Research On The Freeform Surface Design Methods Based On Collimated Beam Shaping

With the development of society and technology, energy consumption increased and people’s increasing lighting requirements, traditional optical elements such as spherical and aspherical surfaces cannot meet the needs any more. It’s hoped that optical elements could achieve more complex illuminations and become more compact and energy saving. Thus freeform surface illumination emerged and developed rapidly. Freeform surfaces have high degrees of freedom and flexible spatial layout. With optical freeform surfaces in an illumination system, the structure of the system could be significantly simplified, the incident beams could be well controlled and some special illuminations could be easily produced. Therefore, freeform surfaces have become a hot spot in the field of optical design in recent years.The beam is defined by the intensity distribution and phase profile and beam shaping is the process of redistributing the intensity or phase of a beam of optical radiation, or redistributing both at the same time. One single freeform surface could only control one of them, while double freeform surfaces could meet the requirements of controlling both the intensity distribution and phase profile simultaneously because of the higher degrees of design freedom. Parallel light illumination is one of the most typical ideal illumination modes. In practical applications, when the effect of the spread angle of the light source to the actual illumination is negligible, it can be considered as parallel light illumination. In this paper, the single freeform surface design method and double freeform surfaces design method are both proposed for solving the illumination problem of parallel light, and detailed analyses are made for the collimated beam with a spread angle.At first, this paper focuses on reshaping the intensity distribution of the collimated beam. The single freeform surface design method in the cylindrical coordinate system based on the elliptic Monge-Ampere (MA) equation is proposed based on Snell’s law and the conservation law of energy, A corresponding mathematical model is established and a numerical method is given for solving this kind of mathematical model. The feasibility of this method is verified by theoretical simulation. Then, a universal single freeform surface design method in the Cartesian coordinate system is proposed to solve the vertex constraint problem in the cylindrical coordinate system. The method is applied to off-axis illumination (OAI) in optical lithography. The L2 Monge-Kantorovich (LMK) theory is used to find an initial design for the iterative scheme of the MA method and four OAI patterns, including two quasar modes and two dipole modes, are achieved by the method. As an important feature of a practical technique, the achieved freeform surface OAI designs have large tolerance to the spread angle of the collimated beam. And more importantly, smooth freeform surfaces which are easier to fabricate are obtained by the integrated MA method.In order to simultaneously control the intensity distribution and phase profile of the beam, a double freeform surfaces design method in the cylindrical coordinate system based on the MA equation is proposed based on the shortcomings of the existing beam shaping methods and freeform surface design methods. A generalized approach is presented to find the numerical solution of the mathematical model. By solving the model, two smooth freeform surfaces are obtained and the incident beam is refracted to produce the prescribed intensity distribution and phase profile. A specific application of laser beam shaping is given to verify the design method. To solve the vertex constraint problem, a mathematical model for double freeform surfaces in the Cartesian coordinate system is proposed to develop the double freeform surfaces design method. And the method has large tolerance to the spread angle of the collimated beam.At last, a double freeform surfaces lens is designed for laser beam shaping with the double freeform surfaces design method. A laser beam shaping system is set up and a series of theoretical simulation analyses are made. The feasibility of this method is verified by manufacturing and experimental test. While the problems exposed in the experimental results show that extremely high machining precision of freeform surface is required in this method. To make this method more universal and practical, double freeform surface design method need to be further improved combined with the actual machining precision.