Light Field = Radiance(Ray)

Transcription

1 The Light Field Concepts Light field = radiance function on rays Conservation of radiance Throughput and counting rays Measurement equation Irradiance calculations From London and Upton Light Field = Radiance(Ray) Page 1

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 Radiance is the quantity associated with a ray Gazing Ball = Environment Maps Miller and Hoffman, 1984 Photograph of mirror ball Reflection direction indexed by normal Image is the radiance in the reflected dir. Page 2

3 The Sky Radiance Distribution From Greenler, Rainbows, halos and glories CS348B Lecture 5 Pat Hanrahan, Spring 2010 Spherical Gantry 4D Light Field Capture all the light leaving an object - like a hologram CS348B Lecture 5 Pat Hanrahan, Spring 2010 Page 3

4 Multi-Camera Array Light Field CS348B Lecture 5 Pat Hanrahan, Spring 2010 Two-Plane Light Field 2D Array of Images 2D Array of Cameras CS348B Lecture 5 Pat Hanrahan, Spring 2010 Page 4

5 Properties of Radiance 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. Page 5

6 1st Law: Conservation of Radiance The radiance in the direction of a light ray remains constant as the ray propagates Quiz Does radiance increase under a magnifying glass? No!! Page 6

7 Measuring Rays = Throughput Throughput Counts Rays Define an infinitesimal beam as the set of rays intersecting two infinitesimal surface elements The differential throughput measures size of the beam: Page 7

8 Parameterizing Rays Parameterize rays wrt to receiver Parameterizing Rays Parameterize rays wrt to source Page 8

9 Parameterizing Rays Tilting the surfaces reparameterizes the rays! Parameterizing Rays: S 2 R 2 Parameterize rays by Projected area Measuring the number or rays that hit a shape Sphere: Page 9

10 Parameterizing Rays: M 2 S 2 Parameterize rays by Sphere: Crofton s Theorem: The Measurement Equation Page 10

11 Radiance: 2nd Law The response of a sensor is proportional to the radiance of the surface visible to the sensor. Aperture Sensor L is what should be computed and displayed. T quantifies the gathering power of the device; the higher the throughput the greater the amount of light gathered Quiz Does the brightness that a wall appears to the sensor depend on the distance? No!! Page 11

12 Irradiance Directional Power Arriving at a Surface CS348B Lecture 4 Pat Hanrahan, 2007 Page 12

13 Irradiance from the Environment Light meter CS348B Lecture 4 Pat Hanrahan, 2007 Irradiance Map or Light Map Isolux contours CS348B Lecture 4 Pat Hanrahan, 2007 Page 13

14 Irradiance Environment Maps N I L(N R ) E(N I ) for N I E(N I ) = 0 N R for R in H 2 (N I ) Compute N R that generates direction R E(N I ) += L(N R ) cos(θ) Δω CS348B Lecture 4 Pat Hanrahan, 2007 Uniform Area Source Page 14

15 Uniform Disk Source Geometric Derivation Algebraic Derivation Spherical Source Geometric Derivation Algebraic Derivation Page 15

16 The Sun Solar constant (normal incidence at zenith) Irradiance 1353 W/m 2 Illuminance 127,500 lm/m 2 = kilolux Solar angle =.25 degrees =.004 radians (half angle) = 6 x 10-5 steradians Solar radiance Polygonal Source Page 16

17 Polygonal Source Polygonal Source Page 17

18 Consider 1 Edge Area of sector Lambert s Formula Page 18

19 Penumbras and Umbras Page 19