The WHAT, the reason why', the WHEN and HOW:
Let's start from WHAT:
The Couder mask is a technical tool of cardboard, or other stiff and Matt material, that prepended to the parabolic mirror in construction to perform on it the Foucault test, serves to measure the Radius Othe Curvature in italian, maybe badly translated automatically in this article in RDC instead of the correct english Radius Of Curvature R.O.C. of the various concentric annuli in which artificially (due to technical simplification of the measurement problems) splits a mirror that, at the end of processing, must be parabolic, so as to be able to assess with the Foucault test, what and where are the manufacturing corrections to be implemented, to ensure that the gradually increased progression of the radii of curvature, of the reflecting surface of each annulus, are close as possible, to the theoretical progression of perfect parabola, taken as a constructive reference.
It often happens that in practical jargon, ROC is called improperly Focus (maybe bad automatically translated in "Fire", and not focus) what in fact is the Radius of curvature "R.O.C." whose focus is exactly half the value. But this practical jargon isn't to much trouble to practice for those who arrived reading up until this point, “nourished” with basic notions on Foucault test.
It is therefore to be assumed that the reader is familiar with the general rules for implementing the Foucault test, in which the Blade (knife edge) of a tester works (normally) moving from right to left, He is hiring in its shade the three characteristic aspects:
- when the blade is inserted (in the light of a slit reflected by the mirror under test) in a location that is before the center of curvature of that zone , she will present its moving shadow Concorde with blade movement, namely (normally) from right to left.
- While When the blade is inserted at the distance of the exact R.O.C, radius of curvature of the zone observed (at the point where the rays reflected from the mirror are crossings) , It will present a feature which is said to shadow “in flat grey colour"”, meaning that the progression that generates this shadow, looks like since done from the center of a ipothetic shutter circular photografic diaphragm, (and therefore (..that is the important..) can not give the impression that the shadow is coming from right nor from the left hand.). And it is precisely this training in the evaluation of the Roc with darkening concentric in colour gray “flat” , which it is made more difficult in the execution of the Foucault test.
- And finally, When the blade is inserted over the R.O.C., It will intercept the reflected rays after their crossing, and then the blade, still entering the light beam from right to left, will show his shadow in progression reversed, ie from left to right.
Between consecutive measurements of ROC of several Windows in the mask, you verify quantitatively the displacement of your values in reference than those of the theoretical parabola of reference , which, with appropriate machining offsets, They may be brought to coincide with it, creating an optically perfect mirror.
It is worth mentioning that these activities of technical verification with the Foucault test takes place in the final stages of the realization (both manual and machine), optical mirrors for telescopes, the majority of which is parabolic, which I am known to be obtained by starting to work a glass disc (with machine); or two discs (by hand); with abrasive brought in powder, applying hand pressure (and then digging) the center of what will become the concave mirror, against the edge of what is the tool, that therefore will possess equal complementary convex curvature.
And it is with this movement, ordered in a series of working strokes (in italian named "corse" alias "races") forward-backward, of suitable shape and amplitude, you get to turn two original glass disks, in two glass discs with complementary surface abraded with an almost perfect spherical shape.
With subsequent phases of refining of the surface roughness of the spherical surface, obtained in a first time with several wets (in italian contrarily named "seccate" alias "dried") working with halving the size of the abrasive grain (carried out from the moment of disappearance of the craters left by the previous coarser grain); and in a second time, holding the tool of a pitch patine and using a very fine abrasive (Cerium oxide), able to clear at a molecular level, any remaining trace of every micro scratches and infinitesimals craters , You will get a shiny surface as is the calm and free water surface
The mask couder. The When and the why:
With the aforementioned processing, accordingly you come to the need to "countersink", ie "parabolizing", the spherical curve until that moment preserved, to become a parabole, Since a spherical surface could not provide a usable refelcted image (...), for the easiest and proper function of Newton telescope.
The difference in shape between the spherical surface and the parabolic is the only radius of curvature of the first, which unique curvature would focus at different points in the image of an object coming from infinity, making it confusing and unreadable from the eyepiece. While a parabolic reflective surface has radii of curvature gradually increasing, as that from the center of the mirror it proceeds towards its periphery, thereby able to converge neatly all the light rays coming from infinity, in a single focal point, thus forming a perfect image, which is then observed with an eyepiece, and therefore enlarged by a magnification that will be greater than the ratio between the focal length of the mirror and that of the eyepiece used.
The continuous measurement of the progressive rays of the plan parabola curvature, is technically impossible, and therefore it is required to get down to appropriate technical compromises.
The first and most important of which, is also a general rule for the solution of any kind of complex problems , and consists in dividing the complex problem into many simples problems..like we see immediately below, in the next lucubration
The Couder mask. the HOW
You create the mask of Couder building a disc of stiff material with a diameter equal to the diameter of the mirror under test, and on it you will trace circumferences that between them ale making
a number of "circular crowns", and each crown will identify a “concentric zone” mirror, It characterized by possessing a so-called "average height "Hm, that identifies the average distance of this annulus, the center mirror.
On each of these "N" circular crowns, we will crops and open in the mask, a pair of diametrically opposite Windows, which will serve to allow them to appreciate in the “flat grey colour” namely’ central obscuration, instantaneous contemporary and characteristic, which occurs only when the tester blade is introduced into the reflected beam to the exact distance of Rdc of that portion of parabola.
Of course there are rules of guidance, to realize the mask, which are as follows:
- Being in a parable continues the change in the DRC, and also continuously increasing starting from the mirror center and proceeding towards the edge; In order to perform measurements that cannot be equally continues (ie on infinitesimal parabola amplitudes), one should come down to compromise to measure on annuli of width a little wider, but still minimum:, and such as not to complicate our assessment of instantaneous and contemporary darkening (that is purpose of Foucault test). Darkening that can no longer be perceived with those features if the window width was much extended by going to affect an area with too large variations, i.e. where it zone radius of the window toward the Center mirro significantly different from the radius toward the periphery of the mirror. This is so even, and even more so, for very short focal ratio mirrors (ie those which have very deep parabolas which have a large variation of radius of curvature in very little lateral displacement towards the edge). This rule is therefore recommended to manufacture for these mirrors of short focal length (for openings not less of F5), a mask with a greater number of control zones, ie windows. But it must be remembered that the Foucault test (and then the mask Couder) is inadequate because inaccurately to complete good quality mirrors, type “Fast”; ie understood as large-diameter (is:=>400mm and focal ratio “short” is: =<F4) , for which you get a better optical quality using the Hartmann test, or one interferometric; or the test of “Caustic” (for technical reasons explained in the article regarding that tests).
- Intuitively, it is understood that the greater the number of windows that have the mask, and the greater the number of measurement points, and therefore the greater the potential accuracy of the resulting parabola. But many windows entail a reduced horizontal extension that can truly become small toward the mirror edge, where this extension is limited and contained, because the radius variations are more sensitive, and thus the evaluation can become very very problematic. The obstacle is usually overcome with the use of a greater number of zones, combined with the use of a camera installed behind the Foucault tester, instead of the human eye. Camera that incorporates the darkening of the zones, while the operator can detect the exact measurement, looking at the image on a monitor, and thus it purified by the multitude of diffraction fringes that plague the eye that looks at the mirror directly, which fringes, together with the small size of the area under test, they would complicate the assessment of the exact ROC.
- The central area of the mirror is that at which the parabola "is flatter" (less deformed), that is, has the variations of tha curvature radius changing less quickly with the lateral displacement; and also that same portion of the mirror will always be obscured by the presence of the secondary mirror of the telescope: So the central area is the one that has the most loose processing tolerance. Therefore, the central measuring window is the widest, and it may optionally also present indifferently a blind central part, as if to cover a center hole of the mirror. This area, however, is still the much critical and important because it is the starting point of all'our measures on the parabolic surface, and mistaken the location of ROC of this base point ... the mistakes they will also affecte all subsequent measurements.
- The pair of windows that is at the edge of the mirror, amplitude should be such as to allow to be able to see well the central darken, at the distance in which you must install the Foucault-meter, that is the center of curvature ROC of the area observed, equal to twice the focal distance of the mirror.
It can indeed be understood that it is not easy to assess the shadows in a pair of windows few mm wide, looking at them from a distance that for a mirror telescope diameter 300 mm F5, it's about 3 meters. Here is a rule of thumb should choose a mask with a number of windows to maintain the amplitude of the extreme windows (which are the most restricted) in about 10 or 15mm.
The Couder mask. CONCLUSIONS and an example of its use with FoucaultMANUALLY performed:
In fact, therefore, and in conclusion, there are no hard and fast rules in the creation of a . Couder mask. Here's an example, and how to use it in practice in manual calculation (... always useful to understand what the various software run without our knowledge, well as on the data of our Foucault test)
Figure 1. Couder mask to 4 zones
Looking at the figure 1, The reference parable declared in it for a mirror diameter 150mm F5, He would have a fire 750mm and therefore a radius R of curvature of the double, in which position the tester Foucauilt, ie 1500mm
For any radius value Hx (see table on the mask image ) It calculates the average radius Hm the resulting window (for the central window, if there is a central hole, the mean radius is equal to half of its diameter).
And finally (bottom row of the table) It is calculated by the value of "Aberration longitudinal theoretical” (Ablt) in each center area (ie in practice quell "error" progressive ball that identifies the desired reference parable) with the formula :
1). Ablt = Hm^2/R
The measures "draft" (It is said “draft” the value of the relative importance of each area measurement, Foucault carried out with the tester) of the areas obtained by the Foucault test, They are not directly usable, mawe need to find the ones that are called “residue”, subtracting the measurements of each area the values of its own aberration ABLT.
Finally all the values found it "reduce"... depriving them of the value of the mirror area taken as a reference.
In practice this important method “reduction”, It is mathematically simulates the real “material displacement” the parable that we measured, by putting it in contact with the reference parable, to a common point in our choice, to then see in reference to that point, as "scatter" the values of the other zones, and find the way for degrees of correction to be implemented more convenient to make our perfect parabola identical to that taken as a reference.
Usually the most convenient point of contact is in the area that is closest to 70% the diameter of the mirror, preferably considered the zero point of the parabola easier achievable, since the parable within the zone 70% is little more dug in the center than the sphere ; while outside the zone 70% is little more countersunk of the sphere.
It is said "parabolization from 70%"
But no one forbids taking other landmarks ("Reducing" our parable to the contact with another great point of reference parable, subtracting all the values found with Foucault, the value of the outlet area as the zero point).
But the two conditions alterenative from the parabolizzazione 70%, are not usually convenient because they require to remove the most large amount of glass , both parabolizing from the center (where you will have to very dig at the edge), that parabolizing from the edge of the mirror (where you will very deepen the center).
The aberration values as "reduced", whether they are POSITIVE directly indicate MANY mm the radius of curvature of the area is TOO LARGE, compared to how it should be (reported to the outlet area as the zero point); If they are NEGATIVE conversely.
The slopes of the graphs instead are the opposite of the values of aberration, and RISE with radius values TOO SMALL, or DESCEND to radius values TOO LARGE.
The use of the graph is very important and immediate for the identification of areas at a glance “that are high” to correct, but it will be covered in detail in’article concerning the execution of the Foucault test with calculations as manuals.
Returning on Couder mask, Its eventual inadequacy is at most date from a too low number of zones, which can result in a disability that prevents a detailed monitoring of the trend of curve a short focal parable, ie very deep. This is understandable because the very pronounced curvature (whose variations are therefore very sudden in the surface confined spaces) and the few zones (so too wides), that would make it difficult or even prevent it from accurately identify in them the “flat grey colour” of the ROC.
This also happens when instead it should make a best control, because that its depth can only be realized with the use of fractional diameter tools compared to that of the mirror, and therefore harbingers of undesired zonal grooves and defects tghat are unknown to full-diameter tools.
In other words, and vice versa, it's a unnecessary complication use a mask with many zones when the processing of the mirror was made with a full-diameter tool, (then this is not a parable of short focal length) as following the implementation of the trappings of polishing strokes, you have the near certainty that the progression between zone and zones will be found to be uniform and free of zonal characteristic errors brought from small diameter tools.
Finally: A spartan little program BASIC for the window calculation of Couder masks, that is fine, and reaches up to calculate 19 zones:
About the BASIC language (daily bread and IT gym us twentysomethings sixties of the last century), I should mention that in BASIC programs you can do it too run on modern computers with Windows 10, downloading and installing a small and simple free program DOSBox, that in a special folder emulates DOS, and which, from the same site can also be chosen “patch” Italian language, and downloaded a valid short and tutorials (in English), or you can watch a movie “How to use DOSBox” on Youtube in Italian .
Programming Environments “Jurassic” GwBasic as IBM or Basica, or the more advanced Microsoft Quickbasic, They are now freely downloadable and useful for editing and debugging programs.
With the use of this small program in BASIC becomes easy with just two attempts and comparisons, choose the mask to be carried out which present the two windows of the outermost zone, in size “readables” from the positioning distance of the Foucault tester .
For example: The mask 4 areas for a mirror 200mm F5, presents area 4 13.5 mm wide which is well observable from the ROC to distance 2 meters (twice the focal); while in 5 areas fifth shrinks 10.6mm; and proving 8 zones, the eighth would shrink to 6.4mm which are too little visible from the same distance of 2 meters.
Anyway, net of reading difficulties indicated, each choice is valid bearing in mind the need to have multiple zones for very short focal ratio mirrors (where it has already reiterated that multiple windows are necessary, each embracing an a more limited area on the mirror, as the curvature of these short focal length parables grows continuously in a very short space).
10 CLS : REM program sccouder.bas
20 DIM hx(20): DIM hm(20): DIM hm2(20)
30 PRINT “SCCOUDER.BAS: Screen size calculation Couder”
40 PRINT “Mirror diameter in mm “;
50 INPUT d
60 PRINT “Number F “;
70 INPUT nf
80 PRINT “Mirror focal length”; nf * O; “mm”;
90 f = nf * O
100 PRINT “Diameter of the central hole of the mirror (zero if no hole)”;
110 INPUT t
120 R = f * 2
130 ry = d / 2
140 hx(0) = t
150 fl = (ry * ry) / R
160 z = INT(fl)
170 PRINT “screen with “; with – 1; “or vice versa”; with; “zones “;
180 INPUT z
190 a = 0:
200 PRINT
210 FOR n = (ry / (with + 1)) TO ry STEP ry / with
220 a = a + 1
230 hx(until
) = SQR(n * ry)
240 hm(until
) = (hx(until
) + hx(until
– 1)) / 2
250 hm2(until
) = hm(until
) * hm(until
) / R
260 PRINT “est.finestra Radius (“; until
; “) Hx(“; until
; “)=”; hx(until
);
270 PRINT “Hm Center window(“; until
; “)=”; hm(until
);
280 PRINT “Aberraz length. Hm ^ 2 / r(“; until
; “)=”; hm2(until
);
290 PRINT “*********************************************”
300 NEXT n
310 END
On internet there are of definitely better…But in programs it reads like things really work, while instead to use them as they are, maybe even beautiful and attractive, piglia what we are given, remaining in blissful ignorance.
Another more modern and good solution, It is provided by the following spreadsheet that indicates the constructive measures of Couder mask, providing the choice between two different number of zones, one of which has an area less than the other, and therefore with the pair of wider extreme windows, providing in this way an easy choice for its better visibility of the critical pair of smaller areas at the edge mirror, which, as known, despite being the most restricted views must be equally well by the distance of the radius of curvature, which it is twice the focal length.
The spreadsheet realizes the window openings gradually narrower from the center to the edge of the mirror, with the calculation in geometric progression of the progression of their parabolic curve with which it will be analyzed.