# decorrelating two image maps — reflected images from laser scattering

I am stuck on a research problem and do not know what kind of methods to use. I hope people in this forum can give me some good ideas, I've always had good brainstorming sessions here.

My problem is that I have a laser and a stack of thin films made up of three different materials. If I shoot the laser at these thin films I get a circular image of the reflected light from the laser scattering on the films. However, the fourth layer is added and I want to measure the change in thickness of the fourth layer, similarly by shooting a laser at this stack. The other three bottom layers are "nuisance" parameters, but their thickness variations are also captured in the pupil image. How do I filter out the observed pupil image so that the information of the three base stacks are eliminated and only the variations of the fourth critical stack are captured? I have 1000 sets (1000 for 3-stack and 1000 for 4-stack) such that for each data point, the 3-stack and 4-stack films have gone through identical process conditions and there is an image for both these stacks. I've thought of maybe signal transforms?

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Each image pixel of the pupil of the film stack is a nonlinear function of the thicknesses but the gradients at each parameter (as well as the image at a certain parameter value) point can be calculated via an optical simulator.

$pix_i(i = 1...n) = f(h_1,h_2,h_3) + \epsilon_i$

where $pix_i$ is a pixel point of the acquired image and $h1,h2,h3$ are the film thicknesses of a 3-film stack. This can now be linearized around $h10,h20,h30$ to

$pix_i(i=1...n) \sim f(h_{10},h_{20},h_{30}) + \frac{df}{dh_i}(h_i = h_{i0}) + \epsilon_i$

• What do you mean by "gradients at each parameter"? – geometrikal Aug 15 '13 at 22:09
• the first-order derivative can be calculated at each pixel point for each height. – Jane Lee Aug 18 '13 at 10:12
• Could you put up an example of 3 vs 4 stacks? – geometrikal Aug 21 '13 at 21:22
• Well, I can't because of confidentiality but they are just thin films with height variations. material A on top of material B ... so on. – Jane Lee Aug 22 '13 at 23:07
• More Qs - Post just a 3 stack then to see what it looks like? Or similar non confidential image? Are the 1000 sets repetitions of the same experiment, or different 4th layer heights? – geometrikal Aug 22 '13 at 23:16