University of Ljubljana

Faculty of Mathematics and Physics

Department of Physics

Seminar 4

Liquid mirror telescopes

Author: Jure Koprčina

Mentor: Tomaž Zwitter

Ljubljana, May 2016

Abstract

Liquid mirror telescopes (LMTs) are a new branch in the family of astronomical

instruments. Their main feature is a reflective liquid in a container that is rotated around a

vertical axis and thus forms a rotational paraboloid which can be used to focus light. It is

possible to build very large liquid mirror telescopes with a reasonably low cost.

Unfortunately, this kind of telescopes can be pointed only directly upward. Nevertheless,

liquid mirror telescopes are of scientific value and can be used for a number of observations. Here we review some of the most important physical properties of this new family of telescopes and

their present contribution to astronomy.

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Table of contents

1 Introduction 2

2 A Rotational Paraboloid 3

3 Basic Design 4

4 Applications of LMTs in Astronomy 5

5 Reflective Surface 6

6 Time Delayed Integration or Drift Scanning 7

7 Disadvantages 9

8 Realized Projects 10

9 Future Plans 11

10 Conclusion 12

11 Literature 12

1 Introduction

In astronomy the problem with glass mirrors in big telescopes is that the mirrors are

heavy and they must be carefully ground and polished, to an accuracy of a few tens of

nanometers, before being coated with a thin layer of aluminum or silver to make them reflective.

Such mirrors also require a complicated support system to prevent temperature changes or the

force of gravity from distorting the surface. The largest, most modern telescopes today use a

system of sensors and actuators that actively controls the shape of the mirror in order to cancel

out these also known by the name active optics [1]. The instruments are a technological

masterpiece, but they cost an enormous amount to build, roughly $10 million for one with a 6-

meter diameter mirror. Therefore, astronomers are looking for more economical solutions. In

this paper we will investigate one of these solutions – liquid mirror telescopes.

Figure 1: The 6-meter diameter Large Zenith Telescope primary mirror that uses mercury to reflect light

[2]

3

2 A Rotational Paraboloid

It is very well known that if a partially filled container is spun about its vertical axis,

then the surface of the liquid in the container takes the form of a rotational paraboloid, which

is the shape of mirrors in most conventional telescopes.

If the container rotates with constant angular velocity ω around its axis of symmetry

which is perpendicular to the surface of the Earth, the liquid then assumes an equilibrium

position such that its surface follows an equipotential surface. At every point, the surface of the

liquid is thus perpendicular to the net force. The liquid is subject to the acceleration of gravity

g

(parallel to the axis of rotation which is taken to be the Z-axis) and to the centrifugal pseudo

acceleration a

which is parallel to the X-axis axis (we assume that the considered point lies on

the X axis). At every point on the surface, the angle α between the normal to the surface and

the parallel to the Z-axis passing through that point is given by [3]:

g

x

g

a 2

tan

(1)

This angle is equal to the angle between the tangent to the curve and the parallel to the X axis

at that point, therefore

g

x

dx

dy 2 . (2)

The result after the integration is:

g

xy

2

22 , (3)

where the constant of integration has been set to zero by placing the origin of the axes at the

vertex of the curve. Equation (3) describes a parabola and can be written in the parametric

form

fyx 42 (4)

Here f is the focal length of the parabola given by

22

gf (5)

Figure 2: Forming of the rotational paraboloid. The gravitational acceleration (vertical force) remains

constant, whereas the centrifugal force (horizontal force) increases with the distance from the axis of

rotation [4].

4

If we choose a liquid with a high reflectivity (for example mercury), the result is the

primary mirror of a telescope. Unfortunately, this kind of mirror can look only directly upward.

The restricted and fixed point of view of this kind of telescopes seems a to be a big obstacle,

but we shall see later that liquid mirror telescopes make a useful piece of equipment even if

they have this restriction.

It can be seen that, for a given value of the acceleration of gravity (we assume the gravity

remains constant) the focal length of the mirror f is determined by the angular velocity alone.

Table 1 gives some relevant parameters for a number of mirrors (the acceleration of

gravity used assumes a terrestrial latitude of 45°). The angular and rim velocities are small and

quite manageable.

Table 1: some parameters for three different f-ratio telescopes at different diameters. [3]

3 Basic Design

The surface of the liquid takes the shape of a rotational paraboloid regardless of the

shape of the container. This is very convenient, because we do not have to smoothen the

container to a great degree, actually we do not have to work the container at all. This way we

avoid the part that usually costs the most. In theory the container could have a flat bottom and

a vertical rim, but to reduce the cost of the reflective liquid (in most cases mercury) and to make

the total weight of the whole mirror as small as possible the container too is the shape of a

rotational paraboloid with the desired focal length. The container is made of a foam core,

laminated with Kevlar. [5]

Mercury is poured in the container which is driven with a synchronous motor with the

desired speed. Mercury is thus spread on the whole surface of the container and forms a thin

reflective layer. After a while the mercury settles and the surface becomes smooth. If during

the operation and observation some disturbance should disrupt the form of the mirror or if dust

should fall on the reflecting surface then the container is stopped, the mercury accumulates at

the bottom and because mercury is denser than most materials all impurities such as dust or oil

can be removed from the surface easily using a skimmer.

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Figure 3: Main components of the liquid primary mirror and the scheme of a working liquid mirror

telescope. [4] The liquid mirror is formed in the container on the air bearing. Light is then reflected to the

focus, where the corrector eliminates the coma. Then light is collected on the detector. [6]

The aperture (the diameter) of this kind of mirror is determined by the size and focal

length of the container, the angular velocity of the container and the amount of mercury.

Theoretically if both focal lengths of the mercury and of the container match and if mercury is

spread in a layer with a thickness of 1mm, then with 1 liter of mercury the mirror area would

be 21m or a diameter of 0.62 meters, which is quite a powerful telescope.

The liquid mirror is of course just the primary mirror of the telescope. Usually there is

a secondary mirror or even a tertiary mirror that reflects the light to the eyepiece or to a

photographic camera or CCD. And every parabolic mirror suffers from an optical aberration,

called coma [7]. Light from a point source (such as a star) in the center of the field is perfectly

focused at the focal point of the mirror. However, when the light source is off-center (off-axis),

the different parts of the mirror do not reflect the light to the same point. The further off-axis,

the worse this effect is. This causes stars to appear to have a cometary coma, hence the name.

Because of coma an optical corrector is needed, that means three or four lenses are placed close

to the focal point, and good image quality can be obtained over an extended field of view.

The use of liquids as a reflective surface is very difficult. They are sensitive to vibrations

and wind, which could cause ripples on the otherwise smooth surface of the mirror. Curved

liquid mirrors need to be rotated with a precise and uniform angular velocity, otherwise the

stars appear blurred and of course the liquid mirror telescope can be pointed only directly

upward and it cannot track stars. Because of Earth's rotation stars seem to drift from east to west

and any astrophotography with liquid mirror telescopes requires really short exposures

otherwise stars would appear as streaks rather than sharp points. Another technique that solves

the problem of drifting stars is the so called drift scanning method that will be explained later.

And the use of mercury is somewhat questionable, because its vapors are toxic.

The main advantage of this kind of telescopes is that they are very cheap compared to

conventional mirrors (for same diameter the cost of liquid mirrors is one or two orders of

magnitude lower), immunity to scratches or cracks, low maintenance costs and little work with

the container of the liquid. And with some tricks the before mentioned disturbances can be

reduced or even completely avoided.

4 Applications of LMTs in Astronomy

The lack of flexibility is not quite as limiting as one might think. For a large number of

scientific studies, fixed pointing is not a hindrance. If the aim is to determine the statistical

properties of a large number of objects, say distant galaxies, it often does not matter what part

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of the sky is probed. One finds distant galaxies everywhere, and the zenith is as good a place as

anywhere else to look. Indeed, it is the best place to direct a telescope to because it offers the

least amount of air in the light path and hence the least amount of atmospheric absorption,

scattering and image distortion. A short list of the scientific applications includes:

• statistical determination of the cosmological parameters H0, q0 and λ0 based upon

surveys for multiply imaged quasars;

• statistical determination of these same cosmological parameters based upon surveys

for supernovae;

• search for quasars and observational studies of large scale structures;

• trigonometric parallaxes of faint nearby objects (e.g. brown dwarfs, etc.);

• detection of high stellar proper motions to probe a new range of small scale kinematics

(stars, transneptunian objects, etc.);

• astrometry of multiple star systems;

• a wide range of photometric variability studies (cf. photometry of stars, RR Lyrae,

micro-lensing effects,

photometry of variable AGN over day to year time scales, etc.);

• detection of low surface brightness and star-forming galaxies, and other faint extended

objects (galactic nebulae, supernovae remnants, etc.);

• galaxy clustering and evolution;

• finally, production of a unique database for follow up studies with 8m class telescopes

(cf. VLT, Gemini, Keck, ...). [8]

For such research programs, liquid-mirror telescopes serve just as well as conventional

telescopes but they don't cost nearly as much. The Large Zenithal Telescope - LZT with a

diameter of 6 meters was built for less than $1 million - an order of magnitude lower than what

one would spend for a conventional telescope of comparable size. So if some of the funds

designated for the construction of telescopes were channeled into instruments that use liquid

mirrors, astronomers doing this kind of research could get considerably more observing time.

If instead of one convential single solid mirror telescope ten liquid mirror telescopes were built

on convenient locations for the same amount of money, the observing time could increase

tenfold.

5 Reflective Surface

Because of its high reflectivity the material most commonly used in liquid mirror

telescopes is mercury. Liquid mercury has a reflection coefficient varying between 0.79 at

310nm to 0.78 at 870nm rising to 0.90 at 1300nm, while conventionally used evaporated

aluminum on glass has a reflectivity of 0.92 at 320nm, rising to 0.98 at 1000nm [3]. At first

sight, aluminum seems to have an advantage over mercury. But these values for aluminum are

for a fresh coating. Large telescope mirrors are never aluminized more often than once a year

and a very large telescope is likely to be aluminized even less often. The aluminum coating

deteriorates as the surface exposed to air is coated with dust, oil, etc. On the other hand, the

mercury layer can be filtered every day if necessary and restored to perfect conditions for the

night. In practice, aluminum and mercury are quite equivalent.

A consideration against the use of mercury as the reflecting liquid is that it can develop

toxic fumes. However, this can be handled safely with proper precautions. Tests have shown

that mercury fumes wouldn't be really dangerous if the observation room had some ventilation

[1].

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Because of toxicity and because mercury freezes at 234.3 K (-38.8 °C), alternatives to

mercury are also investigated. One promising substitute to mercury are ionic liquids, which are

not very reflective but do not evaporate and remain liquid at low temperatures. They can be

covered with a coating of silver so thin that the form of the mirror remains parabolic. Another

substitute are Metal liquid like Films (MeLLFs) – interfacial films of silver nanoparticles that

therefore exhibit high reflection and have the macroscopic properties of a fluid [9]. But for now

the majority of liquid mirrors use mercury.

6 Time Delayed Integration or Drift Scanning

It was mentioned before that liquid mirror telescopes can observe only the zenithal

region of the sky. Because the Earth rotates stars drift through the zenithal region and therefore

it seems impossible to measure any object for a reasonable time because any image of it would

appear blurred. The solution to this problem is a special use of charge coupled devices, or CCDs.

Let’s recall- a CCD chip is a silicon integrated circuit that measures light with a small panel of

up to several million tiny light sensitive pixels that are basically potential wells and converts

the optical image to an electric signal. Usually the CCD grid is constructed from A columns

with the length of B pixels in line. When a photon strikes the CCD sensor it sends an electron

from the silicon to the potential well where it is trapped and held as a small electrical charge.

This way the optical image is stored in the form of an electronic image within the CCD circuit.

If it is known how the optical image will move across the CCD chip it is possible to

manipulate the applied voltages in the CCD circuit in such a way that the electronic image is

shifted to the side of the chip during the exposure [10]. Because the sky is moving in the east -

west direction it is necessary to align the direction of the shift in the same way and applying

voltages to the electrodes in such a way that stored electrons in the potential wells drift along

the chip at the same speed as the drifting image. If that is done correctly, there is no blurring of

the image. When the star reaches the edge of the field of view the corresponding electrons reach

the edge of the CCD. There they are amplified and stored. Because the readout takes place

continuously there is no need for a shutter. Light from a star is accumulated the whole time the

star image is traveling across the CCD chip, typically up to two minutes. This technique is

called Time Delay Integration or "drift scanning" and is often used by astronomers because it

is an efficient way to image a large area of the sky. [11]

Figure 4: The Drift scanning method. [12]

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Zenithal telescopes can only observe declinations that match the geographical latitude

of the observation site (a zenithal telescope positioned in Ljubljana, Slovenia can only observe

the latitude +46.05° and its immediate neighborhood). The field of view is determined by the

focal length of the telescope l (which in case of liquid mirror telescopes is determined by the

angular velocity ω). The stars complete one circle (360°) in one sidereal day (T0=23.934469h

or 86164.0916 s). The CCD chip must be oriented in the east-west direction. The time to read

out a line (shift time) t0 can be calculated from the focal length f, the geographical latitude φ,

the height of the pixels s and the sidereal rate T0 [10]:

0

0 2cos

arctan

T

f

s

t

. (6)

For example: for the focal length 750mm, the height of one pixel on the CCD 9μm, the

geographical latitude 45° the time to read out a line is t0=0,2327 seconds. After this time the

sky has shifted so much that it is necessary to shift the accumulated electrons for one line. The

exposure time for a star is t=B·t0, after that it leaves the field of view. The height of the image

will be the same as the number of columns. The length of the picture, on the other side, depends

of our acquisition time T and can be arbitrarily long. Typically the total acquisition time T for

one picture is around 20 minutes, which produces pictures with the length of L=t0/T and cover

≈5° of the sky.

With this technique, one can let the sky drift into view of the camera for hours on end.

The net result is a series of images that form a strip 360°/T0 ≈15° long for every hour we keep

the exposure going (this statement is true for shooting at the equator; as one moves away from

there to a higher latitude φ, the stars move cosφ·15° every hour). How wide that strip is depends

on the number of columns of pixels on the chip and the focal length of the telescope.

Figure 7: Scan image acquired with an Audine camera and a Canon EF 300 mm F/4 telephoto lens. The

sky moves from the left to the right. At the right we see a ramp corresponding with the start of the scan.

The image has a height of 768 pixels and is 2800 pixels wide. [11]

At the equatorial arc of the sky, the stars move by the rotation of the earth with about

15 arc seconds per second. Near the pole the speed is much lower. In an image north of the

equator, the stars in the northern part of the image move slower than the stars in the middle, the

stars in the south move faster. This will cause a differential trailing in west- east direction. But

with longer focal lengths the field of view decreases, so the difference in speed is not so obvious.

With long focal length the effective exposure time decreases. The array disks caused by

seeing will become bigger. So a shorter focal length should be preferred. The liquid mirror

telescope here has the advantage since very mirrors with small focal lengths can be made easily.

But a paraboloid with a very small f has a very small usable field, because the spherical

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aberration, called coma, strongly affects any object that is not directly in the center of our field

of view [7]. It is therefore crucial to use a suitable optical corrector that corrects the off-axis

areas and therefore enlarges the useful field of view to several minutes of arc and a reasonable

focal length for the optimal performance must be chosen.

7 Disadvantages

As mentioned before liquid mirrors are sensitive to vibrations and wind, which could cause

ripples on the otherwise smooth surface. First LMT’s suffered from three main sources of

ripples that perturbed the surface of the liquid:

Jars of all sort (from the driving mechanism, the bearing and the floor)

Imperfect leveling of the instrument that causes »tidal waves«

Variations of the speed of rotation

Wind and Turbulences

Since the first experiments technology has advanced and today the leveling problem can be

overcome and the jars and the vibrations can be dampened by using an air bearing, which has

precisely ground surfaces separated by a thin film of pressurized air. These bearings are

essentially frictionless, precise and not expensive.

The changes in rotational velocity can come from the roughness of the bearing. The relative

error in rotational velocity is related to the relative error in focal length by df/f=2dω/ω. Let dθ

be the maximum degradation in resolution that can be tolerated, it is related to the focal length

variation by df/f=dθ·const. If we take sec2.0 arcd as a reasonable value and consider a f/1.5

mirror, the stability needed is dω/ω=7·10-7 [3]. This is very high but can be attained with a high

inertia turntable rotating on a frictionless bearing. These conditions are clearly fulfilled for the

large mirrors considered and the air-bearing turntable. To avoid friction between the motor and

the mirror that causes vibrations, a ring of permanent magnets is attached to the rotor of the air

bearing instead. These magnets turn within a magnetic field produced by multiple, usually three

stationary field windings. The rotation rate of the container is measured and if the mirror rotates

to fast or to slow the motor currents are adjusted so the mirror turns with the correct speed. This

way the speed of the mirror is kept constant under almost all observing conditions. [1]

Another disturbing factor is the wind: liquid mirrors need to be protected from it. Not

only that wind gusts can cause waves on the reflecting surface, wind can affect the movement

of the whole rotating container on the turntable. Therefore, it is crucial to put the whole

instrument in an environment that is protected from outside wind. And even if the angular

velocity of the telescope is not big, the outer rim of the telescope in moving with a considerable

speed (in case of the LZT with 2.2 meters per second). Thus the mercury on the outside of the

mirror sees otherwise stationary air moving over it at this rate. As is the case for wind blowing

across water, air becomes turbulent and as a result waves are produced. The solution is to

suspend a very thin film of transparent Mylar plastic a few centimeters above the mercury

(12μm thick on the LZT [13]). This cover rotates with the mirror, trapping the air beneath and

forcing it to rotate at the same speed as the mercury. The vortices are still present, but now they

are above the plastic and cannot affect the reflective liquid surface. The Mylar sheet also

protects against mercury fumes.

10

Figure 8: Because they must be kept spinning, large liquid mirrors are prone to distortions. Toward the outside,

where the mercury moves at high speed, the relative motion can induce turbulence in the air above, subtly

affecting the surface. This test image is of a 2.5-meter-diameter liquid mirror fabricated at the University of

Laval in Canada. [14}

8 Realized Projects

The idea of using a rotating liquid to focus light is nothing new. The Italian E. Capocci

was the first who described this possibility in print in 1850, but he never put the idea into

practice [9]. The concept was initially demonstrated in 1872, when Henry Skey of the Dunedin

Observatory in New Zealand constructed a 35-centimeter-diameter liquid mirror in his

laboratory. First complete liquid-mirror telescopes were built in 1909 by R. W. Wood. His most

successful model used a mirror that was 51 centimeters in diameter. It rotated on a mechanical

bearing and was turned by a motor using a drive belt consisting of fine threads of India rubber.

With this telescope, Wood achieved an angular resolution as little as 2.3’’. Still, Wood's

telescope had many flaws. It was sensitive to vibrations from the drive belt and outside

influences (nearby traffic, footsteps) and it suffered from a small but noticeable wobbling of

the mirror. Because he couldn’t maintain a completely constant spin there appeared fluctuations

of its focal length. And because the rotation axis had to be vertical, the telescope could observe

only a small area of sky directly overhead, and the rotation of the Earth resulted in constant

motion of the images, which means the telescope was useless for astrophotography and barely

useful for direct observations. Because of these problems liquid mirror telescopes weren't

considered usable for astronomy for another 70 years.

Then, in 1982 the Canadian Ermanno Borra decided to revisit the idea and realized that

modern technology could solve the difficulties that Wood experienced. Borra's team used an

air bearing and electronically controlled synchronous motor and constructed mercury mirrors

with a diameter up to 1.5 meters in less than ten years. These mirrors were built in a laboratory

and had a surface so smooth they were basically diffraction-limited - they were as sharp as it is

theoretically possible [15]. First operational telescope using the drift-scanning method was

made in 1994 by Hickson and his team. The diameter was 2.7 meters and they used a four-

element lens corrector to correct coma. The digital images of stars that were obtained with these

telescopes were very sharp and clear - the images were limited by the atmospheric turbulences

and not because of the liquid mirror. NASA Orbital Debris Observatory had a 3-meter diameter

and was used to catalog space debris in Earth orbit [16]. It operated from 1995 to 2002 and later

11

some of its components were used for the Large Zenith Telescope, with 6 meters the biggest

liquid mirror telescope to date.

The LZT was built in 2005 with the purpose to perfect liquid mirror technology to the

size comparable to the largest conventional astronomical telescopes (the largest single primary

mirror in the world is the Subaru telescope having a diameter of 8.2 meters). Located in British

Columbia in Canada, this telescope began regular operation in October 2005. Equipped with a

four-element Richardson prime-focus corrector and thinned 2048x2048 pixel drift-scanning

CCD imaging camera, it is used for astronomical survey observations and also serves as an

engineering test facility for further development of liquid mirror technology. Built at a cost of

less than $1 million dollars, it achieves an image quality and sensitivity comparable to that of a

conventional telescope of equal aperture and is limited primarily by the astronomical quality of

the site [13].

The primary mirror consists of a rotating steel truss and 30 adjustable pads that support

a 6cm thick dish. The dish is fabricated from seven hexagonal segments, plus six smaller pieces,

glued together to form a shell 6.1 meters in diameter. These are made from high-density PVC

foam covered with fiberglass. The foam cores were formed to a concave shape, with 18-meter

radius, by heating to 100C in a large oven. A wall at the rim of the mirror prevents mercury

from spilling. The diameter of the reflecting area is 6.00 meters. [17]

9 Future Plans

Of course there are plans for even better and more sophisticated liquid mirror telescopes.

One of the future projects is the International Liquid-Mirror Telescope with a diameter of 4

meters with a focal ratio of f/2 and a large format CCD camera. It will be built in the mountains

at Devasthal Observatory in India, where conditions for observations are very good (stable

atmosphere, low humidity and many clear nights) [8], [18]. The ILMT will be equipped, at its

prime focus, with a time-delay-integration (TDI) corrector capable of imaging a field of 30x30

arcminutes with a resolution better than one arc second. The ILMT will carry out direct imagery

using a 4K x 4K thinned CCD as the detector working in the TDI mode. The expected limiting

magnitudes are 24.5 at U, B and V bands, 23.5 at R and I band in a single integration [19]. At

the latitude of Devasthal, a band of half a degree covers 156 square degrees, with 88 square

degrees being covered at high galactic latitude (b > 30◦) including the direction of the north

galactic pole [20].

Another future project is the Advanced Liquid-mirror Probe for Astrophysics, Cosmology and

Asteroids (ALPACA) with an 8-meter liquid mirror in Chile. It would have a 2.5-degree field

of view and a drift scanning mosaic camera 240 CCDs [20].

Another idea is that of building observatories with liquid mirrors on the Moon. Because the

Moon has no atmosphere the sky is always dark and there are no atmospheric disturbances so

it makes an ideal observational location, also there is very little seismic disturbance If located

near the Moon's north or south pole the telescope could observe the same area of the sky for a

very long time (even months) and thus detect and study the most distant objects in the visible

universe. Because gravity is weaker on the Moon, bigger mirrors could be constructed and some

plans were made for a liquid mirror telescope with a diameter of 100 meters and a sensitivity

more than 1000 times greater than the James Webb Space Telescope [21], thus capable of seeing

the first stars in the early universe. Lunar telescopes could not use mercury as the reflecting

surface, because mercury would freeze on the Moon. Therefore, it would most likely use low-

12

temperature ionic liquids coated with a thin metallic film (MeLLF) that remain liquid and do

not evaporate. The lower gravity also gives the minor mechanical advantage that the rotational

velocity needed, for a given focal length, is lower. [22]

10 Conclusion

In this seminar I have presented an unconventional type of a telescope which is,

although not suitable for every type of observations, still usable for a number of scientific

observations. Its main advantages are low cost and easy maintenance. I also introduced a

special recording mode of CCDs that allows LMTs to use their full potential. Although LMT

will probably never replace conventional telescopes, they can become a useful addition to

scientific research and because of their low cost compared to other telescopes with

comparable size they are expected to became more popular in the future.

11 Literature

[1] P. HICKSON, Liquid-mirror Telescopes, American Scientist, May-June 2007, Volume 95,

Number 3, Page: 216

[2] http://www.nasa.gov/centers/ames/images/content/180724main_6-mMirror.jpg, (30 May 2016)

[3] E. BORRA, The liquid-mirror telescope as a viable astronomical tool, Royal

Astronomical Society of Canada, Journal, vol. 76, Aug. 1982, pp 245-256

[4] http://www.starosta.com/technical/art/liquid_mirror_.jpg, (30 May 2016)

[5] S. THIBAULT, E. BORRA, Liquid Mirrors: A new technology for optical designers, SPIE Vol. 3482. 0277-786X/98/ [6] HARRIS, W., How Lunar Liquid Mirror Telescopes Work,

http://science.howstuffworks.com/liquid-mirror-telescope2.htm, (29 May 2016)

[7] P. MURDIN, Encyclopedia Of Astronomy And Astrophysics, Page 743

[8] J. SURDEJ et al., The 4m International Liquid Mirror Telescope (ILMT), Ground-based and

Airborne Telescopes, edited by Larry M. Stepp, Proc. of SPIE Vol. 6267, 626704, (2006)

[9] B.K. GIBSON, Liquid Mirror Telescopes: History, JRASC, 85, 158, 1991

[10] http://www.driftscan.com, (29 May 2016)

[11] http://www.astrosurf.com/audine/English/result/scan.htm (29 May 2016)

[12] http://cmhas.wikispaces.com/DriftScanning (30 May 2016)

[13] P. HICKSON, The Large Zenith Telescope: A 6 m Liquid-Mirror Telescope, Publications of the

Astronomical Society of the Pacific, 119: 444455, 2007 April (vol. 119, pp. 444–455)

[14] E. BORRA, Optical Tests of a 3.7-m diameter Liquid Mirror: Behavior under External

Perturbations, doi: 10.1364/AO.39.005651

[15] E. BORRA, A Diffraction-limited f/3 1.5 Meter Diameter Liquid Mirror, 1989ApJ...346L..41B

[16] R. CABANAC, E. BORRA, M. BEAUCHEMIN, A Search for Peculiar Objects with the NASA

Orbital Debris Observatory 3-m Liquid Mirror Telescope, arXiv:astro-ph/9804267v

[17] http://www.astro.ubc.ca/lmt/home.html, (30 May 2016)

[18] http://www.aeos.ulg.ac.be/LMT/, (30 May 2016)

[19] SAGAR, R., New optical telescope projects at Devasthal Observatory, arXiv:1304.2474

[20] http://www.astro.ubc.ca/lmt/alpaca/specs.html (29 May 2016)

[21] http://www.astro.ubc.ca/people/hickson/llmt.html (29 May 2016)

[22] R. ANGEL, A Cryogenic Liquid-Mirror Telescope on the Moon to Study the Early Universe, The

Astrophysical Journal, Vol 680, Number 2, pp. 1582 -1594