FR3131370A1 - METHOD AND DEVICE OF THE BICHROMATIC PYROREFLECTOMETER TYPE FOR DETERMINING THE TEMPERATURE OF A SURFACE - Google Patents

Abstract

The subject of the present invention is a method and a device of the bichromatic pyroreflectometer type for determining the temperature T of a surface (8), the device comprising a first (1a) and a second (1b) source of pulsed laser rays, a head optics (3) consisting of means forming a collimator (31) and means forming a converging lens (30), a first (21a) and a second (21b) so-called emission optical fibers provided for respectively conducting a light wave emitted by the first and the second sources of pulsed laser rays up to the said optical head, a first (4a) and a second (4b) photodiodes, a first (24a) and a second (24b) so-called receiving optical fibers provided to conduct respectively a light wave received by the optical head as far as the photodiodes, the first and second optical fibers for transmission and reception all four being combined in an optical beam (2) called a "bundle". Figure 1

Description

METHOD AND DEVICE OF THE BICHROMATIC PYROREFLECTOMETER TYPE FOR DETERMINING THE TEMPERATURE OF A SURFACE

The present invention lies in the field of non-contact temperature measurements using optical techniques.

The pyroreflectometer is a measuring device that makes it possible to accurately measure the surface temperature of materials.

Just like a pyrometer, it measures the temperature of a surface without physical contact with the material.

However, a pyrometer measures temperatures with an approximation of emissivity. Indeed, to make a measurement with a monochromatic or bi-chromatic pyrometer, it is imperative to have knowledge of the emissivity or emissivity ratio of the surface respectively.

In addition, these quantities must remain constant during the duration of the measurement.

However, these variables depend on the temperature and the surface condition of the material, and it is generally very difficult to access them.

To overcome these difficulties, it is possible to use Pyroreflectometry which combines two measurements on two wavelengths, namely, the measurement of the luminance temperature given by the pyrometer mode of the pyroreflectometer, and a reflectivity measurement bidirectional given by the reflectometer mode of the pyroreflectometer, for each of the wavelengths.

By measuring these physical properties of the material, it is possible to deduce the exact temperature of the surface and the diffusion factor without knowing its emissivity beforehand and without assuming a perfectly diffusing surface.

It is a hybrid method between bichromatic pyrometry and active reflection pyrometry, insofar as it relies on the simultaneous measurements of two luminance temperatures and two monochromatic bidirectional reflectivities, as well as on the introduction of a factor, called “diffusion”, assumed to be independent of the working wavelengths.

Pyroreflectometers are generally made up of three independent entities:

– a transmission and detection unit which allows measurements;

– an optical head which allows illumination and observation of the surface;

– software that allows the analysis of measurements and their processing.

The document KR10-0985341 describes by way of example a device, of the pyrometer type, for measuring the temperature of steel using a semiconductor laser, and in particular, using a semiconductor laser. conductor to increase the surface temperature of the steel and measure the magnitude of the temperature rise that occurs based on the absorption of the steel surface (accurately measure temperature by measuring emissivity steel). The device comprises two oscillating lasers, two optical fibers respectively associated with said lasers. The laser beams transmitted through the optical fibers are focused on the surface. The apparatus also includes two other optical fibers through which thermal radiation collected by light collection means is transmitted to optical filters, to filter thermal radiation energy signals of the first and second wavelengths. The apparatus also includes photodetection means for detecting the filtered thermal radiation of the two wavelengths, and a temperature calculation means for calculating the temperature as a function of these filtered thermal radiation.

However, this type of pyrometer requires heating the surface, which can cause disturbances during temperature measurements. In other words, the temperature measurement process associated with this type of device raises the question of the reliability of the measurements because it is intrusive.

This is why the present invention aims to overcome all or part of the disadvantages listed above.

More precisely, the subject of the invention is a device of the bichromatic pyroreflectometer type for determining the temperature T of a surface, and comprising a first and a second sources of pulsed laser rays, an optical head consisting of means forming a collimator and means forming a converging lens, a first and a second so-called emission optical fibers intended to respectively conduct a light wave emitted by the first and second sources of pulsed laser rays up to said optical head, a first and a second photodiode, a first and a second so-called reception optical fibers intended to respectively conduct a light wave received by the optical head to the photodiodes, the first and second transmission and reception optical fibers all four being united in an optical beam called "bundle ".

Optional, complementary or substitute characteristics of the invention are set out below.

According to a preferred embodiment, the four optical fibers can be silica fibers advantageously coated with a poly imide film, with a thickness of less than 50 microns, preferably less than 20 microns.

According to another preferred embodiment, the four optical fibers can be of substantially equal diameter, the difference between their diameter being less than 10%.

According to yet another preferred embodiment, the four optical fibers can be arranged equidistantly and as close as possible to the axis of the optical beam.

Advantageously, the pyroreflectometer type device may further comprise a sighting laser and a fifth optical fiber connecting said sighting laser to said optical head, said fifth optical fiber being integrated in the center of the optical beam.

Advantageously, the pyroreflectometer type device may also include a range finder.

Advantageously, the pyroreflectometer type device may further comprise a first and a second mode mixer each arranged respectively at the output of the first and second sources of pulsed laser rays, and before the optical beam.

Advantageously, the pyroreflectometer type device may further comprise a coupler or multiplexer at the output of the first and second sources of pulsed laser rays, and a coupler or multiplexer at the input of the first and second photodiodes to combine into a single optical fiber the first and second so-called transmission optical fibers, as well as the first and second so-called reception optical fibers.

The invention also relates to a method for determining the real temperature Tr of a surface using a device of the bichromatic pyroreflectometer type conforming to any one of the embodiments of the invention.

According to this method to determine the real temperature Tr, we first carry out a step of measuring the bidirectional reflectivity ρ ^⊥ (T,λ ₁ ), ρ ^⊥ (T,λ ₂ ) of the surface when the first and the second sources of pulsed laser rays emit at the top of the pulse respectively at a wavelength λ _1, λ ₂ .

Then, we proceed to a step of measuring the luminance temperature T _L1 , T _L2 of the surface for each of the wavelengths λ _1, λ ₂ , when the first 1a and the second 1b sources of pulsed laser rays are outside pulse.

Finally, we carry out a calculation step by iteration on the variable T to determine Tr, such that f(T) =0, for the function defined as follows:

with C2 the Plank constant

According to certain optional characteristics of this method, the calculation step by iteration on the variable T is initiated with a value T0> max (T _L1 , T _L2 ).

According to other also optional characteristics of this process, the wavelengths λ _1, λ ₂ are respectively of the order of 1300 nm and 1550 nm.

Under limit conditions corresponding to cases where:

or

then, the diffusion factor η is calculated according to

and the actual temperature Tr is calculated as the corrective emissivity temperature, as follows:

by recovering the last calculated value of the diffusion factor before the inversion of the reflectivity parameters such as:

The invention also relates to a method for determining the order one temperature of Wien T _{order 1 Wien} of a surface using a bichromatic pyroreflectometer type device conforming to any one of the embodiments of the invention.

According to this method to determine the first order temperature of Wien, we first carry out a step of measuring the bidirectional reflectivity ρ ^⊥ (T,λ ₁ ), ρ ^⊥ (T,λ ₂ ) of the surface when the first and second sources of pulsed laser rays emit at the top of the pulse respectively at a wavelength λ _1, λ ₂ ,

Then, we proceed to a step of measuring the luminance temperature T _L1 , T _L2 of the surface for each of the wavelengths λ _1, λ _2, when the first and second sources of pulsed laser rays are outside the pulse ,

Finally, we proceed to a step of calculating the first order temperature of Wien using the following formula:

According to certain optional characteristics of this process, the wavelengths λ _1, λ ₂ are respectively of the order of 1300 and 1550 nm.

Under limit conditions corresponding to cases where:

or

then, the diffusion factor η is calculated according to:

and the Wien order one temperature T _{order 1 Wien} is calculated as the temperature at corrective emissivity, as follows:

by recovering the last calculated value of the diffusion factor before the inversion of the reflectivity parameters such as:

Other advantages and particularities of the invention will appear on reading the detailed description of implementations and embodiments in no way limiting, and the following appended drawings:

This figure represents a schematic view of a bichromatic pyroreflectometer type device according to one embodiment of the invention.

This figure represents a detailed schematic view of the bichromatic pyroreflectometer type device of the .

This graph represents the function of direct temperature as a function of temperature.

This figure represents the physical phenomenon of reflectivity inversion at high temperatures.

The embodiments described below being in no way limiting, we may in particular consider variants of the invention comprising only a selection of characteristics described, isolated from the other characteristics described even if this selection is isolated within a sentence comprising these other features, if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from prior art information.

This selection includes at least one feature, preferably functional without structural details, or with only part of the structural details if only this part is sufficient to confer a technical advantage or to differentiate the invention from prior art information. .

Figures 1 and 2 each represent detailed views of a bichromatic pyroreflectometer type device according to the principle of the invention.

The latter comprises at least a first 1a and a second 1b sources of pulsed laser rays, an optical head 3 consisting of means forming a collimator 31 and means forming a converging lens 30, a first 21a and a second 21b optical fibers called emission intended to respectively conduct a light wave emitted by the first 1a and the second 1b sources of pulsed laser rays up to said optical head, a first 4a and a second 4b photodiodes, a first 24a and a second 24b so-called reception optical fibers intended to respectively conduct a light wave received by the optical head to the photodiodes 4a, 4b, the first and second optical transmission and reception fibers all four being combined in an optical beam 2 called a “bundle”.

The two sources of pulsed laser rays 1a and 1b must be able to operate on close but not identical wavelengths. Two identical laser drivers are also provided to control laser temperatures and laser intensity. Two optical isolators 11a, 11b can be provided at the output of the lasers.

The optical head 3 is composed of an objective tube, for modifying the distances of the lenses for adjustment, and of several lenses for carrying out collimations 31 or convergences 30. The optical head must be capable of measuring far and on a very small area. The optical head serves to transmit and receive the optical signal. The optical head must make it possible, in association with the beam, to ensure good superposition of the measurement tasks at a given distance. It must also minimize reflections and losses of laser light. To minimize reflections and optical power losses it is necessary to minimize the number of lenses.

To satisfy these criteria, the optical head has a collimator 31 and a converging lens 30. This architecture is the most optimal for adapting to near and far measurements. For a far measurement, we increase the focal length and for a close measurement we decrease the focal length of the converging lens.

The two so-called transmission optical fibers 21a and 21b and the two so-called reception optical fibers 24a and 24b are optical fibers which are brought together in a bundle 2 (called “Bundle” in English) upstream of the optical head. The beam must meet specific criteria for temperature measurements. The measurement surfaces for reflected light and emitted light must be combined for each wavelength, to be in agreement with the theoretical model of the bichromatic pyroreflectometer type device.

The two photodiodes 4a and 4b are identical and have a spectral band belonging to the interval (800:1700), the spectral band not having to exceed the limit of the spectral bands of the optical filters. Two amplifiers with adjustable gain are also provided to amplify the photodiode signal at the photodiode output.

At the input of the photodiodes, an optical filter 40a, 40b is provided for each optical fiber receiving at the study wavelengths with a spectral band of 50nm and transmitting 90%. Filters must have the narrowest possible spectral band and the highest possible transmission. The limit of the attenuation spectral bands of the optical filters must be greater than the detectable spectral band of the photodiodes.

In other words, the filters must be as narrow as possible so that the calculations are as accurate as possible, but these filters must also be as wide as possible to let as much light through as possible. The 50nm spectral band is therefore the good compromise for the temperature ranges measured. On the other hand, it would be possible to use a spectral band of 25nm for the measurement of higher temperatures, or to use a spectral band of 100nm for the measurement of lower temperatures.

Two collimators 41a, 41b which collimate at the study wavelengths are associated with each filter. They allow the light flux to be focused so that it passes through the optical filters with a minimum of loss.

According to a variant, it is also possible to remove the collimators 41a, 41b and integrate the filters into the photodiodes 4a, 4b, the fibers 24a and 24b then each being directly connected to their respective filter.

The device also includes a power supply which makes it possible to power the entire electronic circuit 9, a microcontroller which makes it possible to control the electronic circuit and carry out temperature calculations, an analog-to-digital converter which makes it possible to convert the analog signal from the photodiodes into a digital signal for the microcontroller, converters with analog outputs 4 – 20 mA and 0 – 10 V, which provide a voltage or current corresponding to the surface temperature, Ethernet communication, a temperature display screen and carry out calibrations, as well as an electronic card to connect the electronic elements.

It is the combination of beam 2 which brings together the four optical fibers and the optical head which makes it possible to improve the stability and reliability of the measurement over time.

Advantageously, the four optical fibers are silica fibers coated with a film preferably made of poly imide. The thickness of this film is advantageously less than 50 microns, and even more advantageously less than 20 microns.

Advantageously, the four optical fibers are of substantially equal diameter, the difference between their diameter being less than 10%. For example, we can choose identical fibers with a diameter of 400 microns.

Advantageously, the four optical fibers are arranged equidistantly and as close as possible to the axis of the optical beam 2, so that the fiber cores are very close to each other.

In order to be able to identify where the measurement is made, the bichromatic pyroreflectometer advantageously comprises a sighting laser 5 and a fifth optical fiber 50 connecting said laser to said optical head, said fifth optical fiber being integrated in the center of the optical beam 2.

Advantageously, the bichromatic pyroreflectometer can include a range finder in order to measure the distance between the surface 8 and the optical head.

According to a preferred mode and so as to reduce the optical sensitivity with respect to vibrations, the bichromatic pyroreflectometer can also comprise a first 10a and a second 10b mode mixers each arranged respectively at the output of the first 1a and second 1b sources of pulsed laser rays, and before the optical beam 2.

According to a preferred mode and in order to obtain the most perfect superposition possible for the measurement zones at the two wavelengths λ _1, λ ₂ , the bichromatic pyroreflectometer can include a coupler or multiplexer at the output of the first 1a and the second 1b sources of pulsed laser rays, and a coupler or multiplexer at the input of the first 4a and the second 4b photodiodes to combine into a single optical fiber the first 21a and the second 21b so-called transmission optical fibers, as well as the first 24a and the second 24b so-called reception optical fibers.

The invention also relates to two methods for determining the temperature of a surface 8 by implementing a bichromatic pyroreflectometer type device conforming to an embodiment presented previously.

Each of these processes is based on the theoretical model of the bichromatic pyroreflectometer type device.

The mathematical problem posed by pyroreflectometry can be summarized in the system of equations below:

If we use Planck's law and simplify the identical terms on both sides, we obtain:

This system of equations does not admit of an analytical solution. This system of equations is the basis of the bichromatic pyroreflectometry model. The unknowns of this system are the diffusion factor (η) and the real temperature (T). The elements measured are the luminance temperature and the reflectivity for the two wavelengths. The known elements are wavelengths.

According to the first method which makes it possible to determine the real temperature Tr, we isolate the diffusion factor for the two previous equations:

We subtract the two diffusion factors which are equal to obtain the direct function.

We deduce the function which gives the direct temperature:

with C2 the Plank constant.

In summary, to determine the real temperature Tr of the surface 8, we first proceed to a step of measuring the bidirectional reflectivity ρ ^⊥ (T,λ ₁ ), ρ ^⊥ (T,λ ₂ ) of the surface 8 when the first 1a and the second 1b sources of pulsed laser rays emit at the top of the pulse respectively at a wavelength λ _1, λ ₂ .

Then, we proceed to a step of measuring the luminance temperature T _L1 , T _L2 of the surface 8 for each of the wavelengths λ _1, λ _2, when the first 1a and the second 1b sources of pulsed laser rays are in outside the pulse.

Finally, we carry out a calculation step by iteration on the variable T to determine Tr, such that f(T) =0.

There illustrates the passage through the zero value of the direct temperature function with the difference in reflectivity on the ordinate and the temperature on the abscissa.

This numerical solution has the advantage of not involving any approximation of the mathematical model.

This numerical solution also has the advantage of using an iteration on the temperature instead of an iteration on the diffusion factor.

Furthermore, according to Planck's law, the surface temperature 8 is always higher than the luminance temperature.

Thus, it is not necessary to calculate f(T) from 0°C, but only from the maximum between the two luminance temperatures.

In other words, the calculation step by iteration on the variable T is initiated with T0> max (T _L1 , T _L2 ). This makes it possible to limit the number of iterations

The iteration step on the temperature directly gives the precision on the calculated temperature. It is possible to vary the temperature accuracy by adjusting the iteration step. This type of improvement makes it possible to adjust the number of iterations necessary to the computing power available in the equipment.

Note that the wavelengths λ _1, λ ₂ used could be of the order of 1300 and 1550 nm respectively.

According to the second method which makes it possible to calculate the Wien order 1 temperature, we first proceed to an approximation of the system of equations with the Wien approximation, to the extent that the wavelengths are short.

This system of equations does not admit of an analytical solution, we therefore use a second approximation, namely the polynomial approximation.

The polynomial approximation being more relevant on the natural logarithm function than on the exponential function for low orders, we write the Wien equation system in order to reveal a natural logarithm:

We apply the polynomial approximation of order one to the natural logarithm:

We isolate the diffusion factors for the two equations and subtract them:

We thus obtain the analytical solution of the temperature in bichromatic pyroreflectometry:

In summary, to determine the first order temperature of Wien T _{order 1 Wien} of the surface 8, we first carry out a step of measuring the bidirectional reflectivity ρ ^⊥ (T,λ ₁ ), ρ ^⊥ (T ,λ ₂ ) of the surface 8 when the first 1a and the second 1b sources of pulsed laser rays emit at the top of the pulse respectively at a wavelength λ _1, λ ₂ .

Then, we proceed to a step of measuring the luminance temperature T _L1 , T _L2 of the surface 8 for each of the wavelengths λ _1, λ _2, when the first 1a and the second 1b sources of pulsed laser rays are in outside the pulse.

Finally, we proceed to a step of calculating the first order temperature of Wien using the following formula established previously:

Note that the wavelengths λ _1, λ ₂ used could be of the order of 1300 and 1550 nm respectively.

It is an analytical formula that is easy to use and program, which allows the use of computers with low computing power, more suited to the embedded system.

It allows the calculation of the temperature in real time, more quickly than with the direct temperature formula stated in the previous process, because it does not require resolution by iteration.

Furthermore, the theoretical model of the bichromatic pyroreflectometer type device admits temperature calculation limits.

There are therefore cases for which the direct temperature and the first order temperature of Wien cannot be calculated, and which correspond to the following situations:

In these two cases, it is possible to use an algorithm and calculate a so-called “corrective emissivity” temperature from the luminance temperature values and the bi-directional reflectivities, and by arbitrarily fixing the diffusion factor, considered from then as constant:

The diffusion factor η becomes a “manually” entered parameter.

In summary, outside the limits of the theoretical model of the bichromatic pyroreflectometer type device, the scattering factor η is calculated from the luminance and bichromatic reflectivity temperature measurements, as follows:

Within the limits of the theoretical model of the bichromatic pyroreflectometer type device, the direct temperature and the first order temperature of Wien can no longer be calculated.

They are therefore replaced by the corrective emissivity temperature by recovering the last calculated value of the diffusion factor before the inversion of the reflectivity parameters such as:

Thus, the shows that experimental measurement results, for which the direct temperature and the first order temperature of Wien take the value of the corrective emissivity temperature, when they cannot be calculated. Graph 4 represents time on the abscissa, temperature on the left ordinate and reflectivity on the right ordinate.

Note, the different characteristics, shapes, variants and embodiments of the invention can be associated with each other, in various combinations to the extent that they are not incompatible or exclusive of each other.

Claims (15)

Device of the bichromatic pyroreflectometer type for determining the temperature T of a surface (8), characterized in that it comprises a first (1a) and a second (1b) sources of pulsed laser rays, an optical head (3) consisting of means forming a collimator (31) and means forming a converging lens (30), a first (21a) and a second (21b) so-called emission optical fibers intended to respectively conduct a light wave emitted by the first (1a) and the second (1b) sources of laser rays pulsed to said optical head, a first (4a) and a second (4b) photodiodes, a first (24a) and a second (24b) so-called reception optical fibers intended to conduct respectively a light wave received by the optical head up to the photodiodes (4a, 4b), the first and second optical transmission and reception fibers all four being united in an optical beam (2) called a “bundle”. Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to claim 1, characterized in that the four optical fibers are silica fibers advantageously coated with a poly imide film, with a thickness of less than 50 microns, preferably less than 20 microns. Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to any one of the preceding claims, characterized in that the four optical fibers are of substantially equal diameters, the difference between their diameter being less than 10% Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to any one of the preceding claims, characterized in that the four optical fibers are arranged equidistantly and as close as possible to the axis of the optical beam (2). Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to any one of the preceding claims, characterized in that it further comprises a sighting laser (5) and a fifth optical fiber (50) connecting said laser to said optical head, said fifth optical fiber being integrated in the center of the optical beam (2). Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to any one of the preceding claims, characterized in that it further comprises a telemeter. Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to any one of the preceding claims, characterized in that it further comprises a first (10a) and a second (10b) mode mixers each arranged respectively at the output of the first (1a) and second (1b) sources of pulsed laser rays, and before the optical beam (2). Device of the bichromatic pyroreflectometer type for determining the temperature of a surface (8) according to any one of the preceding claims, characterized in that it comprises a coupler or multiplexer at the output of the first (1a) and the second (1b ) sources of pulsed laser rays, and a coupler or multiplexer at the input of the first (4a) and the second (4b) photodiodes to combine the first (21a) and the second (21b) optical fibers called d into a single optical fiber transmission, as well as the first (24a) and the second (24b) so-called reception optical fibers. Method for determining the real temperature Tr of a surface (8) using a device of the bichromatic pyroreflectometer type according to any one of claims 1 to 8, characterized in that one proceeds
- at a step of measuring the bidirectional reflectivity ρ ^⊥ (T,λ ₁ ), ρ ^⊥ (T,λ ₂ ) of the surface (8) when the first (1a) and the second (1b) sources of pulsed laser rays emit at the top of the pulse respectively at a wavelength λ _1, λ ₂ ,
- at a step of measuring the luminance temperature T _L1 , T _L2 of the surface (8) for each of the wavelengths λ _1, λ _2, when the first (1a) and the second (1b) sources of laser rays pulsed are outside the pulse,
- to a calculation step by iteration on the variable T to determine Tr, such that f(T) =0, with:
[Math1]
with C2 the Plank constant. Method for determining the real temperature Tr of a surface (8) according to claim 9, characterized in that the calculation step by iteration on the variable T is initiated with T0> max (T _L1 , T _L2 ). Method for determining the real temperature Tr of a surface (8) according to claim 9 or 10, characterized in that the wavelengths λ _1, λ ₂ are respectively of the order of 1300 and 1550 nm. Method for determining the real temperature Tr of a surface (8) according to claim 9 or 10 or 11, characterized in that in the cases where:
[Math 2]
or
[Math 3]

then, the diffusion factor η is calculated according to
[Math 4]
and the actual temperature Tr is calculated as the corrective emissivity temperature, as follows:
[Math 5]
by recovering the last calculated value of the diffusion factor before the inversion of the reflectivity parameters such as:
[Math 6]
Method for determining the temperature of order one of Wien T _{order 1 Wien} of a surface (8) using a device of the bichromatic pyroreflectometer type according to any one of claims 1 to 8, characterized in that one proceeds
- at a step of measuring the bidirectional reflectivity ρ ^⊥ (T,λ ₁ ), ρ ^⊥ (T,λ ₂ ) of the surface (8) when the first (1a) and the second (1b) sources of pulsed laser rays emit at the top of the pulse respectively at a wavelength λ _1, λ ₂ ,
- at a step of measuring the luminance temperature T _L1 , T _L2 of the surface (8) for each of the wavelengths λ _1, λ _2, when the first (1a) and the second (1b) sources of laser rays pulsed are outside the pulse,
- at a step of calculating the first order temperature of Wien using the following formula:
[Math 7]
Method for determining the temperature of order one of Wien T _{order 1 Wien} of a surface (8) according to claim 13, characterized in that the wavelengths λ _1, λ ₂ are respectively of the order of 1300 and 1550nm. Method for determining the real temperature of order one of Wien T _{order 1 Wien} of a surface (8) according to claim 13 or 14, characterized in that in the cases where:
[Math2]

or
[Math3]
then, the diffusion factor η is calculated according to
[Math4]
and the Wien order one temperature T _{order 1 Wien} is calculated as the temperature at corrective emissivity, as follows:
[Math5]
by recovering the last calculated value of the diffusion factor before the inversion of the reflectivity parameters such as:
[Math6]
.