Dynamical analysis of free tool rotation on a glass rotating at a constant angular velocity.

This work presents a dynamical analysis of a tool rotating freely due to the action of glass rotating at a constant angular velocity is presented. Preston [J. Soc.

Exact formula to relate optical path differences and transversal aberration components.

An exact equation to relate the optical path differences (OPD) with its transversal aberration components (TAC) is determined. The OPD-TAC equation reproduces the Rayces formula and introduces the coefficient for the longitudinal aberration. The defocus orthonormal Zernike polynomial ( ) is not a solution for the OPD-TAC equation since the obtained longitudinal defocus depends on the ray height on the exit pupil, meaning that it cannot be interpreted as a defocus.

Proof that spot diagram borders are always caustic curves and/or marginal rays II: annular (circular and elliptical) and single hexagonal exit pupils.

In a previous paper [Appl. Opt. 61, C20 (2022)] it was proven that for a circular exit pupil and any optical path differences, the border of any spot diagram is integrated by the caustic surface and/or marginal rays.

Borders of spot diagrams are always caustic surfaces and/or marginal rays.

In this paper, it is proven that for any optical system with a circular exit pupil and wavefronts affected by any aberrations, the borders of all leaving rays are caustic surfaces and/or marginal rays. Several examples are shown for wavefronts affected by linear combinations of Zernike aberrations.

Exact calculation of conic constants and baffles for any two-mirror aplanatic telescope.

To calculate the conic constants of the primary and secondary mirrors of any aplanatic two-mirror telescope, nonexact equations have been used considering third-order approximations, although it was not considered that there is an infinite number of conic constants. In this paper, exact nonlinear equations are obtained; with them, the two conic constants of the mirrors are calculated without approximations. We also find that the conic constants depend on the position at the stop where the calculation is carried out, and there are always residual aberrations.

Lensometer with autocollimation and a square Ronchi grid.

A lensometer based on an autocollimation system and a square Ronchi grid was designed, constructed, and tested. Refractive powers of monofocal, astigmatic, bifocal, and progressive lenses were measured. The focal plane was identified when no spots, or a minimum number of fringes, are observed on the bironchigram (pattern with a square Ronchi grid).

Small petal tools performance for parabolizing optical surfaces.

Small rigid petal tools, driven by a traditional polishing machine, were used to parabolize 20 mirrors 14 cm in diameter and 192 cm of curvature radius. Small rigid circular tools (SCTs), driven manually, were used to parabolize another 20 identical surfaces. A Ronchi test with a square grid was used to evaluate the performance of both techniques.

Local and global surface errors evaluation using Ronchi test, without both approximation and integration.

We have reproduced quantitatively the technique commonly used in optical shop to evaluate surface error from comparison between experimental and simulated Ronchigrams. We used this procedure to evaluate, from Ronchigrams of any number of fringes, the curvature radius and/or conic constant of conic surfaces. The error function is calculated without using integration (numerical or polynomial) so the corresponding problems were avoided.

Use of linear programming to calculate dwell times for the design of petal tools.

Two constraints in the design of a petal tool are, the angles that define it must all be positive, and wear must never be greater than the desired wear. The first constraint is equivalent to that of the positive dwell times of a small solid tool. In view of this foregoing, we present a design of petal tools that are used to generate conic surfaces from their nearest spheres and that correct the profile of a surface that is polished.

Correction of the Preston equation for low speeds.

According to Preston [J. Soc. Glass Technol.

Calculating petal tools by using genetic algorithms.

To pass from a spherical surface to a conic one, it is possible to use a petal tool or a small solid tool that is placed at different time intervals at several radial zones of the glass. Genetic algorithms are applied to calculate the angular sizes of the incomplete annular tools that make up the petal tools. We also present the desired wear results carried out with the petal tool that was designed on the basis of the dwell times of complete annular tools.

Experimental results and wear predictions of petal tools that freely rotate.

It is difficult to calculate the wear produced by free-pinned tools because their angular movement is not entirely predictable. We analyze the wear produced with free-pinned ring tools, using both simulations and experiments. We conclude that the wear of an incomplete ring is directly proportional to the ring's angular size, independently of the mean radius of the ring.

Static and dynamic removal rates of a new hydrodynamic polishing tool.

A new tool for hydrodynamic radial polishing, HyDra, allows for the local polishing of optical surfaces with a controllable wear rate. The results of the removal rate for different polisher types and sizes, applied air pressures for slurry expulsion, and tool height with respect to the working surface, are reported. We present a numerical analysis of the volumetric removal rate for the dynamic experiments as well as a comparison with a similar technique.

Edge effects with the Preston equation for a circular tool and workpiece.

In a polishing process the wear is greater at the edge when the tool extends beyond the border of the workpiece. To explain this effect, we propose a new model in which the pressure is higher at the edge. This model is applied to the case of a circular tool that polishes a circular workpiece.

Sensing a wave front by use of a diffraction grating.

A method is presented to sense the wave front at the exit of an optical surface. This method uses a set of diffracted rays generated when a He-Ne laser impinges on a rectangular diffraction grating. The grating was placed near the curvature center of the surface to be tested.

Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates.

We present a simple algorithm that makes possible the simulation of ronchigrams for any optical system in which it is possible to make an exact ray tracing. We report the simulations for the following grids: the Ronchi classical, square, circular, radial, circular-radial, biparabolic, elliptic-hyperbolic, bipolar, and bielliptic ones.