(short outline)

For all those who still haven’t a clear idea of as a telescope-mirror can be made, and for all those who think and believe that this is something difficult, I wish to make here a short outline of which is the technique, sending back for greater details to the bibliography on the argument.

First of all, I must say that it is not difficult: contrarily to how could be thought, it is easier than to construct the mechanical part of a telescope, since this last one is made up of many parts that must be worked with precision and assembled with as much precision.

In the case of the mirror, instead, made of a single piece, its precision can be pushed without difficulties to measures of the order of 1/30,000 mm and more.
One begins with two discs of glass, possibly equal, one of which serves as tool, while the other will be the mirror. The characteristics of this glass must be the following:

It is not necessary that it is an optical glass, like what we use to make lenses, since the light is reflected on the mirror surface without to cross the glass, so that dispersion- and refractions indices do not have importance. The phases of the working are three: grinding, polishing and figuring.

First phase: grinding

The first phase of the work is the grinding.
One of the two discs is put on a stable support, and fixed with three holders, without to make excessive pressure, so that it can be very firm, but can freely rotate. On this disc is deposited a little abrasive (carborundum n.60 or 80 in order to begin) that is bathed in way to form a kind of cream.

Moving the upper disc ahead and behind on the lower, with regularly irregular movements, and making it turn at the same time regarding the lower, the upper one is consumed mostly in the centers zone, becoming concave, while the other is consumed in the edges, becoming convex. This happens automatically, that one wants or not, to such a point that, inverting the position of discs, one can go back, if necessary, diminishing so the achieved curvature.

The coarse abrasive serves in order to obtain the wanted curvature.
The following increase the curvature only a little and serve mainly in order to achieve a finer grinding.
The grinding phase can last some hours, depending from the mirror diameter.

Second phase: polishing
The successive phase, said of polishing, is obtained with a little different technique:
on the lower disc is deposited a lot of pitch, nearly liquid, on which is then put the other disc (the future mirror), that has already the wanted curvature and the appropriate grinding, so that the pitch becomes convex.

Before making this, it is necessary to make some furrows in the pitch, so that it assumes the aspect of a chocolate tablet, curing that neither furrows nor squares coincide with the center. This to the aim to avoid periodic zonal errors during polishing and figuring. 
Cooled off the pitch, one spreeds on its surface, with a soft brush, a bit oxide diluted in water, and one puts on the pitch the grinded mirror.

The smalls oxide grain (200x smaller than an erythrocyte) sink then in the pitch, but not completely. Moving the mirror ahead and behind on such support, the grains of oxide provoke on the glass innumerable cuts, removing molecule layers and eliminating every unevenness of the surface:

relieves become so smoother and smoother, while pores (produced from the carborundum-grains) become filled up with practically fused glass (to molecular level).

In this way, after some hour of work, the polishing is obtained.
This phase must however continue until the last pore disappears.

It can be useful, to such aim, to control the mirror surface with a microscope (what constitutes other interesting experience).

The cerium-oxide is more energetic, and consumes the glass more quickly.
The iron-oxide, instead, is slower, but allows a better control and to achieve a higher precision.
In the two first phases of the work the mirror assumes a shape that should be spherical.

Before passing to the successive phase, however, it is opportune to make sure that the achieved curvature is really spherical, that is, that it does not have neither irregularities (defects) nor astigmatism.

Third phase: figuring

In order to conclude, one passes to the figuring-phase.
The technique is similar to that used for the polishing, but with a little different movements.
It consists in transforming the spherical curvature in an aspherical one (paraboloid, ellipsoid or hyperboloid, according to the curve one wants to achieve).

The most common is to the paraboloid.
Its curvature can be tested with several methods (Ronchi,
Foucault, etc.), and the figuring must be prolonged until the wanted precision (l/8 to l/20 or more) is achieved.

The time necessary for this operation can vary from a few minutes (with a good pitch and a bit experience) to several hours.

This, to great lines, the way to construct at home a parabolic mirror.

It is a particularly great satisfaction to be able to grind, polish and figure a mirror, and to state that it is able to concentrate in a spot of two or three microns a light-beam of 15-30 or more cm. diameter, achieving so a quality and a precision not always achieved from the mirrors of the industry !