Emissivity Adaptation

 

Abstract

 

The basic assumption behind the operating principle of modern thermal imaging thermometers is a “graybody approximation”. For a graybody, the emittance, reflectance and transmittance are constant for all wavelengths within the wavelengths within the waveband over which the instrument measures.

In reality however, these factors change, and for applications that take place over a wide temperature range, the emissivity variation needs to be taken into account. This work suggests a method for an in-process emissivity identification and adaptation in order to dynamically calibrate infrared temperature measurement systems for applications like heat treatment, welding, cutting etc. A series of experiments has proven that once the spatial and temporal components of emissivity are decoupled, a model can be developed, which in conjunction with direct IR radiocity monitoring can provide information about the required emissivity compensation.

 

 

 


Introduction

 

The ability of infrared thermometers to measure temperature without coming in contact with a particular material is based on the fact that every object emits radiant energy whose intensity is a function of temperature. The general relationship between the radiance of a perfect emitter with wavelength and temperature is expressed by Planck’s law, which is plotted in figure 1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Fig 1:     Planck distribution of radiated energy from a blackbody.

 

A ‘blackbody’ is a hypothetical entity, which absorbs all energy, reflects none and emits energy with perfect efficiency. It is supposed to satisfy the ideal conditions of:

·         Absorbing all incident radiation regardless wavelength and direction.

·         Always emitting the maximum possible amount of energy regardless wavelength for any prescribed temperature.

·         Radiation from a blackbody resembles diffusion; it is independent of direction.

A ‘graybody’ is an entity for which the emittance, reflectance and transmittance are constant for all wavelengths.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Fig 2:     Radiation from a body in space.

 

Radiation coming from any body in space is the sum of the emitted, reflected and transmitted energies. (fig. 2). Opaque bodies do not transmit energy. The ratio of the emittance of a given graybody and the idea blackbody is called emissivity. Thus, emissivity can have the maximum value of 1.0, for the case of a blackbody, and 0.0, for the case of a perfect reflector.

Therefore, it can also be defined as:

 

                               (1)

 

where:                = emissivity

                    = reflectivity

In practice it is a function of both wavelength and temperature.

 

 

Infrared Measurement Theory

 

The three basic modes of heat transfer are conduction, convection and radiation. Thermal radiation can be understood as the heat that leaves an object by way of electromagnetic radiation. Emittance is the ratio of the amount of heat radiated by a material as compared to a black body, and it is always less than one. Shiny, metallic materials tend to have low emittance, while matte, dark colored materials tend to have high emittance. 

Heat transfer by radiation, is described by the Stefan-Boltzmann law:

 

            (2)

 

where:              = heat flow rate

*            = emittance of the material

                *           = 5.67 10-8 [W/m2K4]           

                (Stefan-Boltzmann constant)

                 = temperature at the point of

                                interest [oK]

 = temperature of the

                         surroundings [oK]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Fig 3:     Schematic of optics system of Inframetrics model 600 IR Scanner.

 

Industrial infrared thermometers usually consist of different elements, such as the collecting optics, the radiation detector and some form of indicator. For the system used, the collecting optics, consisting of a germanium window and the focusing lens, are combined with a set of electromechanical servos to perform horizontal and vertical scanning, so that the whole field of view is monitored. The scan mirrors are contained in a sealed evacuated module for increased efficiency. The detector views a thermal reference target 60 times per second and the Mercury/Cadmium/Telluride detector is cooled by liquid nitrogen to 77 oK for maximum thermal sensitivity and spatial resolution. The schematic of the optics system is shown in figure 3.

 

 

Emissivity Model

 

It is obvious, that the emissive capability of steel depends on many parameters. In the present work, an effort is made to isolate the effect of the two main factors that cause spatial and temporal variations of emissivity, the surface condition and the temperature level.

It is assumed that the total value of emissivity is the baseline emissivity of the material, modified by a factor depending on temperature and another one depending on surface conditions, in this case, color bands:

               (3)

 

The baseline emissivity, is a handout value for the particular material. The effect of color and temperature can be decoupled as follows:

 

 

                 (4)

 

where:          is the low temperature emissivity, as this is calculated by the first set of experiments.

 

In the same sense, the effect of color can be isolated as follows:

 

 

                 (5)

 

 

where:      is the reference emissivity, as this is calculated at a ‘clean’ point on the sample in the second set of experiments and shown in figure 13.

 

 

Experimental Method

 

Spatial emissivity distribution

 

Text Box: Fig. 4:     ‘As welded’ sampleThe whole idea was motivated from the observation of the surface of beads conducted with plasma arc on 304 stainless steel plates. In the ‘as welded’ condition, they all had a similar appearance, a series of colored zones, apparently associated with carbonization and other microstructural transformations having taken place during and right after the welding process. Figure 4 is a photograph of one of the as welded samples, where the color pattern is visible.

Initially, a set of low temperature measurements was conducted, in order to identify the spatial distribution of emissivity on the surface of the ‘as welded’ samples. During the experiment, the samples were heated up to 40oC in order to obtain a good resolution of the infrared images. 

 

Fig 5:     Laboratory setup for spatial emissivity

variation measurements.

The spatial variation of emissivity for this particular process, plasma arc welding, is mainly due to microstructural transformations taking place in the material during and after the welding process, and as a result, the appearance of all the samples is similar. Their common characteristic is the repetition of a series of color bands, whose width varies with the welding conditions. Figure 4 is a photograph of the ‘as welded’ surface condition of the specimens. Thus, the low temperature measurements were focused on identifying the influence of surface color on the emissive capability of the steel. It should be noted, that changes in surface roughness and capillary effects of the fusion zone were incorporated in the calculations as an extra color, namely ‘black ridged’. The laboratory setup used for the previously described experiment, is shown in figure 4 and explained in a following paragraph.

Based on the surface appearance, the most prominent color zones were identified by visual observation. Points belonging in these zones were specified as data collection points. The infrared images captured on the VHS tape, as those shown in figures 10a and 10b, were the data source. The data processing methodology is described in full detail in the following paragraph.

 

 

Data processing methodology:

 

Several parameters had to be calculated before the actual emittance could be obtained. Those parameters were the emission level, the relative emission level, the reference emittance, the emission ratio and the averages.

An infrared camera, obtains images of relative emission levels, based on a preset temperature range. The appropriate temperature range is chosen so that the greatest contrast in the image can be obtained without losing any information due to the measurements being too high or too low and therefore out of range. The emission level information was quantitatively calculated based on the values of pixel intensity and the temperature range set on the infrared camera according to the following equation:

         (6)

 

 

where :         =emission level

       =minimum temperature of the range

      =maximum temperature of the range

                    =pixel value

 

The relative emission level was defined as follows:

 

              (7)

 

where:                 = average background

emission level.

                                   = relative emission level

 

The background emission level was measured with a flat, unheated sheet of aluminum foil. If the aluminum sheet is placed directly in front of the sample, then it is assumed that all surrounding emissions are reflected off the sheet and read by the camera.  This is a calibration procedure that takes into account all the emissions that are surrounding the sample but not from the sample itself.

The emission ratio is a particular point’s relative level divided by a reference point’s relative level. The reference point is chosen to be far enough from the weld so that the surface has remained unaffected, thus, its emittance is considered as a baseline. The reference emittance is calculated by the use of the Stefan-Boltzmann law:

 

            (8)

 

The infrared thermometer can give the value of temperature at a point, if its emissivity is known. Therefore, if we set an emissivity value of 1, the IR camera can provide us with a corresponding temperature output :

 

         (9)

 

With an additional direct temperature measurement  on the reference point, the previous equation can be solved for the reference emittance:

 

               (10)

 

where:           = reference emittance

       = IR camera temperature reading on the reference point for  an emissivity value of 1

        = directly measured temperature on the reference point

           =directly     measured temperature of the surrounding area

 

After obtaining the reference emittance value, the emission ratio can be calculated as described above, by the relationship:

                    (11)

 

where :                            = emission ratio

      = relative emission at a point

  = relative emission at the reference point

 

 

Finally, the average emittance is simply the averaged value of all the measurements for the same colored zone for all the samples.

 

               (12)

 

where:    i = color zone number

j = sample number

k = number of measurements for zone i on sample j      

 

 

Experimental Setup

 

Spatial emissivity measurements

 

In order to raise their temperature to the 40 oC level, the samples were heated over a hot plate, and immediately placed vertically in a stable ceramic base. The infrared camera was placed opposite from the samples at a 9cm distance, which gave images of adequate resolution.

Fig. 6:    Laboratory setup for investigating the thermal variation of emissivity.

 

A direct temperature measurement was taken on the samples with a thermocouple for calibration purposes. All the infrared camera readings were recorded on a VHS tape for further processing.

An oven, heated by resistance coils embedded in an open cylinder made of ceramic insulating material, was used to heat the samples. Stainless-Steel samples were placed on a grid-like tray in the center of the oven. Small fans were placed along the rim of the oven to accelerate the heating of the sample by forced convection.

A K type thermocouple was placed in a notch cut into the metal sample, so that the temperature of the sample could be read at any time.  An Intrametrics 600 infrared (IR) camera was focused on the sample at a 58° angle.  The output from the camera was fed to a T.V. monitor and recorded on a VHS tape. The overall setup is shown in figure 6.

 

Fig. 7:    Position of the samples on the grid, before heating.

Figures 7 and 8, show the position of the samples placed on the grid, when the grid is high, out of the oven and when the oven is red-hot respectively.

A thick metal plate covered in a smooth sheet of aluminum foil was placed in front of sample when taking background measurements. Large metal tongs, slightly above the sample, held the metal plate, at a horizontal orientation.

Each sample was placed on the oven’s tray and slowly heated to approximately 480°C.  Starting at 50°C infrared images and measurements were captured every 40°C to 60°C.  When taking the infrared readings, first an appropriate range was selected in the Infrared camera settings, in order to obtain the best resolution for the emission levels being measured.  This way the greatest contrast in the image could be obtained without losing any information due to the measurements being too high or too low and therefore out of range.

 

Fig. 8:    Position of the samples inside the oven.

 

Once an appropriate range was obtained VCR recording of the images was started.   Within the IF camera the emittance of the sample was set equal to 1. The camera was set to point mode, which would allow a nodal temperature reading at a point near the thermocouple notch.   Simultaneously the actual temperature of the sample was read with the thermocouple.  This information, along with the emission level at this point, can be used to calculate a reference emittance value for each image. Color and gray scale infrared images were recorded as well as the range of levels for those images.

Then a flat aluminum sheet was placed in front of the sample, as shown in figure 9, and infrared images were recorded at its appropriate range.  If the aluminum sheet is placed directly in front of the sample, then it is assumed that all surround emissions are reflected off the sheet and read by the camera.

This is a calibration procedure that takes into account all the emissions that are surrounding the sample but not from the sample itself.

 

Fig. 9:    Initializing the IR measurements taking into account background radiation.

 

The video recorded images were transported into computer image processing application (NIH Image 1.61) for analysis. An example of a color infrared radiation field recorded at 350 oC is shown in figure 10.

 

 

 

 

 

 

 

 

Fig. 10: Infrared radiation recorded at 350 oC.

 

 

 

Results

 

The emission field recorded at low temperatures is shown in figures 11a and 11b in color and black and white respectively. The grayscale images were used to convert the image data to temperatures.

The colors shown in figure 11a are not the actual colors of the specimen’s surface, but they are color contours of the emission levels for the chosen temperature range. The colormap is shown at the bottom of the figure; red corresponds to areas emitting the most, and blue to areas that emit less.

Those images were post processed as described in the data post processing methodology and the emissivity data obtained for every color band and for different samples were averaged. The raw experimental data collected, are presented in table …., in the appendix.

 

Fig. 11a: Color map of infrared radiation coming                           from a sample close to room temperature. 

 

 

Fig. 11b: Grayscale map of infrared radiation

 coming from a sample close to room   temperature.  

 

The variation of emissivity over the different color bands as calculated with the previously described methodology is plotted in figure 12.

 

 

Fig. 12: Color related variation of emissivity

 

This experiment helped us define the spatial distribution of emissivity, mainly depending on surface color and roughness. The next step was to define the temperature effect on the emissive capability of steel.  For this case, a different laboratory setup was designed, in order to be able to maintain the samples at high temperatures. This setup has been described above, and is schematically shown in figure 13.

 

Fig. 13: Emissivity variation over a temperature range at a ‘clean’ area of the sample.

 

A series of radiocity measurements were taken at 40-60 oC temperature intervals, up to the 500 oC range. The experimental procedure has already been described in full detail. An extra measurement was also taken at each temperature level on a ‘clean’ area of the sample that had no original surface patterns, neither of color, nor of surface roughness. The values of the emittance at that point were plotted versus temperature in figure 13.

 

Discussion

 

The average (temperature) values are used in calculations related to the effect of temperature where the color effect is not taken into account,   and   the average (color) values are the means of the actual emissivity of a   particular  color band over the whole

 

 

 

 

 

 

 

 

 

 

 

 


 temperature range. The calculated values are presented in table 1.

 

These values are the mean emissivity values measured in low temperature, therefore, they only include the effect of color/surface condition on the baseline emissivity of the material as this last one is found in handbooks. The obtained data after post-processing are summarized in table 2.

 

 

 

 

 

 

 

Table 2: Cold emissivity

 

These values are the mean emissivity values measured at various temperatures at a ‘clean’ unaffected by process transformations point, therefore, they include the combined effect of temperature as well as the effect of changes of color/surface condition during the experiments, such as carbonization during heating. These values are presented in table 3.

 

 

 

 

 

 

 

 

 

 

Table 3: Reference emissivity

 

 

 

 

 

 

 

 

 

 

·         Proposed Model:

 

As analyzed in a previous paragraph, it is assumed that the total value of emissivity is the baseline emissivity of the material, modified by a factor depending on temperature and another one depending on surface conditions, in this case, color bands (eq. 3):

 

The baseline emissivity, is a handout value for the particular material. The effect of color and temperature can be decoupled as follows (eq. 4):

 

where:          is the low temperature emissivity, as this is calculated by the first set of experiments.

 

The experimental value of  can be calculated if we divide the values of table 1 by the values of table 2 that correspond to the same color. The variation of the average values for all colors with temperature is plotted in figure 14.

In the same sense, the effect of color can be isolated as follows (eq. 5):

 

where:      is the reference emissivity, as this is calculated at a ‘clean’ point on the sample in the second set of experiments.

 

Similarly, the experimental value of  can be calculated if we divide the values of table 1 by the values of table 3 that correspond to the same temperature. The variation of the average values throughout the temperature range with color is plotted in figure 15.

 

 

 

 

 

 

 

 

 

 

 

 


Fig. 14: Color related correction factor

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Fig. 15: Temperature related correction factor

 

 

 

·         Calculation of baseline emissivity

 

Based on the proposed model, we can used the equation:  to calculate the baseline value of emissivity and see if it is comparable with handbook values for stainless steel. In order to do this we need to multiply the corresponding values of  ().

 

 

 

 

 

 

 

 

 

 

 

Fig. 16: Experimental estimation of baseline emissivity

The baseline value for the different colors over the temperature range is shown in figure 15 and the mean value for all the colors is found to be 0.417. This value is in very good accordance with handbook values. [Table of Emissivity of various surfaces, Micron Instrument Company Inc., page 8, stainless steel 304, after heating….]

 

 

Error Sources

 

From the first set of experiments it is obvious a variation in emissivity for the different color bands, as seen in the graph in figure …. The colors can be classified in order of increasing emissive capability as follows: caramel, blue, brown, bronze, yellow, black ridged, black flat. As explained before, the ‘black ridged’ area is the fusion zone area where capillary effects and rough surface are all treated as a different color.

The variation in reference emission values is likely due to the different extent of tarnish and impurities on the samples.  For instance sample number two was noticeably dirtier than all the other samples.  Its reference emittance is significantly lower than that of the other samples.  This makes calculated emittance for the different color bands in sample two significantly lower than those for other samples.  However, the ratios to reference emittance values for sample two correspond to those of other samples.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


                                                               

Figure 6: Clean Sample before heating         

Figure 7: Clean sample after heating            

   note the darker color

 

The calculated emittance values for sample number five differ from the other samples.  This is likely due to the unusual color band pattern on sample five.  There are several imperfections on the sample, which are either due to the metal itself or perhaps the welding process.  Emittance calculations were affected by these imperfections and perhaps should not be considered.

As far as the high temperature experiments are concerned, as each sample was heated to 480°C its surface color would begin to change, due to carbonization effects, figures 17a and 17b  This made the overall appearance of the sample darker, changing the colors of the weld regions in some cases.  This transient effect may have been a significant source of error since the location of the color bands might have been changing on the sample surface, over the time of the experiments. However, caution was taken in order to avoid this error, by measuring at the center of each zone.

Another large source of error was the infrared camera itself.  The large size of the oven and the extreme heat generated by it prevented us form placing the camera too close to the sample. Background reflections would have been avoided if a heat shield was available, and if the IR camera was moved close enough for the sample to cover the whole field of view. Unfortunately, the heat shield was not available and the sensor would not operate properly if heat would reach very high levels. For this reason, the sample temperature was not increased more than about 500 oC.. Additionally, the heat from the oven caused a great deal of condensation to form on the camera lens.  The phenomenon was limited by frequent cleaning of the lens to avoid condensation that could greatly affect the infrared images.  Thus, the camera could not be placed closer than  30 cm from the center of the oven, a fact that also reduced the image resolution.

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 18: Schematic of laboratory setup for high temperature measurements.

 

 

Perhaps the greatest source of error, however, was the fact that the thermocouple did not have a good contact with the samples. Placing the thermocouple in a notch on the side of the samples left a great deal of it exposed to the air.  Often, large temperature fluctuations would be noticed, especially at higher temperatures.  This is most likely attributed to the poor contact the thermocouple had with the sample.  This led to a great deal of inaccuracy in the calculations for the reference emittance, which was then used to calculate the emittance of the regions of the weld.  For future experiments, it is suggested that the thermocouples are spot welded on the samples, and at high temperatures, a conductive paste is utilized..

 

 

Applications

 

 

 

 

 

 

 

 

 

 

 

Conclusions

With this work a model for real time calibration of infrared systems is proposed. Experimental observations have proved that emissivity variations in processes that involve significant changes in surface condition and temperature can be broken up in two parts, and calculated in a decoupled way.  The spatial emissivity distribution, which is associated with surface color and conditions, is mapped off-line. Another thermometry method assisting infrared radiocity recordings during an off-line pilot test can provide with data regarding the temperature related emissivity.

When the previous information is available a model relating radiocity and emissivity can be developed. As soon as this model is built, an infrared measurement system can automatically be calibrated using the MIT adaptation law, based on radiocity measurements and model predictions.

 

 

Acknowledgements

 

The authors would like to acknowledge the contribution of undergraduate researchers Greg Angelides, Rafael Jaramillo and Linda McLaren that helped to the conduction of experiments, under the Tufts University Research for Undergraduates 2000 Program.

 

 

References

 

·         IR answers and solutions handbook, IRCON 1997.

·         Holman J.P, “Heat Transfer”,  McGraw Hill, Inc, New York, USA 1997.

·         Mills A.F, “Basic Heat and Mass Transfer”, Irwin, Inc, Chicago, USA 1995.

·         “Model 600 Operator’s Manual”, (Document #05250-200), Inframetrics, Inc. May 1988.