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I'm looking into the section "Reconstructing an object from its shadow" in the book Introduction to the Mathematics of Medical Imaging by Charles L. Epstein.

I have two questions

  1. The tangent point is expressed as a vector which contain two component. The shadow function $h$ multiplied with the orthogonal vector and an $s$ function multiplied with the direction vector. Can anyone tell me why do we have this equation, and what does the $s$ function mean?
  2. And also why do we have $h'D(e) - s(e) = 0$ when it is parallel to the direction vector $\hat \omega$?

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