# Long-Range Multispectral Thermal Imager for Simultaneous Measurement of Distance and Temperature
## 2 Proposed Method  
The multispectral thermal imager is an advanced measurement device that combines multispectral imaging with thermal imaging technology, as shown in Figure 1a. It can simultaneously capture thermal radiation intensity images of the target across multiple wavelength ranges, enabling joint analysis of temperature and spectral information. Compared with traditional single-band thermal imagers, the multispectral thermal imager can more accurately measure the true temperature of the target while correcting for variations in the target's spectral emissivity, making it particularly suitable for measurements in complex environments or high-temperature scenarios. The optical system of the multispectral thermal imager consists of a fixed-focus lens and a multi-aperture spectral splitting lens. The design of the multi-aperture spectral splitting structure, simulated using Zemax, is shown in Figure 1b. This structure utilizes multiple optical apertures to separate the light signal into different spectral bands, enabling simultaneous acquisition of spectral information. Its core lies in employing multiple optical paths or detectors to separate and capture spectral data in parallel. The primary advantage of the multi-aperture spectral-splitting structure is its ability to achieve simultaneous multi-wavelength measurements without compromising temporal precision, making it particularly suitable for spectral measurements of high-speed dynamic targets such as flames and rapid combustion. The multi-aperture spectral-splitting system separates the mixed radiation of the target into energy components of different single-spectral bands through multiple sub-apertures, and its imaging principle is illustrated in Figure 1c. In the depth of field range of the multispectral thermal imager, the measured target with a distance of \(z\) and a height of \(H\) from the prime focus lens becomes a real image with a height of \(u\) from the position with a distance of \(H^{\prime}\) from the prime focus lens. For a prime lens, according to the Gauss formula, as seen in the following:  
\[\frac{1}{F}=\frac{1}{u}+\frac{1}{z} \tag{1}\]  
where \(F\) represents the focal length of the prime lens. The distance of the optical center from the main optical axis of the multi-aperture splitter lens is \(d\). The focal length and image length of the multi-aperture spectroscopic lens are represented by \(u_{0}\) and \(v_{0}\), respectively, and the final imaging size in the focal plane is \(h\). The offset between the focal plane image plane and the head aperture center of the multi-aperture spectroscope is denoted as \(\Delta x\)Since the multiple sub-apertures of the multi-aperture splitter lens are on a plane, using similar triangles to judge the relationship between the objects, we can obtain the following:  
\[\frac{\Delta x}{v_{0}}=\frac{d}{u_{0}} \tag{2}\]  
It can be seen from Figure 1 that \(u\) is the focal length of the primary lens, so the sum of \(u\) and \(u_{0}\) represents the first image plane distance plus the first conjugate distance of multiple apertures, which we denote here by the letter \(k\). In the measurement process, the optical system of the remote multispectral thermal imager is fixed, and the distance  
Figure 1: Remote imaging schematic diagram of multispectral thermal imager. (**a**) A physical image of a remote multispectral thermal imager. (**b**) Zemax simulation diagram of multi-aperture spectroscopic structure. (**c**) Multi-aperture spectroscopic structure imaging model. For several feature points between the two images, a system of equations can be constructed:  
\[\mathbf{M}\cdot H=0 \tag{12}\]  
\[\mathbf{M}=[m_{x1},m_{y1},\dots,m_{xN},m_{yN}]^{\mathrm{T}} \tag{13}\]  
where \(\mathbf{M}\) represents the matrix composed of feature points in two images, and \(N\) represents the sum of all feature points in two images. The basic steps of the RANSAC algorithm based on the homography matrix are as follows:  
1.