system is proposed in this paper, which gives the focus on the vibrating object. It could eliminate the effect of distortion, produced by plane mirrors, prisms, and CCD cameras.

Fig. 2. Depth of field represented by image plane.

Fig. 3. Schema of calibration.


It is well known that distinct images are produced when the object is fixed within the range of the depth of field. In Fig. 2, Plane 1 and Plane 2 are the boundary planes of the depth of field; the numerical value of the depth of field is D. The change in coordinate figures of the X-axis and the Z-axis is only under consideration because of little change in the coordinate figure of the Y-axis.

When point P on the object is projected on the CCD plane, one image will produce two

different image points of point P. In Fig. 3, point P has two image points, lP and rP , in Fig. 3,

when the object is located in Plane 1. Accordingly, when the object is in Plane 2, point P

obtains two image points, '

lP and '

rP . The image-points of lP and '

lP are in the red image,

which are produced by the light that is passed through the red filter, while the two other image points are in the blue image. When the object is situated in an arbitrary position within the range of the depth of field, the image points of point P in each image will lie in lines

'

l lP P and '

r rP P . Obviously, the two functions can be obtained by the pixel coordinates of the

four image points. The pixel coordinates of the four image points can be obtained by

extracting the corner. The functions of the lines '

l lP P and '

r rP P are described in Eq. (1) and

Eq. (2). ( , ),l l l lF f x z (1)

( , ).r r r rF f x z (2)

The two lines must join at point M. Point M and point P are at the same point when the

object is situated in Plane 3. The coordinate of point M ( , )p px z can be obtained by Eq. (1)

and Eq. (2). The two functions can be transformed to Eq. (3) and Eq. (4).

' ( ),l l lx f z (3)

' ( ).r r rx f z (4)

The equation l rz z can be obtained, wherever point P on the object is located. We

define a new variable K, and obtain an equation l rx x , stated as the displacement D

value of the two different pixel coordinates. The function is described in Eq. (5), obtained by subtraction between Eq. (3) and Eq. (4). ' ( ).f z (5)

Then, the Eq. (5) can be transformed to Eq. (6).

( ).z f (6)

As was stated above, when the object is in the depth of field for any position, two image points of any point can be indicated by Eq. (6). The longitudinal displacement of every point can be obtained. Thereby the longitudinal displacement of the whole surface can be obtained.

Along with the vibration of the object, the longitudinal displacement of point P will

change. The function can be described as Eq. (7) and (8), when time is t and t + td .

( ),t tz f (7)

( ).t dt t dtz f (8)

A new variable dz is created, and we get an equation t dt tdz z z , which describes the

vibration within time td . The function of the vibration speed is defined as Eq. (9).

( ).t dt t t dt tz z fdz

dvdt dt dt

(9)

At any moment, the longitudinal displacement of each point on the vibrating object can be calculated, and the value of the vibration deformation is the D value of the longitudinal


displacement at two different moments. For a certain amount of feature points on the object, the longitudinal displacement can be easily calculated. Then, the vibration velocity mode and vibration mode of the whole surface can be calculated by interpolation and fitting.

3. Experimental procedure and results

3.1 Experimental setup

The spectroscopical stereo photogrammetic measuring system is shown in Fig. 4. The internal structure of the box is shown in Fig. 1. This system consists of a CCD camera microvision mv-1300UC, red and blue filters, three plane mirrors, and one dispersion prism. The test object is a slight plexiglas plate with 5*5mm checkerboard patterns. Deformation is engendered by the adjustment of the deformation generator made of microcallipers, and the theoretical value is known.

Fig. 4. (a) Measurement mechanism; (b) test object.

3.2 Image acquisition and process

Between periods of t , a series of images are captured by the CCD color camera. It contains

temporal and spatial information. Figure 5 shows two of them. The left one shows that the test plate had no deformation, and the marks overlap with each other. Another one showed the test plate had a certain deformation, and the marks have an offset in the horizontal direction. Obviously, the different perspectives affect the quality of the images. It leads to some deformations on the image, but the deformations can be eliminated by our calibration method and does not impact the accuracy.

Fig. 5. Image captured in two different times.

It is easy to process the images. The result of separating the red and blue constituents is shown in Fig. 6. For pixel coordinates of the feature points, the Harris method [10] is used to extract them. Then the K in Eq. (9) can be easily calculated. Because of the known quantity

of dt , the value of dv is known. The vibration mode is shown in Fig. 7.

In the experiment, a Plexiglas plate is used. The central part of the Plexiglas plate with checkerboard patterns has the biggest deformation engendered by a deformation generator made of microcallipers, and the value of deformation can be read by microcallipers. At the same time, we can obtain another deformation value of the whole plate by experiment. After


comparing, the point having the biggest deformation, the highest point in Fig. 7, can achieve an accuracy of 0.1 mm. And, under certain conditions, the accuracy can reach 0.02 mm. One is when the test plate has enough smoothness, such as the plate used in aviation; the other is when the vibration has a low scale, usually a range of 1 mm.

Fig. 6. (a) Red constituent; (b) blue constituent.

Fig. 7. Vibration mode.

4. Conclusion

Scanning Doppler laser vibrometry has the advantage of high accuracy, high space definition, and rapid dynamic response, but it is used in static measurement and spot scanning. Shearography also has the advantages of general optic methods, such as non-contact and full-field, but its accuracy is affected highly by the motion of a rigid body. For pulsed holography, it can deal with transient full-field measurement well, but as well as with ESPI, it has a strict measurement environment and is used in precision measurement.

We demonstrate vibration measurement with spectroscopical stereo photogrammetry. It uses the filter to achieve one-lens-one-shot, which avoids the synchronous control problem of two cameras and improves the accuracy of measurement. According to the results, the accuracy reaches 0.02 mm. Since the camera used in this instrument is not a high-speed CCD camera, it cannot be implemented to a high-speed object, but it is feasible.

What’s more, a new calibration approach is used in this system. The calibration target is a switched CCD camera to a vibrating object. It avoids the error of traditional calibration methods and improves a system’s accuracy. Further work should be done on how to divert this method to 2-D from 3-D.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (NNSFC) (50775172).


Documents

Transient full-field vibration measurement using spectroscopical stereo photogrammetry