The aim of this paper is to discuss different models that describe atmospheric transmission in the infrared. They were compared in order to choose the most appropriate one for certain atmospheric conditions. Universal models and different inaccuracies connected with them were analysed in this paper. It is well known that all these models are different, but the aim of this paper is calculate how big the differences are between the characteristics of atmospheric transmission as a function of the distance. There have been models analysed from the literature, and these are used in infrared cameras. Correctly measured atmospheric transmission allows the correct temperature of an object to be determined, which is very vast problem that is discussed in paper.

The atmospheric transmission in the infrared (IR) is an important parameter in
thermovision measurements. This is due to the fact that, when the temperature
of an object is measured, the atmosphere which is between the thermal
imaging camera and the object attenuates infrared radiation emitted by the
object. Additionally, it has been observed, even in laboratory conditions,
that at distance of 1–10 m, the atmospheric absorption, caused by water
vapour and carbon dioxide, is noticeable. The most important role in
absorption of the infrared radiation for the wavelength

Correctly measured atmospheric transmission allows the correct temperature of an object to be determined. In the case of there being no precise model describing the atmospheric transmission in the thermal imager microcontroller (Minkina and Dudzik, 2006, 2009; Minkina et al., 2010), the obtained temperature of the object would be wrong, lower or higher. The atmospheric attenuation depends strongly on the wavelength. For some wavelengths there is very low attenuation over distance of several kilometres, whereas for other wavelengths the radiation is attenuated to close to nothing over a few metres. The attenuation in the atmosphere does not allow the total original radiation from the object to reach the camera. If no correction for the attenuation is applied, then the measured apparent temperature will be lower and lower with increased distance. The influence of distance on the temperature measurement for the short-wave (SW) and long-wave (LW) camera, without taking into account correction of the impact of the atmosphere on the measurement, can be clearly seen in Fig. 1.

The paper compares different methods of calculating the atmospheric transmission coefficient in the infrared which can be found in practice and in the literature. When a model is chosen, such factors as accuracy and the time needed to do the measurements should be taken into consideration. Greater accuracy means a longer time needed for the calculations. In fact, that subject of research about the atmospheric transmission has a wide range, but this paper has some limitations. The paper concentrates only on the atmosphere's impact on the measurement. The effect of the IR radiation emitted by the absorbing atmosphere (Kirchhoff's law) was skipped in this case and will be considered in the subsequent paper. Thermal imaging cameras operate in a particular infrared range, for which the atmospheric transmission coefficient will be different than for the whole band.

The influence of distance to the temperature measurement for the
thermal imaging cameras without taking into account correction of the impact
of the atmosphere on the measurement: (1) LW, 8–12

Depending on a thermovision camera model, there are several different models
of the atmosphere transmittance, such as FASCODE, MODTRAN and SENTRAN
(Anderson et al., 1995; Rothman et al., 2005; Vollmer and
Möllmann, 2010, Pręgowski and Świderski, 1996; Pręgowski,
2001). For example, in the AGEMA 470 Pro SW and AGEMA 880 LW systems, the
manufacturer employs the following simplified equation that describes the
atmospheric transmission in the infrared, using the LOWTRAN model:

The given values are determined in normal conditions of atmospheric
temperature

Characteristics of atmospheric transmission coefficient

The transmittance model defined by FLIR for the ThermaCAM PM 595 camera is a
function of three variables: atmospheric relative humidity

It should be emphasized that the model described with Eq. (

Finally, the thermovision camera measurement model is defined as a function
of five variables (Minkina and Klecha, 2015):

We want to emphasize that the model derived above is a simplified model. In reality, the camera detector receives radiation not only from the object but also from other sources. The simplification can be explained looking at Fig. 4.

Simulation characteristics of the atmospheric transmittance

Explanation of simplifications assumed in the thermovision camera
measurement model (2, 3); ambient temperature

The signal proportional to the ambient radiation intensity and dependent on
ambient temperature

Equations (2) and (3) for calculating atmospheric transmission coefficient

Using experimental studies conducted by Passman and Larmore (1956),
the characteristics of the transmission coefficient can be
calculated precisely. Gas composition influences the results of measurements
carried out using a thermovision camera. In this case, the most important
are the absorbance coefficients: vapour absorbance (

The figure shows the cylinder with height

Vapour absorbance

There is a relationship between the height of the cylinder with water

Taking into account distance

Characteristics of coefficient

A part of the Passman–Larmore table for vapour absorbance

Calculate the atmospheric transmission coefficient for

Using Eq. (

In order to adapt the results to models described in paragraphs 2 and 3, the
average characteristics for the wavelength

A part of the Passman–Larmore table for carbon dioxide absorbance

The tables were obtained on the basis of experimental studies, and that is
why the model seems to give the most accurate value of the atmospheric
transmission coefficient

Characteristics of atmospheric transmission coefficient

The paper of Więcek (2011) gives another atmospheric transmission model in
the infrared

Next, the value of the coefficient

Using Eqs. (

Equation (

In order to compare all models describing atmospheric transmission

Characteristics of atmospheric transmission coefficient

The atmosphere attenuates infrared radiation of an object whose temperature
is measured. In the case of there being no properly designed model including
the atmospheric transmission coefficient in the infrared

The function based on Passman–Larmore measurements was introduced as the
initial model. All models have similar characteristics (Fig. 9, which
becomes more different with the distance; Fig. 10). The model described in
the paper of Więcek (2011) can be much more different from the others if
the calibration point is not appropriate. Practical and experimental models
give similar values of the atmospheric transmission coefficient

It is well known, that all these models are different, but the aim of this paper is to calculate how big the differences are between the characteristics of the atmospheric transmission as a function of the distance.

Characteristics of atmospheric transmission coefficient

Characteristics of atmospheric transmission coefficient

It should be noted that the properly calculated atmospheric transmission
coefficient in the infrared