How to read the fringes of Newton and correct the convex mirror.

As we saw in This article, a convex secondary mirror cannot generally be tested directly (*) . One of the methods used is to refer to a concave mirror which has the same shape of the surface that we want to achieve on the convex mirror.
Overlapping the two mirrors, the analysis of interference fringes with a Newton Interferometer, will highlight the differences between the two surfaces in examination, that precisely gauge and convex mirror.
We know how to evaluate whether the space between the two surfaces is in turn concave or convex, in other words if the contact points between the two glass panes are at the Centre or at the border and we also know how to quantify the difference between the two surfaces depending on the number of Newton's rings.
We will now analyze in detail all other directions we can deduce from & #8217; analysis of interference fringes and to build an effective method for correcting the surface until you reach the desired shape.

To do this we must have our Newton Interferometer and examine the two glasses , with the premise that in this article we will analyze the interference fringes at them across the “tilt”, namely that the thicker spacers placed between the two glass panes in the edge nearest the observer  . (1)

Fig. 1 – Interference fringes

This simulated image, represents two surfaces next to each other, but they still have a difference of about half a wavelength .

Note that the distance between two successive fringe is lambda/2   and you can evaluate the maximum error of the test surface by tracing a diameter and counting just the fringes ( dark ) intersecting the diameter.


The fringe Sundial   passing through the Center is the one that interests us most, Therefore “eyes her out” from everything else and we examine them independently of other.


Fig. 1 – Analysis of single interference fringe

Let us now try to better define the meaning of this scheme, Bearing in mind that the performance of the fringe is a function of the positioning of the spacer thinner (1)


We arbitrarily chose this fringe, so all the following instructions refer to the center of the mirror, but nothing prevents you from choosing another fringe, all that matters is points of contact with the diameter, If we choose a fringe that intersects the only diameter to the edge, then all our considerations will be equivalent but referred to the edge of the mirror.

Why you should use the bangs passing through the Center are:

  • In a system with two mirrors l & #8217; entire optical design based on radii of the Center, both the primary and the secondary, then hold d & #8217; eye the middle part ( which is the one closest to the source sphere ) without modifying it too, working on the rest of the mirror, need to stay within the limits of its tolerance of the schema, an amendment alters substantially over ROC secondary central project parameters, at the risk of being a subordinate not optimized for project scheme.
  • The convex Center is a very delicate, kneading you “flatten” easily, It's the equivalent of the border to concave, a little mistake in the middle and we'll have to remove the glass from the rest of the surface to correct it.

However there are instances when you cannot refer to the fringe passing through the Center. For example, when all the mirror is convex with respect to caliber. In this situation ( as we shall see ) We'll have to refer to the fringe for crochet border and remove glass from the Middle.


Ideally the mirror split into two sectors, that apart the diameter (compared to our vantage point ) and the previous.   in  “North”, We will have all the “missing glass”, namely that, compared to the caliber, would be added in order to conform to the sample surface:

An edge answered back or a “Buca” (the surface gauge champion ) you will always be in this area. In other words, the convex surface in these areas is “lower” compared to the caliber.


Similarly, the whole area “South” than the diameter, represents the portion of glass to be removed in order to conform to the sample surface. A raised edge or a “Knoll” will always be confined to this area, and the trajectory of the fringe will be unequivocally confined in this area.

things actually can become more complicated, When for example a raised edge or a Hill are located in a part of the surface that is, as a whole, lower than the caliber, then we will have at the same time that we will have to remove and add the glass surface, which is clearly impossible, We will therefore always refer to the largest part of the area that needs corrections and   leave local small defects to finishing touches.


In the diagram we can see how the “South” are reachable from the fringe only if its curvature decreases or, If you prefer, If the mirror in that area you “flatten”. Similarly, to access the North zone, the fringe will inevitably increase its curvature and thus become more “cambered”.
In a convex mirror, removing small amounts of glass from a specified area, all we do is increase the curvature of the internal and external the diminish adjacent neighbourhoods, leaving unchanged the curvature in the middle of the field worked.


Closely linked with the previous deductions are radii of the many areas, that will be smaller or larger than the caliber depending on whether they are in the North or the South, and the upward trend will be determined by the trend or drop radius of curvature in the corresponding point.


These results cisuggeriscono how it is possible to intervene on the convex secondary to construct the final figure:

All secondary processing, It boils down to reach even “coarse” a difference of a few fringe with gauge , then step in with the final touches with extreme precision. At that point we examine the Central fringe and the most “that are high, IE those that are   to “South” reference diameter, trying not to touch areas that are already low compared to the caliber.

In theory from time to time we should build and use a tool whose extension is equal to the work area. In practice we resort to other methods:

  1. a special tool sets to annulus working exclusively some zones ( Central, median and device
  2. one tool to void small diameter that can effectively replace all other utensils in corona.

the first solution, faster processing, easier but less accurate techniques,   is most suitable for the early stages, during the parabolizzazione away from the ball until only four or five rings ( Newton ) difference between the two surfaces. The second solution is slower and more difficult but will allow us to intervene with greater accuracy during the minor adjustments.

We'll see in a future article dedicated entirely to the construction of secondary #8217; & hyperbole ( with manual processing ) How to use these techniques, for now let us dwell upon a particular case, our fringe sample and see how you can align the convex mirror at caliber, that is, how do we make “starboard” the fringe without entering into the merit of the techniques and their execution.



Fig. 3 – correction techniques for a convex mirror


Suppose you have all necessary utensils , We start working the area presenting wider deformation in the area “Remove glass”, so in this case, the area between the 50% and the 60% ( about  ) the diameter.
We can do it with a tool in annulus, or with the sub-diameter, the result is the same whether the techniques will be performed correctly ( as we shall see, the two types of tool to be used differently ).
After some sessions we will see the central part of the fringe shift towards the North. the difficulty lies in the fact that in General to evacuate almost as much glass in the entire treated area, Therefore we will make more “Netherlands” all points within the working area.
The result should be similar to that in Figure.


at this point it is not convenient to insist with the same area, as the Central sector would broaden it too with the edge , should move out and working the periphery , lowering it and by conforming with the middle part.


Now we are in the condition that we mentioned before, where all the mirror is convex with respect to the caliber and the fringe through the middle is all in the area “missing glass”. We will now refer to the fringe that intersects the diameter to the edge, that will be almost similar to this central but translated with respect to it in the area “Remove glass” and, in accordance with our previous considerations, We will work the middle part and median trying not to lower our current reference, that is the edge.

The end result should not be very different from the one in the picture. At that point we will repeat the sequence of processes , starting from the (new) deformation that there seems to be the widest, to get close as possible to the theoretical straight fringe (**).

(1)  If the Interferometer which we can observe in axis with the mirrors and the source, the choice of how to position the spacers   of paper does not matter, by rotating the mirrors doesn't change the number of fringes visible, only changes the direction of the curvature of the fringe , basically if we place the spacer thinner towards us rather than on the opposite side, the figures in the article must be rotated 180 degrees.
If instead, the observer is not aligned with the apparatus but notes with a small corner, the choice to place the spacer thinner in the opposite edge to the observer, offers advantages, makes it possible ( Once you've found the right thickness to display a few fringe ) to decrease the number of fringes visible     rotating mirrors,  while in the opposite case, the fringe would increase by number.
(*) actually   some tests as to Ronchi,   can be carried out directly on the convex surface, looking into the mirror “from behind”. Is to place   the mirror with the flat side toward the light source: in this way the concave and convex surface will be seen as you will be able to analyze, Although only in qualitative form, the trend of surface   as for any convergent mirror. There is, of course, take into account the double refraction of light, from the source   arrives at the flat side, through the thickness of the glass, is reflected in the curved surface, back again crossing the thickness of the glass.
(**)  make perfectly straight fringes, does not mean that the figure is “perfect”, but only we could replicate the caliber in a perfect way, even in its flaws.

Leave a Reply