1. CPSC 641 Computer Graphics: Radiometry and Illumination Jinxiang Chai Many slides from Pat Haranhan

2. Light modeling

7. Outline Radiometry and photometry - Radiant intensity - Irradiance - Radiance - Radiant exitance (radiosity) Illumination calculations - Irradiance from environment

8. Radiometry and Photometry

9. Radiometry The goal of a global illumination algorithm is to compute a steady-state distribution of light in a scene To compute this distribution, we need an understanding of the physical quantities that represent light energy Radiometry is the basic terminology used to describe light

10. Photons The basic quantity in lighting is the photon The energy (in Joule) of a photon with wavelength λ is: q λ = hc/λ - c is the speed of light In vacuum, c = 299.792.458m/s - h ≈ 6.63*10 -34 Js is Planck’s constant

11. (Spectral) Radiant Energy The spectral radiant energy, Q λ, in n λ photons with wavelength λ is The radiant energy, Q, is the energy of a collection of photons, and is given as the integral of Q λ over all possible wavelengths:

12. Radiant Energy and Power Power: Watts vs. Lumens - Energy efficiency - Spectral efficacy Energy: Joules vs. Talbot - Exposure - Film response - Skin sunburn Luminance

13. Radiometry vs. Photometry Radiometry [Units = Watts] - Physical measurement of electromagnetic energy Photometry and Colorimetry [Lumen] - Sensation as a function of wavelength - Relative perceptual measurement Brightness [Brils] - Sensation at different brightness levels - Absolute perceptual measurement - Obeys Steven’s Power Law

14. Fluorescent Bulb

15. Sunlight

16. Radiant Intensity

17. Definition: Radiant intensity is the radiant flux radiated from a point on a light source into a unit solid angle in a particular direction. And it is measured in watt per steradian.

18. Angles and Solid Angles Angle Solid angle  circle has 2  radians  sphere has 4  steradians θ l

19. Differential Solid Angles

21. Isotropic Point Source

22. Warn’s Spotlight

24. Goniometric Diagrams

25. Light Source Goniometric Diagrams

26. Radiance

27. Imagine ray of light arriving at or leaving a point on a surface in a given direction. Radiance is simply the infinitesimal amount of radiant flux contained in this ray.

28. Definition: The surface radiance (luminance) is the intensity per unit area leaving a surface. Radiance

29. When the ray is intersecting the surface with an angle θ, the radiance is computed as follows:

30. Radiance Radiance can be leaving, passing through, or arriving at a point on a surface Radiance (arriving)Radiance (leaving)

31. Why do we need radiance? Response of a sensor (camera, human eye) is proportional to radiance Pixel values in image is proportional to radiance received from that direction (not really true).

32. Typical Values of Luminance [cd/m 2 ] Surface of the sun2,000,000,000 nit Sunlight clouds 30,000 Clear day 3,000 Overcast day 300 Moon 0.03

33. Irradiance

34. The Invention of Photometry Bouguer’s classic experiment Compare a light source and a candle Intensity is proportional to ratio of distances squared Definition of a candela Originally a “standard” candle Currently 550 nm laser w/ 1/683 W/sr 1 of 6 fundamental SI units

35. Irradiance Definition: The irradiance (illuminance) is the power per unit area incident on a surface. Sometimes referred to as the radiant (luminous) incidence.

36. Lambert’s Cosine Law A

37. A

38. Irradiance: Isotropic Point Source

44. How to measure the irradiance from the environment?

45. Directional Power Arriving at a Surface

47. Irradiance from the Environment Light meter

48. Typical Values of Illuminance [lm/m 2 ] Sunlight plus skylight100,000 lux Sunlight plus skylight (overcast) 10,000 Interior near window (daylight) 1,000 Artificial light (minimum) 100 Moonlight (full) 0.02 Starlight 0.0003

49. The Sky Radiance Distribution From Greenler, Rainbows, halos and glories

50. Gazing Ball  Environment Maps Miller and Hoffman, 1984 Photograph of mirror ball Maps all spherical directions to a to circle Reflection direction indexed by normal Resolution function of orientation

51. Environment Maps Interface, Chou and Williams (ca. 1985)

52. Irradiance Environment Maps Radiance Environment Map Irradiance Environment Map R N

53. Radiant Exitance (Radiosity)

54. Radiant Exitance Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface. In computer graphics, this quantity is often referred to as the radiosity (B)

55. Directional Power Leaving a Surface

56. Uniform Diffuse Emitter

57. Projected Solid Angle

58. Uniform Diffuse Emitter