Conditions for having identical aberration behaviors of various thick lenses

Solving conceptual thin-lens components with balanced optical aberrations among different optical configurations is essential for lens design from scratch. This paper presents a general and practical method for building conceptual thin-lens components that can be further optimized by Code V (a well-known optical design program) to approach specific aberration targets. The conceptual component consists of a Code V’s lens module and a hologram with zero diffraction order. The latter provides spaces for storing the reference data of incident marginal and chief rays, spherical aberration, central coma, and longitudinal chromatic aberration without affecting the paraxial ray tracing. Those reference data are used to evaluate the real aberrations at different optical configurations by our earlier aberration variation algorithms [Appl. Opt. 55, 10363 (2016)APOPAI0003-693510.1364/AO.55.010363]. The model helps investigate the properties of lenses and solve the balanced aberrations by the optimization process. An example of solving a zoom lens with different optimization goals is given to demonstrate the usage of the method. Detailed design data are listed for verification.

Practical technique for balancing the optical aberrations among conceptual thin-lens components of optical zoom lenses

Chen

2022

Variations of spherical aberration and central coma of conceptual thin lenses

Chen¹

2016

Based on our earlier matrix algorithms [J. Mod. Opt.55, 105 (2008)JMOPEW0950-034010.1080/09500340701308740] for evaluating the variations of Seidel aberrations, new concise equations are derived to directly evaluate the variations of spherical aberration and central coma of conceptual thin lenses when the incident marginal and chief rays are arbitrarily changed. In the earlier algorithms, four cases with distinct translation factors and matrix equations are required according to the relationships of the object and pupil positions; otherwise, division-by-zero errors or insufficient numerical accuracy will be encountered. Conversely, the new versatile equations are always accurate for all kinds of object and pupil positions; one example verifying this property is illustrated. Another example is given to explain why a symmetrical thin lens can provide only one, rather than two, degrees of freedom for correcting Seidel aberrations.

Unique and concise system translation matrices for evaluating optical aberration variations

Chen

2017

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.