The Physikalisch-Technische Bundesanstalt (PTB) expanded its capabilities for the calibration of the spectral responsivity
Due to their measurement principle, pyroelectric detectors can only measure temporal changes in the input radiant power and are, therefore, operated with a chopper wheel to chop the incident radiation. The detector signal, which is typically measured with a lock-in amplifier, depends not only on the amplitude but also on the temporal shape of the chopped radiant power. It is shown that the calculation of the radiant power used for the determination of the spectral responsivity must be based on an accurate approximation of the temporal shape of the chopped radiant flux at the detector. This shape is different for both applied primary methods. It is further shown that the particularities of the lock-in-technique have to be considered in the calculation of the spectral responsivity, including the correct calculation of the detector signal.
The results of the calibration with both approaches are consistent, and the realized measurement uncertainty is in the range between 1 % and 14 %. The pyroelectric detectors were thereby established as transfer detectors for the SI traceable measurement of radiant power in the near-infrared (NIR) and mid-infrared (MIR).
The Physikalisch-Technische Bundesanstalt (PTB) runs different primary
standards to conduct absolute measurements of the spectral responsivity Cryogenic electrical substitution radiometers have been well-established primary detector standards for absolute detector calibrations at the PTB for several years. They measure radiant power traceable to the SI with low uncertainty. The detector calibration for their spectral responsivity is done by relating the output of the detector under test to the measured radiant power (Pohl et al., 2019). Lately, a second approach for SI traceable detector calibrations was established at the PTB by using a primary source standard (Pohl et al., 2021). The radiation of a blackbody can be calculated by Planck's law and is, additionally, spectrally selected by optical bandpass filters and then related to the corresponding detector output signal.
Suitable detectors which have been calibrated against the primary standards
can also be utilized as transfer standards for the dissemination of the
spectral responsivity from the primary standards to other detectors. Thus, SI traceable calibrations of customer devices against these transfer standards require a much lower effort than a direct calibration against the primary standard.
The PTB uses different types of such transfer detectors for different
wavelength ranges. Partially, thermal detectors are applied at wavelengths
above 1.5
The PTB already uses thermopile detectors as near-infrared (NIR) and mid-infrared (MIR) transfer detectors (Pohl et al., 2019). This paper describes the calibration of two pyroelectric detectors, regarding their absolute spectral responsivity
The PTB runs two different measurement approaches for the calibration of radiation detectors in the near- and mid-infrared spectral range. Both approaches are completely independent primary measurement methods for the realization of the spectral responsivity traceable to the International System of Units. The pyroelectric detectors have been calibrated for their spectral responsivity, using both methods.
The first approach for the absolute calibration of detectors regarding their
spectral responsivity uses a cryogenic electrical substitution radiometer
which is a primary detector standard. Electrical substitution radiometers measure the radiant power
The utilized measurement facility consists of a cryogenic electrical
substitution radiometer with a nominal aperture diameter of 5.8 mm and is
equipped with lasers as radiation sources in the infrared spectral range, i.e. a quantum cascade laser (QCL) at 3.96 and 9.45
The second approach for the calibration of detectors for their spectral responsivity is realized by using the radiation from a blackbody radiator, which is a primary source standard. The blackbody radiation can be calculated by Planck's law. Hence, a calibration of the spectral responsivity of the detector with respect to irradiance can be achieved by measuring the corresponding detector output signal. If the aperture size of the detector is known, its spectral responsivity can also be calculated with respect to radiant power (Pohl et al., 2021).
The radiator which was used is called a large-area blackbody (LABB) and is an
almost ideal blackbody with known emissivity of 0.999 and nominal aperture
size of 20 mm in diameter. Its temperature
The blackbody radiation is spectrally selected by using different sets of
accurately characterized optical bandpass filters to obtain information
about the wavelength dependency of the detector responsivity. Sets of two
filters have been applied to improve the attenuation of the out-of-bandpass
radiation. The applied bandpass filters in the spectral range between
1.5
The set-up for the detector calibration at the blackbody is depicted in
Fig. 1. The shutter and precision aperture are temperature stabilized; the chopper wheel for the calibration of pyroelectric detectors was positioned close to the detector aperture. The impact of the chopper position on the calibration result will be discussed in detail in Sect. 3.2.3. The distance
Measurement set-up for the calibration of the spectral responsivity of a pyroelectric detector at the large-area blackbody (LABB) with a precision aperture, two optical filters and a chopper wheel.
In general, the spectral responsivity
However, the output voltage of the lock-in amplifier only reflects the
fundamental oscillation component of the Fourier series of the lock-in amplifier input signal. The frequency of this fundamental component is defined by the chopper frequency. Consequently, for the definition of the spectral responsivity
Furthermore, at most lock-in amplifiers, the DC lock-in amplifier output
voltage is not the fundamental component
In fact, a more reasonable notation would be to multiply the rms value of
the fundamental component of the electrical output signal of the detector
The measurement of the detector signal from the read-out of the output
signal
A lock-in amplifier is used for the read-out of the pyroelectric detector signal with phase-sensitive detection (PSD). This means that input signal contributions with a frequency other than the reference frequency, which is given by the applied chopper frequency, are attenuated close to zero in the DC output signal. This is realized by multiplying the periodic input signal with the sinusoidal reference signal of the lock-in amplifier.
Assuming a sine-shaped input signal, the output
Using commonly known trigonometric identities, this leads to the following:
As shown in Eq. (4), the output of the PSD of the lock-in amplifier consists
of two signal parts, with one at the difference frequency
In order to obtain the value of the signal amplitude
These PSD output signals are usually named
However, it should not be disregarded that this absolute
value
We are now going to use such a lock-in amplifier to measure the signal of a pyroelectric detector. To obtain the spectral responsivity of the detector, the signal of the irradiated detector has to be corrected regularly for the background signal that is produced by the detector when the measured irradiation is blocked by a closed shutter.
In this case, the calculation of the correct detector signal
The reasons for differences in the phases, especially at the blackbody
calibration facility, are, for example, different positions of the parts of the radiation at the chopper wheel when passing the chopper wheel (see details about the chopper wheel in Sect. 4). Even the temperature of the chopper wheel may have an effect on the phases. If the temperature of the chopper wheel is higher than the temperature of the background behind the chopper – e.g. the closed shutter – then the phase may switch by 180
Phase differences between the irradiated and the background measurement
between 20
It has been found that the effect of the phase difference between
Background signal at the cryogenic electrical substitution
radiometer facility measured over several hours. The average values of
As mentioned, the lock-in amplifier transforms the amplitude of the periodic input signal from the detector into a DC voltage at the output. This voltage depends on amplification stages, filter specifications and on the amplitude of the internal reference voltage. Consequently, the lock-in amplifier cannot automatically be assumed to be traceable to the SI from the metrological view of a national metrology institute.
Hence, the PTB handles the lock-in amplifier, including its chopper, as an
inherent part of the pyroelectric detector. This modality is sufficient for
the internal use of the detectors as transfer standards for the dissemination
of the spectral responsivity to customer detectors at PTB. Of course, the
stability of the joint unit of pyroelectric detector and lock-in amplifier
has to be monitored. Also, the individual stability of the pyroelectric
detector (respectively, the lock-in amplifier) will be monitored. Currently, no instabilities larger than the overall measurement uncertainty of either the pyroelectric detector or the lock-in amplifier are known. However, it is
intended to set up an electric calibration method to gain access to SI
traceable values of the detector output voltage amplitudes by calibrating
the lock-in amplifier as an independent measurement device. Until then, the
spectral responsivity of the pyroelectric detector given in volts per watt (
The spectral responsivity of the pyroelectric detector has been defined in
Eq. (1) as the ratio of the detector signal
Definition of the physical quantities concerning the time-dependent course of the radiant power. The input value
The value
The amplitude
In some simple cases (e.g. rectangular or trapezoidal shapes), this shape
factor can be calculated analytically. For example, a rectangular shape has a shape factor of
Finally, the rms value
In our case, the spectral responsivity of the detector is determined from
the DC lock-in amplifier output voltage
To summarize, the amplitude
Consequently, the spectral responsivity must be defined with respect to a
selected temporal shape. Typically, the fundamental sine-shaped component is
used for this definition because only this component participates to the
signal
In this publication, given spectral responsivities are related to a sine wave radiant power modulation and calculated as described by Budzier and Gerlach (2010). The impact of the temporal radiant power shape on the resulting spectral responsivity will be discussed in detail in the following sections. Initial calculations have been performed by approximating these temporal shapes with trapezoidal functions on geometrical considerations. However, it has been found that this is not precise enough to calculate the spectral responsivity with lowest possible uncertainties, especially at the blackbody facility.
Therefore, the temporal shapes of the modulated radiant fluxes behind the
chopper wheel at these facilities have been sampled by turning the chopper
wheel in steps of 0.5
The result of the temporal shape of the radiant flux modulation measured
with the thermopile detector TS-76 at the cryogenic electrical substitution
radiometer facility can be fitted well with a trapezoid function. The
trapezoid shape is basically defined by the beam radius in the plane of the
chopper wheel, which is about 1 mm. Measurement results and trapezoidal fit
are depicted in Fig. 4. The temporal shape of the flux modulation at the pyroelectric detector can be estimated by using the geometric data of the pyroelectric detector as input parameters for the trapezoidal fit. The shape factor
Normalized detector signal of the thermopile detector measured when turning the chopper wheel step by step at the cryogenic electrical substitution radiometer facility (blue), which is in line with the trapezoid-shaped fit (red).
In contrast to the cryogenic electrical substitution radiometer facility, a fit of the chopped radiant flux, using a simple trapezoid-shaped function, is not sufficient at the blackbody facility because the circular shapes of the detector and the blackbody apertures have a strong impact due to the large blackbody and detector aperture compared to the width of the chopper blades (see Fig. 5). Therefore, a model function for an estimation of the temporal shape of the modulated radiant flux at the detector behind the chopper at the blackbody facility will be derived in the following.
Geometry at the blackbody calibration set-up. On the left is the
aperture of the blackbody and on the right the detector aperture. The
chopper (blue) is located between the blackbody and detector. Its vertical
position
In general, the radiant flux
The apertures of the blackbody and the detector are parallel and coaxial
(
If there is no chopper wheel, the integration over
However, for the calibration of the pyroelectric detectors, a chopper wheel
between the detector and the blackbody radiator is necessary as it
periodically shades the detector aperture. For this reason, the integration
in Eq. (15) needs to be carried out, taking into account the shadow of the
chopper on the detector area. The set-up depicted in Fig. 5 is described by the radius
The radius
In the following, the radiant flux
Radiation from an infinitesimal spot at the vertical position
Depending on the chopper position For a chopper position For a chopper position All other positions
Consequently, the irradiated area
The next step is to carry out the integration over
The integration over
Finally, the radiant flux
The temporal shape of the chopped radiant flux can then be calculated by
using the relation between position
The measurement of the signal of the thermopile detector TS-76, when turning
the chopper wheel manually in steps of 0.5
Normalized detector signal of the thermopile detector measured when rotating the chopper wheel in front of the blackbody step by step (blue) and the result of the model function according to Eq. (25) (red).
The calculation of the shape factors
The use of the model function Eq. (25) furthermore enables us to optimize the
positioning of the chopper wheel. Fig. 7 shows the dependence of the shape factor
Theoretical calculation of the shape factors
The theoretical calculation of the shape factor
In general, the calculations show the importance of considering the exact geometrical beam set-up and the accurate temporal shape of the modulated radiant flux especially if the experimental set-up forces one to deviate from an ideal rectangular modulation shape. It should not be forgotten that an appropriate shape factor always has to be applied if one intends on using the calibrated pyroelectric detector for absolute radiometric measurements. Neglecting these considerations leads to a significant measurement error that is easily larger than the overall measurement uncertainty, which will be discussed in Sect. 4.2. In contrast to that, misaligning or a small tilt of the detector can be neglected with respect to the overall uncertainty.
The pyroelectric detectors which have been calibrated regarding their
spectral responsivity at both primary standard facilities are of the type
LIE-651, as manufactured by InfraTec. These detectors have, additionally, been equipped with apertures of a nominal diameter of 4 mm. The diameter of each aperture has been measured traceable to the SI to be able to calculate the radiant flux at the blackbody facility. The detectors do not have any window to avoid the spectral dependencies of the responsivity as effectively as possible. They are, furthermore, implemented in a temperature-stabilized housing, which reduces the influence of variations in the surrounding temperature and leads to a reduced detector noise. The detector housings can be temperature controlled to avoid deviations caused by the temperature sensitivity of the pyroelectric detector, which is typically
The pyroelectric material of this detector type is lithium tantalite
A total of two pyroelectric detectors have been calibrated for their spectral responsivity at both the cryogenic electrical substitution radiometer facility and the blackbody radiator facility. The calculation of the spectral responsivity and correction for the temporal signal shape behind the chopper wheel has been applied, as described in Sect. 3. The calibration results for one of the pyroelectric detectors are depicted in Fig. 8. The results for the second pyroelectric detector are similar, and no significant sample variation was observed.
The spectral responsivity of a pyroelectric detector measured at the cryogenic electrical substitution radiometer facility (red) and the blackbody radiator facility with optical bandpass filters (blue). The error bars indicate the standard measurement uncertainty.
It has to be noted that the sensitive area of the pyroelectric detector is completely irradiated within the area of the aperture at the blackbody radiator facility but only at its centre by the laser radiation at the cryogenic electrical substitution radiometer facility. Hence, the inhomogeneity of the spectral responsivity over the sensitive area leads to a difference in the calibration results between the two different approaches. The observed slight increase of about 1 % of the spectral responsivity at the edges of the sensitive area of the pyroelectric detector compared to that in the centre leads to a systematically higher result for the spectral responsivity of about 0.3 % for calibration at the blackbody radiator facility. This effect is not corrected in the data depicted in Fig. 8.
The measurement uncertainties at the two measurement facilities have been discussed in detail, relative to the calibration of thermopile detectors of type TS-76 (Pohl et al., 2019, 2021). In general, these uncertainty budgets also apply to the calibration of the pyroelectric detectors.
The main uncertainty contribution for the calibration at the cryogenic electrical substitution radiometer is caused by stray radiation. The incident beam in the detector plane has a radius of about 1 mm with a certain amount of stray radiation around that spot. This stray radiation has a different impact on the resulting signal of the pyroelectric detector (respectively, the cryogenic radiometer) due to their different aperture sizes. This leads to the main contribution in the measurement uncertainty budget of the detector calibration. Other influences such as detector noise and wavelength uncertainty are also considered but are comparatively small. The overall measurement uncertainty for the detector calibration is in the range between 1 % and 5 % (Pohl et al., 2019).
The measurement uncertainties for the calibration at the blackbody radiator
range between 5 % and 14 %. The main contributions are as follows (Pohl et al., 2021):
Other sources of uncertainties such as detector noise, temperature
instabilities or geometry are also considered in the overall measurement
uncertainty budget but are not decisive contributions. An additional
uncertainty contribution which is especially related to pyroelectric
detectors is caused by the dependence of the spectral responsivity on the
chopper frequency. The sensitivity of this effect was measured to be about
8 % per hertz at a frequency of 10 Hz. Therefore, the accuracy of the
chopper frequency is of great importance. The chopper frequency is
controlled by the lock-in amplifier SR860, which uses an internal frequency
counter with an accuracy of 25 ppm (parts per million; Stanford Research Systems, 2016). Measurements were conducted with this frequency counter to examine the frequency stability and accuracy of the chopper wheel, which show that the frequency deviation is very small and only of statistical origin. Hence, the resulting uncertainty contribution to the determination of the spectral responsivity is insignificant (
The PTB established two pyroelectric detectors as transfer standards for the
SI traceable measurement of radiant power in the wavelength range between
1.5
In contrast to other types of detectors, pyroelectric detectors measure temporal changes in the input radiant power and are, therefore, operated with chopped radiation. This leads to peculiarities which have to be considered, especially if pyroelectric detectors are used for absolute measurements. The spectral responsivity of this type of detector has to be carefully defined, and clearly stating the definition which is used is recommended. This is especially important since differing definitions are in use.
The beam geometry at the measurement facility determines the temporal radiant flux shape of the chopped radiation at the detector, and this temporal shape has a strong effect on the signal output of the detector and, therefore, has to be considered for the correct calculation of the spectral responsivity. For the same reason, the comprehensive consideration of the temporal shape of the chopped radiant flux is also of great importance if using the calibrated detector for accurate absolute radiometric measurements is intended. In the case of the blackbody radiator facility, it has been found that the factor which considers the temporal shape of the radiant flux ranges between 0.95 and 1.27, depending on the position of the chopper in the set-up. This underlines the importance of an accurate consideration of the temporal shape of the radiant flux to perform correct absolute measurements with pyroelectric detectors and to obtain the lowest possible uncertainties. If the detector signal is measured with a lock-in amplifier, the proper way to correct for background signals, furthermore, has to be noted.
The results of the two calibration approaches are consistent with each other,
and the measurement uncertainties of the calibrations are in the range
between 1 % and 14 %. The calibrated pyroelectric detectors can be
used for the dissemination of the spectral responsivity
All relevant measurement results are shown in the publication in Sects. 3 and 4. However, the underlying measurement data are not publicly available and can be requested from the authors, if required.
TP, PM, JH, UJ and LW worked together on the development and realization of the different measurement approaches, data evaluation and interpretation. JH initiated the work of infrared detector calibration with blackbody radiation. TP, PM and UJ performed the calibration measurements at the cryogenic radiometer and the blackbody radiator facility. TP, PM and LW evaluated the measurement results and wrote the article with contributions from all authors.
The contact author has declared that neither they nor their co-authors have any competing interests.
The component producers/suppliers are mentioned for identification purposes only. Such an identification does not imply any recommendation or endorsement by the PTB, nor does it imply that the producers/suppliers identified are necessarily the best available for the purpose.Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Significant technical support by Marco Schulz, Ingmar Müller and Klaus Anhalt, for the operation of the blackbody radiator, is gratefully acknowledged.
This open-access publication was funded by the Physikalisch-Technische Bundesanstalt.
This paper was edited by Alexander Bergmann and reviewed by two anonymous referees.