Coherent gradient sensor method

The coherent gradient sensor (CGS) method is a full-field interferometric technique that produces fringe patterns by laterally shearing an incident wavefront. This method, developed by Rosakis et al. (1998) for curvature measurement in film-substrate systems, is amenable for use in a variety of experimental configurations in either a reflection or a transmission arrangement. 

The presence of the two gratings in the path of the optical wavefront generates a lateral shift or shearing or optical differentiation of the front. For example, the diffracted beam Ei o, denoted as S xi, X2 + to), is shifted 

The condition for constructive interference of the original and shifted wavefronts is given by 

This equation can be generalized to represent the shearing of the wavefront in either the xi or the X2 direction  

The relation between the optical wavefront and the reflector surface topography can be found by expressing the the specularly reflective, curved 

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Fig. 2.25. Measured normalized curvature versus normalized mismatch strain for Si wafers with W films. The data points represent experiments conducted for different combinations of wafer diameter, wafer thickness and film thickness. The filled circles correspond to curvature measurements made by Finot et al. (1997) using the scanning laser method for the pre-bifurcation data points or the grid reflection method for the post-bifurcation data points. The other symbols denote experiments using the coherent gradient sensor method. Superimposed on the experimental data are the predicted trends for the stable symmetric and stable asymmetric cases replotted from Figure 2.24 with i = 0.26.

The data shown in Figure 2.25 were obtained by means of the wafer curvature scan, the grid reflection method, or the coherent gradient sensor method. The last of these will be discussed further in Section 2.6.2 in the context of a visualization of deformation via Mohr s circle for curvature. The grid reflection method was described in Section 2.3.3, and a typical set of images obtained with this method is shown in Figure 2.26. 

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