Techniques and tools for obtaining symmetrical performance from tilted-component systems

Abstract

Tilted-component systems are known to be characterized by aberrations with unusual field dependences, such as decentered coma and binodal astigmatism. In this paper, the origin of binodal astigmatism in a multielement system from the contributions of individual surfaces is explained in an intuitive manner, as a logical extension of the ordinary aberrations known to all optical designers. The insight provided by this graphical model allows an understanding of why the astigmatism of any given system behaves the way it does, and what needs to be done to convert it to ordinary quadratic behavior, so that what remains can be corrected by a final, rotationally symmetric subsystem. Conditions under which ordinary behavior may be obtained from a system of tilted elements are explored. It is shown that a certain type of symmetry of the primary aberrations may be obtained (regardless of the tilt angles) if the initial, untilted system is monocentric. Graphical displays of the aberration types are used to explore the behavior of the system across the field, and direct optimization of the Zernike coefficients is used to guide the performance of the system.

Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT)

“…Nodal aberration theory for optical imaging systems without symmetry (but with rotationally symmetric components) has emerged as an effective approach to describe the aberrations in misaligned or intentionally decentered/tilted optical systems [1][2][3]. We have recently demonstrated that the theory is well suited for the development of deterministic alignment strategies for astronomical telescopes [4].…”

Meshfree approximation methods for free-form surface representation in optical design with applications to head-worn displays

“…Figoski applied nodal aberration theory to find an alternate solution to a two mirror telescope problem 29 . Rogers illustrated an application of nodal aberration theory to guide the design of a head-worn display 30 .…”

Alignment off-axis optical system using Nodal Aberration Theory

“…Each aberration type develops a characteristic field behavior in a system without symmetry. The astigmatic aberration field system without symmetry (misaligned) has, in general case, contain two zeros, or nodes, neither of which is necessarily located on the center of the image field [2,7] . The coma aberration, which depends linearly on field of view, the aberration field is completely unchanged except that it can move decentered from the center of the image field, if a system that corrected for third-order coma, the introduction of asymmetry will result in an optical system in which the third-order coma is constant in both magnitude and direction over the field of view.…”

“…However, The Nodal Aberration Theory (NAT) for optical system without symmetry (with rotationally symmetric components) has emerged as an effective approach to describe the aberrations in misaligned or intentionally decentered/tilted optical systems [1][2][3][4][5][6] . It has provided a complete mathematical representation of the aberrations of misaligned reflective optical systems in the context of the traditional third-order aberrations of Seidel [1] .…”