Build a Cassegrain secondary mirror (J. Texereau)

convex mirror

TRANSLATION CHAPTER   8 of the BOOK "  CONSTRUCTION   DU  TELESCOPE D ' AMATEUR "

by Jean Texereau

(NOTE: For the readers of French language, It is advised to read this article directly on the book named, (pages 137 – 149) to avoid faults due has the double automatic translation).

The main difficulty of building a telescope Cassegrain combination or variation, is due to the secondary mirror that is convex, and therefore cannot be controlled with Foucault's Method   without the use of expensive tools as auxiliary optical components, because the Foucault test is only applicable on concave mirrors or optical surfaces.

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N.D. T: But the strange exception would directly applicable according to the test method proposed in 1945 by J. H. KING, described in Edition 1998 A.T. book M. 1 on page p. 321, Chapter b. 14 "Testing convex surfaces according to the following figure b. 14.1, that is to install the convex mirror (or plano-convex lens or bi-convex to test), so that it closes with the convex face facing to the ambient air, a pipe-cylinder tank length determined by the radius of curvature of the face, which will be filled with fluid that has the same refractive index test glass. At the other end of the cylindrical vessel is exiting with an optical glass window that is perfectly flat even on a single surface facing towards the outside the pipe. Optical window which will ensure the ability to run through it a normal Foucault test of inner concavity in the mirror (or the lens) viewed from behind, having the same refractive index of glass, obscured, and actually physically eliminated any reflection from all mid surface of optical path immersed in it, except for extreme convex surface, that rear view looks concave.

The King test   Indici rifrazione oli minerali

The generally small size of these mirrors do not oblige to large watertight containers, However, the complication of this direct test is finding a security filling liquid nonflammable and economic that has a identical refractive index (but probably just as close as possible) to that of the glass under consideration, knowing that the index of the glass start from that of the Crown (Bk7) with value 1,5, and climb to normal calcium-sodium glass 1,57, up to the dense Flint glass with value 1,68. The most common transparent liquids that come close enough to those values, are the turpentine and mineral oils, as you read about the image above, that is one of the images attached to the instructions of refractometers for industrial use for the verification of the quality of mineral oils, as reported in the figure above.

End of note

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Since the choice of control method greatly influences the entire working procedure, We will examine the four valid practical methods:

74.   CONTROL“STAR TEST” AROUND the TELESCOPE on a STAR  (see following figure 82 A).

This method applies in normal use of the telescope with a bright star. It is assumed that the full telescope is available and mounted in equatorial mount well stationed and then moved by good clockwise motion with the primary mirror already ok and aluminized; While the secondary on study it is not essential that are metallized.

It takes a great deal of experience to correctly interpret a small defect through the star test, that is the method of Foucault practiced visually on a real star;

This is because the turbulent currents of air make it an illusion that the operator must carry out the photometric equalization on the shadows of the Windows screen of Couder. You could integrate these vortex simply taking images (Foucault-grams) formed by a few minutes of photo pose, but counting on digital images would be laborious because requires the consideration of all rights of photographic photometry. For these reasons, it is preferable to use the method of   Hartmann (2), photographically operated on a bright star as Vega, that would be shooting two images extrafocus separated by a known distance. That way you would be able to record tracks   “light brushes” or isolated light beams from a screen placed at the mouth of the telescope, and it would be enough an exposure time of about one minute with medium sensitivity film,  even if only one of the mirrors is aluminized.

To measure the distance between the images of two bundles of light o a same area you need a micrometer that can read the micron; Since we also know the axial distance that separates the two images, it can easily be deduced the distances of intersection for each zone, even with greater accuracy and safety than that which would result from equalization made visually, on the Foucault test windows.

  1. Application details in the work method Hartmann are given in the book "Lunettes et telescopes" by Danjon and Couder.

fig82

Figure 82

To avoid possible errors, It is better to freshen up a moment ideas referring to the content of the chapter on the calculations for transfering the aberrations to the focal plane (reduction of the aberrations in the focal plane), and at the chapter on the preparation of the inspection report or Check bulletin, as shown in the following figure 52 comes from page 85 Texereau's.

-FIG 52

Figure 52 Check bulletin

It is clear that in a trial with the source placed at infinity the aberrations are at the focus, and then you don't have to do the subtraction of values hm ²/R line 4 Figure 52, regarding subtraction involved only at the center of curvature, namely at the Foucault test whose source is not at the infinity, but it too   to that Centre, alongside the tester knife edge.

Similarly to quickly find the plane of the circle of minimum aberration, because we highlight the longitudinal aberration at the focus (line 5 Fig 52), You must use the values of hm/F and not those of hm/4F.

Finally transverse longitudinal aberration will find themselves using the following formula (16):

formula 16

Other bulletin calculations remain unchanged.

The advantage of a field study of the telescope in the conditions of employment, is the automatic presence of thermal aberrations involved actually, and that in a large telescope are often important .

Unfortunately, with the use of the star test, the cycle of checks and adjustments remains subordinated to the good weather forecast.

(The completion of a secondary Cassegrain diameter 60 centimeters to the Observatory   Meudon asked us almost six months using only this method,  while at the Observatory of Haute Provence a month was sufficient for a minor diameter of almost 52 cm, for a Cassegrain telescope of 193 cm).

In the case of a small tool you can avoid this problem if you   have an enclosed and long enough to be able to install an artificial star   to at least thirty meters away.

The Visual Foucault test in that case would resume his lead since the air in the room can be maintained optically homogeneous, which is not generally easy to get outdoors.

A small mask of Couder homothetic to the normal type, can be positioned against the secondary to achieve direct localization of the tweaks to realize. The source no longer at infinity would look with a slight over-spherical correction, and longitudinal aberration would be much lower than hm ²/R, but not necessarily negligible.

75. Control of the entire optical combination (that is, full telescope) by means of a flat mirror (see above in Figure 82 B) .-

Leon Foucault said that “a flat mirror for Optics is an artificial sky”. If you own a flat mirror without defects and at least equal to the diameter of the primary mirror Cassegrain, You can use it for autocollimation. This method was   followed by G. W. Ritchey in particular for controlling the combination Cassegrain telescope   152 Mount Wilson cm. You will use a Foucault tester in which the source and the knife will be as close as possible, or better   totally free of Parallax using a semitransparent glass (Fig. 82 B). In fact, if the source is off axis, the symmetric reflections occurring are shooting our mirrors in substantially different points. We see that there are altogether five reflections, A first time the telescope with the source at focus, serves as a collimator for providing of parallel rays reflected from the flat toward the combination that becomes telescope.

The defects are then doubled.

You must alluminize the flat mirror and the primary to keep enough light. In the absence of a fully realized mechanic of the telescope, the Assembly must comprise of fine adjustments by means of screws agents on the three mirrors, and despite this, that collimation is a good exercise for a beginner.

This method, like the one above, allow to control only the axial beam.

The fraction of secondary that exceeds this bundle (If you want to extend the field) cannot be whole controlled at one time.

Few amateurs, however, possess a good flat mirror diameter equal to the primary. Good means that   zonal defects are annoying, but a small curvature of the plane is irrelevant to auto-collimation.

76. Hindle Method (see above in Figure 82 C) (2). – You join the convex secondary mirror to check, to a large special spherical mirror test, whose curvature RADIUS is equal to the focal length of the primary mirror of the telescope. The distance d of the vertices is therefore the same in the real telescope.

This time there are only three reflections, and the beam passes twice on the secondary doubling so his defects.

The spherical mirror used in these conditions provides an equivalent stigmatic beam like this of the configuration of a paraboloid with a source at the infinity. The Foucault test thus reveals directly the secondary failures but doubled, as in the preceding method.

Measures must be taken with a small mask of Couder , with aberration reduction calculation as it would with an incident beam parallel.

With a spherical mirror of Hindle a little larger than the primary mirror, You can control a secondary steering for reasons of field.

The obvious disadvantage of this method is practical   the need for a second large mirror for each telescope configuration, so the spherical mirror of Hindle is justified only for a serial production of standard Cassegrain telescopes.

(2) JH HINDLE “a new test for the Cassegranian-Gregory and secondary mirrors” in Monthly Notices by the Royal Astronomical Society, March 1911, reproduced in A.T.M. 1. page. 225.

77 Control a secondary on concave gauge (See above in Figure 82 D).

This method has been found and taught by A. Couder in 1945-1946 optical lab   of the Paris Observatory. And it was also discovered independently by J. P. Hamilton published a good description in 1952 (1).

Explanation of chapters § 51 and 52 of page 93 Texereau's book, at about how you can run interference checks on plane mirrors with a Newton Interferometer easily auto-buildable D.I.Y, allow us to be short

(N.D. T. See equivalent articles about testing Newton's interferometric in this blog   https://www.grattavetro.it/interferometro-di-newton/ and  https://www.grattavetro.it/frange-di-newton-concavita-e-convessita-delle-superfici-in-esame/ ).

It begins with a build of a small spherical concave mirror at least as large as the convex, and having identical curvature RADIUS r2. The verifying of the sphericity of this concave mirror with Foucault does not present any problem, you only need to be careful, with a mirror so small, at extra-axial aberrations in telescope mounting, that can be annoying if the source is not close or confused with the image back.

-fig 83

This spherical mirror will make the Interferential gauge function.

If convex secondary mirror have a polished and transparent back (normal glass Saint-Gobain), the interference fringes can be viewed by placing the light source and the eye close to the center of curvature of the caliber. Three paper spacers, of which one thinner, separates the two glasses, and as usual you have to steer towards us that thinner spacer.

If we assume that our convex mirror is spherical with the same RADIUS of the gauge, the   interference fringes will be straight as a flat glass (view more above fig. 82 D1).

Note that the diameter fringe represents the section deformation of the of meridian of the controlled glass.

So whenever this deformation in relation to a straight line, reaches a inter-fringe, IE the center line between two contiguous fringes, It follows a difference of Lambda / 2 that corresponds to 0,3 μm with the effective wavelength of neon light given by the lamp used in the Interferometer.

(1) J. P. HAMILTON. “A test for the Cassegrain secondary”. in the newspaper of the astronomic  Society of Victoria. February 1952, p. 7.

Especially if we want to make sure that the secondary is hyperbolic, you just have to see if the Central fringe draws well at the progress of the following figure 76 II when the paper thin spacer (in figure called "cale mince") It is positioned as shown above in Figure 82 D2;

-fig76

In addition, the maximum gap for the zone 0.7 can be estimated in tenths of inter-fringe and compared with the deformation calculated by the following formula (15), where b is the known curve deformation coefficient.

formula 15

For example, the fringe represented above in Figure 82 D2 refers to the secondary mirror of the combination proposal as a first example, constructive on page 128 Texereau's book, for which ε Worth 0,12 microns, i.e. (0,12μ x 0.3) = 0,4 inter-fringes.

We note that this method requires the creation of a convex mirror with a radius of curvature strictly imposed and identical to that of the concave caliber made.

To cater to this agreement corresponding to the fringes of the previous FIG. 82 D, It has often taken to the most industrious tweaks of the Hyperbolization proper .

In fact, you can control the hyperboloid although if at the deformation is added the difference of curvature of some fringes between the mirror and its caliber. IT IS’ then just calculate the contour of the new fringes of equal thickness (Note 1).

(1) This family of curves is given up to ± 2 fringe in J. P. HAMILTON cited  above.

If you prefer to operate with equal thickness spacers you must calculate the change in diameter of the new Newton rings corresponding to deformation.

For these reasons we prefer to adjust the RADIUS surfaces at better than a fringe of closeness, before hyperbolizing. This allows more direct control and safer than deformation, Anyway, the approximation to the tenth of inter-fringe is what enough for a modest telescope.

In the case of a significant deformation can be preferred to work figuring the concave caliber that is easy to control precisely with Foucault, using a Couder mask as a paraboloid, but using the values of Δ p’ calculated by the following formula (13) by p. 127, and the value of B2 of the secondary.

formula 13

The secondary is going to be deemed to be completed when we look straight fringes on the warped gauge.

This method is easier to implement for an amateur without control glasses.

Let's now take the practical aspects of the work if you choose this method of verification.

78 General working method of small convex mirrors.

The secondaries of amateur telecopes diameter 200 or 300 mm generally have a diameter between 30 and 80 mm. Achieve exactly one of these mirrors is harder than as one would suppose not having experience in this work.

The working process on a fixed table, If it is easy and effective when you work a disc of 200 x 35 mm becomes increasingly difficult and uncertain if it diameter drops below 150 and especially under the 100 mm in diameter.

In fact with mirrors so small and light, involuntary hand pressures lead to relocation of workpieces and unpleasant surprises. The work by sitting in front of the glass where the tool rotates slowly on a vertical axis, makes things much easier. The foot lathe for opticians in the following figure 84, is considered the best machine for small jobs of precision optics (2).

With you such a lathe you would choose the slowest speed and pedal drive slower and constant as possible at least during the precision polishing.

However, you can improvise a lathe for a random job, directly using the low speed shaft of a motor-worm gearbox, provided that the image does not exceed 15 RPM / min (see following figure 85).

-fig 84-85

Figures 84 – 85

(2) Manufacturer Clavè, 9, Rue Olivier Metra, Paris 20 °

One of those industrial lathes and polishers includes a tool to hold pieces with a standard threaded shank diameter usually as have several wood turning tools. Glasses from work are attached to it by means of glues based on Rosin or pitch like one called "optical cement", or what the French call "Arcanson"(1).

We prefer to mount the glass to work without constraints through special adapters to Bowl receiving your lenses on a disk of cloth loosely.

This fastening (shown in Figure 85) allows you to control or reverse glasses in work without having to get unstuck and re-glue at each reversal of position. There are light alloy bowls adaptation or just hardwood, that can be mounted directly on the rotating axis of lathe, or just be stuck on a rotating table presented by any existing machine tool (see Figure 86).

79 Refining processing of raw edge.

To realize mirror tool can be used as raw material by processing in normal glass Saint-Gobain from 10 until 15 mm thick.

After cutting wheel or diamond glass cutter with classic summary (Fig 60), or with the tool made with a simple iron pipe in shape of Cup that cuts in wet with interposition of Emery grain (Fig. 61) the glass is glued to the Rosin on the wheel to support the piece of the lathe (Fig. 86). Before the Rosin to cool completely, you have to correct the position of the glass so that the faces which are polished tadpole well centered on   support, to ensure both a centred rotation orthogonal to the axis of the machine.

-fig 60-fig 61

A classic way to verify that this centering and orthogonality is satisfied, is to make sure to see the immobility of a reflection image of a lamp or window, coming from the upper surface of the rotating glass.

This centering said “at the light” is made with great care for a lens that has to be   centered since its construction, destined for example to be inserted into an optical system that provides strong convergence, but here in our case of the secondary mirror, a shallower control is amply sufficient.

You have to wait for the complete cooling of the Rosin before beginning the break-in / refinement / regularization of the edge of the glass. If the latter is uneven it starts with a brief equalization with a strip of zinc (see following Figure. 17 A), using a grit Emery 1 minute, by operating a lathe at a speed of about 100 RPM / min.

-fig17

(1) For details on those classic works, refer to the worker of optical glass  accuracy, written by Colonel MUST (And. optical Review).

But to make the glass exactly cylindrical is good an iron articulate on a fixed point, and impelled by a feed screw (see following figure 86). You use the emery of grit 1 minute or 2 minutes as long as the noise abrasion remains uneven , to indicate that it is still uneven surface to even out the mere contact of iron coated with wet Emery , without pressure.

The change of Emery grain will be accompanied by a shift of the moving iron corroded from tangential consumption, or this will be replaced with a brass blade which will provide a nice texture with Emery 10 m and may also serve to smooth the edges that are always fragile.

-86

Squaring edge defects of the mirror are corrected by tilting the iron.

80 roughing.

Glass-glass processing provides two interesting pieces that are both controlled by polished by the method of interference referred to in  (Chapter § 77)

(N.D. T. See equivalent articles about interferometric Newton's testing in this blog:

https://www.grattavetro.it/interferometro-di-newton/ and  https://www.grattavetro.it/frange-di-newton-concavita-e-convessita-delle-superfici-in-esame/ ). .

The convex glass will be the mirror, whose flat back, that will have to be polished, will be protected with shellac varnish against possible damage resulting from working the front face. The concave tool will then be polished to become concave caliber, and is beneficial for it to be made about the 10% larger than the mirror, something that doesn't irritate the abrasion and will disregard any error TDE of inappropriate turned down edge.

The rough grinding occurs as at the fixed table, the glass we make convex is placed bottom, IE supported by lathe holder of piece.

Given the small amount of glass to remove, the emery 1 m or 2 m and strokes of 4/5 d but poorly decentralized , are sufficient to quickly get the desired curvature.

To verify the radius of curvature reached at this stage, is simply to use a mask or template made by cardboardor or zinc, cut directly at the r2 calculated RADIUS of curvature.

Meet that are the desired curvature you must regularize by applying the usual strokes with amplitude 1/3 D . With the same stroles we regularize the surface in reversing the position of the glasses that require two different adjustments on both sides.

After the usual meticulous cleaning and related precautions which prevent unwanted scratches, You can switch to emery grain 5 and 10 m but making a little shorter strokes than 1/3D due to the fact that the cocave tool , that is greater than our mirror,, has the negative trend to turn down its edge.

The reversal of the position mirror – tool should be used not only to correct a curvature RADIUS too long or too short, but also systematically to every wet to keep exactly the same radii complement of two glasses.

The precision of the control possible with a simple model of the curve in cardboard or sheet of zinc (Fig. 20 A, page. 33) leaves something to be desired for precise verification of the radius of curvature of a Cassegrain secondary. The resulting focal length and conjugate points are very sensitive to this parameter.

-20

Therefore, to measure with due precision the deep of the arrow, It can be used a cup spherometer as shown in Figure 87.

-87

The Cup turned into hard steel, its diameter is a little lower than that of the glass to be tested; its annular contact surface is corrected after cementation and/or grain grinding and lapping over hardening with 5 and 10 m, for example on a cast iron table, and the edge that defines the circumference of the contact surface of the Cup must be well alive.

81 Spherometer to Cup (or ring) see previous figure 87.

As you can see right into fig. 87, a micrometer measuring head allows to measure this constant with a precision for convex glass, of Ø1/2 = h1 and concave glass Ø2 / 2 = h2.

The Cup has a 120° axial slots to ensure elasticity and centering to a metal collar type clamp fastener that joins a micrometric measures head type Palmer.

This measuring system adapts very easily to a variety of structures, for example for controls of thickness or parallelism of quartz surfaces for birefringent filters, or for closing plates of telescopes, or for blades of Schmidt, objective lenses, etc …, We would not hesitate to   recommend the best lives possible. For example a step by 1 mm, It is preferable to that of 0, 5 mm, the large diameter chrome drum must be to allow easy reading micron interpolation between notch and notch.

In the event that there is concern of incurring a constant error in measuring a concave glass small radius, the tip of the probe micrometer measuring head (i.e. contact tip measuring rod), should be kept to a maximum diameter of 2 mm, or even polished as a small area of the convex surface. Whereas it would be useless the mechanical complication of a non-rotating head of a measurement screw. The execution of the measure should make it extremely soft rotation of the screw.

Despite whatever you may say the treaties of mechanical measurement, If you avoid using the Torque limiter of the micrometer (which is usually always set too hard) You can define a contact with a fidelity of a micron, with the simple mastery of hardness to maneuver of the drum delicately manipulated.

A first reading serves to annotate the measure corresponding to the zeroing from screw contact and edge of the Cup, and it does so with the spherometer laid on a reference flat. The flat may be an optical piece sacrificed for this purpose, but it's better to   prepare once and for all a finely ground glass surface and polished only for fifteen minutes with a pitch tool, to use for Interferential verify of flatness .

The second reading is done by transferring the spherometer on the glass to be measured.

(N.D. T: With the zeroing of the spherometer, the edge of the cup finds himself on the same level as the Central probe tip; but when the instrument is placed on the convex glass it will touch initially only on the tracer point that will be set back by rotating the micrometer until the edge of the Cup reaches the contact with the glass).

To ensure good reproducibility of the contact pressure of the two experiments to measure, You must maneuver the micrometer screw very slowly and record the feeling of frank contact made, corresponding to a discharge of 1/3 or half the weight of the instrument on the edge of the Cup.

You can then also try the different increasing microns, by appreciating the weight discharges of the sferometer, making it increasingly easy to turn the screw on the glossy surface.

The subtraction of the two readings gives the arrow f within the field of application of the spherometer.

The corresponding radius of curvature r is calculated according to the following (19):formula 19

It is practical to register on the device the constants h12/2  and   h22/2 for convex and concave glasses. Since the term f / 2 is often negligible for astronomical mirrors in which F is small compared to r, one only Division will provide r as in this example where all measurements are in mm:

Uses a cup spherometer with inside diameter of the ring Ø = 52 mm, so   h1= 26; h12 =676; h12/2/ = 338 is the constant to consider for convex glass.

The reading on the flat gave the figure 10,334;

the reading on convex mirror 10,993.

It follows f = 10,993-10,334 = 0,659

the RADIUS searched is then = 338 / 0,659 = 513.

If we want to avoid any detrimental approximation calculation, We will push the Division   to a decimal in addition, Here we will write 512,9 and we're adding f / 2, namely 0, 3   which gives a more accurate radius of 513,2. But we must never forget the physical meaning of the measure limited to the sensitivity of a micron, representing here a within ± 0,8 mm on the RADIUS (1).

82 refinement.

Since the beginning of the refinement of the surface it is necessary to respect the final curvature RADIUS with the best approximation possible. This allows you to often reverse position tool and mirror, and leads more easily to obtain surfaces perfectly combined, that is identical but complementary, namely having exactly the same radius of curvature.

  1. the spherometer in bending to. Couder allows you to bring only the tenth of a micron, While the instruments dial gauges are not generally true to the best of several microns, except when the support brackets are very strict.

For such small mirrors, 2 or 3 wets of each emery 20 m and then 40 are enough to conform the surfaces. The final inspection of the radius of curvature must concentrate on the mirror and on the tool. We need to make sure that the arrows are exactly concordant (of course taking into account the different constant of the spherometer). In fact, with the fine polishing grit would be extremely difficult to achieve a correction of only 2 μ, that is about 7 fringe. A perfect uniformity between the two disks can be obtained with a fine Emery: 60 m or “304” conducting partially the last half polishing wets with the tool above and half by reversing with mirror above.

83 polishing and tweaking.

The two tools can be obtained for example by two thick plywood discs 15 mm-turned on a face exactly to the radius of curvature (tested with good accuracy with picture-cardboard model or zinc) and also turned to the diameter of the corresponding glass to allow the immediate reversal of the position glass – tool

-88

The two wooden discs must be waterproofed (at one time it was accomplished by complete immersion in paraffin, Today there are polyurethane paints).

It begins with a covering of the curve of the tools with a flow of pitch without squares.

To make the casting requires a containment range of masking tape high 50 mm on the perimeter of wooden discs creating a container in which to pour the molten pitch up to a thickness of about 6 mm.

Just cool down is enough you can remove the tape of containment.

It then proceeds to a pressing of pitch on the curve of the glass at first with a great deal of pressure with interposed paper-silk / polyethylene sheet kitchen.

Finally she takes off the paper or polyethylene and run a pressure of best fit with the pitch previously abrasive creamy brushwork (usually cerium oxide and water).

You can then practice a diametrical Groove, or a squaring digging of furrows, (image 88 A) or a spiral a little hollow made with a very sharp scraper. These depressions on the pitch should be maintained or serviced regularly throughout processing to improve adherence.

(N.D. T. The grooves or depressions must always be present in the processing of optical mirrors, and serve to prevent zonal errors due to uneven wear of the pitch, that could inflate at some points or vice versa losing touch in other).

Because the main concern is whether the glasses have radii sufficiently close, It begins with the Polish summarily but evenly over the entire surface, before the gauge tool and then the mirror for .25 of an hour each, then proceed to a first summary interference control.

If it indicates a significant difference in curvature greater than 8 or 10 fringe, It is better to resume polishing to achieve a unification of glasses with greater accuracy.

A concave curvature difference – with glasses that touch the edge – It's harder to retrieve a relative convexity; IT IS’ also be desirable to start with a convexity 3 or 4 fringe, that will lead to a polishing easier.

Being much smoother curvature corrections as the glasses are not completely lucid, It is better not to work soon for the caliber, but push the mirror polishing in approximately 75%, approaching then the curvature of the caliber by means of the simple choice of position under or on top of mirror-tool.

If you need to increase the convexity, convex mirror of course must be under; and vice versa to increase the concavity of the concave. However, We must work so that the gray (understood as surface still opaque) Don't be too unevenly distributed from the Center to the edge.

Polishing the caliber is available (above or below) convenient to reduce residual curvature differences compared to the mirror; Could be useful for this purpose of longer strokes than normal (from 2/3 until 3/4 D) that will help if you need the fix, but care should be taken to deformation! Of course it is superfluous to completely Polish the caliber; as soon as the glasses don't have to one or two rings that you will proceed to the keep in spherical shape of the caliber, who has the approximation that interests us (0,1 fringe). But this is not a task as easy as it may believe those who have no experience.

Such control is done smoothly with the Foucault method (as described in the chapter § 29 and   33, of page. 55 FF.).

-33

Figure 33

If necessary, the tester will be slightly amended by turning towards the knife the exit of   light source and installing a small 90° total reflection Prism that will bring up a few millimeters the light beam of the optical axis and the knife (This means to reduce to a minimum possible the distance from otical axis and light beam of the source slit – knife shown in enormous 25 or 30 mm in the following drawing Foucault tester in Figure 34).

If you want to contain a quantity extra-axial aberrations montage ignorable, We need to reduce the distance between source, knife and board the optical axis, less than 10 mm to a mirror of approximately 500 mm radius,

-34

Figure 34

Similarly to primary mirror, you have to try to get the best possible form. IT IS’ well welcome to fulfill some repetition, given the importance of this result. Working preferably in a room where the temperature is from 20 until 24 ° C.

Use a tool with good pure pitch , quite a little hard for a small glass (the thumbnail must score slightly pitch under heavy pressure), but mostly use pitch that is NOT dried from an abrupt heating, because he would lose the flexibility granted by volatile solvents lost.

Working with strokes 1/3 D for small wets pushed though long over time. Use a low rotational speed of lathe, IT IS’ the back and forth movement practiced hand that must   be winning.

Later, after 3 or 4 wets the pitch must have a surface evenly covered with abrasive (such as cerium oxide), and issue its characteristic smell of softwood much more than it gives out in cold.

It must be ensured to avoid clogged channels of pitch (see previous figure 88 A) so that the tool maintains good contact.

The work is set by the amount of abrasive (iron oxide rouge, or white zircone or Cerium oxides) with water, just as important is the percentage of the two components that will put in each wet. It must be a serious and effective experience to take impeccable wets and a good tool.

Beginners often put too abrasive at a time or too much water; In the course of work, should be sufficient to complete a wet only one brush stroke of abrasive on glass.

Thinking to apply these recommendations to the letter, many are surprised by zonal defects appearing diehards and springing up regularly, whose fault may be an insufficient thermal regime (given by pitch too hard, or wets too short, or insufficient works time) that often results in a surface with turned down edge and center high (see previous figure 33 D).

Center high correcstion is not difficult, and you do so with mirror under and tool over and strokes centered. As regards the Turned Down Egde, which we do not recommend tweaking on a small glass, You'll also want to overlook it, if the exceeding of the gauge diameter will suffice, If not you should try again improving your technique.

Once the Foucault test shows that the caliber is well rounded in the useful portion (see previous figure 33 C ), It only remains to complete the figuration of the convex mirror. The interference fringes observed between spherical caliber and the actual mirror, generally reveal a set of difference in curvature and deformation sometimes used directly to start the Hyperbola. But the normal safest method is to correct for the curve to bring the spherical mirror to get straight fringes of the previous figure 82 D.

It only remains to accomplish the hyperboloid, that is very little compared to the previous job.

When the deformation does not exceed 0, l a 0,2 fringe can be simply a remodeling carried out with the thumb or with index (§ 43). But generally it's best degarnish away the normal tool in form of circular crown of medium radius 0,7 (Fig 88B); used after with strokes a little short from .25 to 1/3D.

In addition to checking the difference in maximum elevation ε about the zone 0,7 (the previous figure 82D), You must verify that the curvature present the desired trend .

Those who are not very familiar with this deformation can cut into a paper mask the Central curvature for a given inter-fringe calculated by the following equation:

formula 14

Image 88 provides some examples of hyperboloid and retouching.

In Figure 88 C the beaded edge is insufficient, a local tool used on the areas to depress you'll complete the action of the crown tool . Sometimes it's the Central relief is not with exact profile (Fig 88 D), you could try a local remodeling, but it is often desirable to resume the puttin in shape after a return towards the sphere.

Certain operators, No matter what they do, fail to prevent the Turned down edge. When this fault is not entirely hidden by the frame of the telescope, There remains a chance to accomplish the secondary mirror with an oversized diameter (Look images 88 IT IS) then use it only on the clear aperture masking or removing the dotted area in fig. 88 and.

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