Glossary of PRIMA
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Glossary of PRIMA |
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The Unit Telescopes (UTs) are the four main telescopes of the VLTI.. They have a diameter of 8.2m and are fixed on the ground, you can observe one UT in its box on the figure 1. A unit telescope has an alt-azimuth mount. In such a mount the telescope tube moves around a horizontal axis called elevation axis. The two bearings which support the tube are mounted on a fork rotating around a vertical axis, called azimuthal axis, thus allowing for pointing over the entire sky. The telescope tube itself consists of a steel structure supporting at the bottom the primary mirror (M1) in its cell, and at the top the M2 Unit by means of metallic beams called "spiders".
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Fig. 1: A Unit telescope |
Fig. 2: An Auxiliary telescope |
The Auxiliary telescopes (ATs), smaller are not fixed (two available
until here, cf fig. 2). With a diameter of 1.8m, the ATs will provide the best
imaging capability of VLTI by complementing the array of the four 8.2m telescopes.
The Auxiliary Telescopes can be placed on any of the 30 possible stations and
provide therefore many interferometric baselines. This will make superior interferometric
imaging possible. The ATs provide the longest possible baseline of the VLTI
(202 meters), fully utilizing the restricted space available on the Paranal
mountain platform. The ATs will be used by the "Narrow Angle Astrometry"
mode of VLTI (measuring extremely accurate positions of objects in the sky).
This requires long baselines as well as regular and long-term monitoring, not
achievable with the 8.2m telescopes.
The isoplanatic angle is the angle between two stars for which the correlation of the wavefront distortions, due to atmospheric turbulence, is sufficiently high. It depends on the wavelength (i.e. ~ 1 arcmin for a wavelength of 2 µm) and on the atmospheric conditions. This angle is given by: qo ~ 0.6 * ro/h
where:
The baseline vector between two telescopes is the three-dimensional vector relying the intersection of the altitude and azimuth axes of a pair of telescopes. The baseline (the modulus of the baseline vector) corresponds to the length separating the two telescopes. You can see on the figure 1 the different possible baselines offered by the telescopes of the VLTI (by joining two telescopes). This disposition allows choosing baselines between 8 and 200m.
Fig. 1: The VLTI array, with the different possible baselines offered by the telescopes disposition
This vector is involved in Interferometry (observation with many telescopes), e.g. into the determination of the OPD.
Considering the case of the VLTI, with two telescopes observing a distant source, the Optical Path Difference (OPD) is the sum of the external path difference and the internal path difference.
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Fig. 1: Optical Path Difference for the VLTI |
On earth, the atmosphere absorbes some radiations corresponding to some precise wavelengths, thus we talk about the transmission of the atmosphere.
Fig. 1: Transmissivity of the atmosphere
This transmission presents some characteristical peaks (cf fig.1 found on this site) that have been precisely defined and called with letters (U,B,V,R,I.Z,J,K,L,M,N). In the parts where the transmission reaches 0 , we can't also observe the radiations corresponding to these wavelengths directly from the earth.
Typically the working domain of PRIMA concerns the K band that belongs to the intervall [2.0,2.4µm].
Magnitude is a scale used by astronomers to measure the brightness of a star.
The first known catalogue of stars was made by the Greek Astronomer Hipparchus in about 120 B.C. and contained 1080 stars. It was later edited and increased to 1022 stars by Ptolemy in a famous catalogue known as the "Almagest". Hipparchus listed the stars that could be seen in each constellation, described their position, and rated their brightness on a scale of 1 to 6, the brightest being 1. This method of describing the brightness of a star survives today. Of course, Hipparchus had no telescope, and so could only see stars as dim as 6th magnitude, but today we can see stars with ground-based telescopes down to about 22nd magnitude.
The mathematic definition of the magnitude is the following: M = -2.5 log ( I / Io ) , where I is the brightness of the observed object and Io a reference brightness taken among rereferences taken by the greeks.
e.g. the star Vega (alpha Lyrae) has thus a magnitude of 0, the ste star Sirius has a negative magnitude of -1.46.
Generally we give the observation band just before the magnitude to precise the spectruum of observation (Ex: K 16).
For more informations about the magnitudes, cf "Methodes de l'Astrophysique" by P. Lena.
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The parsec (PARallax SECond angle) unit is often used in Astronomy, it corresponds to the length between a far star from the earth and the ecliptic plane (Elliptic orbit of earth) when the half of the large axis of the elliptic orbit of earth is seen from the star with an apparent angle of 1 arcsec (cf fig.1).
This unit is noticed pc and 1 pc = 206,265 a.u = 30 000 000 000 000 m = 3,26 light years.
N.B: 1 u.a = one averaged Earth-Sun distance and 1 light year = the length that covers the light for a year.
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Fig. 1: The pc unit |
On each telescope of the VLT, there is three special optical foci, the Cassegrain focus, the Nasmyth focus and the Coude focus. According to the needs, the differents instruments of the VLT will use these foci.
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Fig. 1: The optical foci of the VLT |
First the Cassegrain focus is located just after the secondary mirror (M2), it is able to move in a 2 dimension plane according to the movements of the primary mirror (M1). Using this focus has the main inconvenient to limit the maximal weight of the instrument that would use it because it is directly connected at the primary mirror M1. You can see the Cassegrain focus on the figure 1. To use the Cassegrain focus, M3 is lifted up.
Secondly the Nasmyth Focus is located just after M3, it is on the rotation axis of the telescope. Compared to the Cassegrain focus, the advantage is that we have the possibility to put a heavier instrument but it is always moving with M1 (with a rotating movement). You can see the Nasmyth focus on the figure 1.Moreover, M3 has the possibility to be turned of 180 degrees, offering the possibility to put an another instrument in the new direction. That's why there is in practice two Nasmyth foci, called A and B.
Finally the Coude focus is located after M8, it doesn't belong to the moving part of the telescope and is fixed on the ground. The field is rotating but we can put all the instruments we want without having the precedent limits. You can observe the position of the Coude focus on the figure 1. |
In practice the different foci will be use by the following instruments:
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Cassegrain focus
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Nasmyth Focus
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Coude Focus
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A
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B
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To increase the detected magnitude, PRIMA always uses two objects to work, a bright guide and the faint object we want to study separated by a narrow angle (cf fig.1).
Fig. 1: A bride guide star and a fainter star
Sometimes, the brightness of the faint object we want to detect is drown in the resultant background. We don't "see" any more the object in single exposures. To solve this problem of background, PRIMA will use the "chopping" mode, that consists in pointing alternatively the object, and an another position in the sky without stars within a narrow angle around the searched object. Typically, the system must chop 5 times per second in order to be effective. Afterwards making the difference between the two exposures (with and without the faint object) allows remorring the background and detecting the studied object.
Using this method, an object 10e3 to 10e4 fainter than the background can be detected.
Ideally, the "chopping" must be realized with the mirror closest to the star (M1 mirror), practically the idea is to work with the secondary (M2) mirror with the Unit Telescopes (UTs) ans the M6 mirror with the Auxiliary Telescopes (ATs) (cf the telescope optics layout on the fig. 2).
Fig. 2: VLTI Optics layout
But it has led to some difficulties. Finally the M2 mirror is relatively difficult to move so fast (because of its dimension and weight), moreover to study the beam in the Cassegrain Focus is not very practical (cf the optical Foci of the VLT) .An another solution is to use the Nasmyth Focus near the M3 mirror, but there is always a movement including a limit of weight. The solution to have a fixed beam is to work with the Coude Focus (near M8):
Fig. 3: Coude relay optics
even if the field is rotating, the focus keeps its position. Secondly at the Coude focus, there is Strap as you can see on the third figure (or an adaptative optics sensor) whose role is to stabilize the image of the star in the field of view movement, movement induced by the same atmospheric turbulences, and the fringe stracker stabilizes the movement. Both systems (STRAP and FSU) need the star light. If the beam reaching them is chopped the corresponding cloud loops should be opened and closed 5 times per second, wich is not optimal for the system efficiency.
To avoid this problem, it is prepared to chop the beam with the STS (after the M9 mirror, cf fig. 2). The chopping will not effect STRAP and will only be applied on the faint star, not on the fringe tracker.
For terrestrial interferometry (observing directly from the ground), we have to take care about the presence of the atmosphere and the Longitudinal Atmospheric Dispersion (LAD) that has several consequences for PRIMA.
In vacuum, there is no problem: the different monochromatic fringes have all the same maximum at the same absolute position (cf fig.1) even if due to the different wavelengths, the fringe patterns don't have the same period. Thus the group delay corresponds exactly to the global fringe pattern.
But in the atmosphere the air index of refraction varies with the wavelength under the law: (Leveque, 1997 applicated of the index of refraction formula of Gubler & Tytler, 1998)
where the coefficients have been calculated for the atmospheric prevailing conditions prevailing in the VLTI tunnel, i.e. T = 289 K, P = 743 hPa, and so the following values:
a ~ 199.329e-66 , b ~ 1.129e-6 µm^2 , g ~ 0.009e-6 µm^4
This variation with wavelength of the air index of refraction rises to longitudinal dispersion, i.e. a wavelength dependence of the OPD.
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OPD = (n(l)/n(lo) -1)* L
We have introduced the lenght L corresponding to the geometrical delay (cf fig.1), but each maximum of the monochromatic fringes group is corresponding to a particular lenght L.
For a FSU with a finite bandwith (the K band for example), it has these the following main consequences:
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Fig. 1: Influence of the atmospheric turbulences on the OPD |
Transversal Atmospheric Dispersion deals with the wavelength dispersion by the atmosphere. It deforms the image of the star that is elongated at the moment which the STS sends it on the optical fibers. This aspect will be corrected by the STS. Secondly the pointing depends on the crossed air mass, inducing errors that are automically corrected by the VLTI softwares.
TAD acts principally on the FSU's work and has two mains effects on it:
The Airy's Disk is the the first diffraction's disk given by a natural aperture that has a disk form (for the telescopes of the VLTI, this aperture is given by the size of the telescope itself).
For observing a monochromatic light with the lo radiation, if d is the diameter of the telescope, anf f the focal of the telescope, the radius of the Airy's disk is given by:
R = 1.22*lo*f/d
The diffracted intensity follows a law varying with (card sin)^2 (cf fig.1), in practice we observe then different concentric circles of ligth around the Airy's disk with a decreasing brightness.
Fig. 1: Intensity of diffraction of a circular aperture
The photon flux available for the PRIMA facility (and required in a sufficient quantity in order to pratice imaging or astrometry...) depends mostly on:
1. the celestial object magnitude
2. the telescope collecting areas (that's why the VLTI has been constructed with great telescopes: diameter of 8.2m for the UTs and 1.8m for the ATs)
3. the optical transmission of the atmosphere and of VLTI optical trains
For a given star magnitude, m, the photon flux is given by the following equation: P = a(K band)*10e(-m/2.5) where a (K band) is a proportionality constant.
The FSU uses only the coherent part of this flux, transmitted by its spatial filter. We assume that the coherent flux of each incident beam is equal to its flux multiplied by its Strehl ratio. Actually this Strehl ratio fluctuates rapidly because of the atmospheric turbulences, affecting also the coherent flux.
Moreover, part of the coherent photons are lost in the input of FSU spatial filter, due to the mismatch between the respective intensity distributions of the VLTI and the spatial filter propagation mode.
The Descartes rules explain that for two different spaces 1 et 2 with index of refraction n1 and n2, the refracted beam is defined by: n1*sin i1 = n2*sin i2 (cf fig.1)
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Fig. 1: The phenomenon of refraction |
If n2 < n1, d = n1 * sin i1 = n2 * sin i2, the existence of the refraction is limited by the angle i lim (cf fig. 2), for i1 > i lim, there is no refraction any more. |
Fig. 2: Total Reflection |
With this defined angle i lim, we can have a total reflection, and during this phenomenon the dependence with the wavelength is very small. After a total reflexion, the reflected beam has a supplementary phase determinated by the material index (here the glass), if we choose correctly this index, we can also fix the supplementary phase at p/2, offering a solution for the ABCD Algorithm that requires 4 beams with a phase difference of p/2 between each of the beams.
We have choosen the properties of the reflection to obtain after many reflections (three in practice for the FSU of PRIMA) a phase difference of p/2, thus we obtain 4 beams with the wanted phase difference between each of them. For the first telescope, we send the beam into a K prism (cf fig.1):
Fig. 1: The K prism and the cube beam splitter of the FSU
The perpendicular polarisation is noted s and the parallel polarisation p. After each reflection, we introduce a supplementary phase on the p polarisation, at the exit of the prism, s and p are shifted by p/2. The beam of the second telescope is sent to the same length of glass to keep the symmetry in the longitudinal dispersion. There is thus no differential phase between s and p polarisations. The beams of the two telescopes are sent on a Cube Beam Splitter, where the interferences take place.
To obtain the 4 beams with a phase shift of p/2 needed for the ABCD algorithm in order to reconstruct the group delay (goal of the FSU sub-system), we send each of the two beams that left the cube beam splitter in a polarising cube splitter (cf fig.2):
Fig. 2: Polarising cube splitter
Thus we obtain 4 beams we wanted, that correspond to the ABCD points.
Adaptive Optics (A.O) have for main goal to correct the effects of the atmospheric turbulence on the wavefronts coming from the star. It implies a work with a high frequency (contrary to the Active Optics that are directly applied on the primary mirrors of the telescopes to correct each 30 s the wavefronts to keep them plane). We can approximate the variations of the atmospheric turbulence to 10 ms, it corresponds to the fact that the averaged gap between two wavefronts: s > l (with l the wavelength).
The main idea of the A.O is to measure the wavefront form each 10 ms (in order to follow the atmospheric turbulence). However the primary mirror isn't able to change its form so fast. Thus instead of using directly the primary mirror, A.O will use an another mirror, smaller (its diameter reaches the centimeter level for a thickness of 1.2 mm), on the traject of the ligth beams that can be be deformed faster thanks to a piezo-electric system. This system allows working with frequencies ~ 100 Hz and stabilizing the wavefront.
In fact the corrective optics replace the 8th mirror of the Coude train that coincide with a pupil plane. The A.O system consists in a 60 element bimorph mirror coupled with a curvature WaveFront Sensor (WFS), the WFS detectors are 60 Avalanche Photo-Diodes (APDs).
For a fringe pattern of a polychromatic light, the group delay corresponds to the maximum of the enveloppe function (or the position of the maximum coherence).
Fig. 1: Group delay of a polychromatic light
The group delay can be mathematically defined by the expression:
GD(s0) = Lv + n(s0) * La + Latm
where:
e.g. On the fig.1, the group delay has the abscisse OPD = 0
But the local maximum of the white fringe is able to move inside the enveloppe function. That's why has been introduced the group delay as a reference.
In vacuum, a polychromatic light has a fixed local maximum of the white fringe (cf fig.2). In fact all the different wavelengths composing the polychromatic light have the same absolute maximum for the white fringe at OPD = 0, but are shifted elsewhere.
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But in the atmosphere, the OPD is depending on l , the different wavelengths are shifted even for OPD = 0 (cf fig.3). That's why the global fringe pattern can have a local maximum of the white fringe not corresponding on the group delay. The FSU has in charge to determine the position of the group delay and the shift phase.
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