## 1 Introduction  
The use of light for biomedical imaging dates back to pioneering studies by researchers such as [PERSON] (1843), [PERSON] (1831), and [PERSON] (1929)[1, 2, 3, 4]. Subsequent advances in science and technology have led to the development of various light sources (LASER and LED) and image acquisition sensors, driving the widespread adoption of light in medical and life sciences. Existing imaging modalities have limitations due to ionizing radiation, contrast agents, metal restriction, sophisticated systems, and high costs. Therefore, alternative optical-based imaging techniques with simple, radiation-free, and affordable designs are crucial. Transillumination imaging requires a simple system consisting of light sources, a camera as a detector, and a computer for controlling and processing images. The use of transillumination (diaphanography) to monitor the pathology of human organs has become of interest in recent years, as there have been many new advances related to light source technology, sensor variables, and theoretical, experimental, and clinical results [3; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. However, this method faces great challenges, with a strong scattering of light in biological tissues and time-consuming image processing [24]. Figure 1 shows the transillumination mode and the epi-transillumination mode of the transillumination imaging. Transillumination mode is commonly known by placing the light source on the opposite side of the recording device (typically a camera). The epi-illumination mode can also be considered as a mode of transillumination imaging, utilizing the light source and the recording device positioned on the same side of the object with appropriate lighting conditions. When the lighting conditions are appropriately adjusted to allow the light to diffuse well in the turbid medium, it becomes possible to acquire the distribution of the absorption structure on the surface of the body. The transillumination image is the blurred shadows of the absorbing structures in a turbid medium, such as the collection of point absorbers. As the depth of the absorbing structure increases, the resulting image exhibits progressively more pronounced blurring. Additionally, acquiring light signals when light penetrates thick body parts is challenging. This challenge may also be reflected in breast light or blood vessel finder applications currently on the market [22; 23]. Consequently, de-blurring scattering on observed images has remained a difficulty until recently. To realize transillumination imaging, many studies have been conducted to reduce scattering [24; 25; 26; 27; 28; 29]. [PERSON] et al. have derived a depth-dependent point spread function (PSF) to characterize the scattering of a point light source in biological tissue [24]. The depth-dependent PSF is presented as Equation (1) [24]:  
\[\mathrm{PSF}(\rho)=C\Bigg{(}\mu_{s}^{\prime}+\mu_{a}+\Bigg{[}\kappa_{d}+\frac{ 1}{\sqrt{\rho^{2}+d^{2}}}\Bigg{]}\frac{d}{\sqrt{\rho^{2}+d^{2}}}\Bigg{)}\left( \frac{\exp[-\kappa_{d}\sqrt{\rho^{2}+d^{2}}]}{\sqrt{\rho^{2}+d^{2}}}\right) \tag{1}\]  
where \(k_{d}^{2}=3\mu_{a}(\mu_{s}^{\prime}+\mu_{a})\) and \(C\), \(\mu_{s}^{\prime}\), \(\mu_{a}\), and \(d\) represent the constants concerning \(\rho\) and \(d\), the reduced scattering coefficient, the absorption coefficient, and the depth of the structure, respectively. On the surface, it is possible to divide the light into two components, the composition of direct light that is affected by scattering, the absorption of the scattered environment, and the composition of diffused light. Back-scatter or back-reflection imaging uses a light source and a recording device placed on the same side of the object. By adjusting according to the passing conditions, we can obtain the distribution of absorption structure at the body's  
Figure 1: The transillumination mode and epi-transillumination mode of the transillumination imaging.