Fresnel transform

Question

How is it possible to encrypt multiple images using fresnel transform and inverse the operation to de-multiplex those images?

Answer 1

The particular application the OP is asking about might be better on Theoretical Computer Science or Math, but the long and the short of it comes down to three properties of the transform

• The Fresnel transform is a special case of the Linear Canonical Transform (and also of the Generalized Fresnel Transform (here as free PDF) to make an explicit physics connection).
• The LCT can be represented by 2x2 matrix (exhibited in the wikipedia article and discussed at greater length in the paper by James et. al) and may be composed.
• The representation of the Fresnel transform as a non-zero determinant, which means that ti is invertible, and the inverted matrix also represents an instance of the LCD, which means that the original data may be recovered.

To this we add two facts concerning holograms...

• Holograms represent a Fresnel transform of the a three dimensional data set into a two dimensional representation.
• If we voxelize a 3D space we get a stack of pixelized 2D images (though I imagine this necessitates finding a discrete version of the transform, but that is old hat in numeric analysis).

...and it's obvious, right?

::phew!::