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Reading the following article suggested to me the probable feasibility / experimentability, to transfer even at an amateur level, the application of professional polishing and parabolization of mirrors for telescopes, now of ultra-avant-garde, with a "NON NEWTONIAN LIQUID" tool, which would seem a promising route now missing at an amateur / artisan level, for a significant leap in optical quality of very open mirrors for which now there is only the use of rigid sub-diameter tools.
Is’ I know that a non-Newtonian fluid is stably liquid, but it hardens locally in response proportional to a compression, enough to allow “walk on its waters: ” (https://www.youtube.com/watch?v=f2XQ97XHjVw)
A rotating rubber tool containing that liquid could drag the polishing abrasive acting with greater force caused by the proportional hardening caused by both the centrifugal force given by the variable rotation speed, and by the progressive compression exerted on it by the degree of curvature of the area being processed, to return an instant later perfectly liquid to follow the uniform surface surrounding the area of processing.
ARTICLE ON MIRROR POLISHING BY 8,4 METERS OF THE Giant Magellan Telescope
https://www.space.com/31645-putting-the-polish-on-epic-scale-telescope-mirrors.html
Is’ known to insiders, that to parabolize large diameter mirrors with short or very short focal length by amateur or artisanal work, small diameter tools must be used. Newtonian telescopes made with those mirrors are now in vogue today due to the lower height from the ground that allows you to look into the eyepiece without the need to climb ladders.
These small diameter tools, however, are always carriers of imperfections on the reflecting surface, because working only locally, they never allow a perfect connection between the worked areas and the adjacent ones, such as to respect the minimum tolerance established in ¼ of the wavelength of the yellow-green light of 550 nanometers high.; error which on the glass is equal to 68,75 nanometers between the peak and valley of the asperities of the reflecting surface. Which always leads to a low telescope quality value, which can also be pulled to a less low value, with significant costs, however, due to the time required to correct the surface a thousand times, in the attempts to standardize it to the theoretical parable taken as a constructive reference.
Poor quality becomes visible in the star test, when you see diffraction rings brighter than the adjacent ones, while you have the telescope already well acclimatized.
The article specifies that the work of ultra-fine refinement of mirror polishing from 8,5 meters of the Giant Magellan Telescope was entrusted to a rubber tool filled with a non-Newtonian liquid, it moves slowly on the mirror surface while at the same time it orbits rapidly around itself. The Newtonian liquid becomes rigid due to centrifugal force during the short period of the orbit, while the rest of the content remains fluid over the time it takes to move through the mirror, and flows easily, always matching the shape of the surface, while stiffening smoothes out small-scale irregularities in the mirror surface.
Our doubt / hope / but certainty for the builders of the GMT that arises spontaneously, is that maybe a sub-diameter tool of this type, can work better than a normal our rigid manual sub-diameter, ensuring a contemporary missing action that is much more leveling and connecting the worked area with the surrounding ones.
The tool is very reminiscent of an ice bag turned with a pin in the cap, but what works and can be seen in the image of the article above, it is more realistically made up of an upper aluminum disc of a certain diameter, equipped with a central rotation pin and probably with an upper peripheral ring nut, under the perimeter of which the edge of a flexible rubber disk can be fixed, to form an underlying sac (for example, it could be the fabric of an ice bag cut from the cap and fixed with the ferrule ring on the aluminum disc so as to present externally the internal rubber that waterproofs the external canvas of the bag, so as not to work the weft of the fabric which would remain inside the tool which will contain the Newtonian liquid, like water and corn starch.
To posterity the arduous…experimentation
Very interesting Giulio
However, I am not entirely in agreement on the sub-diameter problem, I try to explain myself:
I don't think the difficulty lies in making the surface uniform, which is possible even with small tools, if by “uniform” we mean a continuity in the change of curvature between the zones, that is, without "jumps" or sudden changes in the radius of curvature between two contiguous areas.Different processing techniques allow to uniform the surface: for example, very narrow W strokes generate a smooth surface without roughness like a full diameter.
The problem if anything ( which is not a problem but an opportunity ) is in the elimination of defects ( zone alte, low or asymmetries of any kind ) when the extension of the defect is greater than the diameter of the tool.For example, if we take an astigmatic surface ( how I got to study thoroughly
), with different radii of curvature ( which can be orthogonal or asymmetrical in the maximum / minimum value of the radius of curvature itself, we will have just one of the cases in which the extension of the defect is greater than the diameter of the tool. If we work with W strokes the entire surface with the full diameter, we will have that the radii of curvature min and max become uniform in an intermediate value,the others consequently become spherical, while with a small sub-diameter they will remain as they are. 
However, after a sufficient number of sessions, we will still have an astigmatic surface, but perfectly uniform in the change of curvatures along each diameter. Practically, in Ronchi we will see lines "inclined" towards the shortest radius of curvature, but perfectly straight, if before they were irregular.
The sub diameter will fail ( with this technique ) to modify the individual radii of curvature, but still it will make them regular "lambda proof" !Not only, We will have a figure with multiple radii of curvature , regular ( taken individually ) and also perfectly connected to each other.
Why does this happen ? for the simple fact that it is in the “nature” of the sub-diameter the ability to machine areas with different curvatures. If this were not the case, it would not be possible to generate a parabola or a "pushed" hyperbola on ultra short focal lengths, where the difference in curvature between center and periphery takes on important values.
If the defect is smaller than the tool diameter, the problem does not arise and we will have the same result as the full diameter: for example in a small "hole" the patina, during races, it will have no contact at the lowest points ( in the bottom of the hole ) remaining "resting" on the edges and, in the long run, will excavate the remaining surface until it reaches the lowest level. At that point there will be full contact between the patina and the glass and uniformity in the figure, having absorbed the defect with the processing.
If the defect is larger than that of the tool ( for example a parabola intended as a "deformed sphere" ) the patina of the sub-diameter will always have a contact within the defective area e, during processing, will remove the same amount of glass over the entire surface, leaving the figure as a whole unchanged. So in these cases, you will have to think differently, sometimes counter-intuitive, and start generating an opposite or identical defect , in some portions of the surface or along some diameters ( interspersed with regularization runs ) depending on the result we want to achieve, but in any case the connection understood as the regularity of the curve, be it constant or variable radius is, in my opinion, a false problem indeed, it is exactly the most important resource of the sub-diameter compared to the solid.
Let's imagine for a moment that the purpose of the processing, for some strange reason, had been to generate a surface with different radii of curvature depending on the direction, such as a toroidal cap. In this case we would not have talked about defects but about the result achieved.
So if a tool allows me to model any curve regardless of symmetry and have control over it during processing, it cannot have limits on the regularity of the curve itself, because it would negate the principle just said.
Principle that is valid, because it is experimentally demonstrable that an astigmatic figure with multiple radii of curvature can be maintained as such, modified or regularized according to the processing technique.
sure, all this in theory ... in practice I suffer from pain !
And, I also believe that to leave the old manual road for the new one, the saying is put into practice that we know what we lose but not what we find.
Especially since a sub diameter with new experimental technologies of a proportional type to that described in the article for telescope by 8,5 meters, in any case, it would certainly have a dimension too large to work amateur telescopes even of important aperture.
Of course, of that application is also fantastic the way of controlling the processing, independently guided by software based on the position of the tool on the surface, compared to a previous mapping of its nanometric asperities. Mapping made by counting the fringe hundredths, reflections from the surface hit with a red laser from 630 nanometers high..
If I'm not mistaken, the accounts, a penny of that light's fringe, measure 6,3 nanometers high.. Which on the glass would damage the wave of light that passes over it twice, in incidence and after reflection, introducing an error on the reflected wave of 12,6 nanometers high., which with respect to the wavelength of the yellow-green visible light of 550 nanometers used for normal telescope, correspond to a terrifying optical precision of the Lambda / 43.6 Large Magellan telescope.
Before reading the article, I had never encountered the practical use of the properties of non-Newtonian liquids, nor a read of the methodology (ingenious) to map the mirror surface with diffraction fringes, to determine where, and how many fringes is the defect to correct, to be able to maneuver the tool up to literally zero out the error.
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