DOCSLIB.ORG

Imaging and Aberration Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Imaging and Aberration Theory Imaging and Aberration Theory Lecture 4: Aberration expansions 2018-11-08 Herbert Gross Winter term 2019 www.iap.uni-jena.de 2 Schedule - Imaging and aberration theory 2019 1 18.10. Paraxial imaging paraxial optics, fundamental laws of geometrical imaging, compound systems Pupils, Fourier optics, pupil definition, basic Fourier relationship, phase space, analogy optics and 2 25.10. Hamiltonian coordinates mechanics, Hamiltonian coordinates Fermat principle, stationary phase, Eikonals, relation rays-waves, geometrical 3 01.11. Eikonal approximation, inhomogeneous media single surface, general Taylor expansion, representations, various orders, stop 4 08.11. Aberration expansions shift formulas different types of representations, fields of application, limitations and pitfalls, 5 15.11. Representation of aberrations measurement of aberrations phenomenology, sph-free surfaces, skew spherical, correction of sph, aspherical 6 22.11. Spherical aberration surfaces, higher orders phenomenology, relation to sine condition, aplanatic sytems, effect of stop 29.11. 7 Distortion and coma position, various topics, correction options 8 06.12. Astigmatism and curvature phenomenology, Coddington equations, Petzval law, correction options Dispersion, axial chromatical aberration, transverse chromatical aberration, 9 13.12. Chromatical aberrations spherochromatism, secondary spectrum Sine condition, aplanatism and Sine condition, isoplanatism, relation to coma and shift invariance, pupil 10 20.12. isoplanatism aberrations, Herschel condition, relation to Fourier optics 11 10.01. Wave aberrations definition, various expansion forms, propagation of wave aberrations special expansion for circular symmetry, problems, calculation, optimal balancing, 12 17.01. Zernike polynomials influence of normalization, measurement 13 24.01. Point spread function ideal psf, psf with aberrations, Strehl ratio 14 31.01. Transfer function transfer function, resolution and contrast Vectorial aberrations, generalized surface contributions, Aldis theorem, intrinsic 15 07.02. Additional topics and induced aberrations, reversability 3 Contents . Repetition... Single refracting surface . Adaptation on optical system terms . Primary monochromatic aberration surface contributions . Extension on several surfaces . Lens contributions . Examples 4 Eikonal Overview . Fermat principle: light takes the fastest way P2 between two points L n(x, y, z) ds 0 The variance of the OPL is zero, stationary point P1 . The OPL is the Lagrange function in optics L L n s , n s the equation of motion is x' x y' y . This is the Eikonal equation of geometrical optics d dr n n ds ds . One ray is fixed by 4 parameters object image optical space angle space system (direction) angle . The general 4x4 functional relation (direction) between object and image space is point s s' restricted by the Fermat principle: r point r' only 4 independent variables . A Legendre transform allows to switch between the variables L(x, y, sx , sy ) nsx x'nsy y' L(x, y, x', y') . Every selection of eikonal variables has at least one case, which is singular 5 Eikonal Overview . Point eikonal: spatial coordinates in dL (x, y, x', y') n's 'dx's 'dy' ns dx s dy object and image space are fixed P x y x y the corresponding angles can be calculated LP LP ns nsy by the differential equations x x y L P LP n'sx ' n's ' x' y' y . Small change of initial ray data in the object space: Fermat principle allows to calculate the corresponding change in the image space A' A R' Q L n's'dr' ns dr s' q' Q' dr s q P' dr' R P . Special case q = 90°delivers the Abbe sine condition nsin u y' m n'sin u' y 6 Refracting Surface I: Basic Eikonal Approach . P, P' points on ray . A, A' arbitrary points on axis 2 2 2 2 . s,s' direction unit vectors of the rays sz 1 sx sy , s'z 1 s'x s'y relationship 2 2 2 2 2 . Real surface equation x y x y z 3 (1 b)... contains system parameters R, b 2R 8R . Angle eikonal, gives the optical path length change in P', if the point P is varied dLA (s,s') n r a ds n'r'a' ds' In coordinate representation dLA n x dsx y dsy z a dsz n'x ds'x y ds'y z a' ds'z y Q surface s' s P P' R n r n' M z A a z a' A' O origin 7 Refracting Surface II: Eikonal .Integration of the differential to get the total optical path length dLA n x ds x y ds y z a ds z n''''' x ds x y ds y z a ds z .Result of 4th order Taylor approximation LA na n'a' 2 2 x y a 2 2 n x sx y sy sx sy 2R 2 2 2 x y a' 2 2 n'x s'x y s'y s'x s'y 2R 2 2 2 2 2 1 b 2 2 2 x y sx sy a 2 2 2 n 3 x y sx sy 8R 4R 8 2 2 2 2 1 b 2 2 2 x y s'x s'y a' 2 2 2 n' 3 x y s'x s'y 8R 4R 8 . Elimination of intermediate variables x, y of the intersection point with the help of the law of refraction 8 Refracting Surface III: Law of Refraction 2 x2 y 2 (1 b)x2 y 2 . Implicite surface equation F(x, y, z) z 0 2R 8R3 . Normal unit vector in the intersection point e F(x, y, z) x (1 b) x2 y2 y (1 b) x2 y2 ex 1 2 , ey 1 2 , ez 1 R 2R R 2R . Law of refraction (n s n's')e 0 . Formulation in components y (1 b) x2 y2 (nsy n's'y )(nsz n's'z ) 1 2 0 R 2R x (1 b) x2 y2 (nsx n's'x )(nsz n's'z ) 1 2 0 R 2R y (1 b) x2 y2 x (1 b) x2 y2 (nsx n's'x ) 1 2 (nsy n's'y ) 1 2 0 R 2R R 2R . Solving for x, y in approximation of 4th order ns n's' ns n's' x R x x , y R y y n n' n n' 9 Refracting Surface IV: Eikonal . Resulting Eikonal function of sx, sy, s‘x, s‘y only (0) (2) (4) LA LA LA LA R 2 2 na 2 2 n'a' 2 2 na n'a' nsx n's'x nsy n's'y sx sy s'x s'y 2(n n') 2 2 R 2 2 2 2 2 2 nsx n's'x nsy n's'y nsx sy n's'x s'y 4(n n')2 1 2 2 2 2 2 2 (1 b)R 2 2 na sx sy n'a's'x s'y nsx n's'x nsy n's'y 8 8(n n')3 . Further re-arrangements for better practical usage: 1. introduction of the pupil coordinates xp, yp instead of the image sides directions s‘x, s‘y 2. switch to the image space ray parameters 3. optional switch to circular coordinates 4. according to Seidel substitution of the system parameter by the paraxial properties of the system and the marginal ray 5. Further approximation in 4th order to get a perturbation representation of the paraxial imaging. This allows a decoupling of the surface contributions 10 Refracting Surface V: Paraxial Optics (2) . 2nd order: paraxial optics 1 LA nR n' R x sx a s'x n sx n n' n n' (2) 1 LA nR n' R y sy a s'y n sy n n' n n' (2) 1 LA n' R nR x' s'x a' sx n' s'x n n' n n' (2) 1 LA n' R nR y' s'y a' sy n' s'y n n' n n' a' n' n n' aa' n' n n n' x' x s n' a' R n' x a' a R . Eliminating s'x, s'y a' n' n n' aa' n' n n n' y' y sy n' a' R n' a' a R . Imaging condition: x‘, y‘ independent from ray directions sx, sy n n' n n' 1. imaging equation a a' R 2. magnification na' x' na' x' x , m n'a x n'a 11 Refracting Surface VI: Pupil Coordinates y yp . Change to pupil coordinates object entrance system for optical systems plane pupil surface . Relations arcsin(sy) x x s x x tanu p x , s p s x x z arcsin(sz) y p sz p p y y y p sy y y p tanu y , sy sz p sz p p s x'x' x'x' p p s'x p s tanu'x , s'x s'z p' s'z p' y'y' p s'y y'y' p tanu'y , s'y s'z p' s'z p' . Approximated to 2nd order x x y y s p , s p x p y p x'x' y'y' s' p , s' p x p' y p' 12 Refracting Surface VII: Eikonal . Eikonal of 4th order 4 4 2 2 (s p) 2 s 2 s (s p) 2 L(4) K x2 y 2 S x2 y 2 A xx yy A 8p4 8p4 p p 2 p4 p p s2 (s p)2 s (s p)3 s3 (s p) P x2 y 2 xx yy D x2 y 2 xx yy C x2 y 2 xx yy 4 p4 p p 2 p4 p p 2 p4 p p 2 2 (n'n)b 1 1 1 1 . Coefficients K ns n's' 3 2 2 R Rs s p Rs' s' p 1.
Load more

Recommended publications
  • Synopsis of Technical Report
    Tzu-Yu Wu October 26, 2011 Opti 521 – Fall 2011 Introductory to opto-mechanical engineering Synopsis of Technical Report J.M. Sasian. ”Design, assembly, and testing of an objective lens for a free-space photonic switching system”, Optical Engineering 32(8), 1871-1878 (August 1993) 1. Introduction In this paper, the design, lens tolerancing, assembly and testing of a lens with a high numerical aperture over a small field of view are discussed. Although this object lens is specifically designed for a free-space photonic switching system, the concepts in aberration corrections and the approaches to reach a high NA within small field of view are applicable in many applications such as microscope objective lens, laser scan lenses. It also serves as a nice guide for a lens designer to understand the whole process of making a lens system which is not only limited to lens design but included tolerancing, lens ordering, the strategy to maintain the budget, assembly and testing details, and the approximate time required for each task. 2. Summary of the synopsis This synopsis mainly focuses on the general concepts in lens design of a fast objective lens with small field of view. It starts with a brief introduction on the lens requirement and lists the common aberration correction methods. Some explanations in aberration corrections are referenced from “Introduction to Lens Design with practical ZEMAX examples” by Joseph M Geary. Lens tolerancing, assembly and testing are included. Details in phonic switching system are neglected. Interested reader can refer the original paper for more details. 3. Lens requirement Lens requirements Focal length: 15mm Focal ratio: 1.5 Field of View: 7 degrees Wavelength: 850 nm Mapping: F-sin( ) ±1.0 Image surface: Flat Performance: Strehl휃 ratio> 0.95휇푚 over the full field Telecentricity: In the image space Lenses: Glass all spherical surfaces Page 1 of 5 4.
    [Show full text]
  • United States Patent (19) 11 Patent Number: 5,838,480 Mcintyre Et Al
    USOO583848OA United States Patent (19) 11 Patent Number: 5,838,480 McIntyre et al. (45) Date of Patent: Nov. 17, 1998 54) OPTICAL SCANNING SYSTEM WITH D. Stephenson, “Diffractive Optical Elements Simplify DIFFRACTIVE OPTICS Scanning Systems”, Laser Focus World, pp. 75-80, Jun. 1995. 75 Inventors: Kevin J. McIntyre, Rochester; G. Michael Morris, Fairport, both of N.Y. 73 Assignee: The University of Rochester, Primary Examiner James Phan Rochester, N.Y. Attorney, Agent, or Firm M. Lukacher; K. Lukacher 57 ABSTRACT 21 Appl. No.: 639,588 22 Filed: Apr. 29, 1996 An improved optical System having diffractive optic ele ments is provided for Scanning a beam. This optical System (51) Int. Cl. ............................................... GO2B 26/08 includes a laser Source for emitting a laser beam along a first 52 U.S. Cl. .......................... 359/205; 359/206; 359/207; path. A deflector, Such as a rotating polygonal mirror, 359/212; 359/216; 359/17 intersects the first path and translates the beam into a 58 Field of Search ..................................... 359/205-207, Scanning beam which moves along a Second path in a Scan 359/212-219, 17, 19,563, 568-570,900 plane. A lens System (F-0 lens) in the Second path has first 56) References Cited and Second elements for focusing the Scanning beam onto an image plane transverse to the Scan plane. The first and U.S. PATENT DOCUMENTS Second elements each have a cylindrical, non-toric lens. One 4,176,907 12/1979 Matsumoto et al. .................... 359/217 or both of the first and second elements also provide a 5,031,979 7/1991 Itabashi.
    [Show full text]
  • Characterisation Studies on the Optics of the Prototype Fluorescence Telescope FAMOUS
    Characterisation studies on the optics of the prototype fluorescence telescope FAMOUS von Hans Michael Eichler Masterarbeit in Physik vorgelegt der Fakultät für Mathematik, Informatik und Naturwissenschaften der Rheinisch-Westfälischen Technischen Hochschule Aachen im März 2014 angefertigt im III. Physikalischen Institut A bei Prof. Dr. Thomas Hebbeker Erstgutachter und Betreuer Zweitgutachter Prof. Dr. Thomas Hebbeker Prof. Dr. Christopher Wiebusch III. Physikalisches Institut A III. Physikalisches Institut B RWTH Aachen University RWTH Aachen University Abstract In this thesis, the Fresnel lens of the prototype fluorescence telescope FAMOUS, which is built at the III. Physikalisches Institut of the RWTH Aachen, is characterised. Due to the usage of silicon photomultipliers as active detector component, an adequate optical performance is required. The optical performance and transmittance of the used Fresnel lens and the qualification for the operation in the fluorescence telescope FAMOUS is examined in several series of measurements and simulations. Zusammenfassung In dieser Arbeit wird die Fresnel-Linse des Prototyp-Fluoreszenz-Teleskops FAMOUS charakterisiert, welches am III. Physikalischen Institut der RWTH Aachen gebaut wird. Durch die Verwendung von Silizium-Photomultipliern als aktive Detektorkomponente werden besondere Anforderungen an die Optik des Teleskops gestellt. In verschiedenen Messreihen und Simulationen wird untersucht, ob die Abbildungsqualität und die Transmission der verwendeten Fresnel-Linse für die Verwendung in diesem Fluoreszenz- Teleskop geeignet ist. Contents 1. Introduction 1 2. Cosmic rays 3 2.1 Energy spectrum . 4 2.2 Sources of cosmic rays . 6 2.3 Extensive air showers . 7 3. Fluorescence light detection 11 3.1 Fluorescence yield . 11 3.2 The Pierre Auger fluorescence detector . 14 3.3 FAMOUS .
    [Show full text]
  • Wavefront Control Simulations for the Giant Magellan Telescope: Field-Dependent Segment Piston Control
    Wavefront control simulations for the Giant Magellan Telescope: Field-dependent segment piston control Fernando Quir´os-Pachecoa, Rodolphe Conana, Brian McLeodb, Benjamin Irarrazavala, and Antonin Boucheza aGMTO Organization, 465 North Halstead St, Suite 250, Pasadena, CA 91107, USA bSmithsonian Astrophysical Observatory, 60 Garden St, MS 20, Cambridge, MA 02138, USA ABSTRACT We present in this paper preliminary simulation results aimed at validating the GMT piston control strategy. We will in particular consider an observing mode in which an Adaptive Optics (AO) system is providing fast on-axis WF correction with the Adaptive Secondary Mirror (ASM), while the phasing system using multiple Segment Piston Sensors (SPS) makes sure that the seven GMT segments remain phased. Simulations have been performed with the Dynamic Optical Simulation (DOS) tool developed at the GMT Project Office, which integrates the optical and mechanical models of GMT. DOS fast ray-tracing capabilities allows us to properly simulate the effect of field-dependent aberrations, and in particular, the so-called Field Dependent Segment Piston (FDSP) mode arising when a segment tilt on M1 is compensated on-axis by a segment tilt on M2. We will show that when using an asterism of SPS, our scheme can properly control both segment piston and the FDSP mode. Keywords: Giant Magellan Telescope, phasing, wavefront control, numerical simulations 1. INTRODUCTION The Giant Magellan Telescope (GMT)1 is a 25.4m diameter aplanatic Gregorian telescope that will be located at the Las Campanas Observatory (LCO), in Chile. The GMT is a segmented telescope, with a primary mirror (M1) composed of seven circular 8.4m segments.
    [Show full text]
  • Zernike Piston Statistics in Turbulent Multi-Aperture Optical Systems
    Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-2020 Zernike Piston Statistics in Turbulent Multi-Aperture Optical Systems Joshua J. Garretson Follow this and additional works at: https://scholar.afit.edu/etd Part of the Optics Commons Recommended Citation Garretson, Joshua J., "Zernike Piston Statistics in Turbulent Multi-Aperture Optical Systems" (2020). Theses and Dissertations. 3161. https://scholar.afit.edu/etd/3161 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. ZERNIKE PISTON STATISTICS IN TURBULENT MULTI-APERTURE OPTICAL SYSTEMS THESIS Joshua J. Garretson, Capt, USAF AFIT-ENG-MS-20-M-023 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENG-MS-20-M-023 ZERNIKE PISTON STATISTICS IN TURBULENT MULTI-APERTURE OPTICAL SYSTEMS THESIS Presented to the Faculty Department of Electrical and Computer Engineering Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science in Electrical Engineering Joshua J.
    [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]
  • Optical Systems for Laser Scanners1 to Provide Yet Another Perspective
    2 OpticalSystemsforLaserScanners Stephen F. Sagan NeoOptics Lexington, Massachusetts, USA CONTENTS 2.1 Introduction .......................................................................................................................... 70 2.2 Laser Scanner Configurations ............................................................................................71 2.2.1 Objective Scanning..................................................................................................71 2.2.2 Post-objective Scanning ..........................................................................................72 2.2.3 Pre-objective Scanning............................................................................................72 2.3 Optical Design and Optimization: Overview .................................................................72 2.4 Optical Invariants ................................................................................................................ 74 2.4.1 The Diffraction Limit .............................................................................................. 76 2.4.2 Real Gaussian Beams .............................................................................................. 76 2.4.3 Truncation Ratio ....................................................................................................... 77 2.5 Performance Issues .............................................................................................................. 79 2.5.1 Image Irradiance ......................................................................................................79
    [Show full text]
  • Utilization of a Curved Focal Surface Array in a 3.5M Wide Field of View Telescope
    Utilization of a curved focal surface array in a 3.5m wide field of view telescope Lt. Col. Travis Blake Defense Advanced Research Projects Agency, Tactical Technology Office E. Pearce, J. A. Gregory, A. Smith, R. Lambour, R. Shah, D. Woods, W. Faccenda Massachusetts Institute of Technology, Lincoln Laboratory S. Sundbeck Schafer Corporation TMD M. Bolden CENTRA Technology, Inc. ABSTRACT Wide field of view optical telescopes have a range of uses for both astronomical and space-surveillance purposes. In designing these systems, a number of factors must be taken into account and design trades accomplished to best balance the performance and cost constraints of the system. One design trade that has been discussed over the past decade is the curving of the digital focal surface array to meet the field curvature versus using optical elements to flatten the field curvature for a more traditional focal plane array. For the Defense Advanced Research Projects Agency (DARPA) 3.5-m Space Surveillance Telescope (SST)), the choice was made to curve the array to best satisfy the stressing telescope performance parameters, along with programmatic challenges. The results of this design choice led to a system that meets all of the initial program goals and dramatically improves the nation’s space surveillance capabilities. This paper will discuss the implementation of the curved focal-surface array, the performance achieved by the array, and the cost level-of-effort difference between the curved array versus a typical flat one. 1. INTRODUCTION Curved-detector technology for applications in astronomy, remote sensing, and, more recently, medical imaging has been a component in the decision-making process for fielded systems and products in these and other various disciplines for many decades.
    [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]
  • Lens Design OPTI 517 Seidel Aberration Coefficients
    Lens Design OPTI 517 Seidel aberration coefficients Prof. Jose Sasian OPTI 517 Fourth-order terms 2 2 W H, W040 W131H W222 H 2 W220 H H W311H H H W400 H H Spherical aberration Coma Astigmatism (cylindrical aberration!) Field curvature Distortion Piston Prof. Jose Sasian OPTI 517 Coordinate system Prof. Jose Sasian OPTI 517 Spherical aberration h 2 h 4 Z 2r 8r 3 u h y1 y 2r W n'[PB'] n'[PA' ] n'[PB'] n[PB] We have a spherical surface of radius of curvature r, a ray intersecting the surface at point P, intersecting the reference sphere at B’, intersecting the wavefront in object space at B and in image space at A’, and passing in image space by the point Q’’ in the optical axis. The reference sphere in object space is centered at Q and in image space is centered at Q’ Question: how do we draw the first order Prof. Jose Sasian OPTI 517 marginal ray in image space? [PQ]2 s Z 2 h 2 s 2 2sZ Z 2 h 2 2 4 4 2 h h h h 2s 3 2 2r 8r 4r [PB] [OQ] [PQ] s 2 1 2 2 s h 2 1 1 h 4 1 1 h 4 1 1 2 2 s r 8r s r 8s s r 2 4 2 h s h s s 1 1 1 u s 2 r 4r 2 s 2 r h y1 y 2r Prof. Jose Sasian OPTI 517 Spherical aberration ' ' [PB] [OQ] [PQ] [PB'] [OQ ] [PQ ] 2 2 2 4 y 2 u 1 1 y 4 1 1 y u 1 1 y 1 1 1 y 1 y ' 2 ' 2 2 2r s r 8r s r 2 2r s r 8r s r 4 2 4 2 y 1 1 y 1 1 8s ' s ' r 8s s r W n '[PB'] n[PB] y 2 u 1 1 1 1 1 y n ' n ' 2 r s r s r y 4 1 1 1 1 n ' n 2 ' 8r s r s r 2 2 y 4 n ' 1 1 n 1 1 ' ' 8 s s r s s r Prof.
    [Show full text]
  • 1 Long Wave Infrared Scan Lens Design and Distortion
    LONG WAVE INFRARED SCAN LENS DESIGN AND DISTORTION CORRECTION by Andy McCarron ____________________________ Copyright © Andy McCarron 2016 A Thesis Submitted to the Faculty of the DEPARTMENT OF OPTICAL SCIENCES In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE In the Graduate College THE UNIVERSITY OF ARIZONA 2016 1 STATEMENT BY AUTHOR The thesis titled Long Wave Infrared Scan Len Design and Distortion Correction prepared by Andy McCarron has been submitted in partial fulfillment of requirements for a master’s degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided that an accurate acknowledgement of the source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: __________________________Andy McCarron Andy McCarron APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: 24 August, 2019 Jose Sasian Date Professor of Optical Sciences 2 ACKNOWLEDGEMENTS Special thanks to Professor Jose Sasian for Chairing this Thesis Committee, and to Committee Members Professor John Grievenkamp, and Professor Matthew Kupinski. I’ve learned all lot from each of you through the years. Thanks to Markem-Imaje for financial support.
    [Show full text]
  • Automated Aberration Extraction Using Phase Wheel Targets Lena Zavyalova, Anatoly Bourov, Bruce W
    Automated aberration extraction using phase wheel targets Lena Zavyalova, Anatoly Bourov, Bruce W. Smith Rochester Institute of Technology, 82 Lomb Memorial Dr., Rochester, NY 14623 ABSTRACT An approach to in-situ wavefront aberration measurement is explored. The test is applicable to sensing aberrations from the image plane of a microlithography projection system or a mask inspection tool. A set of example results is presented which indicate that the method performs well on lenses with a Strehl ratio above 0.97. The method uses patterns produced by an open phase figure1 to determine the deviation of the target image from its ideal shape due to aberrations. A numerical solution in the form of Zernike polynomial coefficients is reached by modeling the object interaction with aberrated pupil function using the nonlinear optimization routine over the possible deformations to give an accurate account of the image detail in 2-D. The numerical accuracy for the example below indicated superb performance of the chosen target shapes with only a single illumination setup. Keywords: aberrations, phase wheel, lithography 1. INTRODUCTION Aberrations are directly related to loss of contrast in the image. Modern lithography lenses require optical path tolerances on the order of several nanometers over extremely large apertures. If the primary aberrations are well- corrected, it is important to know how much wavefront distortion remains. Higher order aberrations are therefore of consequence due to their increased contribution to the total root mean square (rms) wavefront error in large pupils. Measuring the optical aberrations in microlithography projection systems, such as stepper or aerial image microscope, when working from the image space is not trivial.
    [Show full text]