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Spie Press Book

Introduction to Radiometry
Author(s): William L. Wolfe
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Book Description

Radiometry is an essential part of the optical design of virtually every optical instrument, and key to many applications. It is also used to measure the radiation of various objects. This tutorial examines both the techniques of calculating radiative transfer and the measurement of fluxes and radiometric properties of various sorts.

Book Details

Date Published: 6 April 1998
Pages: 200
ISBN: 9780819427588
Volume: TT29

Table of Contents
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Chapter 1. Introduction
1.2 Organization
Chapter 2. Radiometric Quantities, the Language
2.1 Angle and Solid Angle
2.2 Projected Area and Projected Solid Angle
2.3 Definitions of Basic Radiometric Quantities
2.4 Photonic Radiometric Quantities
2.5 Spectral Variables
2.6 Spectral Radiometric Quantities
2.7 Luminous Quantities
2.8 Fluometry
2.9 The Chinese Restaurant System
2.10 Recap
Chapter 3. Radiative Transfer
3.1 The Fundamental Equation of Radiative Transfer
3.2 Lambertian Emitters
3.3 Transfer between a Differential Element and a Disk
3.4 Other Geometries and Distributions
3.5 Recap
Chapter 4. Transmission, Reflection, Emission, and Absorption
4.1 Some Definitions
4.2 The Conservation of Power
4.3 Kirchhoff's Law
4.4 Absorption and Emission
4.5 Transmission and Reflection
4.6 Some Examples
4.7 Relationships among Transmissivity, Reflectivity, Absorptivity, and Emissivity
4.8 Recap
Chapter 5. Radiance
5.1 The Invariance of Radiance in a Vacuum
5.2 Invariance of (Reduced) Radiance across an Interface
5.3 The Invariance of Throughput
5.4 Path Radiance
5.5 Recap
Chapter 6. Sources
6.1 Laser Sources
6.1.1 Fixed-Wavelength Lasers
6.1.2 Tunable Lasers
6.2 Blackbodies
6.3 Cavity Radiators
6.4 Thermal Sources
6.4.1 Nernst Glower
6.4.2 The Globar
6.4.3 The Welsbach and Gas Mantles
6.4.4 Tungsten Bulbs
6.5 Recap
Chapter 7. Detectors
7.1 Detector Descriptions
7.2 Detector Types
7.3 Detector Noises
7.3.1 Johnson Noise
7.3.2 Shot Noise
7.3.3 Photon Noise
7.3.4 Temperature Noise
7.3.5 Generation-Recombination Noise
7.3.6 Excess Noise
7.4 Summary of Noises
7.5 Summary of Detector Properties
7.6 Some Real Problems
7.7 Recap
Chapter 8. Review of Optics
8.1 Photons, Waves, and Rays
8.2 Interference
8.2 Diffraction
8.3 The Thin Lens
8.4 Ray Traces
8.5 Paraxial Ray Traces
8.6 Aberrations
8.6.1 Spherical Aberration
8.6.2 Coma
8.6.3 Astigmatism
8.6.4 Curvature of Field
8.6.5 Distortion
8.6.6 Longitudinal Color
8.6.7 Lateral Color
8.7 Stops and Pupils
8.7.1 Aperture Stops and Pupils
8.7.2 Field Stops and Windows
8.8 Recap
Chapter 9. Normalization
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
Chapter 10. Calibration Standards
10.1 Types of Standards
10.2 Photometric Standards
10.3 Flux Standards
10.3.1 Source Standards
10.3.2 Electrical Substitution Radiometers
10.3.3 Self-Calibrating Detectors
10.4 Synchrotrons
10.5 Material Standards
10.5.1 Reflectance Standards
10.5.2 Transmittance Standards
10.6 Recap
Chapter 11. Measurement Techniques
11.1 Relative and Absolute Measurements
11.2 Errors
11.3 Rules of Measurement
11.4 The Measurement Equation
11.4.1 The Venus Radiometer Example
11.4.2 Spectral Variations
11.5 A Taxonomy of Measurements
11.6 Recap
Chapter 12. Measurement of Fluxes
12.1 Measurement of Power
12.2 Measurement of Incidence
12.3 Measurement of Exitance
12.4 Measurement of Intensity
12.5 Measurement of Radiance
12.6 Calibration Techniques for Radiometers
12.6.1 Distant, Point-Source Method
12.6.2 Distant, Extended-Source Method
12.6.3 Near, Extended-Source Method
12.6.4 Jones Technique
12.7 Recap
Chapter 13. Measurement of Material Properties
13.1 Total Hemispherical Emissivity
13.2 Spectral Directional Emissivity
13.3 Total Directional Emissivity
13.4 Specular Reflectivity
13.4.1 Substitutional Method
13.4.2 The Strong Method
13.4.3 The Bennett-Koehler Method
13.5 Specular Transmittance
13.6 Internal Transmittance and Absorption Coefficient
13.7 Directional-Hemispherical Reflection
13.7.1 The Coblentz Hemisphere
13.7.2 The Paraboloidal Reflectors
13.7.3 The Integrating Sphere
13.7.4 The Gier-Dunkle Cavity
13.8 Directional-Hemispherical Transmittance
13.9 Bidirectional Reflectance and Transmittance
13.10 Refractive Index
13.11 Recap
Chapter 14. Radiometric Temperatures
14.1 Radiometric Temperatures
14.1.1 Radiation Temperature
14.1.2 Radiance Temperature
14.1.3 Ratio Temperature
14.1.4 Color Temperature
14.1.5 Distribution Temperature
14.1.6 Ratio Temperature Difference
14.2 Atmospheric Transmission
14.3 Effective Temperature
14.4 Recap
Chapter 15. Polarization Effects
15.1 Descriptions of Polarization
15.2 Polarization from Dielectrics
15.3 Polarization from Metals
15.4 Polarization from Surface Scattering
15.5 Polarization from Slits
15.6 Polarization as a Result of Atmospheric Transmission
15.7 Representative Mueller Matrices
15.8 Recap
Appendix: Some Geometric Configuration Factors
Preliminaries and Definitions
Plane Parallel Rectangles
Two Perpendicular Plane Rectangles
Contour Integration
Infinite Planes, Concentric Spheres and Infinitely Long Cylinders
Some Other Geometries
Summary and Overview


Radiometry is an essential part of the optical design of almost every optical instrument. Such instruments are usually used to focus and detect radiation for some particular purpose, and for many applications it is absolutely essential to know how much radiation gets to the detector array or film in the image plane and the value of the resultant signal-to-noise ratio or exposure. Radiometry is almost essential in another sense, the measurement of the radiation of various objects. In fact, the word "radiometry" itself means the measurement of radiation. One cannot make the above-mentioned calculations without a knowledge of the flux from the source, whether it be a tungsten bulb or a sun-illuminated vista. Therefore, this text on radiometry involves both the techniques of calculating radiative transfer and the measurement of fluxes and radiometric properties of different sorts.

1.1 History

The most primitive beginnings of radiometry must have been the observation by early man of the different brightnesses of stars and the sensing of the warmth from the sun and the fire (after he invented or discovered it). These were radiometric measurements, but they surely were not quantitative. Greek astronomers, especially Ptolemy and Hipparchus, made good estimates of star magnitudes, and these were extended by Galileo.

The history of quantitative radiometry surely begins with the practice of photometry, the measurement of visible light. It was first put on an organized basis by Pierre Bouguer in 1729 when he described an instrument that could compare the brightnesses of two sources. In 1760 Johann Lambert enunciated the law of the addition of illumination, the inverse square law, cosine law of flux density distribution, and others. Many relatively small advances were made until Becquerel observed the photoelectric effect in 1839. Then the photoconductive effect was discovered by Willoughby Smith in 1873 and the photoemissive effect by Hertz in 1887. These discoveries moved the different measurement instruments out of the realm of human observation and into that of quantitative analyses. Although the eye is a wonderful comparison device, it is notoriously poor at measuring radiation levels. Additional history is available in the very nice photometry text by Walsh and the one on absolute radiometry by Hengstberger.

1.2 Organization

The scheme of this text is to discuss first some of the basic concepts, the language of radiometry, and relatively simple radiative transfer. The methods used to describe the properties of radiators, reflectors, and transmitters are next described. Then ideal and practical sources are covered. Normalization, an interesting part of the field, involving making measurements and calculations of radiative quantities based on responses of certain sensors, is covered next. Radiometric standards are then described, just before measurement and calibration techniques. Radiometric, sometimes known as fake, temperatures are described along with their errors. Concepts of polarization are then discussed, mostly in terms of warnings.

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