WO2008103458A1

WO2008103458A1 - Precision thermometry with background illumination

Info

Publication number: WO2008103458A1
Application number: PCT/US2008/002374
Authority: WO
Inventors: Peter Poulsen
Original assignee: Peter Poulsen
Priority date: 2007-02-23
Filing date: 2008-02-22
Publication date: 2008-08-28

Abstract

Systems and methods can determine the temperatures and/or emissivities of an object (150) that may be semi-transparent or in an environment (160) with background lighting (152). One such system (100) measures the spectra of background lighting (152); light from a target area while the system (100) illuminates the area, light from the area without illumination, and in some embodiments, light from the area while the system (100) illuminates the back of the object. The spectra are typically measured using at least four wavelength bands. Numerical methods using relative measurements can solve for a temperature and/or spectral emissivity of the object.

Description

PRECISION THERMOMETRY WITH BACKGROUND ILLUMINATION

BACKGROUND

[0001] P. Poulsen and S. K. AuIt, "A new method of high precision thermometry," Review of scientific Instruments, 77, 094901, 2006 and U.S. Pat. No. 6,963,816 to Peter Poulsen, issued Nov. 8, 2005, describe methods for determining the temperature of an object from measurements of the spectrum of light emitted and reflected from the object. In general, these thermometry methods use a multi-channel spectrometer and a light source to measure the emitted light and the reflected light from an object surface at an elevated temperature relative to the surrounding environment. The temperature and the emissivity of the surface in each wavelength measured can be determined using knowledge of the spectrum and measurements of the incident, emitted, and reflected light. Alternatively, reflected light can be measured from a reference surface having a known reflectivity and the same geometry as the surface of the object of interest, and the temperature and emissivity of the surface can be determined using the measurements of the reference surface and the measured emitted and the reflected light from the surface of the object.

[0002] The above thermometry methods are generally used in situations where the object is opaque and the effects of background illumination are negligible. However, industrial applications of thermometry often require measurements of temperature to be taken under conditions where background illumination, which may be reflected from or transmitted through the object, significantly adds to the power emanating from an object. Further, many industrially important objects such as semiconductor wafers are transparent or semitransparent at wavelengths of interest in thermometry, e.g., for infrared light. A spectrum method of thermometry that is suitable for application to semitransparent objects and that accounts for the effect of reflected and transmitted background radiation is thus desired.

SUMMARY

[0003] In accordance with an aspect of the invention, systems and methods can determine the temperatures and/or emissivities of objects that may be semi-transparent or in an environment with background lighting. One such system measures the spectra of the background lighting; the light emitted, reflected, or transmitted by an object without illumination; and the light emitted, reflected, or transmitted by the object when illuminated by a light source in the measurement system. Knowledge or measurement of the spectrum of the light source in the measurement system can be employed with the other measurements in the computation of the object's temperature and the object's emissivity and transmissivity as functions of wavelength.

[0004] One specific embodiment of the invention is a process for measuring the temperature or emissivity of an object. The process includes measuring first amounts of light respectively in multiple wavelength bands. The first amounts of light are from the area on an object while a first light source is illuminating the area. Further, second amounts of light that are respectively in the wavelength bands are measured while the first light source is not illuminating the area. Processing of measurements of the first and the second amounts of light can then be used to determine a temperature of the area. Three or more wavelength bands can be employed for the determination of temperature or emissivities in a case without background lighting, and five or more wavelength bands can be employed for the determination of temperature or emissivities in background lighting illuminating both the front and back sides of the object.

[0005] Another specific embodiment of the invention is a system capable of remotely determining the temperature or emissivity of an object. The system generally includes a sensor system, an optical system, and a processing system. The sensor system is capable of measuring amounts of light respectively in at least four or five wavelength bands, depending on the number of background light sources that are present. The optical system is capable of directing the sensor system to sense light from a desired area of an object and capable of turning on and off illumination on the area. The processing system uses measurements of first amounts of light sensed in the wavelength bands while the illumination of the area is turned off and measurements of second amounts of light sensed in the wavelength bands while the illumination of the area is turned on to determine a temperature and/or the spectral emissivity of the area.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Fig. 1 shows a block diagram of a measurement system in accordance with an embodiment of the invention.

[0007] Fig. 2 shows flow diagram of a measurement process in accordance with an embodiment of the invention.

[0008] Fig. 3 shows plots of a reference emissivity as a function of temperature and illustrates a method in accordance with an embodiment of the invention for determining the temperature and emissivities.

[0009] Fig. 4 is a flow diagram of a process for determining a temperature or emissivities of a target area on an object.

[0010] Use of the same reference symbols in different figures indicates similar or identical items.

DETAILED DESCRIPTION

[0011] In accordance with an aspect of the invention, spectral measurements of electromagnetic radiation, e.g., infrared radiation, from the surface of an object can be used to determine the temperature and spectral emissivity of an area on the surface of the object, even when the object is semitransparent and in an environment with background radiation or lighting.

[0012] Measuring the temperature using electromagnetic radiation emitted from an object presents challenges. One challenge is that, in general, the emissivity of the surface of the object is unknown. Even if the emissivity was known prior to heating of the object, heating, oxidation, and other processes can change the emissivity of the surface. Since the emissivity is proportional to the emitted power at each radiated wavelength and generally varies with wavelength, a measurement of the emitted power alone is not sufficient to determine the temperature, even when measurements are performed over a range of wavelengths. Under conditions where the emissivity is subject to some known constraints, for example, for an object known to be a black or gray body emitter, there are methods that can give satisfactory results, but under conditions where the emissivity is an arbitrary function of the wavelength, changes in emissivity can cause significant errors when computing the temperature from an emission only measurement. [0013] Another challenge is that spectral measurements of radiation are often taken under conditions where radiation reflected from the surface of an object or transmitted though the object is a significant part of the radiation from the object. Under these conditions, a measurement of the power and/or the spectrum of the radiation originating at the surface of the object is not a measurement of the emitted radiation alone and will not enable the calculation of the surface temperature even if the emissivity is known. This situation is typical of industrial applications where the environment of the measurement may not be well controlled or where the background radiation is an integral part of the processing environment. For example, background lighting or radiation may originate in the systems used to heat the object. Some examples of such environments include processing equipment for materials such as silicon, glass, metals, and circuit boards.

[0014] In accordance with an aspect of the invention, systems and methods for determining the temperature, the emissivity, and the transmissivity of an object are provided. Some embodiments of the invention can determine the absolute temperature of points or areas on the surface of an object. In some applications, a measurement of emissivity is as important as a measurement of temperature. For example, processes may exist where a change in emissivity is an early warning of a change in one of the parameters of the process. The processes described herein are typically more complex than methods using only a single measurement of power, but the described processes can provide precise information in situations where many prior measurement methods fail. [0015] An instrument used to implement a thermometry process in accordance with embodiments of the invention can generally take many forms, and the form that is employed in a given application will typically depend on cost, the time available to take a measurement, and the accuracy required. However, for purposes of showing one specific embodiment, Fig. 1 illustrates a system 100 that uses measurements of emitted, reflected, and transmitted light from the surface of an object 150 to determine the temperature and/or emissivity of the of the surface. System 100 may be a stand alone instrument (e.g., a thermometry instrument) or may be built into a larger system, for example, as a monitoring system in material processing equipment.

[0016] Object 150 may include or be any type of object or collection of objects such as a room, people, or a work piece for which a temperature or emissivity measurement is desired.

However, in one specific embodiment of the invention, object 150 is a wafer employed in integrated circuit fabrication. As shown in Fig. 1, object 150 is in an environment 160 with background lighting 152, and object 150 may be semitransparent so that light from background lighting 152 that is reflected from or transmitted through object 150 is measured in system 100.

[0017] System 100 includes a light source 110, multiple light sensors 120, and a processing system 130 with interface boards 131 and 132 respectively for communications with light source 110 and sensors 120. A thermometry process as described further below generally depends on measurements of emitted, reflected, and transmitted light from object 150 in multiple bands (or channels) of wavelength, and the number of wavelength bands required for determination of the temperature or spectral emissivity using the disclosed techniques is three plus one additional wavelength band per background light source modeled. Accordingly, a minimum of four wavelength bands need to be measured for a case where object 150 is illuminated on one side, and five wavelength bands need to be measured for a case where object 150 is semitransparent and illuminated on front and back sides. One or more additional wavelength bands may be measured to aid in the evaluation of the errors in the determined quantities. Accordingly, a typical embodiment of system 100 would include light sensors 120 capable of measuring light in five or six distinct wavelength bands. The light sensing can be implemented as shown in Fig. 1 with separate sensors 120 corresponding to each wavelength band, so that sensors 120 measure in parallel the intensities of light in their respective wavelength bands. An alternative configuration might employ a single sensor to serially measure the intensities in two or more of the wavelength bands. In alternative embodiments, each sensor 120 can be a photodiode, a CCD or CMOS image sensor, or a hyperspectral camera sensor.

[0018] The range of wavelengths for each band can range from a narrow wavelength band (e.g., less than about 10 nm) to several μm. The choice of wavelength bands will generally depend on the signal strength obtained in each channel of wavelengths, the change of the emissivity with wavelength, the spectra of the emitted, reflected, and background light, and the error that is acceptable in the measurements. A typical embodiment using InGaAs detectors for sensors 120 can define the measured wavelength bands using six optical bandpass filters having 10-nm bandwidth and central transmission wavelengths that are evenly spaced over a wavelength range from 1 μm to 2.5 μm. This typical embodiment is just an example, and more generally, the wavelength bands selected for a particular application of system 100 will depend on factors such as the expected temperature of object 150, the required accuracy, and the cost of components.

[0019] Light source 110, in general, should include light having wavelengths in or covering every one of the wavelength bands. It is generally useful to have the intensity of light from light source 110 that the surface of object 150 reflects to be of the same magnitude as the intensity of the light emitted from the surface. An example of a suitable light source is a xenon high pressure lamp with a sapphire window that can be mechanically shuttered to control the duration of a light pulse directed into environment 160. For lower cost, an ordinary 12 volt light bulb that is shuttered or switched is often suitable for providing illumination in the near infrared range of wavelengths. Alternatively, a spark system may be employed to create light pulses with short duration for measurements when object 150 moves or changes rapidly. One skilled in the art will recognize, however, that other pulsed light sources may be used.

[0020] In the illustrated embodiment of Fig. 1, light source 110 includes a power supply 112 and a shutter 114 that operate under control of processing system 130, so that a program executed in processing system 130 can turn light source 110 on and off and open or close shutter 114 to permit or prevent a beam of light from light source 110 reaching object 150 in an environment 160. An optical system 140 provides light paths from light source 110 to the environment 160 containing object 150 and from environment 160 to sensors 120. Optical system 140 can include optical fibers, steering optics, or optical switches for directing a beam from light source 110 toward object 150, but the incident beam generally reaches object 150 through free space for remote sensing of the temperature or emissivity of object 150. Fig. 1 illustrates an embodiment in which optical system 140 directs light from light source 110 for normal incidence on either the front or the back of object 150 and directs light emanating normal to the front surface to detectors 120. Alternatively, two separate light sources could be provided, one light source 110 to illuminate the front of object 150 and another light source (not shown) to illuminate the back of object 150.

[0021] Each of light sensors 120 may include a device for measuring the intensity of light in the associated wavelength band, such as, for example, a spectrometer or a still or video digital camera. In the illustrated embodiment, each detector 120 includes a photodiode with an optical filter that selects the spectral band measured by the photodiode. An amplifier system coupled to each photodiode produces an analog signal in a range suitable for analog- to-digital conversion in interface board 132. In yet another embodiment of the invention, a single detector 120 may be employed with interchangeable optical filters to sequentially measure the desired spectral bands.

[0022] Interface board 132, which receives signals from sensors 120 indicating the separate measures for the wavelength bands, may include analog-to-digital converters that provide measurement signals to processing system 130 in a digital format with sufficient accuracy (e.g., 12-bit data) for the processing that system 130 performs. Processing system

130 can be a computer or other system capable of controlling light source 110 via illumination control board 131, receiving data from sensors 120 via interface board 132, and performing calculations as described further below for determination of a temperature and emissivities.

[0023] System 100 can be adapted for thermographic imaging as well as for single point (spot) measurements. In a spot measurement, a target spot is defined by the projection through optical system 140 onto object 150 of the sensing area of sensors 120, and measurements of light from the target spot enable the determination of the temperature and emissivity of the target spot or a volume of object 150 that is around the target spot. The spot is preferably small relative to variations in the temperature or emissivity of the object, so that the temperature and emissivity are substantially uniform in the target spot. In thermographic imaging, optical system 140 is focused to have an object plane corresponding to the surface of object 150 and an image plane corresponding to sensors 120. For thermographic imaging, sensors 120 can be image sensors that produce image data indicative of the spatial intensity in the respective wavelength bands. Processing system 130 can process the image data from sensors 120 to produce a temperature distribution for the surface of object 150, the spatial distribution of the average emissivity in each wavelength band, and the spatial distribution of the error in the computed values of the temperature and the emissivities. With digital image sensors, the image data corresponds to pixels, which can be considered to provide an array of spot measurements that are captured in parallel. Alternatively, the target spot for spot measurements could be scanned across the surface of object 150 to determine spatial distributions of temperature, emissivity, and errors if the scanning time is short compared to the temporal variations in the quantities measured. [0024] The spot measurements (or individual pixels in thermographic imaging) are generally determined under the assumption that the emitted light from an area or volume of object 150 can be described by a single temperature and the assumption that the emissivity and transmissivity are constant over the target area or a relevant volume of object 150. Thus, if object 120 has a large gradient in temperature and/or emissivity, the area viewed by each sensor 120 (or each pixel in sensor 120) must be small enough that the above assumptions are satisfied with sufficient accuracy. The size of the target area is physically determined by the optics employed to transport the radiation to sensors 120. The area viewed in each wavelength channel is preferably the same, viewed in the same geometry, and at the same viewing angles for each sensor 120. If that is not the case, the geometric effects must be included in the formulations for each channel. Correction for geometric effects may be necessary, for example, when one or more optical elements in system 140 have an index of refraction that is a function of the wavelength.

[0025] The optical elements in system 140 that transport the radiation from object 120 to sensors 120 can vary widely depending on the application and user constraints. Optical system 140 typically uses a combination of fiber optics and lenses or mirrors. Sensors 120 receive from environment 160 the emitted, reflected, and transmitted light in multiple wavelength bands, and the selection of the bands measured in a particular sensor 120 can be achieved with filters as shown in Fig. 1 , differences in the wavelength dependence of the sensitivity of sensors 120, or with dispersive optics such as gratings in optical system 140.

[0026] Fig. 1 illustrates a simple implementation of optical system 140 for a spot measurement. In this embodiment, optical system 140 contains optical fibers that transport received light that is emitted by, reflected from, or transmitted through object 150 and splits the received light into six channels corresponding to six sensors 120. Sensors 120 have optical filters that transmit light in associated wavelength bands for measurement. In this configuration, each sensor 120 produces a signal that is a function of the wavelength dependence of the transmissivity of the associated filter and of the wavelength dependence of the response of the sensor 120. Optical system 140 also provides paths or optical fibers that are connected to light source 110 and deliver light to a front or back side of object 150. Light source 110 can be turned on and off, in this case with shutter 114 and directed to either the front or back side of object 150.

[0027] Fig. 2 shows a flow diagram of a process 200 for use of system 100 to measure the temperature or emissivities of object 150. For this use, system 100 can be calibrated as indicated in step 210 to measure the response of sensors 120 and the spectrum of light source

110 when used for front or back lighting. The response of sensors 120 can be measured using a calibration object having a known emissivity and temperature in place of object 150. For example, the calibration object can be a light source that is opaque and has an emissivity of unity, commonly known as a black body source. The measured signals from sensors 120 can then be compared to the expected intensity and calibration constants C₁ can be determined for each wavelength channel. These calibration constants C₁ can be absolute or relative to a selected reference channel. For example, an arbitrary channel may be selected as the reference channel, and the reference channel does not need to be selected prior to the calibration measurement. In practice, a channel that has high signal to noise ratio is preferably selected as the reference channel. [0028] Calibration step 210 also measures the spectrum of light from light source 110. This calibration can be accomplished with object 150 removed from environment 160 by activating light source 110 to direct light from the back side direction and using sensors 120 to measure intensities /, in each wavelength channel i. The spectrum of light source 110 can alternatively be measured by activating light source 110 for reflection from a specular surface having a high and known reflectivity. Both techniques may be required if the spectrum of front side illumination may differ from the spectrum of back side illumination, particularly when separate light sources are employed for illumination of object 150 from different directions.

[0029] Process 200 in a step 220 measures the spectrum of background lighting 152 in environment 160. Background lighting 152 can be measured in a number of ways with object

150 in or removed from environment 160. In particular, while light source 110 is off, the target area of sensors 120 can be pointed away from object 150 and pointed either directly at a source of background lighting 152 or at a specular mirror (not shown) with a known reflectivity that is positioned to reflect light from background lighting 152 into system 100. At least two spectral measurements of the background lighting are generally desired. One measurement indicates spectral components G₁ in the wavelength bands / of light that would be reflected from object 150 and can be determined using a mirror or surface with known reflectivity in place of object 150. A second measurement of the background light can measure spectral components M₁ in the wavelength bands / of light that may be transmitted through object 150 and can be determined with object 150 removed from the environment.

Alternatively, the measurement of background lighting can also be accomplished by measuring the spectrum of the background lighting 152 with a separate instrument, or the spectrum can be computed from the known properties of environment 160.

[0030] In different environments 160, the background lighting 152 may include one or more discrete light sources or diffuse light sources, and the measurement of reflected background lighting G, and transmitted background lighting M, can accurately model many configurations of background lighting. With these types of environments, determination of the temperature or spectral emissivity of object 150 using the techniques described below requires five wavelength bands. However, in some environments, only one type of background lighting G, or M, is significant, and the determination of temperature or spectral emissivity requires only four wavelength bands. In other environments, more than two background lighting spectra may be needed and measured, and calculating the temperature and spectral emissivity of object 150 requires use of more than five wavelength bands.

[0031] Process 200 begins measuring object 150 in a step 230, which measures the light coming from the target spot on object 150 while light source 110 is off. Object 150 in general will only be illuminated by background lighting 152. Accordingly, the light measured in step 230 generally includes light emitted from object 150 and light from the background lighting 152 that was reflected from or transmitted through object 150.

[0032] A step 240 then measures the light from object 150 while the target side of object 150 is illuminated with light from light source 110. For this step, the light measured includes light emitted from object 150, light from light source 110 that is reflected from object 150, and the light from background lighting 152 that reflected from or transmitted through object 150.

[0033] The measurement of step 240 is preferably done with the light from light source 110 co-located with the apertures of sensors 120 in order to ensure that the reflected light is generated and viewed in the same geometry. Typically, sensors 120 and light source 110 view the surface of object 150 in a direction normal to the surface of object 150. However, in some applications it may be useful to use specular angles (i.e., where sensors 120 are located at an angle from the normal), and light source 110 is located at the corresponding specular angle. Such a configuration works as long as the reflectivity of the surface of object 150 does not have an azimuthal angular dependence. [0034] The duration of the illumination for step 240 should be short relative to the time scale of the change in the temperature of the object. If that is not the case, as for measurements varying on a nanosecond time scale, additional knowledge of the underlying physics of the process may be needed. It is also noted that very rapid measurements may require deconvolution of the signals using previously measured instrument response functions. [0035] A step 250 measures the light from object 150 while object 150 is illuminated from an opposite side with light from light source 110. For this step, the light measured includes light emitted from object 150, light from light source 110 that is transmitted through object 150, and the light from background lighting 152 that is reflected from or transmitted though object 150. As described further below, the measurements of step 250 are used to provide information regarding the transmissivities of object 150. Accordingly, step 250 is optional if another method for measuring or determining the transmissivities is used. The concerns regarding the direction and duration of a light pulse for the measurements of step 240 also apply to the measurements in step 250.

[0036] The spectral measurement found in steps 230, 240, and 250 differ from each other and provide information that can be combined with calibration measurements of step 210 and the background measurements of step 220 to determine the temperature, emissivities, and transmissivities of object 150. Process 200 in step 260 determines or calculates the desired quantity or quantities, which may include the temperature T of the target spot, the emissivities ε, of the target spot in the wavelength bands i, transmissivities τ, of object 150 in the wavelength bands /, and errors in the determined quantities. In some exemplary implementations, light source 110 can be continuously pulsed and/or switched to provide a series of spectral measurements that repeatedly cycle through some or all of steps 230, 240, and 250 for determination of a "continuous" reading of a temperature of the target area of object 150. Steps 230, 240, and 250 can be thus replicated in time by pulsing light continuously on and off at a frequency related to the desired time resolution of the measurements, so that (after processing the data) a continuous record of the temperature or other properties of object 150 as a function of time may be obtained.

[0037] Process 200 although described in the context of a spot measurement can also be applied to thermometric imaging. In particular, an imaging system as described above can use an array of pixel sensors, and process 200 as described above for the spot measurements can be followed for each of the pixel sensors of the sensor array. [0038] The processes for determining the local temperature and/or emissivity of a target spot on an object from the measurements as in step 260 of process 200 described above can be better understood from the dependence of the measurements on the characteristics of the object and its environment. In particular, in step 230, sensors 120 produce signals Sj, indicating the radiated power from semitransparent object 150 in respective wavelength bands i. With light source 110 off, the radiated power measured in step 230 includes contributions corresponding to the radiation emitted from the object, background radiation that is reflected from the object, and background radiation that is transmitted through the object. The three terms on the right hand side of Equation 1 provide mathematical expressions for the three signal components when light source in the instrument (e.g., light source 110 of system 100) is turned off. Equation 1 as a whole shows the dependence of a signal 5,- on the average emissivity ε, of the target for wavelength band i, the black body power F₁ (T") in channel i as a function of temperature T, a constant K representing the geometrical relationship between the sensor and the target, the calibration factor C, of the sensor, the intensity JcG₁ in the wavelength band i of the background lighting on the target side of the object, the intensity pMi in the wavelength band i of the background lighting on the opposite side of the object from the sensors, and the transmissivity τ,- of the object for wavelength band i.

Equation 1 : S₁ = S₁F₁ (T) KC^ (I - S₁ - T₁ ) IcG₁KC₁ + T₁PM₁KC₁

[0039] The governing relations for opaque and semitransparent objects appear similar, but, in fact, the definition of reflectivity and emissivity is not the same due to multiple reflections and volume emission within the body of the semitransparent object. The following does not distinguish between the two cases since the form of the equations is the same. [0040] Equation 1 applies the assumption that the reflectivity equals unity minus the emissivity minus the transmissivity for each wavelength band. It is further assumed that the emissivity in each channel is independent of the angle from the normal to the surface. Thus, a situation where a very coarse surface is being illuminated at large angles from the normal might not produce an accurate solution. However, given a sufficient number of wavelength channels, the error in the measurement can be determined as indicated further below. The construction of a thermometry instrument, e.g., system 100 of Fig. 1, is preferably such that all measurement channels have the identical geometrical relationship with the object.

[0041] Factor k in the background intensity kG, is a wavelength independent factor related to the intensity of the background lighting of the target side of the object. The value of the factor k accounts for the intensity of the source and the geometry of the source as it affects the power incident on the target surface. The factor k is also used to compensate for the use of normalized or relative values of the spectrum of the background lighting G,, and as described further below, the value of factor k is initially unknown and is part of the solution that determines the temperature T, the emissivities ε,, and the transmissivities r,-.

[0042] As noted above, a more complex model can be employed when the background light can originate from discrete sources, and the model of frontal lighting of the object as a single spectrum is inaccurate. Multiple sources may be modeled by the use of multiple (and different) k's and G,'s. Thus, the term (l -£, - T^kG₁KC₁ can be replaced by a summation over sources if the environment containing the object of interest is better modeled using multiple background light sources. [0043] Factor /? in the background intensities pM_t is similar in function to factor k and relates to the background lighting on the opposite side of the object from the sensor. The value of p is also initially unknown and will be part of the solution together with the temperature T, the emissivities ε,, and the transmissivities τ,. Again, multiple background light sources on the opposite side of the object of interest can be accounted for using a sum of terms in the manner described above in regard to factor k.

[0044] The multi-band measurements S₁ from step 230 of the power radiated from the target surface are not sufficient to enable a calculation of the temperature without information relating to the value and wavelength dependence of the emissivity and transmissivity. Measurements of step 240 and 250 are thus required. Measurements signals S\ of step 240 measure radiated power in wavelength bands i when a light source in the instrument is illuminating the target side of the object. Accordingly, the radiated power measured in step 240 includes contributions corresponding to the radiation emitted from the object, background radiation that is reflected from the object, background radiation that is transmitted through the object, and illumination from the instrument that is reflected from the object. The difference between signals S₁ and S", is thus reflected radiation Ri that originates from the instrument and is reflected by the object. Equation 2 gives reflected radiation R₁ in terms of the emissivity ε, for wavelength band i, the transmissivity τ,. for the wavelength band i, the intensity /, of the instruments front side illumination, a geometrical factor H independent of wavelength, and the sensor calibration factor C₁ for the wavelength band i.

Equation 2 : S₁ - S\ = R₁ = (1 - ε , - r, )/, HC₁

[0045] The reflected radiation R₁ is obtained by subtracting the signal S, measured in step 230 from the signal S', measured in step 240. The combination of Equations 1 and 2 provide two equations per wavelength band, 2N equations where N is the number of wavelength bands. However, the emissivities ε,, and the transmissivities τ, by themselves provide 2N unknowns, and because of the other unknown values including the temperature T, the measurements of steps 240 and 250 are still not sufficient for a solution indicating the temperature and emissivities of a semitransparent object with background lighting. A measurement of the transmissivities can be employed, which one embodiment of the invention uses measurement signals S", acquired in step 250 of process 200.

[0046] Measurements signals S'\ of step 250 measure radiated power in wavelength band / when a light source in the instrument is illuminating the back side of the object.

Accordingly, the radiated power measured in step 250 includes contributions corresponding to the radiation emitted from the object, background radiation that is reflected from the object, background radiation that is transmitted through the object, and illumination from the instrument that is transmitted through the object. The difference between signals 5", and S", is thus the transmitted radiation Q₁ that originates from the instrument and is transmitted through the object. Equation 3 gives transmitted radiation Q₁ in terms of the transmissivity τ,. for the wavelength band i, the intensity /', of the instruments back side illumination, a geometrical factor H independent of wavelength, and the sensor calibration factor C₁ for the wavelength band i. A calibration measurement So, taken in step 210 with the object removed indicates the spectra of the light source in the instrument when directing light from the back side and is the same as Equation 3 for a free space transmissivity equal to 1. Accordingly, the transmissivites τ,. are equal to the ratio Q₁ISo, , i.e., τ,.= (S₁-S ",)/So,,

Equation 3 : S, - S", =Q, = τ,I\ HC₁

[0047] Equations 1, 2, and 3 when used with the measurements taken in steps 230, 240, and 250 provide three equations per wavelength bands or 3N equations, where N is the number of wavelength bands. As described further below, Equation 1 and 2 can be normalized to remove the geometry factors, leaving 2(N-I) + N equations. The temperature T, the emissivities ε,-, and the transmissivities τ, provide only 2N+1 unknowns, but other quantities such as factors k and p are or can also be treated as unknowns that are independent of wavelength. lfp=0 and k>0, which is the case where only reflected background lighting is significant, the minimum number N of wavelength channels required for a solution is four. If both p and k are non-zero, the minimum number N of wavelength channels is five. In accordance with an aspect of the present invention, multiple wavelength bands are measured in order to allow a complete solution for all unknowns including temperature, emissivities and other quantities, and additional wavelength bands can be measured to estimate an error in the determined solutions.

[0048] Geometric factors H and K can be made to be, and are assumed to be, independent of the wavelength channel. If that is not the case, the dependence of the optical path and magnification on the wavelength must be included in the K and H factors. It is important that the geometry for measuring the emitted light, the reflected light, and the transmitted light be identical for each of the wavelength bands. As described further below, geometric factors H and K can be removed from the solution for the temperature and emissivities through normalization of the equations solved.

[0049] The process preferably should not depend on the measurement of absolute values of the measurement signals. In other words, it is useful if knowledge of the shape of the spectra is sufficient, and the determination process is independent of the distance from the sensors to the surface of the object. To achieve this objective, the equations for measurements of wavelength bands / can be normalized relative to the equations for a reference channel n. In particular, Equations 1 for each value of index i other than the index n for the reference channel can be divided by the Equation 1 for the reference wavelength channel. Similarly, Equations 2 for each value of index i other than the index n for the reference channel can be divided by the Equation 2 for the reference wavelength channel. This normalization removes the geometry dependent factors relating to the sensors and the light source and enables the use of relative values of the known and measured intensity in the wavelength channels. [0050] The values of emissivities £, are unknowns in the normalized Equations 1 and 2, but an emissivity ε_t can be eliminated between the two normalized equations to create an equation in ε_n, k, p, and implicitly in T, the ratio of F₁ IF_n being a known function of T. That equation can then be solved for ε_n and put into a form that depends only on k, p, T, the transmissivities τ, and τ_n, ratios of the spectral inputs /, //„, G₁ IG_n, M₁ I M_n and ratios of the signals and calibration factors S₁ IS_n, R₁I_n IR_nI₁, and C₁ IC_n. The only "cross-terms" in the relation are the ratios G_n IF_n and M_n IF_n . To eliminate the cross terms, the background spectra G₁ and M₁ are normalized to the blackbody spectrum value F₁ by setting the ratios G_n IF_n and M_n IF_n equal to unity. Other options are available that only have the effect of changing the absolute value of G₁ or M₁ and correspondingly the computed value of k or p. The products kG, and pM_t are not affected by the choice of normalization. Equations 4 indicates the algebraic result based on normalized Equations 1 and 2 and the normalization of values G₁ and M₁ as described above.

Equations 4:

^ = [^ - r, )l R_1n - T_n ^ k[F_n I F₁ Ix - T_n ISJR_1n - GJG_n )

+ p{F_n I F Jl I R₁Jr_nS_1n - T₁ [M₁ /M_n )] where

*[! - &. 'KlF_n IF, )+ k[F_n IFjS_1n IR_1n -G₁ IG_n)]

S_1n =S,C_H IS_nC₁ and R_1n = R₁C_nI_n IR_nC₁I₁

[0051] Equation 4 for each wavelength band / other than the band n provides a solution for the emissivity ε_n in the reference channel in terms of variables T, k, and p, the transmissivities τ, and measured quantities. Equations 3 are easily solved as described above for the transmissivities T₁, given the data without absorption by the object and under conditions where light is not scattered out of the optical path by the object and does not reach the sensors or where the scattering effect are mitigated by the use of large sources. Alternatively, the transmissivities τ, of the object can be measured using other techniques.

The solutions or measurements for transmissivities T₁ can be inserted in Equations 4, to provide N-I functions relating emissivity ε_n to temperature T and factors k and/?. Numerical techniques can use these functions to determine a best solution for emissivity ε_n to temperature T and factors k and p. Once the solution for ε_n, k, p, and T is obtained the values of f, can be computed from the original equations describing each measurement.

[0052] If there are no errors in the measurement or in the representation of the physical problem by the equations, the N-I functions represented by the above Equations 4 can be viewed as a set of surfaces in the space of the coordinates ε_n, k, p, and T. The intersection of these surfaces occurs in such a way that one point is common to all. That point is the solution point.

[0053] Actual measurements will have errors. If the errors can be represented as a statistical distribution and the formulation of the problem is correct, the surfaces become probability density distribution functions, and the joint probability density distribution function represents the solution of the problem as well as the error in ε_n, k, p, and T. Once these quantities are known, the governing equations can be used to find the values and the errors of the remaining emissivities in the N-I wavelength bands for i not equal to n. The magnitude and the standard deviation of the N-I distribution functions can be found by variational analysis of the governing equations. The standard deviation of the probability density functions are not only functions of the errors in measurement, but also functions of the values of the emissivities. The relationships for the errors in the case with the opaque object and in the absence of background light were shown by P. Poulsen and S. K. AuIt, "A new method of high precision thermometry," Review of scientific Instruments, 77, 094901, 2006, and the method of analysis for the present case is similar. Notably the errors increase when the emissivities are very small and when the emissivity in the zth channel is nearly equal to that in the nth channel. Thus, this method doesn't apply to a grey surface having equal spectral emissivities. That is a special case for which the solution can be obtained by an emission only measurement. The solution using the probability density functions is somewhat involved but can be found using known methods. An approximate method that is useful as long as none of the spectral bands have emissivities that are nearly equal in value or very small is described below.

[0054] Equations 4 indicate relationships among unknowns ε_n, T, k, and p for known values of measured quantities. In general, a solution for the temperature T can be found for any given values of k and p. In particular, for given values of k and p, Equations 4 gives the reference emissivity ε_n as N-I functions of the temperature T. The plots of the reference emissivity ε_n as functions of temperature T as shown in Fig. 3 illustrate that measurements in different wavelength channels generally produce different functional dependence and therefore different plots. Ideally, if factors k and/? have the correct values, the plots intersect at the solution for the object temperature T and reference emissivity ε_n. In general, there are more than two plots, specifically, N-I plots, where N is the number of wavelength channels, and as a result of measurement errors, the plots will not all intersect at the same point. However, a solution can be found by determining the mean and the standard deviation of the different calculated values of the reference emissivity ε_n at each value of T, and the best solution for the temperature T at the given values of k and p is found to be the temperature having the minimum value of the standard deviation relative to the mean of values for ε_n. The best value of the reference channel emissivity ε_n for the values of A: and/? associated with Fig. 3 is the mean value of the emissivities at the solution temperature.

[0055] A solution can thus be found numerically using Equations 4 and a process 400 illustrated in Fig. 4. In step 410 of process 400, candidate values for T, k, and /? are chosen. Step 420 then uses Equation 4 (N-I) times to calculate values for the reference emissivity ε_n respectively based on the current values T, k, and /? and on the measurements for the wavelength channels other than the reference channel. Steps 430 and 440 calculate a mean and a standard deviation of the calculated reference emissivity values and a ratio of the standard deviation to the mean. If decision step 450 determines that the ratio just calculated is the best found so far in process 400, step 460 records the current values of k,p, T, the mean reference emissivity, and the standard deviation as the best so far. After step 460 or after decision step 450 determines that the ratio just calculated is not the best found so far, step 470 determines whether another combination of values for T, k, and p should be evaluated. In general, steps 410 to 470 can be repeated to vary the values of T, k, and p in any desired manner to find a solution that minimizes the ratio of the standard deviation to the mean of reference emissivity ε_n. The solution for T, ε_n, k, and p is found at the values for T, k and p for which the solution for ε_n corresponds to the minimum value of the standard deviation relative to the mean of ε_n. Once the solution for these quantities is found, the values of the emissivities in the remaining wavelength channels, as well as their errors, can be computed from the governing relations above. [0056] There are multiple ways to find the solution of over- specified systems, of which the above equations are an example. Qualified practitioners will have no difficulty in applying alternative methods to find a solution.

[0057] The method described here is capable of very high accuracy; however, the practitioner must be aware of conditions that contribute error to the measurement, such as sources of light that is inadequately described and measured, multiple reflections between the object and neighboring surfaces, including those associated with the detector assembly, and in general any condition that is not described by the equations that model the radiation processes. In addition there are more subtle conditions relating to both the relative and absolute values of the spectral emissivities that cause errors to be amplified. A valuable feature of the method described above is that, given a sufficient number of wavelength bands for the measurements, the method enables the calculation of the absolute error of the measurement. The thermometry methods discussed here apply to objects with surfaces ranging from specular to Lambertian, and to objects that range from opaque to semitransparent and translucent. Most situations can be addressed by this method, but there are applications that are difficult. These applications typically involve a combination of conditions with multiple discrete sources of background illumination, reflections that cannot be controlled and are not accounted for, and translucent objects that scatter the transmitted light.

[0058] The measurement of the temperature at the surface of an opaque object is a common application. Here, the issues relating to the directional and spectral emissivity of the surface and the sources of background radiation reflected from the surface into the detector are dealt with. In the opaque approximation, the light emitted or reflected is viewed as a surface phenomenon. The background illumination may be described variously as an isotropic radiation field defined by a temperature or an arbitrary spectrum, or it may be described as originating from one or more discrete sources having a known spectrum. [0059] The object may also be semitransparent, absorbing light as it passes through the object; it is possible that the light may scatter and diffuse as it passes through the volume of the object. The light, both internal and external to the volume of the object, reflects at interfaces that are defined by a change in the index of refraction. For the semitransparent case, the emitted light originates in the volume of the object and background light illuminating the object from either side of the object must be accounted for. The radiation field may be uniform and isotropic with a defined temperature or with a known spectrum, or the illumination may originate from one or more discrete sources.

[0060] It is recognized that not every conceivable application is modeled by the equations shown here. The general method can be adapted to specific applications by including a mathematical or numerical description of the specific physical processes in the equations that are used to solve for the temperature and the emissivities. Examples of such processes include wavelength effects on the optics and wavelength dependence of the optical path between the instrument and the object. Such wavelength effects include absorption and emission of light along the optical path.

[0061] Although the invention has been described with reference to particular embodiments, the description is only an example of the invention's application and should not be taken as a limitation. For example, although the above embodiments of processes describe steps in specific orders the order of independent steps in general can be varied. Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention as defined by the following claims.

Claims

What is claimed is:

1. A process comprising: measuring first amounts of light respectively in at least four wavelength bands, wherein the first amounts of light are from an area on an object while a first light source is illuminating the area; measuring second amounts of light respectively in the wavelength bands, wherein the second amounts of light are from the area on the object and measured while the first light source is not illuminating the area; measuring third amounts of light respectively in the wavelength bands, wherein the third amounts of light are from background lighting that is illuminating the object; and processing measurements of the first, second, and third amounts to determine a temperature of the area.

2. The process of claim 1, wherein the plurality of wave length bands comprises five wavelength bands.

3. The process of claim 1, wherein processing further comprises determining emissivities of the area in each of the wavelength bands.

4. The process of claim 1, further comprising: directing light at a side of the object opposite to the area, wherein a portion of the light passes through the object and out of the area; measuring fourth amounts of light respectively in the wavelength bands, wherein the fourth amounts of light are from the area on the object while the light is being directed at the side of the object opposite to the area.

5. The process of claim 4, wherein the light directed at the side of the object opposite to the area is from the first light source.

6. The process of claim 4, further comprising using measurements of the fourth amounts of light to determine transmissivities and using the transmissivities in the processing of the measurements of the first and second amounts.

7. The process of claim 4, wherein measuring the first amounts, the second amounts, and the fourth amounts occur while the object is illuminated by the background lighting.

8. The process of claim 1, wherein measuring the first amounts and the second amounts occur while the object is illuminated by the background lighting.

9. The process of claim 1, further comprising selecting one of the wavelength bands to be a reference band, wherein the processing comprises: determining first ratios of the first amounts to the first amount measured in the reference band; determining second ratios of the second amounts to the second amount measured in the reference band; and determining the temperature from first ratios and the second ratios without otherwise using absolute values of the first amounts and the second amounts.

10. The process of claim 1, wherein the object is semitransparent.

11. The process of claim 1 , further comprising measuring amounts of light respectively in the wavelength bands and originating from the first light source.

12. The process of claim 1, wherein processing the measurements of the first amounts and the second amounts comprises: (a) selecting values for a temperature T and a set factor that depend on background lighting of the object;

(b) determining N-I values for an emissivity ε_n using N-I equations, where the emissivity ε_n corresponds to one of the wavelength bands, N is the number of the wavelength bands, and the N- 1 equations depend on measurements for the wavelength band corresponding to the emissivity ε_n and respectively on measurements for the other wavelength bands;

(c) determining a ratio of a standard deviation of the values of the emissivity ε_n determined in step (b) to a mean of the values of the emissivity ε_n determined in step (b); (d) recording of the value of the temperature T as a solution in response to the ratio determined in a last repetition of step (c) being lower than the ratio determined in any preceding repetition of step (c); and

(e) repeating steps (a), (b), (c), and (d) a plurality of times.

13. A system comprising: a sensor system capable of measuring amounts of light respectively in at least four wavelength bands; an optical system capable of activating the sensor system to sense a spectrum light from a target area, of activating the sensor system to measure a spectrum of background lighting, and of turning on and off first illumination on the target area; and a processing system adapted to use measurements of first amounts of light respectively sensed in the wavelength bands while the first illumination of the target area on the object is turned off, measurements of second amounts of light respectively sensed in the wavelength bands while the first illumination of the target area on the object is turned on, and measurements of the spectrum of the background lighting to determine a temperature of the area.

14. The system of claim 13, wherein the optical system is further capable of turning on and off second illumination that has a direction opposite to a direction of the first illumination, wherein the processing system also uses measurements of third amounts of light respectively sensed in the wavelength bands while the second illumination is turned on to determine the temperature of the area..

15. The system of claim 13, wherein the wavelength bands comprise five wavelength bands.