Figuring a Paraboïdal mirror by thermal predistortion.

Diary of the search for another way of figuring !

Contents table :


In Sky&Telescope February 96 p76-78 was an article that caugth my eyes : refigure your mirror while you observe. Tuning up a mirror electrically, using a potentiometer regulating heat applied to the mirror's back. Mirror correction can be tweaked as nearly perfect as can be judged in the start test. The mirror is one with internal stresses showing seasonal variations, but others should also be curable. From then on I knew heat could be used, but I hated using heat while observing.

Coup-de-foudre (flash of lightning)

Spring 1998 I fell upon a little french booklet : " L'OPTIQUE ASTRONOMIQUE " of Jean Terrien out of 1954. It is part of a well-known serie in french : " que sais-je ?". On page 14 is mentioned that André Couder at the Observatory of Paris parabolized a mirror of 80cm diameter by applying heat with an  electric resistor at the back of the spherical mirror and while it being thermally  warped polishing it spherically !
On page 72 is also mentioned that the 1.93 m mirror of the "Observatoire de Haute-Provence" was polished by Couder in the same way to the diffraction limit.
On the same page on a foot-note is mentioned that Couder used an electric heating procedure in order to make the temperature in a cooling mirror uniform so keeping it's form correct.
That's was it, nothing more, no references and me not sleeping for a couple of nights thinking about it.

Finding a clue

Being a bit addicted to internet-searching I spent desperately several nights on it, but no sign of it. Accidentally browsing Texereau's "How to Make a Telescope" Appendix D featuring a list of the subject that have appeared in "Gleaning for ATM's" of "Sky & Telescope" since November 1941 to December 1983,  I fell upon :  1956 Nov 32 Figuring a Parabolic Mirror by Thermal Deformation, R.E.C. !!!
Instead of sleeping better I was figuring out how I could obtain a copy of   that.

Getting closer

Being a member of a local e-mail list of the Belgian Association of Astronomy I asked help obtaining this article and Tony Dethier promptly answered and asked for my address,  sending it immediately  to me ! I can still remember the thrill when opening the envelope with one copied page !

Finally a method

The Sky&Telescope article was a summary of a translation and referenced to : "Comptes Rendus de l'Academie de Sciences, 235, 491, 1952" featuring a description by Couder !

Figuring a parabolic mirror by thermal deformation

As is well known during a clear night falling temperature causes a parabolic telescope mirror to become slightly overcorrected. Couder noted that this condition can be cured by gentle localized heating of the mirror. This suggested to him the possibility of deforming a spherical mirror before figuring,   so that the action of the tool would lead direcly to a paraboloid. The method was used at Paris to figure a 47-inch f/6 mirror. At the commencement of the work the mirror was nearly spherical. The mirror was then heated in such a way that the deformation of its surface was equal but opposite to the correction desired. One resistance heater, of 28.7 watts, covered a zone at the back of the mirror whose inside and outside radii were 18.5" and 22.8". A second heater dissipating 12 watts, was wound along a groove cut in the edge of the disk at the middle of it's 7.1" thickness. Heating was begun about one hour before starting work, during the pressing of the tool.
Figuring lasted about four hours. Tests following the first three stages of polishing showed ellipsoidal shapes of increasing eccentricity, with a tendency toward the formation of a central depression which Couder counteracted by trimming down the central portion of the tool. The fourth test showed that the surface deviated from a true paraboloid by only 1/6 fringe, the extreme edge being slightly raised. When Couder figured an identical mirror by classical methods in 1931, he needed 28 figuring steps to obtain the same results.

I could sleep better now, but was wondering if the referenced article said more.  But I did have some practical information, the principle being simple but practical realisation seemed not. But I kept being optimistic.

Getting to the source

I did know that the library of the Royal Observatory of Belgium in Ukkel near Brussels is one of the best sources for old works. A friend of mine August Devos, also an ATM, could from time to time ask a local professional Jan Cuypers, related to the Royal Observatory to look something up in the library and copy and send it to him. I contacted also Jan Cuypers explaining my reason for sleepless nights and he too promptly helped me. I couldn't believe my eyes a couple of days later having this article out of 1952 in my hands ! It was only 2 pages long and the summary in S&T appeared to be a good one.  The general procedure was the same, but there were some smaller interesting statements :

  • a reference to an article in Comptes Rendus of 6 december 1950 about the use of a heating element in order to counteract the effect of a mirror cooling down. Putting more energy into it, it's possible to warm up a paraboloid  to a sphere with a sufficient degree of uniformity and precision.
  • the method is compared with the method of B. Schmidt for making a Schmidt corrector-plate by mechanical deformation while polishing. In this method of Schmidt the effect is just the reverse of what we need and it can only be used for very thin plates using vacuum says Couder. He concludes it's only practical  to use thermal  deformations for parabolizing a  thick rigid disk  by  polishing a sphere into a predeformed sphere.
  • Half-time for reaching a thermal equilibrum state was about 40 minutes for this diameter 120 cm 18cm thick disk.
  • The final test was a Hartmann test giving 1/6 fringe deviation of a paraboloid, only the extrem edge was raised.
  • Couder says he could have easily retouced locally, but did not as local retouching gives raise to fine structures diffusing light and the residual error less than the Rayleigh-limit is of opposite sign of the normally observed effect of a mirror cooling down.

If this was not interesting enough to try out I'm not an ATM anymore !

Back to the roots

On may 9th 1998 there was the ATT in Essen (Germany) , one of the biggest astro-meetings in Europe. There I bought the book : "Fernrohre und ihre Meister" by Riekher, because I noticed there was some material in it about Couder. And indeed Couders technique of using heat was described for restoring unwanted mirror deformation by the cooling down of the mirror. The method was applied to a 81cm and 120cm mirror around 1950. The cooling down process makes the mirror colder at the front and at the edges where material is shrinking. This causes a shortening of focal length, but far more harmfull the edges are curling down because the cooling process is also taking place at the edges. By applying a bit of heat this overcorrection can be suppressed, but when applying too much heat overcorrection results.
The reference list mentions :  "Couder, A.:  Thermal distortions of telescope mirrors and their correction. Vistas in Astronomy Bd.I (Ed. by A. Beer) 1955   London and New York pp.372-376" and " Couder, A.: Sur les phenomènes thermiques nuisibles dans les telelscopes a reflexion. Trans. of the Intern. Astron. Union Bd8 (1952) pp 741-746". 

A simple e-mail to Jan Cuypers of the Royal Observatory and the next week I had all three articles in my hands !!

Evidence images !

The 1950 article out of Comptes Rendus confirms the experiments of healing the cooling effects of a 81cm disk, 7.6 cm thick. The edge effect is a kind of spherical aberration : overcorrection 3 times the Rayleigh limit, a hyperboidal form, besides the change in focal length. The heating procudure needs 3 W and for every Watt there's a change of 0.81mm longitudinal aberration of the outer rays. 25W produced an enormous but very regular undercorrection. Half time of the process healing the cooling-down effect was only 8 minutes. The mirror is constantly losing 22W during a night, so a surplus 3W was not sensibly detoriating the images by convection. Much more visible was the amelioration of the images by the disappeared turned down edge ! Solar coelostats are much more detoriated than a normal cooling-down mirror,  so they could benefit a lot of a appropriate heating system at the back.

The 1952 article out of Trans. of the Intern. Astron. Union is dealing with studies for the installation of the 193cm telescope at the "Observatorie de Haute Provence". A first section is dealing with thermal gradients in the surrounding air and the second the thermal mirror-deformations and their corrrection and that this correction can be turned into a help for executing a paraboloid out of a sphere. This second section is almost a copy of the 1950 article described just above, concluding that every mirror could with positive results be provided with such a heating corrector providing there's space available between the supporting systems for the heating element. It's not possible to foresee how much energy is needed for a given disk, but time constants are related to the thickness of the mirror to the second power.
The section about using the heating for producing paraboloids is almost a copy of   the article out of 1952 in Comptes Rendus. However  there's a written account of the discussion afterwards. A first question was about using the heating method for producing Schmidt corrector plates. Couder answered that the Schmidt method with vacuum did not have a time constant of reaction and was much more easier for this type of surfaces. A paraboloid could be produced out of a sphere with the Schmidt method, but by applying pressure at the back-side and holding uniformly  the disk at the edges, which is not easy not using the frontal surface. Not to talk about the necessary force for such disks having a thickness sufficient to be rigid enough. The thermal and pressure method do have a different application field.
Another question was about the practical realisation of heating a disk on the polishing table. Couder describes in detail how it was done : a plastic crown being wound with a thread of constatan of 0.3 mm is put under  the disk directly in contact. Only a sheet of plastic is between it in order to avoid polishing water from reaching the thread. The whole  is thermally isolated from the polshing table, being of metal it can not absorb the produced heat, perhaps creating local gradients due to the   reinforcing ribs in the polishing table. Couder advised also rotating the disk a 1/4 to 1/3 turn, not only prevening astigmatism due to the support but also due to   irregularities in the heating element.
Upon a question Couder is saying that the first application of the heating element besides turning up cooling down edges was the application to solar mirrors and only afterwards producing paraboloids.

A real eye-opener was the article out of 1955 in Vistas in Astronomy. Before I did actually receive the article of Jan Cuypers, Peter Abrahams of the ATM e-mail list did send me a summary of it, saying there were foucaultgrams in it. That was what me made asking the articles to Jan ! The article itself was more or less a translation of former articles. Although some interesting notes :

  • The use of glass instead of bronze for mirrors did make mirrors more rigid, as glass is lighter and stronger. Otherwise glass does not come so quickly to thermal equilibrium as bronze did . So a new problem appeared and up to now it was only partially solved by better kinds of glass, partial isolation of the mirror and forced ventilation. All methods being passive, the heating method is an active one and can be easily tuned.
  • Along with the practical description of the application of the heating element is a drawing !
  • The presence of the supporting points at the edge of the back-side prevent the heating element being applicated up to the edge, causing a narrow turned down edge.
  • Photo's of the foucault-image are showing the mirror in it's normal condition of cooling down : overcorrected. The second when 3W of heat is applied showing good overall correction and the third is showing the over-correction   by applying 25W , comparable in size to that of a spherical mirror. It was this observation that made Couder think of using heat for figuring parabolic or more general aspheric surfaces.
  • Natural variations are much slower than the effects of articial heating and adjustment is easy, excellent correction can be obtained in about a quarter of an hour.
  • The 120cm has been fitted with such a heating arrangement, but also a wire around the edge where there's a groove. Only 10w are needed.
  • There are plans for installing a thermal corrector into the 193cm under construction at  that time.
  • For solar mirrors the heating element could be automated depending on the solar height, state of the sky, state of the surface and the incident angle. Only some Watts would be necessary !
  • besides the former articles, there's a reference to " sur un effet thermique observé dans les télescopes à réflexion", L' Astronomie,63, 253, in 1949 and also to the thesis of Couder out of 1931 referenced   also in Texereau.


Modern application of heat !


In the Proceeding of ICO-16 Satellite Conference on Active and Adaptive Optics on page 301 :" New principle of mirror correction for adaptive optics" . In a first method the use of a laser to deform locally the mirror surface is suggested, but also a more general warming up of the mirror back surface causing a temperature gradient in the disk, giving way to a change in the radius of curvature. However the use in astronomical telescopes is not mentioned.

Playing with a hair-dryer.

In my garage I set up a Ronchi-test on a 11 cm   f/8 apparently made of some plate glass regarding the greenish color of the stuff. I could see with the Ronchi grating before focus very gently curved lines to the outside with the outer edges strongly curving outwards : sign of an attempt of the producer to near a paraboloïd (deepend center) but with turned down edges. I placed 4 lines on the mirror symmetrically.
I then warmed the inner 8.5 cm of the 11 cm disk for about 10s with a hair-dryer of 1200W. I needed about 10 s to reinstall me and have a look at the mirror. I did also an experiment with the addition of a central disk of 6cm diameter and with longer warming up times. All these experiments revealed to me a shortening focal distance and change in the curvature of the lines. I was even able to create  a zonal depression by warming up a ring. When warming up was not done symmetrically, the lines were severly warped. In fact it was clear  to me you can easily let a mirror curl up by applying some heat to the back but it was mostly big fun realizing how sensitive the mirror is. Warming up with a hair-dryer seemed to me not the best way of applying heat so I decided to look for other ways.

Don't break that glass !

Having contact with Luc Arnold for another project of mine I asked him about the method used by Couder. He didn't know it, but knew years ago one did use a device on the 80cm at OHP to counteract turned down edge by falling temperatures. Unfortunately someone put once the normal electricity power to the device instead of the 12V resource and the mirror DID break ! Upon that Texereau made a new one, but the system is not used anymore. He did even contact Jean Texereau to look for related publications but did not find anything new. Nevertheless he did find it intesting himself busy with a 150cm, 22mm thick ordinary glass disk on an active support. I was warned : by warming up a disk too much you can break it.

Looking for a heat source.

I went on for searching a heating system using a resistor and controlling the voltage I put on it. A system suggested by someone using a kind of rope for preventing waterinstallations from freezing was not usable being not enough flexible to make a circle of it. It had also a resistance dependent of temperature and did cost too much. Then I fell upon a old electric curtain at my parents ! I was very sweet for one evening removing the resistor out of it and started playing with it and   calculating how much warmth I could extract out of it related to it's length and the applied voltage. It could be done and it didn't cost anything just some work.

Visiting the place of crime.

In summer 1998 we happened  to be on holidays not so far from OHP in Southern France and I arranged to visit Luc Arnold at OHP to have a look behind the curtains ! It was a marvellous experience and I did visit the dome of the old 80cm !!! It was a sacrified moment realizing this was the instrument I was reading about so much. I imagined it could talk to me, saying well there you are, but it kept silence in it's dome.

ohp80cm.jpg (39156 bytes)


Back to before.

Accidentally I did reread the Sky&Telescope February 96 p76-78 article and did find some new facts by having studied all the above material. For instance the author remarks finding it astonishing his mirror goes through the fase of paraboloïd while changing it's form. He also observes two fases in the changing : first the mirror reacts quickly, but suddenly comes back and  needs more heat to stay where it was, due to the fact that heat is going throught the disk and expanding the upper face also. By applying extra heat one can create a temperature gradient that is stable. He also suggest applying an ellipsoïdal resistor  to the back for curing astigmatism.

Heating or cooling ?

Another idea that can be interesting is to use cooling instead of heating.  Up to now I was thinking about applying heat at the back side so that the edges are curling up as Couder did use.But by cooling the back-side at the middle, the center of the disk would raise and can be polished down with less material removal than at the edges,  the center also being less critical and having less surface ! Yet another way of figuring is to attack the middle and the edges of the mirror being difficult with normal techniques. But perhaps we can heat the mirror at a ring so that both edges and middle are raised a bit. Or we could warm a bit the edges and cool a bit the middle to produce the same effect. This technique gives raise to minimal material removal but seems difficult to control. Drawbacks of cooling is that you can not control it as easily as applying heat and when using it in real-time on-site at the telescope it can cause dew !