- Email: [email protected]
Dynamic photoelasticity using TDI imaging
Optics and Lasers in Engineering 38 (2002) 3–16
Dynamic photoelasticity using TDI imaging Anand Asundi*, M.R. Sajan, Liu Tong School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore Received 5 March 2001; received in revised form 20 August 2001; accepted 20 August 2001
Abstract High-speed photographic systems are necessary for recording and visualization of dynamic events in stress analysis, fluid mechanics, etc. Current imaging systems are fairly expensive and generally not simple to use. Furthermore, most are based on photographic film recording systems requiring time consuming and tedious wet processing of the films. Recently, there is lot of interest in developing and modifying CCD architectures and recording arrangements for dynamic scene analysis. Herein we report the use of a CCD camera operating in the time delay and integration mode for digitally recording dynamic photoelastic stress patterns. Applications in strobe and streak photoelastic pattern recording and system limitations will be explained in the paper. In addition, a scheme for dynamic phase shifting using is also explained. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Dynamic recording; Photoelasticity; Digital imaging; Phase shifting
1. Introduction High speed photographic systems are commonly used for visualizing dynamic phenomena such as stress wave propagation, stress concentration near discontinuities, sports mechanics, ballistics, flow visualization, industrial web inspection, automobile crash studies, etc. In these cases the dynamic scenes are either directly imaged; or, displacement or stress contours obtained using optical interferometric techniques captured. Traditionally, drum camera, high speed image rotation camera,
*Corresponding author. E-mail address: [email protected] (A. Asundi). 0143-8166/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 8 1 6 6 ( 0 1 ) 0 0 1 5 4 - 3
4
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
delayed microflash and Cranz Schardin camera systems have been used for highspeed imaging. Reviews of these devices and methods have been reported in literature [1,2]. While these methods provide high-resolution images, they are expensive and require tedious film processing and recording in a dark room environment. Digital video systems alleviate these disadvantages of the film-based recording systems. Hence they are being widely used for recording and analyzing the stress patterns for static experiments. Conventional video recording systems use a framebased recording operation, attaining a maximum speed of 30 frames per second in the CCIR format. This, however, is not sufficient for most of the dynamic problems in solid and fluid mechanics, where the stress patterns move with velocities in excess of 1000 m/s. Hence development is underway to modify these systems for dynamic photomechanics applications. Conventional cameras operate in the frame-based mode, wherein one field is exposed for a short time, of the order of 20 ms and the photogenerated charges are then transferred to a temporary storage buffer at a faster rate, typically within 0.5 ms. While the next field is being exposed, the charges in the temporary buffer are serially transferred to the data lines. Each display or frame is a combination of the even and odd fields. Thus in the CCIR video format, 30 frames are recorded per second. A solution to the dynamic imaging problem, utilizing the charge transfer time of the frame transfer type CCDs is reported by Hiller and Kowalewski [3]. The event is recorded for 485 ms with a strobe synchronized to the blanking pulses of the video signal. In this method, it may be very difficult to synchronize the dynamic loading with the start of recording. However, while using an explosive type loading, it is possible to derive a trigger pulse from the same video signal to charge the explosive chemicals, which usually have a rise time of 2–4 ms [4]. Application of multiple sensor arrays with individual short duration flash light sources were also investigated. Burger et al. [5] reported the use of five spatially separated charge injection device cameras, coupled with a ruby laser. An Acousto-optic Modulator is used to split the ruby pulse spatially to the cameras. Bretthauer et al. [6], implements a novel scheme using eight CCD sensors and Light emitting diodes in the Cranz Schardin format. Time delay and integration (TDI) is a special operating mode, developed for dynamic stress analysis and automated visual inspection [7,8]. Currently, higher speed and higher resolution type TDI cameras are available off-the-shelf. The high-speed features of the new device for dynamic applications are explored. Details of the camera operation and some demonstrations are provided in the following sections. Furthermore, temporal phase shifting is the standard analysis technique for photoelastic fringe patterns. A novel dynamic phase shifting set-up is described and demonstrated.
2. The TDI camera The Time Delay and Integration (TDI) camera mode utilizes a full frame image sensor, which is actually the forerunner of frame transfer CCD imager. Operation of
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
5
the TDI is akin to the charge sweep during the charge transfer in the frame transfer imager, but with software controlled sweep speeds. The photo-generated charges are shifted row by row along the columns. Following each shift, the accumulated charges are added to the photo-generated charges at the new site. Thus the charges are integrated along the column with an adjustable time delay from one row to the next. Finally, the accumulated charges in the last row are transferred to the output data lines through a serial register. This operation is often compared to that of the traditional drum camera [9]. Originally, the TDI camera mode was designed to record blur free images of moving objects in industrial platforms [10]. If the charge collection sites are moving with the same velocity as the object, a bright and blur-free image of the object is recorded. Since the speed of charge collection sites or the charge integration time can be varied, this was also employed in astronomical imaging and for other low light level applications. Drum cameras were the first devices used in photoelasticity and still continue to be of interest [11]. A brief list of applications of drum camera in photomechanics and related demonstrations are provided by Culver [12]. Since the TDI functions as a digital drum camera, similar applications could be possible with this system. The high speed TDI camera consists of a CCD array of 244 753 pixels. Currently, TDI images saved are one frame size. The maximum scan speed available is 4 ms per line. This speed is more than sufficient for curved surface inspection. However, in dynamic photoelasticity, this may not be sufficient as the stress wave propagation velocity in high modulus materials could be in excess of 1000 m/s. Alternatively, the models could be made with low modulus materials, where the stress wave velocities is reduced considerably to within the limits of the TDI scan rates. High-speed recording is achieved using fast films or short duration flashes, resulting in the reduction of net exposure intensity. Part of the exposure intensity is used to overcome the exposure inertia of the film. For maximum efficiency, traditional methods employ a technique called film-fogging [13]. In this approach, the films are fogged using controlled illumination before recording the actual scene. This process increases the speed of the film by reducing the exposure inertia. The TDI sensor used here provides a similar facility. For these sensors, there is a current bias, which can be applied to the CCD called the dark current, which controls the background rejection. If the dark current bias is set low, extra light is required to overcome the inertia of the CCD. On the other hand, if the dark current bias is higher, the background intensity will be gray, even in the absence of illumination. In such cases, additional light falls on the sensor array produce excess current, resulting in a bright picture. This facility is provided in the camera to compensate for the currents generated at higher temperature. The dark current setting is adjusted so that under the room lighting the CCD output is just above the inertia level. This setting makes sure that the light from the laser diode is completely available at the CCD output. Thus experiments in room lighting is possible. An alternative to this could be achieved by adjusting the TDI scan speed. At the set dark current, higher scan speed reduce the background intensity, while the lower scan speed increase the background intensity.
6
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
3. Experimental set-up and demonstrations 3.1. Dynamic photoelasticity These experiments are performed in a modified static polariscope. The recording geometry is as shown in Fig. 1. A laser diode with 100% depth of modulation is used as the illumination source. This provides a low cost, low power alternative for the bulky and expensive sources such as flash lamps and solid state lasers used in conventional systems. For dynamic photomechanics experiments, the diode laser has two disadvantages. The first one is due to the pulse width, limited by the rise and fall times (250 and 100 ns, respectively). The second limitation is due to the lack of coherence during the short pulse time, which preclude their use in dynamic interferometric studies such as holography and moire! . Expanded light from a laser diode is collimated using lens L1. Lens L2 converges the light beam to the camera lens. The photoelastic model is loaded between the lenses L1 and L2. The model is made of urethane rubber where the stress wave velocity is approximately 200 m/s. 3.2. Streak recording Dynamic photoelasticity experiments were initiated by recording streak patterns of a rectangular strip by Tuzi and Nisida [11]. Later, Flynn and Frocht [14] used this method in direct and oblique incidence formats. In this technique, only a line of interest is illuminated. The temporal variation of stress waves (Photoelastic fringes) across the line is recorded as dynamic photoelastic fringes. The motion of film in the drum camera allows the exposed area to move from the illuminating light strip. In high speed TDI this is possible as the charges accumulated in the exposed area are moving away from the illuminated row in much the same manner. Though the whole field advantage of photoelasticity is sacrificed, it is possible to use low speed devices to record the high-speed information along a line.
Pulse generator Trigger
Time delay
LED Laser
TDI Camera
diode L2
L1 Dynamic scene
Fig. 1. Schematic for Streak/Strobe recording system.
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
7
Fig. 2. Photoelastic specimen and recorded dynamic streak pattern.
The specimen is illuminated along the vertical line shown in Fig. 2(a). This is achieved by inserting a mask after the lens L1 having a slit of width 2 mm. The polariscope is set to the dark field mode and the TDI scanning rate is fixed at 13 ms per line. The camera is aligned such that the scanning direction is perpendicular to the illuminated line. Photoelastic streak pattern due to ball impact is recorded as shown in Fig. 2(b). The columns in the image represent time axis increasing left to right. The stress waves due to impact propagates from top to bottom. The horizontal dark band is the hole. The experiment could also be conducted in bright field polariscope arrangement. But the bright region corresponding to the hole tends to smear the photo-generated charges in the sensor to neighboring pixels, resulting in noise. Generation of the fringes past the loading point and the movement of the fringes can be clearly seen in the figure. Due to the dark field recording arrangement, the velocity of the stress wave front could be estimated from the speed of the first bright fringe. This is easily accomplished from the Fig. 2(b) by counting the number of pixels from left to the bright fringe at any vertical position. Since the line (column) scan time is 13 ms, the horizontal count is multiplied by 13 ms to estimate the time taken by the stress wave to reach the concerned point. The distance traveled by the first and second bright fringes with time is plotted in Fig. 3(a). The velocity of the wavefront (the first bright fringe) decreases as it approaches the hole boundary and then increases again to a relatively steady value after engulfing of the hole. The stress wavefront reflects from the fore position of the hole, damping the propagation of the second bright fringe. Thus the velocity of the second bright fringe is reduced considerably as illustrated in Fig. 3(b). Another interesting point to note is near the aft edge of the hole. When the wavefront engulfs the hole, a compressive stress is exerted at the aft position for a very short time. This is not clear from Fig. 2(b), but is clearly noticeable in the magnified and threshold enhanced area near the aft position as depicted in Fig. 4.
8
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
Fig. 3. (a) Position of the first and second bright fringes and (b) their velocity.
Fig. 4. Magnified view near the hole in Fig. 2b.
After the short compressive stress, the aft position experiences only tensile stress. In a specimen without any discontinuity, the stresses are compressive before the reflections from boundaries start interacting with the propagating waves at any point. Conventionally, compressive stresses are assigned a negative sign and tensile stresses are marked as positive. Correspondingly, the stresses at the aft point goes negative in the beginning and reverts back to positive as shown in Fig. 5 The dynamic stress concentration factor ‘KðtÞ’ is defined as KðtÞ ¼
smax ðtÞ ; snom ðtÞ
ð1Þ
ðtÞ where sðtÞ max and snom are the dynamic maximum and nominal stresses. Hence the stress concentration factor at the aft edge tends to be positive during the short time interval during engulfment of the hole and changes to negative afterwards. This
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
9
Fig. 5.
result is in accordance with the interpretation of Dally and Halbleib [15] on the dynamic stress concentration factors at circular holes in struts. 2.3. Strobe recording Strobe technology has a history of more than a hundred years and its spectrum of applications is recounted by Edgerton [16], the pioneer of strobe photography. The application of ruby laser strobes in recording photoelastic patterns on stationary film, or continuously on high-speed films is illustrated by Taylor [17]. Another interesting application of strobe lighting was the recording of dynamic photoelastic patterns from periodically loaded components [18]. The drum camera like operation of the TDI also facilitates strobe recording [19]. In the strobe mode, the width of the light pulse must be smaller than the scanning time for one line. This is to avoid overlap and thus smearing of the charges between the pixels. The pulse separation is adjusted based on the size of the image. Sufficient time interval must be provided for the photo-generated charges to shift from the illumination area, if frame smearing is to be avoided. The geometry of the photoelastic model is depicted in Fig. 6(a). The specimen is illuminated by a strip of light 16 mm wide along the direction of impact. Dynamic photoelastic patterns obtained after the ball impact are shown in Fig. 6(b). The pulse width and interval are 5 and 130 ms, respectively. The reflection of the higher order fringes due to the reflected stress wavefront at the hole is similar to that in Fig. 2(b). Slow speed TDI cameras are best suited for recording photoelastic fringes from a delayed micro-flash arrangement. Delayed micro-flash is widely used in nondestructive experiments where the flash is triggered at a preset delay after an event such a ball impact. The experiment is repeated by changing the preset delay and recording the scene illuminated again. It is possible to operate a TDI camera at a slow speed so that light integration takes place over a large time interval. Note that
10
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
Fig. 6. (a) Photoelastic specimen (b) dynamic photoelastic patterns due a ball impact on top of the specimen.
Fig. 7. Stress wave propagation in a polycarbonate specimen.
the background illumination may have to be controlled in this case to record a clear picture of the scene of interest. An LED flash of 1 ms duration is sufficient to illuminate a photoelastic specimen of 15 15-cm square. The TDI save mode is turned on before releasing the ball for impact. After the impact, the LED micro-flash illuminates the specimen for 1 ms and the photoelastic fringes are recorded somewhere along the length of the TDI image. It is possible to cut and paste the images recorded after different time delays to visualize a dynamic scene. Fig. 7 depicts propagation of stress waves in a polycarbonate photoelastic model. Photoelastic liquids such as milling yellow provide the potential for using photoelasticity to analyze dynamic fluid mechanics problems. Fig. 8 shows the
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
11
Fig. 8. Dynamic photoelastic patterns generated by a ball dropped into milling yellow solution.
Fig. 9. Schematic diagram for dynamic phase shift photoelasticity.
dynamic fringe patterns generated by the impact of a steel ball into a tank of milling yellow solution.
4. Dynamic phase-shifting photoelasticity 4.1. Experimental set-up Based on the recently developed two-load to phase-shifting technique [20,21], a system for dynamic phase-shifting photoelasticity is developed. The schematic diagram of this system is shown in Fig. 9. This is standard circular polariscope with a Multispec ImagerTM including four groups of quarter wave-plates and analyzers. The operation principle of this system can be described briefly as follows. A beam of light passes through the polarizer and a quarter-wave plate resulting in a circularly polarized light. After transmitting through a stressed birefringent material, its optical energy is split by the Multispec ImagerTM into four paths along the same direction. In each path, a different configuration of quarter-wave plate and analyzer is inserted to generate the required phase-shifted image. The four groups of quarter wave-plates and the analyzer are placed in a single slide, which then is integrated into the Multispec ImagerTM device. Four images are recorded on a single CCD array. The
12
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
A 45 °
135 °
A
Q2
Q2
A Q2
A 45 °
Q2
90 °
Fig. 10. Four configurations of the second quarter-wave plate and the analyzer when the axis of polarizer and the fast axis of the first quarter-wave plate are set as in Fig. 1. Q2 : the slow axis of the second quarterwave plate; A: the analyzer.
Fig. 11. Dark-field image of a ‘‘C’’ shape model subjected to dynamic compression.
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
13
Fig. 12. Schematic diagram of separating the four sub-images in an original image into four individual images.
Fig. 13. Three sets of phase-shifted images recorded at different times during a load cycle.
configurations of four groups of quarter-wave plates and analyzers are shown in Fig. 10. With this system, full-field analysis of a dynamic event is possible. The proposed system demonstrated using a ‘‘C’’ shape model (Fig. 11). The stress in section A is a combination of compression and bending and serves as a good example for evaluation of this system since for beam bending the stress on either side of the neutral axis have opposite signs. Cyclic load is applied using a tensile testing machine, thus generating the dynamic event. The size of the active area of the CCD
14
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
Fig. 14. (a) Isochromatic maps for the three samples obtained by using two-load-step to phase-shifting method.
Fig. 15. Unwrapped phase maps of the three examples and their distributions along the same line. The fringe orders at the end points of specimen are given for comparison.
is 640 480 pixels. A monochromatic filter centered at 575 nm is used with a white light source. A series of images, each of which comprising four phase-stepped images, is recorded. The isoclinic and isochromatic parameters are determined using
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
15
the two-load method using two sets of phase shifted images recorded at two different instants of time. The actual procedure, schematically shown in Fig. 12, involves two steps. First, for a given image, the four sub-images contained in each image are separated into four individual images having the same size and with no physical shift between them. This is achieved by placing a reference mark on the specimen prior to the experiment. Using this reference the four sub-images are cropped from the original image and saved as separate data matrices. With these sub-images, the phase-shift algorithm (20) is then applied. The three sets of images recorded at different times during a single load cycle are shown in Fig. 13. Figs. 14 and 15 show the individually wrapped and unwrapped phase retardation maps after the phase shift algorithm is invoked.
5. Conclusion Application of a TDI camera in dynamic photoelastic recording is demonstrated. High speed TDI provides faster imaging rates. This could be readily used for streak and strobe recording in dynamic photomechanics. Since the CCDs’ are more sensitive than the conventional photographic film, it is possible to use low cost, low voltage semiconductor light sources as micro-flash. The performance of the system is demonstrated by recording streak patterns of dynamically loaded photoelastic models. This experiment suggests the application of line scan sensors for dynamic streak photoelastic investigations. The line scan sensors offer faster scanning rates which could record the dynamic photoelastic patterns from stiffer models with higher stress wave velocities. Dynamic phase shifting can be accomplished using an off-theshelf system to split the light into four components each with an appropriate phase shift. Possibility of use for other dynamic interferometry also exists.
References [1] Dally JW. Introduction to photoelasticity. Exp Mech 1980;20:409–16. [2] Field JE. High-speed photography: techniques and applications. Opt Eng 1982;21:709–17. [3] Hiller WJ, Kowalewski TA. Application of the frame-transfer charge-coupled devices for high speed imaging. Opt Eng 1989;28:197–200. [4] Fang SJ, Hemann JH, Achenbach JD. Experimental and analytical investigation of dynamic stress concentrations at a circular hole. Trans ASME J Appl Mech 1974;41:417–22. [5] Burger CP, Chona R, Khanna SK, Thomas MR. A high speed imaging system employing laser light acousto-optics. Proceedings of the SEM Conference 1994, p. 718–24. [6] Bretthauer B, Meier GEA, Stasicki B. An electronic Cranz Schardin camera. Rev Sci Instrum 1991;62:364–8. [7] Asundi A, Sajan MR. Low-cost digital polariscope for dynamic photoelasticity. Opt Eng 1994;33:3052–5. [8] Asundi A, Chan CS, Sajan MR. 360-deg profilometry: new techniques for display and acquisition. Opt Eng 1994;33:2760–9. [9] Michael GF, Rudolph HD. A large area TDI image sensor for low light level imaging. IEEE Trans Elect Dev 1980;ED-27:688–1693.
16
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
[10] David LG. TDI imaging in industrial inspection. Proc SPIE 1989;1194:36–45. [11] Tuzi Z, Nisida M. Photoelastic study of stresses due to impact. Phil Mag 1936;21:448–73. [12] Culver RS. Measuring dynamic strain profile and history with a drum camera. Exp Mech 1970;10:288–93. [13] Dally JW. In: Lagarde A, editor. Recording systems for dynamic photomechanics, static and dynamic photoelasticity and caustics. Springer, Italy, 1987, p. 248–63. [14] Frocht MM, Flynn PD. On the photoelastic separation of principal stresses under dynamic conditions by oblique incidence. In: Frocht MM, Leven MM, editors. PhotoelasticityFthe selected scientific papers. Pergamon Press, London, 1969. [15] Dally JW, Halbleib WF. Dynamic stress concentrations at circular holes in struts. J Mech Eng Sci 1965;7:23–7. [16] Edgerton HE. Strobe photography: a brief history. Opt Eng 1984;23:SR100–5. [17] Taylor CE, Bowman CE, North WP, Swinson WF. Application of lasers to photoelasticity. Exp Mech 1966;6:289–96. [18] Becker H. Simplified equipment for photoelastic studies of propagating stress waves. Proc SESA 1961;18:214–6. [19] Asundi A, Sajan MR. TDI camera application in dynamic photomechanics. Exp Tech 1994;8(5):9–11. [20] Asundi A, Liu Tong, Chai Gin Boay. Determination of isoclinic and isochromatic parameters using three-load method. Meas Sci Technol 2000;11:532–7. [21] Asundi A, Liu Tong, Chai Gin Boay. Full-field automated photoelasticity using two-load-step method, 2002, in review.
Dynamic photoelasticity using TDI imaging Anand Asundi*, M.R. Sajan, Liu Tong School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore Received 5 March 2001; received in revised form 20 August 2001; accepted 20 August 2001
Abstract High-speed photographic systems are necessary for recording and visualization of dynamic events in stress analysis, fluid mechanics, etc. Current imaging systems are fairly expensive and generally not simple to use. Furthermore, most are based on photographic film recording systems requiring time consuming and tedious wet processing of the films. Recently, there is lot of interest in developing and modifying CCD architectures and recording arrangements for dynamic scene analysis. Herein we report the use of a CCD camera operating in the time delay and integration mode for digitally recording dynamic photoelastic stress patterns. Applications in strobe and streak photoelastic pattern recording and system limitations will be explained in the paper. In addition, a scheme for dynamic phase shifting using is also explained. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Dynamic recording; Photoelasticity; Digital imaging; Phase shifting
1. Introduction High speed photographic systems are commonly used for visualizing dynamic phenomena such as stress wave propagation, stress concentration near discontinuities, sports mechanics, ballistics, flow visualization, industrial web inspection, automobile crash studies, etc. In these cases the dynamic scenes are either directly imaged; or, displacement or stress contours obtained using optical interferometric techniques captured. Traditionally, drum camera, high speed image rotation camera,
*Corresponding author. E-mail address: [email protected] (A. Asundi). 0143-8166/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 8 1 6 6 ( 0 1 ) 0 0 1 5 4 - 3
4
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
delayed microflash and Cranz Schardin camera systems have been used for highspeed imaging. Reviews of these devices and methods have been reported in literature [1,2]. While these methods provide high-resolution images, they are expensive and require tedious film processing and recording in a dark room environment. Digital video systems alleviate these disadvantages of the film-based recording systems. Hence they are being widely used for recording and analyzing the stress patterns for static experiments. Conventional video recording systems use a framebased recording operation, attaining a maximum speed of 30 frames per second in the CCIR format. This, however, is not sufficient for most of the dynamic problems in solid and fluid mechanics, where the stress patterns move with velocities in excess of 1000 m/s. Hence development is underway to modify these systems for dynamic photomechanics applications. Conventional cameras operate in the frame-based mode, wherein one field is exposed for a short time, of the order of 20 ms and the photogenerated charges are then transferred to a temporary storage buffer at a faster rate, typically within 0.5 ms. While the next field is being exposed, the charges in the temporary buffer are serially transferred to the data lines. Each display or frame is a combination of the even and odd fields. Thus in the CCIR video format, 30 frames are recorded per second. A solution to the dynamic imaging problem, utilizing the charge transfer time of the frame transfer type CCDs is reported by Hiller and Kowalewski [3]. The event is recorded for 485 ms with a strobe synchronized to the blanking pulses of the video signal. In this method, it may be very difficult to synchronize the dynamic loading with the start of recording. However, while using an explosive type loading, it is possible to derive a trigger pulse from the same video signal to charge the explosive chemicals, which usually have a rise time of 2–4 ms [4]. Application of multiple sensor arrays with individual short duration flash light sources were also investigated. Burger et al. [5] reported the use of five spatially separated charge injection device cameras, coupled with a ruby laser. An Acousto-optic Modulator is used to split the ruby pulse spatially to the cameras. Bretthauer et al. [6], implements a novel scheme using eight CCD sensors and Light emitting diodes in the Cranz Schardin format. Time delay and integration (TDI) is a special operating mode, developed for dynamic stress analysis and automated visual inspection [7,8]. Currently, higher speed and higher resolution type TDI cameras are available off-the-shelf. The high-speed features of the new device for dynamic applications are explored. Details of the camera operation and some demonstrations are provided in the following sections. Furthermore, temporal phase shifting is the standard analysis technique for photoelastic fringe patterns. A novel dynamic phase shifting set-up is described and demonstrated.
2. The TDI camera The Time Delay and Integration (TDI) camera mode utilizes a full frame image sensor, which is actually the forerunner of frame transfer CCD imager. Operation of
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
5
the TDI is akin to the charge sweep during the charge transfer in the frame transfer imager, but with software controlled sweep speeds. The photo-generated charges are shifted row by row along the columns. Following each shift, the accumulated charges are added to the photo-generated charges at the new site. Thus the charges are integrated along the column with an adjustable time delay from one row to the next. Finally, the accumulated charges in the last row are transferred to the output data lines through a serial register. This operation is often compared to that of the traditional drum camera [9]. Originally, the TDI camera mode was designed to record blur free images of moving objects in industrial platforms [10]. If the charge collection sites are moving with the same velocity as the object, a bright and blur-free image of the object is recorded. Since the speed of charge collection sites or the charge integration time can be varied, this was also employed in astronomical imaging and for other low light level applications. Drum cameras were the first devices used in photoelasticity and still continue to be of interest [11]. A brief list of applications of drum camera in photomechanics and related demonstrations are provided by Culver [12]. Since the TDI functions as a digital drum camera, similar applications could be possible with this system. The high speed TDI camera consists of a CCD array of 244 753 pixels. Currently, TDI images saved are one frame size. The maximum scan speed available is 4 ms per line. This speed is more than sufficient for curved surface inspection. However, in dynamic photoelasticity, this may not be sufficient as the stress wave propagation velocity in high modulus materials could be in excess of 1000 m/s. Alternatively, the models could be made with low modulus materials, where the stress wave velocities is reduced considerably to within the limits of the TDI scan rates. High-speed recording is achieved using fast films or short duration flashes, resulting in the reduction of net exposure intensity. Part of the exposure intensity is used to overcome the exposure inertia of the film. For maximum efficiency, traditional methods employ a technique called film-fogging [13]. In this approach, the films are fogged using controlled illumination before recording the actual scene. This process increases the speed of the film by reducing the exposure inertia. The TDI sensor used here provides a similar facility. For these sensors, there is a current bias, which can be applied to the CCD called the dark current, which controls the background rejection. If the dark current bias is set low, extra light is required to overcome the inertia of the CCD. On the other hand, if the dark current bias is higher, the background intensity will be gray, even in the absence of illumination. In such cases, additional light falls on the sensor array produce excess current, resulting in a bright picture. This facility is provided in the camera to compensate for the currents generated at higher temperature. The dark current setting is adjusted so that under the room lighting the CCD output is just above the inertia level. This setting makes sure that the light from the laser diode is completely available at the CCD output. Thus experiments in room lighting is possible. An alternative to this could be achieved by adjusting the TDI scan speed. At the set dark current, higher scan speed reduce the background intensity, while the lower scan speed increase the background intensity.
6
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
3. Experimental set-up and demonstrations 3.1. Dynamic photoelasticity These experiments are performed in a modified static polariscope. The recording geometry is as shown in Fig. 1. A laser diode with 100% depth of modulation is used as the illumination source. This provides a low cost, low power alternative for the bulky and expensive sources such as flash lamps and solid state lasers used in conventional systems. For dynamic photomechanics experiments, the diode laser has two disadvantages. The first one is due to the pulse width, limited by the rise and fall times (250 and 100 ns, respectively). The second limitation is due to the lack of coherence during the short pulse time, which preclude their use in dynamic interferometric studies such as holography and moire! . Expanded light from a laser diode is collimated using lens L1. Lens L2 converges the light beam to the camera lens. The photoelastic model is loaded between the lenses L1 and L2. The model is made of urethane rubber where the stress wave velocity is approximately 200 m/s. 3.2. Streak recording Dynamic photoelasticity experiments were initiated by recording streak patterns of a rectangular strip by Tuzi and Nisida [11]. Later, Flynn and Frocht [14] used this method in direct and oblique incidence formats. In this technique, only a line of interest is illuminated. The temporal variation of stress waves (Photoelastic fringes) across the line is recorded as dynamic photoelastic fringes. The motion of film in the drum camera allows the exposed area to move from the illuminating light strip. In high speed TDI this is possible as the charges accumulated in the exposed area are moving away from the illuminated row in much the same manner. Though the whole field advantage of photoelasticity is sacrificed, it is possible to use low speed devices to record the high-speed information along a line.
Pulse generator Trigger
Time delay
LED Laser
TDI Camera
diode L2
L1 Dynamic scene
Fig. 1. Schematic for Streak/Strobe recording system.
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
7
Fig. 2. Photoelastic specimen and recorded dynamic streak pattern.
The specimen is illuminated along the vertical line shown in Fig. 2(a). This is achieved by inserting a mask after the lens L1 having a slit of width 2 mm. The polariscope is set to the dark field mode and the TDI scanning rate is fixed at 13 ms per line. The camera is aligned such that the scanning direction is perpendicular to the illuminated line. Photoelastic streak pattern due to ball impact is recorded as shown in Fig. 2(b). The columns in the image represent time axis increasing left to right. The stress waves due to impact propagates from top to bottom. The horizontal dark band is the hole. The experiment could also be conducted in bright field polariscope arrangement. But the bright region corresponding to the hole tends to smear the photo-generated charges in the sensor to neighboring pixels, resulting in noise. Generation of the fringes past the loading point and the movement of the fringes can be clearly seen in the figure. Due to the dark field recording arrangement, the velocity of the stress wave front could be estimated from the speed of the first bright fringe. This is easily accomplished from the Fig. 2(b) by counting the number of pixels from left to the bright fringe at any vertical position. Since the line (column) scan time is 13 ms, the horizontal count is multiplied by 13 ms to estimate the time taken by the stress wave to reach the concerned point. The distance traveled by the first and second bright fringes with time is plotted in Fig. 3(a). The velocity of the wavefront (the first bright fringe) decreases as it approaches the hole boundary and then increases again to a relatively steady value after engulfing of the hole. The stress wavefront reflects from the fore position of the hole, damping the propagation of the second bright fringe. Thus the velocity of the second bright fringe is reduced considerably as illustrated in Fig. 3(b). Another interesting point to note is near the aft edge of the hole. When the wavefront engulfs the hole, a compressive stress is exerted at the aft position for a very short time. This is not clear from Fig. 2(b), but is clearly noticeable in the magnified and threshold enhanced area near the aft position as depicted in Fig. 4.
8
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
Fig. 3. (a) Position of the first and second bright fringes and (b) their velocity.
Fig. 4. Magnified view near the hole in Fig. 2b.
After the short compressive stress, the aft position experiences only tensile stress. In a specimen without any discontinuity, the stresses are compressive before the reflections from boundaries start interacting with the propagating waves at any point. Conventionally, compressive stresses are assigned a negative sign and tensile stresses are marked as positive. Correspondingly, the stresses at the aft point goes negative in the beginning and reverts back to positive as shown in Fig. 5 The dynamic stress concentration factor ‘KðtÞ’ is defined as KðtÞ ¼
smax ðtÞ ; snom ðtÞ
ð1Þ
ðtÞ where sðtÞ max and snom are the dynamic maximum and nominal stresses. Hence the stress concentration factor at the aft edge tends to be positive during the short time interval during engulfment of the hole and changes to negative afterwards. This
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
9
Fig. 5.
result is in accordance with the interpretation of Dally and Halbleib [15] on the dynamic stress concentration factors at circular holes in struts. 2.3. Strobe recording Strobe technology has a history of more than a hundred years and its spectrum of applications is recounted by Edgerton [16], the pioneer of strobe photography. The application of ruby laser strobes in recording photoelastic patterns on stationary film, or continuously on high-speed films is illustrated by Taylor [17]. Another interesting application of strobe lighting was the recording of dynamic photoelastic patterns from periodically loaded components [18]. The drum camera like operation of the TDI also facilitates strobe recording [19]. In the strobe mode, the width of the light pulse must be smaller than the scanning time for one line. This is to avoid overlap and thus smearing of the charges between the pixels. The pulse separation is adjusted based on the size of the image. Sufficient time interval must be provided for the photo-generated charges to shift from the illumination area, if frame smearing is to be avoided. The geometry of the photoelastic model is depicted in Fig. 6(a). The specimen is illuminated by a strip of light 16 mm wide along the direction of impact. Dynamic photoelastic patterns obtained after the ball impact are shown in Fig. 6(b). The pulse width and interval are 5 and 130 ms, respectively. The reflection of the higher order fringes due to the reflected stress wavefront at the hole is similar to that in Fig. 2(b). Slow speed TDI cameras are best suited for recording photoelastic fringes from a delayed micro-flash arrangement. Delayed micro-flash is widely used in nondestructive experiments where the flash is triggered at a preset delay after an event such a ball impact. The experiment is repeated by changing the preset delay and recording the scene illuminated again. It is possible to operate a TDI camera at a slow speed so that light integration takes place over a large time interval. Note that
10
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
Fig. 6. (a) Photoelastic specimen (b) dynamic photoelastic patterns due a ball impact on top of the specimen.
Fig. 7. Stress wave propagation in a polycarbonate specimen.
the background illumination may have to be controlled in this case to record a clear picture of the scene of interest. An LED flash of 1 ms duration is sufficient to illuminate a photoelastic specimen of 15 15-cm square. The TDI save mode is turned on before releasing the ball for impact. After the impact, the LED micro-flash illuminates the specimen for 1 ms and the photoelastic fringes are recorded somewhere along the length of the TDI image. It is possible to cut and paste the images recorded after different time delays to visualize a dynamic scene. Fig. 7 depicts propagation of stress waves in a polycarbonate photoelastic model. Photoelastic liquids such as milling yellow provide the potential for using photoelasticity to analyze dynamic fluid mechanics problems. Fig. 8 shows the
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
11
Fig. 8. Dynamic photoelastic patterns generated by a ball dropped into milling yellow solution.
Fig. 9. Schematic diagram for dynamic phase shift photoelasticity.
dynamic fringe patterns generated by the impact of a steel ball into a tank of milling yellow solution.
4. Dynamic phase-shifting photoelasticity 4.1. Experimental set-up Based on the recently developed two-load to phase-shifting technique [20,21], a system for dynamic phase-shifting photoelasticity is developed. The schematic diagram of this system is shown in Fig. 9. This is standard circular polariscope with a Multispec ImagerTM including four groups of quarter wave-plates and analyzers. The operation principle of this system can be described briefly as follows. A beam of light passes through the polarizer and a quarter-wave plate resulting in a circularly polarized light. After transmitting through a stressed birefringent material, its optical energy is split by the Multispec ImagerTM into four paths along the same direction. In each path, a different configuration of quarter-wave plate and analyzer is inserted to generate the required phase-shifted image. The four groups of quarter wave-plates and the analyzer are placed in a single slide, which then is integrated into the Multispec ImagerTM device. Four images are recorded on a single CCD array. The
12
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
A 45 °
135 °
A
Q2
Q2
A Q2
A 45 °
Q2
90 °
Fig. 10. Four configurations of the second quarter-wave plate and the analyzer when the axis of polarizer and the fast axis of the first quarter-wave plate are set as in Fig. 1. Q2 : the slow axis of the second quarterwave plate; A: the analyzer.
Fig. 11. Dark-field image of a ‘‘C’’ shape model subjected to dynamic compression.
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
13
Fig. 12. Schematic diagram of separating the four sub-images in an original image into four individual images.
Fig. 13. Three sets of phase-shifted images recorded at different times during a load cycle.
configurations of four groups of quarter-wave plates and analyzers are shown in Fig. 10. With this system, full-field analysis of a dynamic event is possible. The proposed system demonstrated using a ‘‘C’’ shape model (Fig. 11). The stress in section A is a combination of compression and bending and serves as a good example for evaluation of this system since for beam bending the stress on either side of the neutral axis have opposite signs. Cyclic load is applied using a tensile testing machine, thus generating the dynamic event. The size of the active area of the CCD
14
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
Fig. 14. (a) Isochromatic maps for the three samples obtained by using two-load-step to phase-shifting method.
Fig. 15. Unwrapped phase maps of the three examples and their distributions along the same line. The fringe orders at the end points of specimen are given for comparison.
is 640 480 pixels. A monochromatic filter centered at 575 nm is used with a white light source. A series of images, each of which comprising four phase-stepped images, is recorded. The isoclinic and isochromatic parameters are determined using
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
15
the two-load method using two sets of phase shifted images recorded at two different instants of time. The actual procedure, schematically shown in Fig. 12, involves two steps. First, for a given image, the four sub-images contained in each image are separated into four individual images having the same size and with no physical shift between them. This is achieved by placing a reference mark on the specimen prior to the experiment. Using this reference the four sub-images are cropped from the original image and saved as separate data matrices. With these sub-images, the phase-shift algorithm (20) is then applied. The three sets of images recorded at different times during a single load cycle are shown in Fig. 13. Figs. 14 and 15 show the individually wrapped and unwrapped phase retardation maps after the phase shift algorithm is invoked.
5. Conclusion Application of a TDI camera in dynamic photoelastic recording is demonstrated. High speed TDI provides faster imaging rates. This could be readily used for streak and strobe recording in dynamic photomechanics. Since the CCDs’ are more sensitive than the conventional photographic film, it is possible to use low cost, low voltage semiconductor light sources as micro-flash. The performance of the system is demonstrated by recording streak patterns of dynamically loaded photoelastic models. This experiment suggests the application of line scan sensors for dynamic streak photoelastic investigations. The line scan sensors offer faster scanning rates which could record the dynamic photoelastic patterns from stiffer models with higher stress wave velocities. Dynamic phase shifting can be accomplished using an off-theshelf system to split the light into four components each with an appropriate phase shift. Possibility of use for other dynamic interferometry also exists.
References [1] Dally JW. Introduction to photoelasticity. Exp Mech 1980;20:409–16. [2] Field JE. High-speed photography: techniques and applications. Opt Eng 1982;21:709–17. [3] Hiller WJ, Kowalewski TA. Application of the frame-transfer charge-coupled devices for high speed imaging. Opt Eng 1989;28:197–200. [4] Fang SJ, Hemann JH, Achenbach JD. Experimental and analytical investigation of dynamic stress concentrations at a circular hole. Trans ASME J Appl Mech 1974;41:417–22. [5] Burger CP, Chona R, Khanna SK, Thomas MR. A high speed imaging system employing laser light acousto-optics. Proceedings of the SEM Conference 1994, p. 718–24. [6] Bretthauer B, Meier GEA, Stasicki B. An electronic Cranz Schardin camera. Rev Sci Instrum 1991;62:364–8. [7] Asundi A, Sajan MR. Low-cost digital polariscope for dynamic photoelasticity. Opt Eng 1994;33:3052–5. [8] Asundi A, Chan CS, Sajan MR. 360-deg profilometry: new techniques for display and acquisition. Opt Eng 1994;33:2760–9. [9] Michael GF, Rudolph HD. A large area TDI image sensor for low light level imaging. IEEE Trans Elect Dev 1980;ED-27:688–1693.
16
A. Asundi et al. / Optics and Lasers in Engineering 38 (2002) 3–16
[10] David LG. TDI imaging in industrial inspection. Proc SPIE 1989;1194:36–45. [11] Tuzi Z, Nisida M. Photoelastic study of stresses due to impact. Phil Mag 1936;21:448–73. [12] Culver RS. Measuring dynamic strain profile and history with a drum camera. Exp Mech 1970;10:288–93. [13] Dally JW. In: Lagarde A, editor. Recording systems for dynamic photomechanics, static and dynamic photoelasticity and caustics. Springer, Italy, 1987, p. 248–63. [14] Frocht MM, Flynn PD. On the photoelastic separation of principal stresses under dynamic conditions by oblique incidence. In: Frocht MM, Leven MM, editors. PhotoelasticityFthe selected scientific papers. Pergamon Press, London, 1969. [15] Dally JW, Halbleib WF. Dynamic stress concentrations at circular holes in struts. J Mech Eng Sci 1965;7:23–7. [16] Edgerton HE. Strobe photography: a brief history. Opt Eng 1984;23:SR100–5. [17] Taylor CE, Bowman CE, North WP, Swinson WF. Application of lasers to photoelasticity. Exp Mech 1966;6:289–96. [18] Becker H. Simplified equipment for photoelastic studies of propagating stress waves. Proc SESA 1961;18:214–6. [19] Asundi A, Sajan MR. TDI camera application in dynamic photomechanics. Exp Tech 1994;8(5):9–11. [20] Asundi A, Liu Tong, Chai Gin Boay. Determination of isoclinic and isochromatic parameters using three-load method. Meas Sci Technol 2000;11:532–7. [21] Asundi A, Liu Tong, Chai Gin Boay. Full-field automated photoelasticity using two-load-step method, 2002, in review.