OPTICAL QUALITY & AND LARGE DIAMETERS :

CHECK BEFORE TO BUY!

SEBASTIEN DEBRUYNE, Commission des instruments de la SAF

DAVID VERNET, Atelier d'optique de l'observatoire de la Côte d'Azur


Sébastien Debruyne and David Vernet wrote this article in "L'Astronomie" for the issue 112 of January 1998, "Bulletin de la Société  Astronomique de France.

The report is simple:  previous material regarding optical quality was mostly made by and available to professionals and not generally known to the amateur. What optical knowledge amateurs did know then was widespread primarily by  “acclaimed opticians"…or worse, the dread “telescope salesmen”...

 

Working with this knowledge, these salesmen found the best customers to be the naive person who relied on the "good" advice from these salesmen with regard to optical quality.  It is here what appears to be an obvious discrepancy:  the salesman becomes both judge and in part, optician.   Indeed, the customer, being unaware of the salesman’s pitch also makes a decision based solely on price in regard to quality and finds it difficult to make the best possible choice without any other facts. Throughout this article, we wish to develop the knowledge of the prospective customer by providing him key elements, which will bring the ability to make decisions necessary to any optical purchase.

We will speak successively about the image, of the quality standards of an optic, classification of the defects and the methods of visualization.  We will underline then the importance of the mirror cell to support the precision of an optic of large diameter (400 mm and more), and then we will give some advice to avoid the traps at the time of the purchase of an optic.

Concept of the image:

The various concepts that we will discuss are to a certain degree abstract and theoretical, but nevertheless essential to the good comprehension of optical quality standards.

 

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figure 1

Diffraction spot and resolving power

The image of a star in an instrument is not a dimensionless point but a small spot (spot of Airy, figure 1) produced by diffraction related to the diameter D of the objective. The angular radius of the first obscure interval of the spot of diffraction is equal to:   r =1,22l /D (radians), or rang »14,1l /D (seconds of a degree) with D expressed in cm.

The linear radius of the diffraction spot of an objective of focal length F is: rlin "1,22l F/D

The linear resolving power at the instrument's focus only depends on the F/D ratio and on l (the image in the blue end of the spectrum is smaller than in the red end.

A. Couder and A.Danjon in their book "Lunettes et Téléscopes" [1] define the limit of resolving power p of a perfect objective. An optics separates two stars of equal magnitude whose angular distance is worth 0,85 times the radius of the diffraction spot: p=0,85.rang»12/D(seconds of degree) with D in cm. The angular resolution on the sky thus depends only on the diameter D of the main optics. Then it is necessary to adapt the system focal length of the instrument (by means of a barlow, or hyperbolic...) so that the sensor in use (CCC, photographic...) is able to fully exploit the theoretical resolving power of the instrument.

Contrast

The contrast C of an image [1] is defined as follows: "Considering two patches unequally luminous of respective brightness B and b, we will call contrast of these patches the relative difference of their brillances: C=(B-b)/B, contrast is equal to 0 between two identical patches, and to 1 when one of the patches is infinitely more brilliant than the other". C thus lies in the interval [ 0,1 ]. The limit of distinction of a detail with vague contour gives a contrast of 0.1 and for a sharp detail contrast is 0.03. This concept is important because contrast gets involved in the Rayleigh criterion as well as that of Françon.

The eye

The eye eye can be regarded as perfect if the pupillary diameter is lower than 1 mm. "Under these conditions, placed behind an instrument having an ocular ring of 0,9mm approximately, the eye would be capable to perceive very small instrumental defects. On the contrary, for pupils higher than 1mm, the eye has its own defects. These defects can be rather important so that those due to the instrument are not perceptible to the eye" [2 ]. To evaluate an instrument, and using the formula of the equipupillar enlargement: g(magnification)=D(diameter of the instrument)/Ø(diameter of the pupil D the eye), we thus see that g(magnification) >D(diameter of the instrument) with D in mm, so that the eye is capable to detect instrumental defects.

Turbulence and its consequences on the image:

notion of speckle (in French "tavelure")

The atmospheric turbulence transforms the plane waves from a stellar object into an irregular surface, embossed and "weavered", which average grid step (r0)) goes from a few centimeters to several meters [ 3 ] [ 4 ]. Thus, for an objective which diameter D is lower than the dimension (r0) of the grid, turbulence will not affect the diffraction spot and the theoretical resolving power will be preserved in short exposures. In long exposures, turbulence makes the diffraction spot "wander" and blurs the image. On the other hand for a telescope whose diameter D is close or higher than the dimension (r0) of the grid, the diffraction is destroyed and leaves place to "a random granular structure due to the constructive two-dimensional interferences (bright spots) and destructive (dark spots) between the luminous vibrations" coming from the grid of the incident wave.

 

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figure 2: Speckles obtained by A.Labeyrie by observing Vega through the 200 inches at Mount Palomar. A speckle has the same size as the diffraction spot.

These grains called speckles are observed easily by examining a star using a strong magnification. "the average size of the granules (l/D) is that of the spot of diffraction of the telescope since the greatest base of interference is the diameter of the aperture, the diameter of the spot image (l/r0) being inversely proportional to the dimension of the bumps on the wavefront. The quality of atmospheric turbulence can be defined on the basis of the number of speckles Ntav present in the image: Ntav"2,3(D/r0)2

Thus, for D=400mm and r0=100mm, Ntav=37. The larger this number, the worse turbulence is" [3]. The deformation of the wavefront Bptv due to turbulence can be evaluated using the relation of Noll

Bptv=(3l /p )(D/r0)5/6

where Bp-v is the deformation in l "peak to valley". For D=400mm and r0=100mm, Bptv=3l.   (Bp-v  =Bptv , PTV stands for "peak to valley").

Awavefront perturbed in such a way by the atmosphere considerably limits the possibilities of the instrument. A large diameter amateur instrument will nearly never give a perfect spot of diffraction, and will reach the theoretical resolution with difficulty.

 

The various way to express optical quality

The quality of an astronomical optics is expressed:

-in an "indirect" manner, while speaking about the defects of the surface of wave (dephasing, concept of l, slope of the defect).

- in a "direct" way by immediately indicating the consequences of the defect on the instrumental image (Strehl ratio).

Optical defects expressed in an indirect way

The defects of the wave surface are quantified in order to compare them with various reference values depending on the desired applications. One then speaks about differences between the wavefront at the exit of the optical system and a theoretical wavefront. These differences are expressed according to the wavelength used by the detector (one will use for example the most significant radiation for the eye, that is to say 0.55 mm). In astronomy, the precision of an optics is always expressed on the wave. Thus a difference of l/10 on the wave is equivalent to a difference of l/20 on a mirror's surface and a difference of l/5 on a lens. A hollow of depth d in a mirror will be traversed twice by the wave, which defect is worth e=d (n-1) =d/2 =d/2. Any serious and honest control sheet must specify the nature of the precision: it is expressed on the wave or on the glass! By convention, we will speak thereafter only about precision on the wave.

Among these wavefront defects, one distinguishes mainly the peak to valley differences (or also crest to crest) and RMS differences. RMS differences are of more recent use [ 5 ]. Let us start initially by examining P-V variations in function of the various tolerance criteria.

The peak to valley variations (P-V)

In order to illustrate this concept of variation peak to valley, let us imagine that one seeks to obtain a plane optical surface. Perfection does not exist, we are thus obliged to fix us tolerances: optics will be regarded as good if it is inside the tolerances. In our case, this is equivalent to define the maximum height difference that exists between the top of the highest defect and the bottom of the deepest canyon of our optics (figure 2, table 1). This concept of maximum height difference remains applicable whatever the shape of optics (spherical, parabolic).

Rayleigh's criterion: the wavefront error (or " tautochronism" error) of the reflected wave near the mirror must be smaller than l/4 (figure 3). This criterion regards spherical aberration. This is equivalent to check that the wavefront is entirely located between two concentric spherical surfaces separated by l/4. The central part of the diffraction spot then only contains 80% of the light energy of the star reflected by the mirror. Rayleigh's criterion assumes a perfect eye and a maximum contrast of 1 between the observed object and the sky background.

 

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Françon's criterion: a defect of l/16 on the wave causes the effectiveness of a perfect eye for a contrast of 0,03 to drop to 92% (this contrast value corresponds to the limit of distinction of a detail with a sharply defined edge). This criterion is much more severe than that of Rayleigh; we will thus use it as the maximum tolerance for the precision of an optics (figure 3). Indeed, beyond this accuracy, the effects on the image are not visible any more [ 2 ] [ 6 ]. Fine-tuning final figuring to obtain a higher precision would be absurd, and without effect on the image! We would like to stress the very interesting work of M.Russel published in the review "Sky and Telescope" of March 1995 [ 6 ]. Indeed, starting from a Jupiter image obtained by the Voyager spacecraft that he treated numerically by computer, he obtained the image that a perfect instrument of 20cm of diameter would give. The optical quality of the instrument was then degraded by introducing spherical aberration and obstruction, he thus obtained new self-speaking images which confirm in an undeniable way the criteria of Rayleigh and Françon. Simulations clearly show that a defect larger than l/4 is unacceptable because the images then are unarguably degraded: fuzzy images, not contrasted, lack of resolution. It is also observed that the central obstruction of a secondary produces a contrast reduction. A defect ranging between l/4 and l/16 affects mainly contrast: the detail is visible on the planet but it is more or less distinct. On the other hand, we can note that there is no obvious difference between a perfect instrument and an optics having a defect of l/16 on the wave. We therefore advise the readers to attentively examine the figures in that article where the criteria referred to above are visualized. The fact of using a computer to carry out this simulation made it possible to M.Russel to be freed from atmospheric turbulence and the instrumental conditions. He thus avoided criticisms which could have been raised about an experimental study where the difficulties would have been insurmountable, for finally giving less convincing results.

Criterion of Couder: the reduced transverse aberration must be smaller than unity [1] (figure 3)

 

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The reduced transverse aberration is defined as the linear radius r0 of a wave element over the linear radius r of the spot of diffraction of the mirror of focal length F. Since r0 =qxF, with q being the slope of the element of wave with respect to the corresponding element of the sphere of reference. When the ratio is lower than the unit, the rays outgoing from the element of wave converge in the spot of diffraction. The criterion of Couder is thus directly associated to the concept of slope of a defect. The more important the slope is, the more luminous energy is rejected far from the focus. We will see the consequences in practise a little further.

The RMS error: when the shape of the wavefront at the exit of an optical system is relatively smooth, the PV rating is a good indicator of the quality of the image. However it is unsuited if the wavefront presents abrupt irregularities. In this case, the RMS rating [ 7 ] reflects in a much more exact way the effect caused by the defect. RMS is the abbreviation of "Root Mean Square" which means average quadratic deviation, or standard deviation, or square root of the variance. For the formulas fans, the variation RMS is calculated in the following way:

 

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where  n is here the number of samples (here measurements; X is the average deviation of the wave compared to the theoretical wave (average of the samples); xi is the variation corresponding to the i-th sample, with i varying of 2 to n.

Let us consider, for example, a optical system perfect but for a bump on its surface. If the bump covers only a very small surface, its effect will be very weak, although P-V variation of the bump on the face of wave is important. In this particular case, RMS variation will be very small and will represent the effect of the bump on the image with a much better accuracy than P-V rating would have done. The relationship between RMS and P-V ratings for the spherical aberration is variable; indeed the denominator of the expression above can vary from 2 to 7: RMS error " P-V error / 3.5. So, the criterion of l/4 of Rayleigh for the spherical aberration corresponds to a variation RMS of l/14. As W.Smith [ 5 ] explains it, the fact that a l/20 RMS rating is more impressive than a l/4 P-V rating contributed to the popularization of RMS ratings among the suppliers of optical systems (table 1). Let us also note that the use of numerical data processing and CCD sensors in the interferometric tests allowed a rapid development of this type of concept which requires heavy calculations! However the RMS rating has the advantage of informing us about the energy distribution of the light in the spot of diffraction as we will see it thereafter, information inaccessible with the P-V rating. Indeed, a mirror can perfectly fill the criterion of Rayleigh or that of Françon, while still having an important transverse aberration; this is why A.Couder considered that the P-V rating was to be mandatorily accompanied by the transverse aberration. We have just noted that these two formulations are complementary. However, speaking only in RMS error in amateur astronomy is vastly dishonest because it is equivalent to knowingly exploiting the ignorance of the customers who confuse the l P-V and the l RMS. Thus you must systematically request the transverse aberration in addition of the l RMS.

The optical defects expressed in a direct manner

The Strehl ratio

The Strehl ratio [5] is the ratio of the intensity of the center of the disc of Airy of an optical system containing an aberration to the corresponding enlightened fraction for a perfect optical system. It is a good measurement of the quality of the image when the optical system is well corrected.

A Strehl ratio of 0.8 corresponds to a P-V error of l/4. The Strehl ratio and RMS error are linked by the following relation:

Strehl Ratio = exp[-(2*pi*rms)²] where rms is expressed in lambda.

For various types of errors, the associated measurement of the image quality are indicated in table 1. The P-V and RMS ratings are given in wavelength. P-V ratings are approximate. Thus it appears that an amount of aberration corresponding to the limit of Rayleigh involves a significant change in the characteristics of the image.

This table corresponds to an instrument not having obstruction. The central obstruction due to a secondary mirror modifies considerably the luminous distribution in the spot of diffraction and the rings.

 

Definition and classification of the defects

In his article in "Ciel et Terre" 1950 [ 8 ], J.Texereau describes the various types of defects which can meet on an optics. Such a recall, today, seems essential to us. Using the slope of the defects and their consequences on the observations (figure 4), we distinguish four main categories: defects of abrasion, defects of form, zoning, and defects of roughness.

 

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Gray pits.

These micro accidents are residuals from fine grinding. They have a depth and width of a few micrometers. (figure5)

 

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figure 5: Mirror of 600mm, F/D= 3,7 observed in the optical shop with a Foucault apparatus which slit was removed. The image of the light source is totally occulted by the knife (strioscopy). One notes the light diffusion caused by the pits and scratches.

The scratches.

They occur during grinding down because of a lack of cleanliness. A relatively deep and long rectilinear scratch causes an additional diffraction spike. If it is curved, the spike will be replaced by diffusion (figure 5)

Sleeks.

They are microscratches produced by the polishing agent or dust which interposes between the mirror and the tool during polishing.

The abrasion defects, negligible if their number is small, are particularly visible after the aluminizing of the mirror and play the same role as dust. These defects are very definitely visible with the Foucault apparatu while moving the knife so as to completely cut the image of the source  in order to carry out strioscopy. Of course one needs a powerful lamp for this Foucault test (halogen 50W, 12V minimum) and remove the slit which here is useless (figure 4).

The defects of form.

They are large amplitude defects (several l to about l/15, figure 3 and 6). They include the residues of spherical aberration and astigmatism which are very well shown by the Foucault test (figure 8) or the wire test. The slope is approximately 10-5 to 10-7. These defects influence primarily the resolution down to l/4, whereas under that, they do not spoil any more but contrast [ 6 ].

 

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figure 6: scale of defects

Zoning.

This is an intermediate defect, from the point of view of its dimension, between the defect of form and the defect of roughness of the ripple type. It consists in a succession of concentric rings which are generated by ring tools or a small tool working on a zone of the mirror (figure 7). It is hard to get definetely categorized because of its amplitude which can vary from l/4 to l/20. Zoning affects mainly contrast. The presence of zones on a mirror is not always noticed easily on the control sheet because that depends on the width of the defects tested for. Thus the notched screen must include many zones otherwise zoning will be averaged (example: 9 zones for a mirror of 600mm with F/D = 4). The turned edge is a particular and localised case of zoning. The turned edge related to the hole of a Cassegrain mirror will have a weaker effect than a turned edge on the external diameter. To convinced oursleves, it suffice to multiply the perimeter by the width of the defect. Moreover, the tolerances are larger in the center of a mirror than at the edge. A suitably dimensioned mask makes it possible to improve intrinsic optical quality by decreasing collecting surface slightly.

 

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figure 7: Schmidt Cassegrain of 300mm controlled by photographic Foucault on a star. The telescope is usable but there remains of the aberration of sphericity and the astigmatism.

 

Defects of roughness: they enter into three categories

Shaped as a centimetric grid (and sometimes called "dog-biscuit") , its amplitude can vary l/10 for the worst optics, to l/100 (figure 6). Even if the ripple is well visible in the Foucault test with a thin slit (figure 9), it appears even more clearly by carrying out a Foucault test with a phase sheet. The effects of the ripple are similar to those of turbulence which breaks apart the rings of the diffraction spot [ 9 ]. That also results in diffusion which attenuates contrasts: the wider the grid is, the closer the defects diffuse to the optical axis. The solid angle of dispersion is worth 14 seconds of degree for a centimetric ripple, and 3 seconds of degree for pitch squares of 5 cm which correspond to a tool of 60cm. A significant ripple will degrade substantially the Strehl ratio.

 

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figure 9: Miroir de 600mm, F/D=3,7 observed in workshop with a Foucault apparatus equipped with a powerful light source and a thin slit. Centimetric ripple is definitely visible: surface is cratered-like! This significant defect is not visible with the caustic test.

It has a millimetre-spaced grid whose amplitude oscillates between 50 Å and 1 Å (figure 6). The solid angle of dispersion is several minutes of degree. The microripple is only visible by the method of the phase contrast (figure 10). From its solid angle, the microripple is a class of defect which will always be interesting to reduce because, neither turbulence, nor the atmospheric diffusion have comparable scattering angles. Optics that do not have a microripple will thus give always images more contrasted whatever the conditions of observation.

 

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figure 10: Mirror of 600mm, F/D = 4,6. Phase control. Phase sheet: aluminium density deposit of 2,8. Harmful surface quality of several tens of angströms. With such a surface quality, a luminous aura of 3 times the Jupiter diameter will be definitely visible around the planet and will degrade significantly the contrast.

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figure 10 (a): Mirror of 600mm, F/D = 4,7. Phase sheet of density 2,23. Excellent surface quality. .

Its influence is negligible in astronomy, on the other hand this type of defects is taken into account for laser applications or space. It is studied using an interferential microscope or a phase contrast microscope.

Summary (figure 4)

The defect of form is very significant because the resolution of the telescope depends on it. Thus as soon as the defect exceeds l/4, the resolution is notably affected. The defect of form also prevents the formation of good images. For defects smaller than l/4, the resolution will remain constant but contrast will be more or less weakened depending on the nature and the importance of the defect. In practice, the improvement of contrast is directly visible on the clearness of the image, on the colors of a planetary image, on the limiting magnitude, which are increased and on the sky background which is decreased. In order to be coherent, going beyond l/4 by filling the criterion of Couder, means that one will be interested in contrast of the image. Thus, the fact of fulfilling the criterion of Françon implies that one must also be interested in all the classes of defects influencing image contrast, if one wants to remain consistent. A good optics is first an optics consistent in all its classes of defects once that the principal criteria are reached.

 

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figure 10 ter: Mirror of 600mm with F/D = 3,3. Controlled by photographic Foucault on a star, the optics suffers from a high zone of Lambda/1,5 and blurs the theoretical spot of diffraction over 12 times its diameter. One sees also a turned down edge, of which the most significant part is already masked on 2 cm. The significant ripple is well visible as well.

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Another mirror, of 500mm with F/D = 3,8. Observed under Foucault test in the workshop. The visible ripple is catastrophic, it decreases severaly the Strehl ratio and breaks up the rings of the diffraction spot as turbulence would do it.

 

Illusions and realities in connection with the final precision of an optics of large diameter (400mm and more): importance of the mirror cell.

When an astronomer buys an optics of large diameter, he/she must know that the precision of the objective obtained in workshop is not the only paramount parameter. The second significant parameter not to neglect is the cell of the mirror which must avoid the flections inherent to thin mirrors.

As soon as ratio R4/e2 (R being the ray of the mirror in cm, e its thickness in cm) exceeds 1600, J.Texereau recommends to compensate for the flections of the mirror by flotation triangles, or better by astatic levers [ 10 ]. For the calculation of the number and distribution of the levers, interested people will refer to the thesis of A.Couder [ 11 ], or to that very recent of L.Arnold [ 12 ] devoted to thin mirrors. In the case of a mirror supported by its three collimating screws and a series of astatic levers, a collimation problem obliges the astronomer to modify the position of the adjustable screws, which in turn obliges it to retune the astatic levers once again. To mitigate this problem, it is advantageous not to touch the three adjustable screws of the mirror, but to connect the mirror cell to the tube of the telescope by a solid system made up of three large pushing bolts and three large drawing bolts. Thus, with this new assembly, it is enough to modify the position of the mirror cell to recollimate the telescope. The three adjustable screws and the astatic levers will remain tuned definitively! It is the principle of the double mirror cell recommended by J.Texereau in its book [ 10 ] or by A.Couder in its thesis [ 11 ].

While the most known role of the mirror cell is to be able to fine tune the collimation of the primary mirror, one should not forget its second function, quite as significant, which is to preserve in the greatest possible proportion the precision of the mirror obtained in workshop. It is not enough to own an optics with l/infinity, controlled under the best conditions in workshop, it is still necessary to be able to tune its mirror cell on the sky with this same precision. To carry out optics, the optician removes the majority of the significant problems: the mirror rests vertically on the edge (when it is thick), maintained by a strap in order to distribute the forces. Moreover as the workshop is at constant temperature, turbulence does not hinder the tests. On the other hand the astronomer is obliged to face the problems avoided by the optician: he observes preferably close to the zenith rather than near the horizon, which requires a good mirror cell to compensate for the deformations of the mirror; as for the problems of turbulence, he/she is well obliged to deal with it, which limits the precision of the visual tests carried out on a star to l/10 according to Texereau [ 8 ]. Thus the mirror cell will be tuned at best at l/10 and it essentially gives the final form to a thin mirror supported by more than three points.

The mirror should imperatively not be constrained by the side holders or the clips which prevent the mirror from falling during an accidental swing of the tube. A gap of a few tenth of millimetres between the holders and the mirror is necessary to allow for the dilation of the machine elements and thus avoid the constraints.

A thin mirror often presents intrinsic astigmatism to which an adjsutment astigmatism is superimposed. The intrinsic astigmatism includes the astigmatism of manufacture which the optician tries to minimize, and astigmatism of folding (sometimes called "potato-chipping") due to the thinness of the mirror. The astigmatism of folding is proportional to the sine of the angle a (zenith, optical axis of the telescope, figure 11), and is such whatever the precision obtained in the workshop. On an equatorial mounting, no passive mirror cell (astatic triangles, levers) can correct this astigmatism which results in a relative closing of the vertical meridian of the mirror and a relative opening of the horizontal meridian. If the mirror is intended for an azimuth mounting standard Dobson, the astigmatism of folding can be possibly corrected by making the mirror astigmatic in workshop. This astigmatism takes much more importance when the mirror is cored, the flections are then increased. One observes very well the astigmatism of folding in workshop, by controlling the mirror on the edge with an artificial star, or better with the wire test where the absence of symetry reflects the presence of astigmatism.

 

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figure 11: Astigmatism of folding of a thin mirror.

The astigmatism of adjustment is cancelled or minimized by tuning the telescope on the sky by means of a star. Only the examination on the sky of the extrafocal unage of a star makes it possible to appreciate the importance of the astigmatism of a complete optical combination under the actual conditions of its use [ 8 ].

The adjustment of a mirror cell equipped with astatic levers is generally done by night, using a star: one must check the homogeneity of illumination and the circularity of the extrafocal image, as well as the ratio between the diameter of the primary and secondary image diameter respectively, ratio which must remain constant. According to J.Texereau, "the dissymetry of the slightly extrafocal image is already visible for a variation of tautochronism of l/10" [ 8 ]. The final shape of the mirror depends on the mirror cell and can at best be of l/10. A question then arises: why buy a large diameter optics with an "announced" irrational precision of l/20 or more, as certain craftsmen advertise? The answer is simple: such a precision is useless, because in any event the mirror cell will be tuned at best to l/10  which is already largely sufficient.

 

How to not be swindled out at the time of the purchase of an optics

 

Tracking down the the generally accepted ideas

No, it is false because excellent photographs are shot with mirrors good to l/2 which give a diffraction spot several times higher than the theoretical spot. During a photographic exposure or CCD, it is impossible to exploit the resolution power at the focus of a telescope. It does not matter the relative opening of the telescope, which can vary F/D=3 with F/D=25, and it does not matter the resolution of the photographic sensors or CCD, atmospheric turbulence will always blur the image during the long exposure. Let us take however the frankly hypothetical case of one night without turbulence, the diffraction spot of the Newtonian telescopes being relatively small (2 micrometer for a F/D=3), it will then still be impossible to exploit the resoloving power of the telescope with the current detectors, which have a resolution varying from 20 to 9 micrometers (CCD or TP 2415).

While an optics is difficult to realize, it is simple to control with the help of some basic knowledge and some precautions. If the manufacturer is honest and sure of his work, he will not see any objection so that optics is controlled elsewhere.

No, because a serious craftsman consistent in the quality of his work will accept readily one more control. A craftsman can carry out good optics for himself, which will allow him to establish his reputation, then sell salad bowls to amateurs who will be in any event unable to see a difference, in particular in the large diameters. Indeed, by brain-washing the neophytes with fallacies, certain manufacturers prevent the user from doubting the quality of optics.

False! Because the control sheet depends on the person who will have produced it. The legal claims in front of courts are not possible because they would involve a true battle of experts and counter-experts on the control methods. Once the purchase carried out, it is very often necessary to live with one's piece of glass and to try to take out the best of it.

Be wary of the labels, especially when they are affixed by the tradesman on all the instruments of their store. In our opinion the label is anything but a quality standard but rather aims to obatin a intentional commercial effect. Without standards recognized by the state or associations of consumers, the tradesman creates his own label so as to decree it systematically later. Such a label thus does not have any value of guarantee.

 

A few advices, as a conclusion

 

 

 

 

 

 

 

 

We make a point particularly of thanking J. Texereau for the many discussions, which we had with him, like for his firm support in the writing of this article. Thank you also in D.Bonneau and L.Arnold for their advices and A.Labeyrie for his technical support about the use of its laboratory of optics of the College of France.

References

[1] A.Danjon et A.Couder- Lunettes et télescopes. Blanchard, réédition 1990.

[2] M.Françon- Vision dans un instrument entaché d'aberration sphérique. Thèse, éditions de la Revue d'Optique, 1945.

[3] D.Bonneau- L'interférométrie des tavelures, "l'Astronnomie", vol. 107, avril1993, p.110.

[4] H.Gié- Le "speckle". Bulletin de l'Union des Physiciens, n°596, juillet-août-septembre 1977, p.1321. M.Henry- Observations à haute résolution en astronomie. Bulletin de l'Union des Physiciens, n°596, uillet-août-septembre 1977, p.1333.

[5] W.J.Smith- Modern optical engineering, the design of optical system, Me Graw-Hill, Inc 1990, New York.

[6] M.D.Russel- Telescopic Performance on the Planets. Sky and Telescope, March 1995, p.90.

[7] A.Marechal et M.Françon- Diffraction, structure des images, influence de la cohérence. Masson 1970.

[8] J.Texereau- Les principaux défauts réels des surfaces optiques engendrés par différentes techniques de polissage. Ciel et Terre n°3-4, mars-avril 1950, p.57.

[9] H.R.Suiter- Star Testing Astronomical Telescope, A manual for optical evaluation and adjustment. Willman Bell 1994, Richmond, USA.

[10] J.Texereau- La construction du télescope d'amateur. Société Astronomique de France 1961.

[11] A.Couder- Recherches sur les déformations des grand miroirs employés aux observations astronomiques. Thèse publiée dans le Bulletin Astronomique de l'Observatoire de Paris, 1932, tome 7, p.201.

[12] L.Arnold- Petites déformations élastiques des plaques et des coques sphériques surbaissées: fonctions d'influence et application à l'optimisation de supports passifs ou actifs de miroirs minces de télescopes et aux miroirs adaptatifs. Thèse présentée à l'Université de Nice, 1995.

 

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