APOGEE INSTRUMENTS, INC.

Infra-Red Transducer Manuscript

EVALUATION AND MODIFICATION OF COMMERCIAL INFRA-RED TRANSDUCERS FOR LEAF TEMPERATURE MEASUREMENT

Bruce Bugbee1, Matt Droter, Oscar Monje, and Bertrand Tanner²
1 Crop Physiology Laboratory, Dept. of Plants Soils, Biometeorology, Utah State University  Logan, UT 84322-4820
² Campbell Scientific Inc., Logan, UT 84321
  
BACK TO IRT PRODUCTS AND SPECIFICATIONS
ABSTRACT
INTRODUCTION
RESULTS
DISCUSSION
FIGURES
REFERENCES
APPENDIX A

ABSTRACT
TOP OF PAGE
Accurate measurement of the leaf to air temperature gradient is crucial for the determination of stomatal conductance and other plant responses in both single leaves and in plant canopies. This gradient is often less than 1°C, which means that leaf temperature must be known to within about ±0.1°C. This is a challenging task, but new, miniature infra-red transducers from Exergen Corporation (Watertown, MA) and Everest Interscience (Tucson, AZ) can be modified and calibrated to achieve this accuracy. The sensors must be modified to add thermal mass and the Exergen sensor requires a measurement of sensor body temperature. Significant error is caused by the discharge of a capacitor in the standard Exergen sensor, but we tested it without the capacitor. The sensors respond rapidly to changes in target temperature, but require 2 to 10 minutes to respond to changes in sensor body temperature, which is often the largest source of error. A new, sensitive method for measuring field of view indicates substantial peripheral vision for both sensors and a wider field of view than specified by the manufacturers. Here we describe sensor output as a function of target and sensor body temperatures, and provide a generic (sensor independent) equation that can be used to achieve ±0.2 C accuracy with Exergen sensors. The equation was developed and verified using two black body calibrators.

INTRODUCTION
TOP OF PAGE
Radiometric surface thermometers, more commonly known as infrared thermometers (IRTs), have many advantages over conventional thermometers for the measurement of surface temperatures, but they require consideration of target emissivity, field of view, and sensor body temperature. Equations for quantitatively determining the magnitude of these errors have been reviewed by Amiro et al. (1983). Conventional thermometers require a probe to be in physical contact with the leaf being measured, which is usually at a different temperature. Consequently, heat is transferred between the probe and the leaf until an equilibrium temperature is reached. The amount by which the probe is cooler or warmer than the leaf affects the temperature of the leaf and induces error in the measurement. In contrast, infrared thermometers do not have this intrusion error, but other sources of error must be corrected for to obtain true target temperature.
Infrared thermometers are filtered to allow only a specific waveband, about 8 to 14 microns, to be transmitted to the IRT detector. This transmitted energy (E) is converted to temperature (T) via the Stefan-Boltzman Law which states E=esT4, where e is the emissivity of the object and s is the Stefan-Boltzmann constant (5.68 x 10-8 Joules m-2 s-1 K-4). Emissivity is defined as the radiation efficiency of a surface as compared to an ideal "black body" emitter. The power radiated by an object (emissivity) at thermal equilibrium in a vacuum must be equal to the power absorbed (absorbtivity).
The following transducers were tested:

Exergen IRt/c-271

Exergen IRt/c-0.21

Everest 3000AL2

POWER SUPPLY:
none
none
± 5V

OUTPUT:
mV
>mV
mV

COST:
$ 199.
$ 299.
$ 795.

SIZE:
13 x 44 mm cylinder
13 x 44 mm cylinder
16 x 32 mm cylinder
1 Sensors from the Exergen Company (Watertown, MA)
• model IRt/c -K-27°C (wide angle) Four replicate sensors were tested
• model IRt/c .2-K-27°C (narrow angle) Four replicate sensors were tested.

2 Sensor from Everest Interscience, Inc. (Tucson, AZ;  ph. 800-422-4342)
• model 3000 AL (narrow angle)

FIELD OF VIEW DETERMINATION

Sensor FOV was determined by recording the target temperature as the IRT was pulled away from a black body cone. The opening of the black body had a diameter of 6 cm and was held at 60 °C. The perimeter of the cone was covered with low-emissivity aluminum foil, which, along with the surroundings, were at 20 °C. The sensor was first placed flush with the cone opening where it viewed 100% of the target and read 60°C. As the sensor was pulled away from the target it began to include the aluminum foil in its field of view. The ratio of target to perimeter at a given distance from the target was determined from the output of the transducer and the relative fractions of radiation emitted by the target and aluminum foil. A sensor with a wide FOV receives more energy from the perimeter at the same distance from the target than a narrow FOV sensor. The difference between the black body temperature and the observed IRT temperature was proportional to the percentage area of target and perimeter within the sensor FOV.

BLACK BODY CALIBRATOR

Accurate calibration requires rigorous control of the sensor body temperature in addition to control of the target black body temperature. A calibration device that independently controlled sensor and target temperatures was built following the design described by Kalma et al. (1988). The calibration unit consists of a separate sensor block and a conical black body. The sensor block accommodates up to four sensors simultaneously. The black body cone was 9 cm long x 3.8 cm diameter. The cone shape increases the effective emissivity of the black body approximately by the ratio of the surface area of the cone to the surface area of the opening (Kalma et al., 1988). The two housings are separated thermally with 6 mm thick insulating material and nylon bolts. The sensors were inserted into cylindrical holes in the sensor block facing the black body. The temperature of the sensor bodies was measured by averaging thermocouples placed beside each of the sensors inside the sensor holes. The temperature uniformity of the sensor block was within ±0.02°C. Similarly, the black body temperature was measured by averaging four thermocouples placed in 1 mm holes drilled in the top, sides, and bottom of the conical housing.

Set point temperatures of both sensor holding block and black body were maintained by four Peltier heaters (Melcor, model no. CP 1.0-127-O5L). Two heaters were placed on opposite sides of each block and fitted with heat sinks. Thermocouple temperatures were connected to an isothermal multiplexer (Campbell Scientific, Inc., model AM25T) that uses a precision RTD for a temperature reference. Temperature was controlled by a datalogger (Campbell Scientific, Inc, model CR10T) using a Proportional Integral Derivative (PID) algorithm in the datalogger that maintained the temperature of the black body to within ±0.03°C.

WATER CONE CALIBRATOR

Water has an emissivity of 0.96 so a water cone calibrator was used to verify the black body calibration of the IRTs. This calibrator consisted of a 2 L beaker filled with water and placed on a magnetic stirring hot plate. The water was rapidly stirred with a large stirring bar so that the vortex produced a deep cone shape on the surface, which increased the effective emissivity of the water. The water temperature was measured by six thermocouples spread out throughout the beaker. Sensors were positioned just above the center of the water cone facing downward. Water temperature was altered by changing the set point of the thermostat on the hot plate. This arrangement provided a simple, low cost method of independently verifying the more complex black-body calibrator.

CAPACITOR INDUCED ERROR IN EXERGEN TRANSDUCERS

Standard Exergen sensors contain a capacitor in their circuit to minimize effects of electromagnetic interference (EMI). The capacitor inside the detector is typically charged by switching currents associated with a thermocouple measurement in multiplexers. The capacitor discharges during measurement and causes errors of up to 3°C in the target temperature. We purchased special Exergen transducers without capacitors and this eliminated these errors. We tested the IRt/c sensors without capacitors in environments with high EMI and their EMI filtering ability appeared identical to sensors with a capacitor. The shielded, twisted-pair thermocouple wire connected to the stainless steel transducer housing seems adequate to filter all the EMI. All measurements reported for Exergen transducers in this paper were conducted with IRTs without capacitors.

CALBRATION FUNCTIONS

When the sensor body temperature is constant, the sensor output is determined only by the target temperature. We quantified the effect of both sensor body and target temperatures by holding the sensor body constant at 15, 20, 25, 30, or 35°C and varying the black body temperature by 9°C above and below the sensor body temperature (Fig 1). The sensor error was defined as the difference between the sensor output and the reference black body temperature.

ADDITION OF THERMAL MASS AND ADDITION OF THERMOCOUPLE FOR SENSOR BODY TEMPERATURE

Because of the slow response time of the sensor bodies to changing temperature, we added thermal mass to the sensor housing to stabilize its temperature. This was accomplished by machining an aluminum cylinder to slide over the existing sensor. Two sizes were tested, 20 and 30 mm diameter. Although the 30 mm diameter was more effective in stabilizing sensor body temperature, we determined that the 20 mm diameter cylinder was adequate in our conditions. We further modified the Exergen sensors by adding a thermocouple inside the external cylinder. This was inserted from the end in a small grove on the inside of the cylinder. Thermal paste was applied to the sensor before insertion to improve heat transfer between the sensor and the external aluminum housing.

RESULTS
TOP OF PAGE

SENSOR RESPONSE TIME

All sensors responded quickly to changes in target temperature, but slowly to changes in sensor body temperature (Table 1). Adding thermal mass to the sensor body dampens rapid changes in temperature and thus improved accuracy in fluctuating air temperature conditions. Response time to changing target temperature was tested by repeatedly pointing the sensor at targets of different temperatures. Response time to changing sensor body temperature was determined in the black body calibrator by holding the target temperature constant and changing the sensor body temperature.

TABLE 1  The response time of the sensors to a 3 °C step change in the black body target or in sensor body temperature.

TABLE 1

TARGET

SENSOR BODY

EXERGEN WIDE
< 1 s
~ 120 s

EXERGEN NARROW
< 1 s
~ 180 s

EVEREST 3000AL
< 1 s
~ 600 s

FIELD OF VIEW

All transducers had a wider field of view than advertised by the manufacturer, but there was no sharp distinction between target and nontarget radiation (Table 2, Figure 1). The fraction of the radiation from the edges may be acceptably small when the nontarget area is at a similar temperature to the target.
FIGURE 1  The sensor field of view expressed as percent of the input signal coming from the target at increasing distances from the target. The target was a black body cone, which had low emissivity aluminum foil around its perimeter. All IRTs accurately measured the cone temperature when they were less than 0.2 diameters away from the target, but the fraction of the target viewed decreased as the distance from the target increased.
TABLE 2  The field of view at which 90 or 99% of the signal comes from the target for the transducers in this study. The field of view as indicated by the manufacturer is shown in the 3rd column. Data from Figure 1.

TABLE 2

90 %

99 %

MANUFACTURER

EXERGEN WIDE

 101° 138° ~90°

EXERGEN NARROW

 80° 128° ~35°

EVEREST 3000AL

 51° 115° ~25°

SENSOR BODY AND BLACK BODY TARGET ERRORS

The error in measurement of the black body target was within the manufacturer’s specifications for both transducers. The output of the Exergen was read as a thermocouple without additional linearization. The mV output of the Everest transducer was linearized with a 5th order polynomial supplied by the manufacturer.
The Exergen sensor error was nonlinear at a constant sensor body temperature and changed from -0.5°C to 1.5 °C as the black body temperature was changed from -9 to +9°C above and below the sensor body temperature (Fig. 2). There was a slightly different curve at each sensor body temperature. The sensor error at all temperatures was less than 0.1°C when the transducer sensor body is held at the same temperature as the target.
FIGURE 2   TOP GRAPH   The errors in the measurement of black body temperature for 4 replicate Exergen IRt/c 0.2 sensors with a narrow field of view. The 4 sensors were purchased on different dates in 1995 and 1996. Each point represents the mean of 3 replicate readings taken on different days. Each data point was reproducible to within 0.02°C. The five groups of lines represent sensor body temperatures from 15 to 35°C.  BOTTOM GRAPH   Measurement error for a single Everest 3000 AL sensor. The four lines in the bottom graph represent sensor body temperatures from 20 to 35 °C. The mV output of the 3000 AL transducer was linearized with the fifth order polynomial supplied by the manufacturer. The error was reproducible on different days and could easily be corrected in software.

LINEARIZATION OF THE EXERGEN NARROW FOV TRANSDUCER

We selected the Exergen narrow FOV sensor for further testing and examined several types of equations to model the nonlinear relation between the sensor error and black body temperature and found that the simplest relation was a parabolic function (Eqn 2).

Error = ( 0.25/p )*[((Apparent Target Temperature - h )2 ) - k ] (2)

This function models error in terms of a directrix coefficient, p, two vertex coefficients (h, k), and the apparent black body temperature. This model describes the error at a single sensor body temperature. In order to describe the entire family of curves in Fig 2, it was necessary to parameterize each of the fitting coefficients (p, h, and k) as a function of sensor body temperature (Fig 3). The final model incorporates three functions (P(sb), H(sb), and K(sb)) which are polynomials describing how the parameters in Eqn 2 vary as a function of sensor body temperature (Eqn 3). A sensor error correction term, SEC, can then be calculated from Eqn 3.

SEC = ( 0.25/P(sb))*[((Apparent Target Temperature - H(sb))2 ) - K(sb) ] (3)

when the sensor body and the target temperatures are measured. The SEC is then used to correct the observed target temperature errors caused by sensor body and target temperatures (Eqn 4).

Corrected Target Temperature = Apparent Target temperature - SEC (4)

The generic (sensor independent) calibration polynomials are:

P(sb) = 26.168 + 2.8291*SB - 0.03329*SB^2 r^2 = 0.708
H(sb) = 5.8075 - 0.08016*SB + 8.49e-3*SB^2 r^2=0.674
K(sb) =-85.943 + 11.740*SB + 0.08477*SB^2 r^2=0.893

The relationship between sensor body temperature and the P, H, and K coefficients could have been fit with linear regression, but the second order polynomial is provides a slightly better fit and is easily implemented in most data acquisition systems. An instruction set for implementing the sensor error correction term in a Campbell Scientific Datalogger is given in Appendix A.

FIGURE 3 The dependence of p, h, and k on sensor body temperature. The dependence of each parameter on sensor body temperature was described by a polynomial denoted H(sb), P(sb), and K(sb).

EXERGEN TRANSDUCER: RESIDUAL ERROR AFTER LINEARIZATION

Figure 4 shows the residual error after implementing the sensor error correction term from Eqn 3 & 4 to the data in Figure 2.

FIGURE 4 GENERIC CORRECTION The residual error after correcting for sensor body and target temperature with one equation for all transducers. The different symbols correspond to different sensors. This generic correction was adequate to achieve 0.2 °C accuracy. CUSTOM CORRECTION. The residual error after correcting each of the four transducers with its own custom correction coefficients. This custom correction was necessary to achieve 0.1 °C accuracy.

INDEPENDENT VERIFICATION OF SENSOR ACCURACY IN A WATER CONE CALIBRATOR

After developing the sensor error correction term, adding thermal mass, and adding a second thermocouple for sensor body temperature, the accuracy was determined using the water cone calibrator. The IRT reading was within 0.2°C of the thermocouples in the stirred water at all temperatures between 14 and 30°C.

ERROR ASSOCIATED WITH DIFFERENT LOTS OF THERMOCOUPLE WIRE

The errors described above are within the limits of error for standard thermocouple wire. We compared 3 types of thermocouple wire from 3 different lots in a rapidly stirred water bath (Omega Eng. USA, 24 AWG).

FIGURE 5  The variation associated with different lots and different types of thermocouple wire. Three, type E thermocouples were used to establish a reference thermocouple response. The type E and type T thermocouples agreed within 0.05°C between 15 and 50°C. The type K wire read consistently below the E and T wire. All thermocouples agreed within about 0.05°C between 18 and 30°C.

DISCUSSION AND CONLCUSIONS
TOP OF PAGE
It was essential to measure and correct for the sensor body temperature of the Exergen IRTs. Increasing the sensor body mass dampened changes in sensor body temperature in fluctuating air temperatures and improved accuracy. A custom calibration equation for each sensor was needed to achieve ±0.1°C accuracy, but ±0.2°C accuracy was attained with a generic calibration equation.
Consideration of the sensor FOV is necessary for optimal IRT placement, particularly with the wide FOV of the Exergen sensors. Our experience indicates that mounting the sensor vertically above the top of the canopy is the most desirable position for measuring canopy temperature. This position prevents the sensor from seeing sky temperature and the wide angle integrates a considerable canopy area.
The Everest sensor came factory calibrated to ±1°C accuracy, and had a narrower FOV than the Exergen sensors, but would require the addition of considerable thermal mass to achieve ±0.2 °C accuracy in fluctuating air temperatures because of the slow response time of the sensor body.
The Exergen sensors must be obtained without the capacitor to achieve the accuracy described in this paper.
Some of the error is associated with the normal variation among different types of thermocouple wire.

REFERENCES
TOP OF PAGE
Amiro, B. D., G. W. Thurtell, and T. J. Gillespie. 1983. A Small Infrared Thermometer for Measuring Leaf Temperature in Leaf Chambers. Jour. Of Experimental Botany. 34:1569-1576.
Fuchs, M. 1990. Canopy Thermal Infrared Observations. Remote Sensing Reviews 5:323-333.
Fuchs, M, and C.B. Tanner. 1966. Infrared thermometry of vegetation. Agron. Jour. 58: 597-601.
Hatfield, J. L. 1990. Measuring Plant Stress with an Infrared Thermometer. HortScience, 25:1535-1538.
Hipps, L. 1989. The Infrared Emissivities of Soil and Artemisia tridentata and Subsequent Temperature Corrections in a Shrub-Steppe Ecosystem. Remote Sens. Environ. 27:337-342.
Huband NDS, and JL Monteith. 1986. Radiative surface temperature and energy balance of a wheat canopy. I. Comparison of radiative and aerodynamic temperature. Boundary-Layer Meteorology 36:1-17.
Idso, S. B., RD Jackson, WL Ehrler, and ST Mitchell. 1969. A method for determination of infrared emittance of leaves. Ecology. 50:899-902.
Kalma J. D., and H. Alksnis. 1988. Calibration of Small Infra-Red Surface Temperature Transducers. Ag. and Forest Meteorology, 43:83-98.
Norman J. M., F. Becker. 1995. Terminology in thermal infrared remote sensing of natural surfaces. Ag. and Forest Meteorology. 77:153-166.

APPENDIX A
TOP OF PAGE

12 GENERIC INSTRUCTIONS FOR MEASURING AND LINEARIZING AN EXERGEN IRt/c 0.2 TYPE K THERMOCOUPLE TRANSDUCER IN A CSI DATALOGGER

Basic equation being implemented (see text): SEC = 0.25/Psb*[{(AppTarget T - Hsb)2}-Ksb]

This basic instruction set can used in a subroutine for up to 25 IRTs per multiplexer.  First measure reference temperature (referenceT) as specified in the AM25T multiplexer manual.
Measure IRt/c apparent target temperature
1: Thermocouple Temp (differential) (P14)1: 1 Rep
2: 21 2.5 mV 60 Hz Rejection Range
3: 1 IN Channel
4: 3 Type K (Chromel-Alumel)
5: 1 REF TEMP LOC [referenceT]
6: 10 LOC [ AppTargetT]
7: 1 Multiplier
8: 0 Offset

Measure Sensor Body Temp (type E t/c)
2: Thermocouple Temp (DIFF) (P14)
1: 1 Rep
2: 21 2.5 mV 60 Hz Rejection Range
3: 2 IN Channel
4: 3 Type K (Chromel-Alumel)
5: 1 REF TEMP LOC [referenceT]
6: 20 LOC [ SensorBodyT]
7: 1 Multiplier
8: 0 Offset

Calculate P, H, & K Coefficients
3: Polynomial (P55)
1: 1 Reps
2: 20 X Loc [ SensorBodyT]
3: 110 F(X) Loc [ Psb]
4: -18.35      C0
5: +7.0435      C1
6: -0.12      C2

4: Polynomial (P55)
1: 1 Reps
2: 20 X Loc [SensorBodyT]
3: 120 F(X) Loc [ Hsb]
4: +21.15      C0
5: -1.12      C1
6: +0.0285      C2

5: Polynomial (P55)
1: 1 Reps
2: 20 X Loc [ SensorBodyT]
3: 130 F(X) Loc [ Ksb ]
4: -499.19      C0
5: +39.97       C1
6: -0.5057      C2
Calculate correction factor (SEC)
6: Z=1/X (P42) {1/Psb}
1: 110 X Loc [Psb]
2: 110 Z Loc [ Psb]

7: Z=X*F (P37) {.25/Psb}
1: 110 X Loc [ Psb]
2: .25 F
3: 110 Z Loc [ Psb]

8: Z=X-Y (P35) {ATT - Hsb}
1: 10 X Loc [AppTargetT]
2: 120 Y Loc [ Hsb]
3: 120 Z Loc [ Hsb]

9: Z=X*Y (P36) {ATT - Hsb}2
1: 120 X Loc [ Hsb]
2: 120 Y Loc [ Hsb]
3: 120 Z Loc [ Hsb]

10: Z=X-Y (P35) {subtract Ksb}
1: 120 X Loc [ Hsb]
2: 130 Y Loc [ Ksb]
3: 130 Z Loc [ Ksb]

11: Z=X*Y (P36) {calculate SEC}
1: 110 X Loc [Psb]
2: 130 Y Loc [ Ksb]
3: 30 Z Loc [SEC]

Calculate corrected target temperature (CTT)
12: Z=X-Y (P35) {AppTarget T - SEC}
1: 10 X Loc [AppTargetT]
2: 30 Y Loc [SEC]
3: 40 Z Loc [CTT]
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