WHAT YOU NEED A FOUCAULT TESTER:
For those who still do not know; It serves to apply the Foucault test on an optical surface, parabolica, reflective, under construction, to infer the fixes to be implemented in order to bring it in to a most high quality.
Given that in a parabolic mirror, the radius of curvature of the surface constantly increases from the center to the edge, the test is applied on such a mirror under construction, notionally divided by a mask “by Couder” in concentric annuli, in whose “zones” measuring the radius of curvature, to control and apply subsequent corrections, so that the resulting Radius progression, are possibly identical with the progeressions of those belonging to a theoretical perfect parabola, taken as a constructive reference. That would mean build a technically perfect optical.
Foucault in practice provide a graph that is the mathematical image of the curve obtained. Which is, (always mathematically) Really “superimposed” to the parable of reference, with a common contact zone of any of the zones taken into consideration, for judging the resulting relative positioning of the other zones, and corrections to apply.
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 it has already exceeded the value of desirable excavation, and to correct "raising" them, you 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 is the type of correction to be applied. And that way, proceeding correction in correction and test in test, It arrives at the conclusion of the processing with the realization of a technically perfect mirror.
That perfection is only a matter of patience and time, the fact that “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 what about the time, which it is also the basis of experience and cunning of the operator, it has, as an amateur enthusiast, a cost equal to zero.
THE SCIENTIFIC PRINCIPLE
on which is based the Foucault test is homologous to that of “Star test” (for example used in the movie of the 400F6 present construction in this blog from which it is this very brief explanation 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 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.
The homology between the star test and Foucault is that in opticals, the image of a light source (like a star) at distance infinity, are formed 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 it is twice the focal distance), It would be formed 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 it happens with this type of Foucault tester.
John Dobson was a great minimalist, that in his life he always wanted to prove that building a telescope is very easy and affordable for everyone, 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, helped to find the correction of an error from the quantitative data that the test provides.
The Foucault test requires another kind of training that is not difficult, and the fact that it is a quantitative and not just a qualitative test, it makes it less coarse and potentially the bearer of better quality optics.
We all therefore have the choice of which method is the most suitable: Star test or Foucault.
TYPE OF TESTER AND TECHNICAL LIMITATIONS OF THE FOUCAULT TEST
They are almost endless construction mode of a Foucault tester, and it can be used for the constructive evaluation of a parabolic mirror potentially of any diameter, However with a focal length of not less than F5.
UNDER WHAT CIRCUMSTANCES’ IT IS NON RECOMMANDED:
1 ) the Foucault test is discouraged on mirrors with focal ratio less than f5 and diameter climbing over 300 mm, because it provides data as less correct, creating poor quality mirrors, that will come out battered for example, from a quality test as the Roddier . test, that however is not applicable as a guide during processing, but only on a full telescope.
The lower accuracy is due to the fact, that the foundation principle of the Foucault test establishes that annuli (called zones) of a parabolic mirror, reflect the image exactly on the optical axis of the mirror.
Which is true for any focal diameter equal to F5 or greater, But only because 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 it is therefore neglected.
While, on the other hand, for short focal lengths the reflection falls on the optical axis only for the central area of the mirror, While for the other zones more and more peripherals, the location of the reflection becomes progressively more and more errata, hand in hand with the decrease of the F-ratio below F5, and with the increase of the diameter of the mirror under construction. And then for these mirrors so “open and so Fast”, whose parabolic curvature is one “bowl” very accentuated deep , the reflections of the other peripheral areas increasingly important because with increasingly restricted tolerances, fall, in spite of this,, gradually increasing in 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, it is very important, because that Center is the starting point of all measurements on the next zones, and an error on this staring point will be added to all the following measures, including the error of the caustic curve.
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 identify with precision, because of this little deformation in that area, that means that the Flat-grey shadow color does not show changes, despite looking for it, 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 error millionths of a millimeter 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 very short focal ratio F3.3, and a diameter of 5 meters.
In light of all this… It should achieve, that the assessment of acquiring such a "short and fast" telescope, It must be made after due consideration. because of the above problems, also in my experience, I know owners of mirrors F4, diameters of over 300mm, they see and complain in their star-tests, bright rings in the diffraction notch in the peripheral areas of the mirror in which the curvature of the "bowl" becomes steeper and more sensitive. Lighting rings that are always the sign of non-uniform parabolic reflective surface, which could also be due to a momentary difference in the local temperature of the mirror during acclimatization; but which generally persisting are a sign of bad processing, made so by the inevitable use of small diameter tools.
FEATURES OF THIS TYPE OF METER:
The tester type covered by this text, It is the most popular and ancient, that presents the independent light source and separated from the blade of the knife with which "cuts" the reflection of the mirror, in order to understand if there is or not in the center of curvature of each reflecting zone under examination.
Jean Texereau, presented by this tester, in a clear Freehand sketch, located in the image # 54 on page 59 of his book "La construction du telescope of amateur" published in 1939, but still valid and free practical teaching source for today “GRATTAVETRO” (Amateur Telescope Macking). (http://www.astrosurf.com/texereau/ ).
I thought to give the image of that sketch, an Italian translation of captions written on it to punch the Texereau, and enter it here below be enlarged with a click to read captions, and also in the gallery at the bottom of this text, to give a better idea of the type of instrument.
In the same gallery I included the annotated images of the constituent pieces 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 advisable above all for the lesser tiredness of the eyes that is obtained by watching the darkening of the 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).
HOW MUST WORK A FOUCAULT TESTER.
For those who still do not know, (others may skip this topic): The tester should be placed at twice the focal length of the mirror in test (which corresponds to the radius of curvature of the reflecting 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) mirror, to the point where you have to find the meter blade, 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. Sharik that, with both movements of the mirror (on adjustable support also in inclination), that the tester, It must be brought to appear on the face of the knife blade facing the mirror, in such a way that more or less tilting the cart which carries the blade, it can intercept ("to cut") completely, and liberate completely, the cone of light coming from the mirror.
Note 1) Personally I found it convenient to put in line with the movement of the carriage, a level red Led, drawing a vertical line on the floor - wall and ceiling in front of the tester to center the mirror first (see last dark picture in Gallery). The level by a few euros, It possesses a magnetic base that I attack on the steel plate that acts as a ballast, placed over the carriage, and which is well aligned to the tester binary.
Note 2) To have greater inertia, stability, and ease of alignment fine tuning 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).
He then puts the slit in place before 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 position (and only from that which is already very close to the central radius of curvature) We see the mirror totally illuminated by the light of the small slit (otherwise, in more distant positions, we will see bright only the blurred outline of the slit).
NOTA3: 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 it is twice the focal.
By extension of this argument, We find that the difference of radiuses that will measure with the meters, It is always slightly less than the mirror Radius square, divided by the radius of curvature (twice the focal length), as the mirror radius is the maximum limit of our measurements, while in practice we will measure drawdowns of zones whose center falls on a smaller radius than the maximum of the soecchio. And this gave us provides the travel distance of the carriage of the tester required to complete the evaluation of all areas, from center to edge of our mirror.
Example: For a mirror 200F6 , that has a radius of mirror 100 mm and focal length (200*6)=1200mm, and then double curvature radius (ie 2400mm);
The maximum travel of the carriage of the tester will be worthHm ^ 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)=2400mm
And the excursion that the tester's cart will have to do, to intercept the light cones of all the zones, It will be slightly lower than the value obtained using the mirror radius, namely:
(100^2)/2400mm = 4,16mm
while for a hypothetical mirror 500F5 the excursion would be (250^2)/ 5000=12,5mm
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 NOTE3.
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 we avvitiamo the inclination of the carriage screw that on top of the column supports the blade, (inclination or introduction of the blade which conventionally takes place from right to left), we will see at some point enter the blade in the light cone, and consequently the mirror principiare to darken in the first pair of windows belonging to the central area of the mirror, ma 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 because: Knowing that the mirror reflects a cone of light, we can already well imagine that if we introduce the blade with the tester in a point of the cone that is BEFORE THE VERTEX OF THE CONE, (we would say in an intrafocal position), we'll see the shadow proceeding 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, on the other hand, we introduce the blade in a point that lies BEYOND 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, and come 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, absolutely not the slightest move the meter from its position… worth the annulment of the entire series of tests.
In practice that exercise is to look for progressive radii of curvature of the parabola, that through the flues of the various zones, and through appropriate calculations, They turn into a graph showing WHERE the bulb is faulty, and also AS it is defective in nanometers, allowing the corrections that gradually lead to optic perfection.
NOTE 4: Recall that if we we place our slit – light source, in the center of curvature of a spherical mirror at the moment or a little dissimilar from the sphere, we will obtain that it will reflect the image of the slit on itself, and therefore inaccessible to the eye.
So Foucault decided to install the source so slightly shifted from the center, to make the reflection accessible.
In fact when you install a source in the center of curvature of a reflective surface, you get the picture of herself; and this optically speaking is the exact counterpart of the fact that if we install a source indefinitely we will get its image exactly in focus.
And that slight shift today is further reduced to around 10mm using a LED, which has a very small diameter compared to that of a car headlight lamp used by the Texereau.
For intuition can understand that this shift introduces a measurement error called astigmatism. But it was already undetectable in size, and therefore negligible when it was 30-35mm, due to the use of a car headlight lamp, while today it is even more negligible with the use of the small LED.
Is’ It is interesting to underline that negligence is valid for lenses with focal ratio equal to or greater than F5, for which the Foucault test is suitable. While for shorter focal lengths, the separation distance of the source from the knife blade, could introduce astigmatism, forcing the use of a tester “Slitless” that is, with the blade of the knife in axis with the slit, which requires special training.
THIS TESTER HAS ONLY TWO TECHNOLOGICAL UPDATES WITH RESPECT TO THE ORIGINAL:
The construction described in the present text, It is consistent with the work shown, except the 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.
2) 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.
WHY’ Is’ USEFUL A SLIDE INSTEAD OF A STENOPEIC HOLE:
The term "source" is also used in physics to indicate a hole, through which the light radiation, ( that can be dual mode, both in the form of photon particle, than in wave form), It 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.
WHY’ CAN NOT BE DONE’ USE A SOURCE MORE’ GREAT:
In the optical quality measurements, It serves to correct the defects on it so that the reflected wave it is not damaged for more than a quarter of the wavelength (Lambda/4), of the light which the human eye is more sensitive (68,75 millionths of a millimeter) that's why you must use a source at maximum pinpoint, in order to obtain measurement values that will be brought back with the calculation, compared with this reference value, and expressed with the fraction "Lambda / n", which presents the best optical quality, the greater is the denominator n.
WHY’ Is’ USEFUL ONE LED DIAMETER 5MM.
A Led smaller 5mm would not be useful because it unnecessarily penalizes the vision of the average human pupil that is wide 5mm.
PIECES OF THE TESTER
I'm:
- 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.
- 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, by a rubbing on a glass, losing sharpening (not useful) and gaining an edge from uniform profile and rectilinear.
- The razor blades (or two half-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, (easy for 10 microns, or bent double for 20 microns), obviously to remove once fixed.
- Modern LEDs brighter are preferred than those dim of the past, however not fatiguing red color.
however not fatiguing red color, however not fatiguing red color, however not fatiguing red color.
however not fatiguing red color: however not fatiguing red color 1,8 volts; however not fatiguing red color; however not fatiguing red color, of 3,5 volts, however not fatiguing red color 15 or 20 milliampere (however not fatiguing red color 30 however not fatiguing red color).
however not fatiguing red color 1,5 however not fatiguing red color 3 however not fatiguing red color, however not fatiguing red color, however not fatiguing red color 4,5 volts, however not fatiguing red color 4,5 volts, however not fatiguing red color (and brightness) to the desired values coming between 10 and 20 milliampere (0,01 e 0.02 Amps).
however not fatiguing red color 20 milliampere (that is 0,02 Amps) however not fatiguing red color, it is calculated it is calculated 1,5 volts exceeding the 3 it is calculated, it is calculated 4,5 it is calculated, In the following way:
stack voltage - voltage Led = (4,5- 3)= 1,5 volts to dissipate.
Then with the Ohm's law R = V / I(ie Resistance [in Ohm] = voltage [in Volt] / current I [in Amper])It calculates the R = (1,5/0,02) = 75 Ohm.
it is calculated, it is calculated, that is (1,5 *0.02)= 0,03 it is calculated 1/8 it is calculated
Wanting to limit the brightness of the LEDs, lighting it with 15 instead of milliamps 20, the resistance would become of (1,5/0,015) = 100 Ohm.
(it is calculated, it is calculated, it is calculated (it is calculated), it is calculated, added to the previous one, it will be able to adjust the light intensity from that maximum to zero).
In certain cases, the junction of the Led, It may be visible as a dark stain on the mirror. It is therefore worthwhile to make the spherical LED head opal, rubbing on a little abrasive from 500 or 800 "grit".
These images make it a better idea to installation
