INSTRUMENTACIÓN

REVISTA MEXICANA DE FÍSICA 51 (1) 104–109

FEBRERO 2005

Apodization of the flat mirror support of a newton telescope
F. Gracia Témich, A. Cornejo Rodrı́guez, and F. Granados Agustı́nInstituto Nacional de Astrofı́sica Óptica y Electrónica,
Apartado postal 51 y 216, C.P. 72000, Puebla, Méx.,
e-mail: temich@inaoep.mx, acornejo@inaoep.mx, fermin@inaoep.mx.
H. John Caulfield
Fisk University,
1000 17th Ave., N Nashville., TN 37047, USA
Recibido el 26 de junio de 2003; aceptado el 24 de septiembre de 2004
An analysis of different structures of the spiders supporting the flat mirror of a Newton type telescope was made, in order to reduce thediffraction effects of the spider on the images produced by the telescope. After applying different numerical solutions used by different
authors, and without satisfactory results, a novel solution based on the analysis of the diffraction pattern of a circular aperture allowed us
to find a satisfactory reduction of the diffraction pattern in the image produced by the support of the secondary flat mirror. Experimentallaboratory results will be shown, using white and He-Ne laser light sources.
Keywords: Diffraction and scattering; optical instruments and equipment.
Se hizo un análisis de diferentes estructuras de las arañas de los soportes del espejo plano de un telescopio tipo Newtoniano, para reducir losefectos de difracción de la araña en las imágenes producidas por el telescopio. Después de aplicar diferentes soluciones numéricas usadas por
diferentes autores, y sin resultados satisfactorios, una nueva solución basada en el análisis de patrones de difracción de aberturas circulares,
nos permitió encontrar una reducción satisfactoria de los patrones de difracción en las imágenes producidos por los soportes del espejo planosecundario. Mostramos resultados obtenidos en el laboratorio, usando fuentes de luz blanca y láser de He-Ne.
Descriptores: Difracción y dispersión; instrumentos y equipos ópticos.
PACS: 42.25.Fx; 07.60.-j

1. Introduction
In Fig. 1a common image obtained with a reflecting telescopeis shown, where the effect of the support system of the secondary mirror on the image are the four bright light lines,
perpendicular to each other at the image. Those diffraction
effects on the images are observed for any kind of reflecting
telescope such as Newtonian, Cassegrain, Ritchey Chrêtien,etc. This effect is produced because the “secondary” mirror
is supported by a mechanical structure of the telescope thatmake it possible to align of the mirrors of the telescope.
To solve the problem of the effects of the spider on thetelescope images, several research papers have been published trough the years giving some solutions, such as thoseworks by Schultz et al. [1],Tuvikine [2], Jacquinot [3]. As aresult, for example, the methods developed by Tuvikine wer
successful in improving the resolution of the images, but collateral diffraction effects on the image appeared; on the other
hand, Schultz, et al. [1], analyzed the problem using a Bessel
aperture, and applying their studies to a Cassegrain telescope;
improvement in the resolution was observed, but the overall
energy in the focal plane was reduced.
Considering the results of the studies mentioned above,
our research was focused, firstly, on finding a mathematicalsolution following some of the steps of the authors mentioned
above, and taking into account other numerical techniques;unfortunately, unsatisfactory results were obtained for the reduction of the diffraction effects on the images observed withF IGURE 1. Image from a two mirror reflecting telescope.

the telescope. Therefore, instead of a mathematical analysis to the problem, it was decided to study carefully the pattern produced by a circular aperture illuminated by a point
source. In accordance with this idea, different apodizers were
designed and tested in the laboratory. This task was accom-

APODIZATION OF THE FLAT MIRROR SUPPORT OF A NEWTON TELESCOPE

plished by studing different structures of the arms of the spider, mainly by overlapping the maximum and the minimumof two close diffraction patterns; as a result, an empirical, but
successful apodizer, was designed, as will be shown in thefollowing sections.

2.

Proposal for the apodization filter

This section will explain how the design for an apodizer, that
could reduce the diffraction effects on the images of a reflecting telescope was found from the overlapping of two diffraction patterns of a circular aperture. The apodizer that was
designed was tested by numerical methods in the laboratory,
placin the apodizer the normal linear spider of the flat mirror of a Newtonian telescope; however the method developed
here can be applied to other types of telescopes. The following paragraphs will explain carefully how the successful
apodizer was designed, and as was mentioned above, after
several trials of combining two diffraction patterns, for a circular aperture, in different ways.

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Figure 2 are shows: Fig. 2a a picture of a Fraunhofer
diffraction pattern of a point source illuminating a circular
aperture, Fig. 2b a diagram of this pattern shows, for the sakeof simplicity, only the first three bright and dark rings; but
also are shown the points O, O2 and O4 corresponding to
the centers of the bright fringes; and O1 , O3 , and O5 which
are the centers for the dark fringes; Fig. 2c the superpositionof two diffraction patterns, as those shown in Fig. 2b; but,
this time, taking care that the “second” dark ring of pattern
A, said point O3 , coincides with the central bright zone ofpattern A’, that is O0 .
As is well known, the position of the two first minima [4]of the diffraction pattern, of a circular aperture, are located at
1.22 and 2.23 units from the center of the pattern. If we convert these two values to centimeters, the magnification of thecentral part of Fig.2.c is obtained and shown in Fig. 2d. For
the drawing of Fig.2.d., the thickness of the dark rings were
calculated taking into account the following considerations:i) the addition of 10% of 1.22 to the central value of 1.22 and;ii) an important conceptual fact for the result of the design of
the apodizer, two main points must be mentioned: first, that

F IGURE 2. a) Airy’s pattern for a circular aperture. b) Diagram for the three inner bright and dark rings of the so called Airy’s pattern. c)
Superposition of two shifted diffraction patterns. d) Magnification of the central region of the two shifted diffraction patterns, mainly with
only the two inter bright and dark rings.

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F. GRACIA TÉMICH, A. CORNEJO RODRÍGUEZ, F. GRANADOS AGUSTÍN, AND H. JOHN CAULFIELD

the second dark ring of the diffraction pattern must be positioned at the central maxima of the second shifted diffraction
pattern, Fig. 2c; and second, that numerical values of the positions of the maxima and minima of the diffraction patterns
must be converted into centimeters for the geometrical drawing.
A magnification of Fig. 2c of the crossing of the two
shifted patterns is shown in Fig. 2d. By crossing the two0
first dark rings centered at O1 and O1 , the structure of theapodizer was found. The shape of the apodizer selected after different trials was the one with two diamond dark zones
D1 and D3 , Fig. 2d, which are the upper and lower intersections of the first two dark rings; and the zone D2 which is anelliptical clear zone between those two dark inner rings.
As has already been mentioned, after trying different
overlapping structures of the diffraction patterns, the overlapping, shown in Fig. 2d, was the apodizer that gave the best
results in our experiments. However, the most important aspect that should be mentioned here, is the fact that the magnification of the pattern shown in Fig. 4d, was done taking into
account the positions of the dark rings of the Airy pattern fora circular aperture, and therefore this method can be applied
for any type of astronomical telescope.

3. Experimental results
The Newton telescope used in our experiment has the following characteristics: diameter 140 mm, focal length 1200 mm,
flat elliptical mirror with 40 mm in the minor axis; the lengthof the linear support of the secondary mirror is equal to 55
mm. For improving the images observed with a Newton telescope in the laboratory, Fig. 3a is shows a scaled size of theapodizer used in the experiment, with physical units in mm.
The new shape for the support of the spider, of the secondary
mirror, were positioned the normal flat support of the mirrorof the telescope, Fig. 3b. Normal supports, as such thoseused, are made from thin metallic blades.

F IGURE 3. Apodizer proposed for the spider of the flat mirror of a
Newtonian Telescope, the apodizer that was designed was locatedupon the normal spider of the flat mirror.

The proper size of the designed apodizer, in particular forthis Newtonian telescope, was constructed by taking the sizeof the apodizer of Fig. 2d; with a length of about 12.5 mm;
and since the length of the support of the telescope is equal to
55 mm, a scale factor was obtained that allowed us to obtain
the real size of the apodizer. Figure 3a shows the real dimension of the apodizer, and Fig. 3b how they look as the spiderof the flat mirror.
Therefore, for other telescopes, the starting point will be
to consider the apodizer size in Fig. 2d; and according to thelength of the linear support of the secondary mirror, either
flat or with a different shape, a scale factor should be derived
for the construction of the real size of the apodizer.
Figure 4 shows a picture of the experimental setup, with
the Newtonian telescope illuminated by a collimated beam.
This picture can be easily understood from the diagram in
Fig. 5a, where the different components of the experimentare described. In order to observe an improvement in theimages observed with the Newtonian telescope. Figure 5bshows the four different structures used of the spider, for our
experiment and simulations. The apodizer designed is compared with the customary spider with three and four arms.
Figures 5b, A and B shows the three arm support systems.
However, for the support in Fig. 5a, screws were used, andin Fig. 5b thick wires were used; in both cases similar diameters for the supporting arms were employed. Figures 5b, C
and D, shows the classical four arm supports schemes, withsimple wires in Fig. 5c and B;the apodizer that was designed
corresponding to Fig. 3a, as in Figs. 5b and D.
Figure 6 shows the experimental images observed withthe telescope for the four different supports, and Fig. 5b forthe spider of the secondary flat mirror. The experiments inthe case of Fig. 6 were conducted using a He-Ne laser as alight source. For a better understanding about the results observed, in the lower right corner of each picture of Figs. 6,
are written the capital letters that correspond to the type of
supporting system of the flat mirror, described in Fig. 5b.
Figure 7 shows the results obtained by numerical simulaR,tion, using a computer program carried out in MATLAB°
but scaled for publication; these simulations mean the Fouriertransform for each of the cases of the spiders of Figs. 5b,
A, B, C, and D. As can be observed, the simulated images,
Fig. 7, have a close resemblance to those images obtained in
the experiment in Fig. 6.
From these experimental and simulated results, the reduction of the diffraction effects became evident when thedesigned apodizer of Fig. 3 was used. This fact can be observed by comparing of the experimental images of Figs. 6cand 6d; and those experimental results are supported by thesimulated images of Figs. 7c and 7d. Therefore, an important conclusion is that the apodizer designed, Fig. 3, that is
located along the linear support of the spider, gave successful
results in diminishing the diffraction effects of conventional
spiders.

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107

F IGURE 4. Picture of the experimental set up with a Newton telescope, and a collimating system illuminating the telescope.

F IGURE 5. a) Scheme of the laboratory experimental set up. b) The
four structures of the spider used in our experiment: A) with threescrew; B) with three wires; C) with four-wire; D) with the proposedfour-arm spider.

F IGURE 7. Simulated Fourier transform for each one of the spiders
shown in Fig. 5b.

Figure 8 shows the experimental results when a whitelight source was used. Hence, similar diffraction patterns canbe observed surrounding the images of the telescope, using
either a He-Ne laser or a white light sources, as can be see in
Figs. 6 and 8, respectively.

4.

F IGURE 6. Experimental results of the telescope images, using awhite He-Ne laser, for each one of the spider structures shown in
Fig. 5b, and the experimental set up of Figs. 4 and 5a.

Analysis of the experimental results

For the three-screw supports shown in Figs. 6a, 7a, and 8a,a rather complicated diffraction pattern could be observed,
with a 6-peak star figure. For the three and four wire supports, six and four lines of diffraction can also be observed as
it is shown in Figs. 6b, 7b and 8b, and Figs. 6c, 7c and 8c,
respectively. For the case of Figs. 6d and 8d, where theapodizer that was designed has been used as support system,
the diffraction effects have been almost eliminated; as canalso be seen in the simulation of Fig. 7d. However a carefulanalysis of Figs. 6d, 7d, and 8d, where the apodizer designed
has been used to show that, even though the diffraction effects have been reduced, some diffraction effects around thecentral area of the images remain. A special comment regarding the simulation patterns, is that they have been scaled for
publication.

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F. GRACIA TÉMICH, A. CORNEJO RODRÍGUEZ, F. GRANADOS AGUSTÍN, AND H. JOHN CAULFIELDTABLE I. Position x and intensity I values of a lineal central scanning of diffraction patterns.

F IGURE 8. Experimental results of the telescope images, using awhite light source, for each one of the spider structures shown in
Fig. 5b, and the experimental set up of Fig. 4.

In order to have a different type of information about thediffraction effects of the flat mirror spiders in the telescope
images, Fig. 9 shows some image irradiance scans along a
horizontal line of the images. These scans correspond to
the four different spider geometries supporting the secondary
mirror. The rotated 45◦ scan in Fig. 9a was done for the special case of the spider with a three-screw support system; andthe horizontal central scans for the other three images of

Figure9b9c9d

x position/ Irradiance value

x/I

x/I

x/I

First secondary maximal

2.2/0.57

3.7/0.47

2.6/0.16

Second secondary maximal

3.7/0.33

4.4/0.30

3.2/0.09

Third secondary maximal

5.6/0.20

5.9/0.20

3.7/0.06

Fig. 6 are shown in Figs. 9b, 9c, and 9d. The best irradianceprofile has been obtained for the designed spider Fig. 8d;
where it can be seen how the diffraction effects have been reduced; since the ripple of Fig. 9d is much smaller (below 0.1)
than the ones seen in Figs. 9b and 9c, whose ripples appeared
close to 0.6 and 0.45, respectively. From a qualitative analysis of Figs. 9b, 9c, and 9d, in Table I records the values of
the intensity with respect to the x coordinate from the central
peak, for the three first secondary maxima, after scaling thesquares of the figure into milimiters.
From Table I and with reference to Figs. 9b, 9c, and 9d, it
can be seen that the position x of the secondary maxima arecloser to the central maxima for Fig. 9d, and also the intensity values drop drastically by about a factor of three for thesame Fig. 9d with respect Fig. 9c.

F IGURE 9. Image irradiance scans, along a line, for each case of the spiders support shown in Fig. 5b; using a He-Ne laser illumination. For
Fig. 6a a rotated scan was done.
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APODIZATION OF THE FLAT MIRROR SUPPORT OF A NEWTON TELESCOPE

5.

Conclusions

It has been shown by experiment at the laboratory, and by
simulations in a computer, that the designed spider based
an empirical study of the superposition of two diffraction
patterns, shifted laterally one with respect to the other, thatthe diffraction effects on the telescope images have been improved. From the results obtained with this type of spider or
apodizer, the diffraction effects on the images of the telescopewere reduced drastically; as can be seen, by comparison, in
Figs. 6, 7, and 8 the diffraction lines perpendicular to the central bright core of the image are diminished. In Fig. 9d theripple of the secondary maxima is decreased in the case of
the spider that was designed. Therefore, the goal that certain
design for the spider can reduce the diffraction effects, wasreached to our satisfaction.
On the other hand, after some analysis of the results, it
is clear that the binary apodizer pattern developed is, in fact,a kind of binary hologram that was first described by Brown
and Lohmann [6], where the radial position selects the phase
information. A Fresnel zone plate, for instance, can be con-

1. A.B. Schultz, T. Vernon Frazier, and E. Kosso, Appl. Opt. 23(1984) 1914.
2. L.M. Tuvikine, Opt. Spectroscopy 10 (1961) 144.
3. P. Jacquinot, Progress in Optics, 3, Chapter II, (Ed. E. Wolf;
North-Holland Publishing Company, Amsterdam, 1964).
4. M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Seven Edition, 439.
5. Pasachoff and Kutner, University Astronomy, Saunders Golden
Sunburst Series, 46, (Philadelphia, 1978).

109

sidered a crude Brown and Lohmann binary hologram, where
the amplitude is modulated by the width of the structure. For
future work, the idea is to concentrate our design efforts on
selecting the widths (amplitudes) that can lead to an optimal
behavior of the spider, according to some measurable criterion. Preliminary results on the topic described were reported
in the OSA Annual Meeting of 2000 [7].

Acknowledgement
One of the authors F.G.T., wishes to thank to CONACyTMéxico for the graduate studies grant. The authors would
like to thank Dr. Octavio Cardona Núñez from INAOE verymuch for his enlightened comments; and Dr. Elfego Ruiz
from IAUNAM, during the process of revision of our paper
for publication, who called our attention to papers of Refs. 8
and 9, where a curved spider can also be used for the reduction of diffraction effects. We are also grateful, to a referee
for his valuable comments, that enriched the content of thepaper in several aspects.

6. B.R. Brown, andA.W. Lohmann, Appl. Opt. 5 (1996) 967.
7. F. Gracia T., F. Granados A., and A. Cornejo R., Apodizationof the flat mirror supports of a Newton telescope, OSA Annual
Meeting, (Rhode Island 2000).
8. L. Ritchter John, Appl. Optics, 23 (1984) 1907.
9. W. Sinnott Roger, Reflection of a telescope maker, Sky & Telescope (September 1989) 313.

Rev. Mex. Fı́s. 51 (1) (2005) 104–109