Flatness Measurement of a Moving Object Using Shadow Moiré Technique with Phase Shifting

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1 Flatness Measurement of a Moving Object Using Shadow Moiré Technique with Phase Shifting Jiahui Pan, Dirk Zwemer, Gregory Petriccione, and Sean McCarron AkroMetrix, LLC, 700 NE Expy., C-100, Atlanta, GA, 3035 ABSTRACT A novel method based on the shadow moiré and phase shifting techniques has been developed to measure the flatness of an object moving at a constant speed. In this method, we propose an angled grating approach to achieve phase shifting with a simple and low-cost system. A grating plane is positioned at a small angle with respect to the axis of motion of the object along a continuous conveyor. While the object is moving horizontally, the vertical distance between the grating and the object changes, creating a series of phase shifts. A camera positioned above the grating captures a series of phase-shifted images for 3-D shape reconstruction. Unlike the traditional shadow moiré technique with phase shifting, this technique removes the need for a high-precision vertical motion system and allows a moving object to be measured without cessation. Since we use a phase calculation algorithm where phase shift is a free variable, the system performance is more tolerant of variations in grating angle and sample speed. The proposed technique has applications in a wide variety of areas such as electronics, metal fabrication, paper, textile, and polymer film industries, where on-line product inspection is a requisite. Keywords Flatness measurement, shadow moiré, phase shifting, angled grating, on-line inspection 1. INTRODUCTION Surface flatness is a common measurement specification in manufacturing industry. Flatness critically affects the reliability and assembly yield of electronic products, the cosmetic appearance and handling characteristics of paper products, as well as the mechanical fit and functionality of fabricated metal components. The ability to distinguish and reject components whose nonflatness exceeds user specifications is valuable on the production line because it allows the manufacturer to maintain product quality, and identify and avoid processing problems in manufacturing. There are many flatness measurement technologies applied in manufacturing. Use of a physical barrier is the simplest method for flatness inspection. In this method, a slot or other physical restriction is set up so that the object will only pass through if it is sufficiently flat. A single point sensor is another approach for flatness evaluation. Usually a height sensor, such as a dial indicator, is applied to multiple points on the sample surface. A calculation is made to acquire surface flatness according to these measures. The barrier and single point sensor methods are inexpensive and good for hand sorting of small quantities. However, they do not provide full-field information or automated quantitative processing. Single point sensor arrays or linescan cameras are then used for on-line automated flatness measurement. The sample passes under the sensors, each of which makes a series of measurements along a single line using optical, direct contact, or other principles. Computerized analysis is used to extrapolate the individual line data into a form that can quantify the flatness. Garcia has proposed a flatness inspection system for steel strip production lines using laser and linescan cameras [1]. The system measures the relative length of the material at five points across the strip width. Flatness indices, which represent the sample flatness, are obtained by length comparison. The measurement system works in real-time, but does not have a full coverage on the measuring surface. In order to achieve full-field data, projection moiré and shadow moiré are used. They are the most widely used techniques for flatness measurement because of their non-contact nature, full-field measurement capability and simple implementation [-]. Phase shifting technique is used together with moiré topography to acquire higher resolution, automatic fringe counting, and high tolerance to spatial variations of the recorded intensity values [5]. However, the use of phase shifting requires the sample surface to be motionless during measurement, which is difficult to implement on some manufacturing lines, where measuring surface flatness on a continuously moving surface is a requirement. For example, some materials are formed, woven or extruded on a continuous basis, such as paper, where the production flow cannot be stopped to make a measurement without introducing flaws into the material. Some other samples cannot readily be stopped and started because of sample characteristics, such as heaviness, or the requirements of the remainder of the production line. There are also some techniques based on moiré topography to measure the flatness of a moving object. Paakkari developed an automatic system

2 for measurement of the flatness of large steel plates based on the projection moiré technique [6]. An intensity-based cumulative method was used for phase calculation, which makes the fringe interpretation possible with one image only, and as a result makes dynamic measurement easy to implement. Zwemer and Hassell have patented a shadow moiré method that can measure surface flatness of a moving object [7]. In this method, a stroboscopic light source is used and acted as an optical shutter for image acquisition. Two images are recorded while the object is moving. Image subtraction and edge counting algorithms are used for fringe analysis. The drawbacks of these methods are their low measurement accuracy and difficulty in automatic data processing compared to the phase shifting method. In this paper, we propose an angled grating method based on the traditional phase-shifting shadow moiré technique to measure the flatness of a moving object. The grating is tilted at an angle with respect to the conveyor bed so that a series of phase shifts will be introduced while the sample passes under the grating. The measurement principle and system setup are presented in Section. In Section 3, a phase shifting algorithm with an undefined constant phase shift is described. With this algorithm, the measurement system is less sensitive to the grating angle and the conveyor speed. Experimental results presented in Section verify the feasibility and effectiveness of the proposed method. It was concluded that the angled grating method is a good means for low-cost and dynamic flatness measurement..1 Shadow Moiré with Phase shifting. PRINCIPLE Shadow moiré is a full-field optical method for measuring relative vertical displacement of continuous opaque surfaces [8-10]. This method is based on the geometric interference of a shadow grating projected on the sample surface and a real grating on a flat reference surface. Fig. 1 shows the principle of the shadow moiré technique. Light passes through the reference grating at an oblique angle,, and casts a shadow of the grating on the sample. This shadow grating is observed back through the reference grating at a different angle,. The overlap of the shadow and real gratings is a periodic function of the distance between them. When the surface of the specimen is curved or warped, a series of dark and light fringes (moiré fringes) are produced as a result of the geometric interference pattern created between the reference grating and shadow grating. Each successive fringe represents a height change of the sample surface of W, the height per fringe. W can be calculated with the following equation: p = tan α + tan β W (1) Where p is the pitch of the grating (center-to-center distance between lines), is the angle of illumination, and is the angle of observation. The analysis of static moiré patterns suffers from the need of cumbersome fringe counting and low accuracy. Phase shifting is then introduced to improve the resolution of the moiré techniques [11-1]. In theory, the measurement resolution of the phase shifting shadow moiré method is 1/56 of a fringe height for use with an 8-bit digitizer. But in practice, the effective resolution can be lower due to the experiment situation [13]. Additionally, the fringe counting process is fully automated and the gradient from fringe to fringe across the sample is automatically determined by using the phase shifting method. A phase shift in the traditional shadow moiré system is typically introduced by vertically translating either the sample or grating using a precision motion system. This makes the measurement system not suitable for measuring a continuously moving object. The reason is that each vertical translation of the grating requires a stabilizing time delay, and the sample must stop to allow the motion system to perform a series of phase shifting during the measurement cycle. Besides, the motion system is typically expensive, especially if sample or grating is large or heavy, and not practical to use in some circumstances such as a heating environment. In this paper, we modify the current shadow moiré system and propose an angled grating approach for measuring the flatness of continuously moving parts without any motion system. Light in Light out Grating p Object Fig. 1 Principle of Shadow Moiré.

3 Phase Grating position Shift Grating position 1 Sample Conveyor (a) Conventional Phase Shifting Static Approach Phase Shift Sample-Image 1 Grating Sample-Image Conveyor (b) Angled Grating Phase Shifting Dynamic Approach Fig. Comparison of static and dynamic approaches of phase shifting.. Angled Grating Method In the conventional phase shifting method, the sample must first be brought to a stop, and then the grating is translated vertically with respect to the sample while images are acquired after specific height shifts. In the angled grating method, the sample is moved continuously along the axis of motion on a belt conveyor. The key feature of this method is the use of a tilted grating, where its plane is aligned at an angle with respect to the axis of motion. The angled grating coupled with horizontal translation of the sample causes the relative height change between the sample and grating. Therefore, the phase-shifted images are created laterally during the movement of the sample without any vertical movement of the grating. The comparison of the two approaches is illustrated in Fig.. The main advantage of the angled grating approach is that the sample does not need to be stopped, which is difficult or impossible in some applications. In addition, the grating does not require vertical translation by means of an expensive highprecision motion system. This approach also allows for a more rapid data acquisition cycle. For example, a typical data acquisition cycle (four images) requires 1- seconds for the conventional phase shifting system shown in Fig. (a), as compared to 150 milliseconds for the angled grating system presented in Fig. (b)..3 System Setup The schematic setup of the angled grating system is shown in Fig. 3. A conveyor carrying a sample moves at a constant speed under a grating mounted above the conveyor and oriented a small angle with respect to the plane of the conveyor. The light source is beside and above the plane of the conveyor bed, with the axis of the line light source parallel to the axes of the ruling lines in the grating plane. A video camera is located above the grating at the same height as the light source to acquire the images. Two photosensors aligned along the direction of motion at the front edge of the grating register the passage of the sample. The speed of each sample is derived from the time difference and known distance between the two sensors. With this Side View Top View Fig. 3 Schematic setup of the angled grating system.

4 speed, a time delay can be properly set so that the image acquisition cycle begins after the sample is completely under the field of view of the camera. In addition, a lateral offset between images can be obtained and used to locate the same points among the intensity images. We use four intensity images to calculate phase and relative displacement in the designated area. Since the conveyor speed is derived before measurement of each sample, the analysis is less sensitive to factors that might vary the conveyor speed, such as electric voltage fluctuations or operator-induced changes. The grating angle should be approximately set such that each shift between images is equivalent to one-quarter of a fringe cycle. The maximum shutter period that can be used is a function of camera resolution, belt speed, and field of view of camera. To capture the image with clarity, the sample should shift less than 1 pixel width while the electronic shutter is open. The size, speed, grating pitch and angle, and other quantitative features of the system are inter-related. Any of these parameters can be varied over a significant range, depending on the application. 3. PHASE SHIFTING ALGORITHM WITH AN UNKNOWN PHASE SHIFT In this work, we use a four-step phase shifting method for the measurement. The common four-step phase shifting algorithm requires a phase shift of 90 degrees. The deviations from this value will introduce significant error into the phase calculation if 90-degree phase shift is assumed. In the angled grating system, if the phase shift must be exactly 90 degrees, a precise relationship is required between the speed of the sample, the angle of the grating, and the interval between image acquisitions, which may be difficult to create and maintain. An improved phase calculation algorithm proposed by Cheng and Wyant [8] was used to address this issue. In this algorithm, the phase shift does not have to be exactly 90 degrees. It can be determined as long as it is a constant between phase steps. Assuming that the phase shift is unknown but constant, the intensity value of each pixel for the four phase-shifted images can be expressed as: ( φ + θ ) ( φ θ ) ( φ 3θ ) ( φ θ ) I = I + cos () 1 0 A I (3) = I 0 + Acos + = I + Acos I () = I 0 + Acos + I (5) Where I 1 to I are the intensity value for each pixel in the four images, I 0 is the intensity bias, A is the intensity modulation, φ is the phase value which is related to the height information, and is the unknown phase shift. Solving for, we obtain: [ 3( I ][ ] ( ) 3) ( I1 ) ( I 3) + ( I1 ) ( I1 ) 3 1 θ = tan (6) and φ at each pixel can be determined as: ( I1 ) ( I 3 ) ( I + I ) ( I + I ) 1 φ = tan tanθ 3 1 (7) With the undefined phase shift angle algorithm described here, the phase can be calculated correctly even if speed or grating angle varies over a wide range from their nominal values. As a result, this algorithm eases the relationship between the vertical phase shift and the horizontal motion of the sample, and makes construction and maintenance of the system much simpler.. EXPERIMENTS A by inch plastic printed circuit board (PCB) was measured as a feasibility test of the angled grating method. The PCB on the conveyor passes under the grating at a known speed of 10 inches per second. The known speed together with the camera frame rate and fringe value is used to design the grating angle with respect to the conveyor plane. If sensors are used at the front edge of the grating, the actual speed of each sample can be determined. This measured speed can be used to set a delay time before the first image is acquired. At this initial experimental stage, the delay time was controlled manually by an operator. A series of four images at fixed time interval is then taken after the delay, while the sample moves under the grating, within the camera field of view. The four phase-shifted images acquired by the camera are shown in Fig. (a) through (d). We can see that the fringe contrast is adequate and the four images have a lateral offset between each. A commercially available

5 part location algorithm is then applied to locate the part and the pixels in the desired measurement area are selected based on the part location results. The phase values of the selected pixels are calculated from the four intensity images with offset, using the constant, but unknown phase shift algorithm described in Section 3. Standard algorithms are used to analyze the phase image as shown in Fig. (e) and the reconstructed displacement data is shown in Fig. (f). This experiment has demonstrated the feasibility of the angled grating method for measuring the flatness of a moving object. The theoretical resolution of this method is ±.5 microns with 100 lines per inch grating and light incidence at 5 degrees. Compared to the static approach, this method may have lower repeatability which needs to be further studied. However, it offers a relatively low-cost system for measuring the flatness of continuously moving parts, which is not achievable with the conventional static shadow moiré system. 5. CONCLUSIONS An angled grating method based on the phase shifting shadow moiré technique is proposed for flatness measurement. Compared to the traditional phase shifting shadow moiré technique, this method removes the need for a high-precision vertical motion system and is able to create phase shift while the measuring object is moving. The unique design of the system enables it to measure sample flatness on a continuous transport system. The relationships involving system parameters, such as grating size and pitch, conveyor speed, camera resolution, and shutter period was discussed. We use a phase calculation algorithm such that the effect of variation in grating angle or conveyor speed is minimized. Preliminary experimental results show the technique to be an effective approach for dynamic or real-time flatness measurement with a wide variety of potential applications in the fabrication and process industries. Future work of error analysis and repeatability study has to be conducted to refine this approach. (a) Intensity image one (b) Intensity image two (c) Intensity image three (d) Intensity image four (e) Phase Image (f) Surface Displacement Fig. An example of data acquisition and processing.

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