WO2014067549A1

WO2014067549A1 - A method for measuring temperature

Info

Publication number: WO2014067549A1
Application number: PCT/EP2012/071393
Authority: WO
Inventors: Petter HAGQVIST
Original assignee: Ptc Innovation Ab
Priority date: 2012-10-29
Filing date: 2012-10-29
Publication date: 2014-05-08

Abstract

A method for measuring temperature of a sample based on the sample'sthermally emitted radiation is provided. The method is based on the assumption that the temperature of the sample at a specific point in time may be determined by using an emissivity of the sample at a preceding point in time, provided that the frequency at which the thermally emitted radiation is measured is sufficiently high. That is, by measuring the radiance from the sample at a high frequency, the change in emissivity and temperature over a short time interval are small enough for the emissivity at one point in time to be used for determining the temperature in a subsequent point in time. Thus, the invention provides for a method for real-time temperature measurements, while allowing for a time-varying emissivity.

Description

A METHOD FOR MEASURING TEMPERATURE

Technical field of the Invention

The present invention relates to a method for measuring the temperature of a sample based on thermally emitted radiation from the sample.

Background of the Invention

Precise temperature measurements are important in many industrial processes for various reasons. For example, in welding, casting, moulding or metal deposition processes, precise temperature information is important for on-line process control and monitoring in order to understand and control the process and to mitigate disturbances and perturbations.

Temperature measurement methods may be divided into contact- based methods, where the sample to be measured is in contact with the measuring device, and non-contacting methods where the sample to be measured is spaced from the measuring device, for the latter the temperature measurement may e.g. be based on information which is radiated from the sample. Due to practical reasons, contact-based methods are not suited for some applications. For example, the sample to be measured may have to be separated from the measuring device due to e.g. temperature measurements on a moving object, or that temperature measurements are sought in temperature ranges above the melting point of the sample. For the latter, contact-based temperature measurement methods are especially adverse since contamination of the sample may occur through melting or alloying.

Many currently deployed non-contacting temperature measuring methods use an instrument measuring thermally emitted radiation from the sample. The measured radiation is then used together with known physical relationships (e.g. radiation related physical relationships) to determine the temperature of the sample. For example, the emitted radiation of a real sample may be compared to that of an ideal black body. The thermal radiation characteristics for an ideal black body with a temperature above absolute zero are described by Planck's law of radiation presented in the following equation:

■ BB,

I (T, λ) is the black body spectral radiance as a function of

temperature and wavelength;

π is pi, approximately equal to 3.14159;

Ci is a constant equal to 3,742 ^* 10⁸ W μηη m^"2;

λ denotes wavelength in μιτι;

e is the Euler's number, approximately equal to 2.71828 (the base of the natural logarithm);

C₂ is a constant equal to 1 .439 ^* 10⁴ μιτι K; and

T is the temperature in K.

Since no real object is an ideal black body, its radiation characteristics may be described as the product of the radiation of a black body and the emissivity of the object. Emissivity, denoted by ε, is the quotient of the emitted radiance, Ι^ε, to the radiance as described by Planck's law, l^BB, low emissivity indicating that the surface is reflective. The definition of emissivity is described in the following equation:

1^ε(Τ, λ, θ, φ)

Ι^ΒΒ (Τ,λ)

where:

ε(Τ, λ, θ, φ) is the emissivity of the sample as a function of

temperature, wavelength, incident inclination angle and azimuth angle;

Ι^ε(Τ, λ, θ, φ) is the spectral radiance thermally emitted from the sample as a function of temperature, wavelength, incident inclination angle and azimuth angle; and

l^BB(T, λ) is the black body spectral radiance as a function of

temperature and wavelength.

Thus, the emissivity of the sample is a function of temperature (T), wavelength (λ), incident inclination angle (Θ) and azimuth angle (φ). However, the emissivity is often assumed to be independent of the viewing direction and therefore, the emissivity is assumed independent of the two incident angles (θ, φ). That is, the emissivity of a sample varies in general with the two parameters, temperature and wavelength. These two parameters may in turn be dependent on for example material and surface characteristics. Thus, by providing the emissivity of a sample, and measuring the spectral radiance of the sample, the temperature of the sample may be determined by using Planck's law and the definition of the emissivity (of course, other versions of Planck's law or any derivation thereof may be used together with the emissivity to determine the temperature of a sample).

The temperature dependency causes a problem since the temperature is used as input to the emissivity, and the emissivity is used to determine the temperature. In other words, the measuring parameter (i.e. the temperature) is an input to the parameter (i.e. the emissivity) used to determine the measuring parameter.

One instrument used for measuring thermal radiation emitted from a sample is a pyrometer. When determining the temperature of the sample using a pyrometer and facing the above mentioned problem with the temperature dependent emissivity, different ways may be adopted to solve the problem. One way is to supply temperature dependent emissivity values to a narrow wavelength pyrometer (since the emissivity is approximately independent of the wavelength over a narrow wavelength) and measure the temperature over this narrow wavelength. Another option is to carry out measurements in two or several wavelength regions, so called multicolour pyrometry. Hereby, the emissivity factor can be eliminated provided that the emissivity-ratios are constant and do not change with temperature.

Another possibility is to know the emissivity and its dependence on various parameters in advance. For certain parameter combinations, such as e.g. temperature and emissivity correlations, extensive studies have been performed for some materials, but it is not feasible to investigate all combinations for all materials. Even if reliable emissivity information is available for the used material of the sample, different dynamic processes, such as e.g. oxidation may affect the surface properties and hence the temperature-emissivity correlation of the sample. Therefore, if the level of oxidation is unknown, the effect of the oxide would give uncertainties in the emissivity calculations.

US 2010/0246631 A1 discloses a temperature monitoring technique for collecting radiation intensity across a broad wavelength range. The method is based on that a solid state spectrometer acquires spectra from a sample in real time and resolves the spectra to a radiation intensity versus wavelength curve. The curve is then fitted to Planck's equation using a non-linear least squares fitting analysis. The method uses a parameter called the amplitude A which is a product of a so called "tooling factor" (system dependent geometrical and sensitivity factors) and the material's emissivity. US

2010/0246631 A1 discloses two ways of carrying out the temperature measurements, either a free fit analysis where the amplitude A may vary freely together with a temperature parameter in order to obtain the best fit, or a locked in mode where the emissivity is assumed to be constant over time.

Hence, none of the methods disclosed in US 2010/0246631 A1 provides for a measurement method where the emissivity of a material takes physical phenomena such as e.g. surface oxidation, into account. Thus, there is a need for an improved temperature measurement method using a more accurate emissivity.

Summary of the Invention

An object of the invention is to overcome the above problems, and to provide for a temperature measurement method utilizing a more accurate, time varying emissivity. This is accomplished by means of a method defined in the accompanying claims.

The present invention is based on the insight that by frequently measuring thermally emitted radiation from a sample, the temperature of the sample at a specific point in time may be determined by using an emissivity of the sample which is approximated with the emissivity of the sample at a preceding point in time. In other words, the inventor has realized that by measuring radiance from the sample at a high frequency, the change in emissivity and temperature over a short time interval are small enough for the emissivity at one point in time to be used for determining the temperature in a subsequent point in time.

Thus, provided that the frequency at which the emissivity and temperature are measured is high enough, the emissivity of the sample at one temperature may be used as a good approximation for the emissivity at another temperature, provided that the temperature of the sample has not changed significantly between the two points in time.

According to a first aspect of the invention, a method for temperature measurement of a sample based on thermally emitted radiation from the sample is provided. The method comprises the steps of:

a) providing a sample to be measured;

b) providing a detector;

c) providing an ith emissivity (ε,) of the sample;

d) measuring an (i+1 )th electromagnetic spectral radiance (Ι^ε,₊ι) from the sample by said detector;

e) calculating an (i+1 )th emissivity-corrected black body spectral radiance (l^EBB +i) based on the ith emissivity (ε,) and the (i+1 )th

electromagnetic spectral radiance (lVi);

f) calculating an (i+1 )th temperature (T_i+i) of the sample based on the (i+1 )th emissivity-corrected black body spectral radiance (l^EBEVn);

g) calculating an (i+1 )th black body spectral radiance (l^BEVn) based on said (i+1 )th temperature measurement (T_i+i);

h) calculating an (i+1 )th emissivity (ε,+ι) based on the (i+1 )th electromagnetic spectral radiance (Ι^ε,₊ι) and the (i+1 )th black body spectral radiance (l^BB _i+i);

j) raising i with the value of one (1 ); and

k) repeating steps c) to j) for a finite number of i;

where i is any integer.

That is, by providing an emissivity e.g. known from experience or previously measured, the temperature of the sample may be continuously measured in real-time, while allowing for the emissivity to vary over time. Hence, the method is based on two assumptions; the emissivity changes with time and temperature in a continuous manner; and that the emissivity at one time may be estimated with the emissivity at a short time period before or after. For the latter, the temperature history of the sample may be calculated backwards with regards to time, e.g. when post-processing the data (e.g. the emissivity and the radiance of the sample). That is, no assumption is made of how the emissivity continuously changes with time and temperature, and no assumption is made of any grey-body behaviour of the sample. Thus, the temperature may be determined without a-priori knowledge of material emissivity characteristics, provided that a reference emissivity is given at some time during the measurement process, e.g. at the beginning of the measurement process.

Owing to this, the method is advantageously used for temperature measurements of materials which have properties that change during the measurement process, such as e.g. oxidising metal surfaces.

The measurement method as described above is advantageously used for temperature measurements above 900 K. Hereby the radiance of the sample may be measured by the detector in the UV-visual spectral range (wavelengths approximately between 100 nm and 760 nm), and hence inexpensive and well-established equipment (e.g. the detector and optics used) may be utilized. Of course, the method is applicable in other regions of the spectral range as well, such as e.g. in the IR spectral range (wavelengths approximately between 0.74 μιτι and 300 μιτι).

It should be understood that the electromagnetic spectral radiation radiated from the sample is a physical quantity dependent on wavelength (i.e. spectral radiation). Furthermore radiance is a measure of, or a calculation based on, the physical quantity radiation that passes through or is emitted from a surface and falls within a given solid angle in a specific direction. Thus, the electromagnetic spectral radiance is a measure of, or a calculation based on, the physical quantity electromagnetic spectral radiation. The

electromagnetic spectral radiance is defined as emitted power per unit area of emitting surface (of the sample), per unit solid angle per wavelength (W m^"2 sr^"1 μιτι^"1) (per wavelength may also be expressed as nm^"1). Throughout the application the electromagnetic spectral radiation of the sample may be referred to as spectral radiation or simply radiation, the fact that the radiation is dependent of wavelength is implicit. Similarly, the electromagnetic spectral radiance of the sample may be referred to as spectral radiance or simply radiance. Furthermore, the expressions measurement of the (spectral) radiation and measurement of the (spectral) radiance are used

interchangeably throughout the application. Moreover, the measurements of, or the calculations based on, the radiation/ radiance are carried out over a spectral range of wavelengths, λ, also referred to as spectral range or range of wavelengths throughout the application. Furthermore, the emissivity of the sample may simply be referred to as emissivity.

It should be noted that the integer i, appertains to the positive natural numbers, i.e. the integer 1 , 2, 3, etc, and that step c) to j) above may be referred to as an iteration step. Moreover, the iteration steps may also be related to the integer i in the same way as the quantities/parameters. Several iteration steps may be referred to as a measurement process.

Furthermore, the phrasing to measure/measuring of a parameter (e.g. temperature) may sometimes be referred to as to determine/determination of the parameter or to estimate/ estimation of the parameter. That is, since most measurements of parameter are some kind of determination or estimation of said parameter, based on information collected from the parameter.

It should be understood that the emissivity provided in step c) is to be used in the beginning of the measurement process, e.g. in the first iteration step, and that in the subsequent iteration steps the emissivity calculated in step h) in one iteration step should be used as the provided emissivity in step c) in the next iteration step. In other words, in the first iteration step, the emissivity provided is known (the emissivity may here be known from e.g. experience or acquired by a previous iteration step or measurement), while the emissivity used for step c) in the second iteration step is the emissivity calculated in step h) in the first iteration step. Furthermore, for step c) in the third iteration step, the emissivity used is the emissivity calculated in step h) in the second iteration step, etc. That is, the emissivity calculated in step h) in the i:th iteration step is used as the provided emissivity in step c) in the (i+1 )th iteration step. Another way of describing the measurement process it that the (i+1 )th emissivity (ε,+ι) from step h) in the (i+1 )th iteration step is replacing the ith emissivity (ε,) in step c) in the (i+2)th iteration step. Of course, if an external reference value of the emissivity is provided sometime during the measurement process, this reference value may be used instead of the emissivity calculated in step h).

According to at least one example embodiment, the step of providing an ith emissivity (ε,), step c), comprises the step of measuring the ith emissivity (ε,) based on any of the following physical quantities: the radiance emitted from the sample; the reflectance of the sample; the temperature of the sample.

This is advantageous as the radiance, the reflectance and the temperature are physical quantities which may be measured by various well- known equipment such as e.g. a spectrometer for the radiance. Of course the emissivity may also be known from reference literature and/or estimated based on the corresponding prevailing conditions, such as e.g. a phase transition of the sample, or provided by other means such as e.g. from complex refractive index based on e.g. quantum mechanics calculations.

According to at least one example embodiment, the step of providing an ith emissivity (ε,), step c), comprises the steps of:

c1 ) providing an ith temperature (T,) of the sample;

c2) measuring an ith electromagnetic spectral radiance (Ι^ε,) from the sample by said detector;

c3) calculating an ith black body spectral radiance (l^BB ) based on said i:th temperature (T,);

c4) calculating the ith emissivity (ε,) based on the ith electromagnetic spectral radiance (Ι^ε,) and the i:th black body spectral radiance (l^BB ).

Hereby, a procedure for providing the emissivity in step c) may be provided for by supplying a temperature measurement of the sample. It should be understood that the procedure described in this embodiment, i.e. step c1 ) to c4) is for providing the emissivity in step c) for e.g. the first iteration step. In later iteration steps, the emissivity in step h) is used as input to step c) in a subsequent iteration step as previously described. However, it should be noted that if an additional/external reliable temperature of the sample is provided later in the measurement process (i.e. in an iteration step not being the first iteration step), said additional temperature may be used as comparison and/or calibration and/or as input to step c) in the method.

According to at least one example embodiment, the ith temperature (T,) is provided by a temperature measurement using an external device, such as e.g. a pyrometer or a thermocouple.

This is advantageous as it provides for a simple reference

measurement of the temperature of the sample. However, it should be noted that the drawbacks using a pyrometer and/or a thermocouple, as previously described, still prevails and that the temperature measured by the external device is to be used as a reference temperature only. That is, the external device may be used some time in the beginning of the temperature process, e.g. before the temperature of the sample has changed, e.g. before the sample has melted, while for the remaining temperature process, when the sample changes temperature when e.g. melting, the method according to step c) to k) above may be used.

According to at least one example embodiment, the ith temperature (T,) is acquired by a previous temperature estimation performed according to a method using the step c) to k) above.

In other words, for a first measurement process, the temperature calculated in step f) according to the method of the invention is used in step c1 ) for a second measurement process. Hereby, the temperature calculated by the method of the invention for a first measurement process may be used as reference temperature in a second measurement process.

According to at least one example embodiment, the (i+1 )th black body spectral radiance (l^BEVn) in step g) is calculated by applying a physical relationship, such as a physical radiation relationship, e.g. Planck's law and/or Wien's displacement law and/or Rayleigh-Jeans law and/or a derivation of any one of the three physical laws. According to at least one example embodiment, the ith black body spectral radiance (l^BB,) in step c3) is calculated by applying a physical relationship, such as a physical radiation relationship, e.g. Planck's law and/or Wien's displacement law and/or

Rayleigh-Jeans law and/or a derivation of any one of the three physical laws. Hereby, a well-known physical relationship may be used to determine the black body spectral radiance, for example by using Planck's law and providing the parameters needed for the corresponding equation, i.e. the temperature of the sample and wavelength range for which the black body spectral radiance is sought.

According to at least one example embodiment, the step of providing a detector, step b), comprises a step of using a broad wavelength detector for measuring the electromagnetic spectral radiance, wherein a measured spectral range of wavelengths (λ) of the electromagnetic spectral radiance is determined by a measurement range of the broad wavelength detector, such that the spectral range of wavelengths (λ) is between 180 nm and 900 nm.

This is advantageous as the spectral range may cover the UV-visual range of the spectra, and thus inexpensive and well-established equipment (e.g. detector and optics used) may be utilized. The detector may measure the radiation from the sample at a frequency of e.g. 20 Hz, that is the detector may perform 20 measurements of the electromagnetic spectral radiance every second (each measurement of the electromagnetic spectral radiance may correspond to a specific iteration step). Of course, using a detector measuring at other frequencies is possible. It should be understood that the frequency of which the detector measures the electromagnetic spectral radiance should be high enough for the temperature and emissivity of the sample to not vary significantly between two consecutive iteration steps and/or two measurements of the electromagnetic spectral radiance. For example, the temperature should not vary more than 2.5 %, preferably not more than 1 %, and most preferably not more than 0.1 % between two consecutive iteration steps.

According to at least one example embodiment, the (i+1 )th black body spectral radiance (l^BEVn) in step g) is calculated by applying the following mathematic relationship, or any derivation thereof:

¹⁺¹ A5(_ec₂/(AT_{i+ 1}) _ _Χ) (3) where: I i+i is the (i+1 )th black body spectral radiance;

λ denotes the spectral range of wavelengths in μηη measured by the detector;

e is the Euler's number approximately equal to 2.71828;

Ti+i is the (i+1 )th temperature estimate in K of the sample;

C₂ is a constant equal to 1 .439 ^* 10⁴ μιτι K; and

oc is indicating the relationship between the above quantities;

such as e.g. jBB _ ^2nC^

i⁺¹ A5 (_e C₂/(AT_{i+ 1}) _ -Q (4) where:

π is pi, approximately equal to 3.14159; and

Ci is a constant equal to 3.742 ^* 10⁸ W μηη m^"2.

Thus, by providing the temperature of the sample and the spectral range of wavelengths of interest for the measurement process (over the measured spectral range), the black body spectral radiance may be calculated.

According to at least one example embodiment, the ith black body spectral radiance (l^BB ) in step c3) is calculated by applying corresponding mathematical relationships as in equation (3) and (4) for the ith black body spectral radiance (l^BB ) and the ith temperature (T,) of the sample.

According to at least one example embodiment, the (i+1 )th emissivity (ε,+ι) in step h) is calculated by applying the physical relationship between the emissivity (ε,+ι), the electromagnetic spectral radiance (l^Ei+i), and the black body spectral radiance (l^BBi+i), according to the following relationship, or any derivation thereof :

'i+1

-i+1 oc jBB (5)

'i+1

such as e.g. εί+ι ^— ! jIBnB (6)

'i+1 where:

ε,₊ι is the (i+1 )th emissivity;

l^Ei+i is the (i+1 )th electromagnetic spectral radiance; and

l^BBi+i is the (i+1 )th black body spectral radiance.

According to at least one example embodiment, the ith emissivity (ε,) in step c4) is calculated by applying corresponding physical relationships as in equation (4) and (5) for the emissivity (ε,), the electromagnetic spectral radiance (Ι^ε,), and the black body spectral radiance (l^BB).

According to at least one example embodiment, the (i+1 )th emissivity- corrected black body spectral radiance (l^EBB ₊i ) in step e) is calculated by applying the physical relationship between the emissivity (ε,), the

electromagnetic spectral radiance (iVi), and the emissivity-corrected black body spectral radiance (l^EBB +i ) according to the following relationship, or any derivation thereof:

such as e.g.

= (8)

According to at least one example embodiment, the (i+1 )th

temperature estimate (T_i+i ) in step f) is calculated by applying a physical relationship, such as a physical radiation relationship, e.g. Planck's law and/or Wien's displacement law and/or Rayleigh-Jeans law and/or a derivation of any one of the tree laws.

It should be understood that the following parameters are vector based quantities: electromagnetic spectral radiance (Ι^ε), emissivity-corrected black body spectral radiance (l^EBB), emissivity (ε), black body spectral radiance (l^BB), wavelength (A); but that the temperature (T) may be a scalar based quantity. The size of the vector based quantities, i.e. the number of rows or columns in the vector, is based on the spectral range of wavelengths (λ), e.g. over the measured range of wavelengths. According to at least one example embodiment, the (i+1 )th

temperature (T_i+i ) calculated in step f) is determined by a dimensional reduction of the (i+1 )th emissivity-corrected black body spectral radiance (l^EBBi+i ). In other words, the vector of the (i+1 )th emissivity-corrected body spectral radiance (l^EBEVn) is used to calculate the scalar of the (i+1 )th temperature (T_i+i ). This may be implemented as a minimisation problem where the difference, e.g. the absolute difference or the square of differences, between each entity in the row or column in the emissivity-corrected body spectral radiance (l^EBB +i ) and each entity in the row or column in the black body spectral radiance is minimised. The black body spectral radiance is a function of the temperature of the sample and therefore can the sum of the absolute differences be minimized with regard to the temperature of the sample. The temperature of the sample corresponding to the smallest value of the sum of the absolute differences is assumed to be the correct

temperature of the sample.

According to at least one example embodiment, the (i+1 )th

temperature estimate (T_i+i ) in step f) is calculated by applying the following mathematic relationship, or any derivation thereof:

T_i+i * 2 C

A In

(7 EBB 5 +

i+l ^Λ

where:

Ti+i is the (i +1 )th temperature estimate in K of the sample;

λ denotes the spectral range of wavelengths in μιτι measured by the detector;

l^EBBi+i is the (i+1 )th emissivity-corrected black body spectral radiance; oc is indicating the relationship between the above quantities; and constants (ττ, Ci ) as previously defined,

such as e.g.

where all parameters and constant are as previously defined.

Thus, in this embodiment, the temperature of the sample is a vector, dependent on the range of wavelengths. A scalar value of the temperature may be then determined by a dimensional reduction of the temperature vector, for example by utilizing some kind of minimisation problem similar to those previously described.

According to at least one example embodiment, the emissivity is based on the approximation that the emissivity varies slowly and continuously in relation to the temperature change of the sample occurring between two consecutive measurements of the electromagnetic spectral radiance measured by the detector, in such a way that ε,+ι ^« ε,. Alternatively, the emissivity at one point in time may be approximated using more historic values of the sample such as e.g. the emissivity and/or temperature from more than one iteration step. For example, the (i+4)th emissivity ε,₊₄ may be a function based on preceding emissivity values and temperature values in such a way that ε,₊₄ = ί(ε,+ι, ε,+2, ε,+3, T_i+i , T_i+2, T_i+3). According to at least one example embodiment, each temperature estimate (T_i+i , T_i+2, T_i+3, etc.) may be derived from each electromagnetic spectral radiance (Ι^ε,₊ι, Ι^ε,₊2, l^Ei+3, etc.) by using the emissivity estimate from a previous temperature estimation (ε,, ε,+ι, ε,+2, etc.) and applying a physical radiation law, such as e.g. Planck's law, in such a way that temperature estimate (T_i+i ) may be derived from the electromagnetic spectral radiance (Ι^ε+ι) by using the emissivity estimate (ε,), where i corresponds to the same integer.

According to at least one example embodiment, the step of calculating the (i+1 )th emissivity, step h), is based on that the (i+1 )th emissivity varies continuously over time and that a local variation of the (i+1 )th wavelength dependent emissivity varies with time in any one of the following ways:

linearly; parabolically; cubically; or by any other polynomial function.

It should be noted that all mathematical relationships described throughout the application may be varied in such a way that each quantity relating to a certain iteration step, e.g. step i, may as well relate to another iteration step, e.g. step i+1 , as long as all quantities within the same iteration step are varied with an equal value (i.e. all quantities relating to iteration step i are raised to iteration step i+1 , while all quantities relating to iteration step i+1 are raised to iteration step i+2).

Furthermore, even though the steps of the method presented here are alphabetically arranged, the steps may be carried out in any another possible order, such as e.g. step d) may be preceding, or be performed

simultaneously, with step c).

Brief description of the drawings

These and other aspects of the present invention will now be described in more detail, with reference to the appended drawings showing example embodiments of the invention, wherein:

Fig 1 schematically illustrates an exemplary experimental set-up for measuring the temperature of a sample based on thermally emitted radiation from the sample;

Fig 2 is a flow chart illustrating an exemplary embodiment of the present invention;

Fig 3 shows a graphical representation of an exemplary embodiment of the invention; and

Fig 4 is a graph showing a comparison of the temperature of a sample measured according to the invention and according to a reference

temperature measurement.

Detailed description of the drawings

In the following description, the present invention is described with reference to a method for temperature measurement of a sample.

Fig 1 is an exemplary experimental set-up for measuring the

temperature of a sample 1 according to at least one example embodiment of the invention. In addition to the sample 1 , the set-up comprises a detector 5, e.g. a spectrometer 5, and a computer 7 for process handling. The

temperature measurement may for example be performed on a metal-alloy, such as e.g. Ti-6AI-4V (titanium alloy with 6 % Al and 4 % V) subject to e.g. welding or a metal deposition process. A general method for determining the temperature of the sample 1 may be performed as described in the following section. Thermally emitted radiation is emitted from the sample, indicated by arrows 3, and detected and measured by the spectrometer 5. The spectrometer 5 is adapted to measure properties of the thermally emitted radiation over a portion of the

electromagnetic spectrum, for example in the range of 180-900 nm if properties of the sample in the UV-visible range of the spectrum are sought. Of course, the spectrometer may be adapted to measure properties over other portions of the electromagnetic spectrum if properties of the sample 1 in other ranges of the spectrum are sought. Subsequently, the spectrometer 5 produces data based on the measured radiation from the sample 1 , and sends the data to the computer 7. The computer 7 is configured with software for data/process handling which executes the methods of the invention and thus, calculates the temperature of the sample 1 in real time and allowing for a varying emissivity of the sample. Alternatively, the data (e.g. the radiance of the sample, the emissivity etc.) is post-processed and the temperature of the sample with regards to time is calculated after the measurements of the sample are completed. Hence the temperature of the sample 1 is determined by converting electromagnetic spectral information into a temperature, allowing varying object emissivity.

An embodiment of the present invention will now be elucidated with reference to the flow chart in fig 2 and the complement schematic illustration in fig 3 which is a graphical representation of an exemplary embodiment of the method according the present invention. At least parts of the method described in relation to fig 2 may preferably be implemented in the software for data/process handling mentioned with reference to fig 1 . In fig 3, parameters with no parentheses are related to an iteration step i+1 while the parameters in parentheses are related to an iteration step i+2 (for the same value of the integer i). The parameters in fig 3 described with reference to fig 2 are for the iteration step i+1 .

In a first step 200, a sample 1 which is subject to a temperature measurement is provided. In a subsequent step 202, a detector 15 is provided, the detector may e.g. be a spectrophotometer 15 as illustrated in fig 3. The spectrophotometer 15 is adapted to measure thermally emitted radiation over a specific range of the spectrum, such as the spectral range of 180 nm to 900 nm. It should be understood that by measuring the emitted radiation over a known spectral range, the wavelengths (λ) which are to be used for the temperature measurement of the sample 1 are defined.

In a subsequent step 204, an ith emissivity ε, of the sample 1 is provided. The ith emissivity ε, may be an estimate e.g. based on known circumstances such as e.g. a phase change of the sample 1 , and/or the emissivity history of the sample 1 and/or other characteristics of the sample 1 . The ith emissivity may alternative be known from a previously performed iteration step or measurement.

In a subsequent step 206, an (i+1 )th electromagnetic spectral radiance l^Ei+i from the sample 1 is measured by the spectrophotometer 15. The electromagnetic spectral radiance, which stems from the thermally emitted radiation from the sample 1 , is indicated as arrows 3 in fig 3.

In a subsequent step 208, an (i+1 )th emissivity-corrected black body spectral radiance l^EBB +i is calculated based on the ith emissivity ε, and the (i+1 )th electromagnetic spectral radiance Ι^ε,₊ι . This may be implemented by e.g. dividing the (i+1 )th electromagnetic spectral radiance Ι^ε,₊ι with the ith emissivity ε,, indicated by a box 18 in fig 3. Furthermore, as illustrated in fig 3, the (i+1 )th electromagnetic spectral radiance Ι^ε,₊ι may have been subject to a smoothing filter FA and a low-pass filter F_t prior to step 208 (the purposes of the smoothing filter FA and the low-pass filter F_t are further explained below).

In a subsequent step 210, an (i+1 )th temperature T_i+i of the sample 1 is calculated based on the (i+1 )th emissivity-corrected black body spectral radiance l^EBB +i . This may be implemented by e.g. inverting Planck's law, indicated by a box 20 in fig 3.

In a subsequent step 212, an (i+1 )th black body spectral radiance l^BB +i is calculated based on the (i+1 )th temperature measurement T_i+i . This may be carried out by e.g. using Planck's law, indicated by a box 22 in fig 3. In a subsequent step 214, an (i+1 )th emissivity ε,+ι is calculated based on the (i+1 )th electromagnetic spectral radiance Ι^ε,₊ι and the (i+1 )th black body spectral radiance l^BB +i . This may be implemented by e.g. dividing the (i+1 )th electromagnetic spectral radiance Ι^ε,₊ι with the (i+1 )th black body spectral radiance l^BB ₊i, indicated by a box 24 in fig 3.

In a subsequent step 216, the method continues with raising the integer i with the value of one (1 ) and in the next step 218, steps 204 to 216 are repeated for a finite number of i. Each set of steps 204 to 216 for a specific value of the integer i may be referred to as an iteration step. An alternative way of elucidating the transfer of one iteration step to the next is illustrated in fig 3, where box 26 is indicating the raise from iteration step i+1 to iteration step i+2. Here the parameters without parentheses are related to iteration step i+1 while the parameter with parentheses are related to iteration step i+2. Thus, after performing iteration step i+1 according to the method, box 26 symbolises the start of iteration step i+2 and the parameters in parentheses are now used in the method for determining the temperature of the sample. That is, in step 204 for iteration step i+1 , the ith emissivity ε, is provided (left hand side of box 26), and in step 214 for the iteration step i+1 , the (i+1 )th emissivity ε,+ι is calculated (right hand side of box 26). By raising the iteration step with the value of one (1 ) in box 26, here indicated with adding the value of one (1 ) to the numeral instead of raising the integer i with the value of one (1 ), the (i+1 )th emissivity ε,+ι calculated in step 214 in the iteration step i+1 is used together with the (i+2)th electromagnetic spectral radiance Ι^ε,₊₂ in the process of determining the (i+2)th emissivity-corrected black body spectral radiance l^BB +₂ in iteration step i+2.

In other words, the (i+1 )th emissivity ε,+ι calculated in step 214 in the (i+1 )th iteration step (e.g. a first iteration step) may be used as the provided emissivity in step 204 in the (i+2)th iteration step (e.g. a second iteration step). Hereby, the (i+1 )th emissivity ε,+ι is used in the iteration step when determining the (i+2)th temperature T_i+2 of the sample (referring to the same integer i). That is, the (i+1 )th emissivity ε,+ι in iteration step i+1 may be used as an approximation for the emissivity used for calculating the (i+2)th temperature T_i+2 of the sample in iteration step i+2 (referring to the same integer i).

It should be noted that all parameters/quantities are vectors except for the temperature. The size of the vectors, i.e. the number of rows or columns in the vectors, may e.g. be determined by the spectral range of wavelengths for which the quantities are measured/calculated. The spectral range of wavelengths may in turn be determined by e.g. the measurement range of the detector 5, 15 (e.g. the spectrophotometer 15).

Thus, the (i+1 )th temperature T_i+i of the sample 1 calculated in step 210 by e.g. inverting the (i+1 )th emissivity-corrected body spectral radiance l^EBBi+i is preferably accompanied with a dimensional reduction. In other words, the vector of the (i+1 )th emissivity-corrected body spectral radiance l^EBBi+i is used to calculate the scalar of the (i+1 )th temperature T_i+i . This may be implemented as a minimisation problem where the difference (e.g. the absolute difference or the square of difference) of each value in the row or column in the emissivity-corrected body spectral radiance l^EBB +i and the black body spectral radiance (which is a function of the temperature of the sample 1 ) are minimized with regards to the temperature of the sample 1 . Thus, the temperature of the sample 1 corresponding to the smallest value of the sum of the absolute differences is assumed to be the correct temperature of the sample 1 .

It should be understood that an iteration step is a collective term for performing step 200 to step 216. That is, each iteration step performs an iteration but the result is not to be considered as a converged value since new measurement data (i.e. a new electromagnetic spectral radiance) is utilized in each iteration step. Furthermore, it should be understood that the order in which the steps are performed are not restricted to the alphabetical order presented here, but any another possible order is conceivable, such as e.g. that step d) may be preceding, or be performed simultaneously with, step c).

As described above, a low-pass filter F_t may be employed by the method. Measurement noise from the detector 5, 15 (e.g. the

spectrophotometer 15) corrupts the true radiance signal and its impact is preferably reduced by employing the filter F_t, which suppresses such noise. Since at least two of the assumptions in the present invention relates to the slow continuous changes in temperature and emissivity any high frequency components of the measured spectral signals in time domain can be considered as noise due to the underlying function having only low frequency characteristics. The filter F_T may be implemented as a second order butterworth filter which acts upon the wavelength channels separately with temporal cutoff frequency.

The purpose of the smoothing filter FA differs from that of the low-pass filter F_T in that the latter minimises measurement noise and the former is designed to mitigate bias in measurement channels within the detector 5, 15. Since the equation for measured spectral radiance is continuous, it is possible to suppress discontinuities and thereby channel bias and errors due to an erroneous calibration through a filter with low-pass characteristics. A simple and computationally efficient method is to employ the Savitsky-Golay smoothing method, which performs local polynomial regression of the signal through a convolution algorithm. It is especially well suited for smoothing of spectra since it retains high frequency components in wavelength domain while giving a smooth and continuous result. This results in the filter being robust towards peaks and notches which are not broadened by the Savitsky- Golay filter as they would be by for example a butterworth filter corrupting neighbouring wavelengths.

When measuring thermal radiation utilizing an instrument (e.g. a spectrometer 5 or a spectrophotometer 15), the instrument's spectral response and calibration function may also be estimated. However these equipment-based parameters may be assumed constant during the measurement process. In practice, the spectral response and calibration function may be included in the value for the emissivity and may therefore easily be eliminated in the calculations during the course of the measurement method.

In order to provide for an ith emissivity ε, of the sample 1 , as in step

204 for e.g. the first iteration step, the following method may be used. In a first step, an ith temperature T, of the sample 1 is provided. This temperature may be a measured value acquired from e.g. a thermocouple or a pyrometer, or known from reference.

In a subsequent step an ith electromagnetic spectral radiance Ι^ε, from the sample 1 is measured by the detector 5, 15. The detector may e.g. be a spectrometer 5 or a spectrophotometer 15.

In a subsequent step an ith black body spectral radiance l^BB is calculated based on said i:th temperature T,.

In a subsequent step the ith emissivity ε, is calculated based on the ith electromagnetic spectral radiance Ι^ε, and the i:th black body spectral radiance l^BBi.

The invention will now be described with relation to a performed experiment and the corresponding results.

Experimental set-up

Materials:

An SPM002-DT spectrophotometer with 2048 channels from Photon Control was used together with an optical head with a focal distance of 200 mm from Lumasense. It was controlled by a custom made LabVIEW-program utilizing spectrophotometer drivers supplied by Photon Control. The spectral range was 190 nm to 870 nm. The spectrophotometer was calibrated for maximum wavelength resolution as supplied from the manufacturer, and not for absolute radiance measurements. This means that the instrument used was not adapted for this type of measurement or modified in any way.

However, it proved to give sufficiently good measurements. It was chosen to illustrate the method's robustness and independence on specialised hardware. Experiments were conducted in an argon atmosphere with less than 50 ppm O2 content as measured by a PBI Dansensor SGI-3 instrument.

Experimental procedure:

A piece of Ti-6AI-4V was heated with an in-house built induction heater. A thermocouple of type S was used to control temperature through a PID-controller and also acted as a temperature reference. Measurements were taken continuously with the spectrophotometer with an exposure time of 20 000 s. These were averaged over 100 ms and recorded to file. The spectrophotometer spot was focused on the surface of the Ti-6AI-4V-piece. As the method is insensitive to absolute radiance values, the positioning is of minor importance as long as it is kept constant and a good signal is acquired.

Method implementation:

The algorithm was implemented using the MATLAB software from

MathWorks Inc.

Results

As illustrated in fig 4, good agreement between measured/estimated temperature (dotted line) and reference temperature (solid line) was found. The difference between reference temperature and estimated temperature was less than 4% of the reference temperature. These error levels were only present for shorter periods, initiated by high absolute second time derivatives of temperature and might be due to uneven temperature distribution throughout the material. The median and mean errors however were below 0,5 %. For the smoothening filer, the Savitzky-Golay filter was used and parameter v, corresponding to the window size for the filter, was set to 99. The results with respect to error in estimated temperature proved to be relatively insensitive to this parameter, and v could be varied with up to 25 % without a significant difference. During the experiment the material oxidised, the results of which were visible to the naked eye after cooling. In the context of this heavy oxidation, the achieved accuracy was satisfactory compared to previously examined methods.

The person skilled in the art realizes that the present invention by no means is limited to the embodiments described above. For example, other measurement methods utilizing the assumption that the emissivity of the sample at one point in time may be approximated with the emissivity of the sample at another point in time are equally applicable by the invention.

Claims

1 . A method for temperature measurement of a sample based on thermally emitted radiation from said sample, said method comprising the steps of:

a) providing a sample to be measured;

b) providing a detector;

c) providing an ith emissivity (ε,) of the sample;

e) calculating an (i+1 )th emissivity-corrected black body spectral radiance (l^EBB+i) based on the ith emissivity (ε,) and the (i+1 )th

electromagnetic spectral radiance (lVi);

j) raising i with the value of one (1 ); and

k) repeating steps c) to j) for a finite number of i;

where i is any integer.

2. A method according to claim 1 , wherein said step of providing an ith emissivity (ε,), step c), comprises the step of measuring the ith emissivity (ε,) based on any of the following physical quantities: the radiance emitted from the sample; the reflectance of the sample; the temperature of the sample.

3. A method according to claim 1 , wherein said step of providing an ith ivity (ε,), step c), comprises the steps of:

c1 ) providing an ith temperature (T,) of the sample; c2) measuring an ith electromagnetic spectral radiance (l^Ei)from the sample by said detector;

4. A method according to claim 3, wherein the ith temperature (T,) is provided by a temperature measurement using an external device, such as e.g. a pyrometer or a thermocouple.

5. A method according to claim 3 wherein the ith temperature (T,) is acquired by a previous temperature estimation performed according to a method using the steps in claim 1 .

6. A method according to any one of the preceding claims, wherein the (i+1 )th black body spectral radiance (l^BB +i ) in step g) is calculated by applying a physical relationship, such as a physical radiation relationship, e.g. Planck's law and/or Wien's displacement law and/or Rayleigh-Jeans law and/or a derivation of any one of the three physical laws.

7. A method according to any one of the preceding claims, wherein the ith black body spectral radiance (l^BB ) in step c3) is calculated by applying a physical relationship, such as a physical radiation relationship, e.g. Planck's law and/or Wien's displacement law and/or Rayleigh-Jeans law and/or a derivation of any one of the three physical laws.

8. A method according to any one of the preceding claims, wherein the step of providing a detector, step b), comprising a step of using a broad wavelength detector for measuring the electromagnetic spectral radiance, wherein a measured spectral range of wavelengths (λ) of the electromagnetic spectral radiance is determined by a measurement range of the broad wavelength detector, such that the spectral range of wavelengths (λ) is between 180 nm and 900nm.

9. A method according to any one of the preceding claims, wherein the (i+1 )th black body spectral radiance (l^BEVn) in step g) is calculated by applying the following mathematic relationship, or any derivation thereof:

where:

l^BBi+i is the (i+1 )th black body spectral radiance;

e is the Euler's number approximately equal to 2.71828;

C₂ is a constant equal to 1 .439 ^* 10⁴ μιτι K;

Ti+i is the (i+1 )th temperature estimate in K of the sample; and

oc is indicating the relationship between the above quantities.

10. A method according to any one of the preceding claims, wherein the (i+1 )th emissivity (ε,+ι) in step h) is calculated by applying the physical relationship between the emissivity (ε,+ι), the electromagnetic spectral radiance (iVi), and the black body spectral radiance (l^BEVn), according to the following relationship, or any derivation thereof :

-i+l oc jBB ^■

'i+l

1 1 . A method according to any one of the preceding claims, wherein the (i+1 )th emissivity-corrected black body spectral radiance (l^EBB +i ) in step e) is calculated by applying the physical relationship between the emissivity (ε,), the electromagnetic spectral radiance (l^Ei+i ), and the emissivity-corrected black body spectral radiance (l^EBB +i ) according to the following relationship, or any derivation thereof: jEBB „ 'i+l

12. A method according to any one of the preceding claims, wherein the (i+1 )th temperature estimate (T_i+i ) in step f) is calculated by applying a physical relationship, such as a physical radiation relationship, e.g. Planck's law and/or Wien's displacement law and/or Rayleigh-Jeans law and/or a derivation of any one of the three physical laws.

13. A method according to any one of the preceding claims, wherein the emissivity is based on the approximation that the emissivity varies slowly and continuously in relation to the change of the sample occurring between two consecutive measurements of the electromagnetic spectral radiance measured by the detector, in such a way that ε, « ε,+ι .

14. A method according to any one of the preceding claims, wherein said step of calculating the (i+1 )th emissivity, step h), is based on that the (i+1 )th emissivity varies continuously over time and that a local variation of the (i+1 )th wavelength dependent emissivity varies with time in any one of the following ways: linearly; parabolically; cubically; or by any other polynomial function.