Three-element trap filter radiometer based on large ... - OSA Publishing

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Research Article

Vol. 55, No. 15 / May 20 2016 / Applied Optics

Three-element trap filter radiometer based on large active area silicon photodiodes S. G. R. SALIM,1,3,* K. ANHALT,2 D. R. TAUBERT,2

AND

J. HOLLANDT2

1

National Institute for Standards (NIS), President Sadat Street, El-Haram, Giza, P.O. Box 136, Egypt Physikalisch-Technische Bundesanstalt (PTB), Abbestraße 2-12, 10587 Berlin, Germany 3 Former guest scientist at the Physikalisch-Technische Bundesanstalt (PTB), Abbestraße 2-12, 10587 Berlin, Germany *Corresponding author: [email protected] 2

Received 1 March 2016; revised 18 April 2016; accepted 18 April 2016; posted 18 April 2016 (Doc. ID 260368); published 12 May 2016

This paper shows the opto-mechanical design of a new filter radiometer built at the Physikalisch-Technische Bundesanstalt, Germany, for the accurate determination of the thermodynamic temperature of high-temperature blackbodies. The filter radiometer is based on a three-element reflection-type trap detector that uses three large active area silicon photodiodes. Its spectral coverage and field of view are defined by a detachable narrow-band filter and a diamond-turned precision aperture, respectively. The temperature of the filter radiometer is stabilized using a water-streamed housing and is measured using a thin-film platinum thermometer placed onto the first photodiode element. The trap “mount” has been made as compact as possible, which, together with the large active area of the chosen photodiodes, allows a wide field of view. This work presents the design of the filter radiometer and discusses the criteria that have been considered in order for the filter radiometer to suit the application. © 2016 Optical Society of America OCIS codes: (120.6780) Temperature; (120.5630) Radiometry; (120.4640) Optical instruments; (120.2440) Filters. http://dx.doi.org/10.1364/AO.55.003958

1. INTRODUCTION Filter radiometers (FRs) are fundamental detection tools in optical radiation metrology. A filter radiometer (FR) with a known spectral response and a well-defined measurement geometry can be used to determine the thermodynamic temperature of blackbody sources, which then allows the establishment of the radiometric spectral radiance and irradiance scales [1,2]. When used with a V λ corrected filter, a link between radiometry and photometry can be obtained, through which the candela and lumen can be realized [3]. Due to the possibility of optimizing their spectral coverage and bandwidth over a wide spectral range, FRs are used in wide-ranging applications as basic detection instruments, for example, in the lighting industry, the medical sector, and remote sensing [4–6]. Typical FRs, especially those used for commercial applications, use single photodiodes as detection elements. This results in significant loss in the incident light due to reflections by the photodiode [7]. On the other hand, trap-designed FRs in which several photodiodes are used, in either a reflection or transmission configuration, absorb almost all incident light reaching the photodiodes, which results in significantly low backreflection as well as improved external quantum efficiency [8,9]. Trap detectors, in general, have considerably reduced sensitivity to the state of polarization of the light they measure [10,11]. These valuable characteristics have made them superior when compared to 1559-128X/16/153958-08 Journal © 2016 Optical Society of America

single element photodiodes in disseminating the accuracy available in the cryogenic radiometer and even in comparing these radiometers when direct comparison is not possible [12]. In 1999 Yamada et al. showed the possibility of using metal– carbon binary eutectic alloys as potential fixed points above the freezing point of copper (T Cu 1357.77 K) [13]. This has been followed by considerable international effort coordinated by the Consultative Committee for Thermometry (CCT) to construct and improve the thermal and radiometric performance of metal (carbide)–carbon (M(C)-C) fixed points [14,15]. This effort is mainly aimed at identifying the thermodynamic temperature of some of these fixed points as well as providing a mise-en-pratique (MeP-K) for the new comprehensive and effective redefinition of the kelvin [16]. Having the ability to deliver the thermodynamic temperature of these fixed points has given FRs further potential [17]; however, their ability to achieve such an objective with low uncertainty levels, expected to be less than 100 mK (k 1) at T Cu , is closely reliant on improvements in their radiometric performance [18]. In accordance with the international research direction to achieve the stated uncertainty, we present a design of a new trap FR built to deliver accurate thermodynamic temperature measurements. The design criteria that have been considered are discussed and presented along with a preliminary evaluation of the FR and an estimation of the expected uncertainty levels.

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2. DESIGN CRITERIA A. Suitability for Application

A typical FR basically consists of an optical sensor combined with a spectral filter and a precision aperture. To measure the thermodynamic temperature, a calibrated FR can be used in “irradiance mode” to measure the radiant flux emitted from the blackbody source through a well-defined geometry [19], as shown in Fig. 1(a). The temperature of the blackbody source in such a case can be determined from the FR voltage V T as Z λ f SλLBB λ; T dλ; (1) V T Cgπ λi

where Sλ is the spectral power responsivity of the FR over the spectral range from λi to λf ; LBB λ; T is the radiance of the blackbody at a temperature T and wavelength λ (as given by Planck’s radiation law); C is a factor that considers the amplifier gain, corrections due to possible nonideal emissivity and uniformity of the blackbody, size-of-source (SSE) and out-of-band (OOB) effects of the FR, as well as corrections related to the possible nonlinearity and temperature dependence of its responsivity; and g defines the geometry of the experiment in terms of the blackbody aperture r 1 , the FR aperture r 2 , and the distance d between them. This geometric factor g can be given as [20] g

2πr 21 r 22 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : r 21 r 22 d 2 r 21 r 22 d 2 2 − 4r 21 r 22

(2)

It is not generally possible for FRs used in the irradiance mode to directly measure the thermodynamic temperature of small aperture fixed points, as this requires an imaging system. However, a lens of known transmittance can be used to image the fixed point cavity onto the FR through a well-defined geometry. This method is known as the “hybrid method” [21]. Although simple, the resultant SSE effect due to adding the lens has to be thoroughly identified [22]. An imaging radiation thermometer can also be used in ‘radiance mode’ to measure the temperature of fixed points, as shown in Fig. 1(b) [23]. The radiation thermometer in such a case compares the radiance of the fixed point with that of a variable temperature blackbody whose thermodynamic

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temperature is determined by a calibrated FR. An absolutely calibrated radiation thermometer can be used to directly measure the thermodynamic temperature of the fixed point. However, the small bandwidths of most laser systems used in the calibration of radiation thermometers can introduce large uncertainties due to interference with optical elements of the thermometers [24]. Meanwhile, their calibration using monochromator-based systems requires a strong signal level [25]. In both cases the reported uncertainty of absolute calibration of the radiation thermometer is generally larger than those reported with FRs [19,22]. In order for the FR to deliver accurate thermodynamic temperature measurements it should ideally have a high signalto-noise ratio. This requires a photodiode with a high shunt resistance along with an optimized irradiance level. The radiometer should also show minimum drift and aging due to the effects of ambient conditions and exposure to thermal radiation. Furthermore, the responsivity of the FR has to be highly linear due to the significant difference in the power level of the calibration source (in the range of nanowatts) and that of the measured blackbody source (in the range of microwatts). Related to this, the FR has to show minimum sensitivity to the difference in polarization state between the calibration and the test source. The radiometer should also have the lowest possible, yet precisely defined, OOB signal. In addition, the FR aperture (and, of course, the blackbody aperture) has to be precise enough to accurately define the measurement geometry and minimize diffraction losses—i.e., it should ideally be a circular, knife-edge aperture of precisely measured diameter. Moreover, the instrument’s field of view (FOV) has to be optimized to suit the measurement geometry, meanwhile showing minimum influence of background stray light sources. B. Photodiode

The application in which the FR is used identifies the spectral coverage of the photodetector used. In the UV, VIS, and NIR optical domains, silicon photodiodes are considered ideal sensors due to their high linearity as well as their uniform surface response and high signal-to-noise ratio [8]. The spectral coverage of silicon photodiodes, along with an application-oriented spectral filter, can enable temperature measurements from 3500 K down to the zinc fixed point (692.6 K) [26]. Three large area silicon photodiodes from Hamamatsu, type S1337-21, have been chosen as detection elements for the FR. This type covers the spectral range from 200 to 1100 nm with maximum responsivity at around 930 nm. C. Spectral Filter 1. Spectral Range

Fig. 1. Thermodynamic temperature measurement by (a) irradiance mode and (b) radiance mode.

The optical properties of the filter directly impact the performance of the FR as a whole as well as its suitability for the application. Interference filters of narrow-band spectral coverage and broadband colored glass filters are commonly used in FRs that measure thermodynamic temperature. Since the spectral coverage of the FR is mainly defined by the in-band (IB) spectral range of the filter, this IB spectral range should be carefully selected so as to enable the FR to reveal minor changes in, thus being more sensitive to, the temperature of the blackbody it measures.

Research Article


The partial derivative of Plank’s law with respect to temperature shows that the change in radiance at a given blackbody temperature is higher at shorter wavelengths compared to that at longer wavelengths. For example, the radiance of a blackbody at 1500 K changes by 0.16% at 400 nm as the temperature varies by 100 mK, while the change is only 0.06% at 1000 nm. Accordingly, FRs having short effective wavelengths can reveal minor changes in the blackbody temperature compared to those having longer effective wavelengths. However, there are other limitations that have to be considered in such a case, such as the reduced response of the silicon photodiode and the relatively low radiant flux of the blackbody, especially when it runs at a relatively low temperature. 2. Out-of-Band Signal

The OOB signal can be defined as the signal measured by the FR in the spectral range it is supposed to block. In order for the OOB signal to be negligible, it should be kept very low compared to the signal transmitted through the IB spectral window—ideally less than the 10−4 level. Otherwise, the FR must be calibrated over the full spectral range of the photodiode response and the OOB signal has to be treated as an integral part of the signal delivered by the FR. The ratio of the OOB to the IB signal can be given as R λi F R λf Si OOB λi Si SλT λLλ; T dλ λf F SλT λLλ; T dλ ; R λf F IB SλT λLλ;T dλ λi F

(3) where Sλ is the responsivity of the silicon photodiode, T λ is the spectral transmittance of the filter, λi F and λf F define the IB spectral range of the filter, and λi Si and λf Si define the spectral range of the silicon photodiode responsivity. To explore the significance of the OOB signal as a function of the blackbody temperature and the filter’s spectral coverage, a simple model has been used. The model uses the spectral responsivity of a silicon photodiode covering the range from 200 to 1100 nm. The spectral profile of the filter is proposed to have a top hat spectral profile shape with 20 nm full width at half-maximum (FWHM), as shown in Fig. 2. The maximum IB transmittance of the filter is supposed to be 0.5, while the transmittance over the OOB spectral range has been taken as 10−6 of the filter’s maximum response. These values are chosen

Fig. 2. Spectral transmittance of a narrow-band filter (principle y axis) and the spectral power responsivity of a silicon photodiode (secondary y axis).

1.E+08

Out-of-band signal level to the in-band signal

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1000 K 1500 K

1.E+06

2000 K

1.E+04

2500 K 3000 K

1.E+02 1.E+00 1.E-02 1.E-04 1.E-06 300

400

500

600

700

800

900

1000

Wavelength /nm

Fig. 3. OOB signal levels at different temperatures as a function of wavelength.

to make the spectral profile of the proposed filter close to that of actual filters commonly in used for such applications [27]. The spectral profile of the filter has been shifted to relocate and center the IB spectral region at different wavelengths starting from 300 to 1000 nm by 100 nm steps. The OOB signal relative to the IB signal has then been calculated at each wavelength and at different blackbody temperatures, as shown in Fig. 3. It can be noticed that the OOB signal levels are significant at shorter wavelengths due to the reduced emitted power from the blackbody compared to that emitted at longer wavelengths— especially when the blackbody is at relatively low temperature. Furthermore, the OOB signal reduces significantly at longer wavelengths, and its dependency on temperature reduces, too. It could also be noticed that at about 900 nm, the OOB levels are almost equal regardless of the temperature of the blackbody. These calculations are based on the assumption that the filter maintains its IB profile although covering different spectral regions along the silicon spectral range. In practice, the width and the transmittance of the IB region as well as the blocking capability in the OOB region vary from one filter to another. Accordingly, the OOB performance of any chosen filter should be investigated in light of its actual spectral profile. D. Backreflection and Polarization

The reflectance of a photodiode depends on its type as well as the angle and the polarization state of the incident light [28]. Some types of silicon photodiodes can show reflectance of more than 30% at shorter wavelengths—depending also on the thickness of the silicon oxide layer. In a single element FR, part of the reflected light is backreflected by the filter. This in turn could make the FR sensitive to the angle of incidence (measurement geometry) and the polarization state of light, especially when there is a tilt between the filter and the photodiode [10]. One of the major advantages in using a trap-design radiometer is the low backreflection, which is better than a few tenths of a percent over most of the silicon spectral range [29]. This in turn results in increased external quantum efficiency and less sensitivity to factors affecting the reflectance. Trap FRs are not meant in general to have ideal quantum efficiency; however, it is required to maximize the absorption of the incident light to have improved responsivity and to minimize the backreflected light by the filter. The backreflection effect can be further minimized by coating the internal surface of the FR, together with the trap mount, with a highly absorbing material.

Research Article The sensitivity of trap detectors to polarization depends on several factors including the reflectance of the photodiodes used, which in turn varies with the polarization state itself and the wavelength. As backreflection is less in transmission trap detectors compared to reflection trap detectors, they are less sensitive to polarization [30]. The polarization sensitivity in reflection trap detectors also depends on the relative orientation of the photodiodes and imperfect alignment on the trap mount [10]. These have to be carefully considered along with the FOV, not only to reduce the polarization effect but also to avoid vignetting errors that might occur in using different geometries of the incident light—i.e., using collimated, convergent, or divergent beams [31]. E. Calibration System

Another important factor that has to be considered, especially for FRs built and calibrated in house, is the availability of a suitable SI-traceable transfer detector along with the technical capabilities required for their calibration. Calibration of FRs at the highest metrological level is generally a multiple-stage process and technically very demanding [32]. The spectral responsivity of the FR has to be determined via one or more calibrated transfer detectors strictly traceable to a cryogenic radiometer, as the primary standard of optical power measurement [33]. The overall relative standard uncertainty of the spectral responsivity of the FR has to be in the 10−4 range in order to apply FRs for state-of-the-art thermodynamic temperature measurement. In addition, FRs require regular testing to monitor any drift and/or aging that may happen during their use. Monochromator-based calibration systems that use broadband sources can be used to calibrate FRs of any spectral coverage within the silicon photodiode spectral response. This, in turn, does not limit the wavelength selection of the spectral filter; however, the calibration uncertainty in this method can be relatively large compared to that obtained using tunable monochromatic laser systems. On the other hand, an interference effect is noticed in FRs using interference filters during their calibration using laser sources. This limits their calibration by broadband sources. For narrow-band glass filters or wedged interference filters, effective wavelengths of 650 and 800 nm may be particularly suitable for laboratories having dye and Ti:sapphire lasers, respectively, as these two wavelengths are in the middle of the tunable range of their lasers. In light of the above considerations and the relatively high cost of the chosen large area photodiodes, it was decided to design a FR with easily interchangeable filters, so that different filters can be used for individual applications. This makes it possible to broaden the use of the FR, for example, by measuring the thermodynamic temperature at different wavelengths or even using it as a radiation thermometer. F. Field of View

With a wide-FOV radiometer, the limitations on the source size and its distance from the radiometer are fewer compared to the case of radiometers having narrow FOV. For FRs used in thermodynamic temperature measurements, the source size is not actually a limitation, as the cavity bottom of the blackbody, either imaged with a lens or not, is usually less than 40 mm in diameter. Meanwhile, long distances between the source and the FR are preferable, as the relative uncertainty


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FR radius ( r2 )

FOV angle θ )

2 rph

d ph

Fig. 4. Tracking light inside the unfolded trap FR.

(due to distance) obtained at long distances is small compared to that obtained at short distances. This in turn makes a FR with relatively narrow FOV suitable for thermodynamic temperature measurements. Meanwhile, the FR should ideally be able to collect considerable signal level at long source distance even when the temperature of the blackbody is relatively low. This, therefore, requires a sufficiently wide FR aperture optimized to collect the minimum background radiation. The FOV depends on the radius of the FR aperture r 2 , and the radius of the projected active area of the photodiode r ph at the maximum distance traveled by a beam inside the FR until it encounters the fifth reflection d ph (this happens at the first photodiode element in the trap configuration), as shown in Fig. 4. The view angle of the radiometer can be given as r ph − r 2 −1 : (4) θ 2 tan d ph In order to allow using a wide FR aperture, the projected active area of the photodiode should be sufficiently large. Furthermore, d ph should be kept short, which means that the trap mount has to be compact and located close to the FR aperture. Given that a filter will be used between the aperture and the photodiode, silicon photodiodes with active areas of 18 mm × 18 mm could be ideal candidates for this requirement—r ph of these photodiodes is almost twice that of the commonly used 10 mm × 10 mm photodiodes. 3. OPTO-MECHANICAL DESIGN The mechanical design of the three-element trap FR is shown in Fig. 5. The design has included improvements to typical designs, such as the ability for easy filter replacement, effective temperature stabilization, and monitoring the actual temperature inside the FR. In this design the filter is placed safely inside one mechanical mount together with the aperture. This mount could be dismantled easily to replace the filter while the photodiodes are kept safely behind an intermediate plate. The holes of the trap mount are 20 mm in diameter each, which is 2 mm wider than the side length of the active area of each photodiode. The active area is placed further back by 1.2 mm to the front surface of the photodiode ceramic mount. This has been considered while designing the trap mount in order to keep the three photodiodes coaxial and centered with

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Trap mount

Photodiode element

Aperture position

Position of the filter

Fig. 6. (a) Photodiodes placed on the trap mount. (b) Cooling housing.

Fig. 5. 3D FR mechanical design.

respect to the optical axis. The surface on which each photodiode is placed on the trap mount is 35 mm wide, which is wide enough to allow easy placement and alignment of the photodiode. This, in turn, makes the FR less vulnerable to beam vignetting errors due to imperfect alignment. In order to reduce polarization sensitivity, the reflection trap FR has been designed such that the second and the fourth reflections are in an orthogonal plane to that of the first and the fifth reflections [29]. The polarization sensitivity of such a design has been proven to be in the 10−5 level [10]. The FR has also been designed such that d ph is 146 mm. The distance between the FR aperture and the center of the first photodiode is only 46 mm. With a 6 mm aperture, the FOV angle is ∼3°. This has been considered enough to enable radiance measurements of a variable temperature blackbody cavity over a wide distance range with minimized influence of stray light sources from the background. The FR-source distance can be measured without touching the aperture, as the reference surface for distance measurement is the front face of the FR. The distance between the aperture and this surface can then be subtracted. All parts of the FR, apart from the cooling housing, are made of aluminum and are black anodized to minimize internal reflection. 4. ALIGNMENT AND CONTROL The photodiodes have been placed and aligned on the trap mount as shown in Fig. 6(a). They have been connected afterwards in parallel and operated in photovoltaic mode. This has been done in a clean laboratory environment with careful attention to static electricity during soldering. A male BNC connector has been used to collect the photocurrent with its ground terminal connected to the FR housing. Since the FR is exposed to a considerable thermal load emitted from the blackbody, the induced thermal effect should be taken into account in order to minimize any expected drift in the FR responsivity. This is particularly important for FRs using interference filters, as their center wavelength can be shifted with temperature change [34]. A water-streamed housing surrounding the FR has been designed to control and stabilize the temperature of the FR. The housing is made of a single brass

piece of 8 mm thickness with an extruded passageway through which water is circulated, as shown in Fig. 6(b). The temperature of the FR is measured using a thin-film platinum resistance thermometer (pt1000). The thin-film thermometer is only 4 mm long and 2 mm wide, which has made it possible to place it inside the FR—on the back of the first photodiode element. This in turn has allowed the actual temperature of the main sensor to be monitored. The two terminals of the thermometer have been connected to a female lemo connector at which the temperature is measured using a four-wire technique. 5. PRELIMINARY EVALUATION Prior to connecting the photodiodes, the shunt resistance of each photodiode was measured. It is important for photodiodes connected in parallel, as in trap detectors, to have matching shunt resistances in order to reduce noise levels. This has been measured by applying voltage levels of 10 mV on the photodiode. The average photocurrent induced by both polarities, after subtracting the photocurrent induced without bias, was used to calculate the shunt resistance. During these measurements the photodiode was placed in a light-tight box far from any electromagnetic fields. The shunt resistance of the three photodiodes agreed to within 30 MΩ with an average of ∼230 MΩ. The spectral profiles of four available interference filters have been tested to be used in the FR using a photodiode array spectrometer and a tungsten lamp. The results are shown in Fig. 7. The nominal maximum wavelengths of the selected filters are 658, 689, 806, and 857 nm. The IB spectral range of the 689 and 857 nm filters has shown extended IB terminals; accordingly, they have been excluded. The increased transmittance over the OOB spectral range, especially at the shorter and longer wavelengths, can be attributed to the presence of stray light inside the array spectrometer or to the poor blocking capabilities of the filters [35]. However, the results have been considered satisfactory to identify the spectral profiles of the filters. The cooling system has been tested by direct exposure of the FR to the thermal load emitted from a blackbody running at 2500 K over an hour. The system has enabled temperature stability to within 0.05°C. A thorough evaluation of the FR

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Table 1. Expected Relative Standard Uncertainty in Thermodynamic Temperature Measurements Relative Uncertainty/ % Δx∕x

Source Uncertainty Filter radiometer responsivity

radiometric performance is ongoing. The results will be presented along with its calibration. 6. UNCERTAINTY ESTIMATION At the Physikalisch-Technische Bundesanstalt (PTB) the FR is used directly without a lens in “irradiance” mode to measure the temperature of variable temperature blackbody sources. The temperature of small aperture sources (fixed points) is measured through an ‘intermediate’ radiation pyrometer and a variable temperature blackbody, as presented in Section 2.A. This section clarifies the sources of uncertainty and estimates their relative values expected to be delivered by the FR. Since the temperature, as given by Eq. (1), is not described explicitly in terms of the other variables, the technique for a “multivariate, implicit, real-valued model” can be used to evaluate its uncertainty [36]. Equation (1) in this case can be written as jλf

Sλj Lλj ; T ∂λj − V T 0;

0.003 0.030 0.073

where G is the amplifier gain, C th is a factor that corrects for the temperature effect on the FR, C SL is the stray light correction, C SSE is a correction due to the SSE, C ϵ is the blackbody emissivity, C d is a correction due to the diffraction effect in the system, C P is a correction due to the polarization effect, and C g is the geometric factor, as given in Eq. (2). The calibration uncertainty of the FR responsivity is limited by the calibration uncertainty of the trap detector against which the FR is calibrated. Usually there are three different spectral ranges of uncertainty: the first is due to the calibration of the OOB region, where the FR responsivity is very low and the dominant source of uncertainty is the signal noise; the second uncertainty range is at the steep changes of the FR’s cut-on and cut-off profiles, where the effective source of uncertainty is the wavelength fluctuation; and the third range is the central part of the IB spectral region, where the main source of uncertainty is the calibration system [37]. For a narrow-band FR of an 800 nm nominal maximum wavelength, the uncertainty of the three spectral regions, as given in Table 1, can produce an uncertainty of about 30 mK (k 1) at the copper point. The repeatability of the FR depends mainly on the stability of the source as well as the temperature stability of the FR during measurements. Due to the effect of temperature on the FR, its temperature should be recorded during measurements so its responsivity can be corrected for any temperature change. The uncertainty in measuring the radii of the apertures depends on their quality and the method used in their calibration.

f C; V T ; Sλi …Sλf X

0.500 0.080 0.027 0.020 0.015 0.010 0.015 0.015 0.010 0.005 0.020 0.005 0.025

Repeatability Amplifier gain Thermal effect Blackbody aperture Filter radiometer aperture Distance Misalignment Stray light Diffraction Size-of-source effect and nonuniformity Polarization Blackbody emissivity Combined relative standard uncertainty (k 1)

Fig. 7. Transmittance of the selected interference filters.

C

OOB: Edges: IB:

(5)

jλi

where f is a function that considers all the uncertainty sources in the experiment including those defined by the correction factor C. Accordingly, the uncertainty can be calculated based on Eq. (5) as 1 0 2 Pjλf ∂f 2 2 ∂f 2 u C u Sλ j jλ ∂C ∂Sλ i 1 B j C u2 T 2 @ 2 A; ∂f ∂f 2 u V T ∂T ∂V T (6)

such that the uncertainty in C is given as 0 2

B u2 C B @

C G

u2 G

2 C Cϵ

2 C C th

u C ϵ 2

u2 C th

2 C Cd

u C d 2

C 2 2 C SL u C SL

2 C CP

u C P 2

1

2 2 C C SSE u C SSE C

2 C Cg

u C g 2

C; A

(7)

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However, an uncertainty level in the submicrometer range can be obtained with high-quality diamond-turned apertures [38]. Since the blackbody aperture is close to the thermal load emitted from the blackbody, the temperature effect on this aperture should be considered by providing suitable cooling. The distance between the apertures can be measured by using either rods of calibrated length or a length-measuring interferometer. Although the interferometer can be more accurate, there is still a dominant source of uncertainty coming from the length of the rod used to move one of the interferometer mirrors [22]. This in turn results in an overall uncertainty of about 0.1 mm, which is comparable to that obtained by only the calibrated rods. The radii of the apertures and the distance between them have a relative sensitivity coefficient twice those of other sources, which is another reason, in addition to the resultant diffraction, for using high-quality apertures. Stray light in the system can be quite challenging due to the difficulty of its “absolute” evaluation. Identifying stray light can be done by excluding the effect of dark and diffracted signals by applying relevant corrections. However, there might still be some components that cannot be corrected—for example, scattered and inter-reflected light coming from the measured source. Due to the unpredictable behavior of those components, their evaluation requires a thorough understanding of the system. A system of reduced stray light levels cannot distinguish stray light from the source stability [39]. Since the FR measures a broadband source through an optical window defined by the filter’s IB region, diffraction losses in the system should ideally be integrated over this optical window. However, it is sometimes calculated at the FR nominal maximum wavelength for simplicity. The difference in size and uniformity between the calibration source and the measured source has to be considered as well, due to the resultant SSE. In addition, the state of polarization of the source and its emissivity are two other sources of uncertainty that should be accounted for. The expanded uncertainty presented in Table 1 shows that the FR can deliver thermodynamic temperature measurements with an uncertainty level of about 80 mK (k 1) at the copper point. The main uncertainty sources come from the calibration of the FR itself and the geometry of the experiment, which are common sources for similar radiance-meter systems [39]. Other uncertainty sources can be kept very low—depending on the efficiency of the system used. 7. CONCLUSIONS A new high-quality FR has been designed and built at the PTB, Berlin, Germany. The FR is made of a three-element reflectiontype trap detector that uses three large area silicon photodiodes, each of 18 mm × 18 mm active area. This, together with careful design, has allowed a wide FR aperture to be used. The temperature of the FR is controlled by a cooling housing and is measured by a thin-film Pt1000 thermometer placed inside the FR. The design enables easy replacement of the filter without affecting the photodiodes or even the aperture. The optomechanical design criteria have been thoroughly investigated and presented. Preliminary evaluation of the FR has shown matching shunt resistances of the three photodiodes, excellent

temperature stability, and alignment. The uncertainty expected to be delivered by the FR has been discussed and showed that an uncertainty of about 80 mK (k 1) at the copper point can be achieved. Acknowledgment. We acknowledge the input of the PTB workshop for the FR fabrication. One of the authors, Saber Salim, expresses gratitude to his colleagues at PTB who were very supportive during his stay at PTB, Berlin.

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