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Файл:Ординатура / Офтальмология / Английские материалы / Lens Design Fundamentals 2nd edition_Kingslake, Johnson_2009.pdf
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- •Lens Design Fundamentals
- •Contents
- •Preface to the Second Edition
- •Preface to the First Edition
- •A Special Tribute to Rudolf Kingslake
- •1.1. Relations Between Designer and Factory
- •1.1.1 Spherical versus Aspheric Surfaces
- •1.1.2 Establishment of Thicknesses
- •1.1.3 Antireflection Coatings
- •1.1.4 Cementing
- •1.1.5 Establishing Tolerances
- •1.1.6 Design Tradeoffs
- •1.2. The Design Procedure
- •1.2.1 Sources of a Likely Starting System
- •1.2.2 Lens Evaluation
- •1.2.3 Lens Appraisal
- •1.2.4 System Changes
- •1.3. Optical Materials
- •1.3.1 Optical Glass
- •1.3.2 Infrared Materials
- •1.3.3 Ultraviolet Materials
- •1.3.4 Optical Plastics
- •1.4. Interpolation of Refractive Indices
- •1.4.1 Interpolation of Dispersion Values
- •1.4.2 Temperature Coefficient of Refractive Index
- •1.5. Lens Types to be Considered
- •2.1. Introduction
- •2.1.1 Object and Image
- •2.1.2 The Law of Refraction
- •2.1.3 The Meridional Plane
- •2.1.4 Types of Rays
- •2.1.5 Notation and Sign Conventions
- •2.2. Graphical Ray Tracing
- •2.3. Trigonometrical Ray Tracing at a Spherical Surface
- •2.3.1 Program for a Computer
- •2.4. Some Useful Relations
- •2.4.1 The Spherometer Formula
- •2.4.2 Some Useful Formulas
- •2.4.3 The Intersection Height of Two Spheres
- •2.4.4 The Volume of a Lens
- •2.5. Cemented Doublet Objective
- •2.6. Ray Tracing at a Tilted Surface
- •2.6.1 The Ray Tracing Equations
- •2.6.2 Example of Ray Tracing through a Tilted Surface
- •2.7. Ray Tracing at an Aspheric Surface
- •3.1. Tracing a Paraxial Ray
- •3.1.1 The Standard Paraxial Ray Trace
- •3.1.2 The (y – nu) Method
- •3.1.3 Inverse Procedure
- •3.1.4 Angle Solve and Height Solve Methods
- •3.1.6 Paraxial Ray with All Angles
- •3.1.7 A Paraxial Ray at an Aspheric Surface
- •3.1.9 Matrix Approach to Paraxial Rays
- •3.2. Magnification and the Lagrange Theorem
- •3.2.1 Transverse Magnification
- •3.2.2 Longitudinal Magnification
- •3.3. The Gaussian Optics of a Lens System
- •3.3.1 The Relation between the Principal Planes
- •3.3.2 The Relation between the Two Focal Lengths
- •3.3.3 Lens Power
- •3.3.4 Calculation of Focal Length
- •3.3.5 Conjugate Distance Relationships
- •3.3.6 Nodal Points
- •3.3.7 Optical Center of Lens
- •3.3.8 The Scheimpflug Condition
- •3.4. First-Order Layout of an Optical System
- •3.4.1 A Single Thick Lens
- •3.4.2 A Single Thin Lens
- •3.4.3 A Monocentric Lens
- •3.4.4 Image Shift Caused by a Parallel Plate
- •3.4.5 Lens Bending
- •3.4.6 A Series of Separated Thin Elements
- •3.4.7 Insertion of Thicknesses
- •3.4.8 Two-Lens Systems
- •3.5. Thin-Lens Layout of Zoom Systems
- •3.5.1 Mechanically Compensated Zoom Lenses
- •3.5.2 A Three-Lens Zoom
- •3.5.4 A Four-Lens Optically Compensated Zoom System
- •3.5.5 An Optically Compensated Zoom Enlarger or Printer
- •Endnotes
- •4.1. Introduction
- •4.2. Symmetrical Optical Systems
- •4.3. Aberration Determination Using Ray Trace Data
- •4.3.1 Defocus
- •4.3.2 Spherical Aberration
- •4.3.3 Tangential and Sagittal Astigmatism
- •4.3.4 Tangential and Sagittal Coma
- •4.3.5 Distortion
- •4.3.6 Selection of Rays for Aberration Computation
- •4.3.7 Zonal Aberrations
- •4.3.8 Tangential and Sagittal Zonal Astigmatism
- •4.3.9 Tangential and Sagittal Zonal Coma
- •4.3.10 Higher-Order Contributions
- •4.4. Calculation of Seidel Aberration Coefficients
- •Endnotes
- •5.1. Introduction
- •5.2. Spherochromatism of a Cemented Doublet
- •5.2.4 Secondary Spectrum
- •5.2.5 Spherochromatism
- •5.3. Contribution of a Single Surface to the Primary Chromatic Aberration
- •5.4. Contribution of a Thin Element in a System to the Paraxial Chromatic Aberration
- •5.5. Paraxial Secondary Spectrum
- •5.7.1 Secondary Spectrum of a Dialyte
- •5.7.2 A One-Glass Achromat
- •5.8. Chromatic Aberration Tolerances
- •5.8.1 A Single Lens
- •5.8.2 An Achromat
- •5.9. Chromatic Aberration at Finite Aperture
- •5.9.1 Conrady’s D – d Method of Achromatization
- •5.9.3 Tolerance for the D – d Sum
- •5.9.5 Paraxial D – d for a Thin Element
- •Endnotes
- •6.1. Surface Contribution Formulas
- •6.1.1 The Three Cases of Zero Aberration at a Surface
- •6.1.2 An Aplanatic Single Element
- •6.1.3 Effect of Object Distance on the Spherical Aberration Arising at a Surface
- •6.1.4 Effect of Lens Bending
- •6.1.6 A Two-Lens Minimum Aberration System
- •6.1.7 A Four-Lens Monochromat Objective
- •6.2. Zonal Spherical Aberration
- •6.3. Primary Spherical Aberration
- •6.3.1 At a Single Surface
- •6.3.2 Primary Spherical Aberration of a Thin Lens
- •6.4. The Image Displacement Caused by a Planoparallel Plate
- •6.5. Spherical Aberration Tolerances
- •6.5.1 Primary Aberration
- •6.5.2 Zonal Aberration
- •Endnotes
- •7.1. The Four-Ray Method
- •7.2. A Thin-Lens Predesign
- •7.2.1 Insertion of Thickness
- •7.2.2 Flint-in-Front Solutions
- •7.3. Correction of Zonal Spherical Aberration
- •7.4. Design Of an Apochromatic Objective
- •7.4.1 A Cemented Doublet
- •7.4.2 A Triplet Apochromat
- •7.4.3 Apochromatic Objective with an Air Lens
- •Endnotes
- •8.1. Passage of an Oblique Beam through a Spherical Surface
- •8.1.1 Coma and Astigmatism
- •8.1.2 Principal Ray, Stops, and Pupils
- •8.1.3 Vignetting
- •8.2. Tracing Oblique Meridional Rays
- •8.2.1 The Meridional Ray Plot
- •8.3. Tracing a Skew Ray
- •8.3.1 Transfer Formulas
- •8.3.2 The Angles of Incidence
- •8.3.3 Refraction Equations
- •8.3.4 Transfer to the Next Surface
- •8.3.5 Opening Equations
- •8.3.6 Closing Equations
- •8.3.7 Diapoint Location
- •8.3.8 Example of a Skew-Ray Trace
- •8.4. Graphical Representation of Skew-Ray Aberrations
- •8.4.1 The Sagittal Ray Plot
- •8.4.2 A Spot Diagram
- •8.4.3 Encircled Energy Plot
- •8.4.4 Modulation Transfer Function
- •8.5. Ray Distribution from a Single Zone of a Lens
- •Endnotes
- •9.1. The Optical Sine Theorem
- •9.2. The Abbe Sine Condition
- •9.2.1 Coma for the Three Cases of Zero Spherical Aberration
- •9.3. Offense Against the Sine Condition
- •9.3.1 Solution for Stop Position for a Given OSC
- •9.3.2 Surface Contribution to the OSC
- •9.3.3 Orders of Coma
- •9.3.4 The Coma G Sum
- •9.3.5 Spherical Aberration and OSC
- •9.4. Illustration of Comatic Error
- •Endnotes
- •10.1. Broken-Contact Type
- •10.2. Parallel Air-Space Type
- •10.3. An Aplanatic Cemented Doublet
- •10.4. A Triple Cemented Aplanat
- •10.5. An Aplanat with A Buried Achromatizing Surface
- •10.6. The Matching Principle
- •Endnotes
- •11.1. Astigmatism and the Coddington Equations
- •11.1.1 The Tangential Image
- •11.1.2 The Sagittal Image
- •11.1.3 Astigmatic Calculation
- •11.1.5 Astigmatism for the Three Cases of Zero Spherical Aberration
- •11.1.6 Astigmatism at a Tilted Surface
- •11.2. The Petzval Theorem
- •11.2.1 Relation Between the Petzval Sum and Astigmatism
- •11.2.2 Methods for Reducing the Petzval Sum
- •11.3. Illustration of Astigmatic Error
- •11.4. Distortion
- •11.4.1 Measuring Distortion
- •11.4.2 Distortion Contribution Formulas
- •11.4.3 Distortion When the Image Surface Is Curved
- •11.5. Lateral Color
- •11.5.1 Primary Lateral Color
- •11.6. The Symmetrical Principle
- •11.7. Computation of the Seidel Aberrations
- •11.7.1 Surface Contributions
- •11.7.2 Thin-Lens Contributions
- •11.7.3 Aspheric Surface Corrections
- •11.7.4 A Thin Lens in the Plane of an Image
- •Endnotes
- •12.1.1 Distortion
- •12.1.2 Tangential Field Curvature
- •12.1.3 Coma
- •12.1.4 Spherical Aberration
- •12.2. Simple Landscape Lenses
- •12.2.1 Simple Rear Landscape Lenses
- •12.2.2 A Simple Front Landscape Lens
- •12.3. A Periscopic Lens
- •12.4. Achromatic Landscape Lenses
- •12.4.1 The Chevalier Type
- •12.4.2 The Grubb Type
- •12.5. Achromatic Double Lenses
- •12.5.1 The Rapid Rectilinear
- •12.5.3 Long Telescopic Relay Lenses
- •12.5.4 The Ross “Concentric” Lens
- •Endnotes
- •13.1. The Design of a Dagor Lens
- •13.2. The Design of an Air-Spaced Dialyte Lens
- •13.4. Double-Gauss Lens with Cemented Triplets
- •13.5. Double-Gauss Lens with Air-spaced Negative Doublets
- •Endnotes
- •14.1. The Petzval Portrait Lens
- •14.1.1 The Petzval Design
- •14.1.2 The Dallmeyer Design
- •14.2. The Design of a Telephoto Lens
- •14.3. Lenses to Change Magnification
- •14.3.1 Barlow Lens
- •14.3.2 Bravais Lens
- •14.4. The Protar Lens
- •14.5. Design of a Tessar Lens
- •14.5.1 Choice of Glass
- •14.5.2 Available Degrees of Freedom
- •14.5.3 Chromatic Correction
- •14.5.4 Spherical Correction
- •14.5.5 Correction of Coma and Field
- •14.5.6 Final Steps
- •14.6. The Cooke Triplet Lens
- •14.6.2 The Thin-Lens Predesign of the Bendings
- •14.6.3 Calculation of Real Aberrations
- •14.6.4 Triplet Lens Improvements
- •Endnotes
- •15.1. Comparison of Mirrors and Lenses
- •15.2. Ray Tracing a Mirror System
- •15.3. Single-Mirror Systems
- •15.3.1 A Spherical Mirror
- •15.3.2 A Parabolic Mirror
- •15.3.3 An Elliptical Mirror
- •15.3.4 A Hyperbolic Mirror
- •15.4. Single-Mirror Catadioptric Systems
- •15.4.1 A Flat-Field Ross Corrector
- •15.4.2 An Aplanatic Parabola Corrector
- •15.4.3 The Mangin Mirror
- •15.4.4 The Bouwers–Maksutov System
- •15.4.5 The Gabor Lens
- •15.4.6 The Schmidt Camera
- •15.4.7 Variable Focal-Range Infrared Telescope
- •15.4.8 Broad-Spectrum Afocal Catadioptric Telescope
- •15.4.9 Self-Corrected Unit-Magnification Systems
- •15.5. Two-Mirror Systems
- •15.5.1 Two-Mirror Systems with Aspheric Surfaces
- •15.5.2 A Maksutov Cassegrain System
- •15.5.3 A Schwarzschild Microscope Objective
- •15.5.4 Three-Mirror System
- •15.6. Multiple-Mirror Zoom Systems
- •15.6.2 All-Reflective Zoom Optical Systems
- •15.7. Summary
- •Endnotes
- •16.1. Design of a Military-Type Eyepiece
- •16.1.1 The Objective Lens
- •16.1.2 Eyepiece Layout
- •16.2. Design of an Erfle Eyepiece
- •16.3. Design of a Galilean Viewfinder
- •Endnotes
- •17.1. Finding a Lens Design Solution
- •17.1.1 The Case of as Many Aberrations as There Are Degrees of Freedom
- •17.1.2 The Case of More Aberrations Than Free Variables
- •17.1.3 What Is an Aberration?
- •17.1.4 Solution of the Equations
- •17.2. Optimization Principles
- •17.3. Weights and Balancing Aberrations
- •17.4. Control of Boundary Conditions
- •17.5. Tolerances
- •17.6. Program Limitations
- •17.7. Lens Design Computing Development
- •17.8. Programs and Books Useful for Automatic Lens Design
- •17.8.1 Automatic Lens Design Programs
- •17.8.2 Lens Design Books
- •Endnotes
- •Index
5.9 Chromatic Aberration at Finite Aperture |
169 |
The longitudinal chromatic aberration for this zone is given approximately by
L0ch ¼ L0a=sinU 0¼ 2aþ4b sin2 U 0
and hence the 0.7 zonal chromatic aberration will be given by
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L0 |
2 a 2b sin2 U 0 |
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Dn sum is z0 ¼ |
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m0 = |
ð chÞz¼ ð þ |
zÞ |
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P |
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sin U |
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But sin U |
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p2 approximately, and the calculated marginal (D – d) |
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Hence |
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X ¼ Sm ¼ a sin2 U m0 |
þ b sin4 U m0 |
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ðLch0 |
Þz¼ 2 X=sin2U m0 |
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(5-13) |
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As a check on this result, we recall that the residual of |
in our cemented |
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telescope doublet was –0.0000578 and sin U0 |
was 0.16659. |
Therefore, we should |
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P |
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expect the zonal chromatic aberration to be –0.00417. By actual ray tracing we find
zonal LF0 ¼ 11:27022
zonal LC0 ¼ 11:27523
F C ¼ 0:00501
The small discrepancy is due to our having neglected the sin6 U0 term in the expression for S.
5.9.5 Paraxial D – d for a Thin Element
We can readily reduce the D – d expression to its paraxial form for a single thin lens element. In this case the length D in the paraxial region becomes
D ¼ d þ Z2 Z1 ¼ d þ |
Y2 |
Y2 |
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2r2 |
2r1 |
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Hence |
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Y2 |
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1 |
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Y2 |
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ðD dÞ ¼ |
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1 |
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¼ 2f 0ðn 1Þ |
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2 |
r2 |
r1 |
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Y2 |
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Dn |
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Y2 |
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ðD dÞ Dn ¼ |
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¼ |
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2f 0 |
n 1 |
2f 0V |
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