On the FPA Infrared Camera Transfer Function Calculation

On the FPA Infrared Camera Transfer Function Calculation

On the FPA infrared camera transfer function calculation

Stefan Datcu*a, Laurent Ibos*a, Simone Matteï**b

aCERTES, Université Paris XII Val de Marne, Créteil, France

bLTM, Université de Bourgogne, Le Creusot, France

Keywords: infrared thermography, transfer function, parametric identification, FPA matrix camera detectors

1.Introduction

In order to obtain a good quantification of the heat flux emitted by a surface using infrared images, it is necessary to calculate accurate values of the surface temperature. Infrared thermograms often present distortion induced by aberration and diffraction phenomena and by electronic noise. A convolution product can model aberration and diffraction distortions and the detector noise is assumed to be stationary and additive. Image restoration can be solved as an ill-posed problem. Its solution is commonly obtained using regularisation methods.

2.Physics

The physical approach used in this work is to study the correspondence between all surface elements of an object M observed by an infrared camera and their images in the image plane (i.e. the detector matrix). The luminance of each surface element M0 of co-ordinates (x0,y0) can be represented in the xOy plane by a two-dimension Dirac distribution . Due to the presence of the optical device distortion, the image of each surface element is a diffusion figure located around the point M(x, y). Generally, in the case of aberration distortion this figure can be assimilated to a diffraction figure [1], which emission distribution can be represented by the camera transfer function h. This function is often considered as position invariant in local regions of the image [1,2].

Considering an object M with a luminance , the emitted radiation E(x',y') in the image plane is given by the convolution product between L0 and h:

(1)

Thus, the radiant heat flux received by the camera detectors is expressed by:

(2)

3.Distortion model and correction protocol

The hypotheses of the model are:

  • The image distortion model is a convolution product,
  • The noise is additive stationary and ergodic.

Generally, we can write:

(3)

The primary purpose is to determinate the transfer function of the camera system. There are four components: the signal transfer function, the optical transfer function, the detector transfer function and the electronic circuit transfer function. We suppose that the electronic circuit transfer function does not depend upon time and detectors position in the FPA matrix. Also, we suppose that the sensibility of the detector is constant on the detector surface. We suppose that all detectors are similar which means that they have the same sensibility and the same noise level (Poisson noise).

We used a camera objective of 45° x 34° field of view. This implies a non-linear behavior of the camera optical system. This behavior constrained us to define a multi-value optical transfer function in order to take into account this non-linearity.

Our approach to determine the camera transfer function is to use a Dirac signal source and to acquire this signal directly [3]. The impulsion response obtained is very noisy due to the low level of the source. Thus, we proceed to a parametric identification in order to model the acquired signal. Three point spread functions are generally used in the imaging systems: the boxcar function, the gaussian function and the exponential function. Using a combination of these functions we have identified the parameters of each of them and the given their evolution curves as a function of the position on the detector matrix.

The final model is:

(4)

where:

  • Np is the number of parameters,
  • r is the radial distance from the center of the matrix (we suppose that the camera transfer function have a radial symmetry),
  • n is the additive stationary noise,
  • f is the theoretical image of the source (i.e. the observed signal),
  • g is the acquired image.

4.Results

We present in this paper the calculation of the camera transfer function obtained for an infrared camera model AGEMA570Elite from FLIR™ and the correction of infrared thermograms obtained on a vertical plane wall surface. Examples of camera impulsion response and transfer function calculated in the center of the detector matrix are presented on the figures below.

Figure 1. Impulsion response of the camera

Figure 2. Calculated transfer function in the center of the detector matrix.

5.References

[1]G. Gaussorgues, La thermographie infrarouge, Technique & documentation, Paris, 1981.

[2]F. Papini, P. Gallet, Thermographie infrarouge, Masson, Paris, 1994.

[3]J.Max, Méthodes et techniques de traitement du signal et applications aux mesures physiques, Masson, Paris, 1989.

*; phone 33 1 45 17 18 44; fax 33 1 45 17 18 42; Centre d’Etudes et de Recherches en Thermique, Energétique et Systèmes (CERTES), IUT de Créteil, Université Paris 12 Val de Marne, 61 avenue du général de Gaulle, 94010 Créteil cedex, FRANCE; **; phone 33 3 85 73 10 42; fax 33 3 85 73 11 20; Laboratoire Laser et Traitements des Matériaux (LTM), Université de Bourgogne, IUT du Creusot, 12 rue de la Fonderie, 71200 Le Creusot, FRANCE

Top View