Theory of aberration fields for general optical systems with freeform surfaces.

  title={Theory of aberration fields for general optical systems with freeform surfaces.},
  author={Kyle H. Fuerschbach and Jannick P. Rolland and Kevin P. Thompson},
  journal={Optics express},
  volume={22 22},
This paper utilizes the framework of nodal aberration theory to describe the aberration field behavior that emerges in optical systems with freeform optical surfaces, particularly φ-polynomial surfaces, including Zernike polynomial surfaces, that lie anywhere in the optical system. If the freeform surface is located at the stop or pupil, the net aberration contribution of the freeform surface is field constant. As the freeform optical surface is displaced longitudinally away from the stop or… 

Aberration analysis for freeform surface terms overlay on general decentered and tilted optical surfaces.

The research result given in this paper offers an important reference for optical designers and engineers, and it is of great importance in developing analytical methods for general freeform system design, tolerance analysis, and system assembly.

Decomposition of the total wave aberration in generalized optical systems.

The proposed method does not place any constraints on the system geometry or the aperture shape and specifies the resulting wavefront error maps using an expansion into Zernike polynomials on near-circular apertures.

Coma full-field display for freeform imaging systems

With the recent advances in optical fabrication technology, the manufacturing of freeform optical surfaces is no longer prohibitive. To spur the development of freeform systems, however, optical

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions.

By analyzing surface contributions to the total wave aberration characterized by Zernike fringe coefficients, it is possible to find solutions corrected for aberrations of orders higher than the order of coefficients used for freeform sag contribution described with the same Zernikes polynomial set.

Design of space-borne imager with wide field of view based on freeform aberration theory

Freeform surfaces have advantages on balancing asymmetric aberration of the unobscured push-broom imager. However, since the conventional paraxial aberration theory is no longer appropriate for the

Computation of astigmatic and trefoil figure errors and misalignments for two-mirror telescopes using nodal-aberration theory.

This paper quantitatively describes the impact of mount-induced trefoil deformation on the net aberration fields of two-mirror telescopes and proposes a modified theoretical formulation for the field-dependent aberration behavior of freeform surfaces based on the framework of nodal aberration theory.

Ray-based optical design tool for freeform optics: coma full-field display.

This research utilizes nodal aberration theory to develop a ray-based method to generate a coma full-field display that circumvents wavefront fitting errors that can affect Zernike polynomial-based full- field displays for highly aberrated freeform starting designs.

Design of a compact freeform optical system via the surface contribution analysis method

The surface contribution analysis method is to find the wave front map at the local intermediate entrance and exit pupil reference spheres for each optical surface by fitting the wavefront errors with Fringe Zernike polynomials to help optical designers find the origins of the main aberrations at the final focal plane.

Analysis of nodal aberration properties in off-axis freeform system design.

Based on the framework of nodal aberration theory (NAT) applied to the coaxial system, the third-order astigmatism and coma wave aberration expressions of an off-axis system with Zernike polynomial surfaces are derived and the relationship between the off- axis and surface shape acting on the nodal distributions is revealed.

Zernike surface contributions as an assisting tool for designing freeform optical systems

A new numerical method is used to study surface-by-surface contributions to the total wave aberration of freeform optical systems and incorporates the field dependency into the wave aberrations and the error of the chief ray is studied separately.



Extending nodal aberration theory to include mount-induced aberrations with application to freeform surfaces.

This paper introduces the path forward for the integration of freeform optical surfaces, particularly those related to φ-polynomial surfaces, including Zernike polynomial surfaces, with nodal aberration theory, and demonstrates a newly identified field dependent contribution to astigmatism.

Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry.

A method for locating the aberration field centers using real-ray-trace data that is entirely model independent and, significantly, that is not restricted to small tilts and decenters, is presented.

Nodal aberration theory applied to freeform surfaces

When new three-dimensional packages are developed for imaging optical systems, the rotational symmetry of the optical system is often broken, changing its imaging behavior and making the optical

Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry.

  • K. Thompson
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2005
It is revealed that in fact there are no new aberrations in imaging optical systems with near-circular aperture stops but otherwise without symmetry, and that the field dependence of an aberration often changes when symmetry is abandoned.

A new family of optical systems employing φ-polynomial surfaces.

A new family of truly nonsymmetric optical systems that exploit a new fabrication degree of freedom enabled by the introduction of slow-servos to diamond machining are presented; surfaces whose departure from a sphere varies both radially and azimuthally in the aperture.

An analytic expression for the field dependence of Zernike polynomials in rotationally symmetric optical systems

Zernike polynomials have emerged as the preferred method of characterizing as-fabricated optical surfaces with circular apertures. Over time, they have come to be used as a sparsely sampled in field

Third-order aberration fields of pupil decentered optical systems.

Nodal aberration characteristics are revealed only by means of the pupil decentration vector and the aberration coefficients of the axially symmetric system, which shows great convenience since parameters of individual surface such as radius of curvature, decenter as well as the shifted center of the Aberration field are not used in the analysis.

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

It is shown that both astigmatic figure error and secondary mirror misalignments lead to binodal astigmatism, but that each type has unique, characteristic locations for the astigmatic nodes.

Basic Wavefront Aberration Theory for Optical Metrology

VIII. IX. X. XI. XII. Sign Conventions Aberration-Free Image Spherical Wavefront, Defocus, and Lateral Shift Angular, Transverse, and Longitudinal Aberration Seidel Aberrations A. Spherical

Calculation of third-order misalignment aberrations with the optical plate diagram

  • A. Rakich
  • Physics
    International Optical Design Conference
  • 2010
The Optical Plate Diagram of C. R. Burch has been generalized to allow the calculation of third-order perturbation aberrations for nominally axially symmetrical optical systems. The plate method has