introduction-to-optics-2nd-ed---f-pedrotti-l-pedrotti-prentice-hall-1993-ww.thuvienvatly.com.92fce.44585

The final result is that light and subatomic particles, like electrons, are both consid- of the chapter... of mechanics and gravity_ In his treatise Optics, Newton clearly regarded rays

Center for Occupational

Research and Development

Waco, Texas

Emeritus Professor of Physics

Air Force Institute of Technology

Ohio

Prentice-Hall International, Inc

PHYSICAL CONSTANTS

Speed of light Electron charge Electron rest mass Planck constant Boltzmann constant Permittivity of vacuum Permeability of vacuum

Preface

Optics is today perhaps the most area of both theoretical and applied physics Since the 1960s the parallel emergence and of fiber optics, and a va-riety of semiconductor sources and detectors have revitalized the field The need for a

ap-parent, both for the student of optics and for the laborer in the field who needs an sional review of the basics

occa-With Introduction to we propose to teach introductory modern optics at an

are written at a somewhat the text assumes as background a good course in introductory physics, at the level usually given to physics and engineering majors, and at least two semesters of calculus The book is written at the level of understanding appro-

physics and mathematics prerequisites as a freshman the traditional areas

of college optics, as wen as several rather new ones, the text can be 11.""",,,,,11 ther a half- or a full-year course We believe that the and

today warrant readjustment of curricula to provide for a full year of

program

For those who are familiar with the first edition, it may be

the major changes introduced in this second edition Two new ch:aJ)ters 11.".11",,, with laser-beam characteristics and nonlinear have been added The new laser chapter now appears, together with the two earlier laser toward the end of the book, where the three function as a unit In addition, the has been

xix

greatly expanded and moved to a later chapter Several new sections have been duced They are Ray and The Thick Lens (Chapter 4), Effect (Chapter 8), and Evanescent Waves 20) Worked examples are now within the text, and 175 new problems have been added to the chapter exercises

intro-Specific features of the text, in terms of coverage beyond the traditional areas, clude extensive use of 2 X 2 matrices in dealing with ray and mul-tiple thin-film interference; three devoted to a chapter on the eye, induding laser treatments of the eye; and individual chapters on holography, coher-ence, fiber optics, Fourier optics, nonlinear and Fresnel equa-tions A final chapter a brief introduction to the optical constants of dielectrics and metals We have attempted to make many of the more specialized chapters indepen-dent of the others so that can be omitted without detriment to the remainder of the book This should be helpful in shorter versions of the course

in-Organization of the material in three major parts follows traditional lines The first part of the book deals with geometrical as a limiting form of wave optics The middle develops wave optics in detail, and the final treats topics generally referred to as modern optics In the first I presents a brief historical review of the theories of light including wave, and photon de-scriptions In Chapter 2, we describe a variety of common sources and detectors of

as well as the radiometric and units of measurement that are used throughout the book In this and the remainder of the text, the rationalized MKS system of units is 3 reviews the geometrical optics covered by in-

physics courses, the usual reflection and refraction relations for rors and lenses Chapter 4 shows how one can extend paraxial optics to of ami-complexity through the use of 2 x 2 matrices Also in this we include an introduction to the ray-tracing that are widely applied computer pro-gramming Chapter 5 presents a semiquantitative treatment of third-order aberration the-ory Chapter 6 discusses the of geometrical optics and aberration

mir-to apertures and mir-to several devices: the prism, the camera, the "",>ni.""" m:u;rOlscope and the telescope The of the eye as the final

in many optical systems is in a separate chapter (7) This explains the functions and the defects of the eye and discusses some of the treatments of these defects that make use of the of laser light

The next section of the text introduces wave or physical with two chapters (8 and 9) that discuss the wave and the superposition of waves Interference nh.>nnlmp,n" are then treated in Chapters 10 and II, the second dealing with both Michel-son and Fabry-Perot interferometers in some detail Although the of coherence

is handled in general terms in discussions, it receives a more and

treatment in Chapter 12 After a brief explanation of Fourier series and the Fourier integral, the chapter deals with both temporal and spatial coherence and presents

a quantitative discussion of partial coherence Chapter i 3 presents, as a

tion of interference, an introduction to holography, including some current aPlpli(;atiions

14 and 15 treat the of We first give a mathematical

2 x 2 matrices to the electric field vector (Chapter 14), fore in detail the mechanisms responsible for the production of p0-

be-larized light (Chapter 15) Thus Chapter 14 uses matrices to describe the various modes

of and types of without reference to the physics of its

more effective Diffraction is discussed in the following three chapters ]7, 18) Since an adequate treatment of Fraunhofer diffraction is too long for a

we have included a separate chapter (17) on the diffraction grating and

Preface

instruments following the discussion of diffraction in Chapter

16 Fresnel diffraction is then taken up in 18

The final chapters are generally more demanding in mathematical sophistication

19 2 x 2 matrices to treat reflectance of thin films Chapter

20 derives the Fresnel equations in an examination of reflection from both dielectric and metallic surfaces The basic elements of a laser and the basic characteristics of laser are treated in Chapter 21, followed by a rather chapter (22) that de-scribes the features of laser beams The and mode structure of laser

sequence, and together with Chapter 23, an essay on laser applications, form

a suitable unit for a minicourse on lasers The other chapters in this final part of the book are self-contained in the sense that no sequence is

,",U'''P'''''' 24 presents a survey of the basic features of fibers with special tention to communication applications Thus of bandwidth, allowed

at-and mechanisms of attenuation at-and distortion are treated here 25 introduces the

of Fourier in a discussion of optical data nr"C'"·",,,

Chapter 26 presents a variety of effects under the umbrella of nonlinear The final chapter (27) considers the propagation of a light wave in both dielectric and metallic media and shows how the optical constants arise

Each of the 27 chapters contains a limited bibliography related to the chapter tents and referred to at times within the text square brackets In addition, at the end of the book, we have included a chronological listing of articles related to optics that have in Scientific American over the I&<;t 40 years or so It is hoped that this list of excellent articles will prove helpful, to the undergraduate student This text is intended to be for either one or two semester sequences The selection of material will on the goals of both teacher and stu-dent As a rough guide, however, a typical one-semester course might include the basic sequenee:

Holography Production of Polarized Fraunhofer Diffraction Fresnel Diffraction Laser Basics

As a further aid to selection, those sections that could be omitted in abbreviated sions of the course are marked with an asterisk See the Contents

ver-We wish to thank the many teachers who have inspired us with an interest in tics and in teaching and the many students who have motivated us to teach with

Guen-and Thomas B Greenslade For their suggestions for improving the second which we have considered very we wish to thank the team of reviewers selected by Prentice Hall: Joel Blatt, Florida Institute of Technology; James Ore-

xxii

gon Institute of Technology~ Harry Daw New Mexico State University; Edward University of Delaware; and Daniel Wilkins, of Nebraska We are grateful to Leno M Pedrotti for his critical reading of most of the new material added in this sec-ond edition For his review and in the chapter on the eye, we are also

to acknowledge and thank Dr Michael Pedrotti, 0.0 We also wish to thank Lawson for her sketch of Einstein that graces page I Finally, we express our tude to the editorial and production staff of Prentice HaiL In particular we are indebted

to our editors, Holly Hodder for the first edition and Ray Henderson for the second and to our production editor, Kathleen Lafferty, who helped us with both editions of this text

Frank L Pedrotti, S.l Leno S Pedrotti

Preface

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34 Reflection in Plane Mirrors 37

3-5 Refraction through Plane Surfaces 38 3-6 Imaging by an Optical System 40

3-7 Reflection at a Spherical Surface 43

Thin Lenses 50

3-10 Velrgeince and Refractive Power 55

3-11 Newtonian Equation for the Thin Lens 57

Problems 58 References 60

Introduction 62

4-4 The Refraction Matrix 66

4-5 The Reflection Matrix 67

4-8 Significance of System Matrix Elements 72

4-9 Location of Cardinal Points for an Optical

*5-2 Third-Order Treatment of Refraction at it Spherical

Interface 89 5-3 Spherical Aberration 93

5-5 5-6

Astigmatism and Curvature of Field Distortion 100

Introduction 151 Biological Structure of the

Functions of the Eye 155 Errors of Refraction and Their Laser

Problems

for Ocular Defects

169 References 171

Introduction 187 SUiJenDOSiti(J~n ~nciple 187 lDerocIsttion of Waves of the Same

1 0 Interference of light 200

Introduction 200

10-3 Double-Slit Interference with Virtual Sources 209

10-4 Interference in Dielectric Films 211

11-2 Applications of the Michelson Interferometer 228

11-3 Variations of the Michelson Interferometer 230

13-1 Conventional versus Holographic Photography 266

13-2 Hologram of a Point Source 267

White-Light Holograms 273 Contents

Appli(;ati1ons of Holography 274 References

Jones Matrices Problems References 297

Production of Polarized light 298

298 IS-I Polarization by .: I", ·,t'"''

Absorption 298 15-2 Polarization Reflection from Dielectric

17-2 Free Spectral Range of a Grating

Resolution a Grating

Introduction 366 18-1 Fresnel-Kirchhoff Diffraction Integml 367 18-2 Criterion for Fresnel Diffraction 369 18-3 The Obliquity Factor 370

18-5 Phase Shift of the Diffracted Light 374 18-6 The Fresnel Zone Plate 374

18-7 Fresnel Diffraction from Apertures with Rectangular

18-9 Applications of the Cornu Spiral 382 18-10 Babinel's Principle 388

388

390

19-1 19-2 19-3

194 19-5

Introduction 391 Tr.ansfer~atrix 392 Reflectance at Nonnal Incidence

Antireflecting Films IreIlecl[mg Films High-Reflectance Layers 402

*20-6 Complex Refractive Index 420

*20-7 Reflection from ~etals 422

Problems 423 References 425

Contents

21

22

Introduction 426 21-1 Einstein's Quantum Theory of Radiation 427 21-2 Essential Elements of a Laser 431

21-3 Simplified Description of Laser Operation 434 21-4 Characteristics of Laser Light 440

21-5 Laser Types and Parameters 451

22-1 22-2-22-3 22-4 22-5 22-6

*22-7

Introduction 456 Three-Dimensional Wave Equation and Electromagnetic Waves 457 Phase Variation of Spherical Waves Along a Transverse Plane 459

Basis for Defining Laser-Beam Mode Structures 459

Gaussian Beam Solution for Lasers 461 Spot Size and Radius of Curvature of a Gaussian

24-3 Bandwidth and Data Rate 504

25 fourier Optics

Introduction 25-1 Optical Data Imaging and Processing

Suggestions for further Reading 581

Articles on Optics from Scientific American 581

Answers to Selected Problems 585

Radiometric and Photometric Tenns 10

Summary of Gaussian Mirror and Lens Fonnulas 54 Summary of Some Simple Ray-Transfer Matrices 70

Cardinal Point Locations in Terms of System Matrix Elements 77

Specific Rotation of Quartz 3/4 Refractive Indices for Quartz 3/6

Refractive Indices for Several Coating Materials

Comparison of Linewidths 441 Laser Parameters for Severa] Common Lasers

400

403

452

128

Medical Fields Involved with Lasers 490

Cbaracterization of Several Optical Fibers 506

Linear and Nonlinear Processes 546 Linear Electro-optic Coefficients for Representative Materials 549 Kerr Constant for Selected Materials 553

Verdet Constant for Selected Materials 554

list of Tables

of quantum electrodynamics, one of the most successful theoretical structures in the

annals of physics

In what follows, we will be content to sketch briefly a few of the high points of this developing understanding I Certain areas of physics once considered to be disci-plines apart from optics-electricity and magnetism, and atomic physics-are very much involved in this account This alone suggests that the resolution achieved also constitutes one of the great unifications in our understanding of the physical world The final result is that light and subatomic particles, like electrons, are both consid-

of the chapter)

1

of mechanics and gravity_ In his treatise Optics, Newton clearly regarded rays of

light as streams of very small particles emitted from a source of light and traveling

in straight lines Although Newton often argued forcefully against positing ses that were not derived directly from observation and experiment, here he adopted

hypothe-a phypothe-article hypothesis, believing it to be hypothe-adequhypothe-ately justified by the phenomenhypothe-a portant in his considerations was the observation that light can cast sharp shadows of objects, in contrast to water and sound waves, which bend around obstacles in their paths At the same time, Newton was aware of the phenomenon now referred to as

Im-Newton's rings Such light patterns are not easily explained by viewing light as a stream of particles traveling in straight lines Newton maintained his basic particle hypothesis, however, and explained the phenomenon by endowing the particles themselves with what he called "fits of easy reflection and easy transmission," a kind

of periodic motion due to the attractive and repulsive forces imposed by material stacles Newton's eminence as a scientist was such that his point of view dominated the century that followed his work

ob-Christian Huygens, a Dutch scientist contemporary with Newton, championed the

view (in his Treatise on Light) that light is a wave motion spreading out from a light

source in all directions and propagating through an all-pervasive elastic medium called the ether He was impressed, for example, by the experimental fact that when two beams of light intersected, they emerged unmodified, just as in the case of two water or sound waves Adopting a wave theory Huygens was able to derive the laws

of reflection and refraction and to explain double refraction in calcite as well

Within two years of the centenary of the publication of Newton's Optics, the

Englishman Thomas Young performed a decisive experiment that seemed to demand

a wave interpretation, turning the tide of support to the wave theory of light It was the double-slit experiment, in which an opaque screen with two small, closely spaced openings was illuminated by monochromatic light from a small source The

"shadows" observed formed a complex interference pattern like those produced with water waves

Victories for the wave theory continued up to the twentieth century In the mood of scientific confidence that characterized the latter part of the nineteenth cen-tury, there was little doubt that light, like most other classical areas of physics, was well understood We mention a few of the more significant confirmations

In 1821 Augustin Fresnel published results of his experiments and analysis, which required that light be a transverse wave On this basis, double refraction in calcite could be understood as a phenomenon involving polarized light It had been assumed that light waves in an ether were necessarily longitudinal, like sound waves

in a fluid, which cannot support transverse vibrations For each of the two

compo-nents of polarized light, Fresnel developed the Fresnel equations, which give the

amplitude of light reflected and transmitted at a plane interface separating two cal media

opti-Working in the field of electricity and magnetism, James Clerk Maxwell

syn-thesized known principles in his set of four Maxwell equations The equations

yielded a prediction for the speed of an electromagnetic wave in the ether that turned

Chap 1 Nature of Light

out to be the measured speed of light suggesting its electromagnetic character From then on, was viewed as a particular region the electromagnetic spec-trum of radiation The experiment (1887) of Albert Michelson and Edward M()rle~v which attempted to detect optically the earth's motion the and the special theory of relativity (1905) of Albert Einstein were of monumental impor-tance Together led inevitably to the conclusion that the assumption of an ether was superfluous The with transverse vibrations of a wave in a fluid thus vanished

If the nineteenth century served to place the wave theory of light on a firm foundation, this foundation was to crumble as the century came to an end The wave-particle controversy was resumed with vigor we mention

some of the key events along the way Difficulties in the wave theory seemed to show up in situations that involved the interaction of light with matter In at the very dawn of the twentieth Max Planck announced at a meeting of the German that he was able to derive the correct blackbody radiation

only by the curious assumption that atoms emitted light in

energy chunks rather than in a continuous manner Thus and quantum

me-chanics were born According to Planck, the energy E of a quantum of

where the constant of proportionality, PlaflCk's constant, has the very small value of

6.63 x 10-34 J-s years later, in the same year that published his theory of

relativity, Albert Einstein offered an explanation of the photoelectric

the emission of electrons from a metal surface when irradiated with light Central to explanation was the conception of as a stream of whose

related to frequency Planck's (1 Then in 1913 the Danish

Bohr once more incorporated the of radiation in his explanation of the emission and absorption processes of the hydrogen atom, providing a physical basis for understanding the hydrogen spectrum Again in the photon model of came to the rescue for Arthur Compton, who explained the scattering of from electrons as particlelike collisions between photons and electrons in which both energy and momentum were conserved

All such victories for the photon or particle model of indicated that light could be treated as a particular kind matter, possessing both energy and momen-tum It was Luis de who saw the other side of the In 1924 he pub-his speCUlations that subatomic are endowed with wave properties

He suggested, in that a particle with momentum p had an associated length of

wave-h

(1

p

hypothesis appeared the years 1927-1928, when Clinton Davisson and Lester

ments that could only be interpreted as the diffraction of a beam of electrons Thus the wave-particle duality came full circle Light behaved like waves in propagation and in the phenomena of interference and diffraction~ it could, however, also behave as particles in its interaction with matter, as in the photoelectric effect

On the other hand, electrons usually behaved like particles, as in the like scintillations of a exposed to a beam of electrons; in other situations were found to behave Hke waves, as in the diffraction produced by an electron

4

Photons and electrons that behaved both as and as waves seemed at first an contradiction, since and waves are very different entities

Gradually it became clear, to a extent through the reflections of Niels

Bohr and especially in his principle of that photons and electrons were neither waves nor particles, but more complex than either,

models like waves and As it turns out, however, the '''~JUJ:',JIV''''~' of a photon or an electron is not exhausted by either model In cer-

attributes stand out We can appeal to no simpler model that is adequate to handle all cases

Quantum mechanics, or wave mechanics, as it is often called, deals with all more or less localized in space, and so describes both light and matter,

Combined with special relativity, the momentum p, A., and speed v for

both material particles and photons are by the same equations:

eQllati!on:s, m is the rest mass and E is the total energy, the sum of rest-mass

and kinetic energy, that is, the work done to accelerate the particle from

The proper expression for kinetic energy is no simply ~mv2,

but mc 2 (y I), The relativistic expression for kinetic energy tmv 2 for

while nonzero rest-mass particles like electrons have a of c,

Eq (1 shows that zero rest-mass particles like photons must travel with the stant speed c The energy of a photon is not a function of its speed but of its fre-

that for a photon, because of its zero rest mass, there is no distinction between its total energy and its kinetic energy The following example illustrates the pn~ce,all1'~ equations

Chap 1 Nature of

Example

An electron is accelerated to a energy of 2.5 MeV Determine its tivistic momentum, de Broglie wavelength, and speed Also determine the same properties for a photon having the same energy as the electron

rela-Solution The electron's total energy E must be the sum of its rest mass

en-ergy and its kinetic enen-ergy,

= 0.511 MeV + 2.5 MeV 3.011 MeV

or

E = 3.011 X 1(1' eV X (1.602 X 10-19 J/eV) = 4.82 X 10-13 J The other quantities are then calculated in order From

p = 1.58 X 10-21 kg-m/s

(1-3):

A = 41.8 X 10-12 m 41.8 pm From Eq (1-5):

v = 2.95 X lOS mJs For the photon, with m 0, we get instead From

p = 1.61 X 10 21

A = 0.412 pm From Eq (l

v = c 3.00 X 108 m/s

(1-6):

Another important distinction between electrons and is that electrons obey Fermi statistics whereas photons obey Bose statistics A consequence of Fermi statistics is the restriction that no two electrons in the same interacting be in

the same state, that is, have the same physical properties Bose statistics

no such prohibition, so that identical photons with the same energy and mentum can occur together in large numbers Because light beams can possess so many similar photons in proximity, the granular structure of the beam is not ordi-narily experienced, and the beam can be adequately represented by a continuous

mo-""U'IaOiU"' •• , wave From this of fields appear as a

A profound consequence of the wave nature of is embodied in the Heisenberg principle of indeterminacy As a result of this principle, particles do not obey deterministic laws of motion Rather, the predicts probabilities Wave functions are associated with the particles through the fundamental wave equa-

that a particle will be found within a region of space during an interval of time Thus

the irradiance (power/area) of these waves at some intercepting surface, also

propor-tional to the square of the wave amplitudes, provides a measure of this probability

that the irradiance of light at a location is proportional to the number of photons

""~_'V"",", through the location per second

PROBLEMS

6

In this way, the interference and diffraction patterns explained by waves can be interpreted as manifestations of particles V<>r'tu'!I", wave amplitudes predict the probabilities of their locations in the same patterns

In the theory called quantum electrodynamics, which combines the pnncllpl(~

of quantum mechanics with those of special relativity, are assumed to

emitting a photon, with a probability that is proportional to the square of the charge There is no conservation law for photons as there is for the charge associated

Essen-tial distinctions between and electrons are removed Both are considered subject to the same principles Through this unification, light is viewed as basically just another form of matter Nevertheless the aspects of

"Slr'firl", and wave of light remain, justifying our use of one or the other description when The wave description of light will be found adequate

to describe most of the optical phenomena treated in this text

1-1 Calculate the de of (a) a golf ball of mass 50 g moving at 20 mls

and (b) an electron with kinetic energy of 10 eV

1-2 The threshold of of the human eye is about 100 photons per second The eye is most sensitive at a of around 550 nm For this determine the threshold in watts of power

1-3 What is the energy, in electron volts, of light photons at the ends of the visible trum, that is, at of 400 and 700 nm?

spec-1-4 Determine the wavelength and momentum of a photon whose energy the mass energy of an electron

rest-1-5 Show that the rest-mass energy of an electron is 0.511 MeV

1-6 Show that the relativistic momentum of an electron, accelerated a potential difference of I million can be conveniently as 1.422 MeV/c, where c

is the speed of light

1-7 Show that the of a photon, measured in angstroms, can be found from its energy, measured in electron the convenient relation,

1-8 Show that the relativistic kinetic energy,

12,400

E(eV)

Ek mc 2

(')' - I) reduces to the classical , when t; ~ c

1-9 A proton is accelerated to a kinetic energy of 2 billion electron volts it'> momentum; (b) its de wavelength; (c) the wavelength of a same total energy

Find (a) with the

1·10 Solar radiation is incident at the earth's surface at an average of 1353 W/m2 on a face normal to the rays For a mean of 550 nm, calculate the number of photons falling on 1 cm2 of the surface each second

sur-1-11 Two parallel beams of radiation with different deliver the same power to equivalent surface areas normal to the beams Show that numbers of photons striking the surfaces per second for the two beams are in the same ratio as their wavelengths

Chap 1 Nature of light

IIEFERENCES

[I] Ronchi, vasco The Nature Cambridge: Harvard '"nIP "ru Press~ 1970~

[2] Hoffmann, Banesh The Strange Story of the Quantum New York: Dover Publications,

1959

[3J vuantum Mechanics New York: Charles Scribner's Feinberg, Gerald "Light." In Lasers and Light, pp 4-13 San Francisco: W H Free- man and Publishers, 1969

[5] Cantor, G N Optics Newton

[6] John Concepts ofClassicai

of electromagnetic radiation can be classified on the basis of their spectral range and the strength of produced (sources) or (detectors) These COllSldler-ations are essential to the production and measurement of electromagnetic

and are discussed in this chapter

2-1 ELECTROMAGNETIC SPECTRUM

8

An electromagnetic disturbance that propagates through space as a wave may be

monochromatic that characterized for practical purposes by a single wavelength,

or polychromatic, in which case it is repre <;entoo by wavelengths, either crete or in a continuum The distribution of energy among the various constituent waves is called the spectrum the radiation, and the spectral implies a de-pendence on wavelength Various regions of the spectrum are re-ferred to by particular names, such as radio waves, cosmic light, and ultraviolet radiation, because of differences in the way they are or detected Most of

dis-the common are given in Figure 2-1, in which the electromagnetic

is displayed in terms of both wavelength (A) and frequency (v) The two quantities are related, as with all wave motion, through the wave vel()(.'ity (c):

The radiation in Figure 2-1 is assumed to propagate in free space, for which, approximately, c 3 x lOS m/s Common units for wavelength shown are

the angstrom (1 A = m), the nanometer (1 nm m), and the

microme-ter (1 p,m = 10-6 m) The regions ascribed to various types of waves, as shown, are not precisely bounded Regions may overlap, as in the case of the continuum from X-rays to gamma rays The choice of label will on the manner in which the

I to- 15

(short-wavelength end) is bounded by the invisible ultraviolet and Intl"nrl"£1 'oi." "

Radiometry is the science of measurement of radiation In the

dis-cussion we present the radiometric or physical terms used to characterize the energy content of radiation Later we briefly discuss some of the more common principles used in the instruments to measure radiation Many radiometric terms have been introduced and however we include here only approved Inter-national System (SI) units These terms and units are summarized in Table 2-1.1

TABLE 2-1 RADIOMETRIC AND PHOTOMETRIC TERMS

(talbot)

or (Ix)

or (cd)

10

Radiometric quantities appear either without or with the subscript e

(electromagnetic) to them from similar terms, to be

de-scribed afterwards The terms radiant energy, (J radiant energy sity, We (J/m 3

den-), and radiant (W watts J/s), need no further

explana-tion Radiant flux density at a measured in watts per square meter, may be

exilance, Me or onto a in which case it is called irradiance,

The radiant flux (<Il,) emitted per unit of solid angle (w) by a point source in a

direction (Figure 2-2) is called the radiant intensity, leo This quantity, often

d<ll

P""""UU; !C""U"!'UC"W""Y Table 2-1 is meant to serve as a convenient summary that can be

re-2 Production and Measurement of light

2-2 The radiant intensity is the flux

•

where sr = steradian The radian intensity Ie a radiating W of power uniformly in all directions, for example, is 4l e l41r Wlsr, since the total surrounding

solid angle is 471" sr

Figure 2-3, is now apparent by calculating the irradiance of a point source on a

spherical surface surrounding the point, of solid angle 471" sr and surface area 41rr2

larger areas, producing an irradiance decreases inversely with the square of the distance

perpendicular to the specified direction, and is given by

Sup-pose a plane or reflector is diffuse, by which we mean that it

radi-ates uniformly in all directions The is measured for a fixed solid angle defined by the fixed aperture Ap at some distance r from the radiating surface, shown in 2-4 The aperture might be the input aperture of a detecting instru-

pn:selnte:d by the surface decreases in such a way

a relation called Lambert's cosine law If the radiance is determined at each angle 0,

it is found to be constant, because the intensity must be by the projected

Sec 2-2

Thus when a (or reflecting) surface has a radiance that is of the

the surface is said to be perfectly diffuse or a Lambertiml surface

We show next that the radiance has the same value at any point along a ray

in a uniform, nonabsorbing medium Figure illustrates a narrow radiation in such a medium, including a central ray and a bundle of

situ-the beam The central ray makes of 91 and 92 ,

-a simil-ar -ar,g;UITlenl, in which we reverse the roles of dA]

dw 2 (dA 2 cos (2) (dAI cos

we can conclude from Eqs (2-7) and (2-8) that Ll = It • " ".,.,", that the radiance

Chap 2 Production and Measurement of light

Suppose, referring to Figure 2-6, that we wish to know the quantity of radiant

power reaching an element of area dA 2 on surface S2 due to the source element dA 1

on surface SI The line joining the elemental areas, of length r12, makes angles of 01 /

one surface by another radiating surface Each

and O 2 with the respective normals to the surfaces, as shown The radiant power is

Radiometry applies to the measurement of all radiant energy Photometry, on the

other hand, applies only to the visible portion of the optical spectrum Whereas diometry involves purely physical measurement, photometry takes into account the response of the human eye to radiant energy at various wavelengths and so involves psycho-physical measurements The distinction rests on the fact that the human eye,

ra-as a detector, does not have a "flat" spectral rsponse; that is, it does not respond with equal sensitivity at all wavelengths If three sources of light of equal radiant power but radiating blue, yellow, and red light, respectively, are observed visually, the yellow source will appear to be far brighter than the others When we use photo-metric quantities, then, we are measuring the properties of visible radiation as they appear to the normal eye, rather than as they appear to an "unbiased" detector Since not all human eyes are identical, a standard response has been determined by the International Commission on Illumination (CIE) and is reproduced in Figure 2-7 The relative response or sensation of brightness for the eye is plotted versus wavelength showing that peak sensitivity occurs at the "yellow-green" wavelength

of 555 nm Actually the curve shown is the luminous efficiency of the eye for topic vision, that is, when adapted for day vision For lower levels of illumination,

pho-when adapted for night or scotopic vision, the curve shifts toward the green, peaking

at 510 nm It is interesting to note that human color sensation is a function of

14

Figure 2·7 CIE luminous efficiency curve The luminous flux to

I W of radiant power at any wavelength is by the product of 685 1m and the

luminous at the same (A) = 685V(A) for each watt of

nation and is totally absent at lower levels of illumination One confirm this is to compare the color of stars, as appear visually to graphic images on color film using a suitable time exposure

dramatic way to human color on illumination is to LIn"",."

35-mm color slide of a scene onto a screen with a low current in the projector

At sufficiently low currents, the scene appears black and white As the current is creased, the full in the scene gradually emerge On the other

in-tense radiation may be visible beyond the of the CIE curve The "",""'.""

an intense laser beam 694.3 nm from a ruby laser is easily seen Even the infrared radiation around 900 nm from a gallium-arsenide semiconductor laser can be seen as a red

Radiometric are now related to photometric quantities the luminous efficiency curve of Figure 2-7 in the way: Corresponding to a ra-diant flux of 1 W at the wavelength of 555 nm, where the luminous rrl""'nr'v

is maximum, the luminous flux is defined to 685 1m Then, for at

A = 610 nm, in the range where the luminous is 0.5 or 50%,1 W ant flux would only 0.5 x 685 or 3421m luminous flux The curve shows thai again at A 510 nm, in the blue-green, the brightness has dropped to

ofradi-50%

Photometric units, in terms of their definitions, parallel radiometric units

is amply demonstrated in the summary and comparison provided in Table 2-1 In

analogous are related by the following eOllatlon:

photometric unit K(A) x raCllornetrlC unit 10) where K (A) is called the luminous efficacy If V (A) is the luminous efficiency, as

on the CIE curve, then Chap 2 Production and Measurement of light

K(A) = 685V(A) (2-11) Photometric terms are preceded by the word luminous and the corresponding units are subscripted with the letter v (visual); otherwise the symbols are the same Notice that the SI unit of luminous energy is the talbot, the unit of luminous inci-dence is the lux (Ix), and the unit of luminous intensity is the candela (cd) Notice also the distinction between the analogous terms irradiance (radiometric) and illumi- nance (photometric)

Example

A light bulb emitting 100 W of radiant power is positioned 2 m from a face The surface is oriented perpendicular to a line from the bulb to the sur-face Calculate the irradiance at the surface If all 100 W is emitted from a red bulb at A = 650 run, calculate also the illuminance at the surface

sur-Solution

irradiance Ee = PIA = 100 W/41r (2 ftl == 2 W/m2

From the CIE curve, V (650 run) = o 1 Thus

illuminance E" = K(A) x irradiance = 685 V(A) x E

E" = 685 x 0.1 x 2 = 137 Im/m2 or lux Thus, whereas a radiometer with aperture at the surface measures 2 W/m2, a

photometer in the same position would be calibrated to read 137 Ix

When the radiation consists of a spread of wavelengths, the radiometric and the photometric terms may be functions of wavelength This dependence is noted by preceding the term with the word spectral and by using a subscript A or adding the A

in parentheses For example, spectral radiam flux is denoted by <fleA or <fle(A) The total radiant flux is then determined by integration over the wavelength region of in-terest:

2-4 BLACKBODY RADIA nON

A blackbody is an ideal absorber: An radiation falling on a blackbody, irrespective

of wavelength or angle of incidence, is completely absorbed It follows that a body is also a perfect emitter: No body at the same temperature can emit more radia-tion at any wavelength or into any direction than a blackbody Blackbodies are ap-proached in practice by blackened surfaces and by tiny apertures in radiating cavities An excenent example of a blackbody is the surface formed by the series of sharp edges of a stack of razor blades The array of blade edges effectively traps the incident light, resulting in almost perfect absorption

black-The spectral radiant exitance MA of a blackbody can be derived on theoretical grounds It was first so derived by Max Planck, who found it necessary to postulate quantization in the process of radiation and absorption by the blackbody The result

of this calculation [I] is given by

MA = 2:~2 ChclAk~ _ I) (2-12)

where A is in micrometers and T is in Kelvin The quantity MJ is plotted in Figure

2-8 for different temperatures The spectral radiant exitance is seen to increase

Figure 2-8 Blackbody radiation spectral distribution at four Kelvin temperatures

The vertical dashed lines mark the visible spectrum, and the dashed curve

(5£7 = 5 x 10 7)

absolute temperature at each wavelength The peak also shifts toward

(dashed vertical lines) at T = 5000 and 6000 K The variation of , the length at which MA peaks, with the temperature can be found by differentiating M"

wave-with to A and setting this equal to zero The result is the Wien displacement

he

T = 5k 2.88 x 103 (!-Lm-K) (2-13)

2 Although Wien's law is often found written in this form, the number 5 is an approximation to

Chap 2 Production and Measurement of

and is indicated in 2-8 by dashed curve If, on the tral exitance of 12) is integrated over all wavelengths exi-tance or area under the blackbody radiation curve at temperature T is

known as the Stefan-Boltzmann law, with u as the Stefan-Boltzmann constant, equal

to 5.67 x 10-8 >N",n-_IK The from real surfaces is always less than that the blackbody or

Planckian source and is accounted for quantitatively by the em".',''''''' E guishing now between the radiant exitance M of a measured and that of a blackbody Mbb at the same temperature, we define

of the is proportional to that of the blackbody and curves are the same except a constant factor The radiation a heated tungsten wire, for example, is close to that of a graybody with E 0.4-0.5

Blackbody radiation is used to establish a color scale in terms of absolute perature The color temperature of a specimen of is then the temperature

tem-of the with the closest energy distribution In this way, a flame can said to have a color of 1900 K, whereas the sun has a

2-5 SOURCES OF OPTICAL RADIATION

Sources of may be natural, as in the case of sunlight and or

as in the case of incandescent or lamps from various sources may also be as monochromatic, spectf'dlline, or continuous The way in which energy is in the radiation determines the color of the light and, conse-quently, the color of surfaces seen under the Jight Anyone who has used a camera is aware the actual color response of depends on the of light used to illu-minate the subject

The following brief survey of sources of light cannot hope to be sive; rather it is intended to direct attention to an extensive area of practical int;nrt1n",_ lion For the purposes of this limited survey, we classify a number of sources as lows:

b Compact short arc

2.4r ~ -c-r -r -r -~

., t)

<:

II)

'i'i .~

Visible

0.8

Ultraviolet

i=vtrAt ""tri.,,1 sun

Sea-level sunlight 1M = 1 air mass)

1.4

Wavelength (,urn)

2.0

surface at sea level: clear day, sun at zenith

2.6

Extraterrestrial solar radiation indicates that the sun behaves approximately as a blackbody with a of 6000 K at its center and K at edge, but the radiation at the earth's surface is modified by absorption in the earth's at-mosphere The annual average of total irradiance just outside the earth's atmosphere

is the solar constant, 1350 W/m 2

• Although solar radiation is not routinely used as a light source in the laboratory, xenon lamps, with appropriate provide an excellent artificial source for solar simulation and are commer-Artificial optical sources that use light produced by a material heated to incan-

descence by an electric current are caned incandescent lamps Radiation arises from

the de-excitation of the atoms or molecules of the material after have been mally excited The energy is emitted over a brood continuum wavelengths Com-

ther-mercially available blackbody sources consist of equipped with a small hole Radiation from the small hole has an emissivity that is essentially constant and equal

to unity Such sources are available at operating temperatures from that of liquid trogen 196°q to 3QOO0c Incandescent sources particularly useful in the infrared

ni-include the Nernst glower This source is a cylindrical tube or rod of refractory

ma-terial (zirconia, yttria, thoria), by an electric current and useful from the Chap 2 Production and Measurement of Light

Typical spectral irradiance from bare element

per 1O-mm 2 area

Wa\lelength Illm)

Figure 2·10 Globar jnfrared source, providing continuous usable emission from

1 10 over 25 /-Lm al a temperature variable up to 1000 K The source is a 6.2-mm

diameter silicon carbide resistor (Oriel Corp., General Stratford,

Conn.)

for higher-temperature operation Radiation over the spectrum

that of a graybody, emissivities approaching unity for tightly coiled filaments Lumen output depends both on the temperature and the electrical power in-put (wattage) During operation, tungsten gradually evaporates from the filament and deposits on the inner bulb surface, leaving a dark film that can decrease the flux out-put by a<; much as 18% the life of the This also weakens the filament and increases its resistance The presence of an

nitrogen or argon, introduced at around 0.8 pressure, to slow down the evaporation More recently problem ha<; been minimized by the addi-

a halogen vapor (iodine, bromine) to the gas in the quartz-halogen or

the bulb free of tungsten reacts with the deposited to form the gas tungsten which then at the hot filament to the E>"."'''

and free the iodine for repeated operation A spectra] curve for a 100-W quartz-halogen filament source is given in 2-11 The lamp approxi-

20

c 3.0 §

2·11 irradiance from a IOO-W quartz halogen lamp, providing

acc:ele:ratles pl!p('trnr\ : sufficiently to ionize the vapor atoms The source

of the electrons may be a heated cathode (thermionic emission), a strong field plied at the cathode (field or the impact of positive ions on the cathode (secondary emission) De-excitation of the excited vapor atoms provides a release of

generally results in a continuous output, in addition to lines teristic of the vapor At lower and current, lines appear,

in monochromatic sources, is to operate at low temperature, sure, and current The sodium arc lamp, for example, radiation almost completely confined to a narrow "yellow" band due to the lines at 589.0 and 589.6 nID The mercury tube is often used to provide, with

pres-the help of isolating monochromatic radiation at wavelengths of 404.7 and nm (violet) 546.1 nm and 577.0 and 579.1 nm (yellow) Other gases or vapors may be used to lines of other desired wavelengths For the highest spectral purity, of the gas are used

When high intensity rather purity is desired, other designs

be-pprh~t~ the oldest source of this kind is the carbon arc, still widely

between two carbon rods in air A 200-A arc lamp may have a peak nance of 1600 The source has a distribution close to that of a gray-body at 6000 K A wide range of spectral outputs is possible by using different ma-terials in the core of the carbon rod When the arc is enclosed in an atmosphere of vapor at pressure, the lamp is a short-arc source and the radiation is

lumi-divided between line and continuous See 2-12 for a sketch of this type of and its The most of these lamps, designed to operate from 50 W to 25 kW, are mercury arc lamp, with comparatively

weak background radiation but strong spectral lines and a good source of ultraviolet; the xenon arc lamp, with practically continuous radiation from the near-ultraviolet

Chap 2 Production and Measurement of Ught

reflector and focusing system (The Eating Corp.)

through the visible and into the and the mercury-xenon arc lamp,

providing essentially the mercury spectrum but with xenon's contribution to the continuum and its own strong spectral emission in the 0.8- to l-lLm range As men-tioned the color quality of the xenon lamp is similar to that of sunlight at 6OOO-K color temperature emission curves for Xe and lamps are shown in 2-13 and 2-14 The hydrogen and deuterium arc lamps are ideal

for ultraviolet spectroscopy because produce a radiance with a continuous background in the ultraviolet region Figure 2-15 shows the typical spectral output

of a deuterium lamp, which produces a line-free continuum from below 180 nm to

400 nm

tubes represent a high output source of visible and near infrared tion produced by a discharge of stored electrical energy through a gas-filled tube The gas is most often xenon The photoflash in contrast, provides high-intensity, short-duration illumination by the rapid combustion of metallic (aluminum

or zirconium) foil or wire in a pure oxygen atmosphere

When a high-intensity point source of radiation is desired in optical tation a useful lamp is the concentrated zirconium arc lamp, with wattages ,,,n',,",,,,, from 2 W to 300 W Zirconium vapor is formed by evaporation from an oxide-

0.008 0.000 0.004 0.003 0.002

Chap 2

Wavelength (nm)

General Catalogue, Stratford, Conn.)

Production and Measurement of light

incan-The familiar fluorescent lamps use low-pressure, low-current electrical

in mercury vapor ultraviolet radiation from excited mercury atoms is converted to visible light by fluorescence in a phosphor on inside of the glass-envelope surface Spectral outputs depend on the particular used "Daylight" lamps, for use a mixture of zinc beryllium

A very different type of source is the low-intensity diode , , a solid-state device employing a p-n junction in a semiconducting crystal The device is hermeticaUy sealed in an optically centered package When a small

re-combination of electrons and holes in the vicinity of the junction LEDs clude the infrared GaAs with a output wavelength near 900 nm and the visible SiC device, with peak output at 580 nm LEDs provide narrow emis-sion bands, as evident in 2-16 Solid solutions of similar cOln~oof1ld

in-materials produce output in a of spectral regions when the alloy is varied

Emission wavelength 111m I

light·emitting diode

The laser is a very important modem source of coherent and extremely

mono-chromatic radiation of very intensity Lasers emit in the traviolet visible, and of the spectrum Because of the central role that lasers play in instrumentation, they are treated in a chapter

Any device that produces a measurable physical response to incident radiant energy

is a detector The most common detector is, of course, the eye Whereas the eye

n '~",,""'C a and subjective response, the detectors discussed here provide

a quantitative and response In view of the role played by the eye

in human vision, it is treated in another

Sec 2-6 Detectors of Radiation