Precision power measurements of terahertz (THz) radiation are required to establish metrological applications in the THz spectral range. However, traceability to the International System of Units (SI) has been missing in the THz region in the past. The Physikalisch-Technische Bundesanstalt (PTB), as the national metrology institute of Germany, determines the spectral responsivity of detectors for THz radiation by using two complementary optical methods: source- and detector-based radiometry. Both approaches have been successfully prototyped, and a pyroelectric THz detector with a well-defined aperture is used to verify the consistency of the two independent calibration methods. These primary investigations led to the design of a new measurement facility for the determination of THz radiant power and the responsivity calibration of THz detectors traceable to the SI.
©2010 Optical Society of America
In the terahertz frequency range of the electromagnetic spectrum neither practical and inexpensive radiation sources nor well characterized and calibrated detectors have been available in the past. In the past two decades, however, remarkable progress was made in the development of THz sources and detectors, like photoconductive antennas, photomixers and quantum cascade lasers, while also many advances in THz spectroscopy and imaging were achieved. Driver of these developments was the increasing number of potential applications of THz radiation in non-destructive materials testing, homeland security, biological and medical sciences, global environmental monitoring and information and communications technology. In order to further improve radiation sources and detectors and their applications metrological methods have to be developed in the THz range to reduce the present uncertainties of their radiometric quantities, such as the radiant power of sources or the responsivity of detectors . This is the specific subject of the “Terahertz Radiometry” project of the Physikalisch-Technische Bundesanstalt (PTB), the national metrology institute of Germany. The idea is to extend optical radiometric methods  which are well established in the visible and infrared spectrum into the THz spectral range and to investigate and overcome possible restrictions caused by the much longer wavelengths, such as 300 µm for a frequency ν = 1 THz.
In this paper two complementary radiometric methods are described, a source- and a detector-based approach to THz radiometry, and present their results. Source-based radiometry is based on a blackbody radiation source which delivers broadband radiation with its radiometric properties only determined by the blackbody temperature. The emitted spectral radiance can be calculated from Planck's law and is used in combination with several well characterized THz filters to determine the irradiance responsivity of THz detectors within the transmitted bandpass of the applied filter combinations .
Detector-based radiometry utilizes an electrical substitution radiometer as a primary detector standard which relies on the substitution of radiant power by electrical heating power. The lowest uncertainty of a spectral radiant power measurement is achieved when performed with a cryogenic radiometer, operated in a liquid helium cryostat, as the primary detector standard and continuous-wave (cw) lasers as monochromatic THz radiation sources . The precise optical power measurement is then used to determine the power responsivity of a THz detector if it is large enough to collect the radiation without clipping any power.
The results of both methods for different types of THz detectors are presented and compared in this paper. Based on these results a dedicated THz calibration facility is now under development at PTB. A core instrument of this new facility is a THz molecular gas laser with a wide tuning range from 1 THz to beyond 5 THz. Its stable THz output power of 10 mW is sufficient to use an electrical substitution radiometer at room temperature as the primary detector standard instead of a cryogenic radiometer.
2. Source-based THz radiometry
Planck’s law of radiation quantifiably describes the spectrum of a blackbody radiator at a given temperature, i.e. it yields its spectral radiance. This is also valid in the THz spectral range for a cavity temperature radiator if the cavity walls show a sufficiently high emissivity to provide an effective emissivity of the cavity very close to unity and if the dimensions of the cavity are large compared to the wavelength of the radiation. In order to use the THz range of the broad spectrum of a blackbody near room temperature it is necessary to suppress the intense radiation in the mid infrared spectral range by an appropriate set of filters. As shown by a specific filter combination in Fig. 1 as an example a suppression of more than six orders of magnitude of the unwanted radiation at shorter wavelengths is necessary to obtain THz radiation with appropriate spectral purity. Both, the high wall emissivity of the cavity radiator and the high and known suppression ratio of the applied filters are the primary challenges of this experiment and have been carefully determined . By knowing the distance between the blackbody and the detector as well as the size of the aperture of the blackbody the spectral irradiance incident on the detector can be calculated. As the radiation homogeneously irradiates the detector its entrance aperture is overfilled, therefore the irradiance responsivity of the detector is calibrated. The incident radiant power can be calculated if the size of the aperture is known and if the responsivity of the detector is spatially uniform i.e. independent of the position inside the entrance aperture. Only in this case the measured irradiance responsivity can be converted to the power responsivity of this detector.
2.1 Experimental setup
The measurement setup for the determination of the irradiance responsivity of THz detectors is described in detail in  and is shown in Fig. 2 . A water-bath blackbody working in a temperature range from 15 °C to 90 °C with a temperature stability of approx. 10 mK is the source for calculable THz radiation. This blackbody consists of a copper cavity with an inner diameter of 60 mm and an inner length of 280 mm. The bottom plate of the cavity is tilted by an angle of 30° with respect to the optical axis. The inner wall of this cavity was coated with Herberts 1356H, a special coating developed for high emissivity in the THz range. An effective emissivity of this THz blackbody near to unity results.
For AC-detection a gold plated optical chopper in front of the blackbody modulates the signal. Its axis of rotation is tilted by 45° with respect to the optical axis. It periodically images in reflection the radiation of a cold reference blackbody on the detector under test. The cold reference consists of a dewar filled with liquid nitrogen and a piece of THz absorbing foam (ECOSORB®) swimming on top of the liquid nitrogen. The foam acts as a surface of high emissivity. The ice coated walls with their high emissivity act as a cavity and enhance the emissivity of the foam. The radiation temperature of this radiator is approximately 77 K. The only optical element in front of the detector is a filter holder containing a combination of up to four low-pass and band-pass filters. The beam path from the filter holder to the THz detector is shielded from radiation of the environment by a cylindrical absorber tube made of ECOSORB®. The diameters of all elements in the beam path are large enough not to change the homogenous radiation field of the blackbody radiator at the detector position. Different types of THz detectors were investigated: pyroelectric detectors at room temperature and silicon-composite bolometers working at cryogenic temperatures. The signal of all detectors is measured with a lock-in amplifier.
2.2 Irradiance responsivity results
The signal of the detector originates from the spectral radiances of the blackbody multiplied by the spectral transmission of the filter combination and by the transmittance spectrum of the air along the beam path. This product has to be integrated over the transmission bandwidth of the filter combination. The resulting irradiance on the detector is calculated from this integral, the known distance from the blackbody to the detector and the area of the blackbody aperture. The result is shown in Fig. 3 for a variety of applied filter combinations. A logarithmic scale is chosen because the irradiance strongly decreases with increasing wavelength according to Planck’s law of radiation (~λ −4).
As an example for calibrated THz detectors the resulting irradiance responsivities of two silicon-composite bolometers of the same type operated at a low temperature by cooling with liquid helium are shown in Fig. 4 . Their responsivities do not change strongly with wavelength. The systematic difference in responsivity by a factor of about two originates from the different construction of both bolometers (entrance window, Winston cone, heat link). The measurements shown in Fig. 4 have been performed with the THz blackbody at 80 °C and the cold reference blackbody at approximately 77 K. The emitted radiation in the mid infrared spectral range changes much stronger with the temperature of the blackbody than in the THz range. This enables a sensitive check that the suppression of the radiation at shorter wavelengths has been correctly determined. When the temperature of the reference blackbody is changed from 77 K to 296 K (23 °C) while the THz blackbody is kept at 80 °C the signal decreases by about 80%. However, the resulting spectral irradiance responsivity of the applied Si-bolometer is in good agreement with the results from the cold reference source as shown in Fig. 5 . In  it was already shown that changing the temperature of the THz blackbody from 80 °C to 23 °C while keeping the cold reference blackbody at 77 K also does not significantly influence the resulting responsivity of a detector.
The result of a pyroelectric detector, a DLATGS (deuterated L-alanine doped triglycene sulphate) detector is shown in Fig. 6 . Due to operation at room temperature the noise equivalent power of the DLATGS is three orders of magnitude higher than that of the silicon bolometer. Its responsivity is three orders of magnitude smaller. In contrast to the bolometer the pyroelectric detector has a well defined aperture of 2 mm in diameter and the incident power can be calculated from the irradiance depicted in Fig. 3. The result is less than 100 pW for the filter combinations with a center wavelength above 400 µm. As a consequence of the low power and the resulting poor signal to noise ratio, the statistical uncertainty of the determined responsivity strongly increases with wavelengths. This limits the calibration of room temperature detectors with blackbody radiation towards longer wavelengths.
3. Detector-based THz radiometry
The basic principle of detector-based radiometry relies on the substitution of the radiation heating of a highly absorbing cavity by electrical heating, which leads to traceability of optical power measurements to the International System of Units (SI). This method is well established in the visible and the near infrared spectral range at PTB . It allows for a precise determination of the spectral radiant power responsivity of radiation detectors and of the associated uncertainty budget. The aim of a pilot measurement was to prove the capability of the method for the first time in the THz region. This is described in detail in .
3.1 Experimental setup
A cw THz quantum cascade laser (QCL) was used for the first calibration of a THz radiation detector against a cryogenic substitution radiometer (CR) which is part of an existing calibration facility for UV and NIR radiation . The QCL came from the German Aerospace Center. This laser system had been well characterized with respect to output power stability, beam profile, emission linewidth, and frequency stability . If the system is cooled to a temperature of 25 K it emits cw laser radiation at a frequency of 2.5 THz. The corresponding wavelength of 120 µm is more than 50 times larger than the wavelengths of radiation used so far with the CR. Therefore the different propagation of the THz laser radiation had to be considered and the design of a suitable optical setup was necessary. To minimize unwanted diffraction effects a TPX lens collected the divergent radiation in a short distance behind the QCL and focused it into the entrance aperture of the CR (Fig. 7 ). Special care was taken to achieve a nearly Gaussian beam profile with a first diffraction minimum ring similar in size and position to the diameter of the entrance aperture of the CR. By this means the uncertainty of the power measurement is reduced considerably .
The difficulties to attain the required Gaussian profile in the focus is illustrated by a video of the QCL beam propagation behind the TPX lens. A thermal imaging camera with a micro bolometer focal plane array (FPA), original designed for the spectral range around 10 µm, is used without optics to record the beam profile at 2.5 THz at different locations along a distance of 400 mm in direction of propagation. Its FPA has 384 x 288 pixels with a pixel size of 51 µm which is large enough for the THz radiation. The video sequence of Fig. 8 (Media 1) starts at 230 mm in front of the focus and stops at 170 mm behind the focus. At the starting point the profile exhibits a complex structure with several local maxima. On its way to the focus the size of the profile is reduced and its shape changes dramatically. Only at a very short distance in front of the beam waist, the power is concentrated in a single central maximum and is converted into the focal axially symmetric Gaussian profile. The focal diameter is small enough to clearly under fill the detector aperture. Behind the focus, the width increases but the shape remains more or less a Gaussian profile.
The calibration procedure consists of two steps. First the power of the QCL is measured by the CR. Then the detector under test (DUT) is moved into the beam at exact the same position as the CR (Fig. 7). To equalize radiation losses in both cases i.e. to minimize errors of comparing the readings of both instruments a wedged window identical to the vacuum window of the CR is placed in front of the DUT and the entrance apertures of the CR are reproduced in front of the detector. By this means a total standard uncertainty of 7.3% could be achieved in this first calibration of a power meter at 2.5 THz traceable to the SI. As explained in Ref. , the largest uncertainty contribution of 7% originates from the limited knowledge of the thickness of the coating inside the absorbing cavity of the CR. All other contribution sum up to only 2%. In summary the difficulties caused by the long wavelength and associated diffraction losses could be solved.
3.2 Power responsivity results
A pyroelectric detector with a cavity absorber in a radiation trap design was chosen as first detector to be calibrated against the CR. The detector head has a built-in chopper which is operated at a frequency of 30 Hz. The head is connected to a power meter with an integrated lock-in amplifier. The power meter electronics converts the detector signal and displays it as power in units of Watts. The user can modify the digital reading by the input of a correction factor larger than one which accounts for radiation losses caused by a non perfect absorption of the cavity absorber. Although the cavity absorber consists of two plane surfaces which abut in the center of the detector there is only a diminutive variation of its responsivity (Fig. 9 ). For calibration its circular entrance aperture of 1 cm2 (diameter 11.3 mm) was reduced by an additional entrance aperture of 5.8 mm diameter which is identical in size to that in front of the CR cavity. During the investigation of its properties it turned out that the responsivity of the trap detector is strongly polarization dependent. This is caused by the 60° angle of incidence for the first absorption inside the cavity absorber. Due to the favorable Brewster condition of p-polarization the correction factor for s-polarized Terahertz radiation is 12% larger than for p-polarized radiation.
For measuring the homogeneity of the pyroelectric trap detector the focal spot size of the QCL was reduced by an aperture of 2.5 mm centered in the focus of the QCL. The detector is placed behind this fixed aperture as close as possible and displaced perpendicular to the beam. The result of a horizontal scan across the full detector aperture is shown in Fig. 9 for three different heights. Obviously, the responsivity does not change more than 5% within a central area of 8 mm diameter. Therefore this pyroelectric trap detector is well suited for THz power measurements because its reading does not change locally within the reduced aperture of 5.8 mm diameter used for the calibration of its power responsivity.
The homogeneity of a silicon-composite bolometer used for calibration of its irradiance responsivity described in section 2 was tested. Due to its operation at low temperatures such a bolometer is three orders of magnitude more sensitive than a pyroelectric detector which necessitates a similar reduction of the radiant power to avoid saturation. By two wire grid polarizers with nearly crossed orientation the laser power was reduced by a factor of 22. In addition, the diameter of the aperture in the focus of the QCL was minimized to 0.7 mm which led to a further power reduction by a factor 8. Thus the bolometer could be operated in a linear regime during its displacement across the beam.
The result of Fig. 10 can be understood by the optical design of the bolometer. Inside the cryostat there is a Winston cone directly in front of the bolometer chip. This is a non-imaging light-collecting entrance cone with a parabolic shape and a reflective inner surface which concentrates the radiation from the large entrance area onto the small bolometer surface. Consequently the measurement of its homogeneity exhibits no plateau but a parabolic change of responsivity. The height of the central maximum depends on the spot size of the incident beam focus. The strong spatial variation of its responsivity clearly indicates that this kind of instrument is not suited to determine the radiant power of an impinging laser beam but rather the irradiance of a spatially extended homogeneous THz radiation field of e.g. a blackbody source (overfilling the large entrance aperture of the Winston cone). The same restriction applies to all detectors with light-collecting entrance cone in front of a small radiation sensitive element such as e.g. typical commercially available Golay cells.
4. Comparison of both methods
For a comparison of both optical methods the power responsivity of the calibrated pyroelectric trap detector was measured also by source-based radiometry. This is possible because its large aperture size of 1 cm2 is exactly known and the homogeneity and the polarization dependence of the power responsivity has been measured before. If used in a quiet environment the pyroelectric trap detector can resolve a power of a few tenths of µW. Due to its construction with a different pyroelectric crystal to achieve a homogeneous response within its large aperture this detector is less sensitive than the DLATGS detector discussed in section 2.2. But it is just sensitive enough to measure the weak THz spectral range of the blackbody radiation behind a THz filter combination with a broad bandwidth and a center wavelength up to 150 µm which results in an irradiance of a few mW/m2.
The results are shown in Fig. 11 . The correction factor introduced in section 3.2 is plotted as a function of the center wavelength of the applied filter combination together with the detector-based result at 2.5 THz which corresponds to a wavelength of 120 µm. The uncertainty bars in this figure are the expanded uncertainty with coverage factor k = 2, i.e. twice the standard uncertainty, yielding a confidence level of 95%. In detector-based radiometry it is the total uncertainty, combining statistical (type A) and systematic (type B) sources of uncertainty according to the guide to the expression of uncertainty measurement (GUM) . The uncertainty of the source-based results is the statistical uncertainty only. Its increase reflects the increasing signal variation when the irradiance of blackbody drops down with increasing wavelength according to Planck’s law. If this is taken into account both methods exhibit a consistent result for the responsivity of the detector.
5. Calibration facility
The measurement conditions of calibrating THz detectors, the experimental results and the associated uncertainties were analyzed and influenced the design of a dedicated THz detector calibration facility which is now set up at PTB using detector-based radiometry for achieving calibration uncertainties less than 10%. A core instrument of this new facility is a THz molecular gas laser optically pumped by an integrated 50 W single-frequency CO2-laser. Its tuning range from 1 THz to beyond 5 THz is based on discrete THz lines in different gases, such as e.g. CH3OH, CD3OH, CH2F2. Stable THz output power is achieved by stabilizing the frequency of the pump laser. This is shown in Fig. 12 by a power variation of less than ± 0.4% over a period of 30 minutes. The remaining small power drift will be corrected for by using a monitor detector during calibration.
The output power of more than 10 mW of the THz molecular gas laser is sufficient to use an electrical substitution radiometer at room temperature as the primary detector standard with the calibration facility. As an advantage, a room temperature radiometer requires no isolation vacuum and therefore an entrance window can be avoided. Room temperature substitution radiometers are used as absolute cavity radiometer systems for measuring the solar irradiance to provide traceability to the world radiometric reference of solar radiation . The measurement standard was introduced as PMO6-CC by the Physikalisch-Meteorologisches Observatorium Davos (PMOD) in Switzerland which serves as the World Radiation Center (WRC) . This instrument is modified to become a new primary THz detector standard. In a cooperation of PMOD und PTB an engineering model is currently tested with the radiation of the THz molecular gas lasers.
It is very important for a primary radiometer that its cavity almost completely absorbs the impinging radiation. For this reason the coating of the engineering model is investigated in regard of its reflection losses in the THz wavelength range. This is illustrated by a measurement on a plane specimen of the cavity absorber. A Fourier transform spectrometer, a VERTEX 80v of Bruker Optik GmbH, is used to determine the specular reflection at an angle of incidence of 12 degree. Both spectra in Fig. 13 originate from slightly lateral shifted mounting positions of the same sample inside the spectrometer. The prominent modulation period which corresponds an optical thickness (n*d) of 75 µm is caused by the beam interference of the front and back side reflection of the coating layer partly transparent in the THz spectral range. The additional periodic fine structure indicates that the thin film heating structure underneath the coating also influences the absorption capability in terms of its magnitude and spectral variation as well. Nevertheless, this first investigation already reveals the modified room temperature substitution radiometer as a promising candidate for a future primary detector standard for THz radiation. The goal of this work at PTB is to expand its present SI-traceable calibration services of power responsivity at 2.5 THz to the whole tuning range of the THz molecular gas laser.
Two optical methods, source-based and detector-based THz radiometry, have been experimentally investigated with respect of their capability to calibrate THz detectors traceable to the SI. Source-based THz radiometry determines the irradiance responsivity at low power levels available with blackbody radiators integrated over the bandwidths of filter combinations which select specific ranges of the THz part of a blackbody spectrum. Detector-based radiometry determines the power responsivity at the specific wavelength of a cw THz laser emitting polarized coherent radiation. First used at 2.5 THz to calibrate a suitable THz detector against a primary detector standard of PTB this method is now applied in a new THz detector calibration facility. A molecular gas laser tunable from 1 THz to 5 THz enables PTB to expand its current calibration services at 2.5 THz with an proved uncertainty of less than 10% to the whole frequency range of this laser in the near future.
The authors would like to thank Heinz-Wilhelm Hübers and Heiko Richter from the German Aerospace Center for providing the QCL in a fruitful cooperation, Peter Meindl and Lutz Werner from the PTB for enabling traceability by their cryogenic radiometer, and Wolfgang Finsterle from the PMOD for the present cooperation to develop a room temperature THz radiometer.
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