Radiometry and Photometry

Transcription

1 Radiometry and Photometry Measuring spatial properties of light Radiant power Radiant intensity Irradiance Inverse square law and cosine law Radiance Radiant exitance (radiosity) From London and Upton Goal is to perform lighting calculations in the physically correct way

2 Radiant Energy and Power Power: Watts (radiometry) Φ vs. Lumens (photometry) Spectral efficacy Energy efficiency P o w e r Heat Radio Infra- Red Ultra- Violet X-Rays IR R G B UV Gamma R a y s Cosmic R a y s Wavelength (NM) Energy: Joules vs. Talbot Exposure Film response Skin - sunburn Photometric luminance Y = V( λ) L( λ) dλ

3 Radiant Intensity

4 Radiant Intensity Definition: The radiant (luminous) intensity is the power per unit solid angle emanating from a point source. I( ω) dφ dω! W "! lm " # = cd = candela % sr $ & # % sr $ &

5 Angles and Solid Angles Angle l = r circle has 2 π radians Solid angle Ω = A R sphere has 4 π steradians 2

6 Differential Solid Angles r sin dφ r d da = ( r d )( r sin dφ ) = r 2 sin d dφ φ

7 Differential Solid Angles r sin dφ r d da = ( r d )( r sin dφ ) = r 2 sin d dφ φ dω da = = sin d dφ 2 r

8 Differential Solid Angles r sin dω = sin d dφ dφ φ r d Ω = = = S 2 π 2π π 1 0 = 4π dω sin d dφ d cos dφ

9 Isotropic Point Source Sphere 2 S Φ = S 2 = 4π I I dω I = Φ 4π

10 Warn s Spotlight ω! Â! I ( ω) = cos s = ( ω Aˆ ) s

11 Warn s Spotlight ω! Â! I ( ω) = cos s = ( ω Aˆ ) s 2π 1 Φ = 0 0 I( ω) d cos dϕ

12 Warn s Spotlight ω! Â! I ( ω) = cos s = ( ω Aˆ ) s 2π 1 1 s 2π Φ = I( ω) d cos dϕ = 2π cos d cos = s

13 Warn s Spotlight ω! Â! I ( ω) = cos s = ( ω Aˆ ) s 2π 1 1 s 2π Φ = I( ω) d cos dϕ = 2π cos d cos = s s + 1 I( ω) = Φ cos 2π s

14 Light Source Goniometric Diagrams

15 Irradiance

16 Irradiance Definition: The irradiance (illuminance) is the power per unit area incident on a surface. dφ E( x) i da! W "! lm " # = 2 2 lux % m $ & # % m $ & Sometimes referred to as the radiant (luminous) incidence.

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

18 Beam Power in Terms of Irradiance E = Φ A

19 Beam Power Falling on the Surface

20 Projected Area A

21 Lambert s Cosine Law A

22 Irradiance: Isotropic Point Source h I = Φ 4π r

23 Irradiance: Isotropic Point Source dω h I = Φ 4π r da dφ = I dω

24 Irradiance: Isotropic Point Source dω h I = Φ 4π r da dω = cos r 2 da

25 Irradiance: Isotropic Point Source dω h I = Φ 4π r da I dω = Φ 4π cos r 2 da

26 Irradiance: Isotropic Point Source dω h I = Φ 4π r da Φ cos I dω = da = E da 4π r 2 E = Φ 4π cos r 2

27 The Invention of Photometry Bouguer s classic experiment Compare a light source and a candle Move until they both appear equally bright Intensity is proportional to ratio of distances squared Definition of a candela Originally a standard candle Currently 550 nm laser with 1/683 W/sr 1 of 6 fundamental SI units

28 Radiance

29 Area Lights Surface Radiance Definition: The surface radiance (luminance) is the intensity per unit area leaving a surface L( x, ω) dω L( x, ω) = di( x, ω) da d 2 Φ( x, ω) dωda da! W "! cd lm " # $ # = = nit $ % sr m & % m sr m &

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

31 Directional Power Leaving a Surface 2 d Φ ( x, ω) = L ( x, ω)cosdadω o o L (, o x ω dω ) da Same da for all directions

32 Radiant Exitance (Radiosity)

33 Radiant Exitance Definition: The radiant (luminous) exitance is the energy per unit area leaving a surface. dφ M( x) o da! W "! lm " = lux # m 2 $ # m 2 $ % & % & In computer graphics, this quantity is usually referred to as the radiosity (B)

34 Area Light Source 2 d Φ ( x, ω) = L ( x, ω)cosdadω o o dω L (, o x ω ) da

35 Area Light Source 2 d Φ ( x, ω) dm ( x, ω) = o = L ( x, ω)cos dω o da dω L (, o x ω ) da

36 Area Light Source dm ( x, ω) = L ( x, ω)cos dω o dω L (, o x ω ) da

37 Area Light Source M = dm ( x, ω) = L ( x, ω)cos dω o H 2 2 H dω L (, o x ω ) H 2 Hemisphere da

38 Uniform Diffuse Emitter M = L cos dω H 2 o L ( x, ω ) = L o o = L o H 2 cos dω dω Uniform means Lo is not a function of direction da

39 Projected Solid Angle Ω! cos dω Ω dω cos dω

40 Projected Solid Angle Ω! cos dω Ω dω cos dω Ω! = cos dω = H 2 π

41 Uniform Diffuse Emitter M = L cos dω H 2 o = = L o πl H o 2 cos dω M dω L o L o = M π da

42 Radiometry and Photometry Summary

43 Radiometric and Photometric Terms Physics Radiometry Photometry Energy Radiant Energy Luminous Energy Flux (Power) Radiant Power Luminous Power Flux Density Irradiance Radiosity Illuminance Luminosity Angular Flux Density Radiance Luminance Intensity Radiant Intensity Luminous Intensity

44 Photometric Units Photometry Units MKS CGS British Luminous Energy Luminous Power Illuminance Talbot Lumen Lux Phot Footcandle Luminosity Luminance Nit Stilb Apostilb, Blondel Lambert Footlambert Luminous Intensity Candela (Candle, Candlepower, Carcel, Hefner) Thus one nit is one lux per steradian is one candela per square meter is one lumen per square meter per steradian. Got it?, James Kajiya