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The measurement of the leaf temperature of forests or agricultural plants is an important technique for the monitoring of the physiological state of crops. The infrared thermometer is a convenient device due to its fast response and nondestructive measurement technique. Nowadays, a novel infrared thermocouple, developed with the same measurement principle of the infrared thermometer but using a different detector, has been commercialized for noncontact temperature measurement. The performances of twokinds of infrared thermocouples were evaluated in this study. The standard temperature was maintained by a temperature calibrator and a special black cavity device. The results indicated that both types of infrared thermocouples had good precision. The error distribution ranged from −1.8 °C to 18 °C as the reading values served as the true values. Within the range from 13 °C to 37 °C, the adequate calibration equations were the highorder polynomial equations. Within the narrower range from 20 °C to 35 °C, the adequate equation was a linear equation for one sensor and a twoorder polynomial equation for the other sensor. The accuracy of the two kinds of infrared thermocouple was improved by nearly 0.4 °C with the calibration equations. These devices could serve as mobile monitoring tools for
Monitoring of the physiological state of forests or agricultural plants has become a basic technique to control the crop environment and to modulate irrigation and fertilization [
Jones [
The performance evaluation of the infrared thermometer is a key step to ensure the accuracy of the measured values. Amiro
Kalma and Alksnis [
The quantitative sensor performance criteria are very important to assess the accuracy and precision. The regression analysis of the linear equation or the higherorder polynomial equation of the relationship between the readout values of an instrument and the standard values of the calibrator is the basic statistical technique used to evaluate performance. The indexes of slope, intercept and the standard deviation are usually selected to evaluate the performance [
The components of an infrared thermometer include an optical system to collect the energy emitted by the measurement subject, the lens to screen the specific wavelength, a detector to convert the energy to an electrical signal, an emittivity adjustment, an ambient temperature compensation circuit and the microprocessorbased electronics to calculate the temperature according to some preset equation. For the infrared thermometer, the received energy is detected and converted into a voltage signal using a pyroelectric or thermopile device. This device requires an external power supply and they are expensive.
A novel selfpowered infrared thermocouple has been recently developed by some manufacturers of infrared thermometers. This device can detect the radiation energy and imitate it as a thermocouple output. Because of the simplicity and compatibility with the thermocouple’s transducer, these units are inexpensive. The limitation is the measuring range [
Recently, more types of infrared thermocouples have been commercialized by manufacturers. This provides an opportunity to apply the technique for monitoring routine temperatures for forest management and agricultural production. The objectives of this study were: (1) to evaluate the performance of infrared thermocouples using a standard temperature calibrator and (2) to determine the adequate calibration equations to improve the accuracy of these sensors.
Two kinds of infrared thermocouples were used in this study, a Sentron SI10AL (Sentron Eng. CO, Ltd, Taiwan) and a Trotec BP20 (Trotec GmbH & CO, Heinsberg, Germany). The respective manufacturer’s specifications are listed in
The standard temperature of the blackbody source was maintained by a TC 2000 temperature calibrator (Instutek AS, Skreppestad Naringspak, Norway). The operating temperature ranged from −40 °C to 150 °C. The temperature of the standard environment was measured by a RTD (resistive temperature detector) thermometer calibrated by the U.S. NIST (National Institute of Standards and Technology). The uncertainty of this equipment from the calibration certificate was 0.03 °C. An aluminum cylinder was installed into the oil bath of this calibrator. The size of this cylinder corresponded to the requirements of the blackbody source [
The target temperature for calibration was maintained at 13, 17, 21, 25, 29, 33 and 37 °C for the Sentron SI10A and at 2 °C intervals for the Trotec BP20 within the same measuring range. The test environment was maintained at 25 °C and the variation of the set room environment temperature was controlled within ±1.5 °C. Several replicate measurements were made for each standard temperature. As one measurement has finished, the infrared thermocouple was taken out from the blackbody cavity for five minutes and then was put into the cavity for further measurement. The signals of the two kinds of infrared thermocouples were indicated in their LCD screens. The error of the data acquisition device was insignificant, according to the manufacturer’s specifications. The sensor signals reached an equilibration state within one second and this was recorded by the visual method.
The performance of these infrared thermocouples was assessed by their accuracy and precision. The accuracy is expressed as the closeness with which a measurement value approached the standard temperature,
The precision
The calibration equations were established using the regression analysis technique. The criteria for selecting of the best equation are the coefficient of determination
The t value of each parameter is calculated as:
The residual plot is a qualitative criterion to evaluate the adequateness of calibration equations. As the data distribution of residual plots indicated a uniform pattern, the model could be recognized as an adequate model. If the residual plots revealed a clearly systematic pattern, a model cannot be accepted.
There are two types of calibration equations. For the classical calibration equation, the readout values of infrared thermocouples were assumed as dependent variables and the standard values of the calibrator were selected as independent variables. For the inverse calibration equation, the standard values maintained by the temperature calibrator were recognized as dependent variables. Because the inverse calibration equation has better predictive ability and is easy to apply [
A polynomial equation could be used to fit the calibration data. However, as higher order parameters were selected, the predicted errors could be increased significantly [
The relationship between the reading values of the Sentron SI10A infrared thermocouple versus standard values maintained by TC2000 calibrator is shown in
A nonlinear distribution of the data scattering was found. The error distribution of the Sentron SI10A is shown in
The errors ranged from −2.0 to 1.8 °C within the range from 13 °C to 21 °C. This revealed an overestimation performance. When the measurement temperature was higher than 25 °C, the errors ranged from −0.6 to −1.8 °C. This represented an underestimation performance. The readout values of the infrared thermocouples should not be recognized as the true values directly. The standard deviations of the measurement values at each standard environment are presented in
Below the measurement temperature of 25 °C, the standard deviations were less than 0.2 °C. In the higher temperature range, the standard deviations were less than 0.1 °C. From the viewpoint of practical applications, this sensor had good precision performance. The estimated parameters and statistics of the calibration equations for this Sentron SI10A infrared thermocouple within the range from 13 °C to 37 °C are listed in
A clear pattern or uniform distribution of residual plots could serve as a qualitative criterion to evaluate the calibration equation. If the data distribution of residual plots indicated a uniform distribution, the model could be recognized as adequate.
A clean systematic pattern of residual plots was found for linear and polynomial equations. However, a random distribution of residual plots was found for the threeorder polynomial equation, indicating that the threeorder polynomial equation was the adequate calibration equation for this sensor within the range from 13 °C to 37 °C. The standard deviation of estimators for the three calibration equations was 0.5541, 0.5410 and 0.3924 °C, respectively.
The nonlinear curves could be viewed as linear lines by narrowing the measurement range. As the measurement data within the narrower range were reevaluated, the calibration equations and statics of the Sentron SI10A infrared thermocouple for the measurement data ranging from 20 °C to 35 °C are presented in
According to the statistical residual plots procedure, the linear calibration equation is recognized as the adequate model by the residual plots. A polynomial equation did not improve the predictive ability by the standard deviations
The distribution between readout values of the Trotec BP20 infrared thermocouple and the standard temperature are shown in
Within the range from 13 °C to 37 °C, the adequate equation was a complex fourorder polynomial equation. The standard deviation of the estimated values for the four calibration equations was 0.8661, 0.7584, 0.7355 and 0.3366 °C, respectively. The results indicated that the sensor required a highorder polynomial equation to decrease the predictive errors. Only the fourorder equation had a uniform distribution of residual plots. As the measurement data were limited over a 20–35 °C range, the regression analysis results are presented in
For the linear calibration equation, the standard deviation of estimated values was 0.8209 °C. A clear systematic pattern of residual plots was found. The twoorder polynomial equation could be recognized as the adequate calibration equation by the residual plot. The predictive error was 0.3322 °C.
To evaluate the reproducibility of the calibration equations, the error distribution of two Sentron SI10A infrared thermocouples from the same manufacturer and the same production batch are shown in
The error distributions of two TROTEC BP20 infrared thermocouples are presented in
From the above results, we can conclude that we must establish a special calibration equation for each infrared thermocouple to ensure the accuracy of its measurement performance.
The results of this study indicated that the accuracy of twokinds of infrared thermocouples could be significantly improved using calibration equations. The form of the adequate calibration equation was influenced by the measurement range. For Sentron SI10A sensors, a threeorder polynomial equation was adequate for the measurement data over a 13–35 °C range. However, a linear calibration equation was valid for a narrower measurement range (20 °C–35 °C). Similar results have been reported on the manuals of some manufacturers [
A linear calibration equation was proposed by Baker
Mahan and Yeater [
In the study of the estimation of stomatal conductance, the difference between canopy and air temperature was below 0.8 °C [
The standard temperature of the black source is maintained by a temperature calibrator and a blackbody source. The uncertainty of the temperature calibrator is within 0.03 °C. The emittity of the blackbody source is nearly 0.9999.
The test environment was maintained at 25 °C and the variation of the setting room environment temperature was controlled within ± 1.5 °C.
The target temperature for calibration was maintained at different range according the practical requirement. The interval of testing temperature is 2 °C.
Three or more replicates are made on each measurement point.
As one measurement is finished, the infrared thermocouple was taken out from the blackbody cavity for five minutes and then was put back into the cavity for further measurements.
The performance of these infrared thermocouples was assessed by their accuracy and precision. The accuracy is expressed as the closeness with which a measurement value approached to the standard value. The error
The calibration equations were established using the regression analysis technique. The criteria for selecting of the best equation are the coefficient of determination
In this study, the performance of twokinds of infrared thermocouples was evaluated. The temperature maintained by the temperature calibrator and a specific black cavity served as the standard temperature. As the reading values of these sensors were used directly as true values, the error distributions ranged from −1.8 °C to 1.8 °C. The accuracy of these sensors could be maintained at nearly 0.4 °C by the calibration equations. The form of the adequate calibration equations was different due to the different manufacturers of infrared thermocouple and the measurement range. Compared with the industrial level infrared thermometer, the main advantage of infrared thermocouples is their cost. From the performance evaluation, these sensors could be applied to
The authors would to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC982313B005032MY3.
The relationship between the readout values of two types of infrared thermocouples
The error distribution of the Sentron SI10A and Trotec BP20 infrared thermocouple. “
The standard deviations of the measured values at each standard environment for the Sentron SI10A and Trotec BP20 infrared thermocouple.
The errors distribution of two SENTRON SI10A infrared thermocouples from the same manufacturer and production batch.
The errors distribution of two Trotec BP20 infrared thermocouples from the same manufacturer and production batch.
Specifications of the thermopile infrared thermometers.
Parameters

Sentron SI10A

Trotec BP20


Operating temperature  0 to 50 °C  0 to 50 °C 
Accuracy  ±1.0 °C (15–35 °C)  ±1.0 °C (21 °C to 200 °C) 
Resolution  0.1 °C  0.1 °C 
Field of view  11 to 1  12 to 1 
Response time  0.1 sec  0.3 sec 
Wavelength  5 ∼ 14 μm  6 ∼ 14 μm 
Signal indication  LCD screen  LCD screen 
The calibration equations and statistics of the SENTRON SI10A infrared thermocouple, measurement ranged from 13 °C to 37 °C.
Linear  T_{s} = −3.0932 + 1.1336 T_{r}  0.9954  0.5541  Clear pattern 
Polynomial  T_{s} = −1.4215 + 0.9858 T_{r} + 0.003 T_{r}^{2}  0.9980  0.5410  Clear pattern 
Thirdorder  T_{s} = −16.0685–1.3945T_{r} +0.1045T_{r}^{2} − 0.0014 T_{r}^{3}  0.9999  0.3924  Uniform 
Clear pattern: the residual plots revealed the systematic clear pattern;
Uniform: the residual plots revealed uniform distribution.
The calibration equations and statistics of the SENTRON SI10A infrared thermocouple within the narrower measurement ranged from 20 °C to 35 °C.
Linear  T_{s} = −6.2284 + 1.2514 T_{r}  0.9935  0.374  Uniform 
Polynomial l  T_{s} = −7.2385 + 1.3287 T_{r} − 0.00145 T_{r}^{2}  0.9940  0.371  Uniform 
Calibration equations and statistics of TROTEC BP20 infrared thermocouple within the ranged from 13 °C to 37 °C.
Linear  T_{s} = 0.8999 + 0.9789 T_{r}  0.9936  0.8661  Clear pattern 
Polynomial  T_{s} = 5.6083 + 0.5440 T_{r} + 0.009037 T_{r}^{2}  0.9953  0.7584  Clear pattern 
Thirdorder  T_{s} = −3.0308 + 1.7307 T_{r} − 0.04161 T_{r}^{2} + 0.000682 T_{r}^{3}  0.9956  0.7355  Clear pattern 
Fourorder  T_{s} = −95.6884 + 18.8478 T_{r} − 1.1713 T_{r}^{2} + 0.03238 T_{r}^{3} − 0.0003204 T_{r}^{4}  0.9991  0.3366  Uniform 
The calibration equations and statistics of TROTEC BP20 infrared thermocouple within the ranged from 20 ° to 35 °C.
Linear  T_{s} = −2.3181 + 1.08489 T_{r}  0.9852  0.8209  Clear pattern 
Polynomial  T_{s} = 29.7702 − 1.3499 T_{r} + 0.04504 T_{r}^{2}  0.9986  0.3332  Uniform 