1 Introduction

The National Institute of Metrology (NIM) has established a standard photoelectric pyrometer for high-temperature scale transfer for the ITS-90 above the silver fixed point since the early 1990s [1]. And then NIM has developed a standard radiation thermometer with center wavelengths of 660 nm, 900 nm, and 1560 nm until now [2]. The optical system of the radiance thermometers commonly consists of a convex lens and field stop. These components are easily contaminated, and the performance may be changed when exposed to air. For this reason, a lens-free irradiation thermometer (LF-IRRT) has been developed since 2009 at NIM. The optical system of the LF-IRRT is a non-imaging optical system and only has two limiting apertures. NIM successfully set up an irradiation thermometer for the temperature range from \(600\,^{\circ }\hbox {C}\) to \(1500\,^{\circ }\hbox {C}\) with a 900 nm center wavelength and a 42 nm bandwidth in 2010 [3]. PTB also successfully developed two kinds of wavelength irradiation thermometers: the first type for the temperature range from \(950\,^{\circ }\hbox {C}\) to \(2300\,^{\circ }\hbox {C}\) with a 802 nm center wavelength and a 26 nm bandwidth; and the second type for the temperature range from \(300\,^{\circ }\hbox {C}\) to \(960\,^{\circ }\hbox {C}\) with a nearly 1600 nm center wavelength and a 96 nm bandwidth [4].

The LF-IRRT with a \(1.55\,\upmu \hbox {m}\) center wavelength based on the InGaAs detector has been developed at NIM, the temperature range of which is from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\). This paper introduces the measurement principle, structure, calibration method, stability, and expanded uncertainty at several temperature points of the LF-IRRT.

2 Experimental Apparatus and Procedures

2.1 Description of Experimental Technique

2.1.1 Principle of Technique

The principle of radiation thermometry involves the relationship between thermal radiation emitted by objects, wavelength, and temperature, the quantitative description of which is the blackbody radiation law. The Planck principle gives the relationship between the blackbody spectral irradiance E and wavelength, and the solid angle of receiving light and temperature,

$$\begin{aligned} E(\lambda ,T, \varOmega )=\varOmega c_1 n^{-2}\lambda \,^{-5}\frac{1}{\pi \exp (c_2 /n\lambda T-1)}. \end{aligned}$$
(1)

Here E is the spectral irradiance of the detecting plane, \(c_{1}\) is the first radiation constant, \(c_{2}\) is the second radiation constant, \(\lambda \) is the wavelength in vacuum, \(\varOmega \) is the solid angle of receiving light, n is the refractive index of the medium, and T is the thermodynamic temperature of the blackbody.

Equation 1 is the general expression for Planck’s law. It describes the relationship among the intensity of blackbody radiation, wavelength, and temperature. The irradiation thermometer uses the interference filter as the monochromator. The photoelectric output from the photocurrent detector is

$$\begin{aligned} I_{\mathrm{P}} =\int _0^\infty \varPhi (\lambda ,T)R(\lambda )\hbox {d}\lambda =\int _0^\infty {AE} (\lambda ,T)R(\lambda )\hbox {d}\lambda . \end{aligned}$$
(2)

Here \(\varPhi \,(\lambda ,\,T)\) is the spectral radiation flux received by the photodetector; A is the area of the rear aperture; T is the thermodynamic temperature of the source; \(E\,(\lambda , T)\) is the irradiance of the radiation thermometer; and \(R(\lambda )\) is the spectral responsivity of the filter and detector. If the irradiation thermometer calibrated at the reference temperature point, \(T_{\mathrm{r}}\), has a photoelectric detector output, \(I_{\mathrm{pr}}\), then

$$\begin{aligned} \frac{I_{\mathrm{P}} }{I_{\mathrm{Pr} } }=\frac{\int _0^\infty {E(\lambda ,T)} R(\lambda )\hbox {d}\lambda }{\int _0^\infty {E(\lambda ,T_{\mathrm{r}} )} R(\lambda )\hbox {d}\lambda }=\frac{E(\lambda _{\mathrm{e}} ,T)}{E(\lambda _{\mathrm{e}} ,T_{\mathrm{r}} )}. \end{aligned}$$
(3)

Here \(\lambda _{\mathrm{e}}\) is the mean effective wavelength between the temperature range of \(T_{\mathrm{r}}\) and T. Substituting the Planck formula into Eq. 3, and then rearranging gives

$$\begin{aligned} T=\frac{c_2 }{\lambda _{\mathrm{e}} \cdot \ln \left\{ {\frac{I_{\mathrm{Pr} } }{I_\mathrm{P} }\left[ {\exp \left( {\frac{c_2 }{\lambda _{\mathrm{e}} T_\mathrm{{r}} }} \right) -1} \right] +1} \right\} }. \end{aligned}$$
(4)

The temperature T and the output of the photoelectric detector \(I_{\mathrm{P}}\) represent a single-valued relationship, even if the effective wavelength \(\lambda _{\mathrm{e}}\) changes slightly with temperature T. Equation 4 is a basic formula for the irradiation thermometer calculating the temperature. In the condition of limiting the solid angle of incident light, the spectral irradiation which is measured by the irradiation thermometer is converted to the corresponding temperature by Planck’s law.

2.1.2 Apparatus

The optical structure of the irradiation thermometer which has four sections is shown in Fig. 1. These four sections are the front aperture, rear aperture, filter, and detector.

Fig. 1
figure 1

Schematic of the optical system showing sections of irradiation thermometer

Full size image

The specifications of the LF-IRRT are listed in Table 1. It is 380 mm long, with a maximum diameter of 90 mm housing section made out of aluminum, the structure is shown in Fig. 2. The temperature range is from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\). The diameter of the front and rear apertures is the same; they are both 3 mm. And the distance between the front aperture and the rear aperture is 300 mm. The filter of the thermometer is an interference filter, the center wavelength of which is \(1.55\,\upmu \hbox {m}\), with the bandwidth and the blocking of the band response being 200 nm and lower than \(10^{-4}\), respectively. The Hamamatsu G8605-25-type InGaAs detector is used, and its working temperature is \(-16\,^{\circ }\hbox {C}\) controlled by a ILX Lightwave LDT-5980. The dark signal of the detector is less than \(1\times 10^{-12}\hbox { V}\). The cavity and the detector unit use isothermal circulating water to maintain a constant temperature. The temperature is controlled at \(25\,^{\circ }\hbox {C} \pm 0.03\, ^{\circ }\hbox {C}\) by a water temperature controller. All the limiting apertures, the baffles, and cavity of the thermometer are black anodized.

Table 1 Specifications of the LF-IRRT
Full size table
Fig. 2
figure 2

Design of LF-IRRT in more detail and with the individual components identified as follows: 1 limiting aperture, 2 output or input temperature controlled liquid, 3 temperature controlled housing, 4 stray light baffles, 5 interference filter, 6 detector, 7 \(\hbox {N}_{2}\) purging, 8 Pt100 sensor, 9 stray light baffles, 10 stray light baffles

Full size image

The standard variable temperature blackbody facility (SVTBB) has been developed at NIM from 2010. This facility includes the sodium heat-pipe and cesium heat-pipe blackbodies, all for which specifications are listed in Table 2. The cesium and sodium heat-pipe blackbodies have been used to calibrate the LF-IRRT from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\) at every \(100\,^{\circ }\hbox {C}\) temperature point. The cavity structure of the cesium and sodium heat pipes is a cylinder with \(31^{\circ }\) “V” notch grooves on the inner wall to increase the cavity emissivity and reduce the influence of the specular reflectance component. The cavity diameter and length are 49 mm and 520 mm, respectively. The normal effective emissivity of the cavity is estimated to be 0.9999, at \(1.6\,\upmu \hbox {m}\), calculated from STEEP3 [5] software based on the assumption of isothermal conditions, perfectly diffuse reflection from the cavity surface, and the value of 0.96 for the emissivity of the paint [6]. Two reference thermometer wells with 220 mm depth are designed behind the cavity bottom on each heat pipe, one for the reference thermometer and the other for the verification of the reference thermometers. The reference thermometers of the Cs and Na are an SPRT and a Au–Pt thermocouple, respectively. The temperature stability of the Cs heat-pipe SVTBB in 10 min is \(0.030\,^{\circ }\hbox {C}\) at \(270\,^{\circ }\hbox {C}\) and \(0.021\,^{\circ }\hbox {C}\) at \(550\,^{\circ }\hbox {C}\). The temperature stability of the Na heat-pipe SVTBB in 10 min is \(0.009\,^{\circ }\hbox {C}\) at \(960\,^{\circ }\hbox {C}\). All the details of the SVTBB are listed in [7].

Table 2 Specification of NIM cesium and sodium heat-pipe blackbody sources
Full size table
Fig. 3
figure 3

Measurement schematic showing the distance between the LF-IRRT and aperture of cavity, the aperture position

Full size image

2.2 Experimental Procedures

2.2.1 Measurement Method

When the LF-IRRT was used to measure the source, the distance between the cavity aperture of the blackbody and the water-cooled aperture placed in the front of the blackbody source is 180 mm. The distance between the water-cooled aperture and the thermometer is 145 mm as shown in Fig. 3. The LF-IRRT measured the center of the blackbody through the aperture for 3 min at every temperature point. The data from the output of the LF-IRRT and the output of the contact thermometer in the heat pipe are sent to a personal computer (PC) at the same time. In order to verify the stability of the LF-IRRT, the Cs and Na heat-pipe temperature points from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\) were measured many times during 1 month. During these measurements, the only amplifier gain settings used for the LF-IRRT were \(10^{8}\) and \(10^{7}\). The ratio of the amplifier gains with these two settings was determined to be 9.92263, and this factor was used to correct the measured output voltages.

2.2.2 Measurement of Temperature and Calibration

The Sakuma–Hattori calibration method is a very commonly used and accurate method [8]. Saunders [9] uses a mathematical derivation to define the physical meaning of each coefficient in the formula. In most cases, as an interpolating method, the Sakuma–Hattori method has the advantage of not requiring the measurement of the effective wavelength of the irradiation thermometer and the system non-linearity. It requires three or more temperature points and then calibrating the thermometer. So it is well suited for calibrating the irradiation thermometer. The Sakuma–Hattori equation is expressed as

$$\begin{aligned} V(T)=\frac{C}{\exp \left( \frac{c_2 }{AT+B}\right) -1}, \end{aligned}$$
(5)

where \(A, \,B\), and C are fitted coefficients that need to be determined. A, B, and C are completely determined by eight temperature points with corresponding output voltages.

2.2.3 Measurement of Size-of-Source Effect

The SSE of the LF-IRRT is measured by the direct method [10]. The source is the ISOTECH-700 variable temperature blackbody at \(500\,^{\circ }\hbox {C}\), the cavity diameter of which is 65 mm. The distance between the aperture and cavity is 15 mm, and the distance between the aperture and the LF-IRRT is 185 mm. The experimental procedure for the SSE is shown in Fig. 4. The field of view of the LF-IRRT is 6.7 mm as calculated from the structure and the distance. The diameter of the apertures of the front of the source range from 10 mm to 65 mm.

Fig. 4
figure 4

Photo of experimental SSE measurement system

Full size image

3 Results

3.1 Temperature and Calibration

Eight temperature points supported by the Cs and Na heat-pipe blackbodies are used to calibrate the LF-IRRT. The voltages of eight temperature points corrected by the emissivity of the cavity and the gain ratio of the amplifier measured by the LF-IRRT are listed in Table 3. And then the \(A,\,B\), and C parameters of the Sakuma–Hattori equation are calculated using these voltages, and results are listed in Table 4. The temperature standard deviation of the residuals on determination of \(A,\,B\), and C is \(0.037\,^{\circ }\hbox {C}\), shown in Table 4 and Fig. 5.

Table 3 Temperature and output current
Full size table
Table 4 LF-IRRT calibration result and standard deviation of the residuals
Full size table
Fig. 5
figure 5

Temperature differences using values of \(A,\,B\), and C from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\)

Full size image
Table 5 Results of the LF-IRRT measurement of the Cs/Na heat-pipe blackbodies between \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\)
Full size table

3.2 Stability of the LF-IRRT

The results are shown in Table 5. The stability or drift of the LF-IRRT is less than \(0.070\,^{\circ }\hbox {C}\) between \(300\,^{\circ }\hbox {C}\) and \(1000\,^{\circ }\hbox {C}\) during 1 month.

3.3 Size-of-Source Effect (SSE) Results

The result for the SSE of the LF-IRRT measured by the direct method is 0.6 % from the source diameter range from 10 mm to 65 mm, which is the average of five measurements made during 1 day, as shown in Fig. 6.

Fig. 6
figure 6

Result of SSE from the source diameter range from 10 mm to 65 mm on average

Full size image

4 Uncertainties

Table 6 Uncertainty analysis of the LF-IRRT (\(^{\circ }\hbox {C}\))
Full size table

There are several aspects contributing to the expanded standard uncertainty, such as the calibration stability of the SPRT for the Cs heat pipe and the Au–Pt thermocouple for the Na heat pipe, the long-term stability of the thermometer, the resistance/voltage measurement from a Fluke 1594A thermometry bridge or a Fluke 8508A voltmeter, the stability of the ice point and switch controller for the Au–Pt thermocouple, the temperature drop of the thermal flux of the cavity bottom, the stability of the blackbody furnace, the uniformity of the cavity bottom of the blackbody, the cavity emissivity, the stability of the LF-IRRT, the RMS of the fit, the alignment, the SSE, etc. following the CCT-WG5 document [11], listed in Table 6. All components of the uncertainty are converted to temperatures. The expanded uncertainties of temperature points from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\) are no larger than \(0.191\,^{\circ }\hbox {C}\).

5 Conclusion

An irradiation thermometer with a \(1.55\,\upmu \hbox {m}\) center wavelength based on the InGaAs is established at the NIM of China, the temperature range of which is from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\). A characteristic of this thermometer is no lens. The stability of the LF-IRRT is better than \(0.070\,^{\circ }\hbox {C}\) between \(300\,^{\circ }\hbox {C}\) and \(1000\,^{\circ }\hbox {C}\) during 1 month. The expanded uncertainties of temperature points from \(300\,^{\circ }\hbox {C}\) to \(1000\,^{\circ }\hbox {C}\) are less than \(0.20\,^{\circ }\hbox {C}\). The size-of-source effect of the LF-IRRT is 0.6 % from the source diameter range from 10 mm to 65 mm.

The new ITS-90 radiation temperature scale facilities with a temperature range from \(-30\,^{\circ }\hbox {C}\) to \(1085\,^{\circ }\hbox {C}\), such as the SVTBB [7], fixed-point blackbodies (In, Sn, Zn, Al, Ag, Cu) [12], the LF-IRRT, and the radiation thermometers based on an InGaAs detector [12] etc., have been established up to now at NIM. The LF-IRRT is a very important transmitted thermometer in industry for its high stability performance.