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Chapter 9:
Normalization
Abstract
The process of normalization is to bring calculations and measurements into consonance with a particular norm. One example is to relate everything to the response of the human eye. It has the advantage of making many calculations and measurements much easier in a particular application, but also has some very subtle and difficult pitfalls. This chapter discusses the process, gives examples, and shows the pitfalls. 9.1 The Need for Normalization There is no such thing as a monochromatic wave. Such a one would have, theoretically, started an eon ago and we would have to wait for the millennium to see it. Practically, a quasi-monochromatic wave has a very narrow spectral band and very little energy. Thus, every radiometric measurement is made over a finite spectral band. This means that the voltage V from a source S(λ) that is detected by a detector with a spectral response ℜ(λ) is given by V=∫S(λ)ℜ(λ)dλ. Under only very restricted conditions can the flux in the band be measured. It is useful to write this another way. The output voltage (current, charge, or other) is given by V=Sℜ∫s(λ)r(λ)dλ. This formulation emphasizes that the source is characterized by a relative spectral distribution, s(λ), with maximum value of 1 and a constant, S, that “de-relativizes” it. The same is true for the detector responsivity, ℜr(λ). Thus, based on Equation 9-2, no matter how clever you are, no matter what you do, unless you have a flat detector, the flux in the band cannot be measured. Only the flux weighted by the detector response can be measured.
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CHAPTER 9


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