Advances in optical design and optimization of miniature zoom optics with liquid lens element

1. Advances in optical design and optimization of miniature zoom optics with liquid lens element 1Cheng-Mu Tsai and 2Yi-Chin Fang 1Dept. of Computer and Communication, Kun Shan University, No.949, Da Wan Rd., Yung-Kang Dist., Tainan City 710, Taiwan. E-mail: jmutsai@gmail.com 2Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology, No. 2, Jhuoyue Rd., Nanzih Dist., Kaohsiung City 811, Taiwan, R.O.C. E-mail: yfang@ccms.nkfust.edu.tw Reporter: Yi-Chin Fang

2. Introduction Discussion of the primary field curvature aberration The optical design of a preliminary telecentric projector lens Suppression of the Petzval field curvature aberration based on a genetic algorithm Simulation result and discussion Conclusions Outline

3. What Issues in Optical System Design There are five primary monochromatic aberrations in optical system Spherical Coma Astigmatism Field Curvature Distortion Two kinds of primary chromatic aberration in optical system Lateral Chromatic Aberration Axial Chromatic Aberration

4. Advance Technology • The task of optimization in optical systems is now undertaken efficiently, partly because • advances in computing • aspherical surfaces • antireflection coatings • new developments in optical glass • From the point of view of optics optimization, ray tracing based on geometrical optics is still more efficient than time-consuming wave aberration calculation based on physical optics;

5. where hp is the radius of the exit pupil, and hmax is the maximum height of the Gaussian image. The five terms on the right-hand side of Equation are called Seidel aberrations. In order of presentation, they are the spherical aberration, coma, astigmatism, field curvature and distortion. Seidel aberrations

6. Seidel Sum (1) • The correlation coefficients SI ~ SV are known as the Seidel Sum, which can be derived from paraxial optics theory as follows:

7. The ray tracing for each parameter

8. Discussion of Petzval aberration • Observing the transverse aberration, it is easy to see that the other Seidel Sum of the primary FCA, SIV, depends on the refractive index and the curvature of the lens system. • The transverse aberration can be derived from where R is the radius of the reference sphere which passes through the center of the exit pupil.

9. Petzval curvature aberrations

10. Derivation of Petzval field curvature aberrations (1) • Assuming that the ratio of the variation of ray tracing from exit pupil to the transverse aberration of the Gaussian image plane is a constant, the distance between the real image and the Gaussian image plane z is

11. Derivation of Petzval field curvature aberrations (2) • According to the spherical wavefront approximation equation, is as follows: • Here CPetzval is the curvature of the Petzval field plane and is equal to nSIV/H2. • Since the Lagrange invariant H is a constant, H = nuh = n'u'h', it will not change as a ray tracing in a different plane. • The Petzval FCA is induced by the refractive index and curvature of the lens system only.

12. Preliminary design of a projector lens

13. Parameters for the preliminary design Basic parameters Zoom parameters

14. Genetic Algorithm (GA) Concept • The concept of the Genetic Algorithm(GA) process is to evolve multiple groups of genes (e.g., factors) into adapting to an environment (that is, a specification) • Advantage • Search the global optimum • The designer just needs less experience when applying in optical system design • Easy to assemble in optical system

15. Genetic Algorithm (GA) Operation The function of the GA process are Initial population Selection Crossover Mutation

16. The gene parameters of the radius of curvature of lenses. Simulation Results (1)

17. The gene parameters of the thickness of a lens. Simulation Results (2)

18. Conclusions We proposed using the GA along with LSD simulations to extensively optimize lens parameters and then further eliminate the Petzval FCA. Through this proposed optimization method, the crossover and mutation operations of the GA, the Petzval FCA has been comprehensively eliminated – up to 88.4%, according to our simulation results.

19. Thanks for your attentions Q & A