TDI imaging—a tool for profilometry and automated visual inspection

Optics and ¸asers in Engineering 29 (1998) 403—411 ( 1998 Elsevier Science Ltd. All rights reserved Printed in Northern Ireland 0143—8166/98/$19.00 PII: S0143–8166(97)00106–1

TDI Imaging—A Tool for Profilometry and Automated Visual Inspection M. R. Sajan,a,* C. J. Tay,a H. M. Shanga & A. Asundib aDepartment of Mechanical and Production Engineering, The National University of Singapore, Singapore-119 260, Singapore bSchool of Mechanical and Prod. Engineering Nanyang Technological University, Singapore-639 798, Singapore (Received 17 October 1997; accepted 28 November 1997)

ABS¹RAC¹ ¹DI imaging is introduced as a solution to industrial web inspection under low-light illumination. In addition to the original purpose of recording clear blur-free images of the objects moving over industrial platforms, it can also be used as a tool for profilometry and automated visual inspection when coupled with proper structured light illumination modules. ¹his paper illustrates a system employing a pulsed laser diode, uniform intensity line generating optics and a high-speed ¹DI imager for recording structured light patterns from rotating cylindrical objects. Defect or shape information is coded as distortions in a regular grating pattern recorded by the ¹DI imager. ¹he shape or defect profile is retrieved by employing Fourier transform and scanning spatial phase detection techniques. ( 1998 Elsevier Science ¸td. All rights reserved.

INTRODUCTION Structured light techniques are widely used in industrial vision systems for profilometry and alignment of components and products. According to the definition of automated imaging association, structured light technique is ‘the process of illuminating an object (from a known angle) with a specific light pattern. Observing the lateral position of the image can be useful in determining the depth information’. Deviations or distortions in the structured light patterns correspond to the shape or defect on the object. Combining the triangulation and Moire principles, the shape or defect profile on the object can be calculated. The majority of the work in this area deals with the *Corresponding author.

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profilometry of flat objects or the so-called 2)5D objects. A large number of industrial products assume cylindrical shape. Conventional automated inspection systems employ point and area sensors to inspect flaws in a particular field of view. It is desirable to have a digital imaging system to record shape or defect information from the complete periphery of cylindrical objects. Video cameras operating in the CCIR or NTSC format are not practical for this work due to their frame-based operation. In CCIR format, the camera is exposed for nearly 40 ms and the frames are transferred as old and even fields. An early report on the measurement of buckling around the periphery of a cylinder is due to Theocaris.1 He used a film-based drum/periphery camera to record shadow and reflection Moire fringes from the periphery of a cylindrical shell through a narrow slit. Lately, Suzuki and Suzuki2 used a similar technique for recording the shape contours of cylindrical objects. In a more recent article, Cheung et al.3 used a CCD camera to record a projected line of light from a cylindrical object. The object is rotated using a step-controlled stage and only one line of image is recorded in each frame after rotating by a step. Typically, this process involves a large number of frames which is time consuming. A faster alternative to this procedure was suggested by Reid and Rixon4 by using a line scan camera. Performance of a TDI imager is similar to that of a drum camera.5 Hence, it is a convenient tool for imaging the periphery of cylindrical objects. Compared to a line scan camera, the alignment is easy and it is possible to replace physical gratings with a modulated structured light illumination. We have demonstrated the use of a TDI system in generating periphery images and shape contours of rotating cylindrical objects.6,7,8 This paper focuses on the Fourier transform and the scanning phase detection (SPD) techniques for retrieving the shape or defect from deformed grating patterns recorded by the TDI imaging systems.

EXPERIMENT Schematic of the experimental set-up is shown in Fig. 1. The test object is a dented can which is mounted on the spindle of a lathe in an industrial workshop. The TDI scanning direction is aligned perpendicular to the axis of rotation. The object is illuminated by a line of light from a laser diode. Conventional laser line projectors employing cylindrical lenses generate a Gaussian intensity distribution resulting in the center of the line being brighter than the ends. This leads to blooming of photo-generated charges which induce streaks in the TDI image. These streaks are sources of noise in the phase unwrapping procedures. However, there are some commercially available specialized optics using either refractive or diffractive optical elements9 which provide a uniform intensity line. In this study, we have used

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Fig. 1. Schematic of the experimental set-up.

a non-Gaussian line generator manufactured by LASIRIS Inc., Canada for generating a line of uniform intensity from a 20 mW laser diode. The TDI camera used in the experiment is capable of scanning up to 250,000 lines/s. Assuming a 250 line peripheral image, this camera is capable of inspecting objects rotating up to 1000 revolutions/s. In the experimental set-up, the spindle speed, however is limited to 31 revolutions/s. Hence, the experiment is performed at a reduced TDI scan rate of 26,666 lines/s. Pulse width and separation are fixed at 20 and 150 ks, respectively. Since the TDI scan speed is still higher compared to the rotational speed of the can, only a third of the peripheral image is captured in the 244 line TDI buffer as shown in Fig. 2. A dent on the surface of the can is coded as distortions in the grating in Fig. 2.

FRINGE ANALYSIS BY THE FOURIER TRANSFORM METHOD Fast Fourier transform method is introduced by Takeda and Mutoh10 for analyzing the shape from a deformed grating pattern. Unlike the phase shifting interferometry method, the shape is retrieved from a single image using the FFT method, which is further accelerated with the availability of DSP processors in digital imaging systems. FFT method consists of taking a Fourier transform of the deformed grating pattern. Resulting Fourier spectrum is symmetrical having side lobes with their width representing the deviation in frequencies compared to a regular grating. The first side lobes correspond to the grating frequency and the subsequent lobes correspond to higher harmonic orders. By filtering one of the first side lobes and shifting it to the center of the spectrum, the regular carrier pattern can be removed. The phase map can then be calculated from the phase angle distribution in the inverse Fourier transform. Selecting one of the side lobes in the Fourier spectrum and translating it to the center is a time-consuming process. A

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Fig. 2. Deformed grating pattern recorded by the TDI camera from a rotating can.

grating with a pitch of 4 pixels generates the side lobes exactly at the mid point of both the halves of the Fourier spectrum as shown in Fig. 3. Thus, it is sufficient to take one-half of the Fourier spectrum instead of selecting the side lobe and shifting it to the center as in the case of higher pitch values of the

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Fig. 3. Power spectrum obtained by performing Fourier Transform operation on a regular grating of pitch"4 pixel.

projected grating. It is also possible to perform the analysis by fixing a threshold selection of the spectrum for each line. This procedure is also time consuming and cuts down spatial information. In this investigation, the pitch of the grating is set to 4 pixels by adjusting the TDI scan frequency and the pulse rate of the laser diode. However, it is important to filter onehalf of the spectrum through a Hann Window before the inverse Fourier transformation is performed. The selection of Hann window suppresses the noises and results in amplification of the center of the spectrum. Once distribution of phase ‘'’ is retrieved using the FFT method, the height deviation around the defective area is calculated using the relation ' p h" 2n tan #

(1)

where ‘p’ is the pitch of the gratings encoded in the TDI image and ‘#’ is the angle between the camera axis and the direction of light projection. Figure 4 shows the height map obtained from the highlighted area in Fig. 3. To compare the effect of filtering a side lobe from the Fourier spectrum using a Hann window, the height map is also calculated without using a Hann window as shown in Fig. 5. Errors on the left and right edges along the X-axis are clearly visible. It is possible to correct this error by choosing an appropriate phase jump threshold while unwrapping the phase angle. This may have to be optimized whenever there is a change in the illumination. Thus, Hann window filtering is the best choice for consistent and faster profile unwrapping.

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Fig. 4. Depth profile unwrapped from the highlighted area in Fig. 2 using the Fourier transform method.

Fig. 5. Depth profile unwrapped from the highlighted area in Fig. 2 without using a Hann window to filter a side lobe in the frequency spectrum.

The shape profile could also be displayed as a random dot stereogram, which is a popular brain teasing medium. It is possible to generate a random dot stereogram either from the intensity or depth profile. We have used the depth profile data retrieved by the FFT method for generating the stereogram. Figure 6 shows the random dot stereogram obtained from the depth map in Fig. 4, which could be viewed by defocusing the eye on the picture plane.

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Fig. 6. Random dot stereogram representing the depth profile in Fig. 4.

FRINGE ANALYSIS BY SPATIAL PHASE DETECTION METHOD In industrial inspection systems, speed is a key factor. Since the FFT method is time consuming, there were efforts to simplify this approach by considering only the first coefficient in trigonometric Fourier series. Toyooka and Tominga11 reported the first application of this in spatial domain where the processing is faster than the regular Fourier transform method by five times. If f is the frequency of the encoded grating and I is the intensity distribution 0 perpendicular to the lines of the grating, then we can define the following integrals over the ith interval of the grating:

P P

(i`1)@fÒ I (x) cos(2nf x) dx (2) i 0 i@fÒ (i`1)@fÒ S[I ]" I (x) sin(2nf x) dx (3) i i 0 i@fÒ C and S are the real and imaginary parts of the first Fourier series coefficient. Assuming that f is sufficiently large compared to the phase gradient over 0 a grating interval, the phase / at the midpoint of the i’th interval is calculated using the relation C[I ]" i

S[I ] i / "tan~1 i C[I ] i

(4)

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Fig. 7. Depth profile unwrapped from the highlighted area in Fig. 2 using the SPD method.

Figure 7 shows the unwrapped depth profile around the dented area on the can obtained using this method. Note that if the phase gradients on the objects is larger as in the case of a sharp defects, the spatial phase detection method generates a lot of errors. It is also susceptible to noise in the image.

CONCLUSIONS A simple and low-cost method using a TDI imager is presented for 360° profilometry of cylindrical objects. Deformed grating patterns corresponding to the shape or defect on the surface of a cylindrical object is encoded using a high-speed TDI camera. The gratings are generated by a pulsed line of light generated by a laser diode. It is important to use non-Gaussian line generators to alleviate the streak noise generated by the TDI scan. Shape or defect information is retrieved from the deformed grating patterns by using Fourier transform and Spatial Phase Detection methods. TDI scan frequency and the laser diode pulse rate are adjusted to record a grating pattern of pitch "4 pixels. This procedure increases the speed of the Fourier transform method. Spatial phase detection is a simplified and faster approach to Fourier transform method. However, it is prone to errors if the phase gradients over a grating interval is large compared to the frequency of the grating.

REFERENCES 1. Theocaris, P. S., Moire topography of curved surfaces. Exp. Mech., 7 (1967) 289—96.

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2. Suzuki, M. & Suzuki, K., Moire topography using developed recording methods. Opt. ¸asers Engng, 3 (1982) 59—64. 3. Cheng, X. X., Su, X. Y. & Guo, L. R., Automated measurement method for 360° Profilometry of diffuse objects. Appl. Opt., 30 (1991) 1274—8. 4. Reid, G. T. & Rixon, R. C., Automatic inspection of quasi-cylindrical objects by phase measuring topography. Proc. SPIE, 665 (1986) 162—7. 5. Michael, G. F. & Rudolph, H. D., A large area TDI image sector for low light level imaging, IEEE Trans. Electron dev. ED-27 (1980) 1688—93. 6. Asundi, A., Chan, C. S. & Sajan, M. R., 360-deg profilometry: new techniques for display and acquisition. Opt. Engng, 33 (1994) 2760—9. 7. Asundi, A. & Sajan, M. R., Peripheral inspection of objects. Opt. ¸asers Engng, 22 (1995) 227—40. 8. Sajan, M. R., Tay, C. J., Shang, H. M. & Asundi, A., Scanning moire and phase shifting with time delay and integration imaging. Opt. ¸ett., 22 (1997) 1281—3. 9. Veldkamp, profile shaping with interlaced binary diffraction gratings. Appl. Opt., 21 (1982) 3209—12. 10. Takeda, M. & Mutoh, K., Fourier transform profilometry for automatic measurement of 3D object shape. Appl. Opt., 22 (1983) 3977—82. 11. Toyooka, S. & Tominga, M., Spatial fringe scanning for optical phase measurement. Opt. Commun., 51 (1984) 68—70.