1. 輻射束輻射束輻射束輻射束 (joule/sec)

2. 光束光束光束光束/光通量光通量光通量光通量(lumen)

3. 光度光度光度光度 (Candela, cd)

4. 輝度輝度輝度輝度 (cd/m2)

5. 照度照度照度照度 (Lux)

6. 光束發散度光束發散度光束發散度光束發散度 (radlux)

7. 反射率反射率反射率反射率 (reflectivity)

8. 電光源效率電光源效率電光源效率電光源效率 (power eff.)

七七七七、、、、色度與色度與色度與色度與CIE色度座標色度座標色度座標色度座標之測定之測定之測定之測定----發光學術語與基本概念發光學術語與基本概念發光學術語與基本概念發光學術語與基本概念

電磁波於單位時間內所傳播的輻射能量電磁波於單位時間內所傳播的輻射能量電磁波於單位時間內所傳播的輻射能量電磁波於單位時間內所傳播的輻射能量 (J/sec)或或或或Watt

F = KΦ Φ Φ Φ (K為視覺度為視覺度為視覺度為視覺度,其大小依波長而異其大小依波長而異其大小依波長而異其大小依波長而異,其最大值為其最大值為其最大值為其最大值為 100,

F為光束為光束為光束為光束

1.輻射束輻射束輻射束輻射束 ΦΦΦΦ (Radiant flux, 單位為焦耳單位為焦耳單位為焦耳單位為焦耳/秒秒秒秒 Joule/sec)

發光光度學常用單位與定義發光光度學常用單位與定義發光光度學常用單位與定義發光光度學常用單位與定義

2.光束光束光束光束/光通量光通量光通量光通量 (luminous, 單位單位單位單位:流明流明流明流明 Lumen)

光源所發出的總光量或單位時間內所通過的光量光源所發出的總光量或單位時間內所通過的光量光源所發出的總光量或單位時間內所通過的光量光源所發出的總光量或單位時間內所通過的光量,

可用照度計加以量測可用照度計加以量測可用照度計加以量測可用照度計加以量測

3.光度光度光度光度I (Luminous intensity,單位為燭光單位為燭光單位為燭光單位為燭光 Cd, candela)

一光源在冇一方向所發出光的強度稱之為光度，假設dω

為一微小立體角，其包含的光束為dF，則此光源箭頭方

向的光度(I)為

I = 光束光束光束光束/立體角立體角立體角立體角= dF/dωωωω 所以所以所以所以 dF = I dωωωω

此立體角內所有方向之光度I 則為 I = dF/dωωωω

對均勻的點光源而言對均勻的點光源而言對均勻的點光源而言對均勻的點光源而言，，，，F (lumen) = 4ππππI (單位為燭光單位為燭光單位為燭光單位為燭光)

其中4π為總立體角

點光源點光源點光源點光源dωI

各種光源的輝度值各種光源的輝度值各種光源的輝度值各種光源的輝度值 (nit)

太陽太陽太陽太陽 165 x 107 月亮月亮月亮月亮 26 x 102

蠟燭蠟燭蠟燭蠟燭 1 x 104 藍空藍空藍空藍空 8 x 103

水銀燈水銀燈水銀燈水銀燈 14 x 104 日光燈日光燈日光燈日光燈 6x 103-1x 104

納氣燈納氣燈納氣燈納氣燈 (200W) 8 x104

4. 輝度輝度輝度輝度 L (Brightness, 單位為單位為單位為單位為nit 或或或或nt = cd/m2或或或或stilb (sb), sb = cd/m2

由一特定的光源發出強度相同時由一特定的光源發出強度相同時由一特定的光源發出強度相同時由一特定的光源發出強度相同時，，，，其發光的面積越大者其發光的面積越大者其發光的面積越大者其發光的面積越大者，，，，則其輝度值則其輝度值則其輝度值則其輝度值

越小越小越小越小。。。。

某一截面的輝度某一截面的輝度某一截面的輝度某一截面的輝度 L (nit)值值值值，，，，為其該方向的光度值為其該方向的光度值為其該方向的光度值為其該方向的光度值 I (cd)，，，，以該截面的以該截面的以該截面的以該截面的

視面積視面積視面積視面積A (m2)除得之值除得之值除得之值除得之值，，，，以以以以L表示表示表示表示

L = I (cd)/A (m2) = nit or cd/m2 or stilb

5. 照度照度照度照度 E (Illumination Intensity,單位為單位為單位為單位為Lux勒克斯勒克斯勒克斯勒克斯)

380-780 nm

(Spectra colorimeter)

(Lux meter)

0.2 – 999 cd/m2

(color analyzer) 測量輝度值與色度值測量輝度值與色度值測量輝度值與色度值測量輝度值與色度值

彩色分析儀彩色分析儀彩色分析儀彩色分析儀---- 輝亮度輝亮度輝亮度輝亮度((((cd/m2))))、、、、對比度對比度對比度對比度、、、、閃爍閃爍閃爍閃爍、、、、色度色度色度色度(x,y)(x,y)(x,y)(x,y)值之測定值之測定值之測定值之測定

Anatomy of Human Eyes

1虹膜虹膜虹膜虹膜

2角膜角膜角膜角膜

玻璃體

4 Rods

5 Cones

3 視網膜視網膜視網膜視網膜

6 水晶體水晶體水晶體水晶體

.7 瞳孔瞳孔瞳孔瞳孔

玻璃體玻璃體玻璃體玻璃體

視神經視神經視神經視神經

Cones (解析度高有色彩分析能力解析度高有色彩分析能力解析度高有色彩分析能力解析度高有色彩分析能力) and rods (感光度高對低照暗輻極敏感感光度高對低照暗輻極敏感感光度高對低照暗輻極敏感感光度高對低照暗輻極敏感)

The distribution of cones and rods in the retina and

where the retina is most sensitive to light (blue graph).

Luminosity response of eyes

– yellow-green is brighter or stronger response to eyes, than R and B.

視網膜視網膜視網膜視網膜(3 types of cones)

Providing high accuracy and the ability to measure absolute color, used in research area

Spectrophotometric method

Tristimulus method

Human eye Problems with difference between individuals and memory characteristics

Small size and portability, used for color difference measurements and QC inspection

3 sensors

Spectral sensors

Chromatic Adaptation（（（（色彩的適應性色彩的適應性色彩的適應性色彩的適應性））））

Chromatic Adaptation (色彩的適應性色彩的適應性色彩的適應性色彩的適應性 )

Block diagram of basic components of a spectrophotometer

A spectrophotometer is a device used to measure the intensity of radiation absorbed at different wavelengths by looking at the spectral reflectance, transmittance or emission.

Inventor: Brace DeWitt; In 1935 Arthur Cobb Hardy received a patent for the spectrophotometer.

The spectral luminous efficiency curves

Scotopic (low light) vision system V’(λλλλ): Driven by rod cells; unable to differentiate different λλλλ’s; provides no saensation of colors

Phototopic (daytime) vision system V(λλλλ) : Driven by cone cells; can differentiate different λλλλ’s: ctreate sensation of colors

507 nm 555 nm

視覺函數視覺函數視覺函數視覺函數V(λλλλ), V’(λλλλ) 曲線曲線曲線曲線

1942與與與與1951年根據亮年根據亮年根據亮年根據亮、、、、暗適應條件下暗適應條件下暗適應條件下暗適應條件下，，，， CIE對對對對200多多多多位觀察者視覺的測定結果位觀察者視覺的測定結果位觀察者視覺的測定結果位觀察者視覺的測定結果，，，，分別推薦了分別推薦了分別推薦了分別推薦了

標準的明標準的明標準的明標準的明視覺視覺視覺視覺(V(λλλλ):峰值峰值峰值峰值555 nm，，，，光譜光效能最高值光譜光效能最高值光譜光效能最高值光譜光效能最高值Km(λλλλ)= 683 lm/W)與暗視覺與暗視覺與暗視覺與暗視覺(V’(λλλλ);峰值峰值峰值峰值507 nm，，，，光譜光效能光譜光效能光譜光效能光譜光效能最高值最高值最高值最高值 Km’(λλλλ) 1699= lm/W)函數曲線函數曲線函數曲線函數曲線。。。。

函數曲線的標準化與函數曲線的標準化與函數曲線的標準化與函數曲線的標準化與Km(λλλλ)、、、、Km’(λλλλ)值測定值測定值測定值測定，，，，在全球光度量測上有了統一的基礎在全球光度量測上有了統一的基礎在全球光度量測上有了統一的基礎在全球光度量測上有了統一的基礎!

S1

投影片 投影片 投影片 投影片 18181818S1 S1 S1 S1 Steven, 2006/5/8

The sensitivity between 700-800 nm is very low, only 380-700 nm is shown.

Color perception by eye and brainThe human retina has three kinds of cones. The response of each type of cone as

a function of l of the incident light.

RGB-cones for the RED-GREEN-BLUE sensitivity also

called as the SML-cones for Short, Medium and Long wavelengths.

The BLUE sensitivity for the B-conesor the S-cones

The GREEN sensitivity for the G-conesor the M-cones

The RED sensitivity for the R-conesor the L-cones

The human retina has three kinds of cones. The response of eachtype of cone as a function of λ λ λ λ of the incident light.

440

545580

x

y

z

Standard Observer

In 1931, the CIE originally defined the standard Observer using a 2o field of view, hence the name "2oStandard Observer"

In 1964, the CIE defined an additional standard Observer, this time based upon a 10o field of view and this is referred to as the "10o Supplementary

Standard Observer“

The 2o standard Observer should be used for viewing angles of 1o to 4o

and the 10o supplementary standard Observer should be used for viewing angles of more than 4o.

An Observer is a person or thing that observes. The sensitivity of each individual's Eye is slightly different; even for people considered to have "normal color vision" , there may be some bias toward red and blue. Also, person's eyesight generally changes with age. Because of these factors, colors will appear differently to each observer.

1. The human eyes

2. The nature of chroma (色度色度色度色度)

3. The standard observers (標準觀查者標準觀查者標準觀查者標準觀查者)

4. Color space (色域色域色域色域)

- chromaticity diagram/coordinates

- color temperature

七七七七、、、、色度與色度與色度與色度與CIE色度座標色度座標色度座標色度座標之測定之測定之測定之測定

- specification and measurements of colors

http://home.wanadoo.nl/paulschils/10.02.htm

CIE 1931 RGB r10(λλλλ), g10(λλλλ), b10(λλλλ) color matching functions

The r10(λλλλ) curve is more than 3 times higher than the others because "red"

wavelengths have low luminance and moderate tinting strength, so more of the

R primary must be used to match the high luminance of the G primary and the

high tinting strength of the B primary.

Color-matching functions of the CIE Standard Observer based on matching stimuli of wavelengths

700.0 (R), 546.1(G), and 435.8 (B) nm.

C R G B≡ ( ) + ( ) + ( )R G B

C R G B(520 nm ) ( ) ( ) + ( )+ ≡R G B

C R G B≡ − ( ) + ( ) + ( )R G B

The three CIE color matching functions (CMFs) are called , Y and Z, and for

practical color matching and display applications. These can be treated as if they

were the spectral response curves for the cone-receptors in the human eye.

While it is convenient to think of X, Y and Z as red, green and blue, owing to

their wide band and substantial overlap (especially of X and Y), this is a crude

approximation. XYZ – tristimulus values; x, y, z : tristimulus response of RGB

CIE 1931 XYZ standard Color matching functionsfor 2°°°° observer

X, Y, z

So the 3 "primary" colors are the virtual colors A, B, and C. Then for a given real color, its components with respect to the primaries are as follows:

x = A/(A+B+C)y = B/(A+B+C)z = C/(A+B+C)

Since x + y + z = 1, if x and y are known then z can be determined.

The CIE diagram is a plot of x vs. y for all visible colors

CIE Chromaticity Diagram (色品圖色品圖色品圖色品圖；；；；色度座標圖色度座標圖色度座標圖色度座標圖)

This is an international standard for primary colors established in 1931. It allows all other colors to be defined as weighted sum of the three "primary" colors. 1)There are no real three colors that can be combined to give all possible colors. 2) Therefore, the standard "primary" colors established by CIE don't correspond to real colors.

The CIE Color Space

• The CIE system characterizes colors by a luminanceparameter Y and two color coordinates x and y which specify the point on the chromaticity diagram.

• the parameters are based on the spectral power distribution of the light emitted from a colored object and are factored by sensitivity curves which have been measured for the human eye.

CIE-1931 Chromaticity Coordinates as the Cartesian Coordinates used to define color in the CIE color space. They are designated as x, y and z and are the ratios of each of the tristimulus values X,Y and Z in relation to the sum of the three. z = 1 - ( x + y )

CIE-1976 Chromaticity Coordinates used to define color in the CIE color space. They are designated as u' and v' u’ = u-uo v’ = v-vo

CIE-1976 U.C.S. CHROMATICITY DIAGRAM

CIE色度座標圖色度座標圖色度座標圖色度座標圖

飽和度飽和度飽和度飽和度

色調色調色調色調

x

x

CIE(Commission Internationale de l'Éclairage )

Additive mixing

Mixing of Colors of light

Mixing paint pigmentsSight of human Eyes

Mixing of Colors of pigments

MAGENTA, YELLOW and CYAN pigment of proper intensities are known as ”The Subtractive Primary

Colors”.

Simple subtractive mixing

Additive color mixtures are always lighter than any of the individual components!

Subtractive color mixtures are always darker than the components separately.

Additive mixing Simple subtractive mixing

Approximate color regions on CIE chromaticity diagram (after Fortner, P. 5, Scien Tech J. 1996)

The boundary represents maximum saturation for the spectral colors, and the diagram forms the boundary of all perceivable hues (色調色調色調色調).

The C.I.E. Chromaticity Diagram

Y2SiO5

Y2SiO5 YAG

YAG

YAG

P22 CRT phosphors

ZnS:Ag (blue)

(Zn,Cd)S:Ag (green)

Y2O3:Eu3+ (red)

The boundary of x, y diagram is bounded by the values of monochromatic light, any color in terms of (x, y)

Tristimulus Fuilters Used in Defining Colors

The energy of any spectral curve:

ER = ΣΣΣΣ(Idλλλλ)R EG = ΣΣΣΣ(Idλλλλ)G EB = ΣΣΣΣ(Idλλλλ)B

1. Take the spectral curves.

2. Multiplying by the overlap of each tristimulus curve.

3. We obtain Tristimulus Values.

Emittance Reflective (scattering)

X = xΣΣΣΣIRdλλλλ X = xΣΣΣΣ IRRRdλλλλ

Y = yΣΣΣΣIGdλλλλ Y = yΣΣΣΣ IGRGdλλλλ

Z = zΣΣΣΣIBdλλλλ Z = z Σ IBRBdλλλλ

x, y, z are the stimulus response of red, green, and blue；；；；而而而而X, Y, Z則稱之為則稱之為則稱之為則稱之為tristimulus values

Because each color gives a set of tristimulus values 但但但但each set之間並未有相互之間並未有相互之間並未有相互之間並未有相互correlation

因為因為因為因為 IR ≠≠≠≠ IG ≠≠≠≠ IB (RGB spectral energy are not equal)

因此有必要將三刺激值因此有必要將三刺激值因此有必要將三刺激值因此有必要將三刺激值 tristimulus values (XYZ) normalized，

並且定義一套並且定義一套並且定義一套並且定義一套 chromaticity coordinates (x, y, z)

Chromaticity coordinates x, y, z 可以定義為可以定義為可以定義為可以定義為

x = X/(X+Y+Z) y = Y/(X+Y+Z) z = Z/(X+Y+Z)

其中其中其中其中 x + y + z = 1

(x, y, z) 稱之為色稱之為色稱之為色稱之為色(度度度度)座標座標座標座標 (chromaticity coordinates)

1) Obtain emission spectrum (利用利用利用利用spectrofluorimeter)

Measuring Emissive Colors 之過程

((((如何將光譜轉換成色度座標如何將光譜轉換成色度座標如何將光譜轉換成色度座標如何將光譜轉換成色度座標????))))

2) 利用利用利用利用 energy of RGB spectral curve:

ER = ΣΣΣΣ(Idλλλλ)R EG = ΣΣΣΣ(Idλλλλ)G EB = ΣΣΣΣ(Idλλλλ)B

等公式等公式等公式等公式，，，，將將將將(Idλλλλ))))積分積分積分積分，，，，以獲得以獲得以獲得以獲得RGB 三原色色光之能量三原色色光之能量三原色色光之能量三原色色光之能量

3) 因為因為因為因為 X = xΣΣΣΣIRdλλλλ Y = yΣΣΣΣIGdλλλλ Z = zΣΣΣΣIBdλλλλ

故可以利用故可以利用故可以利用故可以利用

求取求取求取求取((((x,yx,yx,yx,y))))值值值值 上述上述上述上述 x, y, and z 為為為為the stimulus response of red, green, and blue

x = y = z =

X + Y + Z X + Y + Z X + Y + Z

X Y Z

4) Draw vertical lines on each color function to obtain “weighted functions” to calculate chromaticity coordinates

x: 550-650 nm y: 510-600 nm z: 420-480 nm

One would have a set of lines whose spacing was inversely proportional to peak height.

標準光源A The radiation emitted from an incandescent

tungsten filament operating at 3250K

標準光源標準光源標準光源標準光源 C

Daylight.

The northern skylight at 11:30a.m. at Greenwich, England on Oct. 31, 1931.

Values Related to Color Specification

Comparison of Energy Distribution of Different Light Sources

D65

An approximation of noon sunlight having a correlated color temperature of approximately 4874 K and obtained by a combination Light Source (A) and a special filter.

Light source C

Light source A Light source B

2856 K

6774 K6504 K

標準光源標準光源標準光源標準光源

A: (0.420, 0.395)

B: (0.360, 0.360)

C: (0.315, 0.320)

Any hue (色彩色調色彩色調色彩色調色彩色調) can be specified by (x, y). Illuminants can also be specified.

Color Constancy

Different illuminants (shown in the above diagrams) have different spectral energy distribution and therefore a given object can only reflect different energy distribution.

Colored surfaces appear to retain their approximate daylight appearance even when viewed under LIGHT SOURCES that differ markedly from daylight.

Radiation Curve of Black body

任何溫度下任何溫度下任何溫度下任何溫度下，，，，能完全吸收任何入射波長輻射的熱輻射體能完全吸收任何入射波長輻射的熱輻射體能完全吸收任何入射波長輻射的熱輻射體能完全吸收任何入射波長輻射的熱輻射體，，，，稱之為黑體稱之為黑體稱之為黑體稱之為黑體(black body)。。。。1900年年年年Planck提出光量子理論提出光量子理論提出光量子理論提出光量子理論，，，，導出黑體輻射公式導出黑體輻射公式導出黑體輻射公式導出黑體輻射公式 (Planck equation)

– 處於絕對溫度處於絕對溫度處於絕對溫度處於絕對溫度T之黑體之黑體之黑體之黑體，，，，在波長在波長在波長在波長λλλλ處的光譜能量分布為處的光譜能量分布為處的光譜能量分布為處的光譜能量分布為 Pλλλλ = (c/λλλλ5)(1/ec’/λλλλT-1) 黑體總能量黑體總能量黑體總能量黑體總能量 P = ∫∫∫∫Pλλλλdλλλλ = σσσσT4 (Stephen-Bosemann law)

色溫色溫色溫色溫10000K1000K

Lava

5000K

sun Sirius天狼星天狼星天狼星天狼星