Light Field = Radiance(Ray)

Total Page:16

File Type:pdf, Size:1020Kb

Light Field = Radiance(Ray) The Light Field Light field = radiance function on rays Surface and field radiance Conservation of radiance Measurement Irradiance from area sources Measuring rays Form factors and throughput Conservation of throughput From London and Upton CS348B Lecture 5 Pat Hanrahan, 2004 Light Field = Radiance(Ray) Page 1 Incident Surface Radiance Definition: The incoming surface radiance (luminance) is the power per unit solid angle per unit projected area arriving at a receiving surface dω dA dx2Φ (,ω ) Lx(,ω )≡ i i ddAωi CS348B Lecture 5 Pat Hanrahan, 2004 Exitant Surface Radiance Definition: The outgoing surface radiance (luminance) is the power per unit solid angle per unit projected area leaving at surface dω dA dx2Φ (,ω ) Lx(,ω )≡ o o ddAωi Alternatively: the intensity per unit projected area leaving a surface CS348B Lecture 5 Pat Hanrahan, 2004 Page 2 Field Radiance Definition: The field radiance (luminance) at a point in space in a given direction is the power per unit solid angle per unit area perpendicular to the direction dω dA Lx(,ω ) CS348B Lecture 5 Pat Hanrahan, 2004 Environment Maps L(,θ ϕ ) Miller and Hoffman, 1984 CS348B Lecture 5 Pat Hanrahan, 2004 Page 3 Spherical Gantry ⇒ Light Field Lxy(,,,θ ϕ ) (,θ ϕ ) Capture all the light leaving an object - like a hologram CS348B Lecture 5 Pat Hanrahan, 2004 Two-Plane Light Field 2D Array of Cameras 2D Array of Images L(,,,)uvst CS348B Lecture 5 Pat Hanrahan, 2004 Page 4 Multi-Camera Array ⇒ Light Field CS348B Lecture 5 Pat Hanrahan, 2004 Properties of Radiance Page 5 Properties of Radiance 1. Fundamental field quantity that characterizes the distribution of light in an environment. ∴ Radiance is a function on rays ∴ All other field quantities are derived from it 2. Radiance invariant along a ray. ∴ 5D ray space reduces to 4D 3. Response of a sensor proportional to radiance. CS348B Lecture 5 Pat Hanrahan, 2004 1st Law: Conversation of Radiance The radiance in the direction of a light ray remains constant as the ray propagates 2 2 22 d Φ1 d Φ2 ddΦ12=Φ dA1 dω1 2 L1 dLddAΦ=1111ω dω2 dA2 2 L2 dLddAΦ=2222ω r dA dA ddAωω==12 ddA 11r 2 2 2 ∴L12= L CS348B Lecture 5 Pat Hanrahan, 2004 Page 6 Radiance: 2nd Law The response of a sensor is proportional to the radiance of the surface visible to the sensor. Ω Aperture A Sensor RLddALT==∫∫ ω TddA= ∫∫ ω A Ω A Ω L is what should be computed and displayed. T quantifies the gathering power of the device. CS348B Lecture 5 Pat Hanrahan, 2004 Quiz Does the brightness that a wall appears to the sensor depend on the distance? No!! CS348B Lecture 5 Pat Hanrahan, 2004 Page 7 Irradiance from a Uniform Surface Source Irradiance from the Environment 2 dxΦ=ii(,ω ) Lx (,ωθ )cos dAd ω Lxi (,ω ) dE( x ,ω )= Li ( x ,ωθω )cos d dω θ dA E()xLxd= (,ω )cosθω ∫ i H2 CS348B Lecture 5 Pat Hanrahan, 2004 Page 8 Irradiance from an Area Source A E()xLd= ∫ cosθ ω H2 Ω = Ld∫cosθ ω Ω =ΩL Ω CS348B Lecture 5 Pat Hanrahan, 2004 Projected Solid Angle dω θ cosθ dω ∫ cosθ dωπ= H2 CS348B Lecture 5 Pat Hanrahan, 2004 Page 9 Uniform Disk Source Geometric Derivation Algebraic Derivation cosαπ 2 r Ω= ∫∫cosθφdd cosθ 10 cosα α cos2 θ = 2π 2 h 1 = παsin2 sinα r 2 = π rh22+ Ω= π sin2 α CS348B Lecture 5 Pat Hanrahan, 2004 Spherical Source Geometric Derivation Algebraic Derivation r Ω= ∫ cosθ dω R = π sin2 α α r 2 = π R2 Ω= π sin2 α CS348B Lecture 5 Pat Hanrahan, 2004 Page 10 The Sun Solar constant (normal incidence at zenith) Irradiance 1353 W/m2 Illuminance 127,500 lm/m2 = 127.5 kilolux Solar angle α = .25 degrees = .004 radians (half angle) 22 Ω= π sin απα ≈ = 6 x 10-5 steradians Solar radiance EWm1.353× 1032 / W L == =2.25 × 107 Ω× 610−52sr m ⋅ sr CS348B Lecture 5 Pat Hanrahan, 2004 Polygonal Source CS348B Lecture 5 Pat Hanrahan, 2004 Page 11 Polygonal Source CS348B Lecture 5 Pat Hanrahan, 2004 Polygonal Source CS348B Lecture 5 Pat Hanrahan, 2004 Page 12 Lambert’s Formula γ iiN γ i 3 Ai ∑ A1 i=1 −A2 −A3 nn Aiii=•γ NN ∑∑Aiii= γ NN• ii==11 CS348B Lecture 5 Pat Hanrahan, 2004 Penumbras and Umbras CS348B Lecture 5 Pat Hanrahan, 2004 Page 13 Measuring Rays = Throughput Throughput Counts Rays Define an infinitesimal beam as the set of rays intersecting two infinitesimal surface elements ru(,,112 v u , v 2 ) dA111(,) u v dA222(,) u v 2 dA12 dA dT= 2 x12− x Measure the number of rays in the beam This quantity is called the throughput CS348B Lecture 5 Pat Hanrahan, 2004 Page 14 Parameterizing Rays Parameterize rays wrt to receiver ru(,,,)2222 v θ φ dω222(,)θφ dA222(,) u v 2 dA1 dT==2 dA222 dω dA xx12− CS348B Lecture 5 Pat Hanrahan, 2004 Parameterizing Rays Parameterize rays wrt to source ru(,,,)1111 v θ φ dA111(,) u v dω111(,)θφ 2 dA2 d T== dA1112 dA dω xx12− CS348B Lecture 5 Pat Hanrahan, 2004 Page 15 Parameterizing Rays Tilting the surfaces reparameterizes the rays ru(,, v u , v ) 112 2 dA111(,) u v dA222(,) u v 2 cosθθ12 cos d T= 2 dA12 dA xx12− = ddAω11i = ddAω22i All these throughputs must be equal. CS348B Lecture 5 Pat Hanrahan, 2004 Parameterizing Rays: S2 × R2 Parameterize rays by rxy(,,,)θ φ ω Projected area A()ω Measuring the number or rays that hit a shape Td= ∫∫ωθϕ(, ) dAxy (,) SR22 = Ad(,θϕ ) ωθϕ (, ) Sphere: ∫ 22 S2 TA==44ππ R = 4π A CS348B Lecture 5 Pat Hanrahan, 2004 Page 16 Parameterizing Rays: M2 × S2 Parameterize rays by ruv(,,θφ , ) (,)θφ (,)uv TdAuv= (,) cosθ dωθϕ (, ) ∫∫ MH22 ()N N S π 22 Sphere: TS==ππ4 R S Crofton’s Theorem: 4ππASA= ⇒= 4 CS348B Lecture 5 Pat Hanrahan, 2004 Form Factors Page 17 Types of Throughput 1. Infinitesimal beam of rays cosθ cosθ′ d2 T(, dA dA′′ )≡ dA ()() x dA x xx− ′ 2 2. Infinitesimal-finite beam cosθθ cos ′ dT(,) dA A′′ dA≡ dA () x dA () x ∫ 2 A′ xx− ′ 3. Finite-finite beam cosθ cosθ′ TAA(,′′ )≡ dAxdAx () () ∫∫ 2 AA′ xx− ′ CS348B Lecture 5 Pat Hanrahan, 2004 Probability of Ray Intersection Probability of a ray hitting A’ given it hits A TAA(,)′ Pr(AA′ | ) = TA() A′ TAA(,)′ = ′ πA dA() x cosθ cosθ′ TAA(,)′′= dAxdAx () () ∫∫ 2 AA′ xx− ′ A TA()=π A dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Page 18 Probability of Ray Intersection cosθ cosθ′ TAA(,)′′= dAxdAx () () ∫∫ 2 AA′ xx− ′ =π Gxx(,)()()′′ dAx dAx A′ ∫∫ AA′ dA() x′ cosθθ cos ′ Gxx(,′ )≡ 2 Vxx (,′ ) π xx− ′ 0 ¬visible A Vxx(,′ )= 1 visible dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Form Factor Probability of a ray hitting A’ given it hits A Pr(A′′′′ |ATA ) ( )== Pr( AA | ) TA ( ) TAA ( , ) A′ Form factor definition FAA(,)Pr(|)′′= A A dA() x′ FAA(,′′ )= Pr(| AA ) Form factor reciprocity FAAA(,)′′′= FAAA (,) A TA()=π A dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Page 19 Form Factor Power transfer from a constant source Φ=(,AA′′ ) LTAA (, ) TAA(,′ ) = LT() A′ A′ TA()′ dA() x′ =Φ()(,)A′′FAA A TA()=π A dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Differential Form Factor Probability of a ray leaving dA(x) hitting A’ TdAAdA(,)′ TdAAdA (,)′′ TdAA (,) Pr(AdA′ | ) === TdA() ππ dA = ∫Gxx(,′′ ) dAx ( ) A′ A′ dA() x′ dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Page 20 Form Factor Power transfer from a constant source ddAALTdAAΦ=(,)′′ (,) TdAA(,)′ = LT() A′ A′ TA()′ dA() x′ =Φ()(,)A′′FdAA A dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Radiant Exitance Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface. dΦ Mx()≡ o dA Wlm = lux mm22 In computer graphics, this quantity is often referred to as the radiosity (B) CS348B Lecture 5 Pat Hanrahan, 2004 Page 21 Uniform Diffuse Emitter M = Ldcosθ ω ∫ o H2 Lo(,x ω ) = L cosθ dω o ∫ H2 dω = πLo θ M L = o π dA CS348B Lecture 5 Pat Hanrahan, 2004 Form Factor Irradiance from a constant source ddAAΦ=Φ(,)′′ ()(,) AFdAA ′ Φ()A′ = A′FdAA(,)′ A′ A′ = M()(, A′′ F A dA ) dA dA() x′ EdA()= MA ()(,)′′ FAdA A dA() x CS348B Lecture 5 Pat Hanrahan, 2004 Page 22 Form Factors and Throughput Throughput measures the number of rays in a set of rays Form factors represent the probability of ray leaving a surface intersecting another surface Only a function of surface geometry Differential form factor Irradiance calculations Form factors Radiosity calculations (energy balance) CS348B Lecture 5 Pat Hanrahan, 2004 Conservation of Throughput Throughput conserved during propagation Number of rays conserved Assuming no attenuation or scattering n2 (index of refraction) times throughput invariant under the laws of geometric optics Reflection at an interface Refraction at an interface Causes rays to bend (kink) Continuously varying index of refraction Causes rays to curve; mirages CS348B Lecture 5 Pat Hanrahan, 2004 Page 23 Conservation of Radiance Radiance is the ratio of two quantities: 1. Power 2. Throughput ∆Φ∆()Td Φ Lr()== lim ∆→T 0 ∆TdT Since power and throughput are conserved, ∴ Radiance conserved CS348B Lecture 5 Pat Hanrahan, 2004 Quiz Does radiance increase under a magnifying glass? No!! CS348B Lecture 5 Pat Hanrahan, 2004 Page 24.
Recommended publications
  • Black Body Radiation and Radiometric Parameters
    Black Body Radiation and Radiometric Parameters: All materials absorb and emit radiation to some extent. A blackbody is an idealization of how materials emit and absorb radiation. It can be used as a reference for real source properties. An ideal blackbody absorbs all incident radiation and does not reflect. This is true at all wavelengths and angles of incidence. Thermodynamic principals dictates that the BB must also radiate at all ’s and angles. The basic properties of a BB can be summarized as: 1. Perfect absorber/emitter at all ’s and angles of emission/incidence. Cavity BB 2. The total radiant energy emitted is only a function of the BB temperature. 3. Emits the maximum possible radiant energy from a body at a given temperature. 4. The BB radiation field does not depend on the shape of the cavity. The radiation field must be homogeneous and isotropic. T If the radiation going from a BB of one shape to another (both at the same T) were different it would cause a cooling or heating of one or the other cavity. This would violate the 1st Law of Thermodynamics. T T A B Radiometric Parameters: 1. Solid Angle dA d r 2 where dA is the surface area of a segment of a sphere surrounding a point. r d A r is the distance from the point on the source to the sphere. The solid angle looks like a cone with a spherical cap. z r d r r sind y r sin x An element of area of a sphere 2 dA rsin d d Therefore dd sin d The full solid angle surrounding a point source is: 2 dd sind 00 2cos 0 4 Or integrating to other angles < : 21cos The unit of solid angle is steradian.
    [Show full text]
  • Guide for the Use of the International System of Units (SI)
    Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S.
    [Show full text]
  • RADIANCE® ULTRA 27” Premium Endoscopy Visualization
    EW NNEW RADIANCE® ULTRA 27” Premium Endoscopy Visualization The Radiance® Ultra series leads the industry as a revolutionary display with the aim to transform advanced visualization technology capabilities and features into a clinical solution that supports the drive to improve patient outcomes, improve Optimized for endoscopy applications workflow efficiency, and lower operating costs. Advanced imaging capabilities Enhanced endoscopic visualization is accomplished with an LED backlight technology High brightness and color calibrated that produces the brightest typical luminance level to enable deep abdominal Cleanable splash-proof design illumination, overcoming glare and reflection in high ambient light environments. Medi-Match™ color calibration assures consistent image quality and accurate color 10-year scratch-resistant-glass guarantee reproduction. The result is outstanding endoscopic video image performance. ZeroWire® embedded receiver optional With a focus to improve workflow efficiency and workplace safety, the Radiance Ultra series is available with an optional built-in ZeroWire receiver. When paired with the ZeroWire Mobile battery-powered stand, the combination becomes the world’s first and only truly cordless and wireless mobile endoscopic solution (patent pending). To eliminate display scratches caused by IV poles or surgical light heads, the Radiance Ultra series uses scratch-resistant, splash-proof edge-to-edge glass that includes an industry-exclusive 10-year scratch-resistance guarantee. RADIANCE® ULTRA 27” Premium Endoscopy
    [Show full text]
  • The International System of Units (SI)
    NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303.
    [Show full text]
  • Ikonos DN Value Conversion to Planetary Reflectance Values by David Fleming CRESS Project, UMCP Geography April 2001
    Ikonos DN Value Conversion to Planetary Reflectance Values By David Fleming CRESS Project, UMCP Geography April 2001 This paper was produced by the CRESS Project at the University of Maryland. CRESS is sponsored by the Earth Science Enterprise Applications Directorate at NASA Stennis Space Center. The following formula from the Landsat 7 Science Data Users Handbook was used to convert Ikonos DN values to planetary reflectance values: ρp = planetary reflectance Lλ = spectral radiance at sensor’s aperture 2 ρp = π * Lλ * d ESUNλ = band dependent mean solar exoatmospheric irradiance ESUNλ * cos(θs) θs = solar zenith angle d = earth-sun distance, in astronomical units For Landsat 7, the spectral radiance Lλ = gain * DN + offset, which can also be expressed as Lλ = (LMAX – LMIN)/255 *DN + LMIN. The LMAX and LMIN values for each of the Landsat bands are given below in Table 1. These values may vary for each scene and the metadata contains image specific values. Table 1. ETM+ Spectral Radiance Range (W/m2 * sr * µm) Low Gain High Gain Band Number LMIN LMAX LMIN LMAX 1 -6.2 293.7 -6.2 191.6 2 -6.4 300.9 -6.4 196.5 3 -5.0 234.4 -5.0 152.9 4 -5.1 241.1 -5.1 157.4 5 -1.0 47.57 -1.0 31.06 6 0.0 17.04 3.2 12.65 7 -0.35 16.54 -0.35 10.80 8 -4.7 243.1 -4.7 158.3 (from Landsat 7 Science Data Users Handbook) The Ikonos spectral radiance, Lλ, can be calculated by using the formula given in the Space Imaging Document Number SE-REF-016: 2 Lλ (mW/cm * sr) = DN / CalCoefλ However, in order to use these values in the conversion formula, the values must be in units of 2 W/m * sr * µm.
    [Show full text]
  • Radiometry of Light Emitting Diodes Table of Contents
    TECHNICAL GUIDE THE RADIOMETRY OF LIGHT EMITTING DIODES TABLE OF CONTENTS 1.0 Introduction . .1 2.0 What is an LED? . .1 2.1 Device Physics and Package Design . .1 2.2 Electrical Properties . .3 2.2.1 Operation at Constant Current . .3 2.2.2 Modulated or Multiplexed Operation . .3 2.2.3 Single-Shot Operation . .3 3.0 Optical Characteristics of LEDs . .3 3.1 Spectral Properties of Light Emitting Diodes . .3 3.2 Comparison of Photometers and Spectroradiometers . .5 3.3 Color and Dominant Wavelength . .6 3.4 Influence of Temperature on Radiation . .6 4.0 Radiometric and Photopic Measurements . .7 4.1 Luminous and Radiant Intensity . .7 4.2 CIE 127 . .9 4.3 Spatial Distribution Characteristics . .10 4.4 Luminous Flux and Radiant Flux . .11 5.0 Terminology . .12 5.1 Radiometric Quantities . .12 5.2 Photometric Quantities . .12 6.0 References . .13 1.0 INTRODUCTION Almost everyone is familiar with light-emitting diodes (LEDs) from their use as indicator lights and numeric displays on consumer electronic devices. The low output and lack of color options of LEDs limited the technology to these uses for some time. New LED materials and improved production processes have produced bright LEDs in colors throughout the visible spectrum, including white light. With efficacies greater than incandescent (and approaching that of fluorescent lamps) along with their durability, small size, and light weight, LEDs are finding their way into many new applications within the lighting community. These new applications have placed increasingly stringent demands on the optical characterization of LEDs, which serves as the fundamental baseline for product quality and product design.
    [Show full text]
  • Lighting - the Radiance Equation
    CHAPTER 3 Lighting - the Radiance Equation Lighting The Fundamental Problem for Computer Graphics So far we have a scene composed of geometric objects. In computing terms this would be a data structure representing a collection of objects. Each object, for example, might be itself a collection of polygons. Each polygon is sequence of points on a plane. The ‘real world’, however, is ‘one that generates energy’. Our scene so far is truly a phantom one, since it simply is a description of a set of forms with no substance. Energy must be generated: the scene must be lit; albeit, lit with virtual light. Computer graphics is concerned with the construction of virtual models of scenes. This is a relatively straightforward problem to solve. In comparison, the problem of lighting scenes is the major and central conceptual and practical problem of com- puter graphics. The problem is one of simulating lighting in scenes, in such a way that the computation does not take forever. Also the resulting 2D projected images should look as if they are real. In fact, let’s make the problem even more interesting and challenging: we do not just want the computation to be fast, we want it in real time. Image frames, in other words, virtual photographs taken within the scene must be produced fast enough to keep up with the changing gaze (head and eye moves) of Lighting - the Radiance Equation 35 Great Events of the Twentieth Century35 Lighting - the Radiance Equation people looking and moving around the scene - so that they experience the same vis- ual sensations as if they were moving through a corresponding real scene.
    [Show full text]
  • Radiometry and Photometry
    Radiometry and Photometry Wei-Chih Wang Department of Power Mechanical Engineering National TsingHua University W. Wang Materials Covered • Radiometry - Radiant Flux - Radiant Intensity - Irradiance - Radiance • Photometry - luminous Flux - luminous Intensity - Illuminance - luminance Conversion from radiometric and photometric W. Wang Radiometry Radiometry is the detection and measurement of light waves in the optical portion of the electromagnetic spectrum which is further divided into ultraviolet, visible, and infrared light. Example of a typical radiometer 3 W. Wang Photometry All light measurement is considered radiometry with photometry being a special subset of radiometry weighted for a typical human eye response. Example of a typical photometer 4 W. Wang Human Eyes Figure shows a schematic illustration of the human eye (Encyclopedia Britannica, 1994). The inside of the eyeball is clad by the retina, which is the light-sensitive part of the eye. The illustration also shows the fovea, a cone-rich central region of the retina which affords the high acuteness of central vision. Figure also shows the cell structure of the retina including the light-sensitive rod cells and cone cells. Also shown are the ganglion cells and nerve fibers that transmit the visual information to the brain. Rod cells are more abundant and more light sensitive than cone cells. Rods are 5 sensitive over the entire visible spectrum. W. Wang There are three types of cone cells, namely cone cells sensitive in the red, green, and blue spectral range. The approximate spectral sensitivity functions of the rods and three types or cones are shown in the figure above 6 W. Wang Eye sensitivity function The conversion between radiometric and photometric units is provided by the luminous efficiency function or eye sensitivity function, V(λ).
    [Show full text]
  • Basic Principles of Imaging and Photometry Lecture #2
    Basic Principles of Imaging and Photometry Lecture #2 Thanks to Shree Nayar, Ravi Ramamoorthi, Pat Hanrahan Computer Vision: Building Machines that See Lighting Camera Physical Models Computer Scene Scene Interpretation We need to understand the Geometric and Radiometric relations between the scene and its image. A Brief History of Images 1558 Camera Obscura, Gemma Frisius, 1558 A Brief History of Images 1558 1568 Lens Based Camera Obscura, 1568 A Brief History of Images 1558 1568 1837 Still Life, Louis Jaques Mande Daguerre, 1837 A Brief History of Images 1558 1568 1837 Silicon Image Detector, 1970 1970 A Brief History of Images 1558 1568 1837 Digital Cameras 1970 1995 Geometric Optics and Image Formation TOPICS TO BE COVERED : 1) Pinhole and Perspective Projection 2) Image Formation using Lenses 3) Lens related issues Pinhole and the Perspective Projection Is an image being formed (x,y) on the screen? YES! But, not a “clear” one. screen scene image plane r =(x, y, z) y optical effective focal length, f’ z axis pinhole x r'=(x', y', f ') r' r x' x y' y = = = f ' z f ' z f ' z Magnification A(x, y, z) B y d B(x +δx, y +δy, z) optical f’ z A axis Pinhole A’ d’ x planar scene image plane B’ A'(x', y', f ') B'(x'+δx', y'+δy', f ') From perspective projection: Magnification: x' x y' y d' (δx')2 + (δy')2 f ' = = m = = = f ' z f ' z d (δx)2 + (δy)2 z x'+δx' x +δx y'+δy' y +δy = = Area f ' z f ' z image = m2 Areascene Orthographic Projection Magnification: x' = m x y' = m y When m = 1, we have orthographic projection r =(x, y, z) r'=(x', y', f ') y optical z axis x z ∆ image plane z This is possible only when z >> ∆z In other words, the range of scene depths is assumed to be much smaller than the average scene depth.
    [Show full text]
  • LAND SURFACE EMISSIVITY Long-Wave Infrared (LWIR)
    L LAND SURFACE EMISSIVITY Long-wave infrared (LWIR). For most terrestrial surfaces (340 K to 240 K), peak thermal emittance occurs in the LWIR (8–14 mm). Alan Gillespie Mid-infrared (MIR). Forest fires (1,000–600 K) have Department of Earth and Space Sciences, University peak thermal emittances in the MIR (3–5 mm). of Washington, Seattle, WA, USA Noise equivalent D temperature (NEDT). Random mea- surement error in radiance propagated through Planck’s law to give the equivalent uncertainty in temperature. Definitions Path radiance S↑. The power per unit area incident on Land surface emissivity (LSE). Average emissivity of a detector and emitted upward from within the atmosphere À À an element of the surface of the Earth calculated (W m 2 sr 1). from measured radiance and land surface temperature Planck’s law. A mathematical expression relating spectral (LST) (for a complete definition, see Norman and Becker, radiance emitted from an ideal surface to its temperature 1995). (Equation 1, in the entry Land Surface Temperature). Atmospheric window. A spectral wavelength region in Radiance. The power per unit area from a surface directed À À which the atmosphere is nearly transparent, separated by toward a sensor, in units of W m 2 sr 1. wavelengths at which atmospheric gases absorb radiation. Reflectivity r. The efficiency with which a surface reflects The three pertinent regions are “visible/near-infrared” energy incident on it. (0.4–2.5 mm), mid-wave infrared (3–5 mm) and Reststrahlen bands. Spectral bands in which there is long-wave infrared (8–14 mm).
    [Show full text]
  • Radiant Flux Density
    Schedule 08/31/17 (Lecture #1) • 12 lectures 09/05/17 (Lecture #2) • 3 long labs (8 hours each) 09/07/17 (Lecture #3) • 2-3 homework 09/12/17 (4:00 – 18:30 h) (Lecture #4-5) • 1 group project 09/14/17 (Lecture #6): radiation • 4 Q&A (Geography Room 206) 09/21/17 (Lecture #7): radiation lab • Dr. Dave Reed on CRBasics with 09/26/17 (4:00 – 18:30 h) (Lecture #8-9) CR5000 datalogger 09/28/17 (Lecture #10) 10/03/17 (12:00 – 8:00 h) (Lab #1) 10/10/17 (12:00 – 8:00 h) (Lab #2) 10/20/17 (8:00 -17:00 h) (Lab #3) 10/24/17 (Q&A #1) 10/26/17 (Lecture #11) 11/07/17 (Q&A #2) 11/14/17 (Q&A #3) 11/21/17 (Q&A #4) 12/07/17 (Lecture #12): Term paper due on Dec. 14, 2017 Radiation (Ch 10 & 11; Campbell & Norman 1998) • Rt, Rl, Rn, Rin, Rout, PAR, albedo, turbidity • Greenhouse effect, Lambert’s Cosine Law • Sensors: Pyranometer, K&Z CNR4, Q7, PAR, etc. • Demonstration of solar positions • Programming with LogerNet Review of Radiation Solar constant: 1.34-1.36 kW.m-2, with about 2% fluctuations Sun spots: in pairs, ~11 yrs frequency, and from a few days to several months duration Little ice age (1645-1715) Greenhouse effects (atmosphere as a selective filter) Low absorptivity between 8-13 m Clouds Elevated CO2 Destroy of O3 O3 also absorb UV and X-ray Global radiation budget Related terms: cloudiness turbidity (visibility), and albedo Lambert’s Cosine Law Other Considerations Zenith distance (angle) Other terms Solar noon: over the meridian of observation Equinox: the sun passes directly over the equator Solstice Solar declination Path of the Earth around the sun 147*106 km 152*106 km Radiation Balance Model R R Rt e r Rs Rtr Solar declination (D): an angular distance north (+) or south (-) of the celestial equator of place of the earth’s equator.
    [Show full text]
  • Radiance Products
    PRODUCT DATA RADIANCE™ e-0.25 Attic Barrier Low-e attic barrier for the underside of roof decks Description Features Benefits Radiance™ e-0.25 Attic Barrier is • Low emissivity with 0.21 “e” value Reduces cooling costs in summer formulated to be sprayed on the • Reflects up to 79% of radiant energy Increases interior comfort level underside of the roof deck. When • 100% seamless coverage of attic space More cost efficient than alternative attic systems applied it creates an effective radiant barrier that will stop up to 79% of the • Does not alter electromagnetic fields Will not disrupt attic-mounted antennae or cell potential radiant energy transfer into phone reception the attic. • Breathable Will not increase attic moisture The physics behind Radiance™ • One coat coverage on bare wood and Fast application e-0.25 Attic Barrier is similiar to low-e primed metal glass windows, which reduce the • Application by spray, roller and brush Easy to apply absorption of heat into a building in the summer. The “e” refers to emissivity, which is the ability of a surface to emit or absorb radiant Shelf Life How to Apply energy. The lower the “e” value, the more efficient it is in managing energy Parts A and B: 12 months when properly stored WOOD SURFACES and the greater the energy savings for Storage 1. Apply to a clean, dust-free, dry surface. No need the dwelling. Parts A and B: Store in original containers in a clean, to prime. dry area between 40 and 90° F (4 and 32° C). Keep METAL SURFACES away from direct sunlight.
    [Show full text]