Introduction to Foucault


Foucault is a program to help mirror makers to make good mirrors using the Foucault method.

Foucault is designed to help mirror makers compute all the data in the standard data sheet used in the "How to make a telescope" by Jean Texereau.

All these results are displayed in a test data sheet. It gives the characteristics of the mirror shape and other things such as the depth of glass you have to remove in each zone in order to parabolize the mirror correctly. It is also a means to estimate the quality of the images that will be given by the future telescope.

All the mirror maker has to do is to type the general characteristics of his (or her) mirror.

-> Foucault computes the Hm, Hm2/R and Hm/4f.

->All of this is needed just for the first time and can be saved in a file ( one by mirror).

Then, when testing the mirror with the Foucault test apparatus, type the measurements taken for each zone.

==> Foucault computes the standard parameters of the mirror and draws a graph with a curve representing the general shape of the mirror :it show the depth of glass you need to remove in each zone.

The HistoryList Mode :

Foucault's important feature is its database containing all the measurements taken by the mirror maker on one file per mirror. By this way, the different steps of polishing are kept in the computer. The mirror maker can thus understand better the effect of one peculiar type of stroke on the shape of the mirror. Pieces of information such as the type of stroke, of pitch, how long the polishing worked lasted, etc. can be added by the mirror maker to each set of measurements.

Besides, you can print test data sheets either in the HistoryList mode or in the Calculate mode, already filled or blank for future use. They can be useful to write down your measurements when testing your mirror.


These are the menus of the program:

The Foucault Method

This a summary of the Foucault method to test mirrors.

The Foucault Method to test mirrors is very simple, gives understandable results , and needs less calculations (for standard results).

It will be made in the next version of the help

See the Bibliography if you want to know more about it.

Creating a New File

To create a new file (that will contain all the data about your mirror )

1) Choose New from the File menu. You will have this Dialog Box:

2) Then type the name of the file, the extension will be automatically .mir.

3) After you click OK, you will have this dialog box :

This New Mirror window must be filled completely with all the data describing your mirror :

1) Click the Choose Filename button if you want to change the name of the file.

As a default the extension is .mir.

2) Click the Moving Light check box if you're using a Foucault test apparatus that has a light moving at the same time as the knife.

3) Enter a title (optional). The title can be a brief description of the mirror, or the telescope that it is part of. It will be printed at the top of the document.

4) In the Glass field, enter the type of glass of the mirror, for example Duran 50 or Pyrex.

5) Pressing the tab key or clicking on the boxes, move to the Diameter box and enter the diameter of your mirror, in millimeters.

6) Pressing the tab key, move to the Curvature box and type the radius of curvature of your mirror, in millimeters.

7) Then move to the Radius of Hole box and type the radius of the central hole (if there is one,0 for none) in millimeters.

For typing the parameters of the Couder Screen it is possible to:

* Typing its directly:

- In the Field NB_Zones, type the number of zones of your Couder Screen( between 3 and 10).

- In the field Hx#1, enter the extrem radius of the zone #1, in millimeters.Then do the same with all the other Hx.

* Or ,ask to the computer to calc the parameters: press Suggesting_the_parameters:

Now , you neeed to chooses bteween 3 criteria:

-Number of millimeters of (tirage) by zones: default 1 mm by zones ; if you don't know what to do just press Calc.

-Number of zones: depending of the polisher experience , it is possible to specifie the number of zones ( between 3 and 10) .

-Min Cell Size: You can specifie the min cell size in millimeters for practicals reasons.

It is sugested to make several try and eventually change manually the resultings parameters.

8) Press OK, a minimal test data sheet will be displayed:

Now the file can be saved, by choosing Save from the File menu.

To go on, you have to type the different measurements you will make when testing your mirror with the Foucault test apparatus. Then Foucault will calculate the results.

Adding Measures

To add measures, choose Add Measure from the Calculate menu.

You can change the date of the measure (default is Now) by clicking At and then fill in the date.

Choose the Calculate button, then Foucault calculates the results and displays the test data sheet :

The main result is the line of LF/RO that gives for each zone the radius of the circle of the focus divided by the radius of the diffraction disk So if the LF/RO is less than 1 its means that all the light of this zone goes into the diffraction disk. For the observer, there is no better criterion on the quality of his mirror : it assures him (or her) that all the light will be contained in the diffraction disk!

Experimentally, we can stop polishing the mirror when the LF/RO maximum is less than 0.3.

An other interesting result is the curve named glass depth, it tells you what you need to polish in each zone compared to the perfect parabola wich is represented by a horizontal line.

For example, with this glass depth:

you should deepen the center by polishing in the following way : strokes with an amplitude of 1/2 of the disk diameter, during 20 min, using a lap with a tough pitch,with the mirror on the lap.

Then you could add a work like this:

The works can be useful to remember the effect of the last strokes, for instance.

To polish, you just need the intermediate work and intermediate results, go to the HistoryList mode.

HistoryList Mode

From the View menu choose HistoryList. The window looks like this:

The window shows the different measurements taken at different steps of polishing. By this way, you can take advantage of your previous work to know how to polish. You can also add measurements by hand and write them down on empty forms printed in advance. You will enter them later in the computer.





écran à échancrures

Couder screen or
Zonal Mask

Pantalla de Couder

donner la forme

to Figure


longueur focale

Focal length

distancia focal

rapport F/D

Focal ratio

razon F/D

méthode de Foucault

Foucault method

Método de Foucault

test de Foucault

Foucault test

prueba de Foucault, prueba de la navaja.

appareil de Foucault, foucaultmètre

Foucault test apparatus

Aparato de Foucault





Knife-edge test

prueba de la navaja



herramienta pulidora

taille de miroir

Mirror making

Tallador, fabricante de espejos

diamètre optique

Optical diameter

Diámetro óptico

surface optique

Optical surface

Superficie óptica





to Parabolize





poix à polir






rayon de courbure

Radius of curvature

Radio de curvatura




aberration de sphéricité

Spherical aberration

aberración esférica




bulletin de contrôle

Test data sheet

hoja de control





Build your own telescope by Richard Berry, Willman-Bell Inc., 1994, 2nd edition.The reference book in USA, lot of map and photograph, in english.

Construction du Télescope d'amateur by Jean Texereau, Société Astronomique de France, Paris, 1961, 2nd edition(difficile à trouver..).The bible of the ATMaker, lot of informations but a little bit old.

or the english version :

How to Make a Telescope by Jean Texereau, Willmann-Bell Inc. ed., Richmond VA USA, 1984, 2nd ed.More actual than the french version.

Lunettes et Télescopes by Danjon et Couder, édition Blanche , Paris, 1990.Very nice to know and calculate all the optical systems,but a little bit to old now.

Mon télescope, mon observatoire, Pourquoi pas? by pierre Bourge et Jean-Marc Becker.2nd edition 1985.For starting to make a telescope.

Observations et travaux Nb 10 et 11, Société Astronomique de France, Paris, 1987.Some papers on polishings workshop and Foucault testing.

Réalisez votre télescope by Jean-Marc Lecleire, éditions Jean-Marc Lecleire, le Plessis Robinson, 1997, 1ère éd.Nice book for advanced users,difficult for starters.

Realisez vous même votre télescope, by Michel Lyonnet du Moutier,2nd edition Eyrolles 1983.A other starting book .

Join us

Send a mail to the Autor: Etienne de Foras

Go to the web site of the Autor: Etienne de Foras's Web Page

Go to the Web site of the Atelier d'optique de la SAF

Go to the Web site of the Société Astronomique de France

Thanks to you without anything should be possible..

Claire Bigot : The english documentation.

Ramiro Hernandez :The spanish documentation.

Jean-Jacques Jourdanneau : The debugging.

Gauthier Philippon : Who taught me how to polish a mirror .

MR Lefrancois et Gilbert Morain : The spanish version of Foucault.exe.

And all the members of the atelier of the Sorbonne...