1. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology Improvements of Petzval Field Curvature of HDTV Projector Lens Optics 1 Cheng-Mu Tsai and 2 Yi-Chin Fang 1 Dept. of Computer and Communication, Kun Shan University, No.949, Da Wan Rd., Yung-Kang Dist., Tainan City 710, Taiwan. E-mail: jmutsai@gmail.comjmutsai@gmail.com 2 Institute 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.twyfang@ccms.nkfust.edu.tw Reporter: Yi-Chin Fang

2. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 2 Outline  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

3. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 5 where h p is the radius of the exit pupil, and h max 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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 6 Seidel Sum (1)  The correlation coefficients S I ~ S V are known as the Seidel Sum, which can be derived from paraxial optics theory as follows:

7. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 7 The ray tracing for each parameter

8. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 8 Discussion of Petzval aberration  Observing the transverse aberration, it is easy to see that the other Seidel Sum of the primary FCA, S IV, 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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 9 Petzval curvature aberrations

10. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 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  is

11. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 11 Derivation of Petzval field curvature aberrations (2)  According to the spherical wavefront approximation equation, is as follows:  Here C Petzval is the curvature of the Petzval field plane and is equal to nS IV /H 2.  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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 12 Preliminary design of a projector lens

13. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 13 Parameters for the preliminary design Basic parameters Zoom parameters

14. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 15 Genetic Algorithm (GA) Operation  The function of the GA process are Initial population Selection Crossover Mutation

16. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 16  The gene parameters of the radius of curvature of lenses. Simulation Results (1)

17. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 17  The gene parameters of the thickness of a lens. Simulation Results (2)

18. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology 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. Yi-Chin Fang, Institute of Electro-Optical Engineering, National Kaohsiung First Univ. of Science and Technology Thanks for your attentions Q & A