TSBB09 Image Sensors 2018-HT2. Image Formation Part 1
|
|
- Bruce Francis
- 5 years ago
- Views:
Transcription
1 TSBB09 Image Sensors 2018-HT2 Image Formation Part 1
2 Basic physics Electromagnetic radiation consists of electromagnetic waves With energy That propagate through space The waves consist of transversal electrical and magnetic fields that alternate with a temporal frequency (Hertz) and spatial wavelength (meter) 2
3 Frequency and wavelength The relation between frequency and wavelength is c = c is the speed of light and depends on the medium, c c 0 c 0 = speed of light in vacuum m/s 3
4 Particles and energy Light can also be represented as particles, photons The energy of a photon is E = h = h c / Energy increases with and decreases with h is Planck s constant ( Js) 4
5 Particles and energy Energy depends on the frequency Energy is preserved c 2 and 2 must change with the same factor relative to c 1 and 1 c 1 c 2 < c = 1 2 < 1 If the speed of light changes from one medium to another, the frequency is constant to make the energy constant the wavelength must change 5
6 Spectrum In practice, light normally consists of photons with a range of energies, or waves with a range of frequencies This mix of frequencies/wavelengths/energies is called the spectrum of the light The spectrum is a function that gives the total amount of energy for each frequency or wavelength Monochromatic light consists essentially of only one frequency/wavelength Can be produced by special light sources, e.g., lasers 6
7 Spectrum Less number of photons More number of photons E E Same total energies Natural light Monochromatic light 7
8 Classification of light spectrum 8
9 Polarization The electromagnetic field has a direction Perpendicular to the direction of motion The polarization of the light is defined as the direction of the electric field Natural light is a mix waves with polarization in all possible directions: unpolarized light Special light sources or filters can produce polarized light of well-defined polarization 9
10 Polarization Plane polarization The electric field varies only in a single plane Electric field 10
11 Polarization Circular/elliptical polarization The electric field vector rotates Can be constructed as the sum of two plane polarized waves with 90 o phase shift Conversely: plane polarized light can be decomposed as a sum of two circular polarized waves that rotate in opposite directions 11
12 Coherence The phase of the light waves can either be random: incoherent light (natural light) in a systematic relation: coherent light Coherent light is usually related to monochromatic light sources (e.g. laser) Compare a red LED and a red laser Both produce light within a narrow range The LED light is incoherent The laser light is coherent 12
13 Radiometry Light radiation has energy Each photon has a particular energy related to its frequency (E = h ) The number of photons of a particular frequency gives the amount of energy for this frequency Described by the spectrum Unit: Joule (or Watt second) Is usually not measured directly 13
14 Radiometry The power of the radiation, i.e., the energy per unit time, is the radiant flux Since the energy depends on the frequency, so does the radiant flux Unit: Watt or Joule per second Is usually not measured directly 14
15 Radiometry The radiant flux per unit area is the flux density Since the flux depends on the frequency, so does the flux density Unit: Watt per square meter Can be measured directly! As the energy through a specific area during a specific time interval Irradiance: flux density incident upon a surface Excitance or emittance: flux density emitted from a surface 15
16 Radiometry For point sources, or distant sources of small extent, the flux density can also be measured per unit solid angle The radiant intensity is the radiant flux per unit solid angle Unit: Watt per steradian 16
17 Basic principle Based on preservation of energy A constant light source must produce the same amount of energy through a solid angle regardless of distance to the source The radiant intensity is constant w.r.t. distance The radiant flux density decreases with the square of the distance to the source 17
18 The radiometric chain Light source Sensor Surface 18
19 The radiometric chain Light source Sensor Surface 2 Surface 1 19
20 The radiometric chain Light source 1 Sensor Surface 2 Light source 2 Surface 1 20
21 The radiometric chain Light source 1 Sensor Surface 2 Light source 2 Medium Surface 1 21
22 Interaction between light and matter Most types of light-matter interactions can be represented by n = the material s refractive index a = the material s absorption coefficient Both parameters depend on More complex interactions include polarization effects or non-linear effects 22
23 BREAK 23
24 Light incident upon a surface When light meets a surface Some part of it is transmitted through the new media Possibly with another speed and direction Some part of it is absorbed by the new media Usually: the light energy is transformed to heat Some part of it is reflected For the same material, all three effects depend on the light s wavelength Equivalently: they depend on the light s frequency 24
25 Basic principle Based on preservation of energy: E 0 = E 1 + E 2 + E 3 E 0 = incoming energy E 3 = absorbed energy E 2 = reflected energy E 1 = transmitted energy 25
26 Refraction The light that is transmitted into the new medium is refracted due to the change in light speed a 1 Snell s law of refraction: sina 2 sina 1 = n 1 n 2 = c 2 c 1 a 2 26
27 Absorption Absorption implies attenuation of transmitted or reflected light Materials get their colors as a result of different amount of absorption for different wavelengths Ex: A green object attenuates wavelengths in the green band less than in other bands. 27
28 Absorption The absorption of light in matter depends on the length that the light travels through the material a= e -ax a = attenuation of the light (0 a 1) a = the material s absorption coefficient x = length that the light travels in the material 28
29 Absorption spectrum The spectrum of the reflected/transmitted light is given by s 2 ( ) = s 1 ( ) a( ) s 1 = incident spectrum s 2 = reflected/transmitted spectrum a = absorption spectrum (0 a( ) 1) 29
30 Reflection Highly dependent on the surface type a a a Light is reflected equally much in all directions independent of a Mirror Lambertian surface A real surface is often a mix between the two cases 30
31 Emission Independent of its interaction with incident light (well, almost ): Any object, even one that is not considered a light source, emits electromagnetic radiation Primarily in the IR-band, based on its temperature More on this in the lecture on IR sensors 31
32 Scattering All mediums (other than vacuum) scatter light Examples: air, water, glass We can think of the medium as consisting of small particles and with some probability they reflect the light In any possible direction Different probability for different directions Weak effect and roughly proportional to -4 In general, the probability depends also on the distribution of particle sizes 32
33 Scattering Medium 33
34 Scattering Scattering is not an absorption It rather means that the light ray does not travel along a straight line through the medium There is a probability that a certain photon exits the medium in another direction than it entered. Examples: The sky is blue because of scattering of the sun light A strong laser beam becomes visible in air 34
35 The plenoptic function At a point x = (x 1,x 2,x 3 ) in space we can measure how much light energy that travels in the direction n = (n 1,n 2,n 3 ), n = 1 n x 35
36 The plenoptic function The plenoptic function is the corresponding radiance intensity function p(x,n) (5-dim since x is 3-dim & n has 2 d.o.f) Can also be a function of Frequency Time t p(x,n,,t) (7-dim) (Polarization) 36
37 A light camera A (light) camera is a device that samples the plenoptic function in a particular way Different types of cameras sample in different ways Pinhole-camera Orthographic camera Push-broom camera Light-field camera 37
38 The pinhole camera The most common camera model is the pinhole camera Swedish: hålkamera An ideal model of the camera obscura 38
39 The pinhole camera model Each point in the image plane is illuminated by a single ray passing through the aperture The aperture through which all light enters the camera The image plane This is where we measure the image For an ideal pinhole camera the aperture is a single point The camera front 39
40 The pinhole camera model Mathematically we need only know the location of the image plane and the aperture The rest is physics + practical implementation In fact, it suffices to know the aperture (why?) In the literature, the aperture point is also called camera center camera focal point 40
41 The pinhole camera model The image plane and the camera center define a camera-centered coordinate system (x 1,x 2,x 3 ): Principal or optical axis x 1,x 2 are parallel to the image plane, x 3 is perpendicular to the plane and defines the viewing direction of the camera P=(x 1,x 2,x 3 ) is a point in 3D space Q=(y 1,y 2 ) is the projection of P f = focal distance, the distance between the image plane and the camera center 41
42 The pinhole camera model R is the point where the optical axis intersects the image plane The principal point or the image center The (x 1,x 2 ) plane is the principal plane or focal plane The green line is the projection line of point P All points on the line are projected onto Q Alternatively: the projection line of Q 42
43 The pinhole camera model If we look at the camera coordinate system along the x 2 axis: Two similar triangles give: -y 1 f = x 1 x 3 or y 1 = - f x 1 x 3 43
44 The pinhole camera model Looking along the x 1 axis gives a similar expression for y 2 This can be summarized as: æ ç ç è y 1 y 2 ö = - f æ x ç 1 x ç x ø 3 è 2 ö ø 44
45 The virtual image plane The projected image is rotated 180 o relative to how we see the 3D world Reflection in both y 1 and y 2 coordinates = rotation Must be de-rotated before we can view it In the film based camera, the image is manually rotated In the digital camera this is taken care of by reading out the pixels in the rotated order Mathematically this is equivalent to placing the image plane in front of the focal point 45
46 The virtual image plane Projection lines works as before: from P through the focal point and intersect at Q This defines the virtual image plane Cannot be realized in practice Produces the same image as the rotated image from the real image plane Easier to draw? 46
47 The virtual image plane P = A point in 3D space Q The projection of P onto the virtual image plane O = The camera focal point æ ç è y 1 y 2 ö = f æ x 1 ø x 3 ç è x 2 ö ø 47
48 Lenses vs. infinitesimal aperture The pinhole camera model doesn t work in practice since If we make the aperture small, too little light enters the camera If we make the aperture larger, the image becomes blurred Solution: we replace the aperture with a lens or a system of lenses 48
49 Thin lenses The simplest model of a lens Focuses all points in an object plane onto the image plane object plane a b image plane 49
50 The object plane The object plane consists of all points that appear sharp when projected through the lens onto the image plane The object plane is an ideal model of where the sharp points are located In practice: the object plane may be non-planar: e.g. described by the surface of a sphere The shape of the object plane depends on the quality of the lens (or lens system) For thin lenses the object plane can often be approximated as a plane 50
51 Thin lenses The thin lens is characterized by a single parameter: the focal length f L 1 a + 1 b = 1 f L To change a (distance to object plane), we need to change b since f L is constant a = for b = f L! 51
52 TSBB09 Image Sensors Image Formation Part 2 52
53 Diffraction limited systems Due to the wave nature of light, even when various lens effects are eliminated, light from a single 3D point cannot be focused to an arbitrarily small point if it has passed an aperture For coherent light: Huygens's principle: treat the incoming light as a set of point light sources Gives diffraction pattern at the image plane 53
54 Diffraction limited systems Assume an ideal lens with aperture size D: D D Because of diffraction, a point source infinitely far away (a plane wave) will not be focused onto a single point in the image plane. 54
55 Diffraction limited systems Example: 1D x = vertical position in the aperture 55
56 Diffraction limited systems Each point along the aperture, at position x, acts as a wave source In the image plane, at position x, each point source contributes with a wave that has a phase difference 2 x sin / relative the position at the centre of the aperture, (assuming that x << f) is the angle from point x to the aperture, and assuming that is small it follows that sin tan = x / f We get: 2 x x / ( f) 56
57 Diffraction limited systems The wave function is everywhere characterized by its magnitude A and phase. As is common with sinusoidal signals, we can represent the wave-function mathematically by a complex number: Y = Ae i A phase shift corresponds to multiplying by e i Im Re 57
58 Diffraction limited systems The principle of superposition means that the resulting wave-function at the image plane is a sum/integral of the contributions from the different light sources. For the incoming plane wave, we set its amplitude to 1 and phase = 0: Resulting wave-function Amplitude of incoming light D/2 Y(x) = ò Y ( x )e idf d x = -D/2 ò rect ( x D )eidf d x -» ò rect ( x 2pi x x D )e f sin(p xd f l) l d x = (cmp. Fourier transform) = f l (p xd f l) - 58
59 Diffraction limited systems This phenomena generalizes to 2D: The resulting wave-function is the 2D FT of the incoming spatial amplitude (function of x ) Example: a circular aperture of diameter D (Input amplitude normalized to 1/f ) Y ( r ) = 1 f rect( r l D ) Y(r) = J 1(pr D f l) pr D f l First order Bessel function 59
60 The Airy disk from a single 3D point à à camera front focal plane image plane The Airy disk, the image of a circular pattern projected into the image plane 60
61 The Airy disk The smallest resolvable distance in the image plane, x, is given by Distance to first zero point in Ã(x) lens focal length lens diameter light wavelength 61
62 The Airy disk Conclusions: The image cannot have a better resolution than x No need to measure the image with higher resolution than x! Be aware of cameras with high pixel resolution and high diffraction Image resolution is not defined by number of pixels in the camera! 62
63 The point spread function The Airy disk is also called point spread function or blur disk, circle of confusion Modulation transfer function (MTF) In general the point spread function can be related to several effects that make the image of a point appear blurred Diffraction Lens imperfections Imperfections in the position of the image plane Often modeled as constant over the image Can be variable for poor optical systems 63
64 Depth of field We have now placed a lens at the aperture Points that are off the object plane become blurred proportional to the displacement from the object plane Due to the point spread function, it makes sense to accept blur in the order of x This blur will be there anyway due to diffraction Depth of field d is the displacement along the optical axis from the object plane that gives blur x 64
65 Depth of field D Depth of field (d) x a a b b 1 a + 1 b = 1 f L Insert a = a - d/2 to get the horisontal blur (b -b) Relate horisontal blur to vertical blur x 65
66 Depth of field For a camera where a <, an approximation (assuming d << a) for d is d» 2Dx a(a- f L ) Df L a = distance from lens to object plane f L = lens focal length D = lens diameter x = required image plane resolution d = depth of field 66
67 Depth of field For a lens where a =, points that are further away than d min are blurred less than x where d min = f LD 4Dx 67
68 The F-number f L /D is the F-number of the lens or lens system Example A typical F number of a camera = 8 Blue light = 420 nm wavelength Airy disk diameter x = 1.22 F 4 m For a lens with f L = 15 mm we get d 0.6 m at a = 1.5 m d min 1.8 m at a = This means that the depth of field is within a manageable range 68
69 Lens distortion A lens or a lens system can never map straight lines in the 3D scene exactly to straight lines in the image plane Depending on the lens type, a square pattern will typically appear like a barrel or a pincushion 70
70 Lens distortion Barrel distortion No distortion Pincushion distortion 71
71 Radial lens distortion This effect is called lens distortion (geometric distortion) and can, in the simplest case, be modeled as a radial distortion (y 1, y 2 ) = correct image coordinate (y 1, y 2 ) = r (cos, sin ) (y 1, y 2 ) = real image coordinate (y 1, y 2 ) = h(r) (cos, sin ) Observed point The observed positions of points in the image are displaced in the radial direction relative the image center as described by the pinhole camera model. y 2 Position according to the pinhole camera model y 1 72
72 Radial lens distortion h is approximately a linear function with some non-linear deviation, e.g. The deviation from a linear function usually grows with r Once modeled, we can compensate for the distortion 73
73 Lens distortion Which distortion function h is used depends on the type of lens and other practical considerations: Number of parameters Invertibility More complicated distortion models include angular dependent distortion Cheap lenses => significant distortion Almost no distortion => expensive lenses 74
74 Vignetting Even if the light that enters the camera is constant in all directions, the image plane will receive different amount of illumination This effect is called vignetting 75
75 Vignetting Sometimes used as a photographic effect But is usually unwanted Can be compensated for in digital cameras Image from a digital camera with a very light lens 76
76 Mechanical vignetting B Light from a larger solid angle emitted from point A is focused here A Light from a smaller solid angle emitted from point B is focused here 77
77 The cos 4 law We can see the aperture as a light source in the form of a small area that illuminates the image plane a The flux density decreases with the square of the distance to the light source: cos 2 a The effective area of the detector relative to the aperture varies as cos a The effective area of the aperture relative to the detector varies as cos a 78
78 The cos 4 law This effect exists also in lens-based cameras This means that, in general, there is an attenuation of the image towards the edges of the image, approximately according to cos 4 a Can be compensated for in a digital camera 79
79 Chromatic aberration The refraction index of matter (lenses) is wavelength dependent Example: a prism can decompose the light into its spectrum A ray of white light is decomposed into rays of different colors that intersect the image plane at different points 80
80 Chromatic aberration Sometimes clearly visible if you look close to the edges through a pair of glasses 81
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 informationChapter Ray and Wave Optics
109 Chapter Ray and Wave Optics 1. An astronomical telescope has a large aperture to [2002] reduce spherical aberration have high resolution increase span of observation have low dispersion. 2. If two
More informationChapters 1 & 2. Definitions and applications Conceptual basis of photogrammetric processing
Chapters 1 & 2 Chapter 1: Photogrammetry Definitions and applications Conceptual basis of photogrammetric processing Transition from two-dimensional imagery to three-dimensional information Automation
More informationOPAC 202 Optical Design and Instrumentation. Topic 3 Review Of Geometrical and Wave Optics. Department of
OPAC 202 Optical Design and Instrumentation Topic 3 Review Of Geometrical and Wave Optics Department of http://www.gantep.edu.tr/~bingul/opac202 Optical & Acustical Engineering Gaziantep University Feb
More informationΕισαγωγική στην Οπτική Απεικόνιση
Εισαγωγική στην Οπτική Απεικόνιση Δημήτριος Τζεράνης, Ph.D. Εμβιομηχανική και Βιοϊατρική Τεχνολογία Τμήμα Μηχανολόγων Μηχανικών Ε.Μ.Π. Χειμερινό Εξάμηνο 2015 Light: A type of EM Radiation EM radiation:
More informationBig League Cryogenics and Vacuum The LHC at CERN
Big League Cryogenics and Vacuum The LHC at CERN A typical astronomical instrument must maintain about one cubic meter at a pressure of
More informationApplied Optics. , Physics Department (Room #36-401) , ,
Applied Optics Professor, Physics Department (Room #36-401) 2290-0923, 019-539-0923, shsong@hanyang.ac.kr Office Hours Mondays 15:00-16:30, Wednesdays 15:00-16:30 TA (Ph.D. student, Room #36-415) 2290-0921,
More informationMirrors and Lenses. Images can be formed by reflection from mirrors. Images can be formed by refraction through lenses.
Mirrors and Lenses Images can be formed by reflection from mirrors. Images can be formed by refraction through lenses. Notation for Mirrors and Lenses The object distance is the distance from the object
More informationIntorduction to light sources, pinhole cameras, and lenses
Intorduction to light sources, pinhole cameras, and lenses Erik G. Learned-Miller Department of Computer Science University of Massachusetts, Amherst Amherst, MA 01003 October 26, 2011 Abstract 1 1 Analyzing
More informationINTRODUCTION 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 informationCameras. CSE 455, Winter 2010 January 25, 2010
Cameras CSE 455, Winter 2010 January 25, 2010 Announcements New Lecturer! Neel Joshi, Ph.D. Post-Doctoral Researcher Microsoft Research neel@cs Project 1b (seam carving) was due on Friday the 22 nd Project
More informationObservational Astronomy
Observational Astronomy Instruments The telescope- instruments combination forms a tightly coupled system: Telescope = collecting photons and forming an image Instruments = registering and analyzing the
More informationCS 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 informationChapter 18 Optical Elements
Chapter 18 Optical Elements GOALS When you have mastered the content of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms and use it in an operational
More informationLecture 2: Geometrical Optics. Geometrical Approximation. Lenses. Mirrors. Optical Systems. Images and Pupils. Aberrations.
Lecture 2: Geometrical Optics Outline 1 Geometrical Approximation 2 Lenses 3 Mirrors 4 Optical Systems 5 Images and Pupils 6 Aberrations Christoph U. Keller, Leiden Observatory, keller@strw.leidenuniv.nl
More informationUnit 1: Image Formation
Unit 1: Image Formation 1. Geometry 2. Optics 3. Photometry 4. Sensor Readings Szeliski 2.1-2.3 & 6.3.5 1 Physical parameters of image formation Geometric Type of projection Camera pose Optical Sensor
More informationLENSES. INEL 6088 Computer Vision
LENSES INEL 6088 Computer Vision Digital camera A digital camera replaces film with a sensor array Each cell in the array is a Charge Coupled Device light-sensitive diode that converts photons to electrons
More informationLecture 2: Geometrical Optics. Geometrical Approximation. Lenses. Mirrors. Optical Systems. Images and Pupils. Aberrations.
Lecture 2: Geometrical Optics Outline 1 Geometrical Approximation 2 Lenses 3 Mirrors 4 Optical Systems 5 Images and Pupils 6 Aberrations Christoph U. Keller, Leiden Observatory, keller@strw.leidenuniv.nl
More informationVision 1. Physical Properties of Light. Overview of Topics. Light, Optics, & The Eye Chaudhuri, Chapter 8
Vision 1 Light, Optics, & The Eye Chaudhuri, Chapter 8 1 1 Overview of Topics Physical Properties of Light Physical properties of light Interaction of light with objects Anatomy of the eye 2 3 Light A
More informationWaves & Oscillations
Physics 42200 Waves & Oscillations Lecture 33 Geometric Optics Spring 2013 Semester Matthew Jones Aberrations We have continued to make approximations: Paraxial rays Spherical lenses Index of refraction
More informationDr F. Cuzzolin 1. September 29, 2015
P00407 Principles of Computer Vision 1 1 Department of Computing and Communication Technologies Oxford Brookes University, UK September 29, 2015 September 29, 2015 1 / 73 Outline of the Lecture 1 2 Basics
More informationComputer Vision. The Pinhole Camera Model
Computer Vision The Pinhole Camera Model Filippo Bergamasco (filippo.bergamasco@unive.it) http://www.dais.unive.it/~bergamasco DAIS, Ca Foscari University of Venice Academic year 2017/2018 Imaging device
More informationThe Camera : Computational Photography Alexei Efros, CMU, Fall 2008
The Camera 15-463: Computational Photography Alexei Efros, CMU, Fall 2008 How do we see the world? object film Let s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable
More informationGEOMETRICAL OPTICS AND OPTICAL DESIGN
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
More informationLOS 1 LASER OPTICS SET
LOS 1 LASER OPTICS SET Contents 1 Introduction 3 2 Light interference 5 2.1 Light interference on a thin glass plate 6 2.2 Michelson s interferometer 7 3 Light diffraction 13 3.1 Light diffraction on a
More informationThe Nature of Light. Light and Energy
The Nature of Light Light and Energy - dependent on energy from the sun, directly and indirectly - solar energy intimately associated with existence of life -light absorption: dissipate as heat emitted
More informationCPSC 425: Computer Vision
1 / 55 CPSC 425: Computer Vision Instructor: Fred Tung ftung@cs.ubc.ca Department of Computer Science University of British Columbia Lecture Notes 2015/2016 Term 2 2 / 55 Menu January 7, 2016 Topics: Image
More informationChapter 17: Wave Optics. What is Light? The Models of Light 1/11/13
Chapter 17: Wave Optics Key Terms Wave model Ray model Diffraction Refraction Fringe spacing Diffraction grating Thin-film interference What is Light? Light is the chameleon of the physical world. Under
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. t(x, y) = exp[ jk o ]exp[ jk(n 1) (x, y) ] Find the thickness function for left half of the lens
More informationDiffraction. Interference with more than 2 beams. Diffraction gratings. Diffraction by an aperture. Diffraction of a laser beam
Diffraction Interference with more than 2 beams 3, 4, 5 beams Large number of beams Diffraction gratings Equation Uses Diffraction by an aperture Huygen s principle again, Fresnel zones, Arago s spot Qualitative
More informationName. 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 informationImage 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 informationLecture 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 informationUNIT 12 LIGHT and OPTICS
UNIT 12 LIGHT and OPTICS What is light? Light is simply a name for a range of electromagnetic radiation that can be detected by the human eye. What characteristic does light have? Light is electromagnetic
More informationThe electric field for the wave sketched in Fig. 3-1 can be written as
ELECTROMAGNETIC WAVES Light consists of an electric field and a magnetic field that oscillate at very high rates, of the order of 10 14 Hz. These fields travel in wavelike fashion at very high speeds.
More informationECEN 4606, UNDERGRADUATE OPTICS LAB
ECEN 4606, UNDERGRADUATE OPTICS LAB Lab 2: Imaging 1 the Telescope Original Version: Prof. McLeod SUMMARY: In this lab you will become familiar with the use of one or more lenses to create images of distant
More informationImage Formation and Capture. Acknowledgment: some figures by B. Curless, E. Hecht, W.J. Smith, B.K.P. Horn, and A. Theuwissen
Image Formation and Capture Acknowledgment: some figures by B. Curless, E. Hecht, W.J. Smith, B.K.P. Horn, and A. Theuwissen Image Formation and Capture Real world Optics Sensor Devices Sources of Error
More informationFundamentals of Radio Interferometry
Fundamentals of Radio Interferometry Rick Perley, NRAO/Socorro Fourteenth NRAO Synthesis Imaging Summer School Socorro, NM Topics Why Interferometry? The Single Dish as an interferometer The Basic Interferometer
More informationReflectors 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 informationImage Formation. Dr. Gerhard Roth. COMP 4102A Winter 2015 Version 3
Image Formation Dr. Gerhard Roth COMP 4102A Winter 2015 Version 3 1 Image Formation Two type of images Intensity image encodes light intensities (passive sensor) Range (depth) image encodes shape and distance
More informationBe aware that there is no universal notation for the various quantities.
Fourier Optics v2.4 Ray tracing is limited in its ability to describe optics because it ignores the wave properties of light. Diffraction is needed to explain image spatial resolution and contrast and
More informationAS Physics Unit 5 - Waves 1
AS Physics Unit 5 - Waves 1 WHAT IS WAVE MOTION? The wave motion is a means of transferring energy from one point to another without the transfer of any matter between the points. Waves may be classified
More informationTangents. The f-stops here. Shedding some light on the f-number. by Marcus R. Hatch and David E. Stoltzmann
Tangents Shedding some light on the f-number The f-stops here by Marcus R. Hatch and David E. Stoltzmann The f-number has peen around for nearly a century now, and it is certainly one of the fundamental
More informationTwo strategies for realistic rendering capture real world data synthesize from bottom up
Recap from Wednesday Two strategies for realistic rendering capture real world data synthesize from bottom up Both have existed for 500 years. Both are successful. Attempts to take the best of both world
More informationR.B.V.R.R. WOMEN S COLLEGE (AUTONOMOUS) Narayanaguda, Hyderabad.
R.B.V.R.R. WOMEN S COLLEGE (AUTONOMOUS) Narayanaguda, Hyderabad. DEPARTMENT OF PHYSICS QUESTION BANK FOR SEMESTER III PAPER III OPTICS UNIT I: 1. MATRIX METHODS IN PARAXIAL OPTICS 2. ABERATIONS UNIT II
More information25 cm. 60 cm. 50 cm. 40 cm.
Geometrical Optics 7. The image formed by a plane mirror is: (a) Real. (b) Virtual. (c) Erect and of equal size. (d) Laterally inverted. (e) B, c, and d. (f) A, b and c. 8. A real image is that: (a) Which
More informationChapter 36: diffraction
Chapter 36: diffraction Fresnel and Fraunhofer diffraction Diffraction from a single slit Intensity in the single slit pattern Multiple slits The Diffraction grating X-ray diffraction Circular apertures
More informationSUBJECT: 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 informationOverview. Pinhole camera model Projective geometry Vanishing points and lines Projection matrix Cameras with Lenses Color Digital image
Camera & Color Overview Pinhole camera model Projective geometry Vanishing points and lines Projection matrix Cameras with Lenses Color Digital image Book: Hartley 6.1, Szeliski 2.1.5, 2.2, 2.3 The trip
More informationProjection. Announcements. Müller-Lyer Illusion. Image formation. Readings Nalwa 2.1
Announcements Mailing list (you should have received messages) Project 1 additional test sequences online Projection Readings Nalwa 2.1 Müller-Lyer Illusion Image formation object film by Pravin Bhat http://www.michaelbach.de/ot/sze_muelue/index.html
More informationPHYS 202 OUTLINE FOR PART III LIGHT & OPTICS
PHYS 202 OUTLINE FOR PART III LIGHT & OPTICS Electromagnetic Waves A. Electromagnetic waves S-23,24 1. speed of waves = 1/( o o ) ½ = 3 x 10 8 m/s = c 2. waves and frequency: the spectrum (a) radio red
More informationExperiment 1: Fraunhofer Diffraction of Light by a Single Slit
Experiment 1: Fraunhofer Diffraction of Light by a Single Slit Purpose 1. To understand the theory of Fraunhofer diffraction of light at a single slit and at a circular aperture; 2. To learn how to measure
More informationIMAGE 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 informationExam 4. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: Exam 4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Mirages are a result of which physical phenomena a. interference c. reflection
More informationProjection. Readings. Szeliski 2.1. Wednesday, October 23, 13
Projection Readings Szeliski 2.1 Projection Readings Szeliski 2.1 Müller-Lyer Illusion by Pravin Bhat Müller-Lyer Illusion by Pravin Bhat http://www.michaelbach.de/ot/sze_muelue/index.html Müller-Lyer
More informationThe Camera : Computational Photography Alexei Efros, CMU, Fall 2005
The Camera 15-463: Computational Photography Alexei Efros, CMU, Fall 2005 How do we see the world? object film Let s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable
More informationEE119 Introduction to Optical Engineering Spring 2003 Final Exam. Name:
EE119 Introduction to Optical Engineering Spring 2003 Final Exam Name: SID: CLOSED BOOK. THREE 8 1/2 X 11 SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR PERMITTED. TIME ALLOTTED: 180 MINUTES Fundamental
More informationLlIGHT REVIEW PART 2 DOWNLOAD, PRINT and submit for 100 points
WRITE ON SCANTRON WITH NUMBER 2 PENCIL DO NOT WRITE ON THIS TEST LlIGHT REVIEW PART 2 DOWNLOAD, PRINT and submit for 100 points Multiple Choice Identify the choice that best completes the statement or
More informationImage Formation and Camera Design
Image Formation and Camera Design Spring 2003 CMSC 426 Jan Neumann 2/20/03 Light is all around us! From London & Upton, Photography Conventional camera design... Ken Kay, 1969 in Light & Film, TimeLife
More informationWill contain image distance after raytrace Will contain image height after raytrace
Name: LASR 51 Final Exam May 29, 2002 Answer all questions. Module numbers are for guidance, some material is from class handouts. Exam ends at 8:20 pm. Ynu Raytracing The first questions refer to the
More informationApplications of Optics
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 26 Applications of Optics Marilyn Akins, PhD Broome Community College Applications of Optics Many devices are based on the principles of optics
More information,, Last First Initial UNIVERSITY OF CALIFORNIA AT BERKELEY DEPARTMENT OF PHYSICS PHYSICS 7C FALL SEMESTER 2008 LEROY T. KERTH
1 Solutions Name (please print),, Last First Initial Student Number UNIVERSITY OF CALIFORNIA AT BERKELEY DEPARTMENT OF PHYSICS PHYSICS 7C FALL SEMESTER 2008 LEROY T. KERTH First Midterm Examination October
More informationWarren J. Smith Chief Scientist, Consultant Rockwell Collins Optronics Carlsbad, California
Modern Optical Engineering The Design of Optical Systems Warren J. Smith Chief Scientist, Consultant Rockwell Collins Optronics Carlsbad, California Fourth Edition Me Graw Hill New York Chicago San Francisco
More informationEE119 Introduction to Optical Engineering Spring 2002 Final Exam. Name:
EE119 Introduction to Optical Engineering Spring 2002 Final Exam Name: SID: CLOSED BOOK. FOUR 8 1/2 X 11 SHEETS OF NOTES, AND SCIENTIFIC POCKET CALCULATOR PERMITTED. TIME ALLOTTED: 180 MINUTES Fundamental
More informationOptical System Design
Phys 531 Lecture 12 14 October 2004 Optical System Design Last time: Surveyed examples of optical systems Today, discuss system design Lens design = course of its own (not taught by me!) Try to give some
More informationLaser Telemetric System (Metrology)
Laser Telemetric System (Metrology) Laser telemetric system is a non-contact gauge that measures with a collimated laser beam (Refer Fig. 10.26). It measure at the rate of 150 scans per second. It basically
More informationPHYS 241 FINAL EXAM December 11, 2006
1. (5 points) Light of wavelength λ is normally incident on a diffraction grating, G. On the screen S, the central line is at P and the first order line is at Q, as shown. The distance between adjacent
More informationPerformance Factors. Technical Assistance. Fundamental Optics
Performance Factors After paraxial formulas have been used to select values for component focal length(s) and diameter(s), the final step is to select actual lenses. As in any engineering problem, this
More informationChapter Wave Optics. MockTime.com. Ans: (d)
Chapter Wave Optics Q1. Which one of the following phenomena is not explained by Huygen s construction of wave front? [1988] (a) Refraction Reflection Diffraction Origin of spectra Q2. Which of the following
More informationECEN. Spectroscopy. Lab 8. copy. constituents HOMEWORK PR. Figure. 1. Layout of. of the
ECEN 4606 Lab 8 Spectroscopy SUMMARY: ROBLEM 1: Pedrotti 3 12-10. In this lab, you will design, build and test an optical spectrum analyzer and use it for both absorption and emission spectroscopy. The
More informationLight sources can be natural or artificial (man-made)
Light The Sun is our major source of light Light sources can be natural or artificial (man-made) People and insects do not see the same type of light - people see visible light - insects see ultraviolet
More informationCameras, lenses and sensors
Cameras, lenses and sensors Marc Pollefeys COMP 256 Cameras, lenses and sensors Camera Models Pinhole Perspective Projection Affine Projection Camera with Lenses Sensing The Human Eye Reading: Chapter.
More informationEE-527: MicroFabrication
EE-57: MicroFabrication Exposure and Imaging Photons white light Hg arc lamp filtered Hg arc lamp excimer laser x-rays from synchrotron Electrons Ions Exposure Sources focused electron beam direct write
More informationImage Formation: Camera Model
Image Formation: Camera Model Ruigang Yang COMP 684 Fall 2005, CS684-IBMR Outline Camera Models Pinhole Perspective Projection Affine Projection Camera with Lenses Digital Image Formation The Human Eye
More informationAbsorption: in an OF, the loss of Optical power, resulting from conversion of that power into heat.
Absorption: in an OF, the loss of Optical power, resulting from conversion of that power into heat. Scattering: The changes in direction of light confined within an OF, occurring due to imperfection in
More informationCh 24. Geometric Optics
text concept Ch 24. Geometric Optics Fig. 24 3 A point source of light P and its image P, in a plane mirror. Angle of incidence =angle of reflection. text. Fig. 24 4 The blue dashed line through object
More informationPhysics 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 informationExp No.(8) Fourier optics Optical filtering
Exp No.(8) Fourier optics Optical filtering Fig. 1a: Experimental set-up for Fourier optics (4f set-up). Related topics: Fourier transforms, lenses, Fraunhofer diffraction, index of refraction, Huygens
More informationProjection. Projection. Image formation. Müller-Lyer Illusion. Readings. Readings. Let s design a camera. Szeliski 2.1. Szeliski 2.
Projection Projection Readings Szeliski 2.1 Readings Szeliski 2.1 Müller-Lyer Illusion Image formation object film by Pravin Bhat http://www.michaelbach.de/ot/sze_muelue/index.html Let s design a camera
More informationTransmission electron Microscopy
Transmission electron Microscopy Image formation of a concave lens in geometrical optics Some basic features of the transmission electron microscope (TEM) can be understood from by analogy with the operation
More informationCameras, lenses, and sensors
Cameras, lenses, and sensors Reading: Chapter 1, Forsyth & Ponce Optional: Section 2.1, 2.3, Horn. 6.801/6.866 Profs. Bill Freeman and Trevor Darrell Sept. 10, 2002 Today s lecture How many people would
More informationChapter 23. Mirrors and Lenses
Chapter 23 Mirrors and Lenses Notation for Mirrors and Lenses The object distance is the distance from the object to the mirror or lens Denoted by p The image distance is the distance from the image to
More informationPhysics 431 Final Exam Examples (3:00-5:00 pm 12/16/2009) TIME ALLOTTED: 120 MINUTES Name: Signature:
Physics 431 Final Exam Examples (3:00-5:00 pm 12/16/2009) TIME ALLOTTED: 120 MINUTES Name: PID: Signature: CLOSED BOOK. TWO 8 1/2 X 11 SHEET OF NOTES (double sided is allowed), AND SCIENTIFIC POCKET CALCULATOR
More informationELEC Dr Reji Mathew Electrical Engineering UNSW
ELEC 4622 Dr Reji Mathew Electrical Engineering UNSW Filter Design Circularly symmetric 2-D low-pass filter Pass-band radial frequency: ω p Stop-band radial frequency: ω s 1 δ p Pass-band tolerances: δ
More information12:40-2:40 3:00-4:00 PM
Physics 294H l Professor: Joey Huston l email:huston@msu.edu l office: BPS3230 l Homework will be with Mastering Physics (and an average of 1 hand-written problem per week) Help-room hours: 12:40-2:40
More informationReflection! Reflection and Virtual Image!
1/30/14 Reflection - wave hits non-absorptive surface surface of a smooth water pool - incident vs. reflected wave law of reflection - concept for all electromagnetic waves - wave theory: reflected back
More informationLight: Reflection and Refraction Light Reflection of Light by Plane Mirror Reflection of Light by Spherical Mirror Formation of Image by Mirror Sign Convention & Mirror Formula Refraction of light Through
More informationNotes from Lens Lecture with Graham Reed
Notes from Lens Lecture with Graham Reed Light is refracted when in travels between different substances, air to glass for example. Light of different wave lengths are refracted by different amounts. Wave
More informationLithography. 3 rd. lecture: introduction. Prof. Yosi Shacham-Diamand. Fall 2004
Lithography 3 rd lecture: introduction Prof. Yosi Shacham-Diamand Fall 2004 1 List of content Fundamental principles Characteristics parameters Exposure systems 2 Fundamental principles Aerial Image Exposure
More informationThe diffraction of light
7 The diffraction of light 7.1 Introduction As introduced in Chapter 6, the reciprocal lattice is the basis upon which the geometry of X-ray and electron diffraction patterns can be most easily understood
More informationCriteria for Optical Systems: Optical Path Difference How do we determine the quality of a lens system? Several criteria used in optical design
Criteria for Optical Systems: Optical Path Difference How do we determine the quality of a lens system? Several criteria used in optical design Computer Aided Design Several CAD tools use Ray Tracing (see
More informationPhys 531 Lecture 9 30 September 2004 Ray Optics II. + 1 s i. = 1 f
Phys 531 Lecture 9 30 September 2004 Ray Optics II Last time, developed idea of ray optics approximation to wave theory Introduced paraxial approximation: rays with θ 1 Will continue to use Started disussing
More informationLecture 3: Geometrical Optics 1. Spherical Waves. From Waves to Rays. Lenses. Chromatic Aberrations. Mirrors. Outline
Lecture 3: Geometrical Optics 1 Outline 1 Spherical Waves 2 From Waves to Rays 3 Lenses 4 Chromatic Aberrations 5 Mirrors Christoph U. Keller, Leiden Observatory, keller@strw.leidenuniv.nl Lecture 3: Geometrical
More informationGIST OF THE UNIT BASED ON DIFFERENT CONCEPTS IN THE UNIT (BRIEFLY AS POINT WISE). RAY OPTICS
209 GIST OF THE UNIT BASED ON DIFFERENT CONCEPTS IN THE UNIT (BRIEFLY AS POINT WISE). RAY OPTICS Reflection of light: - The bouncing of light back into the same medium from a surface is called reflection
More informationElectromagnetic Spectrum
Electromagnetic Spectrum The electromagnetic radiation covers a vast spectrum of frequencies and wavelengths. This includes the very energetic gamma-rays radiation with a wavelength range from 0.005 1.4
More informationMirrors, Lenses &Imaging Systems
Mirrors, Lenses &Imaging Systems We describe the path of light as straight-line rays And light rays from a very distant point arrive parallel 145 Phys 24.1 Mirrors Standing away from a plane mirror shows
More informationCameras. Steve Rotenberg CSE168: Rendering Algorithms UCSD, Spring 2017
Cameras Steve Rotenberg CSE168: Rendering Algorithms UCSD, Spring 2017 Camera Focus Camera Focus So far, we have been simulating pinhole cameras with perfect focus Often times, we want to simulate more
More informationIntroduction 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 informationBuilding a Real Camera. Slides Credit: Svetlana Lazebnik
Building a Real Camera Slides Credit: Svetlana Lazebnik Home-made pinhole camera Slide by A. Efros http://www.debevec.org/pinhole/ Shrinking the aperture Why not make the aperture as small as possible?
More informationChapter 16 Light Waves and Color
Chapter 16 Light Waves and Color Lecture PowerPoint Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. What causes color? What causes reflection? What causes color?
More information