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The myopia in the Hubble space telescope
Daniel MALACARA HERNÁNDEZ
Refer this article as: Malacara Hernández, D., The myopia in the Hubble space telescope, Points de
Vue, International Review of Ophthalmic Optics, N63, Autumn 2010
Publication date : 10/2010
Telescope History
The history of the Hubble Space Telescope is full of anecdotes and problems that were satisfactorily
solved over several years. The project started in 1962 when the National Academy of Sciences
recommended that a space telescope be built, at a time when the space programs had not yet
started. It took until 1977 when the United States of America Congress approved the telescope
construction to begin. This was done by means of a NASA contract with Perkin-Elmer Corp. in Danbury
Conn, beginning in 1978.
Eight years later, in 1985 construction of the telescope was concluded. However, the launching of the
space telescope was delayed due to the tragedy of the Challenger Space Shuttle in 1986. The launch
had to wait until April 25, 1990.
Main Telescope Characteristics
To understand better how telescopes work, let us consider two important properties, their resolving
power and their luminosity. The resolving power depends on several factors, such as the aberrations
of the optical system, the diffraction effects, which are large for small apertures of the system, the
dimensions of the image elements (pixels) in the detector and atmospheric turbulence.
In the human eye without refractive defects (emmetropic) the resolving power is mainly limited by
diffraction effects and by the size of the light sensitive elements in the retina. This is approximately
one minute of arc angular diameter. One minute of arc represents a 3 centimeters object size as
observed from a distance of one hundred meters. Then, a person with a 20/20 vision can clearly see
parallel lines separated by 3 centimeters at a distance of 100 meters.
If the diameter of the eye’s pupil was ten times larger and, the light sensitive elements in the retina
(cones) ten times smaller, we could see image details ten times smaller. Thus, one of the main
properties of a telescope, is that we can observe very small details, due to the large diameter of the
main lens or mirror, called the objective. The main limitation for the resolution of a space telescope is
the diameter of the objective.
If the diameter of the pupil is 6 millimeters as in the human eye the resolution would be one minute of
arc. If the diameter is as large as 200 centimeters, the resolving power would also be large so that
object details with only 0.7 arc seconds could be observed. Unfortunately, this result would be valid
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only in outer space, since the atmospheric turbulence reduces the resolving power to a value of about
2 to 3 seconds of arc near sea level or, in the best places to about 0.2 arc seconds, for example, at
the top of a high mountain, where astronomical observatories are located. Thus, we clearly see one of
the advantages of a space telescope. A telescope with an objective with 240 centimeters diameter, as
in the case of the Hubble space telescope, has angular resolution of 0.05 arc seconds.
However it is important to note that the resolving power is not the only important characteristic of an
optical system. The other one is its light energy collecting capacity which determines the brightness
of the image of a star. Thus, the larger the objective diameter is, the larger the light collecting
capacity is. For this reason the human eye pupil opens to about 6 mm in relatively dark places. The
amount of collected light energy is directly proportional to the area of the pupil, in other words, to the
square of its diameter. Thus, a telescope with a pupil diameter of 240 cm as the Hubble space
telescope, collects 160,000 times more light energy than a human eye. This allows the observation of
fainter and more distant luminous objects. This is a second advantage of a large pupil.
Let us consider the light from a star passing thought the pupil of a telescope. The brightness of the
image of this star is directly proportional to the square of the diameter of the pupil and inversely
proportional to the square of the distance to the star. Thus, a telescope with a 240 cm diameter
objective allows the observation of stars 400 times more distant than those observed with the naked
eye (240/0.6 = 400)
Still another advantage of the space telescope over a terrestrial one is that there is no atmosphere
attenuating the light intensity. Summarizing, the Hubble Space Telescope has three very important
characteristics: a) a high resolving power producing more image detail, b) a high luminosity, allowing
the observation of distant celestial objects and c) great transparency, to observe images with more
wavelengths (colours).
The space telescope is a system of two mirrors, a concave primary, also called the objective and a
convex secondary as in Fig. 1. The light from the star illuminates the primary mirror where the light is
reflected towards the smaller secondary mirror. There, the light is again reflected to the image plane,
passing through a small circular aperture at the centre of the primary mirror. The objective has a
diameter equal to two hundred and forty centimeters. It is concave and it does not have an spherical
shape but that of a hyperboloid with rotational symmetry. The secondary mirror is convex and also
has shape of a rotationally symmetrical hyperboloid to produce a good image of the stars. This shape
for the mirrors is necessary due to the large aperture to the system, (pupil). In optical systems with
much smaller pupils, like the human eye or photographic cameras, the optical surface can have the
simpler spherical shape.
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Fig. 1: Schematics of the Ritchey-Chrètièn optical system type for the Hubble Space Telescope. It is
formed by two mirrors, a primary mirror with 240 centimeters diameter and a much smaller
secondary mirror in front of it. Adapted form a figure in the NASA Web page http://hubble.nasa.gov.
In conclusion, if the mirror surfaces were spherical, it would be much simpler to construct them, but
their large size does not permit the formation of a good image. Thus, the image of a luminous point
source, like a star would not be a point as it should be, but a small spot, due to spherical aberration.
This aberration has been well known for over a century. It is relatively easy to observe, for example,
when the light from the sun or a lamp is reflected at the interior of a coffee cup with a reflecting
smooth surface as shown in Fig. 2. If the diameter of the reflected light beam is small, the spherical
aberration is also small and, with little practical importance. However, in the telescope it is of
fundamental importance.
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Fig. 2: Spherical aberration observed with the sun light reflected in the internal face of a coffee cup.
© Daniel Malacara Hernández.
On the other hand, since the angular resolution of the telescope is 2000 times larger than that of the
human eye, the precision with which the telescope surfaces must be polished is much greater than for
a spectacle lens with high quality. As an example, a good spectacle lens can have surface deviations
as large as four to five wavelengths (two thousands of a millimeter). However, the surface of a
telescope must have a precision of a tenth of a wavelength (50 millionths of a millimeter) over its
whole surface. The large size of the mirror surface, its hyperboloidal shape and, the high required
precision make the polishing of the mirror a difficult task. Nevertheless, present optical technology
permits the fabrication and evaluation of the mirrors with these requirements. The main difficulty lies
in evaluation. For this reason, it is frequently said that an optical surface can only be made as good is
permitted by the evaluation method.
The two mirrors for the telescope were made at the Perkin-Elmer Corp. employing the most modern
techniques, using for the first time polishing tools controlled by computer. At the same time, due to
the novelty of the technology used, it was decided to construct simultaneously, another set of
identical mirrors at the Kodak Co., in Rochester, NY.
Optical Tests of the Telescope Mirrors
The testing of an optical concave spherical surface with high precision was basically solved with the
invention of the knife-edge test in France by Leon Foucault in 1858, as illustrated in Fig. 3. This is a
very simple test that only requires a light source with a metallic plate, that has a small pinhole
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located near the centre of curvature of the mirror under test. If the mirror is perfectly spherical all the
light will focus near the centre of curvature, symmetrically located with the illuminating light source. If
the mirror is not perfect but has small surface deformations, the reflected rays will not intersect at a
common point. These deformations become visible by interrupting the deviated rays by means of a
knife, located near the point of convergence of the rays. This knife edge produces shadows that make
the surface deformations clearly visible, as in the Foucault pattern in Fig. 4.
Fig. 3: Schematics of the Foucault test to evaluate concave spherical mirrors. © Daniel Malacara
Hernández.
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Fig. 4: A telescope mirror with spherical errors, as observed with the Foucault test. © Daniel Malacara
Hernández.
The technology to test non-spherical surfaces, which we call aspheric, as in the case of a hyperboloid
with rotational symmetry, is much more complicated. This is a contemporary subject of research,
about which many scientific articles and books have been written. One of the first tests to test
astronomical mirrors with a large size was invented by Joseph Hartmann in Germany in 1904. This
test is similar to the one invented by Foucault. The difference is that instead of using a knife, the
mirror under test is covered with a dark screen with an array of holes as illustrated in Fig. 5. The
reflected light will be formed by many narrow convergent beams, each one coming from each of the
holes on the Hartmann screen. The positions located at a slightly deformed position on a
photographic plate. These images in the form of small spots will appear, as in Fig 6 a. If the mirror
under test is a hyperboloid, the spots will not form a perfect rectangular array, they will be as in Fig. 6
b. The positions of these spots are carefully measured and their deviations from their ideal calculated
position for a perfect ideal surface are calculated. These numbers can be used to calculate the mirror
deformations with a precision of approximately one wavelength.
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Fig. 5: Schematics of the Hartmann test to evaluate spherical as well as aspherical mirrors. © Daniel
Malacara Hernández.
Fig. 6: Hartmann patterns obtained for a) an spherical mirror and b) a hyperboloidal mirror as the one,
used for the Hubble telescope. © Daniel Malacara Hernández.
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Fig. 7: Schematics for the Offner compensator with two mirrors, used to test the primary mirror for the
Hubble telescope. ©Daniel Malacara Hernández.
The Hartmann test has been used traditionally to evaluate the large astronomical telescopes installed
at some mountain observatories. However, the Hubble space telescope was designed to have a much
better image quality than common terrestrial telescopes. For this reason more elaborate techniques
and methods had to be employed to evaluate the quality of the mirrors, as it is shown next.
Optical Tests for the Hubble Space Telescope
The primary and secondary mirrors have a hyperboloidal shape in order to eliminate the spherical
aberration as well as another important aberration called coma. When during the construction of the
optical surface, the light source cannot be located near the centre of curvature as is traditional in the
Foucault and Hartmann tests, the configuration with a hyberboloidal surface would produce spherical
aberration, making high precision testing difficult.
So the main problem in testing a hyperboloid surface is the spherical aberration. It has been common
for about thirty years ago, to construct an optical system with spherical surfaces but with a spherical
aberration that has an opposite sign to that of the mirror. Then the whole system produces a perfect
point image without any spherical aberration. This auxiliary system is known as a “compensator”.
There are many configurations for compensators but the commonest one is formed by a pair of lenses
or a pair of mirrors, placed near the evaluation point, close to the centre of curvature of the optical
surface under test. The compensator with lenses is considered a little less precise than the
compensator with mirrors because the lenses may have some variations in the refractive indices of
the glass. The decision was to use both types of compensator, but to trust more in the results from
the system with mirrors. This compensator was so important that its fabrication was contracted with
the same company, Perkin-Elmer Co, that was to fabricate the telescope mirrors. The compensator
made with two mirrors is shown in Fig. 7. In order to get the desired precision, the assembly of the
system and the mirror separation and other elements have to be set to the required value within the
small prescribed tolerance of a few microns. To assemble the components accurately, during the test,
an Invar rod was carefully made with a precise length to separate some optical elements. If this
changes, a residual undesired spherical aberration might appear in the mirror under test.
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Fig. 8: Images of the spiral galaxy M 100 in the Virgo constellation, taken with the Hubble telescope,
a) before the correction and b) after the correction. Taken from the Hubblesite web page
http://hubblesite.org.
Just what was feared most, had to happen. The optical elements in the compensator were not
correctly assembled. The Invar rod had two thin plastic protections on each end that were not
removed as necessary. This made the separation only 1.3 millimeters longer and the undesired
spherical aberration appeared. The difference at the edge between the obtained mirror surface and
the ideal one was about eight wavelengths, which is close to two hundredths of the thickness of a
human hair. Due to this error the sky image appeared slightly out of focus, lacking the details and
resolution that had been hoped for. In conclusion, the surface of the primary mirror was made with an
error ten times larger than the specified tolerance.
The consequence of this error was so important that the Division of the Perkin-Elmer Company that
made the mirrors and the testing compensator had to be sold off.
Final Correction of the Residual Undesired Aberration
It has occasionally been said that an undesired myopia appeared in the telescope, as in the title of
this article. However, this way of describing it is not technically correct, because there is a
fundamental difference between myopia and spherical aberration. As is well known by all
optometrists, myopia is a general defocusing of the image that has to be corrected with a lens with
the appropriate divergence power to focus the image. On the other hand, in spherical aberration, all
rays near the centre of the pupil are in focus whilst the rays near the periphery of the pupil are
defocused. Hence, the proper “spectacles” have to refocus only the rays on the outer zone of the
pupil without any refocusing any of the rays in the central zone. To say this in a different way, the
spectacles have to introduce spherical aberration with the opposite value to the residual aberration in
the error. To perform this correction, close to the image plane an optical correcting system named
COSTAR (Corrective Optics Space Telescope Axial Replacement) was located. It was manufactured by
Ball Aerospace Co. The installation of this corrector was carried out by specially trained astronauts
aboard the Endeavor shuttle in December, 1993. A total of three missions were required to perform
the complete correction and obtain a telescope with the required image quality.
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Figure 8. shows the images if the spiral galaxy M 100 in the Virgo constellation, taken before and after
correction. The first image is almost the same as one obtained at a terrestrial observatory. Figure 9
shows two images of the nucleus of the Orion nebula, the first one obtained in the 5 metre telescope
at Mount Palomar and the second in the Hubble telescope.
Fig. 9: Images of the center of the Orion nebula taken with, a) the Hubble Space Telescope and b) at
the 500 centimeters diameter Palomar Observatory telescope. Taken from the Hubblesite web page
http://hubblesite.org.
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Fig. 10: The Hubble Space Telescope as seen from Space Shuttle Discovery during its second
servicing mission. Taken from the Hubblesite web page http://hubblesite.org.
Final Commentaries
There are several interesting facts related to all this history. For example, the backup telescope built
at Kodak was never used and it did not have the undesired residual spherical aberration. Another
interesting fact is that the lens compensator, which the builders did not trust much, detected the
residual error. However, they decided to fully trust in the results with the mirror compensator. The
error was so large that it would have been detected even with the traditional Hartmann test but it was
not used. During the four years delay when the mirror was being stored, several universities
requested permission to test the mirror but it was not forthcoming. The reason was that they were
quite confident about all the testing that had been done.
We have to consider that the error was not due to lack of knowledge or to incorrect scientific or
technical concepts. It was only after intensive research that the true reason was determined. The
technician in charge of assembling the mirror compensator neglected to remove the plastic protecting
caps from the ends of the Invar rod spacer. This produced an error in the spacing of the mirrors of the
compensator.
The main conclusion which results from this disastrous experience is that we have to avoid excessive
faith in our results. We have to revise our results and procedures not once, but several times and
better yet, employing different methods.
References
References
D. Malacara, Optical Shop Testing Third Edition, John Wiley and Sons, New York, 2008
National Aeronautics and Space Administration, The Hubble Space Telescope Web page
http://hubble.nasa.gov
The Hubble Space Telescope Optical Systems Failure Report, National Aeronautics and Space
Administration (NASA), November 1990
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