Lab. of Cond. 1Matter Physics
3. Calibration of the detector
Goal of the exercise: Determination of a photodetector’s sensitivity and Stefan-Boltzmann’s
and the inverse-square laws verification.
Description of the experimental set-up:
Model of a black-body (BB). Maximum heating current - 2.5 A.
Autotransformer and safety transformer.
Ammeter.
Thermocouple Pt-RhPt, with a digital multimeter V 544 plugged in.
Mechanical chopper equipped in a reference system (a phototransistor biased with the voltage
of 6 V from the ZS 0.2/6/1 power supply incorporated into the chopper’s cover).
Oscilloscope used to observe the reference current mentioned above.
The examined detector (with the preamplifier powered by the 4.5 V battery).
Selective nanovoltmeter 237 with 233-7-1 preamplifier.
Lab. of Cond. 2Matter Physics
Workflow of the exercise:
1.Assemble the measuring setup according to the scheme shown in Fig.1. Proceed with the
measurement after having your setup checked by the supervisor.
Fig.1.
2. Measure the black-body output slit diameter.
3. Verifying the Stefan-Boltzmann law
During the heating of the black-body (set the autotransformer voltage to about 100 V)
perform the measurement of the detector signal as a function of the temperature until the
temperature reaches 500 K (about 227 0C) for f1  17 Hz and constant distance between the
detector and the emitting slit (about 20 cm).
The modulation frequency measurement is performed using the oscilloscope. A little light
bulb and a phototransistor have been placed opposite to each other in the cover of the
chopper. The light emitted by the light bulb illuminating the phototransistor is modulated in
the same way as the radiation emitted by the black-body illuminating the detector to be
calibrated. The AC signal from the phototransistor is plugged into the oscilloscope, which is
used to measure the period of the voltage.
The temperature is measured by the thermocouple Pt.- PtRh (10% Rh). The electromotive
force of this thermocouple versus the temperature difference (in ºC) is given in Table I,
assuming that the reference junction is a 0ºC temperature. During the exercise the reference
Lab. of Cond. 3Matter Physics
junction is at room temperature therefore the readings from the Table I should
be shifted accordingly.
4. Verifying of the inverse-square law
For the constant temperature of the black-body equal to 500 K, measure the detector signal as
a function of the distance d from the BB emitting slit within the range of 15-50 cm for the
modulation frequency f1. Black-body model reaches its state of the thermodynamical
equilibrium at 500 K once the autotransformer’s knob is set at 60 V.
5. Checking the validity of the approximate relation (3).
For the black-body temperature equal to 500 K, measure the voltage on the detector’s output
at constant distance (20 cm) for two different modulation frequencies. Modulation frequency
is changed by pushing out the right switch in the modulator’s cover.
6. Estimating the detector’s noise signal.
After covering the detector, measure its output voltage for two different modulation
frequencies.
7. After performing the measurements, turn off the power supply of the detectors preamplifier
(unplug the battery).
Lab. of Cond. 4Matter Physics
Data analysis:
1. Verification of the Stefan-Boltzmann law and calibration of the detector.
Plot Udet = f( ) (cf. Eq. (1)). Using the linear regression method, determine the slope of the
line. The slope coefficient of this dependence is the global sensitivity of the detector ( Eq. 2).
Include in the calculations the amplification of the preamplifier 233-7 and the correction
resulting from the shape of the modulation (rectangular modulation). The photosensitive
surface of the detector equals 2 mm2.
2. Verification of the inverse-square law.
Plot Udet = f(1/d2) where d is the distance between the detector and the emitting slit of the
black-body.
3. Determination of the approximate relations between the sensitivity and the modulation
frequency.
The sensitivity of the detector for two different modulation frequencies should be compared.
Check whether the approximate relation (3) is fulfilled.
4. Estimate the parameters of the studied detector, compared to other thermal and photon
detectors.
Literature:
1. R.Nowicki, "Pomiary energii promienistej",WNT 1969, str.49-55
2. J.Piotrowski,A.Rogalski, "Półprzewodnikowe detektory podczerwieni" WNT, 1985, str.13-36
3. Wykład 1, 4 i 9 „Źródła i detektory”.
Lab. of Cond. 5Matter Physics
Equations used for the calculations in the report.
1. The radiation power emitted by the black-body illuminating the detector of surface Ad:

0.45 (T 4  T04 )
Asrc Ad [W ]
d 2
(1)
where d – the distance between the detector and the black-body, Asrc – surface of the slit of
the black-body, 0.45 – factor corresponding to the rectangular modulation of the light, 
Stefan – Boltzmann constant, T – temperature of the black-body (in K), T0 – room
temperature (in K).
2. Voltage sensitivity of the detector (for a fixed frequency):
Ud
(2)
[V / W ]

where Ud is the voltage of the detector’s output (including the amplification of the
preamplifier)
Rv =
3. Approximate relation between the sensitivity and the frequency:
Rv 
cRv

where c= const
(3)
4. How to include the amplification of the preamplifier?
If the voltage of the detector’s output is amplified by an amplifier with the amplification k
[dB] and its measured value equals Um., then the real voltage of the detector Ud is given by:
k = 10 log
U
U 2m
 20 log m
2
Ud
U d

log
Um
k

U d 20

Um = Ud10k/20 
Ud = Um 10-k/20
( e.g. if k = 20 
Ud = Um/10 )
Control questions.
1. Laws of the black-body radiation.
2. Thermal detectors of electromagnetic radiation. Pyroelectric effect.
3. Free electron model.
4. Temperature sensor (so called thermocouple) operations principle.
5. Alternating current (amplitude, root mean square, period, frequency)
(4)