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It claimed Massimo, I agree on everything apart from the fact that the tilt is necessary, In fact, the article that you linked to NortheK, more or less 3/4 the page (just above the short chapter “elliptical fringes”) in the image with the 3 different types of shapes of the fringes which can be seen, leftmost refers precisely to a situation without tilt.
To estimate the value of PV in fact you do as you say, and it is well explained more fully on page 13 dell’ Optical shop testing.
Anyway always interesting article on the NortheK…In the time I have read almost all of them…
And, I said that badly, I meant without a separation layer, with “tilt” It refers to a layer of non-uniform separation, then “inclined”, quite right ?
Even because, if I put two equal surfaces ( almost ) in contact without any separation, there is a risk of “bonding” or at least a strong suction effect ?
It claimed Tilt = tilted and it is also true as you say that if you put in contact two extremely precise surfaces and the negative of the other would form a strong suction effect…
Ok Mirco, thank you
Meanwhile I came to a good 70% polishing, the form does not seem to change and therefore do not think that will complete all before starting the hyperbole, because even with the time it will take to get to K = -5.12, the (the?
) waste pits / and will be a distant memory… 
Rather I was wondering how do you check the roughness was….
For this reason and, not trusting too much with my skills with interferometry ( although simple as this Newton ) I'm putting together the telescope version “prototype” that is, with the wooden components derived from the old Dobson adapted to the new project.
The facts of the test controls and inspections “garage”, I would like to support them with those made directly on the sky, with the help of the star testing and good old network of Ronchi, Their unlike me, hardly wrong…
Tire guess, but I think in qualitative way would try to see the roughness of the floor with Foucault, as it is done with the spherical or parabolic mirrors, but in this case inserting the floor in the optical path of a primary non-wrinkled, as if it were a secondary 45 °, and then placing the side of the Foucault tester roughly to the distance of the radius of curvature to see the primary reflection from the plane.
I would light, and then a little maneuver the orientation of the source to make the less bright lighting, Wherefore normally immediately it puts in prominence the surface roughness (or the infinitesimal dust or dirt) that would occur as usual as clear clouds.
Tire guess, but I think in qualitative way would try to see the roughness of the floor with Foucault, as it is done with the spherical or parabolic mirrors…
Giulio, you do not tell me these things, I really do because then the !
As these fringes of Newton does not convince me at all, certainly not for the validity of the test but as I am doing so… approximate, then I said:
Ok, we can not test the convex surface for obvious reasons, ma…. if we put the mirror on support for Ronchi / foucault test Unlike , What happen ?
Surely the convex part, view from this other side becomes concave with converging reflections, the problems are represented by the sheet of glass that is traversed twice by the light, and the flat surface ( which in this case becomes the front ) that certainly is not flat…
– the flat surface does not contribute to the reflections and even the refractive, in case the non-planarity alters the regularity of the glass layer, and then the local intensity of refraction which, as we know, It contributes together with the curvature of the glass to the determination of the focal length or, rather, since we are using glass as a lens, the refractive power.
but since then the effective refractive index may vary with a shape “almost flat” compared to a flat ? I do not know, for now let's see what happens
Meanwhile, I discovered something fundamental : my LED is not monochrome
Such a pity! 
then a first measure that may come in handy: the radius of curvature (774 mm ), with the contribution of the double refraction of the glass, It brings the focal plane at a distance of 510 mm , therefore shorter, as expected.
The images of Ronchi “unconventional” Instead they say that the surface would not be spherical, but with the periphery growing respect to the center ( we are intra-focal ), However, the trend is very regular and symmetrical, which again makes me think that “quasi-planar face” It affects so imperceptible in this reflection-refraction.
But remember that we are looking at the supposed sphere inside, then the convex mirror surface should be with the lower periphery and higher than the center due, do you agree ?
the mother of all questions at this point would: the shape of the reflective surface is actually so, or it is altered by the double refraction in an irregular manner, ie bringing the ball to look like a oblate sphere ?
A first clue comes from me that the center is a little late with the glossy, so it may actually be “alto” because less achieved by processing, but come on over and we come to the subject of “tests”: roughness
We adjust the web cam grayscale colors to avoid misleading, slightly increase the contrast and try to use the Foucault knife:
And so to the classic image, We made it, roughness there and it shows !
Analysis
: the central bright spot is the reflection of the source on the planar face, the “Sunspots” are dirty / defects of the flat face, the rest I think are actually the “clear clouds” saying Giulio , the irregularities of the reflective surface. Che ne dite ?Hi Massimo, also I do I make Ronchi test “inside out” and indeed because of double refraction to me the mirror curvature becomes much smaller…
In addition I think (Correct me if I'm wrong) that the Ronchi test in this case is to be read to the contrary, in the sense that what we see in intrafocale position now, It would be what we will see in extrafocal position in a classic test of a concave surface…That is if I saw straight lines which, however, near the edge are thrown all outside (intrafocale) I would say that I raised edge, and it is true if you look at the surface on this side, but if I tip the mirror and look at him from the side which then should become the one reflecting the raised edge should become board countered (for complementarity)…
What I like to do, if I have time soon, It is to calculate what should be the shape of the Ronchi lines in the presence of both surfaces perfect, then the front plane and the rear perfectly spherical. In order to understand if the double refraction affects or less on the test results…Well, Meanwhile, I came to the conclusion that the double refraction does not affect the shape of the Ronchi lines
how do I say this ?the first refractive, ie the entry of light-source to the reflective concave part, there is simply no,
1-refraction occurs only in the presence of curved surfaces ( diopters ) that separate two materials with different refractive indices. In the case of a flat surface, as for the lenses, there is no deviation of the light beam. In the case instead that the surface was not flat but spherical with long radius of curvature, similarly would provide a minimum contribution and is imperceptible to the overall focal that the shape of the lines.
2- Also there is a double refraction nell'interferometria, but it is considered irrelevant the first 'crossing of the light on the flat surface.
3-I have found someone far more experienced than me use this method to test the fit of the secondary in Cassegrain ( sin, I was hoping to have invented it
):
http://www.oldhamoptical.com/#!convex-surfaces/ctxnsaid this, we come to what you said Mirco, on the Ronchi lines.
1-We should not worry about how would the Ronchi lines on the convex surface simply because there would be no. The Test of Ronchi, as the area being examined is unique, the detected shape is the same from wherever you look, only changes the direction of increasing or decreasing curvature, which becomes the opposite and complementary, in other words what the convex side “grow up”, from the concave side “decreases” and viceversa.
2-Is’ right instead we should think about the other side of the surface, but not for the shape of the lines, but for the processing techniques ranging think otherwise explain better me:
as you rightly said, the raised edge viewed from the convex becomes retorted ( reversal of the trend of curvature, as we said in step 1 )
This means that if we are working on as you normally do a concave surface, We put in place techniques to remove the glass in the right places to arrive at the correct form.
Looking at the other side, ie having to intervene on the convex surface, we must correct that mistake ( with respect to a same reference surface, ad is. the scope ), but we can not do it with the technique we used in the concave mirror, why, on this side of the mirror, would mean having to add material.
So we have to translate the reference sphere to bring the edge within the volume being processed to see the glass to be removed on the convex surface, to arrive at the same form.
definitely, we have to think “Unlike”, mistakes, as you had already guessed you:
the “central hole” in the concave ( we see only in Ronchi this perspective ), becomes “collina” in convex:
correction: He digs in centrally convex, exactly the opposite of what we would do in the concave.the raised ring in the concave , becomes depressed sector convex
the edge retorted in the concave, It becomes raised edge in the convexbut in all these cases the shape is identical, only changes the point of view and the ability to remove the glass, and then we get to “first postulate” ( theorem ?
) of massimar 
Analyzing the surface of the mirror from the concave portion, the corrections of the shape on the convex part, They are designed to “contrary”, ie using the technique on the concave would generate errors that we want to correct.
I have experienced this on the mirror, later I do the photos and post the results.
Agree on all…
However, I'm doing a little program to verify that the Ronchi lines are not subjected to deviations from the double refraction…Not that I do not trust your words, but you know if you do not put your nose I am not happy…
Quite right !
It would be interesting to find the relation between the second refraction at the focal length of the reflection, maybe starting from the known formulas for the calculation of the focal length of the lenses, whereas the calcium-sodium refractive index of glass is 1,52.Then, made preliminary calculations…
From what I see of the Ronchi lines for a perfect sphere should be seen in (intrafocale) like the ones you would see for a parable in extrafocal. In fact would not exactly identical to those of a perfect parable, but it would be very slightly different, so much so that we almost do not realize the difference…
Using your photos and making a comparison to the good with the Ronchi simulation software you can clearly see how your area, which it is close to a sphere (at least according to the diffraction fringes images) are similar to those of a parabola…As demonstrated by the calculations of the rest… In most calculations tell me that your mirror, due to the double refraction, the center of curvature “altered” It would be to 512.5 mm from the surface under examination… With excellent correspondence with the value you found…
Mirco're a genius ! Now I expect you to explain to me step by step, because I have not figured out how the hell did you, as it interferes and calculates the refraction in the reflection.
Well genius, We do not exaggerate…
I do not know if I will be able to explain it, but I try…I help with a design:
This word, and this in formulas:
For the special software in Excel showing the picture real test, however, you will have to wait because it is not so simple to implement…eh eh…
Great Mirco ! that's where I was wrong, on the first refractive ( and also on the second ) I thought to parallel rays ( I was already “watching” the stars
), but obviously it must be considered the angle of incidence !If we consider a source indefinitely, we will have the first refractive ( I1 = 0 ) for each value of B , then when B tends to 0, ie approaching the optical axis, even the second refraction will tend to zero and then there will never refractions for axial rays.
What does it mean ? which in this case, the focal plane for an infinite source is a caustic, with the vertex equivalent to that of a mirror with the same radius of curvature but without refracting glass front ?
another consideration, reading your maths;
you could put in relation with L XRIT ( and therefore also the angles θ1 and θ4 ) since there is a point at which L and X assume the same value and it is precisely what we used for the test with the source and grating on “alleged” focal plane.I say this because it could be a method, then using the inverse procedure, to calculate the radius of curvature of the convex mirror knowing the source of the distance measurement.
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