Radiometry / Photometry Realistic Rendering Pertinent Questions
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Fundametals of Rendering - Radiometry / Photometry
Fundametals of Rendering - Radiometry / Photometry “Physically Based Rendering” by Pharr & Humphreys •Chapter 5: Color and Radiometry •Chapter 6: Camera Models - we won’t cover this in class 782 Realistic Rendering • Determination of Intensity • Mechanisms – Emittance (+) – Absorption (-) – Scattering (+) (single vs. multiple) • Cameras or retinas record quantity of light 782 Pertinent Questions • Nature of light and how it is: – Measured – Characterized / recorded • (local) reflection of light • (global) spatial distribution of light 782 Electromagnetic spectrum 782 Spectral Power Distributions e.g., Fluorescent Lamps 782 Tristimulus Theory of Color Metamers: SPDs that appear the same visually Color matching functions of standard human observer International Commision on Illumination, or CIE, of 1931 “These color matching functions are the amounts of three standard monochromatic primaries needed to match the monochromatic test primary at the wavelength shown on the horizontal scale.” from Wikipedia “CIE 1931 Color Space” 782 Optics Three views •Geometrical or ray – Traditional graphics – Reflection, refraction – Optical system design •Physical or wave – Dispersion, interference – Interaction of objects of size comparable to wavelength •Quantum or photon optics – Interaction of light with atoms and molecules 782 What Is Light ? • Light - particle model (Newton) – Light travels in straight lines – Light can travel through a vacuum (waves need a medium to travel in) – Quantum amount of energy • Light – wave model (Huygens): electromagnetic radiation: sinusiodal wave formed coupled electric (E) and magnetic (H) fields 782 Nature of Light • Wave-particle duality – Light has some wave properties: frequency, phase, orientation – Light has some quantum particle properties: quantum packets (photons). • Dimensions of light – Amplitude or Intensity – Frequency – Phase – Polarization 782 Nature of Light • Coherence - Refers to frequencies of waves • Laser light waves have uniform frequency • Natural light is incoherent- waves are multiple frequencies, and random in phase. -
Radiosity Radiosity
Radiosity Radiosity Motivation: what is missing in ray-traced images? Indirect illumination effects Color bleeding Soft shadows Radiosity is a physically-based illumination algorithm capable of simulating the above phenomena in a scene made of ideal diffuse surfaces. Books: Cohen and Wallace, Radiosity and Realistic Image Synthesis, Academic Press Professional 1993. Sillion and Puech, Radiosity and Global Illumination, Morgan- Kaufmann, 1994. Indirect illumination effects Radiosity in a Nutshell Break surfaces into many small elements Light source Formulate and solve a linear system of equations that models the equilibrium of inter-reflected Eye light in a scene. Diffuse Reflection The solution gives us the amount of light leaving each point on each surface in the scene. Once solution is computed, the shaded elements can be quickly rendered from any viewpoint. Meshing (partition into elements) Radiosity Input geometry Change geometry Form-Factors Change light or colors Solution Render Change view 1 Radiometric quantities The Radiosity Equation Radiant energy [J] Assume that surfaces in the scene have been discretized into n small elements. Radiant power (flux): radiant energy per second [W] Assume that each element emits/reflects light Irradiance (flux density): incident radiant power per uniformly across its surface. unit area [W/m2] Define the radiosity B as the total hemispherical Radiosity (flux density): outgoing radiant power per flux density (W/m2) leaving a surface. unit area [W/m2] Let’’s write down an expression describing the total flux (light power) leaving element i in the Radiance (angular flux dedensity):nsity): radiant power per scene: unit projected area per unit solid angle [W/(m2 sr)] scene: total flux = emitted flux + reflected flux The Radiosity Equation The Form Factor Total flux leaving element i: Bi Ai The form factor Fji tells us how much of the flux Total flux emitted by element i: Ei Ai leaving element j actually reaches element i. -
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. -
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. -
The Equation of Radiative Transfer How Does the Intensity of Radiation Change in the Presence of Emission and / Or Absorption?
The equation of radiative transfer How does the intensity of radiation change in the presence of emission and / or absorption? Definition of solid angle and steradian Sphere radius r - area of a patch dS on the surface is: dS = rdq ¥ rsinqdf ≡ r2dW q dS dW is the solid angle subtended by the area dS at the center of the † sphere. Unit of solid angle is the steradian. 4p steradians cover whole sphere. ASTR 3730: Fall 2003 Definition of the specific intensity Construct an area dA normal to a light ray, and consider all the rays that pass through dA whose directions lie within a small solid angle dW. Solid angle dW dA The amount of energy passing through dA and into dW in time dt in frequency range dn is: dE = In dAdtdndW Specific intensity of the radiation. † ASTR 3730: Fall 2003 Compare with definition of the flux: specific intensity is very similar except it depends upon direction and frequency as well as location. Units of specific intensity are: erg s-1 cm-2 Hz-1 steradian-1 Same as Fn Another, more intuitive name for the specific intensity is brightness. ASTR 3730: Fall 2003 Simple relation between the flux and the specific intensity: Consider a small area dA, with light rays passing through it at all angles to the normal to the surface n: n o In If q = 90 , then light rays in that direction contribute zero net flux through area dA. q For rays at angle q, foreshortening reduces the effective area by a factor of cos(q). -
Relationships of the SI Derived Units with Special Names and Symbols and the SI Base Units
Relationships of the SI derived units with special names and symbols and the SI base units Derived units SI BASE UNITS without special SI DERIVED UNITS WITH SPECIAL NAMES AND SYMBOLS names Solid lines indicate multiplication, broken lines indicate division kilogram kg newton (kg·m/s2) pascal (N/m2) gray (J/kg) sievert (J/kg) 3 N Pa Gy Sv MASS m FORCE PRESSURE, ABSORBED DOSE VOLUME STRESS DOSE EQUIVALENT meter m 2 m joule (N·m) watt (J/s) becquerel (1/s) hertz (1/s) LENGTH J W Bq Hz AREA ENERGY, WORK, POWER, ACTIVITY FREQUENCY second QUANTITY OF HEAT HEAT FLOW RATE (OF A RADIONUCLIDE) s m/s TIME VELOCITY katal (mol/s) weber (V·s) henry (Wb/A) tesla (Wb/m2) kat Wb H T 2 mole m/s CATALYTIC MAGNETIC INDUCTANCE MAGNETIC mol ACTIVITY FLUX FLUX DENSITY ACCELERATION AMOUNT OF SUBSTANCE coulomb (A·s) volt (W/A) C V ampere A ELECTRIC POTENTIAL, CHARGE ELECTROMOTIVE ELECTRIC CURRENT FORCE degree (K) farad (C/V) ohm (V/A) siemens (1/W) kelvin Celsius °C F W S K CELSIUS CAPACITANCE RESISTANCE CONDUCTANCE THERMODYNAMIC TEMPERATURE TEMPERATURE t/°C = T /K – 273.15 candela 2 steradian radian cd lux (lm/m ) lumen (cd·sr) 2 2 (m/m = 1) lx lm sr (m /m = 1) rad LUMINOUS INTENSITY ILLUMINANCE LUMINOUS SOLID ANGLE PLANE ANGLE FLUX The diagram above shows graphically how the 22 SI derived units with special names and symbols are related to the seven SI base units. In the first column, the symbols of the SI base units are shown in rectangles, with the name of the unit shown toward the upper left of the rectangle and the name of the associated base quantity shown in italic type below the rectangle. -
RADIATION HEAT TRANSFER Radiation
MODULE I RADIATION HEAT TRANSFER Radiation Definition Radiation, energy transfer across a system boundary due to a T, by the mechanism of photon emission or electromagnetic wave emission. Because the mechanism of transmission is photon emission, unlike conduction and convection, there need be no intermediate matter to enable transmission. The significance of this is that radiation will be the only mechanism for heat transfer whenever a vacuum is present. Electromagnetic Phenomena. We are well acquainted with a wide range of electromagnetic phenomena in modern life. These phenomena are sometimes thought of as wave phenomena and are, consequently, often described in terms of electromagnetic wave length, . Examples are given in terms of the wave distribution shown below: m UV X Rays 0.4-0.7 Thermal , ht Radiation Microwave g radiation Visible Li 10-5 10-4 10-3 10-2 10-1 10-0 101 102 103 104 105 Wavelength, , m One aspect of electromagnetic radiation is that the related topics are more closely associated with optics and electronics than with those normally found in mechanical engineering courses. Nevertheless, these are widely encountered topics and the student is familiar with them through every day life experiences. From a viewpoint of previously studied topics students, particularly those with a background in mechanical or chemical engineering, will find the subject of Radiation Heat Transfer a little unusual. The physics background differs fundamentally from that found in the areas of continuum mechanics. Much of the related material is found in courses more closely identified with quantum physics or electrical engineering, i.e. Fields and Waves. -
CHAPTER 2: Radiometric Measurements Principles REFERENCE: Remote Sensing of the Environment John R
CHAPTER 2: Radiometric Measurements Principles REFERENCE: Remote Sensing of the Environment John R. Jensen (2007) Second Edition Pearson Prentice Hall Energy-matter interactions in the atmosphere at the study area and at the remote sensor detector RADIANT ENERGY (Q): is the energy carried by a photon. Unit: Joules (J) RADIANT FLUX (Φ): is the time rate of flow of radiant energy. Unit: watts (W = J s-1) Φ = dQ = Joules = Watts dt seconds A derivative is the instantaneous rate of change of a function. RADIANT INTENSITY (I): Is a measure of the radiant flux proceeding from the source per unit solid angle in a specified direction. Unit: watts steradian-1 I = dΦ = watts dω steradian Solid Angle (ω ó Ω): Is equal to the spherical surface area (A) divided by the square of the radius (r). Unit: steradian Ω = A/r2 Radiance (L) Radiance in certain wavelengths (L)is: -the radiant flux (Φ) -per unit solid angle () -leaving an extended source area L in a given direction () Acos -per unit projected source area (A) Units: watts per meter squared per steradian (W m-2 sr -1 ) L is a function of direction, therefore the zenith and azimuth angles must be considered. The concept of radiance leaving a specific projected source area on the ground, in a specific direction, and within a specific solid angle. FIELD RADIOMETRY Lλ Radiance (L) REFLECTANCE Sample Radiation () R() = __________________ Reference Radiation () x100 = Reflectance Percent REFLECTANCE RADIANCE FLUX DENSITY Irradiance is a measure of the amount of radiant flux incident upon a surface per unit area of the surface measured in watts m-2. -
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. -
Radiometric and Photometric Measurements with TAOS Photosensors Contributed by Todd Bishop March 12, 2007 Valid
TAOS Inc. is now ams AG The technical content of this TAOS application note is still valid. Contact information: Headquarters: ams AG Tobelbaderstrasse 30 8141 Unterpremstaetten, Austria Tel: +43 (0) 3136 500 0 e-Mail: [email protected] Please visit our website at www.ams.com NUMBER 21 INTELLIGENT OPTO SENSOR DESIGNER’S NOTEBOOK Radiometric and Photometric Measurements with TAOS PhotoSensors contributed by Todd Bishop March 12, 2007 valid ABSTRACT Light Sensing applications use two measurement systems; Radiometric and Photometric. Radiometric measurements deal with light as a power level, while Photometric measurements deal with light as it is interpreted by the human eye. Both systems of measurement have units that are parallel to each other, but are useful for different applications. This paper will discuss the differencesstill and how they can be measured. AG RADIOMETRIC QUANTITIES Radiometry is the measurement of electromagnetic energy in the range of wavelengths between ~10nm and ~1mm. These regions are commonly called the ultraviolet, the visible and the infrared. Radiometry deals with light (radiant energy) in terms of optical power. Key quantities from a light detection point of view are radiant energy, radiant flux and irradiance. SI Radiometryams Units Quantity Symbol SI unit Abbr. Notes Radiant energy Q joule contentJ energy radiant energy per Radiant flux Φ watt W unit time watt per power incident on a Irradiance E square meter W·m−2 surface Energy is an SI derived unit measured in joules (J). The recommended symbol for energy is Q. Power (radiant flux) is another SI derived unit. It is the derivative of energy with respect to time, dQ/dt, and the unit is the watt (W). -
Causes of Color Radiometry for Color
Causes of color • The sensation of color is caused • Light could be produced in by the brain. different amounts at different wavelengths (compare the sun and • Some ways to get this sensation a fluorescent light bulb). include: • Light could be differentially – Pressure on the eyelids reflected (e.g. some pigments). – Dreaming, hallucinations, etc. • It could be differentially refracted - • Main way to get it is the (e.g. Newton’s prism) response of the visual system to • Wavelength dependent specular the presence/absence of light at reflection - e.g. shiny copper penny various wavelengths. (actually most metals). • Flourescence - light at invisible wavelengths is absorbed and reemitted at visible wavelengths. Computer Vision - A Modern Approach Set: Color Radiometry for color • All definitions are now “per unit wavelength” • All units are now “per unit wavelength” • All terms are now “spectral” • Radiance becomes spectral radiance – watts per square meter per steradian per unit wavelength • Radiosity --- spectral radiosity Computer Vision - A Modern Approach Set: Color 1 Black body radiators • Construct a hot body with near-zero albedo (black body) – Easiest way to do this is to build a hollow metal object with a tiny hole in it, and look at the hole. • The spectral power distribution of light leaving this object is a simple function of temperature Ê 1 ˆ Ê 1 ˆ E(l) µ 5 Á ˜ Ë l ¯ Ë exp(hc klT )-1¯ • This leads to the notion of color temperature --- the temperature of a black body that would look the same Computer Vision - A Modern Approach Set: Color Measurements of relative spectral power of sunlight, made by J. -
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).