chapter 9, Normalization

from: Introduction to Radiometry

Author(s): William L. Wolfe

Published: 06 April 1998

Chapter DOI: http://dx.doi.org/10.1117/3.287476.ch9

Chapter Page Count: 13 pages

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Front Matter

1. Introduction

2. Radiometric Quantities, the Language

3. Radiative Transfer

4. Transmission, Reflection, Emission, and Absorption

5. Radiance

6. Sources

7. Detectors

8. Review of Optics

9. Normalization

10. Calibration Standards

11. Measurement Techniques

12. Measurement of Fluxes

13. Measurement of Material Properties

14. Radiometric Temperatures

15. Polarization Effects

A. Some Geometric Configuration Factors

Back Matter

Preview

Chapter Contents

9.1 The Need for Normalization
9.2 Effective Values
9.3 Photometry
9.4 An Illuminating Example
9.5 Other Normalizations
9.6 Normalization to the Peak
9.7 Normalization to the Average
9.8 Normalization to the Bandwidth
9.9 A Nasty Denormalization
9.9 Recap

Excerpt

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

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

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.

http://dx.doi.org/10.1117/3.287476.ch9

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