GEOMETRICAL OPTICS AND OPTICAL DESIGN

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "GEOMETRICAL OPTICS AND OPTICAL DESIGN"

Transcription

1 GEOMETRICAL OPTICS AND OPTICAL DESIGN Pantazis Mouroulis Associate Professor Center for Imaging Science Rochester Institute of Technology John Macdonald Senior Lecturer Physics Department University of Reading New York Oxford OXFORD UNIVERSITY PRESS 1997

2 Contents Rays and the Foundations of Geometrical Optics 1.1. Waves, Wavefronts, and Rays The Pinhole Camera Propagation of Wavefronts, Reflection, Refraction Fermat's Principle Irradiance and the Inverse-Square Law The Basic Postulates of Geometrical Optics 15 Review of Elementary Ray Optics Plane Surfaces Reflecting Surfaces Refracting Surfaces Curved Surfaces: Focusing Focusing in the Paraxial Region Graphical Ray Tracing for Thin Lenses Graphical Ray Tracing for Mirrors 31 Imagery by a Single Surface and a Thin Lens The Sign Convention The Paraxial Approximation 39

3 x CONTENTS 3.3. Imagery by a Single Surface The Conjugate Equation Power and Focal Lengths of a Surface Mirrors Imagery by a Thin Lens Thin Lens Conjugate Equation Power of a Thin Lens in Air Focal Lengths of a Thin Lens Thin Lens Refraction: The General Case Many Surfaces in Contact Throw Imagery of an Extended Object. Magnification The One-Component Design Problem Other Types of Magnification The Angular Size of an Object Visual Magnification Longitudinal Magnification. Imagery of a Volume Gaussian Optics The Paraxial Height and Angle Variables Paraxial Ray Tracing for Systems of Many Surfaces Notation Magnification Paraxial Ray Tracing through Many Surfaces The Optical Invariant Principal Planes 70 AAA. Definition and Properties of the Principal Planes Power and Focal Lengths of a General System Reference to an Arbitrary Set of Conjugates Afocal Systems Location of Principal Planes Power and Principal Planes of a System of Two Separated Components Thick Lenses: Power and Location of Principal Planes Nodal Points, Measurement of Focal Length Additional Topics in Gaussian Optics Newton's Form of the Conjugate Equation Imagery of a Tilted Plane Summary of Gaussian Optics The Two-Component Design Problem 88

4 5. Putting It All Together Stops and Pupils Entrance and Exit Pupils Numerical Aperture, F Number Depth of Focus, Depth of Field Pupils: Off-Axis Imagery Pupil Matching Paraxial Marginal and Pupil Rays How to Find the Stops Size of a Lens or Surface (Clear Aperture) Two-Ray Forms of Я Significance and Use of the Marginal and Pupil Rays Connecting Paraxial and Finite Optics The Sine Condition The Tangent Condition Gaussian Predesign The Two-Lens System with Fixed Pupil Positions The y-y Diagram Light Flux Transmission through Optical Systems Radiometry versus Photometry Radiometric (Photometric) Quantities and Units Flux Emitted into a Cone by a Lambertian Source Flux Collected by a Lens Irradiance of an Image Radiance (Luminance) of an Aerial Image Photometry of Illumination Systems Off-Axis Illumination Illuminance from a Large Source Luminance of a Distant Source 132 CONTENTS xi 6. Gaussian Optics of Optical Instruments and Components The Telescope Visual Telescopes Astronomical Telescopes and Resolution Information Capacity of an Optical System Laser Beam Expander The Microscope Magnifying Power and Resolution Microscope Illumination Systems Projection Systems The Overhead Projector Aspherics in Illumination Systems Other Projection Systems The Eye Basic Anatomy Geometrical Parameters 152

5 xii CONTENTS Scene Luminance and Retinal Illuminance Refractive Effects and Accommodation Resolution and Acuity Contrast Sensitivity Reflecting Prisms Geometrical Aspects of Reflection Tunnel Diagram. Effect of a Plane Block of Glass Common Prism Types Some Instrumental Applications of Reflecting Prisms Cylindrical and Anamorphic Optics Image of a Point through a Cylindrical Lens Image Illuminance through a Cylindrical Lens Gradient Index Optics Snell's Law The Parabolic Index Profile Paraxial Ray Tracing for Gradient Index Media Gaussian Constants of GRIN Rods The Optical Invariant Diffractive Optics The Diffraction Grating Holographic Optical Elements Binary Optics Introduction to Aberrations Chromatic Aberration Characterization of Dispersion Chromatic Effects for a Thin Lens The Achromatic Doublet and Related Concepts Secondary Spectrum. Apochromatic Correction Introduction to Monochromatic Aberrations The Origin of Monochromatic Aberrations Wavefront and Ray Aberrations Canonical Coordinates The Wave Aberration Function. Classification of Aberrations The Wave Aberration Polynomial for Rotationally Symmetric Systems Classical Aberration Types Ray Intersection Patterns and Spot Diagrams Longitudinal Aberration Aberration Tolerances Example: Computation of Wave and Ray Aberration Computation of Primary Aberrations The Seidel Aberration Coefficients The Paraxial Refraction Invariants 227

6 CONTENTS xiii Surface Contribution to the Wavefront Aberration The Seidel Aberration Formulae Special Aberration-Free Cases. The Aplanatic Meniscus Chromatic Aberrations Design Example: A Simple Camera Objective Astigmatism and Field Curvature Primary Aberrations of a Reflecting Prism (Plane-Parallel Plates) Primary Aberrations of a Spherical Mirror Aberrations of a Thin Lens in Air Central Aberrations (Stop at the Lens) Shape-Independent Aberrations The Shape Factor and the Magnification Parameter Shape-Dependent Aberrations The Corrected Doublet A Practical Aberration Primer Thin-Lens Aberrations with a Remote Stop The Eccentricity Parameter Stop-Shift Effects for a Single Surface Stop-Shift Effects for a General System and a Thin Lens Stop-Shift Theorems Example: The Petzval Projection Lens The Two- and Three-Component Solution with Fixed ЪК The Two-Component Solution The Three-Component Solution The Cooke Triplet Optical Design The Optical Design Process Making the System Real: Thickening, Total Aberration Design Example: Operating Spectacles Optimization Pupils and Pupil Imagery Pupil Aberration Off-Axis Pupil Shape and Vignetting Off-Axis Image Formation and Canonical Coordinates Aspherics A Brief Guide to Optical Design Software 289

7 xiv CONTENTS Appendix 1. Matrix Methods in Paraxial Optics 294 Al.l. The Conjugate Matrix 296 A 1.2. Relation between A,B,C,D and 5,5',К 298 Appendix 2. Gaussian Beam Ray Tracing 300 A2.1. Basic Characteristics of Gaussian Beams 300 A2.2. Paraxial Equations for Gaussian Beams 303 A2.3. Thin Lens in Air 306 A2.4. The General System: Principal Planes 308 A2.5. Two-Ray Formulation of Gaussian Beams 311 Appendix 3. Finite Ray Tracing 317 A3.1. Vector Form of Snell's Law 318 A3.2. The Surface Equation and the Surface Normal 318 A3.3. Surface Transfer 319 A3.4. Refraction 320 Appendix 4. Shift of Focus 322 A4.1. Longitudinal Focal Shift 322 A4.2. Transverse Focal Shift 324 Appendix 5. Two Computer Programs 327 A5.1. Thin Aplanatic Doublet Design (Stop at the Lens) 327 A5.2. Paraxial Ray Tracing and Seidel Aberration Computation 331 Appendix 6. Thin-Lens Bending Program 341 Bibliography 349 Index 351

Lecture 4: Geometrical Optics 2. Optical Systems. Images and Pupils. Rays. Wavefronts. Aberrations. Outline

Lecture 4: Geometrical Optics 2. Optical Systems. Images and Pupils. Rays. Wavefronts. Aberrations. Outline Lecture 4: Geometrical Optics 2 Outline 1 Optical Systems 2 Images and Pupils 3 Rays 4 Wavefronts 5 Aberrations Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl Lecture 4: Geometrical

More information

SPIE. Lens Design Fundamentals PRESS. Second Edition RUDOLF KINGSLAKE R. BARRY JOHNSON

SPIE. Lens Design Fundamentals PRESS. Second Edition RUDOLF KINGSLAKE R. BARRY JOHNSON Lens Design Fundamentals Second Edition RUDOLF KINGSLAKE R. BARRY JOHNSON AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an imprint

More information

Lens Design I. Lecture 10: Optimization II Herbert Gross. Summer term

Lens Design I. Lecture 10: Optimization II Herbert Gross. Summer term Lens Design I Lecture : Optimization II 5-6- Herbert Gross Summer term 5 www.iap.uni-jena.de Preliminary Schedule 3.. Basics.. Properties of optical systrems I 3 7.5..5. Properties of optical systrems

More information

Geometric optics & aberrations

Geometric optics & aberrations Geometric optics & aberrations Department of Astrophysical Sciences University AST 542 http://www.northerneye.co.uk/ Outline Introduction: Optics in astronomy Basics of geometric optics Paraxial approximation

More information

Long Wave Infrared Scan Lens Design And Distortion Correction

Long Wave Infrared Scan Lens Design And Distortion Correction Long Wave Infrared Scan Lens Design And Distortion Correction Item Type text; Electronic Thesis Authors McCarron, Andrew Publisher The University of Arizona. Rights Copyright is held by the author. Digital

More information

Image Formation. Light from distant things. Geometrical optics. Pinhole camera. Chapter 36

Image Formation. Light from distant things. Geometrical optics. Pinhole camera. Chapter 36 Light from distant things Chapter 36 We learn about a distant thing from the light it generates or redirects. The lenses in our eyes create images of objects our brains can process. This chapter concerns

More information

Chapter 34 Geometric Optics (also known as Ray Optics) by C.-R. Hu

Chapter 34 Geometric Optics (also known as Ray Optics) by C.-R. Hu Chapter 34 Geometric Optics (also known as Ray Optics) by C.-R. Hu 1. Principles of image formation by mirrors (1a) When all length scales of objects, gaps, and holes are much larger than the wavelength

More information

Chapter 26. The Refraction of Light: Lenses and Optical Instruments

Chapter 26. The Refraction of Light: Lenses and Optical Instruments Chapter 26 The Refraction of Light: Lenses and Optical Instruments 26.1 The Index of Refraction Light travels through a vacuum at a speed c=3. 00 10 8 m/ s Light travels through materials at a speed less

More information

Chapter 23. Light Geometric Optics

Chapter 23. Light Geometric Optics Chapter 23. Light Geometric Optics There are 3 basic ways to gather light and focus it to make an image. Pinhole - Simple geometry Mirror - Reflection Lens - Refraction Pinhole Camera Image Formation (the

More information

Name. Light Chapter Summary Cont d. Refraction

Name. Light Chapter Summary Cont d. Refraction Page 1 of 17 Physics Week 12(Sem. 2) Name Light Chapter Summary Cont d with a smaller index of refraction to a material with a larger index of refraction, the light refracts towards the normal line. Also,

More information

Optical Signal Processing

Optical Signal Processing Optical Signal Processing ANTHONY VANDERLUGT North Carolina State University Raleigh, North Carolina A Wiley-Interscience Publication John Wiley & Sons, Inc. New York / Chichester / Brisbane / Toronto

More information

The Brownie Camera. Lens Design OPTI 517. Prof. Jose Sasian

The Brownie Camera. Lens Design OPTI 517. Prof. Jose Sasian The Brownie Camera Lens Design OPTI 517 http://www.history.roch ester.edu/class/kodak/k odak.htm George Eastman (1854-1932), was an ingenious man who contributed greatly to the field of photography. He

More information

Chapter 29/30. Wave Fronts and Rays. Refraction of Sound. Dispersion in a Prism. Index of Refraction. Refraction and Lenses

Chapter 29/30. Wave Fronts and Rays. Refraction of Sound. Dispersion in a Prism. Index of Refraction. Refraction and Lenses Chapter 29/30 Refraction and Lenses Refraction Refraction the bending of waves as they pass from one medium into another. Caused by a change in the average speed of light. Analogy A car that drives off

More information

Geometrical Optics Optical systems

Geometrical Optics Optical systems Phys 322 Lecture 16 Chapter 5 Geometrical Optics Optical systems Magnifying glass Purpose: enlarge a nearby object by increasing its image size on retina Requirements: Image should not be inverted Image

More information

Introduction to Light Microscopy. (Image: T. Wittman, Scripps)

Introduction to Light Microscopy. (Image: T. Wittman, Scripps) Introduction to Light Microscopy (Image: T. Wittman, Scripps) The Light Microscope Four centuries of history Vibrant current development One of the most widely used research tools A. Khodjakov et al. Major

More information

Lecture Outline Chapter 27. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 27. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 27 Physics, 4 th Edition James S. Walker Chapter 27 Optical Instruments Units of Chapter 27 The Human Eye and the Camera Lenses in Combination and Corrective Optics The Magnifying

More information

Image formation. Types of Images

Image formation. Types of Images Image formation A. Karle Physics 202 Nov. 27, 2007 Chapter 36 Mirrors Images Ray diagrams Lenses As usual, these notes are only a complement to the notes on the whiteboard. Types of Images A real image

More information

CHAPTER 33 ABERRATION CURVES IN LENS DESIGN

CHAPTER 33 ABERRATION CURVES IN LENS DESIGN CHAPTER 33 ABERRATION CURVES IN LENS DESIGN Donald C. O Shea Georgia Institute of Technology Center for Optical Science and Engineering and School of Physics Atlanta, Georgia Michael E. Harrigan Eastman

More information

Course Syllabus OSE 4240 OPTICS AND PHOTNICS DESIGN, 3 CREDIT HOURS

Course Syllabus OSE 4240 OPTICS AND PHOTNICS DESIGN, 3 CREDIT HOURS Regardless of course type; e.g., traditional, media-enhanced, or Web, syllabi at UCF are required to include: Course title and number Credit hours Name(s) of instructor(s) Office location Office or Web

More information

CHAPTER 18 REFRACTION & LENSES

CHAPTER 18 REFRACTION & LENSES Physics Approximate Timeline Students are expected to keep up with class work when absent. CHAPTER 18 REFRACTION & LENSES Day Plans for the day Assignments for the day 1 18.1 Refraction of Light o Snell

More information

TOPICS Recap of PHYS110-1 lecture Physical Optics - 4 lectures EM spectrum and colour Light sources Interference and diffraction Polarization

TOPICS Recap of PHYS110-1 lecture Physical Optics - 4 lectures EM spectrum and colour Light sources Interference and diffraction Polarization TOPICS Recap of PHYS110-1 lecture Physical Optics - 4 lectures EM spectrum and colour Light sources Interference and diffraction Polarization Lens Aberrations - 3 lectures Spherical aberrations Coma, astigmatism,

More information

PHYS 160 Astronomy. When analyzing light s behavior in a mirror or lens, it is helpful to use a technique called ray tracing.

PHYS 160 Astronomy. When analyzing light s behavior in a mirror or lens, it is helpful to use a technique called ray tracing. Optics Introduction In this lab, we will be exploring several properties of light including diffraction, reflection, geometric optics, and interference. There are two sections to this lab and they may

More information

1) An electromagnetic wave is a result of electric and magnetic fields acting together. T 1)

1) An electromagnetic wave is a result of electric and magnetic fields acting together. T 1) Exam 3 Review Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) An electromagnetic wave is a result of electric and magnetic fields acting together. T 1) 2) Electromagnetic

More information

Converging and Diverging Surfaces. Lenses. Converging Surface

Converging and Diverging Surfaces. Lenses. Converging Surface Lenses Sandy Skoglund 2 Converging and Diverging s AIR Converging If the surface is convex, it is a converging surface in the sense that the parallel rays bend toward each other after passing through the

More information

Physics, Chapter 38: Mirrors and Lenses

Physics, Chapter 38: Mirrors and Lenses University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 38: Mirrors and Lenses Henry Semat

More information

Exercises Advanced Optical Design Part 5 Solutions

Exercises Advanced Optical Design Part 5 Solutions 2014-12-09 Manuel Tessmer M.Tessmer@uni-jena.dee Minyi Zhong minyi.zhong@uni-jena.de Herbert Gross herbert.gross@uni-jena.de Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str.

More information

Microscope anatomy, image formation and resolution

Microscope anatomy, image formation and resolution Microscope anatomy, image formation and resolution Ian Dobbie Buy this book for your lab: D.B. Murphy, "Fundamentals of light microscopy and electronic imaging", ISBN 0-471-25391-X Visit these websites:

More information

Optical Engineering 421/521 Sample Questions for Midterm 1

Optical Engineering 421/521 Sample Questions for Midterm 1 Optical Engineering 421/521 Sample Questions for Midterm 1 Short answer 1.) Sketch a pechan prism. Name a possible application of this prism., write the mirror matrix for this prism (or any other common

More information

INDEX OF REFRACTION index of refraction n = c/v material index of refraction n

INDEX OF REFRACTION index of refraction n = c/v material index of refraction n INDEX OF REFRACTION The index of refraction (n) of a material is the ratio of the speed of light in vacuuo (c) to the speed of light in the material (v). n = c/v Indices of refraction for any materials

More information

Chapter 23. Mirrors and Lenses

Chapter 23. Mirrors and Lenses Chapter 23 Mirrors and Lenses Mirrors and Lenses The development of mirrors and lenses aided the progress of science. It led to the microscopes and telescopes. Allowed the study of objects from microbes

More information

Chapter 34: Geometric Optics

Chapter 34: Geometric Optics Chapter 34: Geometric Optics It is all about images How we can make different kinds of images using optical devices Optical device example: mirror, a piece of glass, telescope, microscope, kaleidoscope,

More information

CREATING ROUND AND SQUARE FLATTOP LASER SPOTS IN MICROPROCESSING SYSTEMS WITH SCANNING OPTICS Paper M305

CREATING ROUND AND SQUARE FLATTOP LASER SPOTS IN MICROPROCESSING SYSTEMS WITH SCANNING OPTICS Paper M305 CREATING ROUND AND SQUARE FLATTOP LASER SPOTS IN MICROPROCESSING SYSTEMS WITH SCANNING OPTICS Paper M305 Alexander Laskin, Vadim Laskin AdlOptica Optical Systems GmbH, Rudower Chaussee 29, 12489 Berlin,

More information

INTRODUCTION THIN LENSES. Introduction. given by the paraxial refraction equation derived last lecture: Thin lenses (19.1) = 1. Double-lens systems

INTRODUCTION THIN LENSES. Introduction. given by the paraxial refraction equation derived last lecture: Thin lenses (19.1) = 1. Double-lens systems Chapter 9 OPTICAL INSTRUMENTS Introduction Thin lenses Double-lens systems Aberrations Camera Human eye Compound microscope Summary INTRODUCTION Knowledge of geometrical optics, diffraction and interference,

More information

Master program "Optical Design"

Master program Optical Design University ITMO, Russia WUT, Poland Department of Applied and Computer Optics Photonics Engineering Division http://zif.mchtr.pw.edu.pl Master program "Optical Design" (ACO Department), St. Petersburg

More information

Properties of optical instruments. Visual optical systems part 2: focal visual instruments (microscope type)

Properties of optical instruments. Visual optical systems part 2: focal visual instruments (microscope type) Properties of optical instruments Visual optical systems part 2: focal visual instruments (microscope type) Examples of focal visual instruments magnifying glass Eyepieces Measuring microscopes from the

More information

Reflectors vs. Refractors

Reflectors vs. Refractors 1 Telescope Types - Telescopes collect and concentrate light (which can then be magnified, dispersed as a spectrum, etc). - In the end it is the collecting area that counts. - There are two primary telescope

More information

For rotationally symmetric optical

For rotationally symmetric optical : Maintaining Uniform Temperature Fluctuations John Tejada, Janos Technology, Inc. An optical system is athermalized if its critical performance parameters (such as MTF, BFL, EFL, etc.,) do not change

More information

Lens Design II. Lecture 8: Special correction features I Herbert Gross. Winter term

Lens Design II. Lecture 8: Special correction features I Herbert Gross. Winter term Lens Design II Lecture 8: Special correction features I 2015-12-08 Herbert Gross Winter term 2015 www.iap.uni-jena.de Preliminary Schedule 2 1 20.10. Aberrations and optimization Repetition 2 27.10. Structural

More information

13. Optical Instruments*

13. Optical Instruments* 13. Optical Instruments* Objective: Here what you have been learning about thin lenses is applied to make a telescope. In the process you encounter general optical instrument design concepts. The learning

More information

Journal of Modern Optics Publication details, including instructions for authors and subscription information:

Journal of Modern Optics Publication details, including instructions for authors and subscription information: This article was downloaded by: [National Chiao Tung University 國立交通大學 ] On: 28 April 2014, At: 06:01 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954

More information

Image Formation Fundamentals

Image Formation Fundamentals 03/04/2017 Image Formation Fundamentals Optical Engineering Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens Imaging Conjugate Points Imaging Limitations

More information

Fundamental Paraxial Equation for Thin Lenses

Fundamental Paraxial Equation for Thin Lenses THIN LENSES Fundamental Paraxial Equation for Thin Lenses A thin lens is one for which thickness is "negligibly" small and may be ignored. Thin lenses are the most important optical entity in ophthalmic

More information

Lens Principal and Nodal Points

Lens Principal and Nodal Points Lens Principal and Nodal Points Douglas A. Kerr, P.E. Issue 3 January 21, 2004 ABSTRACT In discussions of photographic lenses, we often hear of the importance of the principal points and nodal points of

More information

CHAPTER 3 OPTICAL INSTRUMENTS

CHAPTER 3 OPTICAL INSTRUMENTS 1 CHAPTER 3 OPTICAL INSTRUMENTS 3.1 Introduction The title of this chapter is to some extent false advertising, because the instruments described are the instruments of first-year optics courses, not optical

More information

Lens Design II. Lecture 8: Special correction features I Herbert Gross. Winter term

Lens Design II. Lecture 8: Special correction features I Herbert Gross. Winter term Lens Design II Lecture 8: Special correction features I 2017-12-04 Herbert Gross Winter term 2017 www.iap.uni-jena.de 2 Preliminary Schedule Lens Design II 2017 1 16.10. Aberrations and optimization Repetition

More information

Lenses- Worksheet. (Use a ray box to answer questions 3 to 7)

Lenses- Worksheet. (Use a ray box to answer questions 3 to 7) Lenses- Worksheet 1. Look at the lenses in front of you and try to distinguish the different types of lenses? Describe each type and record its characteristics. 2. Using the lenses in front of you, look

More information

SUBJECT: PHYSICS. Use and Succeed.

SUBJECT: PHYSICS. Use and Succeed. SUBJECT: PHYSICS I hope this collection of questions will help to test your preparation level and useful to recall the concepts in different areas of all the chapters. Use and Succeed. Navaneethakrishnan.V

More information

Chapter 2 - Geometric Optics

Chapter 2 - Geometric Optics David J. Starling Penn State Hazleton PHYS 214 The human eye is a visual system that collects light and forms an image on the retina. The human eye is a visual system that collects light and forms an image

More information

An Indian Journal FULL PAPER. Trade Science Inc. Parameters design of optical system in transmitive star simulator ABSTRACT KEYWORDS

An Indian Journal FULL PAPER. Trade Science Inc. Parameters design of optical system in transmitive star simulator ABSTRACT KEYWORDS [Type text] [Type text] [Type text] ISSN : 0974-7435 Volume 10 Issue 23 BioTechnology 2014 An Indian Journal FULL PAPER BTAIJ, 10(23), 2014 [14257-14264] Parameters design of optical system in transmitive

More information

Optical Design Lab Suresh Sivanandam Dunlap Institute for Astronomy and Astrophysics, University of Toronto

Optical Design Lab Suresh Sivanandam Dunlap Institute for Astronomy and Astrophysics, University of Toronto Optical Design Lab Suresh Sivanandam (sivanandam@dunlap.utoronto.ca) Dunlap Institute for Astronomy and Astrophysics, 1.Introduction and Objective Optical design is a critical part of astronomical instrument

More information

Lecture PowerPoint. Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoint. Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli Lecture PowerPoint Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the

More information

OPTICS DIVISION B. School/#: Names:

OPTICS DIVISION B. School/#: Names: OPTICS DIVISION B School/#: Names: Directions: Fill in your response for each question in the space provided. All questions are worth two points. Multiple Choice (2 points each question) 1. Which of the

More information

Properties of optical instruments

Properties of optical instruments Properties of optical instruments Visual optical systems part 1: afocal systems (telescope type) A basic optical description of the eye Power: 60 diopters (at rest) Equivalent to a single spherical surface,

More information

1.1 Singlet. Solution. a) Starting setup: The two radii and the image distance is chosen as variable.

1.1 Singlet. Solution. a) Starting setup: The two radii and the image distance is chosen as variable. 1 1.1 Singlet Optimize a single lens with the data λ = 546.07 nm, object in the distance 100 mm from the lens on axis only, focal length f = 45 mm and numerical aperture NA = 0.07 in the object space.

More information

Area of the Secondary Mirror Obscuration Ratio = Area of the EP Ignoring the Obscuration

Area of the Secondary Mirror Obscuration Ratio = Area of the EP Ignoring the Obscuration Compact Gregorian Telescope Design a compact 10X25 Gregorian telescope. The Gregorian telescope provides an erect image and consists of two concave mirrors followed by an eyepiece to produce an afocal

More information

Parity and Plane Mirrors. Invert Image flip about a horizontal line. Revert Image flip about a vertical line.

Parity and Plane Mirrors. Invert Image flip about a horizontal line. Revert Image flip about a vertical line. Optical Systems 37 Parity and Plane Mirrors In addition to bending or folding the light path, reflection from a plane mirror introduces a parity change in the image. Invert Image flip about a horizontal

More information

Lenses. Images. Difference between Real and Virtual Images

Lenses. Images. Difference between Real and Virtual Images Linear Magnification (m) This is the factor by which the size of the object has been magnified by the lens in a direction which is perpendicular to the axis of the lens. Linear magnification can be calculated

More information

Computer Generated Holograms for Optical Testing

Computer Generated Holograms for Optical Testing Computer Generated Holograms for Optical Testing Dr. Jim Burge Associate Professor Optical Sciences and Astronomy University of Arizona jburge@optics.arizona.edu 520-621-8182 Computer Generated Holograms

More information

R 1 R 2 R 3. t 1 t 2. n 1 n 2

R 1 R 2 R 3. t 1 t 2. n 1 n 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71/2.710 Optics Spring 14 Problem Set #2 Posted Feb. 19, 2014 Due Wed Feb. 26, 2014 1. (modified from Pedrotti 18-9) A positive thin lens of focal length 10cm is

More information

Physics 3340 Spring Fourier Optics

Physics 3340 Spring Fourier Optics Physics 3340 Spring 011 Purpose Fourier Optics In this experiment we will show how the Fraunhofer diffraction pattern or spatial Fourier transform of an object can be observed within an optical system.

More information

Three-Mirror Anastigmat Telescope with an Unvignetted Flat Focal Plane

Three-Mirror Anastigmat Telescope with an Unvignetted Flat Focal Plane Three-Mirror Anastigmat Telescope with an Unvignetted Flat Focal Plane arxiv:astro-ph/0504514v1 23 Apr 2005 Kyoji Nariai Department of Physics, Meisei University, Hino, Tokyo 191-8506 nariai.kyoji@gakushikai.jp

More information

PHY 431 Homework Set #5 Due Nov. 20 at the start of class

PHY 431 Homework Set #5 Due Nov. 20 at the start of class PHY 431 Homework Set #5 Due Nov. 0 at the start of class 1) Newton s rings (10%) The radius of curvature of the convex surface of a plano-convex lens is 30 cm. The lens is placed with its convex side down

More information

A Course on Foundations of Optical System Analysis and Design (FOSAD)

A Course on Foundations of Optical System Analysis and Design (FOSAD) A Course on Foundations of Optical System Analysis and Design (FOSAD) Lakshminarayan Hazra Department of Applied Optics and Photonics University of Calcutta 92 Acharya Prafulla Chandra Road, Kolkata 700

More information

Chapter 34. Images. Copyright 2014 John Wiley & Sons, Inc. All rights reserved.

Chapter 34. Images. Copyright 2014 John Wiley & Sons, Inc. All rights reserved. Chapter 34 Images Copyright 34-1 Images and Plane Mirrors Learning Objectives 34.01 Distinguish virtual images from real images. 34.02 Explain the common roadway mirage. 34.03 Sketch a ray diagram for

More information

AP Physics Problems -- Waves and Light

AP Physics Problems -- Waves and Light AP Physics Problems -- Waves and Light 1. 1974-3 (Geometric Optics) An object 1.0 cm high is placed 4 cm away from a converging lens having a focal length of 3 cm. a. Sketch a principal ray diagram for

More information

VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES

VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES Shortly after the experimental confirmation of the wave properties of the electron, it was suggested that the electron could be used to examine objects

More information

( ) Deriving the Lens Transmittance Function. Thin lens transmission is given by a phase with unit magnitude.

( ) Deriving the Lens Transmittance Function. Thin lens transmission is given by a phase with unit magnitude. Deriving the Lens Transmittance Function Thin lens transmission is given by a phase with unit magnitude. t(x, y) = exp[ jk o ]exp[ jk(n 1) (x, y) ] Find the thickness function for left half of the lens

More information

Refraction, Lenses, and Prisms

Refraction, Lenses, and Prisms CHAPTER 16 14 SECTION Sound and Light Refraction, Lenses, and Prisms KEY IDEAS As you read this section, keep these questions in mind: What happens to light when it passes from one medium to another? How

More information

Chapter 34: Geometrical Optics (Part 2)

Chapter 34: Geometrical Optics (Part 2) Chapter 34: Geometrical Optics (Part 2) Brief review Optical instruments Camera Human eye Magnifying glass Telescope Microscope Optical Aberrations Phys Phys 2435: 22: Chap. 34, 31, Pg 1 The Lens Equation

More information

Finite conjugate spherical aberration compensation in high numerical-aperture optical disc readout

Finite conjugate spherical aberration compensation in high numerical-aperture optical disc readout Finite conjugate spherical aberration compensation in high numerical-aperture optical disc readout Sjoerd Stallinga Spherical aberration arising from deviations of the thickness of an optical disc substrate

More information

c v n = n r Sin n c = n i Refraction of Light Index of Refraction Snell s Law or Refraction Example Problem Total Internal Reflection Optics

c v n = n r Sin n c = n i Refraction of Light Index of Refraction Snell s Law or Refraction Example Problem Total Internal Reflection Optics Refraction is the bending of the path of a light wave as it passes from one material into another material. Refraction occurs at the boundary and is caused by a change in the speed of the light wave upon

More information

Geometric Optics. Ray Model. assume light travels in straight line uses rays to understand and predict reflection & refraction

Geometric Optics. Ray Model. assume light travels in straight line uses rays to understand and predict reflection & refraction Geometric Optics Ray Model assume light travels in straight line uses rays to understand and predict reflection & refraction General Physics 2 Geometric Optics 1 Reflection Law of reflection the angle

More information

University of Rochester Department of Physics and Astronomy Physics123, Spring Homework 5 - Solutions

University of Rochester Department of Physics and Astronomy Physics123, Spring Homework 5 - Solutions Problem 5. University of Rochester Department of Physics and Astronomy Physics23, Spring 202 Homework 5 - Solutions An optometrist finds that a farsighted person has a near point at 25 cm. a) If the eye

More information

Tolerancing in Zemax. Lecture 4

Tolerancing in Zemax. Lecture 4 Tolerancing in Zemax Lecture 4 Objectives: Lecture 4 At the end of this lecture you should: 1. Understand the reason for tolerancing and its relation to typical manufacturing errors 2. Be able to perform

More information

CS 443: Imaging and Multimedia Cameras and Lenses

CS 443: Imaging and Multimedia Cameras and Lenses CS 443: Imaging and Multimedia Cameras and Lenses Spring 2008 Ahmed Elgammal Dept of Computer Science Rutgers University Outlines Cameras and lenses! 1 They are formed by the projection of 3D objects.

More information

Chapter 34 Geometric Optics

Chapter 34 Geometric Optics Chapter 34 Geometric Optics Lecture by Dr. Hebin Li Goals of Chapter 34 To see how plane and curved mirrors form images To learn how lenses form images To understand how a simple image system works Reflection

More information

Dr. Todd Satogata (ODU/Jefferson Lab) Monday, April

Dr. Todd Satogata (ODU/Jefferson Lab)  Monday, April University Physics 227N/232N Mirrors and Lenses Homework Optics 2 due Friday AM Quiz Friday Optional review session next Monday (Apr 28) Bring Homework Notebooks to Final for Grading Dr. Todd Satogata

More information

IMAGE FORMATION. Light source properties. Sensor characteristics Surface. Surface reflectance properties. Optics

IMAGE FORMATION. Light source properties. Sensor characteristics Surface. Surface reflectance properties. Optics IMAGE FORMATION Light source properties Sensor characteristics Surface Exposure shape Optics Surface reflectance properties ANALOG IMAGES An image can be understood as a 2D light intensity function f(x,y)

More information

Basic Optics System OS-8515C

Basic Optics System OS-8515C 40 50 30 60 20 70 10 80 0 90 80 10 20 70 T 30 60 40 50 50 40 60 30 70 20 80 90 90 80 BASIC OPTICS RAY TABLE 10 0 10 70 20 60 50 40 30 Instruction Manual with Experiment Guide and Teachers Notes 012-09900B

More information

ii) When light falls on objects, it reflects the light and when the reflected light reaches our eyes then we see the objects.

ii) When light falls on objects, it reflects the light and when the reflected light reaches our eyes then we see the objects. Light i) Light is a form of energy which helps us to see objects. ii) When light falls on objects, it reflects the light and when the reflected light reaches our eyes then we see the objects. iii) Light

More information

IMAGE SENSOR SOLUTIONS. KAC-96-1/5" Lens Kit. KODAK KAC-96-1/5" Lens Kit. for use with the KODAK CMOS Image Sensors. November 2004 Revision 2

IMAGE SENSOR SOLUTIONS. KAC-96-1/5 Lens Kit. KODAK KAC-96-1/5 Lens Kit. for use with the KODAK CMOS Image Sensors. November 2004 Revision 2 KODAK for use with the KODAK CMOS Image Sensors November 2004 Revision 2 1.1 Introduction Choosing the right lens is a critical aspect of designing an imaging system. Typically the trade off between image

More information

Two Fundamental Properties of a Telescope

Two Fundamental Properties of a Telescope Two Fundamental Properties of a Telescope 1. Angular Resolution smallest angle which can be seen = 1.22 / D 2. Light-Collecting Area The telescope is a photon bucket A = (D/2)2 D A Parts of the Human Eye

More information

Activity 6.1 Image Formation from Spherical Mirrors

Activity 6.1 Image Formation from Spherical Mirrors PHY385H1F Introductory Optics Practicals Day 6 Telescopes and Microscopes October 31, 2011 Group Number (number on Intro Optics Kit):. Facilitator Name:. Record-Keeper Name: Time-keeper:. Computer/Wiki-master:..

More information

Lecture 17. Image formation Ray tracing Calculation. Lenses Convex Concave. Mirrors Convex Concave. Optical instruments

Lecture 17. Image formation Ray tracing Calculation. Lenses Convex Concave. Mirrors Convex Concave. Optical instruments Lecture 17. Image formation Ray tracing Calculation Lenses Convex Concave Mirrors Convex Concave Optical instruments Image formation Laws of refraction and reflection can be used to explain how lenses

More information

Chapter 36. Image Formation

Chapter 36. Image Formation Chapter 36 Image Formation Real and Virtual Images Real images can be displayed on screens Virtual Images can not be displayed onto screens. Focal Length& Radius of Curvature When the object is very far

More information

Gaussian Ray Tracing Technique

Gaussian Ray Tracing Technique Gaussian Ray Tracing Technique Positive Lenses. A positive lens has two focal points one on each side of the lens; both are at the same focal distance f from the lens. Parallel rays of light coming from

More information

Design of diffractive singlets for monochromatic imaging

Design of diffractive singlets for monochromatic imaging Design of diffractive singlets for monochromatic imaging Dale A. Buralli and G. Michael Morris The Seidel aberrations of a rotationally-symmetric diffractive lens with an arbitrary phase profile are presented.

More information

JPN Pahang Physics Module Form 4 Chapter 5 Light. In each of the following sentences, fill in the bracket the appropriate word or words given below.

JPN Pahang Physics Module Form 4 Chapter 5 Light. In each of the following sentences, fill in the bracket the appropriate word or words given below. JPN Pahang Physics Module orm 4 HAPTER 5: LIGHT In each of the following sentences, fill in the bracket the appropriate word or words given below. solid, liquid, gas, vacuum, electromagnetic wave, energy

More information

Multi-Element Overview

Multi-Element Overview Intro Lenses Overview........ 128 Windows Achromats 425-675nm Cemented Doublets. 132 425-675nm Fast Achromats..... 133 1064/633nm Air-Spaced...... 134 1064/532nm Air-Spaced...... 135 Aplanats Visible....................

More information

General Physics Experiment 5 Optical Instruments: Simple Magnifier, Microscope, and Newtonian Telescope

General Physics Experiment 5 Optical Instruments: Simple Magnifier, Microscope, and Newtonian Telescope General Physics Experiment 5 Optical Instruments: Simple Magnifier, Microscope, and Newtonian Telescope Objective: < To observe the magnifying properties of the simple magnifier, the microscope and the

More information

Using molded chalcogenide glass technology to reduce cost in a compact wide-angle thermal imaging lens

Using molded chalcogenide glass technology to reduce cost in a compact wide-angle thermal imaging lens Using molded chalcogenide glass technology to reduce cost in a compact wide-angle thermal imaging lens George Curatu a, Brent Binkley a, David Tinch a, and Costin Curatu b a LightPath Technologies, 2603

More information

Person s Optics Test KEY SSSS

Person s Optics Test KEY SSSS Person s Optics Test KEY SSSS 2017-18 Competitors Names: School Name: All questions are worth one point unless otherwise stated. Show ALL WORK or you may not receive credit. Include correct units whenever

More information

Diffractive Lenses for Extended Depth Of Focus and Presbyopic Correction

Diffractive Lenses for Extended Depth Of Focus and Presbyopic Correction Diffractive Lenses for Extended Depth Of Focus and Presbyopic Correction G. Michael Morris and Dale Buralli Apollo Optical Systems, Inc. 330 Clay Road Rochester, NY 14623 E-mail: morris@apollooptical.com

More information

10.2 Images Formed by Lenses SUMMARY. Refraction in Lenses. Section 10.1 Questions

10.2 Images Formed by Lenses SUMMARY. Refraction in Lenses. Section 10.1 Questions 10.2 SUMMARY Refraction in Lenses Converging lenses bring parallel rays together after they are refracted. Diverging lenses cause parallel rays to move apart after they are refracted. Rays are refracted

More information

Conformal optical system design with a single fixed conic corrector

Conformal optical system design with a single fixed conic corrector Conformal optical system design with a single fixed conic corrector Song Da-Lin( ), Chang Jun( ), Wang Qing-Feng( ), He Wu-Bin( ), and Cao Jiao( ) School of Optoelectronics, Beijing Institute of Technology,

More information

Techniques of Designing Eyepieces using ATMOS. Rick Blakley October 28, 2012

Techniques of Designing Eyepieces using ATMOS. Rick Blakley October 28, 2012 Techniques of Designing Eyepieces using ATMOS Rick Blakley uranoport@msn.com October 28, 2012 1 1) Introduction: Ray tracing eyepieces requires skills of the sort one must muster for tracing any design,

More information

The Optics of Mirrors

The Optics of Mirrors Use with Text Pages 558 563 The Optics of Mirrors Use the terms in the list below to fill in the blanks in the paragraphs about mirrors. reversed smooth eyes concave focal smaller reflect behind ray convex

More information

Kolmogorov Turbulence, completed; then Geometrical Optics for AO

Kolmogorov Turbulence, completed; then Geometrical Optics for AO Kolmogorov Turbulence, completed; then Geometrical Optics for AO Claire Max ASTR 289, UCSC January 19, 2016 Page 1 Finish up discussion of Kolmogorov Turbulence from previous lecture Page 2 Structure function

More information

Photographic zoom fisheye lens design for DSLR cameras

Photographic zoom fisheye lens design for DSLR cameras Photographic zoom fisheye lens design for DSLR cameras Yufeng Yan Jose Sasian Yufeng Yan, Jose Sasian, Photographic zoom fisheye lens design for DSLR cameras, Opt. Eng. 56(9), 095103 (2017), doi: 10.1117/1.OE.56.9.095103.

More information

PHYS 1020 LAB 7: LENSES AND OPTICS. Pre-Lab

PHYS 1020 LAB 7: LENSES AND OPTICS. Pre-Lab PHYS 1020 LAB 7: LENSES AND OPTICS Note: Print and complete the separate pre-lab assignment BEFORE the lab. Hand it in at the start of the lab. Pre-Lab Start by reading the entire prelab and lab write-up.

More information