NASA/TM-- 1998-208808

Self Calibration of a 2-wavelength Pyrometer

Daniel Ng

Lewis Research Center, Cleveland, Ohio

November 1998

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NASA/TM-- 1998-208808

Self Calibration of a 2-wavelength Pyrometer

Daniel Ng

Lewis Research Center, Cleveland, Ohio

National Aeronautics and

Space Administration

Lewis Research Center

November 1998
NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

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Self Calibration of a 2-wavelength Pyrometer

Daniel Ng

NASA Lewis Research Center

Introduction

Pyrometers require calibrations to determine their instrument constants before they can be

used in remote temperature measurements (Ref. 1) These constants reflect the combined

effects of detector response, the transmissivities of intervening optical media (windows

and gases) and the emissivity of the measured surface. We describe here the principle and

the demonstration of a self calibrating 2-wavelength pyrometer.

Me_od

The basic hardware of the pyrometer is a spectrometer equipped with detector or

detectors sensitive at two wavelengths. In response to radiation from a radiating surface,

the detector response at different wavelengths are simultaneously recorded during a time

in which the measured surface experienced a temperature excursion over an unknown

range.

V(_,,t) is the response of the pyrometer detector at wavelength _, at time t when the

temperature of the emitting surface is T(t). The response of the detector to radiation

emitted from the measured surface is a voltage given by

V(/],, t) = gxex'cxL()_,T(t)) (1)

where g)_is the detector's spectral electrical response constant to radiation at wavelength

_,, e)_is the emissivity of the emitting surface and and "c)_is transmissivity of the

intervening medium or window. The intensity of the radiation arriving at the detector is

ex'cxL(_,,T(t)) where

c1 1

L()_,T(t)) (2)

_5 (exp(c 2 / )_T(t))-1)

is the spectral radiation intensity of a black body at temperature T(t) obeying Planck's

equation, c1 and c2 are the radiation constants.

Assuming no time dependence in gx, ex and "cx, a new quantity A(_,) is defined:

A(_)= gxexvx (3)

The assumption of no time dependence in g_, e_ and "c_is in general valid for most

materials. It is most true for g_ because detectors have good short and long term stability.

e_ of a surface may vary by a large amount due to oxidation or thermal changes during the

temperature excursion. Variation of "c_could be due to absorption by gases whose

concentration in the optical path may vary. At the two wavelengths _1 and _2, data are

recorded from time t = 0 to t = tfinal. Consider the following quantities:

NASA/TM--1998-208808 1
v(;_,o)=A(;_>(;_,r(o))

v(;_,0=A(;_>(;_,r(0)

V(;_,0)=A(;_>(;_,r(o))

v(;_,0=A(;_)L(;_,r(0)

Eqn (6) can be transformed into

&

exp _ =Lv(22,0) ,_ + 1

Similarly Eqn (7) is transformed into

_2

exp i,l:.A( ,Cl _ =kv(22,t) _ +1 ]c2

(4)

(5)

(6)

(7)

(8)

(9)

The ratio of Eqn (4) and Eqn (5) is

V(2,,0) exp(c 2/21T(0))-1

y(t)- V()_,t) - exp(c 2/_-1 (10)

Eqns (8) and (9) are used to eliminate T(0) and T(t) from Eqn (10) and define

1

x(_2,,)- v(_2,,) (11)

from which we obtain

x_

v(&,o) -_ -1

Y(t)-v(_'t)-[ A(_) cl 1_ =[ cl ]_ +' -' A(_)_x(_,t)+l -1

(12)

Analyzing y(t) as defined by Eqn (10) as a function of X(_,2,t) which is defined by

Eqn (11) will determine the constant A(_,2). With A(_,2) determined, the temperature in

Eqn (2) at any time t is determined to be

c2/_

T(t) = Ln (A(_) I (13)

NASA/TM--1998-208808 2
Experiment

To illustrate the working of this pyrometry method, a commercial

spectrometer/radiometer was used. It possessed an indium antimonide/mercury cadmium

telluride detector and a filter wheel monochromator for radiation from 1.3 to 14.5 gm.

Normal radiometer calibration was omitted. The spectrometer was exposed to radiation

from a black body furnace whose temperature was gradually increased from room

temperature to 1300 K. The temperature of the furnace was constant during the time the

spectrometer acquired a spectrum. At each temperature, the detector output voltage

spectrum was recorded (Fig 1). In Figure 1, the different traces in the spectrum

correspond to different temperatures. The temperature of the black body furnace was

measured using a chromel-alumel thermocouple.

Results

Voltage data at different times (hence at different temperatures) for radiation at

wavelengths _, = 2 and _, = 5 gm were transformed according to Eqns (10) and (11). Two

analyses were performed on the data. In the first analysis, one wavelength was treated as

_,1 while the other wavelength was treated as _,2 • In the second analysis, the designation

of )_1 and )_2 was reversed. The results are shown in Fig. 2 and Fig. 3. Calculations

performed according to Eqn (12) for the value of A0_) are shown in both figures. The

value of A0_) was determined using the least squares method. With the determined values

of A0_) used in Eqn (13), the temperatures at different times are calculated. Comparison

of these temperatures with the thermocouple produced temperatures are shown in Fig. 4.

The agreements are excellent. The straight line through the data is a plot of slope equal 1.

Conclusion

The working of a self calibrating 2-wavelength pyrometer is demonstrated. The pyrometer

calibration constant is automatically determined by the pyrometer. The voltage response

of detectors at two different wavelengths at many different unknown temperatures was

analyzed to determine the calibration constants and used to measure temperatures at

subsequent times.

References

. DeWitt, D.P., Nutter, G.D., Theory and practice of Radiation Thermometry, John

Wiley & Sons, New York, 1988.

NASA/TM--1998-208808 3
VOLTAGE SPECTRUM

1.4

1.2

_" 1.0

LU- 0.8

(.9

<

_- 0.6

d

O

> 0.4

11i // _!_ "_,,,

o.o ....

0 2 4 6 8 10 12 14

WAVELENGTH, gm

Figure 1

16

6

5

v 4

3

2

1

0

[3

0

[]•

PLOT OF y(t) vs x(t)

X1 = 2 gm

X2 = 5 i_m

[]

• [3

.... I .... I .... I

50 x(t) 100 150

Figure 2

NASA/TM--1998-208808 4
120

100

80

_v 60

40

20

0

PLOT of y(t) vs x(t)

X1 = 5 _m

X2 = 2 pm

/

/

/D

[]

/

/

•[3

[]

I

[]p•D•• I I I I I I I I I I

0 1 2 3 4 5 6

x(t)

Figure 3

I

7

15OO

v 1000

CC

W

t--

W

O

CC

>- 500

13_

0

TEMPERATURE

0 500 1000

TC (K)

Figure 4

I

1500

NASA/TM--1998-208808 5
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November 1998

4. TITLE AND SUBTITLE

Self Calibration of a 2-wavelength Pyrometer

6. AUTHOR(S)

Daniel Ng

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135- 3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546- 0001

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Technical Memorandum

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WU-523-21-13-00

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REPORT NUMBER

E-11398

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--1998-208808

11. SUPPLEMENTARY NOTES

Responsible person, Daniel Ng, organization code 5510, (216) 433-3638.

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Subject Category: 35 Distribution: Nonstandard

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12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Pyrometers require calibrations to determine their instrument constants before they can be used in remote temperature

measurements. These constants reflect the combined effects of detector response, the transmissivities of intervening

optical media (windows and gases) and the emissivity of the measured surface. We describe here the principal and the

demonstration of self calibrating 2-wavelength pyrometer.

14. SUBJECT TERMS

Pyrometer; Emissivity; Calibration; Temperature measurement

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OF REPORT

Unclassified

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15. NUMBER OF PAGES

11

16. PRICE CODE

A03

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