# Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization
## 1 Introduction  
Gaussian Laser beam has been widely used in the field of lighting [1], detection [2], and satellite communication [3]. However, for the applications of optical therapy, laser projection [4], and lithography [5], etc., it is necessary to homogenize Gaussian beam into a flat-topped beam. Aspheric lens group method [6; 7; 8], free-form lens method [9; 10; 11; 12], diffracted optical elements (DOEs) [13; 14; 15], and microlens array (MLA) [16; 17; 18; 19] are usually used to achieve laser beam homogenization. For the aspheric lens group method, the energy distribution of Gaussian beam is spatially modulated to form a uniform distribution in a specific position. The energy utilization rate and spot uniformity are both high up to 90%, which can be applied to lasers with high power [8]. In 2008, [PERSON] [9] proposed a design method for the beam shaping of double free-form surface lens, which shapes the collimated incident laser beam into the collimated outgoing beam with the required energy distribution. In 2013, [PERSON] proposed that the inhomogeneity of the laser beam can be eliminated by energy mesh dividing, expansion, and superposition [12]. This method has a high freedom of design which can effectively realize the high uniformity of the laser beam. However, the aspheric lens group is composed of two traditional aspheric lenses: concavelens and convex lens. Due to the large appearance size of the overall homogenization structure, the miniaturization, and integration of the optical system cannot be realized. For the free-form lens, the mesh division of lens surface is fine and each mesh surface will be designed separately, which brings high machining accuracy requirements and increase the machining difficulty. Diffractive optical elements (DOEs) with high integration can control the intensity distribution accurately with high diffraction efficiency. When the DOEs are used to homogenize the laser beam, the more the number of steps in the structure, the better the homogenization effect will, while the processing difficulty will increase as well. Meanwhile, the energy utilization rate, that is, diffraction efficiency will depend on the number of steps. For example, when the number of steps is two, four, eight, or sixteen, the energy utilization rate will be 40.5%, 81%, 94.9%, and 98.6%, respectively [20]. In addition, the DOEs operate in a very narrow wavelength band and is sensitive to the change of the wavelength, which limits the applicability of lasers with different wavelengths. The binary DOEs is always designed for a single wavelength. When the other wavelength is used to irradiate the DOEs, the central zero order strong intensity will be produced, which greatly reduces the uniformity of the homogenization spot. The method of MLA has the advantages of high energy utilization rate, small volume and high integration. In addition, it is not sensitive to the intensity distribution of incident light. The incident laser beam is divided into a series of sub-beams, which are superimposed on each other in the far field to eliminate the inhomogeneity between different sub-beams and form a homogenized spot [16; 17]. The MLA is a refractive continuous surface structure with less stray light and it is suitable for beam homogenization of different lasers with a high energy utilization rate. In recent years, a lot of related research work on the method of laser beam homogenization by means of using refractive MLA have been carried out. The imaging MLA (double periodic MLAs) beam integrator system was designed by [PERSON] for fiber injection to obtain uniform speckle pattern at the output end of the fiber [21] and the research results are applied in industry [22]. The higher the Fresnel number of the MLA, the sharper the edge of the homogenized spot will be, which is diffracted by the MLA. The uniformity of the homogenized spot is related to the number of sub-beams, which are divided by the MLA. However, periodic MLA is only suitable for the laser beam with poor coherence.