DCS14 Design and Correction Lecture 11 Correction

Total Page:16

File Type:pdf, Size:1020Kb

DCS14 Design and Correction Lecture 11 Correction Design and Correction of Optical Systems Lecture 11: Correction principles II 2014-06-18 Herbert Gross Summer term 2014 www.iap.uni-jena.de 2 Preliminary Schedule Law of refraction, Fresnel formulas, optical system model, raytrace, calculation 1 09.04. Basics approaches Dispersion, anormal dispersion, glass map, liquids and plastics, lenses, mirrors, 2 16.04. Materials and Components aspheres, diffractive elements Paraxial approximation, basic notations, imaging equation, multi-component 3 23.04. Paraxial Optics systems, matrix calculation, Lagrange invariant, phase space visualization Pupil, ray sets and sampling, aperture and vignetting, telecentricity, symmetry, 4 30.04. Optical Systems photometry Longitudinal and transverse aberrations, spot diagram, polynomial expansion, 5 07.05. Geometrical Aberrations primary aberrations, chromatical aberrations, Seidels surface contributions Fermat principle and Eikonal, wave aberrations, expansion and higher orders, 6 14.05. Wave Aberrations Zernike polynomials, measurement of system quality Diffraction, point spread function, PSF with aberrations, optical transfer function, 7 21.05. PSF and Transfer function Fourier imaging model Rayleigh and Marechal criteria, Strehl definition, 2-point resolution, MTF-based 8 28.05. Further Performance Criteria criteria, further options Principles of optimization, initial setups, constraints, sensitivity, optimization of 9 04.06. Optimization and Correction optical systems, global approaches Symmetry, lens bending, lens splitting, special options for spherical aberration, 10 11.06. Correction Principles I astigmatism, coma and distortion, aspheres Field flattening and Petzval theorem, chromatical correction, achromate, 11 18.06. Correction Principles II apochromate, sensitivity analysis, diffractive elements Overview, photographic lenses, microscopic objectives, lithographic systems, 12 25.06. Optical System Classification eyepieces, scan systems, telescopes, endoscopes 13 02.07. Special System Examples Zoom systems, confocal systems 14 09.07. Further Topics New system developments, modern aberration theory,... 3 Contents 1. Field flattening and Petzval theorem 2. Field lenses 3. Chromatical correction 4. Achromate and apochromate 5. Diffractive elements 6. Miscellaneous 4 Petzval Theorem for Field Curvature . Petzval theorem for field curvature: 1 n 'n n ' k k 1. formulation for surfaces m Rptz k nk nk 'rk 2. formulation for thin lenses (in air) 1 1 Rptz j n j f j . Important: - no dependence on bending - no dependence on stop location . Natural behavior: image curved object towards system plane . Problem: collecting systems with f > 0: If only positive lenses: R always negative ptz R ideal optical system real image . Typical scaling for single lens: image plane R shell ptz n 1.6 f 5 Petzval Theorem for Field Curvature . Goal: vanishing Petzval curvature 11 h 1 1 and positive total refractive power j R j n f f ptz j h1 f j j for multi-component systems . Solution: General principle for correction of curvature of image field: 1. Positive lenses with: - high refractive index - large marginal ray heights - gives large contribution to power and low weighting in Petzval sum 2. Negative lenses with: - low refractive index - samll marginal ray heights - gives small negative contribution to power and high weighting in Petzval sum 6 Flattening Meniscus Lenses . Possible lenses / lens groups for correcting field curvature . Interesting candidates: thick mensiscus shaped lenses r 2 2 1 n 'n 1 n 1 d k k d Rptz k nk nk 'rk n f n r1r2 r1 1. Hoeghs mensicus: identical radii 2 (n 1) d - Petzval sum zero F' nr 2 - remaining positive refractive power 2. Concentric meniscus, r r d - Petzval sum negative 2 1 - weak negative focal length 1 (n 1)d (n 1)d F' - refractive power for thickness d: R n r r d ptz 1 1 nr1(r1 d) 3. Thick meniscus without refractive power n 1 1 (n 1)2 d Relation between radii 0 r2 r1 d n Rptz nr1 nr1 d (n 1) 7 Correcting Petzval Curvature r r . Triplet group with + - + 1 2 r 3 d/2 collimated n2 n1 . Effect of distance and 1/Rpet [1/mm] -1 refractive indices 10 SF66 / FK3 / SF66 10-2 BK7 -3 10 r1 50 70 100 [mm] From : H. Zügge 8 Field Curvature 1 F . Correction of Petzval field curvature in lithographic lens j R j n for flat wafer j h j . Positive lenses: Green hj large F Fj j h1 . Negative lenses : Blue hj small . Correction principle: certain number of bulges Microscope Objective Lens a) . Possible setups for flattening single meniscus the field lense . Goal: b) - reduction of Petzval sum two meniscus lenses - keeping astigmatism corrected c) symmetrical triplet d) achromatized meniscus lens e) two meniscus lenses achromatized f) modIfied achromatized triplet solution Field Flatness one waist two waists . Principle of multi-bulges to reduce Petzval sum 1 1 n' r k n f p k k . Seidel contributions show principle Petz Petz 1. bulge 1. waist 2. bulge 2. waist 3. bulge 0.2 0 -0.2 10 20 30 40 50 60 Size Reduction by Aspheres 1. bulge 2. bulge 3. bulge 10 8 . Sensitivity of refractive lenses 6 spherical 4 for aspheres 2 0 1.5 1 coma 0.5 0 0.5 0.4 0.3 astigmatism 0.2 0.1 0 0.4 0.3 0.2 distortion 0.1 0 5 10 15 20 25 30 35 40 45 50 55 sum pupil aspherical 12 Flattening Field Lens Effect of a field lens for flattening the image surface 1. Without field lens 2. With field lens curved image surface image plane image flat shell image field lens 13 Field Lenses . Field lens: in or near image planes . Influences only the chief ray: pupil shifted . Critical: conjugation to image plane, surface errors sharply seen marginal ray chief ray field lens in intermediate original lens L image plane 2 shifted pupil pupil lens L1 14 Field Lens im Endoscope Ref : H. Zügge 15 Chromatical Aberrations . Various cases of chromatical aberration correction a) axial and lateral color corrected b) axial color corrected F FC C MR CR FC FC c) lateral color corrected d) no color corrected F C C F F C F C 16 Axial Colour: Achromate (a) (b) (c) . Compensation of axial colour by appropriate glass choice . Chromatical variation of the spherical aberrations: spherochromatism (Gaussian aberration) . Therefore perfect axial color correction BK7 BK7 F2 BK7 N-SSK8F2 (on axis) are often not feasable n = 1.5168 n = 1.5168 1.6200 n = 1.5168 1.6177 = 64.17 = 64.17 36.37 = 64.17 49.83 F= 1 F = 2.31 -1.31 F = 4.47 -3.47 r p r p r p 1 1 1 486 nm 588 nm 656 nm z z z -2.5 0 -0.20 0 0.20 -100 0 100 Ref : H. Zügge Achromate . Achromate: - Axial colour correction by cementing two Crown in different glasses front - Bending: correction of spherical aberration at the full aperture - Aplanatic coma correction possible be clever choice of materials . Four possible solutions: - Crown in front, two different bendings - Flint in front, two different bendings Flint in front . Typical: - Correction for object in infinity - spherical correction at center wavelength with zone - diffraction limited for NA < 0.1 - only very small field corrected solution 1 solution 2 Achromate: Realization Versions . Advantage of cementing: solid state setup is stable at sensitive middle surface with large curvature . Disadvantage: a) flint in front loss of one degree of freedom . Different possible realization forms in practice edge contact cemented b) crown in front edge contact cemented contact on axis broken, Gaussian setup Achromate : Basic Formulas . Idea: 1. Two thin lenses close together with different materials 2. Total power F F1 F2 F F 3. Achromatic correction condition 1 2 0 1 2 . Individual power values 1 1 F1 F F F 2 1 2 1 1 1 . Properties: 2 1. One positive and one negative lens necessary 2. Two different sequences of plus (crown) / minus (flint) 3. Large -difference relaxes the bendings 4. Achromatic correction indipendent from bending 5. Bending corrects spherical aberration at the margin 6. Aplanatic coma correction for special glass choices 7. Further optimization of materials reduces the spherical zonal aberration Achromate: Correction sMR' . Cemented achromate: 6 degrees of freedom: aplanatic 3 radii, 2 indices, ratio 1/2 case . Correction of spherical aberration: diverging cemented surface with R positive spherical contribution 1 for nneg > npos case with 2 solutions . Choice of glass: possible goals case with 1. aplanatic coma correction one solution and coma 2. minimization of spherochromatism case without solution, correction 3. minimization of secondary spectrum only spherical minimum . Bending has no impact on chromatical correction: is used to correct spherical aberration at the edge . Three solution regions for bending 1. no spherical correction 2. two equivalent solutions 3. one aplanatic solution, very stable Achomatic solutions in the Glass Diagram flint crown negative lens positive lens Achromat Achromate . Achromate . Longitudinal aberration . Transverse aberration . Spot diagram 486 nm 587 nm 656 nm y' = 486 nm axis rp 1 = 656 nm sinu' = 587 nm 1.4° 486 nm 587 nm 656 nm 2° s' [mm] 0 0.1 0.2 Coma Correction: Achromate Image height: y’ = 0 mm y’ = 2 mm Achromat . Bending of an achromate Pupil section: meridional meridional sagittal bending Transverse y' y' y' - optimal choice: small residual spherical Aberration: 0.05 mm 0.05 mm 0.05 mm aberration (a) - remaining coma for finite field size . Splitting achromate: additional degree of freedom: - better total correction possible (b) - high sensitivity of thin air space . Aplanatic glass choice: vanishing coma (c) . Cases: a) simple achromate, Achromat, splitting sph corrected, with coma (d) b) simple achromate, coma corrected by bending, with sph Achromat, aplanatic glass choice c) other glass choice: sph better, coma reversed (e) d) splitted achromate: all corrected e) aplanatic glass choice: all corrected Wave length: Ref : H.
Recommended publications
  • Chapter 3 (Aberrations)
    Chapter 3 Aberrations 3.1 Introduction In Chap. 2 we discussed the image-forming characteristics of optical systems, but we limited our consideration to an infinitesimal thread- like region about the optical axis called the paraxial region. In this chapter we will consider, in general terms, the behavior of lenses with finite apertures and fields of view. It has been pointed out that well- corrected optical systems behave nearly according to the rules of paraxial imagery given in Chap. 2. This is another way of stating that a lens without aberrations forms an image of the size and in the loca- tion given by the equations for the paraxial or first-order region. We shall measure the aberrations by the amount by which rays miss the paraxial image point. It can be seen that aberrations may be determined by calculating the location of the paraxial image of an object point and then tracing a large number of rays (by the exact trigonometrical ray-tracing equa- tions of Chap. 10) to determine the amounts by which the rays depart from the paraxial image point. Stated this baldly, the mathematical determination of the aberrations of a lens which covered any reason- able field at a real aperture would seem a formidable task, involving an almost infinite amount of labor. However, by classifying the various types of image faults and by understanding the behavior of each type, the work of determining the aberrations of a lens system can be sim- plified greatly, since only a few rays need be traced to evaluate each aberration; thus the problem assumes more manageable proportions.
    [Show full text]
  • Representation of Wavefront Aberrations
    Slide 1 4th Wavefront Congress - San Francisco - February 2003 Representation of Wavefront Aberrations Larry N. Thibos School of Optometry, Indiana University, Bloomington, IN 47405 [email protected] http://research.opt.indiana.edu/Library/wavefronts/index.htm The goal of this tutorial is to provide a brief introduction to how the optical imperfections of a human eye are represented by wavefront aberration maps and how these maps may be interpreted in a clinical context. Slide 2 Lecture outline • What is an aberration map? – Ray errors – Optical path length errors – Wavefront errors • How are aberration maps displayed? – Ray deviations – Optical path differences – Wavefront shape • How are aberrations classified? – Zernike expansion • How is the magnitude of an aberration specified? – Wavefront variance – Equivalent defocus – Retinal image quality • How are the derivatives of the aberration map interpreted? My lecture is organized around the following 5 questions. •First, What is an aberration map? Because the aberration map is such a fundamental description of the eye’ optical properties, I’m going to describe it from three different, but complementary, viewpoints: first as misdirected rays of light, second as unequal optical distances between object and image, and third as misshapen optical wavefronts. •Second, how are aberration maps displayed? The answer to that question depends on whether the aberrations are described in terms of rays or wavefronts. •Third, how are aberrations classified? Several methods are available for classifying aberrations. I will describe for you the most popular method, called Zernike analysis. lFourth, how is the magnitude of an aberration specified? I will describe three simple measures of the aberration map that are useful for quantifying the magnitude of optical error in a person’s eye.
    [Show full text]
  • Wavefront Aberrations
    11 Wavefront Aberrations Mirko Resan, Miroslav Vukosavljević and Milorad Milivojević Eye Clinic, Military Medical Academy, Belgrade, Serbia 1. Introduction The eye is an optical system having several optical elements that focus light rays representing images onto the retina. Imperfections in the components and materials in the eye may cause light rays to deviate from the desired path. These deviations, referred to as optical or wavefront aberrations, result in blurred images and decreased visual performance (1). Wavefront aberrations are optical imperfections of the eye that prevent light from focusing perfectly on the retina, resulting in defects in the visual image. There are two kinds of aberrations: 1. Lower order aberrations (0, 1st and 2nd order) 2. Higher order aberrations (3rd, 4th, … order) Lower order aberrations are another way to describe refractive errors: myopia, hyperopia and astigmatism, correctible with glasses, contact lenses or refractive surgery. Lower order aberrations is a term used in wavefront technology to describe second-order Zernike polynomials. Second-order Zernike terms represent the conventional aberrations defocus (myopia, hyperopia and astigmatism). Lower order aberrations make up about 85 per cent of all aberrations in the eye. Higher order aberrations are optical imperfections which cannot be corrected by any reliable means of present technology. All eyes have at least some degree of higher order aberrations. These aberrations are now more recognized because technology has been developed to diagnose them properly. Wavefront aberrometer is actually used to diagnose and measure higher order aberrations. Higher order aberrations is a term used to describe Zernike aberrations above second-order. Third-order Zernike terms are coma and trefoil.
    [Show full text]
  • Digital Light Field Photography
    DIGITAL LIGHT FIELD PHOTOGRAPHY a dissertation submitted to the department of computer science and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy Ren Ng July © Copyright by Ren Ng All Rights Reserved ii IcertifythatIhavereadthisdissertationandthat,inmyopinion,itisfully adequateinscopeandqualityasadissertationforthedegreeofDoctorof Philosophy. Patrick Hanrahan Principal Adviser IcertifythatIhavereadthisdissertationandthat,inmyopinion,itisfully adequateinscopeandqualityasadissertationforthedegreeofDoctorof Philosophy. Marc Levoy IcertifythatIhavereadthisdissertationandthat,inmyopinion,itisfully adequateinscopeandqualityasadissertationforthedegreeofDoctorof Philosophy. Mark Horowitz Approved for the University Committee on Graduate Studies. iii iv Acknowledgments I feel tremendously lucky to have had the opportunity to work with Pat Hanrahan, Marc Levoy and Mark Horowitz on the ideas in this dissertation, and I would like to thank them for their support. Pat instilled in me a love for simulating the flow of light, agreed to take me on as a graduate student, and encouraged me to immerse myself in something I had a passion for.Icouldnothaveaskedforafinermentor.MarcLevoyistheonewhooriginallydrewme to computer graphics, has worked side by side with me at the optical bench, and is vigorously carrying these ideas to new frontiers in light field microscopy. Mark Horowitz inspired me to assemble my camera by sharing his love for dismantling old things and building new ones. I have never met a professor more generous with his time and experience. I am grateful to Brian Wandell and Dwight Nishimura for serving on my orals commit- tee. Dwight has been an unfailing source of encouragement during my time at Stanford. I would like to acknowledge the fine work of the other individuals who have contributed to this camera research. Mathieu Brédif worked closely with me in developing the simulation system, and he implemented the original lens correction software.
    [Show full text]
  • Ethos 13 Pkg.Pdf
    WARRANTY REGISTRATION FORM We sincerely thank you for your purchase and wish you years of pleasure using it! Tele Vue Warranty Summary Eyepieces, Barlows, Powermates, & Paracorr have a “Lifetime Limited” warranty, telescopes & acces- sories are warranted for 5 years. Electronic parts are warranted for 1 year. Warranty is against defects in material or workmanship. No other warranty is expressed or implied. No returns without prior authoriza- tion. Lifetime Limited Warranty details online: http://bit.ly/TVOPTLIFE 5-Year/1-Year Warranty details online: http://bit.ly/TVOPTLIMITED Keep For Your Records Dealer: ________________________________ City/State/Country: ______________________ Date (day/month/yr): ______/______/________ 13.0 Ethos (ETH-13.0) Please fill out, cut out, and mail form below within ® 2-weeks of product purchase. Please include copy of sales receipt that has your name, the Tele Vue 32 Elkay Drive dealer name, and product name. Chester, NY 10918-3001 Cut out mailing address at left, tape to envelope, insert form & sales receipt in envelope and apply U.S.A. sufficient postage to envelope. 13.0 Ethos (ETH-13.0) How did you learn about this product? c Dealer c Friend c Tele Vue Blog c CloudyNights.com c TeleVue.com ______________________________________ c Social Media/Magazine/Other(s): Name Last First ______________________________________ Street Address What made you decide to buy this and your com- ments after using the product? ______________________________________ City State/Province ______________________________________ Postal Country Code Email*: _________________________________ Purchase Information Phone: _________________________________ Dealer: ________________________________ Astro Club: ____________________________ City/State/Country: ______________________ *c Check to receive email blog / newsletter Date (day/month/yr): ______/______/________ Ethos 6, 8, 10, & 13mm 100° Eyepieces Thank you for purchasing this Ethos eyepiece.
    [Show full text]
  • (S15) Joseph A
    Optical Design (S15) Joseph A. Shaw – Montana State University The Wave-Front Aberration Polynomial Ideal imaging systems perform point-to-point imaging. This requires that a spherical wave front expanding from each object point (o) is converted to a spherical wave front converging to a corresponding image point (o’). However, real optical systems produce an imperfect “aberrated” image. The aberrated wave front indicated by the solid red line below corresponds to rays near the axis focusing near point a and rays near the margin of the pupil focusing near point b. optical system o b a o’ W(x,y) = awf –rs entrance pupil exit pupil The “wave front aberration function” describes the optical path difference between the aberrated wave front and a spherical reference wave (typically measured in m or “waves”). W(x,y) = aberrated wave front – spherical reference wave front 1 Optical Design (S15) Joseph A. Shaw – Montana State University Coordinate System The unique rotationally invariant combinations of the exit-pupil and image-plane coordinates shown below are x2 + y2, x + yand All others are combinations of these. y x exit pupil image plane For rotationally symmetric optical systems, we can choose the “meridional” plane as our plane of symmetry so that we only need to consider rays that pass through the pupil in the plane. Then = 0 and our variables become the following … = 0 → x2 + y2, y We now convert to circular coordinates in the pupil plane and replace with to match Geary. y x2 + y2 → 2 = normalized exit-pupil radius y → cos = exit-pupil angle from meridional plane → = normalized height of ray intersection in image plane exit pupil image plane 2 Optical Design (S15) Joseph A.
    [Show full text]
  • Coma Aberration
    Coma aberration Lens Design OPTI 517 Prof. Jose Sasian Coma 0.25 wave 1.0 wave 2.0 waves 4.0 waves Spot diagram 2 2 W H, , W200 H W020 W111H cos 4 3 2 2 2 W040 W131H cos W222 H cos 2 2 3 4 W220 H W311H cos W400 H ... Prof. Jose Sasian Coma though focus Prof. Jose Sasian Cases of zero coma 1 u WAAy131 2 n •At y=0, surface is at an image •A=0, On axis beam concentric with center of curvature •A-bar=0, Off-axis beam concentric, chief ray goes through the center of curvature •Aplanatic points Prof. Jose Sasian Cases of zero coma Prof. Jose Sasian Aplanatic-concentric Prof. Jose Sasian Coma as a variation of magnification with aperture I 1 u WH131 , AAyH 2 n Prof. Jose Sasian Coma as a variation of magnification with aperture II S S’ m=s’/s Prof. Jose Sasian Sine condition Coma aberration can be considered as a variation of magnification with respect to the aperture. If the paraxial magnification is equal to the real ray marginal magnification, then an optical system would be free of coma. Spherical aberration can be considered as a variation of the focal length with the aperture. u sinU U U’ u' sinU ' Prof. Jose Sasian Sine condition On-axis L Sine condition YY’ L' O’ h YY’ O’ UU’L' L O h’ PP’ PP’ Optical path length between y and y’ is Optical path length between O and O’ is Laxis and does not depend on Y or Y’ Loff-axis = Laxis + L’ - L L = L + h’ n’ sin(U’) - h n sin(U) Lhsin( U ) L ''sin(') hU off-axis axis u sinU hn' 'sin( U ') hn sin( U ) u' sinU ' That is: OPD has no linear phase errors as a function Prof.of field Jose of Sasian view! Imaging a grating m sin(U ) d d sin(U ) m d'sin(U ') Prof.
    [Show full text]
  • Generation of Third-Order Spherical and Coma Aberrations by Use of Radially Symmetrical Fourth-Order Lenses
    Lo´pez-Gil et al. Vol. 15, No. 9/September 1998/J. Opt. Soc. Am. A 2563 Generation of third-order spherical and coma aberrations by use of radially symmetrical fourth-order lenses N. Lo´pez-Gil Section of Neurobiology and Behavior, Cornell University, Ithaca, New York 14853-2702 and Laboratorio de O´ ptica, Departamento de Fı´sica, Universidad de Murcia, 30071 Murcia, Spain H. C. Howland Section of Neurobiology and Behavior, Cornell University, Ithaca, New York 14853-2702 B. Howland 4913 Regent Street, Madison, Wisconsin 53705 N. Charman Department of Optometry and Vision Science, University of Manchester Institute of Science and Technology, P.O. Box 88, Manchester, M60 1QD, UK R. Applegate Department of Ophthalmology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78284-6230 Received December 24, 1997; revised manuscript received April 28, 1998; accepted May 1, 1998 We have extended the method of Alvarez [J. Am. Optom. Assoc. 49, 24 (1978)] to generate a variable magni- tude of third-order spherical and/or coma aberration by using a combination of fourth-order plates with a mag- nification system. The technique, based on the crossed-cylinder aberroscope, is used to measure the wave- front aberration generated by the plates. The method has been applied to correct the third-order spherical aberration generated by an artificial eye as well as the coma produced by a progressive addition ophthalmic lens. The simplicity of the method and its relatively low cost make it attractive for partial correction of the aberrations of the eye. © 1998 Optical Society of America [S0740-3232(98)03709-0] OCIS codes: 220.1000, 220.1010, 220.4830, 220.0220, 170.4460, 170.4470.
    [Show full text]
  • I. Reflective and Refractive Telescopes II. Telescope Optics III
    I. Reflective and Refractive Telescopes II. Telescope Optics III. Optical Aberrations IV. Telescope Configuration V. Telescope Mount VI. Observatory and Observatory site Vahram Chavushyan 28th ISYA Tonantzintla, 25th July to 12th August, 2005 9 Telescopes serves three main functions: (1) they are light collectors. The simplest telescopes simply focus light rays to a small area.; (2) Resolve light so that finer details can be seen; (3) Magnification: making objects look bigger (closer) 9 Two main types: refractive and reflective 9 As we are observing objects at very large distances, light can be assumed to come from infinity and can be represented as parallel rays f o = focal length of objective Basic Refractor real image formed here Basic Reflector f o = focal length of primary 9 For research telescopes or for astrophotography, we will place the analyzer (e.g. photometer, spectrometer) at the location of the focal plane 9 For visual observations, we need an eyepiece to properly collect the light through the objective lens or the primary mirror into the eye f f o e © C.R Kitchin: Telescope and Technique Note: Focal point of objective and eyepiece coincide 9 Lens Formula: 1 / o + 1 / i = 1 / f o i where o = object distance from lens, i = images distance from lens, f = focal length of lens 9 Linear magnification m: m = - i / o where m > 0 if the image is erect, |m|>1 if enlarged Reference: Optics by Hecht and Zajac (Addison-Wesley) 9 One of the most important number that characterize a telescope is its focal ratio (or, f/ number) Focal length of primary focal ratio = Aperture diameter of primary 9 E.g.
    [Show full text]
  • Design and Correction of Optical Systems
    Design and Correction of optical Systems Part 12: Correction of aberrations 1 Summer term 2012 Herbert Gross 2 Overview 1. Basics 2012-04-18 2. Materials 2012-04-25 3. Components 2012-05-02 4. Paraxial optics 2012-05-09 5. Properties of optical systems 2012-05-16 6. Photometry 2012-05-23 7. Geometrical aberrations 2012-05-30 8. Wave optical aberrations 2012-06-06 9. Fourier optical image formation 2012-06-13 10. Performance criteria 1 2012-06-20 11. Performance criteria 2 2012-06-27 12. Correction of aberrations 1 2012-07-04 13. Correction of aberrations 2 2012-07-11 14. Optical system classification 2012-07-18 3 Contents 12.1 Symmetry principle 12.2 Lens bending 12.3 Correcting spherical aberration 12.4 Coma, stop position 12.5 Astigmatism 12.6 Field flattening 12.7 Chromatical correction 12.8 Higher order aberrations 4 Principle of Symmetry . Perfect symmetrical system: magnification m = -1 . Stop in centre of symmetry . Symmetrical contributions of wave aberrations are doubled (spherical) . Asymmetrical contributions of wave aberration vanishes W(-x) = -W(x) . Easy correction of: coma, distortion, chromatical change of magnification front part rear part 2 3 1 5 Symmetrical Systems Ideal symmetrical systems: . Vanishing coma, distortion, lateral color aberration . Remaining residual aberrations: 1. spherical aberration 2. astigmatism 3. field curvature 4. axial chromatical aberration 5. skew spherical aberration 6 Symmetry Principle . Application of symmetry principle: photographic lenses . Especially field dominant aberrations can be corrected . Also approximate fulfillment of symmetry condition helps significantly: quasi symmetry . Realization of quasi- symmetric setups in nearly all photographic systems Ref : H.
    [Show full text]
  • Theory of Mirror Telescopes. K. Schwarzschild
    Investigations into geometrical optics. II Theory of mirror telescopes. by K. Schwarzschild. Presented by F. Klein during the meeting of 22 January 1905. § 1. Introduction. 1. In the competition between refractors and reflectors, the reflectors are at present gaining ground. Many and various of the former doubts concerning the precision and stability of large mirrors have been dismissed by the technical progress of recent years. At present glass mirrors with a silver-plated front side are commonly used. As the thickness of the silver layer turns out very even from experience, the exact form giving process used in the fabrication of lenses is also suitable for the fabrication of mirrors. Warping and temperature related strain can be reduced to a harmless measure by suitable mounting (Ritchey, Chicago). The low weather resistance (the silver layer quickly loses its high gloss) is compensated for by arranging the elements in such a way that the mirror can easily be taken out and can be freshly silvered during the course of a single day. With this obstacle removed, the advantages of reflecting telescopes are plainly shown, two of which stand in first place. The first to emphasize is the economic advantage offered by reflectors. An ordinary achromatic lens has four polished surfaces, the reflecting telescope (apart from the small plane mirror) has only one and the quality demand of the glass mass of the mirror (although it must be good) is not the very highest. Consequently, the price ratio between lenses and mirrors of the same diameter can rise up to 10:1 with large dimensions.
    [Show full text]
  • Basic Wavefront Aberration Theory for Optical Metrology
    APPLIED OPTICS AND OPTICAL ENGINEERING, VOL. Xl CHAPTER 1 Basic Wavefront Aberration Theory for Optical Metrology JAMES C. WYANT Optical Sciences Center, University of Arizona and WYKO Corporation, Tucson, Arizona KATHERINE CREATH Optical Sciences Center University of Arizona, Tucson, Arizona I. Sign Conventions 2 II. Aberration-Free Image 4 III. Spherical Wavefront, Defocus, and Lateral Shift 9 IV. Angular, Transverse, and Longitudinal Aberration 12 V. Seidel Aberrations 15 A. Spherical Aberration 18 B. Coma 22 C. Astigmatism 24 D. Field Curvature 26 E. Distortion 28 VI. Zernike Polynomials 28 VII. Relationship between Zernike Polynomials and Third-Order Aberrations 35 VIII. Peak-to-Valley and RMS Wavefront Aberration 36 IX. Strehl Ratio 38 X. Chromatic Aberrations 40 XI. Aberrations Introduced by Plane Parallel Plates 40 XII. Aberrations of Simple Thin Lenses 46 XIII.Conics 48 A. Basic Properties 48 B. Spherical Aberration 50 C. Coma 51 D. Astigmatism 52 XIV. General Aspheres 52 References 53 1 Copyright © 1992 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-408611-X 2 JAMES C. WYANT AND KATHERINE CREATH FIG. 1. Coordinate system. The principal purpose of optical metrology is to determine the aberra- tions present in an optical component or an optical system. To study optical metrology, the forms of aberrations that might be present need to be understood. The purpose of this chapter is to give a brief introduction to aberrations in an optical system. The goal is to provide enough information to help the reader interpret test results and set up optical tests so that the accessory optical components in the test system will introduce a minimum amount of aberration.
    [Show full text]