Gil Abramovich, Kevin Harding, Matthew Radebach, Kevin Kenny, Zhaohui Sun, Martha Gardner, Dirk Padfield, Ralph Isaacs, Joe Ross, Ming Jia, Li Tao, Guiju Song and Jianming Zheng

Adaptive filters for speckle removal can halve the measurement variations for systems using fringe projection with infinitesimal penalty in process time.

A popular way to extract 3D data from an industrial part is to project onto it structured light, such as fringes, and capture the pattern using one or more cameras.^{1} Distortion in the projected pattern provides the shape data. Although algorithms for fringe 3D data retrieval are common and convenient, they are susceptible to image noise, usually in the form of speckles. In fringe projection metrology systems, the light source (especially laser) or surface texture creates speckle noise that significantly reduces performance.^{2}

Our measurement method^{3} addresses 3D shapes, such as the edge break as shown in the center panel in Figure 1. Speckle noise (left panel) reduces the sinusoidal appearance of a profile, which is perpendicular to the fringes. This results in inadequate gage repeatability and reproducibility (GR&R). Here we present a method for improving this property by removing noise while preserving fringe data.

While speckle noise has a wide bandwidth in the frequency domain, fringes are typically narrowband, with dominant frequency changes based upon surface curvature. In our approach, noise removal algorithms either incorporate a bandpass filter (BPF) or a bandstop filter (BSF). A BPF passes the frequency band of the fringes, but a BSF rejects the speckle noise frequency band in a direction perpendicular to the fringes. In addition, the algorithm may contain a low-pass filter (LPF) along the fringes in order to further reduce speckle noise (see Figure 2).

We investigated several algorithms based on a six-sigma approach^{4} that evaluated development, the down-selection process, parameter optimization, and verification.

**Figure 1.** Close-up (left) and wider view (center) of a surface image with speckle noise. Right: profile intensity values for the horizontal white line in the surface image. Note speckles and local profile ‘jumps’.

**Figure 2.** Image enhancement for fringe projection preferably incorporates a bandpass filter in the direction perpendicular to the local fringe direction and a low pass filter parallel to it.

Our candidate algorithms included the curvature anisotropic diffusion^{5} (CAD) algorithm and two original Gabor-based algorithms.^{6} Curvature-driven CAD removes random noise with minimal effect on non-random feature edges, and iso-brightness contours are viewed as a level set. One of the ‘home-grown’ candidates, algorithm 2 (A2), consisted of edge orientation detection followed by a 2D Gabor filter: that is, local fringe orientation is first measured, then the filter applied for noise removal. Finally, algorithm 3 (A3) is the most specific and assumes that edge directions are parallel to one of the image axes. This algorithm applies line shifting that temporarily produces vertical fringes, then a global 1D horizontal Gabor BPF and 1D vertical Gaussian LPF. Finally, line shifting is reversed to obtain a speckle-free image.

**Figure 3.** Enhanced images (from the validation set): A-D with Algorithm 3; E-F with Algorithm 2.

Each algorithm incorporates a set of control parameters. A2, for example, is sensitive to orientation detection filter size and Gabor noise-reduction filter size. We investigated GR&R sensitivity to variations in parameter values, and evaluated the acceptable ranges using fractional factorial design of experiments (DOE). This led to elimination of the CAD algorithm because processing proved excessively long for our real-time requirements. We then used a full factorial DOE that included parameter values from within a reduced range for each of the remaining algorithms. We performed regression, first to extract the transfer function for each algorithm, and then optimaized it.

A3 delivered 50% or better improvement on GR&R for all tested edge types, using an independent image set. A2 provided a slight performance advantage for round edges but failed in the presence of abrupt edge direction changes, such with chamber edges. Figure 3 gives examples of the enhanced images.

In summary, we improved performance for fringe projection phase-shift analysis sensors by adaptive Gabor-based image enhancement filters. Future modifications will include removing minor line-shift errors (`jumps') apparent with A3, and improved handling of sharp corners when using oriented Gabor filters (A2).

Gil Abramovich, Kevin Harding, Matthew Radebach, Kevin Kenny, Zhaohui Sun, Martha Gardner, Dirk Padfield

GE Research

Niskayuna, NY

Ralph Isaacs, Joe Ross

GE–QTC

Cincinnati, OH

Ming Jia, Li Tao, Guiju Song, Jianming Zheng

GE–CTC

Shanghai, China

References:

6.

G. Abramovich, K. Harding, R. Isaacs, M. Radebach, K. Kenny, Z. Sun, J. Ross, M. Jia, L. Tao, G. Song, J. Zheng, M. Gardner, D. Padfield, Image Enhancement for Phase Shift Analysis Sensors, *Proc. SPIE* 6382, 2006.