Modulation Transfer Function of the Thermal Imaging Monocular

The modulation transfer function (MTF) of thermal imaging monocular (TIM) was investigated in this article. TIM consists of a lens, a microbolometric matrix (MBM), an electronic system of video signal amplification and processing, a micro display and an eyepiece. The monocular is considered as a linear invariant incoherent system. It’s MTF is equal to the product of the modulation transfer functions of the components. For the convenience of practical application, it is proposed that all MTFs are considered as a function of the angular spatial frequency in the space of objects. An example of TIM MTF calculation with given characteristics was considered. The study of the MTF showed that the spatial impact of the MBM, which is determined by matrix structure, has the greatest influence on the deterioration of this function.


Introduction
Thermal imaging systems are widely used in various fields of human activity, including security systems, medical thermal diagnostics, aeronautical and space systems, remote sensing of the Earth's surface, military affairs, etc. [1][2][3][4][5]. In many cases, such systems are small-dimensional thermal imaging monoculars (TIM) in which the heat-contrast image of an object is observed by the operator on the display screen with the help of an eyepiece. The main characteristics of TIM are the spatial and temperature resolution, the maximum detection and recognition distances. They depend on the modulation transfer function (MTF) of the monocular [6][7][8]. Significant amount of scientific papers [9][10][11][12][13][14][15] are devoted to investigation of the thermal imagers MTF, the main components of which are the lens and the radiation detector. At the same time, there is a lack scientific and technical information about the development of methods for determining the MTF of a TIM, which consists of objective lens, microbolometric matrix (MBM), electronic system, display and eyepiece. Therefore, the development of such methods for determining the generalized MTF of thermal imaging monocular is an important task. 1 Problem formulation The purpose of the article is to develop a method for determining the modulation transfer function of a thermal imaging monocular, which includes lens, microbolometer matrix, electronic system, display and an eyepiece that will optimize the characteristics of the monocular to solve a particular observation problem.   One-dimensional spatial MTF of a MBM can be approximated by function [9] ( ) = sinc( ) sinc( ), where is a period of the matrix structure and is a size of sensitive pixel area.
The temporal MTF of the MBM is a spatial low pass filter, which is approximated by the function [7] where is a constant time of the microbolometer.
The MTF of the matrix display is approximated by a function similar to the MBM MTF, i.e.
The eyepiece MTF is approximated by a function similar to lens MTF, i.e. The relationship between the spatial and temporal frequencies is determined as [7] = , Hz, where is angular pixel matrix size and is one pixel generation time.
The relationship between the angular spatial frequencies in the observation space The lens forms an image of Foucault test with linear period ′ and angular spatial frequency The Test object Lens MBM Screen display Eyepiece Operator Fig. 3. The relationship between the angular spatial frequencies in the observation space ′′ and the space of objects Taking into account (10) and (11), we get the is an electronic magnification of TIM.
The angular magnification of the "TIM-operator" system is defined as (Fig. 3) Therefore, (12) can be presented in the form Let put the MTFs of individual TIM components as functions that depend on the angular spatial frequency in the object space (Fig. 3).
The lens MTF is determined by (3), where = . Then The spatial MTF of MBM is defined from (4), which we represent in the form The temporal MTF of MBM is determined from (5) taking into account (8). So, we have The MTF of the display is determined by (6) taking into account (12) ( ) = sinc The MTF of the eyepiece can be expressed by (7) which, similarly to the lens MTF (15) and taking into account (12) will be where is a variable angle of field of view, mrad.