Building and using the Foucault tester by “the Texereau”


For those who don't know yet; need to apply the Foucault test on an optical surface, parabolic, reflective, under construction, to infer the fixes to be implemented in order to bring it in to a most high quality.

Since in a parabolic mirror, the radius of curvature of the surface constantly increases from the Center to the edge, the test applies on such a mirror under construction, artificially divided by a mask “by Couder” in concentric circular crowns, in whose “zones” We measure the radius of curvature, to control and implement subsequent corrections, so that the resulting Radius progression, are possibly identical with the progeressions of those belonging to a theoretical perfect parabola, taken as constructive reference. Which would mean building a technically perfect optics.

Foucault in practice provide a graph that is the mathematical image of the curve obtained. Which is, (always mathematically) actually “superimposed” to the parable of reference, with a common contact zone of any of the zones taken into consideration,to judge the consequent relative positioning of the other zones, and corrections to be applied.

Other zones may in fact be too "high", (and therefore scratchable with abrasion grit to lower them); or already ok, (do not touch); or too "low", (where we have already exceeded the value of excavating desirable, and to correct "raising" them, yiou need lower all other zones; Or take as a common point of contact, another cheaper zone (if there are).

Based on the evaluation of that chart, the operator decides from time to time which type of correction to be applied.   and in that way, proceeding in correction and test into test, We come to the conclusion of a technically perfect mirror.

That perfection is just a matter of patience and time, because the “n” fixes affect always only one infinitesimal of millionths of a millimetre thick surface glass, such as to never irreversibly affect the previous work. And as for the time, that is also the light of the experience and guile of the operator, It has as a keen amateur a cost equal to zero.


underpinning the Foucault test is homologous to that of the “Star test” (as used in the movie 400F6 building on this blog is taken this brief explanation by John Dobson lasting 3 minutes).

The difference compared to the star test is that the Foucault test is quantitative, i.e. it tell us is where exactly is the error, and how extensive and deep it is; While the star's test is just grossly qualitative , as is the Ronchi test. because it can only show where is the error but, I can't provide the precise quantitative "how much" characteristics useful to draft effectively fix.

Homology between the star test and Foucault is that in optics, the image of a light source (like a star) at distance infinity, it forms at the focal distance of the parabolic mirror.

While the image of a light source placed in the center of curvature of the reflective surface (which is twice the focal length), you would form on itself, and then it would be impossible to use as a guide to building an optical construction, except moving the light source laterally of a little corner, to be able to see the image to the side of the source and at minimum distance from it, as is the case with this type of Foucault tester.

John Dobson was a great minimalist, that in his life he always tried to prove that build a telescope is very easy and affordable for anyone, how effectively would be one star test that requires no tools if the human eye... but conscious and well trained.

The system invented by Foucault is also’ it home made, but requires the tester tool , and another type of eye, I would say minus expert, also because it helps to find a fix for an error, by quantitative data that provide.

The Foucault test requires another type of training, not harder, but the fact that it's a quantitative test and not only qualitative, it makes it less coarse and potentially a carrier of controlled and better quality optics.

To all of us so the choice of the most suitable personally method.


Are almost endless ways of building a Foucault tester, and it can be used for the constructive evaluation of a parabolic mirror potentially of any diameter, but with focal length not less than F5.


1 ) the Foucault test is discouraged on mirrors with focal ratio less than f5 and diameter climbing over 300 mm, because it provides data gradually less correct, creating poor quality mirrors, that will beat up from a quality test as the Roddier. Test not applicable as a guide in progress, but only full telescope.

A minor correctness is due to the fact, that the founding principle of the Foucault test provides that circular crowns (called zones) of a parabolic mirror, reflect the image exactly on the optical axis of the mirror itself.

Which is true for any focal diameter equal to F5 or greater, But why the discrepancy between the optical axis and the real position of the reflection, is so minimal as to be in these cases not measurable, and is therefore neglected.

But for the short focal lengths, the reflection falls on the optical axis only for the central zone of the mirror, While for other zones via via peripherals, the location of the reflection becomes progressively more errata, hand in hand with the decrease of the F-ratio below F5, and with the increase of mirror diameter under construction. And then for these mirrors so “open and so Fast”, whose parabolic curvature is one “Bowl” very deep accentuated, the reflections of the other outlying zones increasingly important, and with increasingly restricted tolerances, fall in spite of this, gradually in increasing distance from the optical axis, along a trumpet-pavillon shaped curve called the "caustic curve".

2 ) Also it should be noted that the exact identification of the center of curvature of the central zone of the mirror, is very important, because that Center is the starting point of all measurements on the next zones, and his error would be added to all the following measures, including the caustic curve error.

In fact, the central zone of a mirror may seem the least inportant, because despite its wider tolerances, and his remaining masked by the shadow of the secondary mirror, its exact Center is also very difficult to pinpoint, because of little deformation present in that area, that means that the Flat-grey color does not show changes, Despite looking for her, we moves significantly in longitudinal way the tester cart, and with this, wronging measurement.

To these difficulties is added also the greatest, coming from the depth of such very open parables, that is incompatible with the use of an auto-leveling tools having diameter equal to the diameter of the mirror; and it is therefore necessary for them to use small diameter tools, which digging only locally, makes it almost impossible to keep the entire curved surface within the entry level quality tolerance, of the famous and very few 68,75 millionths of a millimeter of error between peak and Valley, of the differences with respect to the theoretical parabola taken as constructive reference.

Therefore, these very open mirrors require the use of more technical tests other than Foucault,, such as the Hartmann test,, or the Caustic test, , created in 1936 to make the HALE telescope of Mount Palomar, first large telescope to have a short focal ratio F3 .3, and a diameter of 5 meters.

In light of all this…   Should achieve, that the assessment of acquiring such a "short and fast" telescope, must be made after due consideration. Because of the above problems, also in my experience, I know owners of mirrors F4, of diameters over 300 mm, and of different origins, that in their star tests complain bright diffraction rings into the notch, in the peripheral zones of the mirror in which the curvature of the "bowl" becomes more sensible.


The tester type covered by this, is the most popular and ancient, presenting the light source is independent and separate from the blade of the knife with which they "cut" the reflection of the mirror, in order to figure out if you are in the center of curvature of each reflective area under consideration.

Jean Texereau, presented by this tester a clear Freehand sketch, located in Figure # 54 to page 59 his book "La construction du telescope of amateur" published in 1939, but still valid and free source of practical teaching for “GRATTAVETRO” (Amateur Telescope Macking). ( ).

I thought I'd give the image of that same sketch, an Italian translation of the captions written on it by Texereau, and inserting it below Click to read captions zoomable, and also in the image gallery below this text, to get a better idea of the type of instrument.

In the same gallery I posted pictures with commentary of constituent parts my version, "Orthodox" at the thought of Texereau. Version that has always worked well, Although I have not added a web-cam very useful for sharing results, and especially recommended for less fatigue of the eyes that is obtained by looking at the darkening of shadows on a monitor, rather than directly with the naked eye; being in that case also in a position not the most comfortable and disturbed by diffraction fringes.

((It often happened to me with the desirable and more sensitive fine slits well aligned to the blade,, to see fringes of diffraction that fictitiously replicate the sight of the "cutting edge" of the blade. which, by now, is not detected by the web-cam . So the follow the foucault test at the monitor is more profitable and restful than following it with the naked eye).


Only for those who don't know yet, (others may skip this topic): The tester should be placed at twice the focal length of the mirror in test (that matches the radius of curvature of the reflective surface), on a table in front of the mirror (that dues of the distance often is on another table).

The measuring distance is measured starting from the central recess (Sagitta) of the mirror, to the point where you have to find the blade of the tester, well aligned with the optical axis of the mirror.

To align the Led should light up and remove the slit from in front it, in order to make the LED lightball well traceable, reflected from the mirror in test. Cue ball that, with both mirror movements (tilt adjustable support), that of tester, must be brought to appear on the face of the knife facing the mirror, so that tilting more or less the cart which carries the blade, It can intercept ("cut") completely, and completely free, the cone of light coming from the mirror.

Note 1) I personally have found it convenient to put aligned with carriage movement, a level red Led, that draws a vertical line on the floor – wall and ceiling in front of the tester to center initially the mirror (see last dark picture in Gallery). The level by a few euros, has a magnetic base that I attack the steel plate that acts as a ballast, placed over the carriage, and that is well aligned to the track of the meter.

Note 2) For greater inertia, stability, and easy fine adjustment of the alignment manually, I put the tester on a larger table, that becomes the alone I move. (I have experienced that is a valid system I copied from the video on the realization of 200F6 in this blog).

The slit is then replaced in its place in front of the LED, and then we puts the eye (or a web-Cam) at one point a little further back to where was the "cue ball" Led light, between the source (that must be on our left hand conventionally) and the knife blade (conventionally on our right hand). From that location (and only from that which is already very close to the central RADIUS of curvature)  We will see the mirror fully illumined by the light of the small slit (otherwise, in more distant locations, We will see only the blurred outline of slit light).

Note3: And this total enlightenment happens because we have positioned the tester to a dual focal distance, where exactly is the vertex of the cone of reflection from the center of the mirror in test (zone 1), so it is no longer necessary to move the tester to track down the vertex of the cones of the other zones reflected gradually recede from the first zone, at a value euquals of squared radius of their Center, divided by the radius of curvature R, which is twice the focal length.

By extension of this reasoning, We find that the difference of radiuses that will measure with the meters, is always slightly less than mirror Radius squared, divided by the radius of curvature (double the focal length). And this gives us the distance meter cart needed to complete the assessment of all areas, from the Center to the edge  of our mirror.

Example: For a mirror 200F6 , that has a radius of mirror 100 mm and focal length (200*6)= 1200 mm, and then double-radius of curvature (i.e. 2400mm);

The maximum excursion of the cart will be worth     meterHM ^ 2/R

Where in this case Hm^2 is the square of the radius of the mirror,

While R is the radius twice the focal length (2*1200)= 2400

And the excursion that the tester's cart will have to do, to intercept the light cones of all the zones, will be slightly less than the value obtained using the radius of the mirror, namely:

(100^2)/2400mm = 4.16 mm

While for a hypothetical mirror 500F5 the excursion would be (250^2)/ 5000= 12.5 mm

We note then that a run of 25 mm of the tester cart, and therefore also of the Palmer micrometer used to push the carriage, it would be enough to build very large mirrors.

End of note 3.

We now install the Couder mask in front of the mirror, which will show us pairs of horizontal diametral windows, each pair open on a specific circular crown of the mirror that participates in the formation of the reflecting parabola.

If now screw on the locking screw tilt of the cart that supports the blade Stud top, (tilt or introduction of the blade that is conventionally from right to left), we will see at some point enter the blade in the light cone, and consequently the mirror commences to dimming first in pair of Windows belonging to the central area of the mirror, but the blade's shadow will proceed in three different ways, depending on whether the current position of the tester's carriage is BEFORE, or AFTER, or IN THE CENTER of the radius of curvature of the zone of the mirror in question..

This is because: Knowing that the mirror reflects a cone of light, we can already well imagine that if we introduce the blade by standing with the tester in a point that is BEFORE the vertex of the light cone, (we would say the intrafocus position), We will see the shadow proceed from right to left, that is in according to the movement of the blade. Because with the knife we intercepted light rays, BEFORE they cross each other at the vertex of the cone.

If instead we introduce the blade at a point which is AFTER the vertex of the cone, (We would say the location extrafocus), We will see the shadow proceed as opposed to the real movement of the blade, from left to right, because with the knife we have intercepted the light rays after they have crossed the vertex of the cone.

If finally we introduce the blade in to the point that is the vertex of the cone, We will see the zone evenly darkening concentrically, as would be the case following the closure of a hypothetical circular photographic diaphragm. All without allowing us to appreciate if the shadow came from the right or fron thre left.

The purpose of the Foucault test is to find the vertex of the cone of light (which is the center of the radius of curvature of each zones of the series presented by the Couder mask. See note 4), and measure with a Palmer micrometer the measures called "Drawings", moving only the cart of the tester back and forth, with the push of the micrometer only, and inserting and extracting the blade, without absolutely move the tester from his position… under penalty of cancellation of the entire series of tests.

In practice that exercise is to try turning radii progressive parable, that through the tubes of the many areas, and through appropriate calculations, are transformed into a graphic that shows where the reflector is faulty, and also what is defective in nanometers, allowing corrections that gradually lead to optical perfection.

NOTE 4: Recall that if we let our cleavage – light source, in the center of curvature of the mirror when spherical or slightly dissimilar from the sphere, We will achieve that it will reflect the image of slit on itself, and therefore inaccessible from view.

So Foucault sought to install the source so slightly offset from the Centre, to make the reflection accessible.

In fact, when you install a spring in the center of curvature of a reflective surface, you get the picture out of herself; and this optically speaking is the exact counterpart of the fact that if we install a source at infinity we get his picture in the cast is exactly

And   that slight shift 10 mm are possible today using an Led, that is very small in comparison to that of a car headlight lamp.

For insight we can understand that this shift introduces an error of measurement called astigmatism. But it was already small and is negligible when it was   30-35 mm using the car headlight lamp, It is mostly negligible now with the use of Led.

But the interesting part of this note is with focal lengths for which the Foucault test is eligible. And it is

on the source itself the image of Doing local mind for positioning the Foucault tester, You must arrange in the middle where we have the fact of using a slit poIL   VERTEX of the CONE which is the center of the radius of curvature of each zone of the series presented by Couder mask, and that is achieved by using a point source located in the center of curvature of the reflective area


The building described in this text, is consistent with the work indicated, unless minimal technological variants available today, who were not at the time of the edition of the book.

THE USE OF ONE LED as a light source, rather than a car headlight bulb THE USE OF A PALMER MICROMETER with precision of one hundredth of a millimeter, instead of the use of a threaded bar M6 pitch 1mm, operated with a solid wooden disc whose circumference is covered by a strip of paper with 10 divisions. Which allowed the Texereau to read the tenth of a millimeter ... However, it is already sufficiently precise and useful for this purpose., and.

THE USE OF A PALMER MICROMETER with precision of one hundredth of a millimeter, instead of the use of a threaded bar M6 pitch 1mm, operated with a solid wooden disc whose circumference is covered by a strip of paper with 10 divisions. Which allowed the Texereau to read the tenth of a millimeter … However it is already sufficiently precise and useful for this purpose..

The modern digital micrometers, Palmer type, are today easily purchased for little money, on stalls from used or scrap, due to the frequent breaking of the digital display. But these instruments preserve the mechanical precision part of the micrometer, easily recyclable in the Foucaul tester.

The diameter of a 5 mm commercial Led, reduces down to just 10 mm the distance between the knife blade of Foucault and the slit that serves as a light source of the tester, against the 30 – 35 mm shown in drawing of Texereau. And with 10 mm of wheelbase you work a focal ratio F5 best placed anti-astigmatism, with respect to the use of a bulky lamp like that of a car headlight.


The term "source" is also used in physics to denote a small hole, through which the light radiation, ( that can be dual mode, either in the form of particle photon, than in wave form), presents the phenomenon of diffraction, that happens when the wave behavior of light rises and becomes visible.

The diffraction effects are detectable with the "diffraction notch" formed by a central light dot surrounded by alternately light and dark rings, due to the addition (light) or subtract (dark) of the phases of the light waves passing through the obstacle (small hole ), when the wavelength of the light is comparable with the size of the small hole.) or subtract (dark) of the phases of the light waves passing through the obstacle (small hole), when the wavelength of the light is comparable with the size of the small hole..

A wide slit from 10 until 20 microns, it replaces very well the pinhole of equal diameter, preserving entirely its physical function , but providing the human eye with a much brighter vision with its extension in height of 5m.


In measurements of optical quality, need correct defects on it so that the reflected wave is not damaged for more than a quarter of the wavelength (Lambda/4), of light that the human eye is most sensitive (68,75 millionths of a millimeter) that's why you should use a source at puntiformità, to obtain measured values that will be returned with the computation, in comparison with this reference value, and expressed as the fraction   "Lambda/n", presenting the best optical quality, the higher the denominator n.


A smaller sized Led 5 mm would not be useful because it penalizes pupil average human vision that is unnecessarily wide 5 mm.



  • A base plate of the tester (see picture 1) of 30x20cm in 15mm thick plywood,
  • A cart (see picture 2) of 21x13cm in wood as above, which can perform a 35mm long forward-to-back stroke by sliding on two inverted V shaped skids in contact with the track in brass tube, The carrriage can be inclined with a knob to M6 screw that points on a glass sliding plate, glued with double-sided adhesive on the base of the tester. The knob, by turning the screw, brings the carriage to make an arc, inclining towards the source, in order to intercept the light rays coming from the mirror under examination;
  • ; A 25x25x130mm square-section wooden batten column supports the Foucault blade, fixed with double-sided adhesive tape, on a support plate with only one central screw that allows it to be oriented and aligned perfectly with the image of the slit before each test. The alignment is done by placing a magnifying glass in place of the observer's eye, through which you will see the image of the slit not visible from the naked eye, to which is superimposed the image of the blade to be oriented, so that at his movement, extinguishes in one stroke the whole extension of the slit. The blade of the knife may well be a razor blade, bit is necessary to flatten the cutting edge by rubbing it with a few passes on a glass plate. This because the sharpening of the blades, and of all the blades in general, presents some undulations on the blade seen by profile, which optically are sources of interference and must be rectified).
  • A column as above in square section wooden strip of 25x25x200mm as a support of the Led source and the slit,
  • 2 Two pieces of aluminum angular 40x40x4mm long 60mm for the heads of the sliding track of the trolley, with a hole for mounting the Palmer micrometer.
  • A sliding track of the trolley, consisting of a threaded bar M6 32cm long, covered by a brass tube type for domestic curtains, 29 cm long.
  • A cutout of glass 120x30x4mm on which slide the inclination pin of the trolley, to be glued to the base of the tester with double-sided adhesive tape.
  • And it is’ useful a ballast piece of iron weighing about 1 kg to be fixed over carriage for stability and inertia.
  • Under the cart is a rubber band attached to the other end of the tester base, to ensure continuous traction that keeps to zero the clearance between the trolley and the pushing or pulling Palmer micrometer.
  • On the top of the shaft of the micrometer is fixed with a piece of plastic thermo-shrink tube, a small steel ball that avoids to induce involuntary twisting motion to the chariot during rotation of Palmer.
  • The slit consists of an aluminium plate 5x5 mm with hole diameter 5mm placed in front of the Led, on this plate you can place two half razor blades with sharp previously "rectified" as mentioned above, from a rubbing on a glass, losing the edge (not useful) and gaining an edge from uniform and straight profile.
  • The razor blades (or two half razor blades) they can be fixed with their facing cutting edges in front of the vertical slit, fastened them with double-sided tape, and inserting between them, like adjusting spacer, a piece of magnetic tape from videocassette, (simple for 10 microns, or double folded to 20 microns), obviously to remove once fixed.
  • Modern LEDs brighter are preferred than those dim of the past, Anyway not red color.

I find that the color blue is giving me less hassle of green.

These LEDs typically have a rated voltage of 3 volts, and a current of 20 milliamper (Max 30).

So they are powered easily with a lasting flat battery 4,5 volts, interposing a fixed resistor that adjusts the current (and the brightness) to the desired values coming between 10 and 20 milliamper (0,01 and 0.02 Amper).

The resistor in this case is calculated to make them dissipate the tension of 1,5 volts that exceeds the 3 volts compared to 4,5 of the battery, as follows:

Battery voltage – mains voltage Led = (4,5- 3)= 1,5 volts to be dissipated.

Then with Ohm's law R = V / I (i.e. Resistance [in ohms] = Voltage [in volts] / current I [in Amper])calculating the R = (1,5/0,02) = 75 Ohm.

Wanting to limit the Led brightness, turning it on with 15 milliamper instead of 20, the resistance would become of (1,5/0,015) = 100 Ohm.

In some cases the Led junction, may be visible as a dark spot on the mirror. It is therefore worthwhile to make satin ball Led head, passing over a little abrasive from 500 or 800 "grit".

The following images make for a better idea of the mounting

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