Abstract

New unique and concise translation matrices are derived for evaluating the aberration variations of conceptual and real lenses when the paraxial marginal and chief ray paths are arbitrarily changed. They are helpful in investigating the general behaviors of lenses and optimizing the balanced aberrations of lens components in prime and zoom lenses. These new matrices, with a dimension of 9×9 for monochromatic aberrations and a dimension of 4×4 for chromatic aberrations, are derived based on our earlier algorithms of which four cases with distinct translation factors and matrices are required according to the relationships of the original and new positions of the object and pupil; otherwise, division-by-zero errors or insufficient numerical accuracy will be encountered. As a comparison, the new matrices have several advantages. First, by introducing four meaningful equivalent optical invariants, multiplying the old matrices, and simplifying the new matrices, they have concise expressions to significantly reduce the calculation time. Second, they are unique and always accurate to apply for all kinds of object and pupil positions without suffering any mathematical problems, i.e., four separated algorithms are no longer necessary. Third, due to the unique property, the component contributions of original aberrations to new aberrations can be directly evaluated and analyzed.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Variations of spherical aberration and central coma of conceptual thin lenses

Chaohsien Chen
Appl. Opt. 55(36) 10363-10369 (2016)

Aberration correction of zoom lenses using evolutionary programming

Sourav Pal
Appl. Opt. 52(23) 5724-5732 (2013)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (8)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (6)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (95)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription