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Shouldn't the Maximum Magnitude of the Scatter Vector be 1?
- By Dan Hill
- Published 1 September 2006
- Frequently Asked Questions
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The Magnitude of the Scatter Vector
The simple answer is no: the maximum magnitude of the scatter vector is 2. If we refer to the diagram included in the Scattering section of the Non-Sequential Components chapter in the ZEMAX User’s Guide, note that vector x is the scatter vector. Vector x is the difference between the projection of the specular ray vector (β0) and the projection of the scattered ray vector (β). Note that the projections are not unit vectors, although the scattered ray vector, S-hat, and the specular ray vector, R-hat, are unit vectors.

It is the magnitude of the scatter vector which is plotted along the x axis of the plot in the Scatter Function Viewer:

So how is it possible that the magnitude of the scatter vector, x, can be 2? Well, imagine the case where the scatter ray vector (S- hat) and specular ray vector (R-hat) lay on the plane of the surface, but point in opposite directions. Thus, if they lie in the plane of the surface, their “projections” are equivalent to the unit ray vectors themselves. Measuring the magnitude (thus the magnitude of the scatter vector, x) from “tip-to-tip” of these two vectors is equal to 2.

Since ||b|| = 1 and ||b0|| = 1, then ||x|| = 2!
1 Response to "Shouldn't the Maximum Magnitude of the Scatter Vector be 1?" 
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said this on 07 Sep 2006 9:30:56 PM PDT
Cleared up something I had not understood. Thanks!
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