Studies On The Design Of Off-axis Display Systems With Anastigmatic Free-form Surface

The off-axis reflective system is widely used in the fields of head-mounted display,visual display and ultra-thin projection because of its advantages of flexible structure,no obscuration,folding optical path,etc..Optical systems is becoming lightweight,integrated and novel,and the traditional optical components can not meet the requirement of optical systems.Free-form surface has been more and more widely used in off-axis system for that it has large degree of freedom,and it can control the direction of the ray at each position according to the requirements.Thus,the design and application of free-form surfaces has being hotspot issues in the field of optical design.After studying the current design method of free-form surface,a direct design method of free-form surface based on the principle of anastigmatism is present in this paper.The design anastigmatic surface can be sued for astigmatism correction at each field of view for an imaging optical systems effectively,and it can also make the systems become more lightweight.Which can meet the requirements of large field of view,miniaturization,lightweight for off-axis display systems.The design surface can be directly applied to the design of off-axis display systems,and also can be used as an initial surface for further optimization.The main work of this paper are shown as follows:(1)The description and design methods of optical free-form surfaces are studied.The description methods of free-form surfaces can be divided into two type: one is described with parametric polynomial,the other is described with normal polynomial.The advantages and disadvantages of each description method are discussed.The design methods of free-form surfaces can be divided into two type: iterative optimization method and direct mapping method.The design principles of each methods are studied.The Manufacturing and testing methods of free-form surface is also discussed in this paper.Based on the studies of the free-form surface,an dual-channel off-axis helmet mounted display(HMD)is designed with a Zernike polynomial free-form surface.The field of view of the system is 40°× 30°,and the exit pupil diameter is 8mm,and the eye relief is above 30 mm.The system is compact and has good image quality.It show that the system designed with Zernike polynomial free-from surface has good performance.(2)With the studies of the principle of anastigmatism,a design method of free-from surface based on the ordinary differential equation is proposed,to correct residual astigmatism or realize anastigmatism by itself.A more directly design method of the anastigmatic surface is proposed for its simplicity with the discrete approximation.During the design of the anastigmatic reflector,the mapping between object surface and image surface is unconstrained,and the shape of the image source surface is also a part of the design result.With the solution,a single-reflector HMD system with 40°×30 ° field of view is designed.The MTF at Nyquist frequency of each filed is above 0.15 to meet the quality requirements of HMD systems.The model is built with the residual astigmatism introducedby a glass substrate,and an reflector that can correct the residual astigmatism introduced by the glass substrate is designed.(3)Based on the curvature equation and the Codington equations,the design method of the anastigmatic surface is extended to three-dimension.A design method of an anastigmatic free-form surface based on partial differential equation is developed in the case of with residual astigmatism of not,and the numerical solution of the partial differential equations is calculated by with the initial data on the meridian surface.With the designed anastigmatic surface,a single-reflector off-axis HMD system with the field of 40°×30° is designed.The astigmatism of the system is well corrected,and the MTF at Nyquist frequency above 0.15.The results designed with a rotationally symmetric and a non-rotationally symmetric anastigmatic surface are compared with each other,and the image quality of them has no significant difference.However,in the result designed with the non-rotationally symmetric surface,the image source plane is more flat than the result designed with rotationally symmetric surface.Thus,if the plane image source is used,the system will achieve a larger field of view when it is designed with a non-rotational symmetric anastigmatic surface.(4)The applications of rotationally symmetric and a non-rotationally symmetric anastigmatic surface is analyzed.A dual-channel off-axis HMD with the field of view of40°×30° is designed with a non-rotationally symmetric anastigmatic combiner and a curved flexibe OLED,which has only two components,and it provides a lightweight solution for the HMD system.The total length is 54 mm,and the exit pupil diameter is 5mm,and the eye relief is 23.6 mm.The all MTF of each filed at 25lp/mm is above 0.2.A virtual reality system with field of view of 40°×30° is designed with a rotationally symmetric anastigmatic surface,which can realize monocular stereo vision.A optical model is built,in which the points in the virtual image with visual distance ranging from several meters to infinity conjugate with the points on the image source surface at each field.The program written in the macro-language is used to get the coordinates of the points.The designed offers dynamic accommodation and convergence cues for observers,so that they can feel more real when they use the system.