The calibration of uncooled thermal infrared (IR) cameras to absolute temperature measurement is a time-consuming, complicated process that significantly influences the cost of an IR camera. Temperature-measuring IR cameras display a temperature value for each pixel in the thermal image. Calibration is used to calculate a temperature-proportional output signal (IR or thermal image) from the measurement signal (raw image) taking into account all technical and physical properties of the IR camera. The paper will discuss the mathematical and physical principles of calibration, which are based on radiometric camera models. The individual stages of calibration will be presented. After start-up of the IR camera, the non-uniformity of the pixels is first corrected. This is done with a simple two-point correction. If the microbolometer array is not temperature-stabilized, then, in the next step the temperature dependence of the sensor parameters must be corrected. Ambient temperature changes are compensated for by the shutter correction. The final stage involves radiometric calibration, which establishes the relationship between pixel signal and target object temperature. Not all pixels of a microbolometer array are functional. There are also a number of defective, so-called “dead” pixels. The discovery of defective pixels is a multistep process that is carried out after each stage of the calibration process.
In recent years, thermography has had a dramatic development with annual growth rates of over 20 % (Mounier, 2011). This development will have an even more dynamic impact in the future. Enabling this huge market success are infrared (IR) image sensors based on microbolometer arrays, which have excellent thermal and spatial resolution (Kruse, 1997; Vollmer and Möllmann, 2010). Also, because no cooling is required, they have low power consumption and have a low entry-level price.
Mainly due to the rapid development of micro- and nanotechnology,
microbolometers have become significantly cheaper and more efficient. While
early in 2000 the maximum image size was
An uncooled IR camera consists of the following main components (Fig. 1)
(Budzier and Gerlach, 2011):
IR optics sensor arrays processor-based camera electronics. vision display device and temperature-measuring image device
Both these components and the calibration process play an especially crucial
role in ensuring the quality of an IR camera. The calibration is implemented
both in the hardware and the software (firmware). For the two device
concepts
there are different calibration concepts (Budzier, 2014).
Vision devices display the measured radiation distribution of the scene qualitatively. They serve primarily as a night vision device. This class of devices is produced in very large quantities. They are used in military applications, security technology and increasingly in automotive technology (night driving aid). The aim of calibration is to produce as closely as possible an optically flawless image. This process is referred to generally as “smooth out”.
Structure of an uncooled IR camera with microbolometers.
Temperature-measuring IR cameras also display a temperature value for each pixel. Here, after the “smooth out”, a radiometric calibration must also be carried out. Practically every pixel of an IR camera is a separate pyrometer. The main problem is that the calibration parameters of microbolometers depend on both the ambient temperature and the camera temperature (Budzier and Gerlach, 2011).
In the following text the calibration of temperature-measuring, uncooled
IR cameras will be described for microbolometer arrays This
article is a summarized presentation of the habilitation thesis of Budzier (2014).
Optical channel in an uncooled IR camera.
Camera model for the calculation of the IR image (explanation in text).
The theoretical basis for the calibration is based on a radiometric model of the thermal uncooled IR camera. In this case, the sensor array including the sum of radiant fluxes from the object and from inside the camera will be considered (Fig. 2).
A pixel “sees” inside the camera essentially the edge and the bracket
(front panel) of the optics and its own sensor housing. In addition, the
pixel gives out emissions in the entire half-space. The irradiance
The reduced solid angle
Since the pixel receives radiation from the entire half-space, the
reduced solid angle
In order to determine the radiance
Modern microbolometer arrays do not contain Peltier elements in a
vacuum housing. These are called TEC-less microbolometers (TEC:
thermo-electric cooler). The microbolometer is no longer stabilized to a
constant temperature, i.e. the sensor temperature
The dependence of the offset and the sensitivity of a microbolometer array
cannot be derived from the physical properties of a bolometer resistance
without information concerning the signal processing. Since the internal
signal processing of a microbolometer array is not known in detail for
reasons of company in-house security, the array must be regarded as a black
box. In general, the following polynomials can be assumed for the
temperature dependence of the offset
Extension of the camera model from Fig. 3 for the calculation of the IR image for TEC-less microbolometers.
A radiometer, where each individual pixel of an IR camera can be determined, measures the radiant flux of the object and generates an output signal which, as a result of the calibration, is proportional to the temperature of the object (DeWitt and Nutter, 1989). A radiometric IR camera displays as accurately as possible the true temperature of a black body. The calibration is used here to calculate a temperature-proportional output signal (IR image) from the measurement signal (raw image) taking into account all technical and physical properties of the IR camera. The steps necessary for this are summarized in Fig. 5.
In the following section, the non-uniformity correction (Sect. 3.1), the temperature-dependent correction (Sect. 3.2), the defective pixel correction (Sect. 3.3), the shutter correction (Sect. 3.4) and the radiometric calibration (Sect. 3.5) will be presented in detail. There will be no further discussion of the operating point setting which depends significantly on the microbolometer used and would correspond to the example provided by the manufacturer's procedure.
Flow chart of radiometric calibration.
Schematic of the two-point correction procedure, using the example of two pixels. Dashed curves: the value “offset” is shifted parallel to the standard curve.
Because of the technology, the individual pixels of a microbolometer have uniquely different operating points (DC bias values) and sensitivities and, thus, differing characteristics. During the correction of this non-uniformity all pixels are converted onto a single characteristic curve, the so-called standard characteristic curve. This process is referred to as “smooth out” because the IR image now with uniform illumination has no structure and so is smooth. According to this characteristic adjustment, all pixels behave the same and subsequent calibration steps can be exemplarily performed on any pixel or on any group of pixels.
The description of the pixel characteristic curve is often a function of the
object temperature
The characteristic curve corrections described in the literature (Schulz and Caldwell,
1995, and Wallrabe, 2001) also refer to photon sensors, whose function
Firstly, it is assumed that both the sensor temperature and the ambient temperature are constant.
The linear relationship between the voltage of the pixel
In order to reduce the calculation during real-time correction, Eq. (13),
If the temperature of the microbolometer is not constant, as is the case for
TEC-less microbolometers, the sensor sensitivity and offset parameters
change with temperature (Eqs. 8–10). To correct this temperature
dependence, the polynomials of Eqs. (8) and (9) must be determined. For this
purpose, the pixel voltages
Due to the difficult manufacturing process for microbolometer arrays, all pixels have different parameters such as operating points, characteristic curves and noise. Pixels that either do not work or whose parameters vary greatly from the mean are defined as non-functional or defective. Defective pixels are generally referred to as “dead” pixels.
Pixel defects manifest themselves as defective pixels in the IR image. Their actual value can only be estimated with the help of neighbouring pixels. The measured value at this point of the IR image is not reconstructable. Therefore, the number of dead pixels is an important quality characteristic of microbolometers. Normally not more than a maximum of 1 % of all pixels should be defective.
A pixel is considered defective if any of the following conditions is met.
The operating point is outside of the previously defined voltage range The sensitivity differs more than The noise voltage is 1.5 times greater than the average noise voltage of the array.
In addition, a group of defective pixels exist, which, although they do not
meet the above criteria, behave differently and are classified as defective.
These are, for example, short circuits between adjacent pixels or non-linear
characteristics of individual pixels. Figure 7 shows a raw image with a
plurality of defective pixels (black dots).
Raw image with 1926 defective pixels (0.6 %):
Typical subdivision of infrared microbolometer arrays in the mid (zone A) and marginal zones (zone B).
Defective pixels occur not only individually but also in clusters. A cluster of dead pixels is a group of at least two defective pixels that are adjacent or gather together in a corner. Clusters are characterized by their size, that is, by the number of defective pixels. In the image section in Fig. 7b clusters are clearly visible. Particularly critical are defective rows or columns, because, despite a correction in the IR image, they are always conspicuous. A column or row is usually considered defective if more than 50 % of the pixels do not work.
Specification of allowable defective pixels.
Since the number of defective pixels of a microbolometer is an important quality attribute, the manufactures will always indicate in their specifications the maximum permissible number of defective pixels. In the centre of an IR image defective pixels are particularly noticeable. Therefore, the image area is divided into at least two zones (Fig. 8). In the central region (zone A) higher demands are placed on the functionality of pixels than of those on the edges. Table 1 shows a specification of permissible defective pixels.
The detection of defective pixels proceeds in three steps (flow chart in
Fig. 5).
The first defective pixel detection must be done before the uniformity correction.
Here all defective pixels are detected that are located outside of the
previously defined range of variation of the pixel operating points. These
are primarily pixels which are outside the control range and, thus, affect
the position of the standard curve. Furthermore, all pixels which are too
noisy are eliminated. The second defective pixel detection is performed using the calculated gain
and offset values according to the characteristic curve correction. Here
defective pixels are identified that have too great a deviation from the
standard curve. The third defective pixel detection is carried out at the end of the
calibration. In this case, all defective pixels which have not yet been
detected are recorded. This is done by considering the IR image with
different adjustments and richly contrasting scenes.
While the first two defective pixel detections can be performed
computationally, the final detection is carried out manually. This also
means to verify the correction of the cluster and, if necessary, to change
the correction method.
There is no reading at the location of a defective pixel. This can only be estimated from the surrounding area. The aim of the recalculation of the pixel value is always to produce a high-quality visual image, i.e. so that an observer of the IR image may not notice any defective pixels. The calculation of the pixel value is carried out by methods of image pre-processing, such as with median operators.
In order to calculate the radiance and the object temperature from Eq. (5),
the radiance
The starting point for consideration is that the radiance of the camera
interior space was determined using a known ambient temperature and thus a
known camera temperature
When the shutter is open, the pixel voltage is
The projected solid angle
For each pixel the voltage
Histogram of the raw image at the operating point showing a black
body with a temperature of 150
Effect of two-point correction.
Histograms of
Temperature dependence of
Shutter characteristic curve. Parameter: camera temperature of the respective measurement points.
Object temperature
The previous corrections in Sect. 3.1 and 3.4 lead to all pixels of the
IR image having the same behaviour and the IR image not being dependent on
the ambient temperature. Finally, the radiometric calibration calculates the
temperature of the object to be measured from the grey values of the pixel.
It works with a voltage object temperature characteristic, so for each grey
value
According to Horny (2003) it is possible to approximate the sensor output
signal with a Planck curve:
In the following, the calibration process will be illustrated by an example.
The calibration process begins with the setting of the operating point.
Figure 9 shows a histogram of the raw image with optimized operating point
(dynamic range of
After the operating point has been fixed, in the first defective pixel detection procedure, all pixels which lie outside of the dynamic range are defined as defective. Figure 10 shows the effect of a two-point correction of the pixel graph, in which the variation of the values of the individual pixels occurring in the raw image (Fig. 10a) is eliminated. The recognizable characteristic stripe structure is formed by the column-wise arrangement of “blind” bolometers. The optical image resulting from the natural vignetting of the optical signal and delivered to the image edge is also always present in raw image where in Fig. 10a it is hardly recognizable by the content of the thermal image.
By analysing the offset and gain values calculated in the two-point
correction (Fig. 11), in a second defective pixel detection procedure more
abnormal pixels that lie outside a defined scatter band can be sorted out.
Fixed limits of
For TEC-less microbolometers, the temperature dependence of the offset values and the sensitivity has now to be determined (Fig. 12). The regression analysis includes the known relationships between camera or sensor temperature and the respective measured variables. These are for the sensitivity of a polynomial of the second order (see Eq. 9) and the offset values for a third-order polynomial (see Eq. 8).
After correction of the non-uniformity, the correction of the ambient
temperature dependence is carried out. The so-called shutter characteristic
curves are recorded, which represent the ratio of the shutter-open signal to
shutter-off signal as a function of the temperature of the camera (Fig. 13).
For this, the camera temperature (in Fig. 13 from 3.9
to 47.3
Subsequently, the radiometric calibration is carried out by determining the
signal voltage
Finally, a third defective pixel detection takes place during the final check. Here visually conspicuous pixels are rejected by visual inspection.
The calibration of an uncooled IR camera is a complex and lengthy process,
which significantly affects the cost of an IR camera. Depending on the
measurement technology used, such as black bodies, references and climatic
chambers, the proposed calibration allows for the measurement of absolute
temperatures with a maximum measurement uncertainty of about
For rapid changes in temperature of the camera, the shutter needs to be frequently operated, e.g. several times within 1 min. Since the operation of the shutter always causes an interruption of the measuring process, the user should operate the shutter as little as possible or even completely avoid using it. For the shutterless operation of IR cameras, however, much more complex calibration algorithms are required, which build on those described here. Such an approach is pursued by Tempelhahn et al. (2014).