Aspherical

Even if the first attempts at making aspherical lenses had been successful, chromatism (Fig. 6, which was not properly understood, would have prevented such lenses to deliver acceptable images anyway. Solutions to the problem of chromatic aberrations had been delayed by Newton himself, who incorrectly... 

The poor reflectivity of speculum and the tighter figure tolerance, combined with the difficulty to accurately measure aspherical surfaces have slowed the evolution of the reflecting telescope down. These issues are of a pure technological nature optical solutions for reflecting telescopes were derived in the... 

As noted before, short focal ratios imply severe difficulties in generating the aspherical departure from an ideal sphere. It is, however, directly related to the telescope length, hence to the structure and building sizes, which are major cost positions and performance issues in a telescope project -cost of large structures and buildings, improbable thermal equilibrium hence local turbulence, misalignments and flexures, etc. 

In the first case, lets consider what happens to a perfect light wave when it impinges on a mirror. In general mirrors can be described as flat (which is less interesting) spherical, conic or aspheric. 

With spherical segments, optical figuring and testing is a proven and reliable process, well suited for mass-production. Serial production of diffraction-limited, large optics is already under way for laser fusion projects, with European suppliers increasing their capacity to approximately 1,000 m2 per year Aspherical segments would certainly be feasible as well, but the inherent risk and potentially lower quality need to be properly evaluated. In figuring optical... 

In the design presented here, the compensation of the enormous spherical aberration of the primary mirror inevitably falls on the quaternary one. With a FI. 42 spherical primary mirror, the aspheric departure to be figured into the quaternary is as large as 14 mm. 

Besides the increase of reflections implied by Owl optical design, a price to pay for the spherical primary mirror solution is the difficulty to compensate for its spherical aberration, and in particular the horrendous aspherization of the quaternary mirror (which is conjugated to the primary). A possible test setup has been identified and the state of current technology allows for cautious hope industrial studies are however still required to confirm feasibility and evaluate implied cost and schedule. 

The first part of the presentation will deal with the fabrication of aspheric mirrors of varying degrees of difficulty and explaining how the difficulty is related to the optical parameters of the surfaces. In general, the same difficulties arise in testing of aspheres in the same order and for the same reasons, so this chapter will serve as somewhat of an introduction to the optical testing chapter as well. 

The secret is to build a primary that is aspheric to get the desirable optical properties of these designs while keeping the segments as close as possible to a shape that is spherical or can be polished almost as easily as a sphere such as a toroid, a surface with two constant radii. To study this idea further, consider a mirror that is a parabola of revolution. We use a parabola because the more realistic hyperboloid is only a few percent different from the parabola but the equations are simpler and thus give more insight into the real issues of fabrication. The sagitta, or sag, of a parabola is its depth measured along a diameter with respect to its vertex, or... 

If this expression for the aspheric departure from spherical is expanded and recast in terms of commonly accepted optical aberrations, we find the departure is made up of a linear combination of aberrations and alignment terms shown in Tab. 1. The k is the conic constant if the asphere is not a parabola and the... 

The original bend and polish idea is due to Bernard Schmidt who built what has become known as a Schmidt telescope with a spherical primary and an aspheric corrector plate that introduces exactly the right amount of spherical aberration to cancel the spherical aberration that would be introduced by the spherical primary (Schmidt). The corrector has to be thicker at the edge in proportion to the radial distance in the aperture to the fourth power to provide the needed correction. 

Abstract This lecture addresses the optical testing of concave aspheric mirrors. Examples of measurements of low order aberrations are shown. There are noises and bisases due to environmental effects, such as air turbulence, mirror temperature. Methods of interferometric testing are discussed. 

Keywords optical testing, mirror segments, aspheric mirrors... 

The projector chosen for Keck is an afocal Gregorian telescope (see Ch. 3) which expands the beam to a full 50-cm round profile. The final lens is placed with the plane surface facing the sky and the aspheric surface ground to give a 1/10 wave (rms) transmitted wave front. A back reflection from the last surface is used to monitor the quality of the wave front as it leaves the dome. 

To = temperature of the solvent at which tan A goes through a maximum. These values are presented in Table II. VSE (the Stokes-Eeinstein volume) is calculated for a spherical molecule if the molecule is aspherical this calculation (VSE) is called Vapparent The Vapparent can be smaller or larger than the Stokes-Einstein volume and varies from the equivalent sphere volume obtained by solution of equations 3,4 and 5. 

---