Sn
eso
r P
hys
ics
Seres István 2 http://fft.szie.hu
Fotometry
Used quantities:
angle: length fo arc/radius
Solid angle: area/radius squared
r
i
r
i
2r
Asr
Central angle of a circle: 2 (radian)
Central angle of a sphere: 4 (steradián)
(steradián = sr)
Sn
eso
r P
hys
ics
Seres István 3 http://fft.szie.hu
Fotometry
The solid angle of an elementary area:
2r
cosdAd
d
r
dA
dA cos
Sn
eso
r P
hys
ics
Seres István 4 http://fft.szie.hu
FotometryOverview:
Radiometrical quantity Unit Fotometrical quantity
Unit
Emitted power (Φe) W Luminous flux (Φv)
lm
Irradiation (Ee)
(Power density)
W m-2 Illumination (Ev) lx
Irradiation density (Le) W m-2 sr-1
Brilliancy (Lv) cd m-2
Sn
eso
r P
hys
ics
Seres István 5 http://fft.szie.hu
Fotometry
Luminous flux
Spectral sensitivity of the eye(visibility function)
Sensitivity max of the human eye: 555 nm
Power: 1 wattLuminous flux: 683 lumen
Maximal spectral utilization
watt
lumen683Km
Sn
eso
r P
hys
ics
Seres István 6 http://fft.szie.hu
Fotometry
láthatósági függvény
0
0.2
0.4
0.6
0.8
1
350 450 550 650 750
hullámhossz (nm)
(nm) V
480 0.139
490 0.208
500 0.323
510 0.503
520 0.71
530 0.862
540 0.954
550 0.995
555 1
560 0.995
570 0.952
580 0.87
590 0.757
600 0.631
610 0.503
620 0.381
630 0.265
640 0.175
Luminous flux
Sn
eso
r P
hys
ics
Seres István 7 http://fft.szie.hu
Fotometry
The energy emitted by a unit time:
dt
dW n/ /lumelm
)683(,__max:
_:)(
__:
)(
1
2
1
WlmnutilizatiospectralimalKm
functionvisibilityV
powerspectralemitted
dVKm
e
e
Luminous flux
Sn
eso
r P
hys
ics
Seres István 9 http://fft.szie.hu
Fotometry
Illumination:Luminous flux on a unit surface
/lux/E
lxdA
dE
Sn
eso
r P
hys
ics
Seres István 11 http://fft.szie.hu
Fotometry
Fotometers
Important properties of light sensors
1. The spectral dependence of the sensor is coincidence with the visibility function V(λ)
2. The photocurrent is proportional to the illumination
3. The angled irradiation is detected as the cosine of the incliment angle
Sn
eso
r P
hys
ics
Seres István 12 http://fft.szie.hu
Fotometry
Photometers
•Subjektiv photometry
• Photocell
• semiconductor diode
Sn
eso
r P
hys
ics
Seres István 14 http://fft.szie.hu
Fotometry
Subjective photometry
Weber photometer
Bunsen fotometer:
Relative measurement