Radiometry, photometry, measuring color

Transcription

1 Radiometry, photometry, measuring color Lecture notes are done by Géza Várady, based on the lecture notes of Prof. János Schanda University of Pécs, Faculty of Engineering and Information Technology, Dept. of IT

2 Radiometry, photometry, measuring color Radiometry deals with optical radiation, in terms of physical radiation Photometry deals with the amount of radiation, that is sensed by the human eye, thus, weighted with the spectral sensitivity (what does a number mean? - communication) Color measuring tries to give objective quantities equvivalent to perception of colours

3 Electromagnetic radiaton Optical radiation: electromagnetic radiation with the wavelengths between 100 nm 1 mm Visible radiation: 380 nm 780 nm Light: perception caused by visible radiation

4 Electromagnetic spectum X-ray ultraviolet visible Infrared Microwaves Radiowaves radiation

5 Radiometric quantities P d P point-like radiator radiates in directions ε,φ (epsilon, gamma) d (dω - omega) solid angle: The quotient of the area of the cut of piece of the sphere by the conical beam and the square of the radius of the sphere: d=da/r 2 Different definition: the apparent area of an object viewed from a given point. The closer little and far away big objects seem the same. (square law). Unit: steradian (sr) (Ray tracing, 3D)

6 Radiometric quantities P point-like radiators efficiency (power) can be wavelengthdependent. The wavelength dependency (or function) of a given X quantity is signed by λ: X(λ) X(lambda). The distribution in the next picture is the derivative function by the wavelength, thus, it s integral gives the unit itself (the area under the curve).

7 Spectrum-dependent quantities Relative intensity Wavelength dependency: X() Filter throughput Spectral distribution: wavelength dx/d X Eg. CRT monitor phosphors spectral distribution

8 Radiometric quantities Name Symbol Unit radiant energy Q joule, 1 J 1 kgm 2 s -2 radiant flux (power) (phi) or F watt (Js -1 ) irradiance E Wm -2 radiant intensity I Wsr -1 radiance L Wm -2 sr -1

9 Radiometric quantities relations Radiant flux (power) Power distribution, F watt (Js -1 ) d/d Wm -1 Radiated energy Q joule, Q Φ dt 1 J 1 kgm 2 s -2 irradiance E d /da E Wm -2 Radiant intensity I d /d I Wsr -1 radiance L d 2 /(ddacos) L Wm -2 sr -1

10 Irradiance ~= the quotient of the (incoming radiant flux on a given area of the surface) and (the area of the surface) E d /da d da

11 Radiant intensity, point-like source ~ is understood only for point-like sources: the radiant flux radiated into unit solid angle toward a given direction d I P d I d /d

12 n d A Radiance L d Def.: The radiant flux d radiated into d unit solid angle, in direction of angle from n (the normal of the da surface element) L d 2 /(ddacos), Spectral radiance: L dl /d = d 3 /(ddacosd)

13 Inverse square law d Id (I d /d ) d da 2 /d2 (steradian definition!) d /da 2 E 2 = d d A 2 (Id)/dA 2 = (IdA 2 )/(da 2 d 2 ) P d d = E 2 I / d 2 (irradiance = radiant intensity/ d 2 )

14 Lambert radiator Radiance is direction-independent: L() const.; L(,) const. L d n d P d A

15 Mirroring and diffuse reflection Incoming radiance Diffuse reflection Mirroring reflection

16 Lambert (reflection) surface Equally diffuse reflecting surface No mirroring reflection Reflection coefficient: = refl / in refl = in cos The reflected radiance is directionindependent: L refl ( )= const.

17 Lambert reflector Irradiance: E Reflected radiance, directionindependen: incoming beam normal of surface reflected beam Radiance vector L E reflecting surface

18 Photometry Our vision reacts for optical radiation according to it s spectral sensitivity Visual basic experiment: brightness matching Colorfull test source Comparison source

19 Flicker photometry It s hard to match brightness between different colors At a given frequency (10 20 Hz domain) color information disappears and only intensity information (brightness) is perceived (color info. is slow, intensity info. is fast).

20 Flicker photometer Circle sector Comparison source mirror motor Half-pass mirror monochromator Observers eye shutter Test source Radiation measurement

21 Visibility functions By flicker photometry: International Comission on Illumination (Comission Internationale d Éclairage, CIE) standardized in 1924 the V( ) function (daylight, photopic vision) In 1954 the V ( ) function (dark, scotopic vision)

22 Visibility functions 1 0,9 relative sensitvity 0,8 0,7 0,6 0,5 0,4 0,3 V'( ) V( ) 0,2 0, w avelength, nm

23 Experimental basics of photometry symmetry: if AB, then BA; transitivity: if AB and BC, then AC; proportionality: if AB, then AαB; additivity: if AB, CD and (A+C)(B+D), then (A+D)(B+C) where A, B, etc.. are stimuli: the multiplication of radiance and the visibility function at given wavelength: eg. AL V(), generalized we can write the spectral distribution of radiance: S V().

24 Basics of photometry According to the above, we can summarize the monochromatic components: S V( ) 780nm V k ) e, V( 380nm d This gives the connection of radiometry and photometry. In this example: luminous flux radiant flux. (ɸ v, ɸ e )

25 Basics of photometry Daytime (photopic) vision: V(), cones work Nighttime (scotopic) vision: V (), rodvision; uses rhodopsin only low-light, additivity and proporcionality holds: 780nm ' ' e, v k 380nm V' ( ) d

26 Photometric quantities and units k and k are constants: 780 nm K e, ( ) V( ) v m 380 nm d Where K m = 683 lm/w and we can define the unit of luminous flux: lumen. The unit of luminous intensity is the candela. (K m = 1700 lm/w) Luminous flux: lm, unit: lumen.

27 Photometric quantities and units Luminous intensity: quotient of the luminous flux starting from a point-like source toward a given direction at an infinitesimal (very small) solid angle and the solid angle: I v d d v symbol: cd, unit: candela, 1 cd = 1 lm/sr

28 Definition of candela The unit of luminous intensity in SI, one of the base units. Roughly speaking, it is used to express how bright a beam of light is. Symbol, cd. (it used to be 1 candle) The luminous intensity, in a given direction, of a [light] source that emits monochromatic radiation of frequency hertz and that has a radiant intensity in that direction of watt per steradian (w/sr).

29 Luminous flux [lm] from lumious intensity 1 m lightingdefinitions.html = 1 sr 2 1 m 1 cd luminous intensity point-like source

30 Luminance (light level) Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted or reflected from a particular area, and falls within a given solid angle. d 2 d L v 2 d v dda cos 1 1 da 1 unit: cd/m 2, symbol: L v

31 Illuminance the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelengthweighted by the luminosity function to correlate with human brightness perception E d v / da unit: lux, symbol: lx; 1 lx = 1 lm/m 2 2

32 Contrast, contrast ratio contrast: where L t is the targets luminance L b is the backgrounds luminance contrast ratio: c c v L t L L L t b b L b

33 Efficiency, Efficacy Radiant efficieny, symbol: e (eta) the quotient of the radiated and absorbed power of the radiator Luminous efficacy, unit: lm/w the quotient of the output luminous flux and the absorbed power of the radiator (what we really see as well)

34 Luminous efficacy of sources Type of lightsource Lum. Efficacy (lm/w) Incandescent lamp 14,4 (2%) Halogene lamp 17 (2,5%) Compact fluorescent lamp High-pressure metalhalid lmap (MH) 85 (10%) 90 (11%) High-pressure Na lamp 116 (17%) Low-pressure Na lamp (orange light) 206 (30%) LED 4,5 300 (0,6 44 %)

35 Mesopic photometry IT jobs: CAD lab, traffic control, etc.. Road lightning 3 cd/m cd/m 2 luinance levels Our eyes spectral sensitivity goes from V( ) to V ( )

36 Scotopic, mesopic and photopic regions lg( cd/m ) szkotopos mezopos fotopos

37 Visibility functions 1 0,9 relative sensitivity 0,8 0,7 0,6 0,5 0,4 0,3 V'( ) V( ) 0,2 0, w avelength, nm

38 Change of lum. efficacy L, lamp: cd/m 2 Na cd/m 2 Hg (Natrium) (Mercury) Photopic: 0,05 0,05 Mezopic: 0,028 0,061 Scotopic: 0,01 0,07 Difference between luminance perception and detail perception!

39 Measuring color Color perception in our brains Quantitative description: color stimulus, that initiates perception Colour-matching Colur-stimuli: additive color mixing : monitor subtractive color mixing: color film, printer

40 Grassmanns laws 1. Every color stimuli can be created as the additive mixture of three, independent color stimuli. Independency means, that no stimuli can be mixed by the two others. 2. For color matching, only the three basic color stimuli count, the spectral distribution does not. 3. By changing one component stimulus continiously, the resultant stimuli will change continiously

41 Basic experiment of the additive colour-matching Comparison lightsource Intensity control Test lightsource

42 Additive color-match The followings hold Distributivity, (A+B)*C = AC + BC, Additivity, f(a+b) = f(a) + f(b) Proportionality, Comparison stimuli: red: 700 nm green: 546 nm blue: 435 nm

43 colour matching functions rgb color match fn. 0,40 0,35 0,30 0,25 G( ) R( ) 0,20 B( ) 0,15 0,10 0,05 0,00-0, ,10-0,15 wavelength, nm r( ), g( ), b ( )

44 Tristimulus-values R k S r ( ) d G k S g( ) d B k S b ( ) d

45 CIE 1931 color stimulus system

46 CIE XYZ trirtimulus values (color stimulus components), self-luminaires (lightsources) X k S x( ) d; Y k S y( ) d; Z k S z( ) d ( x( ), y( ), z( )) Color matching functions The y function is the V( ) function, if k=683 lm/w

47 Color stimulus or hue coordinates x X X Y Z y X Y Y Z

48 Color stimulus or hue coordinates 0,9 0,8 0,7 0,6 0,5 520 nm 510 nm 500 nm 540 nm G 560 nm 580 nm R, G, B: cathod ray tube basic stimuli (yellow) y 0,4 0,3 0, K 7000 K K 2000 K 600 nm R 650 nm Planck radiator line (magenta) 0, nm B 450 nm 400 nm 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 x

49 CIE Chromaticity diagram

50 Color measurement of secondary radiators (not self-luminous) d x S k X ) ( ) ( ) ( d y S k Y ) ( ) ( ) ( d z S k Z ) ( ) ( ) ( d 1 ) ( ) S( y k where S( ) illuminants spectral power distribution ( ) spectral reflection of surface

51 Color Temperature The color temperature (CT) is the temperature that the ideal black-body radiator (Planck radiator) is at, with comparable hue to that of the lightsource CT is only meaningful for that sources, that are somewaht close to a black-body radiator Black-body radiaton (Flash simulator):

52 Correlated Color Temperature The correlated color temperature (CCT) is the temperature that the ideal blackbody radiator (Planck radiator) is at, with comparable hue to that of the lightsource which lightsources x,y coordinates are the closest to the planckian locust

53 Standard spectral distributions and lightsources CIE A illuminant (incandescent light) CIE B illuminant (Daylight, 4874K) CIE C illuminant (Daylight, 6774 K) CIE D series of illuminant (Daylight with different K, eg. D 65 Daylight, 6500K

54 Standard spectral distributions and lightsources

55 Standard spectral distributions and lightsources

56 Standard spectral distributions and lightsources CIE A (incandescent lamp CCT-2856K) CIE B (direct sunlight at noon -- CCT 4874K) CIE C (cloudy day -- CCT 6774K)

57 CIE A- and D65 spectral power distribution wavelength

58 2 viewing angle: CIE 1931 (XYZ) CIE Color spaces

59 CIE Color spaces CIE 1960 (UCS) More perceptual uniformity U=(2/3)X V=Y W=1/2(-X+3Y+Z)

60 CIE Color spaces CIE L*,a*,b* (CIELAB) 1976 L is lightness and runs from 0 (black) to 100 (white) a red-green axle b blue-yellow axle Distances are more or less linear with perceptional differences

61 CIE Color spaces CIE L*,a*,b* (CIELAB) 1976 L is lightness and runs from 0 (black) to 100 (white) a red-green axle b blue-yellow axle Distances are more or less linear with perceptional differences