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Field evaluation of the temperature stability of a multispectral radiometer
REMOTE SENSING OF ENVIRONMENT 17:103-108 (1985)
103
SHORT COMMUNICATION Field Evaluation of the Temperature Stability of a Multispeetral Radiometer RAY D. JACKSON U.S. Water Conservation Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Phoenix, AZ 85040
BARRETT F. ROBINSON School of Electrical Engineering, Purdue University, West Lafayette, IN 47907
Measurements of radiance from a calibrated barium sulfate painted reflectance panel, made during the course of routine field experiments, were used to evaluate the effect of detector temperature on the voltage output from silicon (Si) and lead sulfide (PbS) detectors of a multiband spectral radiometer. The four Si detectors were found to be nearly independent of temperature changes. However, the voltage output from the three PbS detectors decreased linearly with increasing detector temperature at a rate of 4 - 5 % ° C 1, which is considerably more than expected from manufacturer's specifications for the instrument. The error in reflectance values caused by a detector temperature change of I ° C was less than 0.25% of value for the Si detectors, but was about 2.5% of value for the PbS detectors. A correction factor was derived to adjust measured voltages to a reference temperature and to compute corrected reflectances. The correction factor can be derived from analysis of field measurements of radiance from a calibrated reflectance panel, if the detector temperature is known at the time of measurement.
Introduction
Temperature stability (repeatable performance at different ambient temperatures) is an essential feature for field radiometers. When absolute radiance values are required, ambient temperature changes will affect unstable detectors and cause errors in the data. When data are transformed into reflectances, stability is crucial if the detector temperature changes between the time that a standard reflectance panel is measured and the time of target data collection. Radiometers that measure reflected and emitted radiation within the wavelength interval of 0 . 4 - 1 5 / , m use detectors whose voltage response can be altered by the temperature of the detector (Slater, 1980). ©Elsevier Science Publishing Co., Inc., 1985 52 Vanderbilt Ave., New York, NY 10017
To circumvent this problem, temperature compensation circuits may be included as an integral part of detector configurations. However, adequate temperature insensitivity is not always achieved. During the course of a 5-month field experiment in which reflectance measurements were made with a multiband spectral radiometer over a wheat canopy, it became evident that certain bands were sensitive to ambient temperature changes. Conventional methods for evaluating this temperature sensitivity require specialized facilities and equipment (e.g., a stable radiance source) that are not always available at field locations. This report describes a method, based on field measurements, for correcting the output voltage of a multispectral radiometer to 0034-t257/85/$3.30
104
compensate for changes in detector temperature and to compute corrected reflectances.
Equipment and Procedure The data reported here were obtained with an eight-band multispectral radiometer specifically designed for field use (Robinson et al., 1979). This instrument, the Barnes 12-1000 Modular Multispectral Radiometer 1 (MMR), mimics the spectral bandwidths of the Thematic Mapper (TM), with one additional band at 1.15-1.30 gm (Table 1). MMR bands 1-4 have silicon (Si) detectors, bands 5-7 have lead sulfide (PbS) detectors, and the thermal band (MMR-8) detector is lithium tantalate (LiTaO3). The manufacturer's instruction manual states that each detector has a thermistor-based temperature compensation circuit to reduce variations in output voltage due to ambient temperature changes. Temperature stability of the Si channels is given as 1% for a 5 °C temperature change of air blowing around the instrument for 20-min periods within the ambient temperature range of 15-35°C. Temperature stability of the PbS channels is given as 2% for the same conditions. Robinson et al. (1981) tested the prototype instrument and found that the temperature stability of the PbS channels was twice the manufacturer's specifications and concluded that compensation using the detector temperature monitor might be required for conditions other than as specified. The temperature sensitivity of the thermal band was discussed
I Trade names and company names are included for the benefit of the reader and do not imply endorsement by the U.S, Department of Agriculture or Purdue University.
R. D. JACKSON AND B. F. ROBINSON
by Jackson et al. (1983) and will not be considered here. The experimental procedure consisted of measuring the radiance from a calibrated BaSO4-painted panel 2 at the start, the midpoint, and the end of the measurements over a wheat canopy. The entire sequence required about 20 min to complete, with the measurements centered at 1035 MST (1735 CUT), the approximate local time of Landsat-4 overpass. Measurements were made on cloud-free days from January to May 1983. The instrument was placed out-of-doors for at least 30 min to allow it to approach ambient temperature. Detector voltage outputs (Vt~g,t) were recorded with an Omuidata Polycorder 1 and later transferred to a computer. After subtracting the dark levels (Vd~rk), the voltages were divided by the gain settings, thus normalizing 'all data to a gain of 1. The voltages for each detector were then divided by the BaSO4 panel reflectance (pp~u,,0 that had been corrected for sun zenith angle effects (Robinson and Biehl, 1979; Kimes and Kirchner, 1982). This procedure yielded voltage values that approximated those that would have been obtained if the BaSO4 panel had been a perfect lambertian reflector. The temperature of the MMR detectors was indirectly measured by monitoring a thermistor embedded in an aluminum plate in close thermal contact with the detectors. The thermistor output was used as a measure of the seven detector temperatures. To isolate the temperature effect, it was necessary to adjust the voltages to represent those expected under identical irradiance conditions. Accordingly, the 2L. L. Biehl. personal communication.
R A D I O M E T E R TEMPERATURE STABILITY
105
TABLE 1 Nominal Wavelength Intervals for the Eight-Band Barnes 12-1000 MMR and the Corresponding Thematic Mapper Bands. MMR BA~,rD 1 2 3 4 5 6 7 8
W A v E t ~ o ' r a (/zm)
TM BAND
0.42-0.50 0.52-0.60 0.63-0.69 0.76-0.90 1.15-1.30 1.55-1.75 2.05-2.30 10.5-12.5
1 2 3 4
:I
MMR t -
(1)
where Vr is the voltage at the reference zenith angle 0r (taken as 45°), V the adjusted voltage V = (Vt~get - Vdark)/ (gain × Ppanel), and O= the zenith angle at the time w h e n V was measured. This procedure is not exact because it does not account for diffuse radiation and is affected by atmospheric scattering,
5 7 6
3
voltages were adjusted to a constant zenith angle, i.e.,
Vr= V(cos Or)/(COSOz),
--
~1 ~ [ ~-~r 3 o~ > e r-~ 3 ,.,
f
Voltages from the four bands with Si detectors, adjusted to a voltage that would correspond to the radiance at Or---45 o, are plotted versus the detector temperature in Fig. 1. Figure 2 shows similar data for the three bands having PbS detectors. Slopes and intercepts from linear regression are given in Table 2. These data show that the output voltage from the Si detectors are acceptably independent of detector temperature, changing less than 0.5%°C -~ , whereas the PbS detector outputs change as much as 4-5% °C 1. At least three factors contribute to the scatter of data points about the regression lines in Figs. 1 and 2: 1) Diffuse radiation was ignored in correcting the voltage data
i
i
.~. .--.'~'--~... • , ~ '.~ ~'~~-Sj~' ~ ~
~,
MMR-2-
b~)
c~ (K
Results and Discussion
i
MMR- 3 3
ii MMqRIo
20
30
qo
DETECTOR TEMPERATURE F I G U R E 1. Adjusted voltages versus detector temperature for four M M R bands with silicon detectors.
to a reference radiance, 2) the change in atmospheric scattering from one measurem e n t to the next was not accounted for, and 3) the correction of the BaSO 4 panel reflectance for nonlambertian effects may not have been sufficiently accurate. Generally, the first two factors would introduce random errors, whereas the third factor could be biased. However, the re-
I(X~
R. D. J A C K S O N A N D B, F. R O B I N S O N 3
Table 2. Equation (2) can be written in the forin
v = (a + B'r)L, MMR- S L~J 4.9
where a , . = AL~, b, = BL,, and L r is the radiance of the calibration panel which has been adjusted to a reference sun angle of 45 ° . For any radiance level (L) the output voltage (V) for any detector temperature ( T ) will be
i 2
F0
>
tEb
(3)
l
Ld F-O3 MNR- 6 3
V = (A + B T ) L .
MMRl0
(4)
Since it is desired to adjust the measured voltage values to a standard temperature (To), we define
7 20
30
t+0
v o = ( A + BTo )L,
DETECTOR TEMPERATURE
FIGURE 2. Adjustedvoltagesversusdetectortempera ture for three MMRt)andswithlead sulfidedetectors. stdts clearly define a linear relation between normalized voltages and the detector temperature. The relation can be expressed as V~ = a,. + b,T,
(5)
where Vo is the voltage that the radiance L woldd produce at a temperature T0. Dividing Eq. (5) by Eq. (3) and rearranging, we obtain ~, L, A / B ÷ I'o . . . . . . . . Vr L A/B+T'
(6)
(2) from Eq. (1)
where a,. and b r a r e the intercept and slope. Values of a~ and b,, corresponding to a zenith angle of 45 ° are given in
V,. V
L, I,
TABLE 2 Slopes, Intercept, and r 2 Values Besulting from I,m ear Regression of Adjusted Voltages and Detector Temperatures. M M B BAND
SLOPE
INTERCEPTS
r ?
1 2 :3 4 5 6 7
0.0005 ~ 0.0022 0.0049 + 0.(X)08 0.0505 0.0362 0.0395
1.9:32 3.651 2.070 1.793 5;.301 2.325 2.552
0.007 0.032 0.438 0.029 0.969 ().9~,3 0.97S
cos 0~ cos 0 '
(7)
RADIOMETER TEMPERATURE STABILITY
107
which is valid at any detector temperature within the region of interest. The voltage (V), measured at any temperature (T), can be adjusted to its corresponding value at a reference temperature (T0) by multiplying by a correction factor (13), which is defined as t~ -
V° V
"/
a:
O I.-k.d
b._
z o ~J Ld P~
A / B + T° - ar/b~ + To A/B + r a,./br+T"
0 kJ
I J
(8) Figure 3 shows the relation of 13 to the detector temperature for a reference temperature of 25°C. Values of a , and br for MMR bands 5 and 6 (Table 2) were used in the calculation. Values of 13 for MMR-7 were intermediate between bands 5 and 6. Since the ratio a , / b , was nearly the same for the three detectors, the use of a single average correction factor for the three PbS bands would cause only a small error ( < 1% at 0°C and < 5% at 50°C). The error in target reflectance when the MMR temperature changes following measurement of the reflectance standard is of interest. The uncorrected reflectance factor (O) is adjusted to the reference temperature by
(9)
Oo = o B ,
where p = V / V o , and Vop is the voltage measured for the reflectance standard corrected to the reference temperature (To). Using Eqs. (9) and (8) and rearranging yields
T P=Po
lo
80
40
SO
TEMPERRTURE
F I G U R E 3. T h e voltage a n d reflectance correction factor (/~) as a [unction o | d e t e c t o r t e m p e r a t u r e for TO = 25°C.
linear function of the detector temperature with a slope of a
d o / d T = Oo/(To + a , / b r ) .
(11)
Equation (11) is a measure of the sensitivity of reflectance measurements to temperature drift after the reference panel measurement was taken. The sensitivities for the four Si and the three PbS detectors are given in Table 3. The Si bands are adequately insensitive to temperature changes, but sensitivity of the PbS channels may be as much as 2.5%°C - 1. T A B L E 3 Sensitivity ( d p / d T ) of Reflectance Values to D e t e c t o r T e m p e r a t u r e C h a n g e s Following the M e a s u r e m e n t of the Reflectance Standard.
d p/ dT M M R Bn_~D 1 2 3 4 5 6 7
~ ,
(10) which shows that the reflectance factor is
20
DETECTOR
a r/br )
To+ar/b, + To+ajb
J
~For a
10% reflector.
(°C + + -
l)
0.0003 0.0006 0.0025 0.0004 0.0258 0.0255 0.0257
REFLECTn.NCE Era~oR (% o C - l)~ + + -
0.003 0.006 0.025 0.004 0.258 0.255 0.257
108
B. 1). JACKSON AND B. F. ROBINSON
Concluding Remarks
References
Although the results reported here may not apply directly to other instruments, the large sensitivity of PbS detectors to temperature changes suggests that this factor should be evaluated for instruments that are used under conditions where temperature effects may pose a problem. If the instrument temperature change is monotonic, the error in target reflectance caused by detector temperature sensitivity can be reduced by measuring reflectance panel radiances before and after the target measurements and interpolating to the time that the targets were measured. The data required for evaluating the temperature effect can be obtained during the course of field measurements. If reflectance standards are measured at a number of different ambient temperatures, and the detector temperature and the time (for stm zenith angle calculations) are noted, an analysis such as that described here can be used to evaluate the effects of changing temperatures, to correct the measured voltage to a reference temperature, and to compute corrected reflectances.
Jackson, R. D., Dusek, D. A., and Ezra, C. E. (1983), Calibration of the thermal channel on four Barnes Model 12-1000 multi-modtdar radiometers, WCL Report 12, U.S. Water Conservation Laboratory, Phoenix AZ, pp. 75. Kimes, D. S., and Kirchner, J. A. (1982), Irradiance measurement errors due to the assumption of a Lambertian reference panel, Renugte Sens. Environ. 12:141-149. Robinson, B. F., and Biehl, L. L. (1979), Calibration procedures for measurement of reflectance factor in remote sensing field research, Soc. Photo-opt. Instrum. Eng. 196:16--26. Robinson, B. F., Bauer, M. E., DeWitt, D. P., Silva, L. F., and Vanderbilt, V. C. (1979), Multiband radiometer for field research, Soc. Photo-opt. Instrum. Eng. 196:8-15. Robinson, B. F., Bucldey, R. E., and Burgess, J. A. (1981), Performance evaluation and calibration of a modular mtdtiband radiometer for remote sensing field research, Soc. Photo-opt. I~'trum. Eng. 308:146 157. Slater, P. N. (1980), Renu~te Sensing: Optics and Optical Systevn~s', Addison-Wesley, Reading, MA, p. 575. l~eceit ed 13 January 1984, revised 23 ]uly 1,98.4.
103
SHORT COMMUNICATION Field Evaluation of the Temperature Stability of a Multispeetral Radiometer RAY D. JACKSON U.S. Water Conservation Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Phoenix, AZ 85040
BARRETT F. ROBINSON School of Electrical Engineering, Purdue University, West Lafayette, IN 47907
Measurements of radiance from a calibrated barium sulfate painted reflectance panel, made during the course of routine field experiments, were used to evaluate the effect of detector temperature on the voltage output from silicon (Si) and lead sulfide (PbS) detectors of a multiband spectral radiometer. The four Si detectors were found to be nearly independent of temperature changes. However, the voltage output from the three PbS detectors decreased linearly with increasing detector temperature at a rate of 4 - 5 % ° C 1, which is considerably more than expected from manufacturer's specifications for the instrument. The error in reflectance values caused by a detector temperature change of I ° C was less than 0.25% of value for the Si detectors, but was about 2.5% of value for the PbS detectors. A correction factor was derived to adjust measured voltages to a reference temperature and to compute corrected reflectances. The correction factor can be derived from analysis of field measurements of radiance from a calibrated reflectance panel, if the detector temperature is known at the time of measurement.
Introduction
Temperature stability (repeatable performance at different ambient temperatures) is an essential feature for field radiometers. When absolute radiance values are required, ambient temperature changes will affect unstable detectors and cause errors in the data. When data are transformed into reflectances, stability is crucial if the detector temperature changes between the time that a standard reflectance panel is measured and the time of target data collection. Radiometers that measure reflected and emitted radiation within the wavelength interval of 0 . 4 - 1 5 / , m use detectors whose voltage response can be altered by the temperature of the detector (Slater, 1980). ©Elsevier Science Publishing Co., Inc., 1985 52 Vanderbilt Ave., New York, NY 10017
To circumvent this problem, temperature compensation circuits may be included as an integral part of detector configurations. However, adequate temperature insensitivity is not always achieved. During the course of a 5-month field experiment in which reflectance measurements were made with a multiband spectral radiometer over a wheat canopy, it became evident that certain bands were sensitive to ambient temperature changes. Conventional methods for evaluating this temperature sensitivity require specialized facilities and equipment (e.g., a stable radiance source) that are not always available at field locations. This report describes a method, based on field measurements, for correcting the output voltage of a multispectral radiometer to 0034-t257/85/$3.30
104
compensate for changes in detector temperature and to compute corrected reflectances.
Equipment and Procedure The data reported here were obtained with an eight-band multispectral radiometer specifically designed for field use (Robinson et al., 1979). This instrument, the Barnes 12-1000 Modular Multispectral Radiometer 1 (MMR), mimics the spectral bandwidths of the Thematic Mapper (TM), with one additional band at 1.15-1.30 gm (Table 1). MMR bands 1-4 have silicon (Si) detectors, bands 5-7 have lead sulfide (PbS) detectors, and the thermal band (MMR-8) detector is lithium tantalate (LiTaO3). The manufacturer's instruction manual states that each detector has a thermistor-based temperature compensation circuit to reduce variations in output voltage due to ambient temperature changes. Temperature stability of the Si channels is given as 1% for a 5 °C temperature change of air blowing around the instrument for 20-min periods within the ambient temperature range of 15-35°C. Temperature stability of the PbS channels is given as 2% for the same conditions. Robinson et al. (1981) tested the prototype instrument and found that the temperature stability of the PbS channels was twice the manufacturer's specifications and concluded that compensation using the detector temperature monitor might be required for conditions other than as specified. The temperature sensitivity of the thermal band was discussed
I Trade names and company names are included for the benefit of the reader and do not imply endorsement by the U.S, Department of Agriculture or Purdue University.
R. D. JACKSON AND B. F. ROBINSON
by Jackson et al. (1983) and will not be considered here. The experimental procedure consisted of measuring the radiance from a calibrated BaSO4-painted panel 2 at the start, the midpoint, and the end of the measurements over a wheat canopy. The entire sequence required about 20 min to complete, with the measurements centered at 1035 MST (1735 CUT), the approximate local time of Landsat-4 overpass. Measurements were made on cloud-free days from January to May 1983. The instrument was placed out-of-doors for at least 30 min to allow it to approach ambient temperature. Detector voltage outputs (Vt~g,t) were recorded with an Omuidata Polycorder 1 and later transferred to a computer. After subtracting the dark levels (Vd~rk), the voltages were divided by the gain settings, thus normalizing 'all data to a gain of 1. The voltages for each detector were then divided by the BaSO4 panel reflectance (pp~u,,0 that had been corrected for sun zenith angle effects (Robinson and Biehl, 1979; Kimes and Kirchner, 1982). This procedure yielded voltage values that approximated those that would have been obtained if the BaSO4 panel had been a perfect lambertian reflector. The temperature of the MMR detectors was indirectly measured by monitoring a thermistor embedded in an aluminum plate in close thermal contact with the detectors. The thermistor output was used as a measure of the seven detector temperatures. To isolate the temperature effect, it was necessary to adjust the voltages to represent those expected under identical irradiance conditions. Accordingly, the 2L. L. Biehl. personal communication.
R A D I O M E T E R TEMPERATURE STABILITY
105
TABLE 1 Nominal Wavelength Intervals for the Eight-Band Barnes 12-1000 MMR and the Corresponding Thematic Mapper Bands. MMR BA~,rD 1 2 3 4 5 6 7 8
W A v E t ~ o ' r a (/zm)
TM BAND
0.42-0.50 0.52-0.60 0.63-0.69 0.76-0.90 1.15-1.30 1.55-1.75 2.05-2.30 10.5-12.5
1 2 3 4
:I
MMR t -
(1)
where Vr is the voltage at the reference zenith angle 0r (taken as 45°), V the adjusted voltage V = (Vt~get - Vdark)/ (gain × Ppanel), and O= the zenith angle at the time w h e n V was measured. This procedure is not exact because it does not account for diffuse radiation and is affected by atmospheric scattering,
5 7 6
3
voltages were adjusted to a constant zenith angle, i.e.,
Vr= V(cos Or)/(COSOz),
--
~1 ~ [ ~-~r 3 o~ > e r-~ 3 ,.,
f
Voltages from the four bands with Si detectors, adjusted to a voltage that would correspond to the radiance at Or---45 o, are plotted versus the detector temperature in Fig. 1. Figure 2 shows similar data for the three bands having PbS detectors. Slopes and intercepts from linear regression are given in Table 2. These data show that the output voltage from the Si detectors are acceptably independent of detector temperature, changing less than 0.5%°C -~ , whereas the PbS detector outputs change as much as 4-5% °C 1. At least three factors contribute to the scatter of data points about the regression lines in Figs. 1 and 2: 1) Diffuse radiation was ignored in correcting the voltage data
i
i
.~. .--.'~'--~... • , ~ '.~ ~'~~-Sj~' ~ ~
~,
MMR-2-
b~)
c~ (K
Results and Discussion
i
MMR- 3 3
ii MMqRIo
20
30
qo
DETECTOR TEMPERATURE F I G U R E 1. Adjusted voltages versus detector temperature for four M M R bands with silicon detectors.
to a reference radiance, 2) the change in atmospheric scattering from one measurem e n t to the next was not accounted for, and 3) the correction of the BaSO 4 panel reflectance for nonlambertian effects may not have been sufficiently accurate. Generally, the first two factors would introduce random errors, whereas the third factor could be biased. However, the re-
I(X~
R. D. J A C K S O N A N D B, F. R O B I N S O N 3
Table 2. Equation (2) can be written in the forin
v = (a + B'r)L, MMR- S L~J 4.9
where a , . = AL~, b, = BL,, and L r is the radiance of the calibration panel which has been adjusted to a reference sun angle of 45 ° . For any radiance level (L) the output voltage (V) for any detector temperature ( T ) will be
i 2
F0
>
tEb
(3)
l
Ld F-O3 MNR- 6 3
V = (A + B T ) L .
MMRl0
(4)
Since it is desired to adjust the measured voltage values to a standard temperature (To), we define
7 20
30
t+0
v o = ( A + BTo )L,
DETECTOR TEMPERATURE
FIGURE 2. Adjustedvoltagesversusdetectortempera ture for three MMRt)andswithlead sulfidedetectors. stdts clearly define a linear relation between normalized voltages and the detector temperature. The relation can be expressed as V~ = a,. + b,T,
(5)
where Vo is the voltage that the radiance L woldd produce at a temperature T0. Dividing Eq. (5) by Eq. (3) and rearranging, we obtain ~, L, A / B ÷ I'o . . . . . . . . Vr L A/B+T'
(6)
(2) from Eq. (1)
where a,. and b r a r e the intercept and slope. Values of a~ and b,, corresponding to a zenith angle of 45 ° are given in
V,. V
L, I,
TABLE 2 Slopes, Intercept, and r 2 Values Besulting from I,m ear Regression of Adjusted Voltages and Detector Temperatures. M M B BAND
SLOPE
INTERCEPTS
r ?
1 2 :3 4 5 6 7
0.0005 ~ 0.0022 0.0049 + 0.(X)08 0.0505 0.0362 0.0395
1.9:32 3.651 2.070 1.793 5;.301 2.325 2.552
0.007 0.032 0.438 0.029 0.969 ().9~,3 0.97S
cos 0~ cos 0 '
(7)
RADIOMETER TEMPERATURE STABILITY
107
which is valid at any detector temperature within the region of interest. The voltage (V), measured at any temperature (T), can be adjusted to its corresponding value at a reference temperature (T0) by multiplying by a correction factor (13), which is defined as t~ -
V° V
"/
a:
O I.-k.d
b._
z o ~J Ld P~
A / B + T° - ar/b~ + To A/B + r a,./br+T"
0 kJ
I J
(8) Figure 3 shows the relation of 13 to the detector temperature for a reference temperature of 25°C. Values of a , and br for MMR bands 5 and 6 (Table 2) were used in the calculation. Values of 13 for MMR-7 were intermediate between bands 5 and 6. Since the ratio a , / b , was nearly the same for the three detectors, the use of a single average correction factor for the three PbS bands would cause only a small error ( < 1% at 0°C and < 5% at 50°C). The error in target reflectance when the MMR temperature changes following measurement of the reflectance standard is of interest. The uncorrected reflectance factor (O) is adjusted to the reference temperature by
(9)
Oo = o B ,
where p = V / V o , and Vop is the voltage measured for the reflectance standard corrected to the reference temperature (To). Using Eqs. (9) and (8) and rearranging yields
T P=Po
lo
80
40
SO
TEMPERRTURE
F I G U R E 3. T h e voltage a n d reflectance correction factor (/~) as a [unction o | d e t e c t o r t e m p e r a t u r e for TO = 25°C.
linear function of the detector temperature with a slope of a
d o / d T = Oo/(To + a , / b r ) .
(11)
Equation (11) is a measure of the sensitivity of reflectance measurements to temperature drift after the reference panel measurement was taken. The sensitivities for the four Si and the three PbS detectors are given in Table 3. The Si bands are adequately insensitive to temperature changes, but sensitivity of the PbS channels may be as much as 2.5%°C - 1. T A B L E 3 Sensitivity ( d p / d T ) of Reflectance Values to D e t e c t o r T e m p e r a t u r e C h a n g e s Following the M e a s u r e m e n t of the Reflectance Standard.
d p/ dT M M R Bn_~D 1 2 3 4 5 6 7
~ ,
(10) which shows that the reflectance factor is
20
DETECTOR
a r/br )
To+ar/b, + To+ajb
J
~For a
10% reflector.
(°C + + -
l)
0.0003 0.0006 0.0025 0.0004 0.0258 0.0255 0.0257
REFLECTn.NCE Era~oR (% o C - l)~ + + -
0.003 0.006 0.025 0.004 0.258 0.255 0.257
108
B. 1). JACKSON AND B. F. ROBINSON
Concluding Remarks
References
Although the results reported here may not apply directly to other instruments, the large sensitivity of PbS detectors to temperature changes suggests that this factor should be evaluated for instruments that are used under conditions where temperature effects may pose a problem. If the instrument temperature change is monotonic, the error in target reflectance caused by detector temperature sensitivity can be reduced by measuring reflectance panel radiances before and after the target measurements and interpolating to the time that the targets were measured. The data required for evaluating the temperature effect can be obtained during the course of field measurements. If reflectance standards are measured at a number of different ambient temperatures, and the detector temperature and the time (for stm zenith angle calculations) are noted, an analysis such as that described here can be used to evaluate the effects of changing temperatures, to correct the measured voltage to a reference temperature, and to compute corrected reflectances.
Jackson, R. D., Dusek, D. A., and Ezra, C. E. (1983), Calibration of the thermal channel on four Barnes Model 12-1000 multi-modtdar radiometers, WCL Report 12, U.S. Water Conservation Laboratory, Phoenix AZ, pp. 75. Kimes, D. S., and Kirchner, J. A. (1982), Irradiance measurement errors due to the assumption of a Lambertian reference panel, Renugte Sens. Environ. 12:141-149. Robinson, B. F., and Biehl, L. L. (1979), Calibration procedures for measurement of reflectance factor in remote sensing field research, Soc. Photo-opt. Instrum. Eng. 196:16--26. Robinson, B. F., Bauer, M. E., DeWitt, D. P., Silva, L. F., and Vanderbilt, V. C. (1979), Multiband radiometer for field research, Soc. Photo-opt. Instrum. Eng. 196:8-15. Robinson, B. F., Bucldey, R. E., and Burgess, J. A. (1981), Performance evaluation and calibration of a modular mtdtiband radiometer for remote sensing field research, Soc. Photo-opt. I~'trum. Eng. 308:146 157. Slater, P. N. (1980), Renu~te Sensing: Optics and Optical Systevn~s', Addison-Wesley, Reading, MA, p. 575. l~eceit ed 13 January 1984, revised 23 ]uly 1,98.4.