Research Papers

Optimized Mask Image Projection for Solid Freeform Fabrication

[+] Author and Article Information
Chi Zhou

Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089chizhou@usc.edu

Yong Chen1

Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089yongchen@usc.edu

Richard A. Waltz

Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089rwaltz@usc.edu


Corresponding author.

J. Manuf. Sci. Eng 131(6), 061004 (Nov 10, 2009) (12 pages) doi:10.1115/1.4000416 History: Received October 10, 2008; Revised September 29, 2009; Published November 10, 2009; Online November 10, 2009

Solid freeform fabrication (SFF) processes based on mask image projection have the potential to be fast and inexpensive. More and more research and commercial systems have been developed based on these processes. For the SFF processes, the mask image planning is an important process planning step. In this paper, we present an optimization based method for mask image planning. It is based on a light intensity blending technique called pixel blending. By intelligently controlling pixels’ gray scale values, the SFF processes can achieve a much higher XY resolution and accordingly better part quality. We mathematically define the pixel blending problem and discuss its properties. Based on the formulation, we present several optimization models for solving the problem including a mixed-integer programming model, a linear programming model, and a two-stage optimization model. Both simulated and physical experiments for various CAD models are presented to demonstrate the effectiveness and efficiency of our method.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 17

A DLP-based system based on optimized pixel blending

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Figure 18

Light intensities for different gray scale levels

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Figure 20

A dragon test case for dimensional accuracy study

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Figure 21

A simple test case for surface quality study

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Figure 1

A mask image planning framework based on optimized pixel blending. In our method, we first used a desired subpixel resolution to slice an input 3D CAD model into a set of 2D images. For each image, we use geometric heuristics to set the pixels’ gray scale values; we then solve the first optimization model to refine the gray scale values for minimizing the blending errors; finally, we solve a second optimization model to get the gray scale values for maximizing separation of boundary pixels with different values.

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Figure 2

Principle of pixel blending. The light energy of three pixels A, B, and C has different shapes and sizes.

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Figure 13

Three test images

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Figure 14

An example of LP1 with IIS. In this case, we set thresholds δ1=2.0 and δ2=1.4. The pixels with values (2.0) and (1.4) in (b) are corresponding to the black and white pixels in (a), respectively. The pixels with values (1.9) and (1.5) are corresponding to the pixels which cannot be satisfied by LP1.

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Figure 15

The accumulative effects of LP1 and LP2 for the dragon model; (a) the accumulative effects of the whole image for LP1; (b) the accumulative effects of a local profile for LP1. The color bar indicates the values of the accumulative effects. The dotted line indicates the target boundary of the profile; and (c) the accumulative effects of the same profile for LP2

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Figure 16

The accumulative effects in the boundary region of the dragon model for LP1 and LP2. In each figure, the horizontal line is the index number and the vertical line is the accumulative values. Two thresholds δ1 and δ2 are also marked in the figure.

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Figure 19

A simple test case for dimensional accuracy study

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Figure 22

Surface quality measurement setup and surface quality comparisons between the traditional and optimized pixel blending methods

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Figure 3

Problem description. Each of the w×h big pixels (i,j) was further divided into n×n small pixels (p,q). The elliptic contour lines represent the convolution effects by each pixel (i,j).

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Figure 4

Problem formulation of pixel blending

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Figure 5

The existence of a solution for a pixel blending problem depends on a given image. (a) Pixels in a checker board are all independent constraints. Therefore no solution exists. (b) Pixels in a layer of a hearing aid shell have plenty of redundancy. A solution exists such that the pixel blending result is the same as the target image.

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Figure 6

Steps of geometry heuristic

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Figure 7

(a) A square pattern is given as the target image, which is also the blending result by the optimization method (in this case, we set n=5); (b) the blending result generated by the geometric heuristic (we can see errors around the corners); (c) the mask image obtained by the optimization method; and (d) the mask image obtained by the geometric heuristic method.

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Figure 8

Standard mixed-integer programming model

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Figure 9

Linear programming model.

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Figure 10

Boundary pixels B have both 0 and 1 in its neighbors. Boundary region B are all the pixels that are within 3σ distance from B. The circle regions in the left and right sides represent the convolution region for the big pixels with values 1 and 0, respectively.

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Figure 11

Framework of the optimization model with prior knowledge

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Figure 12

The second stage optimization model



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