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Home , Apostilb, Brightness, Lambert (unit), Luminance, Luminous efficacy, Luminous flux

445.664

Light-Emitting Diodes

Chapter 16. Human eye sensitivity and photometric quantities

Euijoon Yoon

445.664 (Intro. LED) / Euijoon Yoon

Human vision

Ganglion cell (circadian receptor)

• Cones: provide sensitivity • Rods : color insensitive • Color perception depends on .

• regime: High light level vision regime (during daylight) • regime: Low light level vision regime (at night)

445.664 (Intro. LED) / Euijoon Yoon

1 Three different vision regime

• Photopic vision : human vision at high ambient light level (daylight condition) • Scotopic vision : human vision at low ambient light level (at night) • Mesopic vision : light level between the photopic and scotopic vision regime

445.664 (Intro. LED) / Euijoon Yoon

Normalized spectral sensitivity

• Night- vision is weaker in the spectral range • Stronger in the spectral range as compared to day-time vision

445.664 (Intro. LED) / Euijoon Yoon

2 History of photometric units

• Photograph shows plumber’s . • A plumber’s candle emits a of 1 (cd). The cd is historical origin of all photometric units. • photometric unit is relevant when it comes to light perception by a human being.

• First definition (now obsolete) : The luminous intensity of a standardized candle is 1 cd.

• definition (now obsolete) : 1 cm2 of platinum (Pt) at 1042K ( of solidification) has a luminous intensity of 20.17 cd.

• Third definition (current) : A monochromatic light source emitting an optical of (1/683) at 555 nm into the solid of 1 (sr) has a luminous intensity of 1 cd.

• and candle are obsolete units. Candlepower and candle measure luminous intensity and are approximately equal to 1 cd.

445.664 (Intro. LED) / Euijoon Yoon

Luminous , , and

• : A light source with a luminous intensity of 1 cd emits a luminous flux of 1 lm into a of 1 steradian.

• An isotropic light source with a luminous intensity of 1 cd emits a total luminous flux of 4π lm = 12.56 lm.

• Illuminance : If a 1m2 surface receives a luminous flux of 1 lm, then the illuminance of the surface is 1 . lm/m2

Ex) Moonlight 1 lux; 10 lux; home 30-300 lux, office desk light 102-103 lux; surgery light 104 lux; direct 105 lux

• Luminance is the luminous intensity emitted per unit area of a light source. Luminance is a figure of merit for displays. Typical displays have a luminance of 100- 500 cd/m2.

445.664 (Intro. LED) / Euijoon Yoon

3 Exercise: Photometric Unit

• A 60 W has a luminous flux of 1000 lm. Assume that the light is emitted isotropically from the bulb (a) What is the luminous efficiency (i.e., the number of lumens emitted per Watt of electrical input power) of the light bulb? A: 1000 lm / 60 W = 16.7 lm/W (b) What number of standardized emit the same luminous intensity? A: luminous intensity per steradian =1000 lm /4p = 80

(c) What is the illuminance, Elum, in units of lux, on the desk located 1.5 m below the bulb? A: 1000 lm / 4p (1.5)2 m2 = 35.4 lm/m2 = 35.4 lux (d) Is the luminous level obtained under (c) sufficiently high for reading? A: Yes.

445.664 (Intro. LED) / Euijoon Yoon

Exercise: Photometric Unit

(e) What is the luminous intensity, Ilum, in units of candela, of the light bulb? A: 1000 lm / 4p sr =79.6 lm/sr = 79.6 cd (f) Derive the relationship between the illuminance at a distance r from the light bulb, measured in lux, and the luminous intensity, measured in candela? 2 2 A: Elum * 4p r / 4p = Ilum Æ Elum r = Ilum (g) Derive the relationship between the illuminance at a distance r from the light bulb, measured in lux, and the luminous flux, measured in ? 2 A: Elum 4p r = Flum (h) The definition of the cd involves the optical power of (1/683) W. What, do you suppose, is the origin of this particular power level? A: Historical origin: 1/683 of the 555 nm light source has the same intensity as the candle.

445.664 (Intro. LED) / Euijoon Yoon

4 Typical illuminance in different environments

Illumination condition Illuminance Full moon 1 lux Street lighting 10 lux Home lighting 30 to 300 lux Office desk lighting 100 to 1000 lux Surgery lighting 10000 lux Direct sunlight 100 000 lux

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The projected surface area

• Aprojected = Asurface cosΘ (Θ is the angel between the direction considered and the surface normal) • The luminous intensity of LEDs with lambertian emission pattern also depends on the angle Θ according to a cosine lqw • Thus, the luminance of LEDs is a constant, independent of angle

445.664 (Intro. LED) / Euijoon Yoon

5 Common units

Conversion between common Si and non-Si units for Unit Common name Unit Common name 1 cd/cm2 1stilb (1/π) cd/m2 1 (1/π) cd/cm2 1 (1/π) cd/ft2 1 foot-lambert 1 cd/m2 1 nit

Luminance Luminance Typical values for Device Device (cd/m2) (cd/m2) the luminance of displays Display 100 (operation) Organic LED 100-10000

Display 250-750 (max) III-V LED 1 M-10M

Photometric Unit Dimension Radiometric unit Dimension Photometric and Luminous flux lm W corresponding (optical power) radiometric units Luminous intensity lm/sr = cd W / sr Irradiance Illuminance lm/m2 = lux W / m2 (power density) Luminance lm/(sr m2)=cd/m2 W / (sr m2)

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CIE eye sensitivity function

• CIE 1931 function : current photometric standard in US • The CIE 1978 function, which can be considered the most accurate description of the eye sensitivity in the photopic vision regime

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6 Eye sensitivity function and

• The conversion between radiometric and photometric units is provided by eye sensitivity function,V(λ)

•Visible range: 390 - 720 nm

• Definition of Lumen: - Green light (555 nm) with power 1W has luminous flux 683 lm

• Efficacy of radiation gives number of lumens per optical Watt.

• Among LEDs with same output power, green LEDs are brightest.

445.664 (Intro. LED) / Euijoon Yoon

Luminous flux and efficiency

Luminous flux (unit: lm) lm Φ = 683 V (λ)P(λ)dλ lum ∫ W λ ( V ( λ ) : eye sensitivity function, P ( λ ) : the power spectral density) Luminous efficacy (unit: lm/W) Φ ⎡ lm ⎤ ⎡ ⎤ = lum = ⎢683 ∫V (λ)P(λ)dλ⎥ /⎢∫ P(λ)dλ⎥ P ⎣ W λ ⎦ ⎣λ ⎦ - the conversion efficiency from optical power to luminous flux

Luminous efficiency (unit: lm/W) Φ = lum IV - The luminous efficiency is the product of luminous efficacy and electrical-to-optical power conversion efficiency. - The luminous efficiency is highly relevant figure of merit for visible- LEDs.

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7 Luminous efficiencies of different light sources

Luminous Light sourse efficiency Edison’s first light bulb (C filament) 1.4 lm/W Incandescent filament light bulbs 15-20 lm/W sources Quartz halogen light bulbs 20-25 lm/W Fluorescent Fluorescent light tubes 50-80 lm/W sources vapor light bulbs 50-60 lm/W HID (High- intensity Metal halide light bulbs 80-125 lm/W discharge) High pressure sodium vapor light 100-140 lm/W bulbs

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Summary of photometric, radiometric, and quantum performance measures for LEDs

Figure of merit Explanation Unit

Luminous efficacy Luminous flux per optical unit power lm/W

Luminous efficiency Luminous flux per input electrical unit power lm/W

Luminous intensity efficiency Luminous flux per sr per input electrical unit power cd/W

Luminance Luminous flux per sr per chip unit area cd/m2

Power efficiency Optical output power per input electrical unit power %

Photons emitted in active region per electron Internal quantum efficiency % injected

External quantum efficiency emitted from LED per electron injected %

Escape probability of photons emitted in active Extraction efficiency % region

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8 and linearity of human vision

• Brightness: lack of standardized scientific definition – Brightness is an attribute of visual perception and is frequently used as synonym for luminance and (incorrectly) for the radiometric term radiance • For point source, – Brightness (in the photopic vision regime) can be approximated by the luminous intensity (cd) • For surface source, – Brightness can be approximated by luminance (cd/m2) • Standard CIE – Assumption: human vision is linear within the photopic regime – Isotropically emitting blue point source and red point source have the same luminous intensity

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Circadian rhythm and circadian sensitivity

• Circadian rhythm of circadian cycle – The human wake-sleep rhythm has a period of approximately 24 hrs. – The wake-sleep rhythm of humans is synchronized by the intensity and spectral composition of light. – to inappropriately high intensities of light in late afternoon or evening can upset the regular wake-sleep rhythm. – Retinal ganglion cells have an optical sensitivity.

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