Control of Linear Astigmatism Aberration in a Perturbed Axially Symmetric Optical System and Tolerancing

Abstract

Linear astigmatism aberration is undesirable because it rapidly degrades image quality. We discuss some techniques to control and mitigate this aberration, and provide a comparison of lens systems that have been desensitized for linear astigmatism aberration.

Surround-View Fisheye Optics in Computer Vision and Simulation: Survey and Challenges

“…Due to the mass production and time constraints of producing camera systems, this optical aberration cannot be eliminated. To compensate for astigmatism, optical systems could sometimes end up being rebuilt several times, but this is industrially undesirable [56], [57]. To correct linear astigmatism, a manufactured lens can be rolled on its mechanical seat so that one surface becomes tilted by an angle of α measured in arc minutes which can be estimated by (3) [56]: where d is the lateral displacement of the lens due to rolling and R is the radius of curvature of the surface on the seat.…”

“…To compensate for astigmatism, optical systems could sometimes end up being rebuilt several times, but this is industrially undesirable [56], [57]. To correct linear astigmatism, a manufactured lens can be rolled on its mechanical seat so that one surface becomes tilted by an angle of α measured in arc minutes which can be estimated by (3) [56]: where d is the lateral displacement of the lens due to rolling and R is the radius of curvature of the surface on the seat. Finally, a thin optical wedge is added to the optical system just before the light reaches the image plane as described by [56], [58]:…”

“…where n is the index of refraction of the wedge, u is the slope of the first order marginal ray before entering the wedge, ū is the slope of the first order chief ray before entering the wedge in image space respectively, and y is the marginal ray height at the wedge [56]. Figure 7 demonstrates these parameters on a sample optical wedge-shaped as a rectangular prism.…”

Split achromatic doublet problem and lens element centering in a drop-in barrel

“…When the surfaces are tilted, the aberrations that can result are line-of-sight change, uniform astigmatism, uniform coma, linear astigmatism, field tilt, and smile and keystone distortion. 7,8 Because of the small perturbation uniform astigmatism is usually negligible; however, uniform coma and linear astigmatism usually contribute to limit the image sharpness. If the lens system is optically fast, spherical aberration and uniform coma may be significant; if the field of view is large, then linear astigmatism can also be significant.…”

“…When in a symmetric lens system, the radii and surfaces spacing are perturbed from their nominal values, the main result is a change in focus, magnification, and in the fourth order aberrations 7 of spherical W040, coma W131, astigmatism W222, field curvature W220, and distortion W311. When the surfaces are tilted, the aberrations that can result are line-of-sight change, uniform astigmatism, uniform coma, linear astigmatism, field tilt, and smile and keystone distortion 7 , 8 . Because of the small perturbation uniform astigmatism is usually negligible; however, uniform coma and linear astigmatism usually contribute to limit the image sharpness.…”