# Study on the Light Field Regulation of UVC-LED Disinfection for Cold Chain Transportation
## 3 Research Methodology
### Design of the Proposed Optical System  
Figure 2 presents the schematic diagram of the proposed system, in which a UVC-LED chip with a wavelength of 275 nm was used as the light source. Three collimating lenses (lens 1-3 in the Table 1) were used to realize the collimation of LED light, then a pair of microlens arrays (lens 4) and a focusing lens (lens 5) were used to regulate the uniformity of the light beam, thereby ensuring that the UVC light can realize the disinfection effect of the ice layer in cold chain transportation. The parameters of lenses are listed in Table 1. The proposed system provides an effective solution to stop the spread of global viral epidemics via disinfection during cold chain transportation. The luminance of LEDs is defined as the amount of luminous flux emitted by the unit area of the light source surface in the unit solid angle of the normal direction, which is expressed as:  
\[L=\frac{d\phi}{dS\cos\theta d\Omega} \tag{1}\]  
The luminous intensity of the light source is expressed as the luminous flux emitted within a unit solid angle, namely:  
\[I=\frac{d\phi}{d\Omega} \tag{2}\]  
Therefore, the light distribution curve for a Lambert type LED light source can be expressed as follows [26]:  
\[I(\theta)=I_{0}\cos^{m}\theta \tag{3}\]  
where, \(\theta\) is the included angle between the luminous direction of the light source and the plane normal, and \(I_{0}\) is the intensity value of the normal direction. The value of \(m\) is generally provided by the LED manufacturer, and the ideal \(m\) value of an LED light source is 1. Figure 1: **(a)** Ice with a convex spherical surface; **(b)** ice with a concave spherical surface; **(c)** ice with a conical surface. Figure 2: The schematic diagram of the proposed uniform UVC-LED disinfection system by microlens arrays. Light field regulation is a method to control light field by using optical devices such as microlens arrays and a cylindrical mirror. It is widely used in lighting systems in recent years. LEDs are optically designed twice before they become lighting products to realize light field regulation [27,28]. According to the LED light distribution curve, when the light source is directly used for illumination, uneven light spots will be formed on the receiving surface. The light distribution curve of a Lambert-type LED is a cosine distribution, so the effect of strong lighting in the middle and low lighting at the edge will occur, and the LED will have a large divergence angle. In current disinfection systems, a multi-chip or multi-device combination is carried out to achieve the uniformity of the lighting surface. However, the light field formed in this way is unable to meet the requirements of the uniformity of illumination in the entire illuminated area. Therefore, in the proposed system, the uniformity of the LED collimated beam is accomplished by using microlens arrays in conjunction with a focusing lens. The essence of light uniformity is to transform the uneven lighting surface in the spatial domain into a uniform lighting surface. After homogenizing the illumination surface of a Lambert beam, the light intensity of the central area can be reduced and that of the edge area can be increased to improve energy utilization. To achieve this, the following principles must be met [29]:  
Consider the radius of the LED circular spot after collimation as \(b\), and the spot is divided into \(M\) uniform parts along the radial direction of the light. Then, the total power contained in the \(N\)-th uniform area is:  
\[P(N)=\int\limits_{0}^{\frac{N}{M}b}I_{0}\cos^{m}\theta\cdot 2\pi rdr \tag{4}\]  
The power of the \(N\)-th annular region is:  
\[\left\{ \begin{array}{l}P_{N}=P(N,z)-P(N-1,z)=\frac{\pi c}{2}\bigg{\{}\exp \biggl{[}-2\frac{2u(N-1)^{2}}{M^{2}}\biggr{]}-\exp\biggl{(}-2\frac{uN^{2}}{M^{ 2}}\biggr{)}\bigg{\}}\\ u=b^{2}/w^{2}\end{array} \right. \tag{5}\]  
Assuming that the illuminated area is a rectangular area and the length-width ratio of the rectangular area is \(\beta\), the following can be obtained:  
\[\left\{