WO2001059488A1

WO2001059488A1 - Process for obtaining biquadratic optical surfaces and in particular schmidt correctors

Info

Publication number: WO2001059488A1
Application number: PCT/IT2000/000043
Authority: WO
Inventors: Pietro Sgarbi
Original assignee: Pietro Sgarbi
Priority date: 2000-02-11
Filing date: 2000-02-11
Publication date: 2001-08-16

Abstract

The present invention concerns a process to obtain biquadratic surfaces, in particular Schmidt correctors, characterised in that it includes the positioning of two transparent plano-parallel optical plates (18, 19) adequately spaced. The plates (18, 19) are connected to one another on the periphery in such a way so as to allow their radial expansion. Moreover, the application of an equally distributed deforming force (P) on the given plates is foreseen, in particular induced by means of an optical fluid (41), and regulated by a central expansion compensator (49), so as to obtain biquadratic surfaces.

Description

PROCESS FOR OBTAINING BIQUADRATIC OPTICAL SURFACES AND IN PARTICULAR SCHMIDT

CORRECTORS

DESCRIPTION 5 The present invention refers to a process to obtain biquadratic optical surfaces, in particular Schmidt correctors, and product acquired with the aforementioned process.

In the Schmidt type cameras for astronomical photography, in short, telescopes devised to realise astronomic photographs, the only process for

10 obtaining the corrector plate necessary in the aforementioned cameras due to the employment of spherical mirrors instead of parabolic mirrors, consists of an extremely accurate surface processing beginning with a piano-parallel plate, with zonal works, entirely executed by hand or partially by machine (cf. "Albert Ingalls, Amateur Telescope Making, Volumes 1, 2, 3, Ed.

15 Williarnann Bell Inc."; "Allan Mackintosh, Advanced Telescope Making

Techniques - Optics, Ed: William Bell Inc."; " Allan Mackintosh, Advanced Telescope Making Techniques -Mechanical, Ed. William Bell Inc."; "F.A.Jenkins, H.E.White, Ottica, Ed. Istituto Editoriale Universitario"). The high degree of precision required to obtain this corrector plate,

20 characterised by its biquadratic surfaces, necessitates several hours spent in the hands of an expert specialist, with the resulting elevated production costs.

Moreover, during this type of processing there arises the need for periodic optical controls.

25 The evolution of the Schmidt camera, still in use, has led to the realisation of other optical systems such as Schmidt - Cassegrain and Baker - Schmidt whose main prerogative is to obtain shorter instruments with equal luminosity in order to avoid the main defects which affected the Schmidt originals, that is their length in relation to their exposure.

30 Corrector plates with biquadratic surfaces realised with the process above, or rather through the removal of glass, are foreseen even for the more recent cameras, with the resulting elevated production costs.

In view of the state of the method described, the aim of the present invention is to dramatically reduce the cost of manufacturing the corrector plate used in all the types of instruments which are derived from the original

Schmidt configuration, maintaining the same optical quality and surface precision whilst eliminating the manual operations involved when removing the glass and the optical controls required during the processing phase of the corrector plates, limiting them to a single final control. In accordance with the present invention, this object is achieved by means of a process for obtaining biquadratic surfaces, in particular Schmidt correctors, characterised in that it includes the use of two transparent piano- parallel plates, adequately distanced from one another and connected to one another at the periphery in order to allow their radial expansion, and the application of an equally distributed deforming force on these plates so that their distance at the centre is greater than that at their periphery, thereby inducing a biquadratic deformation on the surface of the plates so that the two plates will assume a shape similar to a single plate worked on both surfaces an expansion compensator being placed at the centre of the two plates.

Preferably it is foreseen that an optical fluid medium is inserted between the two piano-parallel plates to exercise the said deforming force in an equal manner on the surface of the two plates.

Thanks to the present invention it is not necessary to complete an initial piano-parallel processing of the internal surfaces of the two plates if the optical medium adopted has the same refraction index as the material used for the plate.

The new process overcomes the inconvenience of a manual working of the plate because a curve automatically deformed to the maximum extremity of the plate itself is achieved without further processing. The new process devised is applicable to all of the optical combinations which foresee a Schmidt-type corrector, and more precisely: classic Schmidt, Schmidt - Cassegrain, Baker - Schmidt, Newton - Baker; moreover, it is applicable to the classic Newton in order to improve the general performance.

A further advantage introduced by the new process is the dramatic reduction in the intermediate optical controls required to verify the shape of the surface obtained.

The characteristics and the advantages of the present invention will be made evident by the following detailed description of an embodiment thereof, illustrated as a non limiting example in the enclosed drawings, in which:

Figure 1 shows a classic configuration of the Schmidt system in accordance with the known technique; Figure 2 shows a classic configuration of the Schmidt - Cassegrain system in accordance with the known technique;

Figure 3 illustrates a classic configuration of the Newton - Baker system in accordance with the known technique;

Figure 4 illustrates a configuration of the Newton classic system; Figure 5 shows the family of curves utilised by all correctors for the reduction of optical aberrations;

Figure 6 shows the course of the two plates deformed by the process according to the present invention;

Figures 7 and 8 compare the theoretical optical curve with that obtained in accordance with the present invention;

Figure 9 shows the final configuration of the corrector obtained in this way.

A classic configuration of the Schmidt camera is shown in Figure 1.

According to what is illustrated in this Figure note the presence of a Schmidt corrector 1 with biquadratic surface, a concave spherical mirror 2 and a focal surface 3.

Moreover, note that the mirror 2 has a radius r and an apex V, positioned on an optical axis 6, whilst the focal surface 3 has a radius rl and is concentric on the surface of the focal F mirror 2. The corrector 1 deviates the incident rays 4 and 5 to compensate for the spherical aberration of mirror 2, whilst the coma is eliminated by positioning the corrector 1 in the centre of curvature C. 'Spherical aberration' is intended as the inability of a spherical mirror to carry parallel incident rays onto the same focal point in different positions on its surface, whilst "coma" is intended as the comet tail shaped image which is caused by the impossibility of focalising a punctiform image if this lies outside the optical axis as a consequence of the incidence of oblique beams.

The corrector 1 is realised by means of a highly accurate surface processing starting from a piano-parallel plate of glass with hand-made zonal works subsequently executed to give the corrector a very slight spherical curvature.

The shape to be given to the corrector 1 plate surface is not unique. That is to say that there is not only one but an entire family of valid equations which eliminate the aberrations caused by mirror 2; for practical reasons a specific shape is chosen, as for example that which allows a lesser removal of glass when the same correction is required (see Figure 5).

Moreover, the shape of the corrector 1 must be able to keep the residual chromatic aberration caused by the corrector itself at a minimum, which aberration, however, in the case of traditional correctors, is always kept to very low values due to the thinness of the plate.

In as much as it concerns the correction of the chromatic aberration which is always present in this type of instrument even if in small quantities, it is sufficient to process only one surface provided that an appropriate coefficient shape is chosen (k factor later explained). First Wright and then Linfoot demonstrated that it is possible to utilise even two surfaces. The chromatic aberration can also be eliminated in this way. (cf. "E. H. Linfoot, Monography Note Royal Astronomical Society, num. 1, pag. 104 and 154, year 1944").

A classic configuration of the Schmidt - Cassegrain system is shown in Figure 2.

According to what is shown in this illustration note the presence of a biquadratic Schmidt corrector 1 positioned before the focus F of mirror 2, unlike Figure 1, where the corrector is positioned in the centre of curvature C or rather at twice the distance; this system employs a convex secondary mirror 7 which can be either spherical or hyperbolic.

The main prerogative of this type of instrument is to obtain systems shorter than that shown in Figure 1 because the longer the optical tube, that is the longer the telescope is, the higher is the cost of the entire instrument with a ratio estimated at 1 :6 (for example a 2m telescope would be six times the price of a lm long telescope).

A classic configuration of the Newton - Baker system is shown in Figure 3.

According to what is shown in this Figure note the presence of a holed Schmidt corrector 8, a parabolic mirror 9 whose focus F is placed on the optical axis 6 and is positioned beyond the said corrector 8 and the achromatic doublet 10.

Moreover, note that the presence of the parabolic mirror 9 does not create the spherical aberrations typical of the mirrors shown in Figures 1 and 2 and that the coma problem is eliminated with the introduction of the achromatic doublet 10, even if the doublet 10 does, however, cause a spherical aberration which must be corrected by means of the corrector 8.

Figure 4 illustrates a classic Newton system which can be distinguished from the previous Newton - Baker system in that its configuration can be reduced to a primary parabolic mirror 9 and a secondary elliptic plane mirror 60, whose function is to perpendicularly deviate the image to the optical axis.

Figure 6 shows the course of two plates deformed by the process according to the present invention.

According to what shown in this Figure note an abscissa axis indicating the radius of the plate expressed in centimetres, and an ordinate axis indicating the deformation which the said plate undergoes expressed in centimetres (the diagram is not to scale).

Moreover, note the presence of two curves 11 and 12 representing the deformation undergone by the two surfaces of a piano-parallel plate of glass subjected to the process of the present invention.

The process according to the invention takes advantage of the elastic property of the glass to deform the plates maintaining the surfaces parallel between them in order to obtain a permanent shape, such as that shown in Figure 6. This consists of a bending corresponding to the biquadratic surface required, the shape being acquired by means of an equally distributed pressure. This is practicable in as much as the deformations undergone by the plates are extremely small and are, therefore, rigorously elastic (Hooke's law).

The inner space which is formed is filled with an adequate optical medium 13. This optical medium 13 will be a fluid, such as distilled water and 60% to 98% glycerine solution or a mineral oil with a low viscosity and a low freezing point (such as the type used for achromatic doublets) for applications with diameters greater than 10 - 13 cm, otherwise it is possible to use a case-hardening vegetable resin or other synthetic case-hardening resins (such as cyano-acrylate, epoxy, etc.) for applications with diameters less than 10 - 13 cm.

In particular cases where the fluid has the same refraction index as the glass of the plate employed (up to the third decimal Figure), there is the remarkable advantage of not having to optically process the inner surfaces, as a common processing according to the best tolerances obtainable from the optical industry is sufficient.

Unlike the classic process, in which the glass is removed as shown in Figures 1, 2 and 3, the process according to the invention cannot be applied to only one surface of the plate whilst leaving the other flat, but necessarily requires the simultaneous deformation of the two surfaces which will, in this way, remain parallel to each other as is shown in Figure 4.

So as not to introduce an undesired affect deteriorating the optical characteristics of the system it is sufficient to take into account the thickness and the refraction indexes of said parameters and, in accordance with these parameters, to adapt the total amount of the deformation to achieve the same correction as would be achieved with a single surface processed.

In accordance with the invention, the process always requires the presence of two plates adequately distanced and supported at the edge by a fixed support or free support. The plates which constitute the corrector can be of different thicknesses (that which involves a deformation different from one plate to another) in such a way that it is possible to obtain a better chromatic correction as foreseen in the solution indicated by Linfoot.

The fundamental parameters are: a) elasticity coefficient; b) rigidity coefficient (or flexural rigidity); c) elasticity module; d) Poisson's module (or Poisson's ratio); e) thickness of the plate; f) refraction index; g) dispersion index; h) total inner pressure.

It can be noted that by modifying one or more parameters, a more or less wide variation of the surface shape and of its maximum deformation is obtained. The environmental conditions foreseen for the correct operation are: a) thermal excursion from - 10 °C a + 25 °C, that is with a Δ = 35 °C; b) a barometric pressure excursion from 780 rnm/Hg (maximum high pressure at sea level) to 560 mm/Ffg (minimum pressure at a height of 2500 mt.).

With these operational conditions the only optical control required is to be carried out on the already assembled corrector and consists of testing the calibration of the inner pressure between the two plates, simultaneously verifying the quality of the image obtained by means of an interferometer or Ronchi reticule positioned in the focus of the instrument.

The maximum deformation is calculated on the basis of the physical characteristics of the glass employed in order to realise the plates constituting the corrector. The various physical parameters of the calculation provide a large degree of freedom in obtaining a series of curves, greater than with the processing system for removal of the material.

The equation which describes the conditions of elastic deformation for a system with a circular plate fixed at the edges and loaded with a weight P equally distributed on the entire surface , is given as: = [P / (64*D)] * (R² - ι²) (1) where the "w" indicates the movement induced by the force P, "r" a generic point belonging to the plate; P the total weight applied; D coefficient of the rigidity of the plate, where D is:

D = E*h³ / 12 (1 - μ²) (2) with E elasticity module, h the thickness of the plate and μ Poisson coefficient.

The tensile stress sustained by the plate due to its fitting is determined by the following equation: σ_eq = 3 / 4 (P*R² / h²) (expressed in Kg/cm) (3)

Another example of deformation of a circular plate, with radius R and thickness h, with an edge simply supported, with a weight P (indicated with a plurality of arrows) equally distributed on the entire surface of the plate is described by the following equation: w = (P / 16D) * (a*R² - b*R²*r² + c*r⁴) (4) with D as the rigidity of the plate (see equation 2).

The coefficients a, b and c are calculated on the basis of the contour conditions and in this case: a = l / 4 (5 + μ) / (l + μ); b = l / 2 (3 + μ) / (H- μ); c = l / 4 (5) In the examples shown the applied weight P force must always be symmetrical in respect to the centre of the plate.

An expert technician recognises that, from an optical point of view, the Schmidt corrector must always have a surface shape given by the only family of equations shown in fig. 5, that is of the following type:

Δ = (x⁴ - krV) / [4(n - 1) R³] (6) where Δ is the deviation of the plate surface; x is the radius of a generic point on the plate (x = 0 the centre of the plate); k is the shape factor and is comprised between - 1 and + 3; r is the semi-diameter of the plate; R is the curvature radius of the primary mirror; n is the refraction index of the plate.

Moreover, where it is necessary to express the distance of the plate from the primary mirror the following type of equation must be used:

Δ = - (F - M)r² / [2(n - 1)E * F] + M * r⁴ / [16 * (n - 1) * E * F³] (7) where M is the primary focus, F is the equivalent focal, E is the distance of the plate from the primary mirror, n is the refraction index, r is a generic point on the surface.

For the best correspondence between the optical curves corresponding to equations 6 or 7 and the equation 1 it is preferable that the plate has a fixed type support. Under these conditions, choosing a shape factor k = 2, the two curves turn out to be practically identical (see Figures 7 and 8) (cf.

"Resistenza dei materiali" by Nsevolod Feodosev, Editori Riuniti).

With the said system a curve automatically deformed to the extreme border of the plate is achieved without further processing. This was particularly critical in the traditional technique. For examples of correctors applied to systems such as the classic

Schmidt, the Schmidt - Cassegrain and the classic Newton, the calculation values used for the comparison of optical results obtainable with the process according to the invention are summarised in the following table:

Note that the use of standard borosilicate glass (in initials BK3) is foreseen for all of the examples considered.

The final configuration of a corrector obtained in accordance with the process of the present invention is shown in Figure 9.

According to what is shown in this Figure, note that the two plates 18 and 19, of glass and other transparent material, with adequate space between them, have a central hole 29 through which it is possible to obtain the connections for the external collimation of a secondary mirror 40 connected to a small disc 47. In fact, through a semisphere 43 with a prefixed diameter tightly housed in a spherical seat 64 of disk 65 and a stem 45 provided with bucket springs 66 used to connect the semisphere 43 to a contact conical surface 46 with three grub screws 44 screwed in a cover 67 which in turn is screwed to the external body 68 of the compensator 49, the support plane 47 of the secondary mirror 40 is precisely positioned within the smallest fraction of degrees, to the advantage of the collimation and, therefore, the quality of the focus image of the connection.

The two plates 18 and 19 are hermetically sealed thanks to the presence of a couple of gaskets 42 with a predetermined thickness glued to the external wall of an expansion compensator 49 and another couple of gaskets

48 glued to a barrel 21.

The barrel 21 in this way allows a radial expansion of the two plates 18 and 19 that is, one plate "slides" onto the other, so that the traction generated by the bending at the centre can be discharged without creating an undesired deformation.

The two plates are spaced by a suitably sized annular gasket 62 placed near to the external edge.

An optical medium 41 is inserted between plates 18 and 19. The optical medium 41 is a fluid in cases where the diameter of plates 18 and 19 is greater than approximately 10 - 13 cm, but can also be a vegetable case- hardening resin, as for example the so-called Canada balsam, or synthetic if the diameter of plates 18 and 19 is lower. The fluid can be inserted after the corrector has been assembled with the exception of membrane 50. In fact there is only air between the two plates 18 and 19 and the fluid is injected, through a needle (not shown in the Figure) with the same diameter as the special holes 63 made on the body of the compensator 49, until it goes out of the other holes. The air present between the two plates 18 and 19 is vented in this way.

The deformation of the two plates 18 and 19, as shown in Figure 6, is therefore caused by the optical medium inserted, with a predetermined pressure obtained thanks to the screwing down of a threaded and graduated ring 52 which compresses the optical medium 41 thereby creating the deformations foreseen by the theory described previously in accordance with equation 1. The expansion compensator 49 is located centrally on plates 18 and 19 and acts by means of an elastic membrane 50 so as to maintain the difference in pressure between the outside (ambient pressure) and the inside (pressure exerted on the optical medium 41 by the membrane 50) constant thanks to the holes 63 in order to guarantee a constant deformation, which must imprint a shape such as that shown in Figure 6.

The function of the membrane 50 of the expansion compensator 49 is to absorb the volumetric variations induced by variations in temperature and/or variations in atmospheric pressure caused by the different heights at which the instrument is operated. The difference in pressure between the inside and outside is kept constant thanks to the variability in volume of the optical medium determined by the movement of membrane 50.

Moreover, note the presence of a threaded ring 52 in Figure 9 which allows the recalibration of membrane 50 and, therefore, the pressure exerted on the two plates 18 and 19 when, for example, the conditions exceed those previously mentioned (temperature lower than approx. - 10 °C or height greater than 2500 metres); the maximum limits foreseen are - 30°C and + 40°C for the temperature and 4.000 metres for the altitude. The recalibration operation is carried out by moving the threaded ring 52 to the positions already set on the body of the compensator while the instrument was being assembled.

In the event the optical medium 41 is inside plates 18 and 19, it is possible to carry out a chromatic filtering for special applications as fluids accomplishing this function can be used thanks to their selective fransmissivity, as for example certain fluorides or oils or also the compounds used for the production of gelatine filters. Other fluids, besides those already mentioned, may also be used (a solution of distilled water and 60% to 98% glycerine, low viscosity mineral oil), according to the glass employed for the two plates 18 and 19. In fact the refraction index of the glass, in the case of lanthanum, can reach n = 2.036, making it convenient to use silicon oil or mineral oil with a very low grade of viscosity.

It is always advisable to execute the anti-reflection coating even with the new process but only on the external surface in as much as the optical medium 41 guarantees the optical continuity between the first front surface and the last rear one.

The corrector in accordance with the invention, exemplified in fig. 9, is applicable to any of the optical systems cited.

In the case of the Schmidt - Cassegrain system, besides the corrector fitted with the expansion compensator, a secondary mirror able to eliminate the residual coma is needed, as also in cases where traditional correctors are employed, in that the position of the plate does not allow for a total elimination of this aberration. However, with the exception of the above, the new system allows a total elimination of the spherical aberration to the edge of the plate. Moreover, glasses with high refraction indexes, especially those with lanthanum, turn out to be more suitable; to this purpose it is calculated that if it were possible to deposit a layer of germanium even of only 0.5 microns on the external surfaces of both plates, the glass employed could be normal glass with a low index, BK3 type, which is much more economical than the lanthanum type. The fluid must have a refraction index analogous to that of the glass employed and, as stated previously, it is better if it is identical.

Reducing the image field to 1.5°, against the 3° design ones, value more suitable to this type of configuration, even the residual coma falls within the acceptable range of values even with glasses whose index is around the mean values of the BK3, that is about 1.472. In practise the correction of the coma is partly carried out by the corrector and partly carried out by the secondary mirror which, not having to correct the spherical aberration, will be spherical and not hyperbolic. The process is further simplified given that, being able to work directly on the corrector, the secondary mirror can be realised first and only on the design data. This, from an industrial point of view, can be translated as a remarkable standardisation and, therefore, simplification of the process. The corrections will be referred in this way to the calibration of the corrector. In the case of the classic Newton system, where the primary mirror is parabolic, the corrector must only correct the coma and a minimal (usually very little) residual of spherical aberration. Working then in systems usually exposed from f/4 on (up to about f/8), the deformation required is sufficiently contained. These systems are advantageous when the corrector can adopt a shape factor k=2 as in this way it is possible to almost totally remove the coma with the single corrector on an image field of even 4°, leaving a very low residue and employing, in this case, a very economical glass such as the BK3 or the BK7. The other characteristics of the Newton configuration are not affected, given the low power of the corrector, and the field continues to be practically flat. Even the solution worked out by Baker could be simplified in this manner, eliminating the need to insert an achromatic doublet in the area immediately before the focal plane. In the specific case of instruments of this type already realised (and above all, already in use) this system allows the realisation of a simple transformation "kit", economic and easy to install, which converts the classic Newton into a highly correct instrument with a field more than optimal even for amateur photographers. The system has also been studied for exposures up to f/3 giving the same results and thereby indicating the possibility of realising very simple and compact instruments above all suitable for wide field photography. The corrector can be also used with other applications employing catadioptric systems for photographic use.

Claims

1. Process for the realisation of biquadratic surfaces, in particular Schmidt correctors, characterised in that it includes the positioning of two transparent piano- parallel plates (18, 19), adequately spaced and connected at the periphery in order to allow their radial expansion, the interposition of an expansion compensator (49) in a central position between the two plates (18, 19) and the application of a deforming force (P) equally distributed on the said plates (18, 19) so that their distance to the centre is greater than that to their periphery, inducing in this way a biquadratic deformation on their surfaces, so that the two plates (18, 19) assume a shape similar to a single plate processed on both surfaces.

2. Process in accordance with claim 1, characterised in that an optical fluid medium (41) is inserted between the two piano-parallel plates (18, 19) to exercise the given deforming force (P) in an equal manner on the surface of the two plates (18, 19).

3. Process in accordance with claim 1, characterised in that the given deforming force (P) is regulated through a membrane (50) connected to the body (68) of the compensator (49) through a threaded and graduated ring- nut (52), in such a way so as to vary in a predetermined manner the pressure that the optical medium (41) exerts on the plates ( 18 , 19) .

4. Process in accordance with claim 1, characterised in that the central expansion compensator (49) comprises means (43-47, 66, 67) to collimate a secondary mirror (40).

5. Process in accordance with claim 4, characterised in that the means (43-47, 66, 67) to collimate the secondary mirror include a small supporting disc (47), a semisphere (43) connected in turn to the small disc (47), a disc (65) with a spherical seat (64) against which the semisphere (43) leans, sealed onto the spherical seat (64), a stem (45) connected to the semisphere (43), a counteracting spring (66) to keep the semisphere (43) in contact with the spherical seat (64), a conical tip (46) positioned on the other extremity of the stem (45) and in contact with the adjusting dowels (44) located on a cover (67) screwed to the body (68) of the compensator (49) in such a way so as to allow the micrometric regulation of the small disc (47).

6. Process in accordance with claim 1, characterised in that the two plates (18, 19) are sealed on the peripheral edge by means of gaskets (42,

48).

7. Process in accordance with claim 1, characterised in that the two plates (18, 19) have the same thickness.

8. Process in accordance with claim 1, characterised in that the two plates (18, 19) have different thicknesses.

9. Corrector obtained with the process in accordance with any of the preceding claims, characterised in that it includes two transparent piano- parallel plates (18, 19), adequately spaced on the periphery so as to allow their expansion in a radial direction, an expansion compensator (49) in a central position between the two plates (18, 19), and mediums (41) to apply a deforming force (P) equally distributed on the plates (18, 19) so that their distance to the centre is greater than that to their periphery, in this way inducing a biquadratic deformation on their surfaces so that the two plates (18, 19) assume a shape similar to a single plate processed on both surfaces.

10. Corrector in accordance with claim 9, characterised in that the means (41) for applying the deforming force (8) are composed of an optical fluid medium.