APPL-1008 / Page 1 of 31
`Apple Inc. v. Corephotonics
`
`

`

`~·" .•
`
`;' : .
`
`,.
`
`The Manual of Photography
`Ninth Edition
`
`I
`I
`J I
`
`APPL-1008 / Page 2 of 31
`
`

`

`The Manual of Photography
`Photographic and digital imaging
`
`Ninth Edition
`
`"
`
`Ralph E. Jacobson
`MSc, PhD, CChem, FRSC, ASIS Hon., FRPS,
`FBIPP
`
`Sidney F. Ray
`BSc, MSc, ASIS, FBIPP, FMPA, FRPS
`
`Geoffrey G. Attridge
`BSc, PhD, ASIS, FRPS
`
`Norman R. Axford
`BSc
`
`Focal Press
`OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI
`
`APPL-1008 / Page 3 of 31
`
`

`

`Focal Press
`An imprint of Butterworth-Heinemann
`Linacre House, Jordan Hill, Oxford OX2 8DP
`225 Wildwood Avenue, Woburn, MA 01801-2041
`A division of Reed Educational and Professional Publishing Ltd
`-@.__ A member of the Reed Elsevier plc group
`The I/ford Manual of Photography
`First published 1890
`Fifth edition 1958
`Reprinted eight times
`
`The Manual of Photography
`Sixth edition 1970
`Reprinted 1971, 1972, 1973, 1975
`Seventh edition 1978
`Reprinted 1978, 1981, 1983, 1987
`Eighth edition 1988
`Reprinted 1990, 1991, 1993, 1995 (twice), 1997, 1998
`Ninth edition, 2000
`
`© Reed Educational and Professional Publishing Ltd 2000
`
`All rights reserved. No.part of this publication may be reproduced in.
`any material fo1m ·(including photocopying or storing _in any medium by
`electronic means imc! whether or not transiently or incidentally to some
`other use of this publication) without the written permission of the
`copyright holder ~xcept in accordance with the provisions of the Copyright,
`Designs and Patents Act 1988 or under the terms of a licence issued by the
`Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London,
`England WlP OLP. Applications for the copyright holder's written
`permission to reproduce any part of this publication should be ad\lfessed .
`. to the publishers
`
`Under the terms of the Copyright, Designs and Patents Act 1988, Sidney Ray asserts his moral
`rights to be identified as an author of this multi-authored work
`.
`'
`British Library,. Cataloguing in Publication Data
`The rhanuat of photography: photographic and
`digitaI imaging - 9th ed.
`1. Photography - Handbooks, manuals, etc.
`I. Jacobson, Ralph E. (Ralph Eric), 1941-
`771
`rsaN 0.240 51574 9
`
`Library of Congress Cataloguing in Publication Data
`The manual of photography: photographic and digital imaging. - 9th ed./Ralph E.
`Jacobson ... [et al.].
`p.cm.
`Originally published in 1890 under the title: The Ilford manual of photography.
`Includes bibliographical references and index
`ISBN 0 240 51574 9 (alk. paper)
`I. Jacobson, R. E.
`1. Photography.
`
`TR145 .M315 2000
`771- dc21
`
`00-042984
`
`Composition by Genesis Typesetting, Rochester
`Printed apd bound in Great Britain
`
`RLANrA
`_TREE
`
`~~
`
`British frmt for
`Come' 11atw11 Volu11tecrs
`
`FOR BVERY TITLB THAT \VB PUBLISH, BUTTBRIVORTH·HBINBMANN
`WILL PAY FOR BTCV TO PLANT AND GARB FOR A.TREB.
`
`APPL-1008 / Page 4 of 31
`
`

`

`Contents
`
`1
`
`2
`
`3
`
`4
`
`Preface to the first edition of The
`tiford Manual of Photography
`(1890)
`
`Preface to the ninth edition
`
`Imaging systems
`Ralph E. Jacobson
`The production of images
`Photographic and digital imaging
`General characteristics of reproduction
`systems
`Imaging chains
`The reproduction of tone and colour
`Image quality expectations
`
`Fundamentals of light and vision
`Ralph E. J acobson
`Light waves and pa1ticles
`Optics
`The electromagnetic specti·um
`The eye and vision
`
`Photographic light sources
`Sidney F. Ray
`·Characteristics of light sources
`Light output
`Daylight
`Tungsten-filament lamps
`Tungsten-halogen lamps
`Fluorescent lamps
`Metal-halide lamps
`Pulsed xenon lamps
`Expendable flashbulbs
`Electronic flash
`Other sources
`
`The geometry of image
`formation
`Sidney F. Ray
`Interaction of light with matter
`Image formation
`The simple lens
`Image formation by a compound lens
`Graphical consti·uction of images
`
`ix
`
`xi
`
`1
`
`1
`2
`
`5
`6
`6
`7
`
`9
`
`9
`10
`10
`11
`
`16
`
`16
`21
`25
`25
`26
`27
`27
`27
`28
`29
`38
`
`39
`
`39.
`41
`42
`43
`45
`
`The lens conjugat6' equation
`Field angle of view
`Covering power of a lens
`Geometiic distortion
`Depth of field
`Depth of field equations
`Depth of focus
`Perspective
`
`5
`
`The photometry of image
`formation
`Sidney F. Ray
`Stops and pupils
`Aperture
`Mechanical vignetting
`Image illumination
`Image illuminance with wide-angle
`lenses
`Exposure compensation for close-up
`photography
`.
`Light losses . and lens ti·ansmission
`Flare and its effects
`T-numbers
`Anti-reflection coatings
`
`6 Optical aberrations and lens
`performance
`Sidney F. Ray
`Introduction
`Axial chromatic abenation
`Lateral chromatic abenation
`Spherical abenation
`Coma
`Curvature of field
`Astigmatism
`Curvilinear distortion
`Diffraction
`Resolution and resolving power
`Modulation transfer function
`
`7 Camera lenses
`Sidney F. Ray
`
`Simple len.ses
`Compound lenses
`
`45
`48
`49
`49
`50
`53
`56
`57
`
`61
`
`61
`62
`62
`63
`
`66
`
`67
`68
`68
`69
`69
`
`72
`
`72
`72
`74
`75
`76
`77
`77
`78
`79
`80
`81
`
`83
`
`83
`83
`
`v
`
`APPL-1008 / Page 5 of 31
`
`

`

`vi Contents
`
`Development of the photographic lens
`Modem camera lenses
`Wide-angle lenses
`Long-focus lenses
`Zoom and varifocal lenses
`Macro lenses
`Teleconverters
`Optical attachments
`Special effects·
`
`8
`
`Types of camera
`Sidney F. Ray
`Survey of development
`Camera types
`Special purpose cameras
`Automatic cameras
`Digital cameras
`Architecture of the digital camera
`
`9 Camera features
`Sidney F. Ray
`Shutter systems
`The iris diaphragm
`Viewfinder systems
`Flash synchronization
`Focusing systems
`Autofocus systems
`Exposure metering systems ··
`Battery power
`Data imprint;ing
`
`1 (j
`
`. .
`Camera movements
`Sidney F. Ray
`Introduction
`Translational movements
`Rotational movements
`Lens covering power
`Control of image sharpness
`Limits to lens tilt
`Control of image shape
`Perspective control len$eS
`Shift cameras
`
`11 · Optical filters
`Sidney F. Ray
`Optical filters ·
`Filter sizes
`Filters and focusing
`Colour filters for black-and-white
`photography
`Colour filters for colour phot.ography
`Special filters
`Polarizing filters
`Filters for darkroom use
`
`12
`
`13
`
`14
`
`15
`
`85
`88
`91
`93
`95
`98
`99
`100
`102
`
`104
`
`104
`107
`113
`115
`120
`125
`
`131
`
`131
`136
`138
`143
`144
`151
`154
`160
`161
`
`163
`
`163
`165
`165
`166
`168
`170
`171
`173
`174
`
`176
`
`176
`178
`178
`
`179
`182
`183
`186
`189
`
`Sensitive materials and image
`sensors
`Ralph E. Jacobson
`Latent image formation in silver
`halides
`Image formation by charge-coupled
`devices
`Production of light-sensitive materials
`and sensors
`Sizes and formats of photographic and
`electronic sensors and media
`
`Spectral sensitivity of
`photographic materials
`Geoffrey G. Attridge
`Response of photographic materials to
`short-wave radiation
`Response of photographic materials to
`visible radiation
`Spectral sensitization
`Orthochromatic materials
`Panchromatic materials
`Extended sensitivity materials
`Infrared materials·
`Other uses of dye sensitization
`Determination of the colour sensitivity
`of an unknown material
`Wedge spectrograms
`Spectral sensitivity of digital cameras
`
`Principles of colour photography
`Geoffrey G. Attridge
`Colour matching
`The first colour photograph
`Additive colour photography
`Subtractive colour photography
`Additive processes
`Subtractive processes.
`Integral tripacks
`
`Sensitometry
`Geoffrey G_. Attridge
`The subject
`Exposure
`Density
`Effect of light scatter in a negative
`Callier coefficient
`Density in practice
`The characteristic (H and D) curve
`Main regions of the negative
`characteristic curve
`Variation of the characteristic curve
`with the material
`Variation of the characteristic curve
`with development
`
`191
`
`191
`
`193
`
`195
`
`200
`
`205
`
`205
`
`206
`207
`208
`208
`208
`209
`209
`
`210
`210
`211
`
`213
`
`213
`214
`214
`214
`215
`217
`217
`
`218
`
`218
`218
`. 219
`220
`220
`221
`222
`
`223
`
`225
`
`225
`
`........... -------- -
`
`APPL-1008 / Page 6 of 31
`
`

`

`91
`
`l91
`
`l93
`
`.95
`
`~00
`
`:05
`
`~05
`
`~06
`rn
`~08
`~08
`'.08
`'.09
`'.09
`
`:10
`:10
`~11
`
`13
`
`:13
`:14
`:14
`:14
`.15
`.17
`.17
`
`18
`
`.18
`.18
`.19
`20
`20
`21
`22
`
`23
`
`25
`
`25
`
`Gamma-time curve
`Variation of gamma with wavelength
`Placing of the subject on the
`characteristic curve
`Average gradient and (;
`Contrast index
`Effect of variation in development .on
`the negative
`Effect of variation in exposure on the
`negative
`Exposure latitude
`The response curve of a photographic
`paper
`Maximum black
`Exposure range of a paper
`Vaiiation of the print curve with the
`type of emulsion
`Variation of the print curve with
`development
`Requirements in a print
`Paper contrast
`The problem of the subject of high
`contrast
`Tone reproduction
`Reciprocity law failure
`Sensitometric practice
`Sensitometers
`Densitometers
`Elementary sensitometry
`Sensitometry of a digital camera
`
`The reproduction of colour
`Geoffrey G. Attridge
`Colours of the rainbow
`Colours of natural objects
`Effect of the light source on the
`appearance of colours
`Response of the eye to· colours
`Primary and complementary colours
`Complementary pairs of colours
`Low light levels
`Black-and-white processes
`Colour processes
`Formation of subtractive image dyes
`Colour sensitometry
`Imperfections of colour processes
`Correction of deficiencies of the
`subtractive system
`Masking of colour materials
`Problems of duplication
`The chemistry of colour image
`formation
`Chromogenic processes
`Silver-dye-bleach process
`Instant colour processes
`Alternative method fodnstant
`photography
`
`226
`227
`
`227
`228
`228
`
`228
`
`229
`230
`
`231
`231
`232
`
`232
`
`233
`234
`234
`
`235
`236
`238
`239
`240
`241
`244
`245
`
`247
`
`247
`247
`
`248
`248
`249
`250
`250
`250
`251
`254
`254
`258
`
`259
`260
`261
`
`263
`263
`268
`269
`
`271
`
`17
`
`Contents vii
`
`Photographic processing ·
`Ralph E. Jacobson
`Developers and development
`Developing agents
`Preservatives
`Alkalis
`Restrainers (anti-foggants)
`Miscellaneous additions to developers
`Superadditivity (synergesis)
`Monochrome developer formulae in
`general use
`Changes in a developer with use
`Replenishment
`Preparing developers
`Techniques of development
`Obtaining the required degree of
`development
`Quality control
`Processing following development
`Rinse and stop baths
`Fixers
`Silver recovery
`Bleaching of silver images
`Washing
`Tests for permanence
`Drying
`
`273
`
`273
`273
`276
`276
`277
`277
`278
`
`279
`282
`283
`284
`285
`
`289
`292
`293
`293
`294
`296
`298
`299
`300
`301
`
`18
`
`302
`
`Speed of materials, sensors and
`systems
`Ralph E. Jacobson
`302
`Speed of photographic media
`302
`Methods of expressing speed
`305
`Speed systems and standards
`ISO speed ratings for colour materials . 306
`307
`Speed of digital systems
`308
`Speed ratings in practice
`
`19 Camera exposure determination
`Sidney F. Ray
`Camera exposure
`Optimum exposure criteria
`Exposure latitude
`Subject luminance ratio
`Development variations
`Exposure determination
`Practical exposure tests
`Light measurement
`Exposure meter calibration
`Exposure values
`Incident light measurements
`Exposure meters in practice
`Photometry units
`Spot meters
`In-camera metering systems
`Electronic flash exposure metering
`Automatic electronic flash
`
`310
`
`310
`311
`311
`312
`313
`313
`315
`315
`316
`318
`318.
`320
`323
`324
`324
`329
`333
`
`16
`
`APPL-1008 / Page 7 of 31
`
`

`

`viii Contents
`
`20 Hard copy output media
`Ralph E. Jacobson
`Hard copy output
`Photographic papers
`Type of silver halide emulsion
`Paper contrast
`Paper smface
`Paper base
`Colour photographic papers
`Processing photographic paper
`Pictrography and Pictrostat
`Dry Silver mate1ials
`Cylithographic materials/Cycolor
`Thermal imaging materials .
`Materials for ink-jet printing
`
`21
`
`Production of hard copy
`Ralph E. Jacobson
`Photographic printing and enlarging
`Types of enlargers
`Light sources for enlarging and
`printing
`Lenses for enlargers
`Ancillary equipment
`Exposure determination
`Conventional image manipulation
`Colour printing
`Colour enlarger design
`Types of colour enlarger
`Methods of evaluating colour negatives
`for printing
`Digital output
`Evaluating the results
`
`336
`
`336
`336
`336
`337
`338
`339
`339
`340
`344
`345
`346
`346
`347
`
`348
`
`349
`349
`
`353
`354
`355
`355
`358
`359
`362
`363
`
`365
`367
`370
`
`22
`
`Life expectancy of imaging media 372
`Ralph E. Jacobson
`Life expectancy of phqtographic media
`Processing conditions
`Storage conditions
`Atmospheric gases
`Toning
`Light fading
`Life expectancy of digital media
`
`372
`373
`··375
`376
`377
`378
`379
`
`23' Colour matters
`Geoffrey G. Attridge
`Specification by sample
`The physical specification of colour
`Specification of colour by synthesis
`Colour gamuts
`Summing up
`
`24
`
`25
`
`Theory of image formation
`Norman R. Axford
`Sinusoidal waves
`Images and sine waves
`Imaging sinusoidal patterns
`Fomier theory of image formation
`Measuring modulation transfer
`functions (MTF)
`Discrete transforms and · sampling
`The MTF for a CCD imaging array
`Image quality and MTF
`
`Images and information
`Norman R. Axford
`Image noise
`Photographic noise
`Quantifying image noise
`Practical considerations for the
`autocorrelation function and the
`noise power spectrum
`Signal-to-noise ratio
`Detective quantum efficiency (DQE)
`Information theory
`
`26 Digital image processing and
`manipulation
`Norman R. Axford
`Linear spatial filtering (convolution)
`Frequency domain filtering
`Non-linear filtering
`Statistical operations (point, grey-level
`operations)
`Image restoration -
`Edge detection and segmentation
`Image data compression
`
`Index
`
`383
`
`383
`384
`384
`389
`392
`
`393
`
`394
`395
`397
`398
`
`406
`408
`411
`411
`
`413
`
`413
`413
`417
`
`419
`420
`422
`426
`
`428
`
`428
`429
`433
`
`434
`438
`442
`443
`
`.447
`
`APPL-1008 / Page 8 of 31
`
`

`

`Lble for
`:rays of
`rared as
`~ne for
`lumina(cid:173)
`linate a
`::an be
`mit the
`typical.
`bin the
`Lination
`local
`
`Lductor
`emits
`hs by
`meous
`t light
`ape of
`to a
`led in
`form.
`>ically
`•stems
`80nrn
`ligital
`
`ma tic
`blue)
`:er to
`lmay
`h.s to
`Dis-
`2nm)
`ns to
`
`ion al
`ston,
`
`·and
`
`·obe.
`
`!ogy.
`
`the
`
`edn.
`
`•lied
`
`4 The geometry of image formation
`
`Interaction of light with matter
`
`Imaging generally records the interaction of light or
`radiation with the subject, except for self-luminous or
`emissive subjects and uses lenses or optical systems
`to fo1m an image at the photoplane of a camera. There
`are four principal effects of the interaction of light
`with an object, namely absorption, reflection, trans(cid:173)
`mission, and chemical change. The first two of these
`always occur to some extent: transmission occurs in
`the case of translucent or transparent matter; and
`chemical change occurs under approp1iate circum(cid:173)
`stances. The absorbed light energy is not destroyed,
`but converted to another such as heat, or sometimes
`electrical or chemical energy. This chapter details the
`behaviour of reflected or transmitted light, and the
`formation of an optical image.
`
`Transmission
`
`Some transparent and translucent materials allow
`light to pass completely through them apait from
`absorption lOsses. Such light is said to be transmitted
`and the transmittance (T) of the matyrial is the ratio
`of emergent luminous flux to incident luminous flux.
`Direct transmission (sometimes miscalled 'specular
`transmission') refers to light transmitted without
`scatter, as for example by cleai· optical glass. If
`selective absorption takes place for particular wave(cid:173)
`lengths of incident white light,. then the material is
`seen as coloured by transmitted light, as in the case of
`a camera filter. If scattering occurs, as in a translucent
`medium, the light undergoes diffuse transmission,
`which may be uniform or directional or preferential.
`The transmittance of such a medium may be defined
`as in either a general or in a specific direction.
`
`Reflection
`
`Depending· on the nature of the surface, particularly
`its smoothness, the reflection of light may be direct or
`diffuse. Direct or specular reflection is the type of
`reflection given by a highly polished surface such as
`a mirror, and. is subject to the laws of reflectiOn
`(Figure 4.1). Light incident on the surface is reflected
`at an angle equal to the· angle of inc;:idence. (The
`angles of incidence and reflection are both measured
`
`Normal
`I
`I
`I
`
`Incident ray
`
`Reflected ray
`
`~ A /
`"<(V.
`
`:::::::::::::::;:::;::::::::::::::::::::;::::::::::::::::::::::::::::::::::::::::::::::::::~:::::::~:~:~:~:~:~:~:~:
`
`Figure 4.1 Specular reflection of an incident light ray by a
`plane minor; i = r
`
`from the nonnal, i.e. the line perpendicular to the
`surface at the point of incidence.) The surface
`b1ightness of a directly reflecting smface is highly
`dependent on viewpoint. A perfectly .diffuse or
`Lambertian surface, on the other hand, reflects the
`incident light equally in all dii'ections;
`thus its
`brightness or luminance is seen as constant irrespec(cid:173)
`tive of viewpoint. Few surfaces have such extreme
`properties; shiny smfaces usually produce some
`scattered light, and matt surfaces (Figure· 4.2) may
`show a
`'sheen'. Reflection from most surfaces
`combines both direct and diffuse reflection and is
`known as mixed reflection. Depending on the proper(cid:173)
`ties of the incident light, the nature of the material and
`angle of :incidence, the reflected light may· also be
`partially or completely polarized. Objects are seen
`mainly by diffusely reflected light which permits the
`perception of detail and textme, qualities not found in
`specular surfaces such as miiTors.
`Reflectance (R) is defined as the ratio of the
`.reflected luminous flux to the incident luminous flux,
`and (as with transmittance) this may be defined as
`either general or in a specific direction. · Smfaces
`
`Incident ray
`
`Reflected rays
`
`Figure 4.2 The diffuse reflection of an incident light ray by
`a matt surface
`
`39
`
`APPL-1008 / Page 9 of 31
`
`

`

`I I .
`
`I !
`
`40 The geometry of image formation
`
`Glass
`
`Refractive index
`
`/
`
`Crown
`Flint
`Dense flint
`
`1.46-1 .53
`1.53-1 .65
`1.65-1.92
`
`Air
`
`A
`-190°--..,--
`1
`I
`I
`
`Normal
`
`Incident
`ray
`
`Figure 4.3 An obliquely incident light ray undergoing refraction when passing from air to glass
`
`commonly encountered have refl.ectances in the range
`0.02 (2 per cent) (matt black paint) to 0.9 (90 per
`cent).
`
`Refraction
`Whe~ a ray of llght being transplitt~d in one medi~m
`passj':S -into anqther o~ different optical properties its
`direction is changed at .the interface except in the case
`when it enters normally, i.e. perpendicular to the
`inierface. This deviation, or refraction of · the ray
`results from a change in the velocity of light in
`passing from one medium to the next (Figure 4.3).
`Lenses utilize the refraction of glass to.form images.
`Light travels more slowly in a denser medium, and a.
`decrease (increase) in velocity causes the ray to be
`bent towards (away from) the normal. The ratio of the
`velocity in empty space to that within the med~um is
`kn_own as the refractive index (n) of the medium. For
`two media of refractive indices n1 and n2 where the
`angles of incidence and refraction are respectively i
`and r, then.the amount of refraction is given by Snell's
`Law:
`
`(1)
`
`Taking n1 as being air of refractive index approx(cid:173)
`imately equal to 1, then the refractive index of the
`··
`medium n2 is given by
`
`sin i
`
`sin r
`
`(2)
`
`The velocity of light in an optical medium depends
`on its wavelength, and refractive index varies in a
`non"linear manner. with wavelength, be;ing greater for
`blue ·light than for red light. A quoted value for
`
`refractive. index (n,i) applies only to one particular
`wavelength. The one usually quoted (nd) refers to the
`refractive index at the wavelength of the d line in the
`helium spectrnm (587 nm).
`When light is transmitted by clear optical glass
`solids or p1isms, refraction causes effects such as
`deviation, dispersion and total internal reflection
`(Figure 4.4). Deviation is the.change of direction of
`the emergent ray with respect to the direction of the
`incident ray. In the case of a parallel-sided glass
`block, the emergent ray is not deviated with respect to
`the original incident ray; but it is displaced, the
`amount depending on the angle of incidence and the
`thiclmess of the block and its refractive index. A non(cid:173)
`parallel-sided prism deviates the ray by two refrac(cid:173)
`tions, the deviation D depending on the refracting
`angle A of the prism, and on its refractive index. But
`when white light is deviated by a prism it is also
`dispersed to form a spectrum. The dispersive power
`of a prism is not directly related to its refractive index
`and it is possible to almost neutralize dispersion by
`using two different types of glass together, whilst
`retaining some deviation. In achromatic lenses this
`allows rays of different wavelengths to be brought to
`a common focus (see Chapter 6).
`For a ray of light emerging from a dense medium
`of refractive index n2 into a less dense medium of
`refractive index n1 , the angle of refraction is greater
`than the angle of incidence, and increases as the angle
`of incidence increases until a ·critical value Cic) is
`reached. At this angle of incidence the ray will not
`emerge at all, it will undergo total internal-reflection
`(TIR).
`At this critical angle of incidence, ic = sin-1
`(nrfn 2 ) . For air (n1 = 1), also for glass with n2 = 1.66,
`ic is 37 degrees. TIR. is used in reflector prisms to give
`almost 100 per cent reflection as compared with 95
`per cent at best for uncoated front-surface mirrors. A
`45 degree prism will deviate a collimated (i.e.
`parallel) beam through 90 degrees by TIR; but for a
`
`APPL-1008 / Page 10 of 31
`
`

`

`The geometry of image formation 41
`
`K
`
`Refracted
`ray
`Normal
`
`d = t sin i ( 1 - .! )
`n
`
`(a)
`
`s
`
`D=A(n -1)
`
`Figure 4.5 Formation of an image by a pinhole. The
`bundles of rays from points on the subject S pass through
`pinhole P and diverge to form an image I on photoplane
`surface K. The image is inverted, reversed, smaller and lacks
`sharpness
`
`(b)
`
`ray
`
`Image formation
`
`Normal
`
`Incident
`ray
`
`lncii:lent
`ray
`
`Air
`
`·incident ray
`(white light)
`
`rticular
`s to the
`e in the
`
`tl. glass
`:uch as
`F[ection
`:tion of
`, of the
`i glass
`:pect to
`~d, the
`md the
`Anon(cid:173)
`refrac(cid:173)
`racting
`:x. But
`is also
`power
`~index
`ion by
`whilst
`es this
`1ght to
`
`.edium
`um of
`7eater
`: angle
`Cic) is
`ill not
`ection
`
`sin- 1
`: 1.66,
`ogive
`ith 95
`ors. A
`' (i.e.
`for a
`
`Red
`Green
`Blue
`
`Angle i = Angler
`Angle i > Angle c
`
`(c)
`
`(d)
`
`Figure 4.4 Various consequences of refraction of light by
`glass prisms. (a) A monochromatic light ray passing
`obliquely through a·parallel-sided glass block, and resultant
`displacement d. (b) Refraction of monochromatic light caused(cid:173)
`by its passage through a prism, and resultant deviation D ,
`( c) Dispersion of white light by a prism. ( d) Total internal
`reflection in a right-angled prism, critical angle C
`
`widely diverging beam the angle of incidence may
`not exceed the critical angle for the whole beam, and
`it · may be necessary to metallize the reflecting
`surface.
`
`When light from a subject passes through an optical
`system, the subject may appear to the viewer as
`being in a different place (and probably of a
`different size). This is due to the formation of · art
`optical image. An optical system may be as simple
`as a plane mirror or as complex as a highly
`corrected ·camera lens. A simple· method of image
`formation -is via a pinhole in an opaque material
`(Figure 4.5). Two properties of this image are that
`it is real, i.e. it can be formed on a screen as rays
`from the object pass through the pinhole, and that,
`as light travels· in straight lines, the
`image is
`inverted, and laterally reversed left to right as
`viewed fiom behind a scattering (focusing) screen.
`The ground-glass focusing screen of · a technical
`camera when used with a pinhole shows such an
`image.
`·
`A pinhole is limited in the formation of real
`images, as the sharpness depends on the size of the
`pinhole. The optimum diameter (K) for a pinhole is
`given by the approximate fmmula:
`
`J( = ,fV
`25
`
`(3)
`
`where v is the distance from pinhole to screen. A
`larger hole gives a brighter but less sharp image. A
`smaller hole gives a less bright image, but this is also
`less sharp owing to diffraction (see Chapter 6).
`Although a pinhole image does not suffer from
`curvilinear distortion, as images produced by lenses
`may do, its poor transmission of light and low
`resolution both limit its use to a few specialized
`applications.
`
`APPL-1008 / Page 11 of 31
`
`

`

`42
`
`T/11! ge11111et1)' q/' i111age formation
`
`,
`'
`,
`' /
`
`'
`
`' ,
`
`I
`
`'
`
`I
`
`I
`
`--r-
`(a)
`
`A
`
`"
`
`~
`~
`~
`
`P1·
`
`(b)
`
`Figure 4.6 Negative and positive lenses. (a) A simple
`positive lens considered as a series of prisms. (b) Formation
`of a virtual image of a point object by a negative lens
`
`The $imple lens
`
`A lens is a system of one or more pieces of glass or
`e'lements with (usually) spherical surfaces, all of
`whose centres are on a common axis, the optical (or
`principal) axis. A simple or thin lens is a single piece
`of glass ot ·element whose axial thiclmess is small
`compared with its diameter, whereas a compound or
`thick lens consists of several air spaced components,
`some of which may comprise several elements
`cemented together, to correct for aberrations. A
`simple lens may be regarded as a number of prisms,
`as shown in Figure 4.6. Light diverging from a point
`source P 1 and incident on the front surface of the
`positive lens is redirected by refraction to form a real
`image at point P2 . These rays are said to come to a
`focus. Alternatively, by using a negative ·lens, the
`incident rays may be further diverged by the refrac(cid:173)
`tion of the lens, and so appear to have originated from
`a virtual focus at point P3 .
`·
`The front and rear surfaces of the lens may be
`convex, concave or plane; the six usual configura(cid:173)
`tions of simple spherical lenses are shown in . cross(cid:173)
`section in Figure 4.7. A meniscus lens is one in which
`the centres of curvature of the surfaces are both on
`the same side of the 1ens. Simple positive meniscus
`lenses are used as close-up lenses for cameras. While
`the same refracting power in dioptres is possible with
`various pairs of curvatures, the shape of a close-up
`lens is important in deteq:nining its effect on the
`quality of the image given by the lens on the
`camera.
`· The relationships between the various parameters
`of a single-element lens of refractive index nd, axial
`thiclmess q and rndii of curvature of the surfaces R 1
`
`I I
`
`I
`
`[
`TI
`[
`
`(b)
`
`Figure 4.7 Simple lens. (a) Lens parameters; A, optical
`axis; C1, C2 , centres of curvature with radii R 1 and R2 ; V1
`and V 2 , vertices of spherical surfaces; 0, optical centre; 11,
`refractive index; t, axial thickness; D, diameter. (b) Shape
`configurations: plano-convex, plano-concave, equi-biconvex,
`equi-biconcave, positive meniscus, negative meniscus
`
`and R2 required to give a focal length for (refractive)
`power K are given by the general 'lensmakers'
`formula':
`
`K = !_ = '(n~ _ l) (-1 _ ~) + (Cnct - I)q)
`.
`· .
`f
`Ri
`nctR1R2
`R1
`For f measured in millimetres, power K = 1000/f in
`dioptres. For a thin lens, equation (4) simplifies to
`
`(4)
`
`K = !_ = (nct - I) (~ - -
`: f
`
`Ri
`
`1
`
`)
`R1
`
`(5)
`
`Image formation by a simple positive lens
`
`Irrespective of their configuration of elements, cam(cid:173)
`era lenses are similar to simple lenses in their image(cid:173)
`forming properties. In particular, a camera lens
`always fo1ms a real image if the object is at a distance
`of more than one focal length. The formation of the
`image of a point source has been discussed, now let
`
`APPL-1008 / Page 12 of 31
`
`

`

`0 '·
`
`l..--f
`I
`I
`I
`I
`
`(a)
`
`(b)
`
`Figure 4.8 hnage formation by a positive lens. (a) For a
`distant subject: F is the rear principal focal plane; (b) for a
`near subject: focusing extension E = (v - f); I is an inverted
`real image
`
`us consider the formation of the image of an extended
`object.
`If the object is near the lens, the position and size
`of the optical image can be determined from the
`refraction of light diverging to the lens from two
`points at opp9site ends of the object. Figure 4.8
`shows this for a simple lens. The image is inverted,
`laterally reversed, minified, behind the lens and
`real.
`To a first approximation, a distant object can be
`considered as being located at infinity. The rays that
`reach the lens from any point on the object are
`effectively parallel. As before the image is formed
`close to the lens, inverted, laterally reversed and real.
`The image plane in which this image is formed is
`te1med the principal focal plane (F) . For a flat distant
`object and an 'ideal' lens, every image point lies in
`this plane. The point of intersection of the focal plane
`and the optical axis is termed the rear principal focus
`(or simply the focus) of the lens, and the distance
`from this point to the lens is termed the focal length
`(j) of the lens. Only for an object at infinity does the
`image distance or conjugate (v) from the lens corre(cid:173)
`spond to the focal length. As the object approaches
`the lens (i.e. object distance u decreases), the value bf
`v increases (for a positive lens). If the lens is· turned
`round, a second focal point is obtained; the focal
`length remains the same. The focal lengths of thick
`lenses are measured ·from different points in the lens
`
`ical
`,; V1
`·e; n,
`tape
`on vex,
`
`active)
`iakers'
`
`(4)
`
`00/f in
`es to
`
`(5)
`
`lens
`
`, cam(cid:173)
`mage(cid:173)
`lens
`l
`stance
`of the
`ow let
`
`The geometry of image formation 43
`
`configuration (see below). Finally, the distance of the
`focus from the rear surface of a lens is known as the
`back focus or back focal distance. This is of
`importance in camera design so that optical devices
`such as reflex milrnrs or beam-splitting prisms can be
`located between lens and photoplane.
`
`Image formation by a compound
`lens
`..
`
`A lens is considered as 'thin' if its axial thiclmess is
`small compared to its diameter and to the object and
`image distances and its focal length, so that measure(cid:173)
`ments can be made from the plane passing through its
`centre without significant error (Figure 4.9a). With a
`compound lens of axial thiclmess that is a significant
`fraction of its focal length, these measurements
`plainly cannot be made simply from the front or back
`smface of the lens or some point in between.
`However, it was proved by Gauss that a thick or
`compound lens could be treated as an equivalent thin
`one, and thin-lens f01mulae used to compute image
`properties, provided that the. object and image
`conjugate distances were measured from two theoret(cid:173)
`ical planes fixed with reference to the lens. This is
`referred to as Gaussian optics, and holds for paraxial
`conditions, i.e. for rays whose angle of inciqence to
`th,e optical axis is less than some 10 degrees.
`Gaussian optics uses six defined cardinal or Gauss
`points for any si.D.gle lens or system of lenses. These
`are two principal focal points, two principal points
`and two nodal points. The corresponding planes
`through these points orthogonal to the optical axis are
`called the focal planes, principal planes arid nodal
`planes respectively (Figure 4.9b). The focal length of
`a lens is then defined as the distance from a given
`principal point to the corresponding principal focal
`point. So a lens has two focal lengths, an object focal
`length and an image focal length; these are, however,
`usually equal (see belqw) .
`The definitions and properties of the · cardinal
`points are as follows:
`(1) Object principal focal point (F1): The point
`whose image is on the axis at infinity in the
`image space.
`Image principal focal point (F2 ) : The point
`occupied by the image of an· object on the axis
`at infinity in the object space.
`(3) Object principal point (P1) : The point that is a
`distance from the object principal focal point
`equal to the object focal length F 1. All ·object
`distarices are measured from this point.
`Image principal point (P2): The point at a
`distance from the image principal focal point
`·equal to the image focal length F2 • All irriage
`distances are measured from this point. The
`principal planes
`through
`these points are
`
`(4)
`
`(2)
`
`APPL-1008 / Page 13 of 31
`
`

`

`44 The geometry of image formation
`
`u
`
`v
`
`(a) Simple lens
`
`Front principal
`plane
`(nodal plane)
`
`Rear principal
`pl