ADDITIVE MANUFACTURING BASED ON MULTIPLE CALIBRATED PROJECTORS AND ITS MASK IMAGE PLANNING

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1 Proceedings of the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference August 15-18, 2010, Montreal, Quebec, Canada DETC ADDITIVE MANUFACTURING BASED ON MULTIPLE CALIBRATED PROJECTORS AND ITS MASK IMAGE PLANNING Chi Zhou Yong Chen* Daniel J. Epstein Department of Industrial and Systems Engineering University of Southern California Los Angeles, CA 90089, U.S.A. *Author of correspondence, Phone: (213) , Fax: (213) , ABSTRACT Additive manufacturing (AM) processes based on mask image projection such as digital micro-mirror devices (DMD) have the potential to be fast and inexpensive. More and more research and commercial systems have been developed based on such digital devices. However, a digital micro-mirror device such as a digital light processing (DLP) projector has limited accuracy and resolution. Based on the principle of pixel bling, we present a novel AM process by using multiple DMDs to significantly improve the accuracy and resolution of built components. In order to achieve the desired pixel bling result for a given layer, it is critical to plan the mask images that will be used by the multiple projectors. In addition, the mask image planning needs to compensate the calibrated light intensity in a projection image that is usually non-uniform and non-linear. We present a general optimized pixel bling method based on direct discrete search (DDS). Its mathematic model and computing method for the mask image planning are presented. Various test cases have been performed to verify its effectiveness and efficiency. KEYWORDS Additive Manufacturing, Mask Image Projection, Pixel Bling, Multiple Projectors, Optimization. 1 INTRODUCTION Current market trs such as consumer demand for variety, shorter product life cycles, and higher product quality have resulted in the need for more efficient and robust manufacturing paradigm. Additive manufacturing (AM) can fabricate parts directly from computer-aided design (CAD) models without part-specific tooling and fixtures. Thus it can significantly shorten product development cycle while satisfying customized design requirements. In this paper, we are interested in the AM processes based on mask image projection devices. In this process, the 3-Dimentional (3D) CAD model of an object is firstly sliced by a set of horizontal planes. Each slice is then converted into a 2-Dimentional (2D) image which serves as a mask corresponding to the layer to be built. The mask image is then projected by a light projection device onto a surface to form the layer of the object. By repeating the process, 3D objects can be formed on a layer-bylayer basis. This process can form a whole layer of multiple objects simultaneously and dynamically. Therefore, it provides a potentially faster approach that is indepent from part size and geometry. It also removes the requirement of an accurate XY motion control subsystem. Therefore the process can be relatively inexpensive. Several research systems have been developed before based on the mask image projection process [1-15]. Both light crystal display (LCD) and digital micromirror devices (DMD) have been used as light projection device, and visible-lightcured photopolymer or UV curable resin have been used as the raw material. LCD as a dynamic mask has limited optical efficiency including large pixel size, low filling ration, low switching speed, low optical contrast, etc [9]. Compared with LCD, DMD (Texas Instruments, Dallas, TX) offers better performance in terms of optical fill factor and light transmission, thus it is more widely used for projection based stereolithography. Several commercial systems based on DMD have also been developed such as the Perfactory system from Envisiontec Gmbh [16] and the V-Flash system from 3D Systems Inc. [17]. Sophisticated modeling and algorithms have been proposed to facilitate the performance and improve the resolution of sliced images [18-19]. Physical curing process is also investigated and process parameters are calibrated to improve the resolution [20-22]. Due to the limited pixel number of a DMD device (e.g pixels), most research systems [1-15] use a platform 1 Copyright 2010 by ASME

2 that has a small area size (less than 5 5 mm) to achieve high accuracy and resolution. Therefore the systems can mainly fabricate micro parts. Hence the related process is named mask projection micro stereolithography. In this paper, we are interested in building parts with much larger size. Accordingly a platform with much larger area is required (e.g mm as used in our system). Hence we name our process mask projection large-area stereolithography. An illustration of the process is shown in Figure 1. Notice each pixel s size related to such a bigger platform increases accordingly (e.g. ~0.265 mm in our system). This poor resolution, without intelligent mask image planning, can not guarantee good part quality. To improve the resolution and accuracy of such a process, we proposed an optimized pixel bling method in our previous work [23]. By intelligently manipulating pixels gray scale values in a projected image, we can achieve exposure levels within a layer in a resolution that is higher than a pixel size. In addition, the optical components (lens and mirrors) have inherent accuracy limitations. Therefore, each pixel has some fuzziness or image blurring. To study the effects of optical defects, we also presented a calibration method to capture the non-uniformity of a projection image for a low-cost off-theshelf DLP projector [24]. 2 OVERVIEW OF OUR PREVIOUS WORK 2.1 Pixel Bling for Projection-based AM Process As one of the most important process parameters, a well planned mask image is especially important for the mask projection large-area stereolithography. An optimization pixel bling method [23] has been presented for the mask image planning. The method is mainly based on: (1) the light intensity of a pixel follows Gaussian distribution; (2) the light beam of a pixel will spread to its neighboring pixels; (3) the light intensity at any position is actually the sum of the light intensities contributed by all the neighboring pixels (defined as pixel bling); (4) a desired energy input can be achieved by intelligently manipulating the grayscale values of each pixel; (5) such exposure energy will then lead to a cured layer with desired shape. We mathematically formulate the pixel bling problem in an optimization model, and use optimization tools to solve the problem. Both simulation and physical experiments have been carried out to validate the effectiveness and efficiency of the optimized pixel bling method. Figure 2(a) shows an example of dimensional accuracy study. Notice the traditional slicing method will lose the small portion while the pixel bling method can get the shape quite close to the original one. Figure 2(b) shows the case of surface quality study. It is obvious that the building result based on the optimized pixel bling method will result in a much better surface quality. (a) Dimensional accuracy study Figure 1: Large-area mask projection stereolithography. In this paper, we investigate the use of multiple projectors in the mask projection large-area stereolithography, especially the mask image planning for multiple projectors. As one of the most important process parameters in the projection based AM processes, the mask images play a critical role in improving the accuracy and resolution of a built component. The remainder of the paper is organized as follows. Section 2 gives a brief review of our previous work including optimized pixel bling and projection image calibration. In Section 3 we present an overview of different ways of using multiple projectors in the projection-based AM process. We present a mathematical model and a direct discrete search (DDS) method for the mask image planning in Section 4. Our investigation on the setting of critical parameters is presented in Section 5. The experimental result and analysis are discussed in Section 6. Finally, we conclude and discuss future work in Section 7. (b) Surface quality study Figure 2: Two test cases for optimized pixel bling [23]. 2 Copyright 2010 by ASME

3 2.2 Projection Image Calibration for Optimized Pixel Bling A single Gaussian function is assumed to approximate the light intensity of each pixel in the pixel bling method presented in [23]. This assumption may not be suitable for a low-cost off-the-shelf DLP projector. Due to the low cost optic components used in such a projector, the projection image may have distortion and the light intensity is non-uniform. These geometric and energy differences would affect our pixel bling results. We presented a novel method to calibrate such non-uniformity of projection image [24]. Based on a built calibration system, the calibrated result for an off-the-shelf DLP projector is shown in Figure 3. It shows that (1) the pixels are non-uniformly distributed in the image; (2) The shapes and orientations of the pixels are changing gradually and smoothly; (3) The center portion has less distortion; (4) The pixels are not evenly distributed. Other experiments also show that: (5) the distribution is consistent for different grayscale levels. The part quality for large-area mask projection stereolithography can be significantly improved by incorporating the calibration results in the mask image planning framework. techniques for such purpose are shown in Figure 4 and Figure 5 respectively. Projector 1 Projector 2 Projector 4 Projector 3 Projector 5 Projector 6 Projector 7 Projector 4 Projector 8 Projector 9 Platform Figure 4: Multiple projectors by overlapping areas [25]. Figure 3: Pixel calibration framework and relate results for a DLP projector [24]. 3 OVERVIEW OF PROCESSES BASED ON MULTIPLE PROJECTORS 3.1 Motivation As discussed before, due to the limited pixel number of a DMD device, the most commonly used approach for building parts with high resolution is to shrink down the working area. For example, for a typical DMD chip that has pixels, we need to shrink down the platform size to 5 5 mm 2 in order for a pixel size to be ~5μm. Previous methods on using multiple projectors to achieve a bigger building area have been following such a strategy. Two most commonly used Projector Projector 4 Platform Figure 5: Bigger area by moving projectors [26]. 3 Copyright 2010 by ASME

4 In Figure 4, the technique is based on arranging multiple projectors side by side so each projector will cover a smaller portion of the building platform [25]. In Figure 5, another technique is based on mounting a projector on a linear XY stage, which will then translate the projector to cover the whole building platform [26]. However, these two techniques either need lots of projectors or need very accurate linear XY stage. Both of them also have high cost but low efficiency. Thus, it is desirable to develop a new method that can use a small amount of projectors and can achieve high efficiency and low cost. 3.2 Multiple Projectors Based on Optimized Pixel Bling Instead of shrinking down the working area of a projector, we present a novel process by following a different strategy of using multiple projectors. Our approach is based on the aforementioned optimized pixel bling method. As shown in our previous work [23], the pixel bling of light intensity provides us tremous capability in selectively solidifying resin into a desired shape. We can improve the accuracy without reducing the working area of the projector. However, finding a good solution to achieve desired shapes is sometimes difficult especially for geometries with complex features. This is mainly due to the limited design variables (i.e. number of pixels) while the constraints are tight. Hence the feasible search space is limited. If multiple projectors are used, we may get multiple times design variables compared to those in one projector. Consequently the accuracy and resolution of a given image may be further improved by solving a related optimization model. We propose a novel way of using multiple projectors to achieve a higher accuracy and resolution. The core idea of the proposed method is illustrated in Figure 6. Suppose the light intensity K c related to the critical energy level E c is 0.5. Consider two ideal pixels with sizes mm. If we set their light intensity at 0.35, only the overlapping region ( mm) will be cured, since its light intensity (0.7) is greater than K c. Therefore, it is feasible to build a feature that is smaller than the pixel size of each projector. Hence, the main idea of the mask projection large-area stereolithography based on multiple projectors is: (1) arrange multiple DLP projectors to have a designed overlapping area as shown in Figure 6.right, i.e. shifting each of n projectors by 1/n of a pixel; and (2) control pixels light intensity and exposure time intelligently to achieve desired energy distribution after pixel bling. A feasibility study based on the simulation of ideal pixels has been performed. A test example is shown in Figure 7. For a sliced image of a hearing aid shell (refer to Figure 7.left), three projection images at a lower resolution can be computed (refer to Figure 7.right). The three images are positioned such that each image is shifted by 1/3 of a pixel size (refer to Figure 6.right). The overlapped images will have a pixel bling result that is close to the input image at a 3 resolution compared to that of the projection images (refer to Figure 7.middle). Compared to the previous methods in Section 3.1, the significant benefits of our method are: (x1, y1) (1) Less number of projectors is required. Compared to the technique as shown in Figure 5.a, the proposed method will only require 2 and 3 projectors (instead of 2 2 and 3 2 projectors), respectively, to achieve 2 and 3 times higher XY resolution. (2) No moving mechanisms are needed. Compared to the technique as shown in Figure 5.b, the proposed building process will consequently be much faster and have a lower cost. K1 = 0.35 K = 0.7 (x3, y3) K2 = 0.35 liquid (x1, y1) Solid (x3, y3) liquid Figure 6: Multiple projectors based on optimized pixel bling. Figure 7: Input image with 3x resolution of each projector. 4 MODEL AND ALGORITHM BASED ON MULTIPLE CALIBRATED PROJECTORS 4.1 Mathematical Model We first illustrate the pixel bling process in Figure 8 before presenting the mathematical model. The 3D solid model (a) is firstly sliced by a set of horizontal planes. Each slice is converted into a 2D image (b) by some sampling methods. In our case, we use super sampling. That is, the sampling resolution is n times higher than the projector s resolution. Hence for each pixel of the projecting image, we subdivide it into n n sub-pixels and use the sub-pixel resolution as the 2D image s resolution. According to the target image (b), we use some algorithms (e.g. Geometric algorithm, linear programming optimization and iterative optimization algorithm) to get a mask image (c). The grayscale level of each pixel H in mask image (c) represents the corresponding light intensity. Since each pixel follows a Gaussian function (d) [24]. The mask image will convolute with the Gaussian function and get the accumulated intensity (e) as I = H G. According to the polymerization reaction process, the material will be cured only when the energy is greater than the critical energy. Thus, we 4 Copyright 2010 by ASME

5 get the bling result (g) as F ' = T( I), where T is the gate function (f) with threshold of critical energy and F ' (g) is a binary image representing the bling result. Comparing the bling result F ' with the target F, we get the error image E (h), and the colorful pixels show the errors. Hence our objective is to minimize the errors while satisfying the given constraints. H G I T F' Figure 8: Pixel bling process. In the original model presented in [23], we assumed the DLP projector is uniform and all the pixels have an identical standard Gaussian distribution. However, the calibration results showed that the commercial projectors have certain distortion for pixels at different regions [24]. Thus the original model needs to be adjusted based on the calibration result for multiple projectors. Besides, we also have to consider the effects from all the multiple projectors for each small pixel and integrate the shifting parameters in the model. Considering all the factors, the mathematical model for the mask projection micro stereolithography based on multiple projectors is presented as follows. Let m denote the number of projectors, x, t y denote the offset of projector t, the update t model is shown as follows: Where: F' 2 1 ( p x0 x )cos( ) ( 0 )sin( ) t θ q y y t θ Gtpq ( H ) = A exp 2 σ x A 2 ( p x0 x )sin( ) ( 0 )cos( ) t θ + q y y t θ σ y H A =, σ H 1 3 x H σ x =, σ 1 3 y H σ y E (1) (2) = (3) I =, I = 1,2, 255 (4) 255 In the model, x 0, y 0, A, σ x, σ y are the calibrated parameters for big pixel (i, j) with full light intensity (gray scale =255 or H =1). A, σ x, σ y are the Gaussian parameters for big pixel (i, j) with partial light intensity (gray scale<255 or H <1). Compared to the original model, the objective function and the constraints are almost the same. However, the Gaussian parameters are different and derived from the calibrated data. Hence the new formulated model is much more complicated and harder to solve than the original model. Even though all the calibrated parameters are constant coefficients, the shape parameters are not linearly decreasing with the light intensity. Thus the new model can not be solved by linear programming solvers. Moreover, due to the physical constraints, the light intensity has limited levels, i.e, H can only take 255 discrete numbers. Hence the new model loses the continuity. All the derivative based optimization methods are not applicable anymore. In the original model, the two linear programming models can only be solved with small scale problems with simple geometry. For more complicated problems, there are no feasible solutions because of mutually exclusive constraints. In our previous work, we also resorted to an advanced tool infeasibility analysis feature (IIS) of CPLEX, which can give us a good solution and report the hard constraints. However, for multiple calibrated projectors, we found this solution is far worse than the optimal solution for most cases. Thus, a new computing method is needed for solving the optimization model defined in (1). In 2D printing industry, an iterative direct binary search (DBS) method has been widely used and verified to be effective in creating high quality halftone images [27-28]. Instead of binary variables considered in the DBS method, the variable H in our model is discrete and can take 255 values. Hence, inspired by the DBS method, we proposed an iterative method named direct discrete search (DDS) to solve the optimized pixel bling for multiple calibrated projectors. 4.2 DDS Algorithm Starting with an initial solution, the direct discrete search method iteratively scans the original image in raster order and gradually perturbs the light intensity of pixels in the boundary region. It accepts the changes that can reduce the error and progressively updates the best solution. The DDS method has no specific mathematical requirement on the model. However, it is a heuristic optimization method, like any other local optimization method, DDS can not necessarily find the global solution. But it can give us a sub optimal solution in reasonable time, thus it is more flexible and robust than linear programming solver and can properly fit our purpose. Similarly to [23], we conduct a two-stage optimization process based on error and separation respectively. Error is the difference between the bling result and target, which is discussed in the previous subsection. Since our problem is a multi-objective optimization problem, after achieving the optimal error, we further separate the pixels with different values (0 or 1) to the largest extent without increasing the error. In Figure 8(e), we are expecting the light intensity for each black pixel is as high as possible, whereas for each white pixel 5 Copyright 2010 by ASME

6 the light intensity is as low as possible. Higher separation is better for polymerization and can achieve higher surface smoothness. To reduce the computation cost, we take advantage of the prior knowledge and only consider the variable and constraints that are associated with the boundary regions. Since the main framework for the two stages are identical except the objective, we will only present the frame work for the first stage (i.e. optimizing the error). The DDS algorithm is shown in Figure 9. //first stage for minimal error use geometric method to get an initial solution as input Initialize by recording the current effects as the best effects, the current light intensities as the best light intensities, and the current error as the best error for each iteration for each projector p for each big pixel (i, j) p perturb light intensity of (i, j) p if ( i, j) p Β p, then for each small pixel ( p, q) S update accumulated effects according to recorded best effect and best light intensity update current error if current error < best error, then update best error, best effect and best light intensity else change back current error, current effect and current light intensity Figure 9. Framework of the DDS algorithm. We can notice in the algorithm: (1) DDS is an iterative optimization method. Hence a maximum iteration number can be set as the termination criteria. (2) The light intensity has 256 levels. We perturb the light intensity of a big pixel by randomly picking a new level in [0, 255]. (3) We only consider the pixels that can affect the boundaries. For the interior pixels, we trivially set them as 1 or 0 according to the target. This strategy has no affect on the optimization result but can improve the efficiency dramatically. (4) We use the calibrated parameters to calculate the accumulated effect of all the small pixels that are affected by the big pixel, and update the errors accordingly. Since a big pixel only affects a small region, the computational cost can be reduced. (5) We judge the new solution by comparing the result related to that of the best solution we ever have. Accordingly the best solution can be updated. Figure 10 shows the optimization process for a test case of a dragon tail model. As can be seen from the figure, the two optimization criteria, error and separation [23], are optimized based on the DDS method. In stage 1, the error (indicated by red line) gradually decreases; in stage 2, the separation (indicated by blue line) gradually increases. We show the corresponding bling results in the figure. Compared to the given image, the related errors are also given in the figure (green and red pixels are extra and missing portions respectively). Figure 10: Optimization process for DDS method. 5 THEORETICAL DEVELOPMENT ON MULTIPLE PROJECTORS According to our calibration result, the light intensity of a pixel follows a Gaussian distribution as shown in Figure 11. Compared to an ideal pixel, such a Gaussian distribution is essential in order for the optimized pixel bling to work. Figure 11: Gaussian distribution approximation. In order to understand the effects of the sizes of a Gaussian distribution especially its variances (σ ), we first illustrate the convolution models of five neighboring pixels in 1-dimension. An example is shown in Figure 12 for three different variances (σ = 0.75, 1, and 1.5). It can be noticed that different Gaussian distributions will lead to different characteristics in the convolution results. Hence it is critical to understand the relation between the variance in the Gaussian distribution and the achievable optimization result. This can provide us guidelines in hardware construction especially in optics design. 6 Copyright 2010 by ASME

7 (a) σ = 0.75 (b) σ = 1 (c) σ = 1.5 Figure 12: Convolution effects with different Gaussian distribution. Based on the aforementioned DDS method, we test different cases under different variances ( σ ) and different subdivision levels ( n ). The results on such relation are shown in Figures 13 and 14. As can be seen from Figure 13, both the tests on dragon model and round-mech model under different subdivision levels have the similar results between the error and variances. The best solution can be achieved when the variance is ~1.0, which is the variance we used in our prototyping system. Using two projectors essentially doubles the variance and makes the problem harder. Thus, we may need to adjust the variances of each projector in the multiple projectors system. As a comparison, we run the same simulation based on two projectors. The results are shown in Figure 14. Based on the simulation results, the best solution can be achieved when the variance is ~0.75. In addition, comparing the results in Figure 13 and 14, the errors reduce significantly. This verifies that, the more projectors we have, the higher accuracy and resolution we can obtain. (b) Round-Mech Model Figure 13: Error comparison under different variances and subdivision levels (one projector). (a) Dragon Model (a) Dragon Model (b) Round-Mech Model Figure 14: Error comparison under different variances and subdivision levels (two projectors). 7 Copyright 2010 by ASME

8 6 TESTING RESULTS AND ANALYSIS 6.1 Dimensional Accuracy Tests For comparison between a single projector and multiple projectors, we adopt the same test cases as shown in [23] to verify the proposed method. Four test cases are shown in Figure 15, which include a square, round-mech part, dragon and dragon tail models. In all the tests, we assume σ =1.0. (a) Square (b) Round-mech Figure 16: Dragon tail model at different portion projector. Table 2: Comparison between different projectors for dragon tail model. #Projectors Methods (0) (1)Left (2)Left (3)Right (4)Right Center Top Bottom Top Bottom Geometric DDS Geometric DDS Geometric DDS (c) Dragon (d) Dragon tail Figure 15: Three test images. The test results of the four models are given in Table 1. It is shown from the results that the multiple projectors based systems can improve the accuracy and surface quality. In addition, better accuracy can be achieved with more projectors. It is also indicated by the results that the DDS algorithm can solve very complex geometries effectively for the multiple projector based systems. Table 1: Comparison between different projectors for square, round-mech and dragon models. #Projectors Methods Geometric DDS Geometric DDS Geometric DDS n= square n= n= n= round n= n= n= dragon n= n= We also position the dragon tail model at different portion of the projection image (refer to Figure 16). As shown in the figure, pixels have various orientations and sizes at different positions. Based on the calibrated results, we use Gaussian functions with different parameters in the optimization process. The results for different number of projectors are shown in Table 2. It can be seen that, compared to the geometric method, the DDS method can dramatically improve the surface quality. 6.2 Feature Resolution Tests The resolution is one of the most important criteria in micro-fabrication processes. The proposed multiple projectors based model and DDS method may be applicable to the microfabrication processes by achieving both high resolution and large building area at the same time. To verify its effectiveness in improving the building resolution, we test the method by using a two dimensional array model. Figure 17(a) shows the CAD model and Figure 17(b) shows a sliced layer image. The cross section of each rod is a square whose size is 4 4 pixels. (a) CAD model (b) Cross section Figure 17: A test case of a 2D array model. The simulation results are shown in Table 3, including the mask image, accumulated light intensity, bling result and the generated errors by Geometric method and DDS method. Table 3 (a) and (b) show the results for one projector and two projectors respectively. For this complex problem, both the geometric method and DDS method based on one projector can not generate part as the target. The errors are indicated by the green color around the corners of the squares. Even with two projectors, the geometrical method can still not solve the problem. Only the DDS method based on the two projectors system can solve the problem and exactly achieve the target. 8 Copyright 2010 by ASME

9 Table 3: Comparison between different projectors for 2D array model. (a) One projector Mask Image Accumulated Effect Bling Result Error Geometric 160 DDS+ Calibration 160 Mask Image (b) Two projectors Accumulated Effect Bling Result Error Geometric 160 DDS+ Calibration 0 9 Copyright 2010 by ASME

10 7 CONCLUSION AND FUTURE WORK Mask image planning is an important process planning step for the mask projection large-area stereolithography. Optimized pixel bling is a mask image planning technique that can significantly increase the accuracy and resolution of such additive manufacturing process. To further improve its accuracy and resolution, we propose a novel process based on multiple calibrated projectors. We present the mathematical model for the mask image planning of the process. Due to the nonlinear and discrete nature, a direct discrete search method is presented for the mask image planning, which is robust and flexible for pixels with complex calibrated parameters. Various cases have been tested to verify the effectiveness of the proposed process. Our future work includes the following: (1) we would like to conduct physical experiment to practically verify the proposed method; (2) the current DDS method perturbs the light intensity with uniform probability. 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