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Hi Massimo,
And, let's say that your argument seem right, and also intuitively I would think so, But then placing the values in the formulas the results are different from the expectations.
I agree, and also the outcomes they say, that teta1 = teta2 and that are equal to 0 for a source located at infinity and then anything before refractive.
But then the light beams are deflected by the curved surface, however, that redirects them to cone and this slight inclination generates the second refraction. Keep in mind that for very small angles the sine of an angle practically coincides with the same value of the angle, then for the Snell formula the outgoing angle is 1.52 times greater than the angle incident (1.52 = Refractive index glass), which is no small.
Although I fully agree with you that in exactly on the optical axis theory should be no refraction…
But it is also true that exactly the optical axis can not tell where the fire fall, because those rays intersect the axis at all points (so in theory any point of that line is the “focus”)… 
However, I have compiled an Excel spreadsheet that would simulate the sights of Ronchi varying the parameters. The leaflet was designed to show the lines of Ronchi ONLY for a BALL surface and the test run backwards, ie illuminating the glass on the side of the flat surface. In fact it can even simulate a classic concave surface, as if we were performing the typical test, just put equal to 1 the refractive index of the glass (this will eliminate its contribution to the refractions).
https://www.grattavetro.it/wp-content/uploads/2016/04/Ronchi-Foucault-inverso.xlsx
P.S: the sheet has a mountain of stones inside, I seem to have controlled well enough before you upload it to the site, but it could be that I ran away a little digression or some other little thing. So if you were to appear strange results let me know that I try to fix…Anyway, at the moment, in all the tests they did the results have always been consistent…Try to play…
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…
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…
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…
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…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…
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…
Hi Massimo, I'm writing about it now a little article that I hope to publish soon.
Anyway, the rectilinear shape of the fringes or slightly see the curve because there is a slight tilt between the two surfaces under analysis. If you see slightly curved it is because you are viewing a small portion of a circular fringe that would have its center far outside mirror (precisely because of the tilt). If you can remove the tilt, and ensure that the two surfaces are perfectly parallel then you will see the circular fringes if there is a slight difference between the two radii of curvature, otherwise you would see even a (because it already would be bigger mirror) if the two curves are perfectly identical.
To get the beautiful straight fringe (then with tilt in the tests) indicating that it was possible to generate the mirror surface “equal” to that of the gauge it is necessary that the two curvatures of the tool and for the caliber are precisely equal, or otherwise barely different. This means that to test a flat surface I'll need a reference flat surface, to test a ball I'll need to have a ball as a reference, a parable a parable as a reference and so on. If this does not happen, such as, for example, if we want to test a parabola with a reference surface which is a sphere, I will never see the straight lines, but I see it deformed a certain amount, quantity that must be measured and checked to see if the surface under test is good or not.
Clear that evaluate, also to the eye in a straight line, rather one that must have a precise shape or curvature is far easier, for this generally is used to give the mirror and the tool the same curvature and the same conic constant. Well crap just does not say, and then as you know Massimo, We homebuilders we arrange with all the imagination and we are not lacking…
Also I have not yet made an interferometer worthy of the name, and when I arrange how I like you too…
Regarding the fringes would say they are pretty straight sign that you're doing well (as usual) and that you're not moving far away from the scope…
If you position the surfaces so as to obtain the circular fringes, how do you come out?
What about Massimo, very good sfera..complimenti…
I am happy to see and read that a slight edge retorted may be normal to form in a mirror with a short focal ratio since even in my mirror-caliber formed a slight edge…fiuhh… Ah, forward to the polishing of the convex mirror, I suggest you check immediately with the interference fringes that the two curvatures are not too far apart and to intervene immediately with any corrective action, otherwise (as it has happened to me) the two curves deviate very far in a short time, and now, do I have to lose a great deal to groped to fix the problem…
Classics drawbacks that you learn to deal with the first realizations…
good job…ciao… hello Giulio, thank you so much, I forgot to look in the book of Malacare, it's written all over…
It is true as you say that you have to look at the spacing between the fringes and actually seeing an exponentially smaller and smaller spacing, which means that the distance between the two surfaces increases more and more, but this happens is that the mirror has a greater curvature of’ tool, whether it has a lesser curvature of the tool (at the end of the relative distance it is always the same)…
The only way to understand which of the two situations is present is press on one of the two and see how they move the fringes…I think the answer is well explained on page 7 also with two beautiful drawings…
Now I do not have much time, but after I read it carefully and I understand the question well…Meanwhile, thanks again…
Ciao… Hi everyone, in the short time I have available svuto I began to fix the shape of the tool surface, now finally approaches the ball, although there is still a little hole in the center and the slight edge retorted…
I also continued to mirror polishing, but here is the problem I can not solve.
To verify the shape of the mirror, sufficient to analyze the interference fringes that are created when they mate mirror and tool. Just begun the step of polishing (of entrabi) you saw 6-7 concentriche fringe, but then, continuing the work, the number of these fringes rose gradually up to twenty…This is a sign that the 2 curvature are moving further away, but I can not figure out if I should increase or decrease the curvature of the mirror to approximate the curvature (I tried to continue the polishing with mirror above, with mirror under etc., but the number of fringes seems to me more and increase…bah )…
Ah, by pressing with the finger above the mirror you see the fringes move inwardly…any suggestions?To build and test a convex optical surface is necessary to proceed in a somewhat 'different from how we proceed to realize for example the primary of a newton. The entire process for manufacturing, for reasons of time, no I describe it here, especially since I have already done magnificently in this article Giulio:
In summary then, it will be necessary to give the tool concave surface of the same curvature and conic constant of the mirror that you intend to accomplish, as this will serve as a reference against which will be evaluated that the convex mirror, through interference fringes with an interferometer of the Newtonian type.
This type of interferometer is extremely simple to implement and it will describe the construction later, as soon as I have all the necessary components. The actually fringes can see already putting just under a neon lamp, but it serves a type of monochromatic illumination for not having interference fringes of different colors, for this it is necessary to build the equipment specially. Hi everyone, after finishing the session with grain 80 They moved gradually to the grits 220 400 600 ed 800…And at this point it is time to polishing:
First I made the two full-diameter tools into pitch, one for the mirror, and one for the concave glass, I have to say being able to peck the right hardness at the first attempt ...
During processing just you feel that the glass bites the pitch and forming the white froth cerium oxide and is heard that ssssssss sssssss typical of when things are going the right way ...As stated from the beginning, My intention was to be able to do even polishing machine with full-diameter tools but after a short polishing session, just enough to start pondering the surface, I made the first Ronchi test set noting that the configuration of the machine could not get a nice spherical surface. So I did several tests, but I've never found one that could generate a nice smooth surface. I noticed that it would be necessary to use a smaller tool type 75-85% the diameter in order to obtain a good ball (as I got to experience in working with 400 f4.8).
Anyway I made a good portion of polishing machine and now I am continuing, until the gloss, Hand with classic races 1/3 COC in order to fix the shape and get to the ball.Tomorrow if I have a bit 'of time I hope to post some pictures of the tests.
Hi Massimo, after the hiatus'd say you're off to a…
the windows have already dug, changed the grits and now you're shining, but my camera was you who built scooter… A question: why you have opted for a modified tool star plus at 90% the diameter? how come you have not used the full standard diameter? There are special reasons?
Anyway great job as always, I can not wait to see the evolution of the work…
