The Study On Vector Aberration Theory For Off-axis Optical System

Off-axis optical system, namely optical system with tilted component, is onestructural style for designing wide-field reflecting optical system. Vector aberrationtheory is the significant and adaptive method to analyze off-axis optical system. Theprimary coverage in this dissertation is research of vector aberration theory,calculation of vector aberration theory and optical design of off-axis optical systemunder guidance of vector aberration theory. As a direct extension of rotationallysymmetrical wave aberration theory, expression of vector aberration theory can bewritten in a vector approach; aberration field of off-axis optical system appears thecharacteristic of aberration nodal and aberration displacementï¼› Replacement ofrotationally symmetrical axis in centred system, Optical Axis Ray is to describeoff-axis optical system. The first-order properties of decentered and tilted opticalsystems are analyzed in detail, the relation formula between aberration contributioncenter and decenter and tilt of each optical component is derived. Based on first-orderproperties of off-axis optical system, vector aberration theory is given by the ways ofwavefront aberration and Seidel aberration. Two independent sets of aberrations areintroduced by each surface: one induced by the base sphere and the other induced bythe aspheric departure of the surface. These two sets of aberration terms can becombined vectorially to yield the final aberration contribution for the surface. The fivethird-order aberrations in decentered and tilted optical systems are described in detail. The distortion is analyzed based on a collinear transformation between the object andimage spaces.Seidel aberration for third-order vector aberration theory is given. Thus vectoraberration theory can be used to calculate the aberration of off-axis optical system.Equations for third-order coma are derived by a vector approach. Coma-freecondition to remove misalignment induced coma was obtained. The coma-free pointin two-mirror telescopes is found as a conclusion of our coma-free condition, whichis in highly agreement with the result solved by R. N. Wilson using Schiefspieglertheory. By this way the aberration calculation of off-axis optical system isimplemented using vector aberration theory. This is the key originality innovation inthe dissertation.It is pointed out that vector aberration theory is very effective in the aberrationanalyses of off-axis optical system; vector aberration theory can be used to calculateaberration of off-axis optical system; vector aberration theory can give useful designinsights for off-axis optical system. Based on the vector aberration theory conceivedby Shack, we design an tilted-component four-mirror optical system by cancel out its3rd-order coma and balance the astigmatism. Some problems in the design oftilted-component optical system are generalized, and some solutions are supplied forreference.