## 1. Characterization parameters of basic optical properties of light diffusion films

In order to accurately describe the diffusion effect of the light diffusion film, firstly, the photometric index of the light diffusion film is defined, and then the basic optical properties of the surface light diffusion film are accurately quantified.

(1) transmittance and haze: transmittance represents the ratio of the luminous flux through the sample to the luminous flux incident on the sample, that is, the total transmittance, expressed as τ t. τ 1 represents the light intensity of the incident light, and τ 2 represents the total light intensity transmitted through the sample, then:

Haze represents the ratio of the scattered light flux to the transmitted light flux that deviates from the direction of incident light through the sample, which reflects the scattering effect of light passing through the sample. Expressed by H (in this experiment, only scattered light fluxes more than 2.5 degrees away from the direction of incident light are used to calculate haze)

(2) luminous flux: the part of radiant flux that can stimulate the human eye is called luminous flux, expressed by the character φ, the unit is lumen (lm), the definition formula:

**2theoretical basis of light scattering.**

### 2.1 Light scattering mechanism and classification.

Light scattering refers to the phenomenon that light diffuses in all directions after passing through a non-uniform material and deviating from its incident direction. For single particle scattering, the particles can be divided into many small electric dipoles. When light passes through, each dipole will be excited and vibrate because of the external electromagnetic field. The vibration frequency of the dipole is the same as that of the external excitation field, so the secondary radiation is scattered in all directions. At an infinitely distant point P, the superposition of each dipole scattered wave forms the scattered field of that point.

Rayleigh scattering and Michaelis scattering theory (Mie scattering theory) are the most commonly used scientific theories to study the phenomenon of light scattering. According to the size of scattered particles, light scattering can be divided into two kinds: one is that the size of scattered particles is equal to or larger than the wavelength λ of the incident light, which is called Mie scattering. Mie scattering theory is a classical algorithm for solving the analytical solution of the interaction between spherical scatterers and electromagnetic fields, and the other is that the size of scattered particles is less than 1 × 5-1 × 10, which is called Rayleigh scattering.

### 2.2 Mie scattering theory.

The size of the diffusion particles involved in this paper is less than 5 μ m, which belongs to the scope of application of Mie scattering theory.

The regular scattering sphere is shown in figure 2-1. According to the Mie scattering theory, the linearly polarized light with wavelength λ and intensity I 0 propagates positively along the z axis, and the direction of electric field vibration is parallel to the x axis. The spherical center of the diffused particle is the coordinate origin O, the diameter is d, and the refractive index relative to the surrounding medium is m.

Then the scattered light intensity of a certain point P in the scattered light field is

In the formula, r is the distance between point P and the center of the sphere, θ is the scattering angle, and 1 and 2 are the intensity functions of polarized scattered light in the orthogonal direction, which can be expressed as follows:

According to Mie scattering theory, the expressions of scattering amplitude functions are as follows:

Where a_{n} and b_{n} are Mie scattering coefficients, and the expressions are as follows:

Where z means an or ma. Jn+1/2 (z); H (2) naught 1 beat 2 denotes Bessel function of semi-integral order and Hank function of the second kind respectively. The other represents the scattering function, and the expression is as follows:

Where Pn and P (1) n denote Legendre function and first order Legendre function respectively.

According to the Mie scattering theory, the scattered light intensity of P at a certain point in the scattered light field is related to the diameter and relative refractive index of the particles. The relative refractive index and diameter of diffused particles will affect the scattering characteristics, which can be predicted by Mie scattering theory. According to the introduction of light diffuser in the first chapter, organic light diffuser is mainly used in the market at present, including PMMA, silicone, PS and so on. The refractive indices of the three materials are 1.49, 1.43 and 1.55, respectively. In this experiment, the matrix resin is UV curable resin, and its refractive index is 1.49. The relative refractive index m of the three kinds of optical diffuser is 1, 0.96 and 1.04 respectively. In order to achieve the best properties of the diffusion film, we choose silicone and PS microspheres as light diffuser. The effects of particle size, doping concentration and diffusion film thickness on the diffusion film are verified by software simulation and experiments. For details, please see the next decomposition.