This is a newer and I think easier to understand version of the LIT equations. The original equations can be found here. And of course, both produce the same results.

LIT is a Fixed Source Test and as such, the angle of the source ray s is equal to the angle of reflection ray r as measured with respect to the Normal per Fig-1:

• Alpha represents the angle s and r.
• The slope of the Normal is -z' per Fig-4.
• The slope of a perpendicular to the Normal is +1/z' per Fig-3.

The Normal vector (per Fig-1 equation 2) of the form y=mx+b is y=-z'x+zz'+h, where zz'+h is the b term. Knowing z, the other side of that right triangle is found using similar triangles where the derivative z' serves as the other triangle with similar sides. Derivative z' and 1/z' are used in many places in Fig-1 in this manner which has greatly simplified this new version of the LIT equations, which gets exactly the same results as the old.

Excels Solver (Root finder) is used to find the numerical solution to the LIT differential equations, which can be simply summarized as:

z is varied (using a Root finder) until Yz of Fig-2 equation 12 is nearly equals to Ym (the slit images as measured by ImageJ).

Instead of using Z=-Kz of Fig-4 to compute the Foucault, Z=(h-Rz'+zz')/z' is used instead being it avoids multiplying by K=-0 when the conic is a sphere.