A method using a freeform surface lens for LED secondary optic design is proposed in this paper. By Snell's Law, the differential equations are given to build the relationship between the normal direction of a freeform surface and its input/output ray vectors. Runge-Kutta formulas are used to calculate the differential equations to design the freeform surface. Moreover, the optical model for uniform illumination is simulated and optical performance is analyzed. A practical freeform surface lens for LED uniform illumination is fabricated using an injection molding method. By the process, our system demonstrates a uniform illumination with a divergence half-angle of 6 degrees and an efficiency of 78.6%.

Using light field reconstruction technique, we can display a floating 3D scene in the air, which is 360-degree surrounding viewable with correct occlusion effect. A high-frame-rate color projector and flat light field scanning screen are used in the system to create the light field of real 3D scene in the air above the spinning screen. The principle and display performance of this approach are investigated in this paper. The image synthesis method for all the surrounding viewpoints is analyzed, and the 3D spatial resolution and angular resolution of the common display zone are employed to evaluate display performance. The prototype is achieved and the real 3D color animation image has been presented vividly. The experimental results verified the representability of this method.

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The Monge-Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L(2)-Kantorovich (LMK) theory. An efficient approach is proposed to find the optimal mapping of the LMK problem. The characteristics of the new approach are introduced and the limitations of the LMK theory in illumination design are presented. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design.

We propose a method of designing a freeform lens array for off-axis illumination (OAI) in optical lithography to produce desired OAI patterns and improve efficiency. Based on the Snell law and the conservation law of energy, a set of first-order partial differential equations are derived and the coordinate relations for each OAI pattern are established. The contours of the freeform lens unit are calculated numerically by solving the partial differential equations, and the freeform lens array is obtained by arraying the lens units. Moreover, the optical performance for each OAI pattern is simulated and analyzed by software. Simulation results show that the irradiance distribution of each OAI pattern can be well controlled with a maximum uniformity of 92.45% and a maximum efficiency of 99.35%. Also, analysis indicates that this method has the advantages of reducing the complexity of the exposure system and having good tolerance to the input intensity variations of the laser beam.