Studies On The Q-type Characterization Function Of Free-form Surface And Its Application In Imaging Optical Systems

With the increasing demands for the use of various photoelectric products,the traditional optical systems,which are composed of spheres or power series aspheres,have been unable to meet the requirements of high performance,small size and low cost.At the same time,due to the rapid development of ultra precision optical fabricating technology and testing technology,high-precision fabricationand test of free-form surfacebecome possible,because of its higher degrees of freedom and flexible spatial layout,it can simplify the structure of system to the greatest extent,and significantly improve the optical system performance.It gradually becomes a new generation of optical components.This paper analyzes the main description and design methods of optical free-form surface,and the mathematical models of free-form surface that is represented by Q-type function polynomial are studied emphatically.And the free-form surface is applied to the specific imaging optical systems.The main study work is as follows:(1)By using the theoretical analyzing method,the mathematical construction characteristics of three expression forms of Q-type function polynomial are studied(including the Q-con polynomial,Q-bfs polynomial and Qbfs extendedpolynomial).And the features advantages of Q-type function polynomial in characterizing optical free-form surface are also studied.(2)The application of electronic endoscope objective optical system designwith free-form surface,which is represented by Q-con type function polynomial.The designed system's field of view(FOV)is 110°,focal length is 1mm,F number is 3.3,and the total length is 7.89 mm,in the full FOV,the modulation transfer function(MTF)values are greater than 0.37 at the Nyquist spatial frequency of 156lp/mm that is approaching to the diffraction limit.And they meet the requirements of electronic endoscope for large field of view,high imaging quality and miniaturization.Compared with the traditional power series aspheres design,the Q-con type free-form surface is easier to fabricate and it can effectively reduce the assembly difficulty of the system.(3)The application of panoramic fish-eye lens optical systemdesign with free-form surface,which is represented by Q-bfs type function polynomial.The designed fish-eye lens' s FOV is 180°,focal length is 14 mm,F number is 3.5 and it is used for monitoring.The design results meet all the requirements.And under the same computing platform and structural parameters,a fish-eye lens is designed with power series aspheres.Analysis and comparison of the two designs,the Q-bfs type free-form surface has higher system aberration correction ability,and it can effectively improve the system optimization design efficiency.And the designed Q-bfs free-form surfaces have smaller fabricating difficulty,it is advantageous to improve the fabricating efficiency and lens yield of optical element.The two kinds of designed surfaces are fabricated and tested,the results are consistent with the theoretical analysis.