Dual sensor radiation pyrometer
This invention relates to a pyrometer for measuring the temperature of heated products such as a steel slab or billet in a heating furnace, and more particularly to a dual sensor radiation pyrometer that accurately determines the product temperature in the presence of a substantial amount of reflected external radiation. 
     Accurate knowledge of the temperature of a steel slab or billet in a reheating furnace is necessary to reduce fuel costs and to increase productivity. It is generally impractical to use contact methods for product temperature determination. A far more practical method for temperature determination is the measurement of thermal radiation emitted by the product. A fundamental problem in measuring thermal radiation is that the radiation received by a sensor sighted on the product consists of two components, the radiation emitted by the product and the radiation emitted from the furnace walls that is reflected from the product surface into the sensor. 
     One method of eliminating the reflected radiation component is to shield the product area viewed with water-cooled sight tubes. This method has been limited to furnaces operating at low temperatures, and it is not useful where product movement could damage the equipment or where there is a wide variety of product sizes. 
     Another method is to use an additional sensor to measure or infer the amount of reflected radiation which must be subtracted from the radiation received from the product. This method may be reasonably accurate, but using an additional sensor viewing the furnace emitted radiation, either directly or from a water-cooled target, requires additional viewing ports and careful selection of viewing areas. The method is unsatisfactory where furnace temperatures are not uniform. 
     Still another method is to use two sensors operating at different wavelengths sighting on the product whose outputs may be mathematically manipulated to compute the product temperature. The mathematics may be of sufficent complexity to require the use of a digital computer or a dedicated microprocessor and thus obviate the possibility of a flexible stand-alone type of instrument capable of operating in real-time. The accuracy of this method is dependent upon the accuracy of mathematical relationships used, which may be a fixed correction factor or a factor based on the ratio of the sensor outputs. 
     It is, therefore, an object of my invention to provide a non-contacting pyrometer that accurately measures the surface temperature of an object inside a furnace in the presence of reflected radiation. 
     Another object is to provide a pyrometer that is capable of measuring such temperature in real-time and which may be used as a stand-alone instrument over a range of furnace temperatures and a range of objects inside the furnace. 
    
    
     These and other objects will become more apparent after referring to the following specification and drawings in which 
     FIG. 1 is a schematic drawing of the preferred embodiment of my invention, 
     FIG. 2 is a schematic drawing of a second embodiment of my invention, 
     FIG. 3 is a schematic drawing of a third embodiment of my invention, and 
     FIG. 4 is a partial schematic drawing showing a circuit eliminating flame effects. 
    
    
     Referring now to FIG. 1, reference numeral 2 is a first infrared sensor, preferably a silicon photodiode positioned to receive radiation, both reflected and emitted from a heated slab S in a reheating furnace (not shown). Sensor 2 has a narrow band filter to provide responses only to specific wavelengths over the operating temperature range. A second sensor 4, also a silicon photodiode, is positioned to receive radiation from slab S at the same location as sensor 2. Sensor 4 has a narrow band filter to provide responses to specific wavelengths different from sensor 2, preferably sensor 4 is responsive to longer wavelengths than sensor 2. The output of sensor 2 is connected to the input of a first operational amplifier 6 which has a voltage output 8, linearly proportional to the radiation received by sensor 2, and a feedback resistor 10. The output of sensor 4 is connected to the input of a second operational amplifier 12 which has a voltage output 14, linearly proportional to the radiation received by sensor 4, and a feedback resistor 16. 
     Output 8 of amplifier 6 is connected to the input of a first logarithmic amplifier 18. Amplifier 18 has an output 19 connected to the input of an inverted 20. Inverter 20 has an output 22 connected to a first input of an adder circuit 24. 
     Output 14 of amplifier 12 is connected to the input of a second logarithmic amplifer 26. Amplifier 26 has an output 28 connected to the input of a first function generator 30 and to the input of linearizing circuit 32. Function generator 30 has an output 34 connected to a second input of adder 24. 
     Adder 24 has an output 36 connected to the input of a second function generator 38. Function generator 38 has an adjustable resistor 40 for adjusting the gain of an amplifier in generator 38 and an output 42 connected to a first input of a multiplier circuit 44. Circuit 32 has an output 46 connected to a second input of multiplier 44. Multiplier 44 has an output 48 connected to a temperature indicator 50. 
     Steel slab reheating furnaces operate in a temperature range from 2100° F. to 2500° F., with final slab temperatures ranging from 2100° F. to 2300° F. Over these operating ranges, silicon photodiodes are commonly used as sensors for infrared radiation. These sensors respond to near infrared radiations from about 1.1 micron wavelength to wavelengths in the visible range, but may be equipped with narrow-band filters to provide responses only to specific wavelengths in this range. 
     Sensors 2 and 4 approximately linearly convert incoming radiation into a current output when operating in a short-circuit mode. The current output is converted by amplifiers 6 and 12 to voltage outputs 8 and 14, designated as V 1  and V 2  respectively, linearly proportional to the amount of radiation received by each sensor. 
     If sensors 2 and 4 view a surface temperature, T s , for slab S, the amount of radiation, R, received by each sensor under narrow-band conditions is given by Wien&#39;s Law: 
     SENSOR 2 
     
         R.sub.λ.sbsb.1 =C.sub.1 E.sub.s λ.sub.1.sup.-5 e.sup.-C.sbsp.2.sup./λ.sbsp.1.sup.T.sbsp.s         (1) 
    
     and, 
     SENSOR 4 
     
         R.sub.λ.sbsb.2 =C.sub.1 E.sub.s λ.sub.2.sup.-5 e.sup.-C.sbsp.2.sup./λ.sbsp.2.sup.T.sbsp.s         (2) 
    
     where 
     C 1  =a constant 
     C 2  =0.014388 M K 
     λ=wavelength, meters 
     T s  =surface temperature, °K 
     E s  =surface emittance 
     Correspondingly, voltages V 1  and V 2  may be given as 
     
         -V.sub.1 =C.sub.3 E.sub.s e.sub.-C.sbsp.2.sup./λ.sbsp.1.sup.T.sbsp.s (3) 
    
     
         -V.sub.2 =C.sub.4 E.sub.s e.sup.-C.sbsp.2.sup./λ.sbsp.2.sup.T.sbsp.s (4) 
    
     where 
     
         C.sub.3 =C.sub.1 F.sub.1 R.sub.f1 λ.sub.1.sup.-5 
    
     
         C.sub.4 =C.sub.1 F.sub.2 R.sub.f2 λ.sub.2.sup.-5 
    
     F 1  and F 2  are sensor constants, and 
     R f1  and R f2  are values of feedback resistors. 
     If V 2  is divided by V 1 , the basis of &#34;2-color&#34;pyrometers, the resulting ratio, V R , is independent of E s , assuming E s  is the same for both λ 1  and λ 2 . ##EQU1## 
     If the slab S at temperature T s  is placed inside a furnace operating at temperature T f  (where T f  &gt;T s , as the furnace is heating the slab) sensors 2 and 4 will receive additional radiation from the furnace which is reflected from the surface. Assume that the furnace will have an effective emittance which approaches 1.0 in value as T s  approaches T f  (black body condition); the furnace emittance will therefore be considered to be 1.0. Assume also that the surface will reflect exactly (1-E s ) of the furnace-emitted radiation (the view factor for furnace radiation is 1.0) and assume also that the furnace temperature in the area being viewed is uniform. Under these assumptions the radiation emitted by the furnace will be identical in form to Equations 1 and 2, substituting T f  for T s  and (1-E s ) for E s . 
     The total radiation received by sensors 2 and 4 will then produce outputs found by summing the surface emitted radiation and the furnace reflected radiation as follows: 
     
         -V.sub.1 =C.sub.3 [E.sub.s e.sup.-C.sbsp.2.sup./λ.sbsp.1.sup.T.sbsp.s +(1-E.sub.s)e.sup.-C.sbsp.2.sup./λ.sbsp.1.sup.Tf ] (6) 
    
     and, 
     
         -V.sub.2 =C.sub.4 [E.sub.s e.sup.-C.sbsp.2.sup./λ.sbsp.2.sup.T.sbsp.s +(1-E.sub.s)e.sup.-C.sbsp.2.sup./λ.sbsp.2.sup.Tf ] (7) 
    
     If typical values are assigned to the factors in the equations and the results plotted, it is apparent that as the difference between T f  and T s  increases, the difference between the values of V 1  and V 2  and the voltages without reflected radiation also increases. If these voltages are converted to temperatures, the errors in temperature indications become readily apparent. If adjustments are made for emittance, then the indicated temperature error would approach zero as T s  approaches T f . When the temperatures are equal, black body conditions, the indicated temperatures would be the same. If V 2  is divided by V 1 , the resulting ratio, V R , decreases as the slab surface temperature increases, provided V 2  is derived from the sensor receiving the longer wavelength radiation. This indicates that as temperature increases, the amount of shorter wavelength radiation increases more rapidly than the amount of longer wavelength radiation. The addition of reflected radiation from the higher-temperature furnace would also result in a lower V R  than the value of V R  for the slab surface only. This difference in responses of the sensors when T s  is not equal to T f  as compared to the sensor responses when T f  is equal to T s  is applied to determine the actual slab temperature. 
     If the sensors receive a combination of both reflected and emitted radiation, Equations 3 and 4 may be rewritten to determine indicated temperatures T e1  and T e2  as follows: 
     
         -V.sub.1 =C.sub.3 e.sup.-C.sbsp.2.sup./λ.sbsp.1.sup.Te.sbsp.1 (8) 
    
     and, 
     
         -V.sub.2 =C.sub.4 e.sup.-C.sbsp.2.sup./λ.sbsp.2.sup.Te.sbsp.2 (9) 
    
     assuming an emittance of 1. T el  is not equal to T e2  except when the slab and furnace are at the same temperature, black body conditions. Under such conditions V R  may be readily determined from equation 5 and therefore given a value of V 1  or V 2 , the other can be calculated. However, the calculated values, V el  or V e2 , derived in this manner, will not be equal to V 1  or V 2  except when T s  is equal to T f . The differences between V el  and V 1 , and between V e2  and V 2 , or combinations thereof may be applied to provide an adjustment factor which yields a reasonably accurate readout of slab surface temperature. 
     Adjustment factors, CF, may be developed as follows: ##EQU2## 
     There are several methods for applying these adjustment factors to determine slab temperature. The indicated temperature T el  or T e2  may be corrected, V R  may be corrected or the voltage outputs V 1  or V 2  may be corrected. The choice would depend on the effect of surface emittance, the size of the error to be corrected and the simplicity of the required circuit. Since it appears that surface emittance effects all three methods in about the same manner, the first method appears preferable because it appears to have the lowest change in the required correction factor for a given change in the adjustment factor utilized and the circuitry is not complex. 
     In the first method, correcting the indicated temperature a temperature correction factor, TCF, is developed to provide the slab temperature T S  from the indicated temperature, T e2  according to the following equation: 
     
         T.sub.S =T.sub.e2 ×TCF                               (13) 
    
     Knowing the response characteristics of the sensor, TCF may be calculated for various combinations of surface and furnace temperatures. If the values of TCF are plotted against adjustment factors CF1, CF2 and CF3, the plots are independent of combinations of assumed surface and furnace temperature provided the sensors respond in an exponential mode. Using curve fitting techniques, equations may be derived from the plot for calculating TCF from each of the adjustment factors. 
     In FIG. 1, radiation received by sensor 4 is converted to signal 14, V 2 , by amplifier 12. V 2  is converted to a logarithmic signal 28, 1V 2  by amplifier 26. Function generator 30, provides an altered output 34, 1V el . Since the V R  function and the inputs and outputs of circuit 30 are all logarithmic, circuit 30 is preferably a circuit which changes or alters the gain or slope and zero shift of the straight-line logarithmic graph of equation 5. 
     Radiation received by sensor 2 is converted to signal 8, V 1  by amplifier 6. V 1  is converted to a logarithmic signal 19, 1V 1  by amplifer 18. Inverter 20 makes adder 24 function as a subtractor, providing output 36, the logarithm of adjustment factor CF1 of equation 10, by subtracting 1V, from 1V el . 
     Circuit 38 provides output 42, TCF, using the empirical equation derived from the plot of TCF and CF1 and with resistor 40 set for surface emittance. Output 28, 1V 2 , of amplifier 26 is connected to circuit 32 which provides a linearized, output 46, T e2 , which is a temperature indication according to the radiation received by sensor 4. Signals 42 and 46 are combined in multiplier circuit 44 according to equation 13 to provide output 48, T S , to a suitable indicating instrument 50 for actual surface temperature readout. 
     In the second method, correcting V R , a ratio correction factor RCF is developed to provide V RSC , the value of V R  resulting from the actual slab surface temperature according to the following equation: 
     
         V.sub.RSC =RCF×V.sub.R                               (14) 
    
     where V R  is the ratio of V 2  divided by V 1 . 
     The value of RCF may be plotted against CF1, CF2 and CF3 and using curve fitting techniques. Equations may be derived from the plot for calculating RCF from each of the adjustment factors. 
     Referring to FIG. 2 which shows a circuit using the second method and in which the same circuit elements have the same numbers and same functions as in FIG. 1, an output 52 of amplifier 18 is connected to an input of a third function generator 54. Generator 54 has an altered output 56 connected to a first input of a first subtractor circuit 58. Output 52 is also connected to a first input of a second subtractor circuit 60. Output 28 of amplifier 26 is connected to a second input of subtractor 60. Subtractor 58 has an output 62 connected to the input of fourth function generator 64. Function generator 64 has an adjustable resistor 66 and an output 68 connected to an input of a multiplier 44. Subtractor 60 has an output 70 connected to the input of a second linerize circuit 72. Circuit 72 has an output 74 connected to the input of a fifth function generator 76. Generator 76 has an output 78 connected to a second input of multiplier 44. Multiplier 44 has an output 48 connected to a suitable indicator 50. 
     In FIG. 2, radiation received by sensor 4 is converted to signal 14, V 2 , by amplifier 12. V 2  is converted to a logarithmic signal 28, 1V 2 , by logarithmic amplifier 26. Radiation received by sensor 2 is converted to signal 8, V 1 , by amplifier 6. V 1  is converted to a logarithmic signal 52, 1V 1 , by logarithmic amplifier 18. Signal 52, 1V 1 , and signal 28, 1V 2 , are subtracted in circuit 60 to provide signal 70, log V R . Linearizer circuit 72 converts signal 70, log V R  to signal 74, V R . Circuit 76, using equation 5, provides an output 78, which is the uncorrected temperature indication derived from V R  and the known V R  -T characteristics of the sensors. 
     Signal 52, 1V 1  is converted to signal 56, 1V e2 , by circuit 54 which is similar to, and functions in the same manner as, circuit 30 of FIG. 1. Output 56, 1V e2 , of circuit 54 and signal 28, 1V 2  are combined in subtractor circuit 56 to provide signal 62, CF2, according to equation 11. Circuit 64 provides output 68, RCF, using the empirical equations derived from the plot of RCF and CF2, and setting resistor 66 set for surface emission. Signal 68, RCF, and signal 78, indicated temperature based on V R , are combined in circuit 44 according to equation 14 to provide signal 48 to a suitable indicating instrument 50 for actual surface temperature and readout. 
     In the third method, correcting either V 1  or V 2 , a voltage correction factor, VCF, is developed to provide a corrected V, V c , from the actual amplified voltage output of the sensor according to the following equation 
     
         V.sub.c =V.sub.CF ×V                                 (15) 
    
     where V is the amplified output of one of the sensors, and V c  is the corrected voltage which is converted to a signal representing the actual slab surface temperature. 
     The value of VCF may be plotted against CF1, CF2 and CF3, and using curve fitting techniques, equations may be derived from the plot for calculating VCF from each of the correction factors. 
     Referring to FIG. 3 which shows a circuit using the third method and in which the same circuit elements have the numbers and same functions as in FIG. 1, output 36 of adder circuit 24 is connected to an input to a sixth function generator 80. Function generator 80 has an output 82 connected to an input of multiplier 44. Output 14 of amplifier 12 is also connected to an input of multiplier 44. Multiplier 44 has an output 84 connected to an input of a seventh function generator 86. Circuit 86 has an output 48 connected to an indicating instrument 50. 
     In FIG. 3 radiation received by sensor 4 is converted to signal 14, V 2 , by amplifier 12 and connected to multiplier 44. Signal 14 is also converted to a logarithmic signal 28, 1V 2 , by amplifier 26. Function generator 30, according to equation 5, provides an output 34, 1V e1 . Radiation received from sensor 2 is converted to signal 8, V 1 , by amplifier 6. V 1  is converted to a logarithmic signal 19, 1V 1 , by amplifier 18. Inverter 20 makes adder 24 function as a subtractor providing output 36, CF1 of equation 10, by subtracting 1V 1  from 1V e1 . 
     Circuit 80 provides output 82, VCF of equation 15 using the empirical equation derived from the plot of VCF and CF1, and with resistor 40 set for surface emittance. Signals 82 and 14 are combined in multiplier 44 according to equation 15 to provide signal 84, V c , the corrected output. Circuit 86 converts V c  to a temperature indication, signal 48, on the basis of the temperature-voltage characteristics of sensor 4. Actual surface temperature is shown on indicator 50. 
     Signals 8 and 14 each have two components, radiation emitted by the surface and radiation reflected from the surface. In typical furnace operations, the sum of these two components is relatively steady which allows all components to operate as expected and to provide an accurate determination of surface temperature from signals 8 and 14. However, it is possible that sensors 2 and/or 4 may pick up radiation from the flame coming from the furnace burners and thus add erroneous and erratic values to signals 8 and or 14. To minimize errors caused by flames, a first valley picker circuit 88 is connected to the output of amplifier 6 and a second valley picker circuit 90 is connected to the output of amplifier 12 as shown in FIG. 4. The valley picker circuits act to eliminate the fluctuating signals above the base signal representing the reflected and emitted radiation from the slab surface. 
     The presence of flame effects can be determined by comparing the difference between the temperature readout based on correcting the output of sensor 2 with the temperature readout based on correcting the output of sensor 4. 
     The preferred embodiment has been described with sensor 4 sensitive to the longer-wave length radiation. This is preferred since T e2  then is closer to the true slab temperature than T e1 . However, the invention, in all embodiments, will also function correctly with V 1  and V 2  reversed. 
     In addition, while equations 10, 11 and 12 describe these adjustment factors, only equations 10 and 11, CF1 and CF2 are illustrated in the three methods. A computer program was developed to calculate the pyrometer response for combinations of furnace and surface temperatures with readouts of T e1  and T e2  and the results of using CF1, CF2 and CF3 to calculate the slab surface temperature. The results show that any of these adjustment factors result in fairly accurate readout of slab surface temperature over a wide range of combinations of furnace and slab temperatures. Circuitry for developing CF2 is similar to as circuitry for developing CF1. Circuitry for CF3 requires additional multiplication.