Study on refraction character of astigmatic optical system with matrix method

In optometry and vision science, simplified models are usually used to analyze and calculate refraction character of astigmatic optical system on the assumption that lenses are thin and close enough to each other. However, in fact those lenses do have stated center thickness and lens space between them. The simplified models are not suitable for accurate analysis and system design. In this paper, first, accurate mathematic model for single astigmatic-power lens is established with matrix method. Next, models are established for complicated astigmatic optical system. Then, comparison between accurate and simplified models is made by calculating the difference on dioptric power due to different position and lens space. Results show that when using astigmatic lens combination to test human vision parallel light should pass lower power lens first and then higher power lens, otherwise big error will be induced. Finally, uncertainty is evaluated and discussed for astigmatic optical system on the base of accurate mathematic models. Conclusion is that uncertain from front and back surface radii is the biggest, secondary is from refractive index and lens space, and uncertain from lens thickness is the least.