The modulation transfer function measures the extent to which the thermal imaging system faithfully reproduces the scene, and it is the result of the interaction of the components with different spatiotemporal frequency characteristics. In models such as NVTHERM, it is usually assumed that the thermal imaging system is a linear system, and each point on the target is imaged by the point spread function, and the image formed by the image surface is accumulated after the innumerable points of the object surface are convolved with the point spread function. result. Figure 14.2 illustrates the role of the modulation transfer function in the imaging process. The modulation transfer function of an infrared thermal imaging system is mainly determined by four components: an optical system, a detector, a circuit, and a display.
Thermal imaging systems have a wide range of wavelengths, and the received scene radiation is incoherent, and its optical system can be considered a diffraction limited optical system. The transfer function of a diffraction-limited optical system depends on its wavelength and aperture. For a common circular aperture, the modulation transfer function under diffraction constraints is
Where is the cutoff frequency, which is determined by the wavelength and the F number, . In addition to diffraction, the imaging process is also affected by aberrations in the optical system. The dispersion circle energy distribution caused by the aberration is a Gaussian function with a circular symmetry form with a standard deviation of and a modulation transfer function of
The total modulation transfer function of the optical system can be obtained by combining the above two factors.
The detector has the effect of spatial sampling and integration on the incident image. The spatial integral will generate high frequency confusion, and its modulation transfer function is
W is the effective detection length of the pixel. The effect of the electronic circuit on the signal is mainly low-pass filtering, which is usually described as a multi-stage RC low-pass filter whose modulation transfer function can be expressed as
Where is the 3db attenuation frequency of the electronic circuit. The time frequency of the electronic circuit is converted to the spatial frequency by the scanning speed of the IRFPA. The point spread function of the CRT display is approximated as a Gaussian distribution function, assuming that the modulation transfer function of the CRT display is
Where is the spatial feature frequency. Therefore, the modulation transfer function of the entire system is
An infrared thermal imaging system can be viewed as a linear system. From the linear theory, there is a definite relationship between the output function and the input function. This relationship is called the optical transfer function.
Where and are the Fourier transforms of the input and output functions, respectively. Let be called the modulation transfer function of the system. Therefore, the modulation transfer function can reflect the response of the infrared thermal imaging system to image signals of different spatial frequencies.
If the input function is a step function, its derivative is a δ function, then . According to the Fourier transform theory,
If the input image satisfies the step function requirement, we can use Equation (14-10) to calculate the modulation transfer function of the system.