In this presentation on Radiometry and Photometry we will look at Radiometry, the detection and measurement of radiation across the full electromagnetic spectrum, including ultraviolet, visible and infrared radiation. Photometry is concerned only with the visible portion of the spectrum, from about 380 to 780 nanometers.

1. LED Fundamentals
Radiometry &
Photometry
08-03-2011

2. Definitions, Units and Symbols
 Radiometry – deals with the detection and measurement of electromagnetic radiation
across the total spectrum
 Photometry – subfield of radiometry; radiometric power scaled by the spectral response
of the human eye
LED Fundamentals | Radiometry & Photometry | Page 2

3. Definitions, Units and Symbols
 Radiometry – deals with the detection and measurement of electromagnetic radiation
across the total spectrum
 Photometry – subfield of radiometry; radiometric power scaled by the spectral response
of the human eye
Radiometric Photometric
Quantity Symbol Units Quantity Symbol Units
Radiant Power Φe W Luminous Flux Φv lumens (lm)
Radiant Intensity Ie W/sr Luminous Intensity Iv lm/sr
2 2
Irradiance Ee W/m Illuminance Ev lm/m
2 2
Radiance Le W/m -sr Luminance Lv lm/m -sr
“e” = “energetic”
“v” = “visual”
v visual
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4. Converting to Photometric Units
 Power (Watts) is converted to luminous
flux (lumens) via the relation:
Φv = flux (lumens)
780
 v  K  Pe   V   d Pe = Power
V = photopic response function
380 of the human eye
1
0.9
K = constant (683 lm/W for
0.8
photopic)
0.7
Relative Sensitivity
0.6
0.5
0.4
R
0.3
0.2
0.1
0
400 450 500 550 600 650 700 750
Wavelength (nm)
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5. Convert Radiometric to Photometric
Pe   V   Pv  
1
1 1
0.8 0.8
0.8
0.6 ensity [a.u.] 0.6 0.6
0.4 0.4
04 0.4
inte
0.2 0.2
0.2
0 0
400 450 500 550 600 650 700 750 0 400 450 500 550 600 650 700 750
400 450 500 550 600 650 700 750
W avel eng t h ( nm) W aveleng t h ( nm)
Wavelegth [nm]
780
 v  K  Pe   V   d
380
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6. Solid Angle
Surface Area = A
Sphere radius = R
Solid Angle Ω = A/R2
Units: Steradians (sr)
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7. Projected Solid Angle
Solid angle area (d)
 Solid Angle Area d

Area of projected
solid angle (cos  d)
Unit sphere
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8. Projected Solid Angle
d  sin  d d
d proj  cos  d
2 
α
 proj    cos sin  d d
0 0
 projj   sin  2
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9. Photometric Units and Symbols
Photometric Units
Metric English
Quantity Symbol Units Name Units Name
Luminous Flux Φ lumens (lm) lumens
candela (cd)
Luminous
I lm/sr or
Intensity
candlepower
2 2
Illuminance E lm/m lux (lx) lm/ft Ft-candle
2 2
Luminance L cd/m nits cd/π*ft Ft-Lambert
I
E
L
LED Fundamentals | Radiometry & Photometry | Page 9

10. Lambertian Source
 Brightness (luminance) is
independent of angle
L   L0 
 Intensity falls off as cosθ I ( )  I 0 cos
 Many LEDs are very nearly
Lambertian sources
I0
I 0 cos 

LED Fundamentals | Radiometry & Photometry | Page 10

11. Lambertian Source
Total flux in a 2θ cone:

  2  I  'sin  ' d '
0

  2  I 0 cos  ' sin  ' d '
0
  I 0 sin 2 
The total flux of a Lambertian
source of 1 cd is lumens.
LED Fundamentals | Radiometry & Photometry | Page 11

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