Time delay and integration imaging for internal profile inspection

Optics & Laser Technology 30 (1998) 459±465

Time delay and integration imaging for internal pro®le inspection C.J. Tay*, S.L. Toh, H.M. Shang Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, 119260 Singapore Received 7 September 1998; received in revised form 2 December 1998; accepted 2 December 1998

Abstract A time delay and integration imaging technique is presented and applied to internal surface contour measurement. Using the proposed optical arrangement, inspection of pro®les of objects which are mounted on the internal surface of a hollow cylinder can be carried out. Tests conducted on objects with diameters ranging from 40 to 214 mm show good agreement with results obtained from conventional pro®lometer. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Time delay and integration imaging; Internal pro®le; Inspection; Pro®lometer

1. Introduction In recent years, interferometry has been widely used to determine the shape of an object. According to the de®nition of automated imaging association, structured light technique is the process of illuminating an object (from a known angle) with a speci®c 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. The majority of the work in this area deals with the pro®lometry of ¯at or the so-called 2.5D objects. A study in the pro®le measurement of a 3D di€used object was carried out by Cheng [1] using the triangulation principle with structured illumination. A thin structured light was projected onto a test object and the resulting deformed light beam was re-imaged onto a 2D array. The height of the object surface along the light beam could be determined through demodulation of the deformed light line. This method has limitations caused by the surface roughness and varying surface re¯ectivity. It, however, is relatively fast and simple. The method was extended by Asundi [2±4] to include a 3608 acquisition and display of the object surface

* Corresponding author. Tel.: 65-8742557; fax: 65-7791459. E-mail address: [email protected] (C.J. Tay)

using a pulsating laser diode and a rotating platform. The recording of the images and the grating patterns on a moving object was made possible by the introduction of the time-delay-and-integration (TDI) camera. The TDI camera operated much like the conventional analog drum camera [5]. The phase shifting and logical moire routine were adopted to analyze the grating pattern quantitatively. A 3D sensing approach known as phase measuring pro®lometry based on the use of sinusoidal grating projection and digital phase shifting technique was developed by Halioua [6]. The method had many applications in the aerodynamic and medical ®elds. However, it employed the phase-shift algorithm which was more suitable for parallel data acquisition. The phase shifting method required image intensity values of 4±5 phase-shifted images. However, using the Fourier transform (FT) method, the object pro®le could be generated from a single image [7]. Using a method based on additive and subtractive phase modulated electronic speckle pattern interferometry and the Fourier analysis, Wang [8] was able to study the shape variation of an object. The method reduced the time needed for fringe acquisition to only one single frame instead of four or ®ve. The FT method was also adopted by Sajan [9] for the inspection of the pro®le of a moving object. The undeformed and deformed gratings on a moving object were recorded and analyzed to obtain a phase map of

0030-3992/98/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 0 - 3 9 9 2 ( 9 8 ) 0 0 0 7 8 - 4

460

C.J. Tay et al. / Optics & Laser Technology 30 (1998) 459±465

the object. The object pro®le was subsequently obtained by phase unwrapping. The FT method appeared to give accurate results in the investigation. In this study a method based on that of Asundi [2] is presented and applied to internal surface contour measurement. Previous works in this area were limited to inspection of external pro®le or defects which are readily observable from the external surface where a light source could be directed. In this study the technique has been extended to include inspection of internal wall of a hollow cylinder with a quantitative assessment of the accuracy of the method. Tests were conducted on cylinders with diameters ranging from 40 to 214 mm and the results show good agreement with that obtained from conventional pro®lometer. 2. Theory In projection light systems, the image of a light pattern projected on the surface of a test object exhibits deviations and distortions compared to the pattern projected on an original undeformed reference plane. Using the triangulation principle, the pro®le of the object surface can be inspected and quanti®ed. As shown in Fig. 1, the height h of a point A on the object at a distance Dx from the origin C is given by the relation: hˆ

Dx N…x†p ˆ tan y tan y

…1†

where y is the angle of illumination, p the pitch of the grating and N the number of fringes in a moire pattern

generated by superimposing the reference pattern over the image of the object pattern. The light wave amplitude on C can be expressed in the general form: go …x,y† ˆ a…x,y† ‡ b…x,y†cos…2pf0 x†,

…2†

where f0 denotes the fundamental (carrier) frequency of the observed light wave and a(x,y ) and b(x,y ) represent the unwanted irradiance variation due to nonuniform light re¯ection or transmission by the object. The light wave amplitude on A can be expressed as: g…x,y† ˆ a…x,y† ‡ b…x,y†cos‰2pf0 x ‡ f…x,y†Š

…3†

where f(x,y ) represents a phase angle introduced due to the object height. The Fourier transform G( f,y ) of the recorded wave amplitude g(x,y ) is given by: G… f,y† ˆ A… f,y† ‡ C… f ÿ f0 ,y† ‡ C  … f ‡ f0 ,y†

…4†

Taking the inverse Fourier transform of C( f,y ) with respect to f yields c(x,y ). The phase distribution may then be calculated using the expression f ˆ tanÿ1

Im‰c…x,y†Š , Re‰c…x,y†Š

…5†

where Im[c(x,y )] and Re[c(x,y )], denote the imaginary and real parts of c(x,y ) respectively. The phases generated using Eq. (5) are wrapped in modules of 2p and must be unwrapped to generate the object pro®le.

Fig. 1. Optical arrangement.

C.J. Tay et al. / Optics & Laser Technology 30 (1998) 459±465

3. Experimental work To overcome the diculty of detecting internal defects and allow optical access into the concave inner surface of the cylinder, a special optical arrangement is required. The system consists principally of a laser diode light source with a pulsating unit and a TDI camera coupled to a PC (see Fig. 2). Two sets (leading-in and leading-out) of front-faced plane mirrors each attached to a mechanical slider block inclined at an angle of 458 to the illumination direction. In the leading-in set, the upper mirror (mirror A) is tilted at 458 downwards while the lower mirror (mirror B) is tilted at 458 upwards. The mechanical slider blocks are mounted on a vertical rod supported by an adjustable post holder and suspended inside the test specimen (a hollow cylinder with an internal radius of 107 mm and 3 mm thickness) with mirror A exposed above the rim of the cylinder. The cylinder is mounted on a rotating stage with a variable speed. The internal surface of the cylinder is illuminated by directing the light source at mirror A. The depth of illumination on the cylinder surface is controlled by adjusting the position of mir-

461

ror B. This capability allows the entire inner wall section to be accessed. Using a similar arrangement, the image of the illuminated surface is captured by the leading-out mirrors placed with their axes parallel and rotated at an angle to the leading-in mirrors. A simple structured light pattern having alternate bright and dark lines is directed at mirror A by pulsing the laser diode at a suitable frequency. The TDI camera used 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 present set-up the period of the pulse train ranges from 4.8 to 6.7 ms and the corresponding scanning speed of the TDI camera ranges from 48,000 to 70,000 lines/min. Images of the illuminated surface are recorded by the TDI camera. Subsequent tests are carried out on two other objects. An object with a moderately curved pro®le and a radius of curvature 50 mm (object A) and a hemispherical object with a radius of 20 mm (object B). Objects A and B are mounted on the internal surface of the cylinder as shown in Figs 3 and 4 respectively.

Fig. 2. Experimental set-up.

462

C.J. Tay et al. / Optics & Laser Technology 30 (1998) 459±465

Fig. 3. Object A mounted on cylinder.

4. Results and discussion To ensure that the multiple re¯ections through the proposed arrangement of mirrors do not introduce any signi®cant optical distortion, the cylinder was tested at various rotational speeds. Fig. 5 shows a typical fringe pattern obtained on the hollow cylinder with a reference marker, which is used to determine the cylinder diameter. Any optical distortion would be readily observed from the pitch, thickness and linearity of the fringes. From the fringe thickness, pitch, scanning

speed of the TDI camera and the relative position of the reference marker, the internal diameter of the cylinder is determined as shown in Table 1. It is seen that the scatter in diameter readings recorded using the proposed technique ranges from ÿ0.9 to +1.8% of the nominal diameter which is within acceptable limits for most practical applications. The results also suggest that the optimum conditions for the present experimental set-up appear to be at a stage rotational speed of 45 rpm with a pulse train period of 6.0 ms and a scanning speed of 62,689 lines/min. A compari-

Fig. 4. Object B mounted on cylinder.

C.J. Tay et al. / Optics & Laser Technology 30 (1998) 459±465

463

Fig. 5. Fringe pattern on hollow cylinder.

Table 1 Internal diameter of cylinder Rotational speed (rpm)

35 40 45 50

Pulse train period (ms)

4.6 5.3 6.0 6.7

Scanning speed (lines/min)

48758 55724 62689 69655

Internal diameter (m)

% variation

present results

method A

0.213 0.219 0.215 0.218

0.210 0.215 0.215 0.216

1.4 1.9 0.0 1.0

Fig. 6. Fringe pattern on object A.

Fig. 7. Fringe pattern on object B.

son of the present results with that of the conventional dial gauge pro®lometer (method A) is also included in Table 1. As can be seen, at the optimum test conditions the agreement is excellent with no discrepancy between the two sets of results. Figs 6 and 7 show the respective fringe patterns obtained on object A and B. In Fig. 6 two sets of fringe pattern are observed, one set represents the cylinder (used as a base) pro®le and the other rep-

resents object A. The fringes on object A are shifted slightly to the right. The amount of shift is proportional to the relative height of the object surface from the base. The fringe density on the right hand side of object A is higher than the left hand side. Considering the direction of object rotation and light source illumination, this would indicate that the gradients are negative on the right side and positive on the left. When the rotation is in the opposite direction, the

464

C.J. Tay et al. / Optics & Laser Technology 30 (1998) 459±465

Fig. 8. A 3D plot of object A.

Fig. 9. A comparison of results for object A.

Fig. 10. A comparison of results for object B.

C.J. Tay et al. / Optics & Laser Technology 30 (1998) 459±465

converse is true. The fringe data are analyzed using an image processing software and a 3D plot of object A is shown in Fig. 8. In previous works [2±5], a quantitative assessment of the accuracy of the TDI technique is not readily available. Hence, measurements along a cross-section of the object are also taken using method A and the results are compared with the present technique (Fig. 9). The Y-axis represents the object height and for convenience, the number of pixels is plotted along the X-axis. As can be seen the results generally agree well. A maximum discrepancy of 16% at a pixel value of 30 is observed. Similar results are obtained for the hemispherical object (Fig. 10). It is seen that there is good agreement between method A and the present results and the maximum discrepancy at the optimum test conditions is less than 6%.

5. Concluding remarks This paper presents a new method for internal surface contour measurement using the time delay and integration method. The imaging is carried out by a system of optical arrangement, which enables the internal surface of a cylinder to be inspected without any signi®cant optical distortion. The results obtained

465

using the proposed method compared well with those of conventional pro®lometer. Hence, the results suggest a potential for the proposed method to be developed into a technique for internal surface inspection in industry. References [1] Cheng X, Su XY, Guo LR. Automated measurement method of fringe analysis for 360 pro®lometry of di€use objects. Appl. Optics 1991;30:1274±8. [2] Asundi A, Chan CS, Sajan MR. 360-deg pro®lometry: new techniques for display and acquisition. Opt. Eng. 1994;33:2760±9. [3] Asundi A, Sajan MR. Dynamic recording using a TDI camera. Appl. Optics 1994;33:8102±5. [4] Asundi A, Sajan MR. Peripheral inspection of objects. Opt. Laser Eng. 1995;22:227±40. [5] Asundi A, Sajan MR. Digital drum camera for dynamic recording. Opt. Eng. 1996;35:1707±13. [6] Halioua M, Liu H. Optical 3D sensing by phase measuring pro®lometry. Opt. Laser Eng. 1989;11:185±215. [7] Takeda M, Ina H, Kobayashi SJ. Fourier-transform method of fringe analysis for computer based topography and interferometry. Opt. Soc. Am. 1982;72:156±60. [8] Wang L, Krishnaswamy S. Shape measurement using additive± substractive phase shifting speckle interferometry. Meas. Sci. Technol. 1996;7(12):1748±54. [9] Sajan MR, Tay CJ, Shang HM, Asundi A. Time delay and integration imaging for inspection and pro®lometry of moving objects. Opt. Eng. 1997;36:2573±8.