DEVELOPMENT OF COLOR IMBALANCE NORMALIZATION METHOD WITH VANDERMONDE MATRIX INTERPOLATION FOR SURFACE PROFILE ARTIFACT CORRECTION IN DIGITAL COLOR FRINGE PROFILOMETRY

• Main Author: Ari Irwanto, Decky
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/65256
• Institution: Institut Teknologi Bandung

Digital Color Fringe Profilometry (DCFP) applies an encoding process to 3 sinusoidal fringe images with phase difference 120° for each red, green, and blue channel to produce a color fringe image that is projected to the reference surface and the object surface. The method gives a chance measurement with single projection for 3 different phases. The camera records images of the projected fringe on surfaces and the computer program processes them to produce a 3D surface profile measurement. The depth of the object causes a phase change in the fringe pattern. Utilization of commercial level projector and camera in measurement system causes the recorded fringe pattern distorted due to noise, nonlinear intensity, and color imbalance. Color imbalance is the addition of harmonic components to the fringe pattern which varies for each of the red, green, and blue channels. Distortion level determines phase information quality and determines the level of harmonic ripple on the reconstructed surface. One of the methods to overcome the color imbalance problem in DCFP is the fringe harmonic reduction method using band-pass filter and Hilbert transform. Phase Shifting Interferometry (PSI) was used to determine the wrapped phase of the normalized fringe. This approach allows the occurrence of wrapped phases due to noise (residual), thus extraction of absolute phase requires an advance phase unwrapping method with a large computational cost. In this study, an alternative method was developed to overcome the color imbalance problem using an interpolation approach based on the Vandermonde matrix. The preprocessing step for normalizing the color fringes is applying a filter to the sinusoidal fringe in each color channel to determine the estimated distortion trend line for each fringe line. The type of filter used is a 1st order Savitzky-Golay filter with parameter M=50 followed by a 4th zero-phase Butterworth Low Pass Filter with a normalized cut-off frequency 0.038. The point of intersection between the ascending fringe pattern and the estimated line is denoted as ti. Next, a horizontal line is drawn from ti so that the horizontal line intersects with a descending fringe pattern that is after ti. The intersection of the horizontal line with the descending fringe pattern is denoted ui. The middle value of the x-coordinate between ti and ui is the x-coordinate position of the maximum peak. The middle value of the x-coordinate between ui and ti+1 is the x-coordinate position of the minimum peak. The center position on the x-coordinate between the 2 points of intersection of the fringes with the estimated line is the x-coordinate position of the minimum peak or maximum peak. 3rd order polynomial interpolation based on the Vandermonde matrix can reconstruct the ideal fringes from the minimum peak to the maximum peak or vice versa based on the x-coordinate positions at the minimum peak (y=-1), maximum peak (y=1), and 2 points (x,y) based on the sinusoidal function added between the x-coordinate of the minimum and maximum peaks. The extraction of the wrapped phase on the normalized fringes utilizes the Hilbert transform. The absolute phase is obtained by adding a multiple of 2? every time there is a phase discontinuity in the wrapped phase. The average absolute phase difference of each RGB channel at the same x-coordinate between the fringe pattern on the reference plane and the fringe pattern on the object surface represents the depth of the object at the x-coordinate in 1 line of fringes. The test of the proposed method was carried out on two test objects, a dynamic membrane surface with 3 peaks (object-A) and a staircase (object-B). The test results on object-A, the proposed method can reconstruct the membrane surface in the range of 0-11.8 cm at 2 different peak heights. The test results on object B produce a inclined surface on the object component that is perpendicular to the reference plane. The inclined surface arises due to the frequency limitation of the fringes of the device which is not able to sample the high frequency sinusoidal component of the step shape on a surface perpendicular to the reference plane. The test results were compared with a spot scanning-based triangulation mechanism using a laser. In the measurement range of 4.1 cm to 10 cm, excluding errors due to inclined surfaces, the measurement error is in the range of -5.76% to 1.79%.