Singlet lenses free of all orders of spherical aberration

  title={Singlet lenses free of all orders of spherical aberration},
  author={Juan Camilo Valencia-Estrada and Ricardo Flores-Hern{\'a}ndez and Daniel Malacara-Hern{\'a}ndez},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
This paper describes a method to design families of singlet lenses free of all orders of spherical aberration. These lenses can be mass produced according to Schwarzschild's formula and therefore one can find many practical applications. The main feature of this work is the application of an analysis that can be extended to grazing or maximum incidence on the first surface. Also, here, the authors present some developments that corroborate geometrical optics results, along with the axial thick… 

Figures from this paper

Analytic conic constants to reduce the spherical aberration of a single lens used in collimated light.

Here, analytic equations for the conic constants, principal surfaces, and caustic surfaces are provided, and also approximations at the third and fifth orders formed by conic lenses, in order to reduce the spherical aberration at these orders.

General formula for bi-aspheric singlet lens design free of spherical aberration.

A rigorous analytical solution for the bi-aspheric singlet lens design problem and the input is the first surface of the singlet, which must be continuous and such that the rays inside the lens do not cross each other.

Paraboloid–aspheric lenses free of spherical aberration

Abstract A method to design singlet paraboloid-aspheric lenses free of all orders of spherical aberration with maximum aperture is described. This work includes all parametric formulas to describe

General formula to design a freeform singlet free of spherical aberration and astigmatism: comment

In their article -Appl. Opt. 58, 1010_1015 (2019)- Gonz\'alez-Acu\~na et al claimed:"an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism."

General formula to design a freeform singlet free of spherical aberration and astigmatism: comment.

This work presents the complete solution of an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism, which can only be applied when the object and image are both real, and the image is inversed.

Superconical aplanatic ovoid singlet lenses.

Within the framework of the theory of rigorously stigmatic optical systems, making use of Cartesian surfaces for the construction of stigmatic ovoid singlet lenses, the same functionality of optical systems involving a set of spherical lenses is achieved.

Calculation of a lens system with one or two aspherical surfaces having corrected spherical aberration.

  • A. MikšP. Pokorný
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2020
The paper presents a detailed theoretical analysis of characteristics of a rotationally symmetric lens system with one or two aspherical surfaces having corrected spherical aberration and reduced

Catadioptric interfaces for designing VLC antennae.

A model to design bi-aspherical catadioptric lenses with limited image diffraction using a first refractive Cartesian oval surface that does not introduce any spherical aberration is presented.

Spherical Aberration-Corrected Metalens for Polarization Multiplexed Imaging

We present a terahertz spherical aberration-corrected metalens that uses the dynamic phase to achieve polarization multiplexed imaging. The designed metalens has polarization–dependent imaging



Analytic aspheric coefficients to reduce the spherical aberration of lens elements used in collimated light.

A comparison of the aspheric coefficients obtained through the analytic formulas and commercial optical design software is presented, showing good agreement, which is useful in reducing spherical aberration.

Finite conjugate spherical aberration compensation in high numerical-aperture optical disc readout.

The Wasserman-Wolf-Vaskas method is used to design biaspheric objective lenses that satisfy a ray condition that interpolates between the Abbe and the Herschel conditions, making the analytical theory a good approximation for any objective lens used in practice.

Thick lenses free from spherical aberration designed by using exact ray tracing

We obtained novel analytic expressions which permit us to realize the optical design of any thick lens, this analysis include both first and exact order design. We employ the conic constant of the

Optical Aberration Coefficients. XII. Remarks Relating to Aberrations of any Order

This paper concerns itself with certain general details of the “Lagrangian” theory of aberration coefficients previously developed by the author. They are: (i) the general relation between various

On the Image Sharpness in the Central Field of a System Presenting Third- and Fifth-Order Spherical Aberration*

It is customary in photographic lenses to leave some third-order spherical aberration to partially compensate the higher order terms. However, so far no satisfactory answer has been given to the

Optical Aberration Coefficients. VIII. Coefficient of Spherical Aberration of Order Eleven

On the occasion of developing the theoretical basis for the calculation of the coefficient of quaternary spherical aberration it was suggested that it would be desirable to proceed to coefficients of

Explicit representations of all refractive optical interfaces without spherical aberration.

The following explicit model, valid for high aperture refraction with homogenous and isotropic materials, encompasses all explicit solutions of the first-order nonlinear differential equation

Wide angle lenses with aspheric correcting surfaces.

Refracting elements having aspheric correcting surfaces near the center of curvature are analyzed and typical forms of the correcting surfaces have been determined, both by third-order theory and by numerical integration of exact equations.

Caustics in a meridional plane produced by plano-convex conic lenses.

Using the caustic formulas and a paraxial approximation, analytic expressions are derived to evaluate the spherical aberration to the third order, and a formula to reduce this aberration is provided.

Two-Surface Refracting Systems with Zero Third-Order Spherical Aberration

An analysis is made of refracting systems consisting of two spherical surfaces. Solutions are found for those systems having zero third-order spherical aberration. These are in the form of four