Correct 2d-diffraction image for different scattering angles after refraction.

Hello,

my Problem: Given is an intensity image (real positive integers in a 2048*2048 Matrix) from a forward scattering experiment. That means around the directly transmitted beam in the center of the matrix i have a diffraction image with the scattering angle corresponding to the size of the scattering object. For example a laser shining into water with small particles and recording the image downstream the sample. The recorded scattering angle in air is different from the "real" scattering angle inside the sample (in this case the water filled cuvette). I want to correct all pixels with respect to their "real" scattering angles, as if my detector was inside the water.

e.g. a feature in the image is at 500 pixels distance from the center, I know the CCD-sample distance and all refractive indices. So I can calculate the scattering angle in water simply using Snell's law and get a new (pixel) distance in a corrected image.

The recorded scattering angle is rather large (>20°) such that the small angle approximation (sin(x) = x) is no longer valid. The outermost pixels will not only be shifted along their connection line to the center of the diffraction pattern but also distorted. The total intensity (sum(sum(image)) must be equal after the transformation. Resampling the matrix to calculate the new pixel intensities will be necessary.

I saw the mapping toolbox offers a large variety of Map projections and i guess that maybe an azimuthal projection could be what I need.

1. Can someone tell me if there is already a projection/algorithm that would fit the problem described above? What is the according syntax? 2. If not, what would a solution look like? I don't expect a finished script but maybe a roadmap how to develop an algorithm by myself.

Thanks for all feedback. /Stefan.

Answer 1

[Image Analyst]

If you can figure out the mathematical equation, then you can do something like what Steve demonstrates here: http://blogs.mathworks.com/steve/2006/08/04/spatial-transformations-defining-and-applying-custom-transforms/

[Stefan]

Thanks, i have to work through this tutorial! So far it looks promising.