by: Giulio TiberinI

 

The spectrum of the visible electromagnetic radiation, with the wavelengths expressed in nanometers (millionths of a millimeter)

The realization of a parabolic mirror for the telescope is actually an activity in which the unit of measurement most important and decisive for the quality of the instrument and its performance, and it is expressed in "nm", ie the millionth of a millimeter, equivalent to billionth of a meter.

In the grinding or "scratching glass" operations, the reference number of the most important of all is 0.00000006875 m, that is “for friends” 68.75 nanometers high..

Such is the extent of the "MPE", that is, the MINIMUM "machining tolerance" that can present the reflective surface of a parabolic mirror so that it can be considered “as soon as” good, or entry level, expressing the maximum permissible deviation with respect to the values of the precise theoretical parabola taken as a reference for processing.

But why 68.75, and not another number?

The reason is given by the combination of two phenomena linked to the behavior of the human eye, and to the reflection of a mirror:

THE TWO COMPONENTS LIABLES:

1) The human eye, that has its greater sensitivity in the perception of light yellow-green color liyng in the electromagnetic spectrum of white light, . Spectrum which is known to contain the radiation of all the visible colors "rainbow", from red to violet (see wavelenghts in the above image).

This yellow-green light has a wavelength of 550 nanometers high. (0,55 microns).

2) The reflection that we have for the wavefront of the light coming from the observed object with the telescope, Which front first will contacts (incidence), to the face of the mirror:  And if in that contact point on the surface the mirror there are an imperfection with respect to the parable of reference, this would alter the wavefront incident, dommaging it in a value equal to the imperfection encountered.

The same is then immediately reflected wave, and in his passing again on that same imperfection already encountered “in his incomings”, it would be further damaged, for the second time, doubling the amount of the error previously acquired.

Then: An error on the glass creates a double amplitude error in the reflecting wave, and so in telescope vision.

The combination of the two components means that:

Because An error on reflected wave that is equal to one quarter of the yellow-green wavelength , (137.5 nanometers high.) can be detected in the telescope sight…but still acceptable; And sincewe have seen that this error doubles during the reflection: Here it is necessary that the mirror surface is doubly precise, that is at least the eighth of yellow-green wavelenght (68.75 nanometers high.), because in practical use, doubling the error value you will get the famous 137.5 nanometers, or the fourth Lambda (1/8+1/8=1/4, and 68.75 68.75 = 137.5 nanometers high.) that make perceive at the eye the error present, but it is at the "entry level" limit value for the quality of a reflective optics.

Those 68.75 nanometer precision in machining are a very, very small value, but well eye detectable by the simple test of Foucault (that is able to amplify 600 thousand times any error on the reflecting surface).; and yet perfectly accessible and correctable , in the handmade processing .

NOTE: The sensible and curious question that would rise to the assertion that the error what it is “It is visible but still acceptable” is:  But what the eye sees through a telescope with such an acceptable error?

And the answer brings up the wave behavior of light causes, up to an error of the reflecting surface of a quarter of the wavelength (lambda/4), a source point (like a star), high-magnification view with an optical instrument, You will NOT see it as a simple bright dot but you will feel of them one diffraction pattern (see following figure on the left side) formed by a central point that contains the 84% of the light, surrounded by a dark ring and a first clearer outer ring containing the 7% , then by a further dark ring and a second ring still clear outermost containing only the 3% , and so on with other rings always less obvious.

20To give an example indicative, a half-wave error (lambda/2, equal to lambda / 4 on the glass) carried by a reflected light wave, It transfers a sensitive part of’ 84% of light contained in the central area of ​​the diffraction notch dot, the first outer bright ring increases so that its illumination, With the result that the telescope sight, the image instead of being punctiform, It will perceive enlarged in a wider stain, which it extends almost to join the central point with the first light ring (see figure above, On the right side) . And it is this enlargement that clearly demonstrates a loosing of "pin-pointing", and a sure loss of contrast , that is, the cancellation of the fine details of objects, that would have been visible at a high magnification, in a more accurate optic..

Closed NOTE.

MAN VS MACHINE

The following statement would seem a contradiction in our era of widespread and sophisticated automation. But in order to realize a mirrors grinding machine, such precision is necessary to invent this machine "messy" in its repetitiveness, like is messy a man's manual action.

This is curious, but stems from the fact that the realization of a parabolic mirror, for example, diameter 300mm, It is the result of approximatelynear hundred thousand "Past forward – and forth” (..Strokes is "passate" for italians) processing for abrasion of the glass; Each of which removes an infinitesimal part of glass.

Such a long process in terms of time, and very little incisive in unitary glass removal, is more governed by the statistic that not from the precision of a single “stroke” of work.

The amateur astronomer who looks to Do It Yourself, in the first instance is definitely impressed by the amount of manual work in relation of a missor realization, not realizing immediately that those awesome "100000" (strokes) manuals backward and fortward, only then correspond more or less to 28 hours of actual manual labor, (or one hour a day for less than a month).

He is therefore immediately and mistakenly attempting to orient himself towards the realization of a simple machine to shorten a job that is only apparently simple..

But in that case underestimates that a parabolic mirror is not a simple "shaked vegetables"; And the machine that produces a mirror is not a "vegetables mixer", where anyone, simply pressing a button, start the mixer “doing everything by itself”.

It is not technically possible to build or use a machine to complete the complex processing of a decent quality mirror, without previously having traveled and knew very well how to perform that work in MANUAL MODE, accompanied by its inevitable and numerous corrections to be applied to return to that very restricted tolerance of which here you are talking.

In fact, statistically errors of opposite sign committed by man working in a natural way, will self elide them, in a manual processing, acting according to simple rules, that make he remains "more or less" around empirical but resolutory parameters, because TESTED BY TWO CENTURIES of good manual processes.
While an amateur car is not sophisticated or professional, performing thousands of strokes mechanically PRECISES, and "all the same", (that is NOT able to imitate the work within certain "random" limits, of the human work by hand) will only multiply by number the errors in different areas of the mirror, also greatly increasing the severity of certain of them. Where insted manual labor with random strokes would have easily eliminated the one and the other.

It goes without saying that a simple rotating table amateur machine can instead help considerably in the partial phase of the initial hogging a curve and rough grinding of a mirror, which will then be corrected and finished by hand…. AS ONLY BY HAND YOU CAN DO BETTER..

 

Comments (10)

  1. Avatar

    fulvio_

    Finally, I understand where they come out of these blessed 68.75 nanometers high. (lambda/4). Thanks Giulio
    In another forum you wrote (there was talk of metallic mirrors):
    [… precision polished that you have to get on the glass (or on the reflective metal) a mirror, is at least 68.75 millionths of a millimeter peak / valley, just to have a mirror “Lambda/4” which it is the limit “entry level” acceptability… ]
    I would be grateful if you could (you could) explain what is' virtually’ (blank on which you are working) this “distance peak / valley” which must not exceed 68.75 nanometers high.. That, there must be no 'bumps’ compared to a 'theoretical surface’ perfectly smooth larger than this critical threshold?
    Congratulations on your article.

    • Avatar

      Giulio TiberinI

      Exactly Fulvio.
      This because: With the measurement method of Foucault, which it is still the most widely used though nineteenth-century, (but for this doable with an extremely simple tester and with a little training), It examines the parabolic curve fabricated manually, comparing the reflection of some pairs of windows formed in the diametrical “of Couder mask” to verify what their optical focus; and to verify that the progression of the focal circumference of the crowns which they belong windows, is the nearest possible to the progression of the theoretical parabola taken as a reference.
      This does not take into account the entire surface but only a diameter, and it is assumed that those who have done the work it did following a few basic rules that do not allow to make local errors, but ensure that the surface is all very uniform.
      It goes without saying that the draft values ​​measured with the simple tester, who have given us the broken line that approximates the curve measured on our parable (broken segments are made up of as many pairs of Couder mask windows), It will be inserted in a graph between two copies of the reference parabola….How's “ham between two slices of bread”..
      In this way we see materially “How far is it” our broken (prosciutto)the perfect parabola (slices of bread) that we want to achieve, and therefore we're going to correct several times to get as close as possible to perfection.

      Our we are broken then touch a spot on one of two containment parables; and two on the other points.

      The point that touches the parable indicates “peak” place the dish from which to measure the greatest distance from it in our broken, which it is the point of “valle”.
      That on the glass asperities distance must be less than 68,75 nanometers because the light wave coming from the star will be damaged by it a first time in incidence, and a second time reflected emerging, and its accumulated error in the two passages will be 68.75 + 68.75 = 137,5 nanometers which is precisely one quarter of the wavelength “Lambda” of light to which the eye is most sensitive, ie Lambda / 4.
      I hope to not have you confused ideas. But it also asks smoothly.

    • Avatar

      Giulio TiberinI

      Methods most recent measurement, sophisticated and not within the reach dell'astrofilo,no longer indicate the two extremes “peak and valley” relative error, but find a “"Efficace value"” which it is a mean square (RMS) the entire surface.

      The amateur, however, happily does without those precise and modern industrial control methods, and it continues to produce equally mirrors above the commercial quality, even just using the simple TWO COMPLEMENTARY methods of measurement, which are the Ronchi test (which shows the qualitative trend of the entire surface, What that Foucault can not show) and the complementary Foucault (which quantifies the errors and indicate which areas and what should be corrected. What the Ronchi test can not do ).

  2. Avatar

    fulvio_

    I am rereading more times I grasped the meaning of the speech (… although some details escape me. What however not essential since at the moment I have no glass to be tested). What really beyond the understanding of a non 'grattavetri’ It is how it is possible to achieve such precision values (order of nanometers) relying on the large number of past and on the elimination of errors due to chance 'controlled’ the same pass. Are you so, I have written in many different ways and all made mirrors are also irrefutable confirmation. But it is a very difficult concept to assimilate desk.
    Two observations / curiosity: I saw that the points (draft values?) of 'broken’ the graph you posted deviate all excess (or defect not know) compared to the ideal parable. Is’ what happens in practice always, or it can happen that the measures to detect excess deviations And for defect?
    then I did not understand why a deviation of 50 nanometers correspond to a lambda processing / 11.
    He 68.75 nanometers correspond to lambda / 4 we (I think):
    lambda/4 = [550/(68.75+68.75)]
    and then:
    lambda/11 = [550/(25+25)]
    in the case of a deviation of about fifty nanometers (say their 50) It should not be:
    lambda/5.5 =[550/(50+50)]?

  3. massimar

    massimar

    I post in these interesting considerations, to say that the problem of accuracy “nanometrica” of the surface it is longer in its extent than in its realization. Consider the fact that past with pitch tool and cerium oxide have a next zero effectiveness, a single backward and forward movement is able to affect only some of the glass molecule, “to dig” 50 or 60 nanometers is not as straightforward as you might think. We need a good working session with cerium and elbow grease. It would be much more difficult to imagine digging or modify the surface of a millimeter, which involves machining hours.

    Otherwise , optical test ( Foucault in a particular way ) They are subject to personal errors of assessment, therefore the quality of the measurement is subject to the operator's experience and ability, an error on the measurement of the draw of an area of ​​a tenth of a millimeter ( on a radius of curvature of three meters ) It may seem a pittance, but it is equivalent to a substantial deviation from the actual surface profile, that would lead us to intervene by digging a few hundred nanometers glass and then other sessions with cerium, in an attempt to correct a virtual error and at the same time obtain the opposite result, ie, an even more evident departure from the theoretical reference figure.

  4. Avatar

    fulvio_

    Massimar wrote:
    [… Otherwise , optical test ( Foucault in a particular way ) They are subject to personal errors of assessment, therefore the quality of the measurement is subject to the operator's experience and ability… ]

    But then,, 'as a layman',, you will forgive me, but the question arises as to how you can rely on buying a lambda / x . Because if we add to the experience and the skill of the operator a deplorable factor 'malice',, it does not come out. . An account is a 'commercial' mirror ’ ((I think I understand that they are of quality just 'sufficient'’ quality to reduce production costs) ) and the user is aware of this. . But if you throw a bundle of money for a craft or 'industrial' quality mirror ’ of quality ((which I know… Zambuto) ... Zambuto) you want all the lambda. .
    Or maybe those who work 'quality'’ use those more sophisticated measurement methods ((maybe OBJECTIVES) ) that Giulio was talking about? ?
    ((Maybe I'm going OT about the topic of the article.. In case you can ignore / delete the comment by an administrator).).

    • Avatar

      Giulio TiberinI

      Nerd. The companies have at their disposal machines capable of performing interferometric tests that are not as subjective as those of the amateur. .
      But the amateur “experienced” sees ((as well as Foucault and Ronchi)) also by the star test if that mirror has some flaws. . The star test is a kind of Foucault done “on the field”.

  5. Avatar

    Giulio TiberinI

    Your comments Fulvio, are beautiful, timely and interesting..
    I begin by saying the graph with a green background (title “"tautochronism waste on the wave" ... ”… apart from the archaic voice "tautochronism" that optically would mean isocrony in the coming of light to the focus) ): Those 41 nanometers are already in effect the error on the reflected wave, , and which are then already double of the 22,1 nanometer on the glass. .
    But this error on the glass you can see from the blue background chart below the one in question,, taken from this worksheet::
    https://www.grattavetro.it/wp-content/uploads/2014/12/UltimoRitocco-1200×721.jpg

    In this excerpt we see better:
    https://www.grattavetro.it/wp-content/uploads/2014/12/Lambda11-vetro-da-togliere.jpg

    But I would send you the original spreadsheet, , so you could from time to time copy the values of the 17 row of the same checks (17 series of drafts in the gray table below from E65 to j65 down to E83 - – J83 ) in the boxes E,,F,G,H,And the more ,J 12 to see each step relative to the realization, graphics (and correction of errors including).
    If you write me an email to redazione@grattavetro.it I will send it to you.

    As for the accuracy of the test, I agree with the observation made by Massimar; the detections of such small sizes are very subjective and therefore “dancers”. But in substance, When you do some series of measures and see that the values ​​remain between the lambda / 8 and lambda / 10, six mathematically safe to have in hand an ultra exceptional mirror, even if you have the certainty that the lambda you have measured both the real and definitive

    The measures are expressed in defect or in excess by the slope of the graph broken: A line that goes down indicates a curvature radius of that area too large; while a line that conversely salt. This too you will find it on different writings not only my.

    And this rise or fall also says the glass scratcher (that can only “to remove material”), that the areas to be machined to correct the parable (almost always) only those with a broken rising. Otherwise you have to turn down any shape back slightly towards the ball.

    If French is not a problem for you, you get the book for free “the construction of the amateur telescope” chapters or whole and always in .PDF format . I'm 280 pages representing “The bible” the grattavetro. from the site: http://www.astrosurf.com/texereau/

  6. massimar

    massimar

    It Fulvio, like Julius says the “professionals” have other available tools, but here we are talking about is amateur homebrewing which, if done with the right skills, experience and dedication,, can lead to results even higher than the most noble optics, , but in any case it remains an eventuality, , this is not the end goal of the ATM "grattavetri" , which mainly wants to understand, , experiment and create with his own hands ...…

    Is’ equally clear that those who have built over time a name and credibility in the industry, , as the company you mentioned, , certainly did not make mistakes on the measurement of the lambda, , also because we say it clearly, , in a mirror lambda / 8, , if all the rest of the telescope is up to it, , just put your eye to no longer need so many certificates..

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