I. C. Atmospheric and physical constraints
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I. C. Atmospheric and physical constraints |
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The VLTI has been constructed to observe the sky directly from the earth. There is actually some projects of space interferometers, like the DARWIN facility. In vacuum, there is on an astronomical observation point of view no problem, the beams are coming directly from the stellar objects without perturbations. However, on the ground, we have to take into account the important effects of the atmosphere on the beams coming from vacuum and crossing it on the one hand and of the physical constraints imposed by the ground on the other hand. To limit these effects, the setting of the VLTI has been chosen in Paranal, a desert in the middle of Chile Atacama desert where there are 360 observation nights per year, and where the air is not very turbulent offering a good seeing (cf the picture below showing the Atacama desert looked from the sky). We will see what is exactly the influence of the atmosphere on PRIMA, and what are the main other physical constraints in order to introduce the solutions proposed by the PRIMA facility.
View from Vacuum of the Atacama desert
Warning! The Netscape and Mozilla navigators don't recognize the greek letters, that could disturb the good reading of this page. |
The atmosphere is turbulent. These turbulences are first characterised by the deformation of the wavefronts seen by one telescope, then by a supplementary OPD called the atmospheric piston between two telescopes and finally by the phenomenon of anisoplanetism. But what are the origins of such turbulences? More than eventual clouds, the gases composing the atmosphere move, the temperature and the pressure vary constantly, so is the index of refraction of air varying with time and space.
The atmospheric turbulences will affect the path of the light beams.To introduce the atmospheric turbulence phenomenon, let's consider parallel light beams coming from space (cf fig.1) without taking care of the atmosphere in a first time. In optics (and in particular in Interferometry) we talk about wavefronts.
Fig. 1: General traject of the beams from the star to the fringes trough the VLTI optic train
When a star (or an another stellar object) produces light, there is an isotropic distribution of the light beams, the wavefronts are spherical (like a stone falling into water produces spherical waves). If we observe these beams far enough from the star (in particular with two telescopes of the VLTI on Earth, cf fig.1), we can locally approximate the spherical wavefronts as plane wavefronts. That will be exactly the case of a telescope in orbit around Earth for example.
But when the plane wavefronts penetrate the atmosphere, the perturbations due to the turbulences modify the form of the wavefronts and they are not plane any more. The variation of the index of refraction implies different speeds of the light waves for different beams. The new form of the wavefronts is varying continuously (cf fig.2) depending on the local atmospheric conditions.
Fig. 2: Animation of the atmospheric piston
click here or on the picture to see the animation
a) Image degradation:
Looking on the figure 2, we can clearly see that for one telescope the wavefront is not plane any more on the aperture. Without correction, this has for main consequence a degradation of the images. It will be corrected with a system of Adaptive Optics (A.O) in charge of deforming the telescopes to bring the wanted correction (cf solutions brougth by PRIMA).
b) Interferometric piston:
In the inferometric case, the wavefront reaching one telescope will be delayed compared to the other by the atmospheric turbulences. This difference is called the atmospheric piston (cf P on the fig. 2) and its value is varying with time (cf fig. 3). The degree of turbulences in atmosphere is characterized by the amplitude of the variation. For an integration time long enough, the average value of the atmospheric piston is null (cf fig.3).
Fig. 3: Values of the atmospheric piston each intervall Dt
Due to the atmospheric turbulences and to this atmospheric piston the fringe pattern in a telescope interferometer shows a dynamic behaviour. It is smeared out after few 100 ms (depending on the observation wavelength). Thus, if the integration of the observation is too long , we loose the visibility and won't distinguish fringes any more!
c) Anisoplanetism and differential piston:
If we succeed to stabilize the fringes of the bright star with an appropriate correction (cf solution brought by PRIMA) comes another problem, because the faint object is not aligned with the bright star. The path of the light beams are different (and in particular in the atmosphere) when the telescopes are looking both stars. There is a differential piston between both stars. Its amplitude is lower than that of the single star piston.
These differential perturbations will cause some small oscillations of the fringes of the fainter star (jitter). In practice we will never observe fixed and stable fringes.
a) The basis of the VLTI:
The two telescopes that will be used by PRIMA (for any combinaison taken among the UTs and the ATs) are fixed on the terrestrial ground, a mountain in the middle of a desert at an altitude of about 2600m. However this ground isn't perfectly stable. Thus, movements of the ground (in general at the µm or mm level) are induced by such general phenomenons as terrestrial tides or settings of the ground. One has to measure precisely these movements in order to correct for their influence on the geometrical delay between the two incident beams, i.e. deleting exactly the optical path difference induced.
b) The atmospheric dispersion:
We must take care of some additional phenomenons when we want to extract and correct some signals: the longitudinal atmospheric dispersion (LAD) concerns the traject of the light beams in and outside the VLTI and the transversal atmospheric dispersion (TAD) concerning the pointing of the stars, these two notions are not developped here but in the glossary.
c) Mobility of the ATS:
The ATs have been constructed in order to have the possibility to have a larger choice of baselines (in practice 8 to 200m). However, the repeteability of their movements does not reach the µm level, they never have exactly the same position.
d) Pupils position:
In PRIMA the baseline of the exact positions of the entrance's pupils. These ones are given by M1 and M2 (the primary and the secondary mirrors) combination and are located well below M1. But as the telescopes are not fixed to be able to pick up the stars, the positions of the pupils are not fixed with time.
Faced with such constraints, to perform its requirements of accuracy, PRIMA has brought the following corrections.
Adaptive Optics system (AO) take care of correcting at high frequency (to follow the fast atmospheric variations each 10 ms) the wavefronts deformed by atmospheric turbulence on each telescope. To realize it, instead of deforming the primary telescope each 10 ms (which is technically impossible) adaptive optics deforms a small mirror (with a diameter of some centimeters and a thickness of 1.2 mm) thanks to a piezoelectric system at a frequency of some hundreds of Hz. Thus the wavefront can be stabilized and a diffraction limited image observed. A.O however doesn't correct for atmospheric piston.
Faced with such atmospheric and physical constraints to interferometric observations, PRIMA has brought some new concepts to push back the limiting observations due to these effects.
a) The increasing of the sensitivity:
Because of the atmospheric piston, without any correction, the fringes are permanently moving. But PRIMA has as an objective to increase the sensitivity of the VLTI to allow it observing objects up to 5 magnitudes fainter.
Until PRIMA, the compromise between long integrations to have the highest number of photons and shorter integrations to keep the best visibility was limited by these atmosphere turbulences. In fact, without PRIMA, in order to freeze the fringe pattern, the maximum exposure time is limited to few 10 ms (observed 2 µm wavelength). If a bright object, close enough to the faint object, is used to measure the fringe position and then to stabilize the fringes in a closed loop system, the maximum exposure time on the faint object can be extended by many magnitude (from milliseconds to several seconds).
PRIMA allows observing a bright star and measure the position of its fringes with very short expositions (inferior to 10 ms) with a correction to bring them to a reference position (the "0" position, the absolute position of the white fringe) thanks to the delay lines (the actuator) and the fringe sensor unit (FSU) B (the sensor).
Afterwards we will be able to integrate longer and get more sensitivity.
b) Astrometry:
Moreover, PRIMA wants to perform micro-arsecond astrometry, i.e. to measure the relative position of two stars with micro-arcsecond accuracy. To realize it, the telescopes have to measure the differential optical path difference (DOPD cf fig.5) with nanometer accuracy meaning the same accuracy for the measure of the delay lines displacements.
Fig. 5: Differential OPD
When the fringes of the bright star are stabilized, we can observe the fringes of the fainter object and the fringes of the bright guide star with the FSU A. The relative distance between the two fringes packages, DOPD is measured by PRIMA metrology and allows determining the angle a between the two stars with the formula (cf fig.5):
where B is the baseline, i.e. the distance between the two telescopes.
e.g. With a baseline of 100m and a DOPD measured with an accuracy of 10nm, the angle measurement accuracy is around 10e-10 rad ~ 20 µarcsec, knowing for a physical comparison that 2 mas represent the size of a human on the moon viewed from the earth.
c) Phase referenced Imaging:
PRIMA will finally enable phase referenced imaging. The current VLTI instruments (MIDI, VINCI) are just giving the visibility modulus. PRIMA allows measuring the phase, meaning the relative position of the white fringe of the two stars. The phase is in fact an essential part to realize better imaging: fig.6 shows us two objects reconstruction when the amplitude of the complex visibility of the one is crossed with the phase information of the other. It shows clearly the importance of the phase compared to the amplitude.
Fig. 6: Comparison betwee the respective influence of phase and amplitude of the complex visibility in reconstructed imaging process
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We will use two stars. The brightest is used as a reference (the white fringe occupes the "0" position), and we measure the phase difference f with the fainter object: the relative distance between the two fringe patterns is given by the formula:
How do we find the image of the object? We will realise maps of measured visibility and phase (cf the complex visibility in Interferometry tutorial) as a function of the baseline. Typically to realize such maps (in practice the (u,v) maps), we take a fixed baseline and we measure a point of the amplitude of the complex visibility, and a point of its phase. Because of the earth rotation, the baseline is rotating too, when we observe the measured point for a long time, the measurement points move in the (u,v) plane along elliptical curves (Typically the period of an observation is 8 hours). Then we change the baselines and do the operation again. When we have enough points on the (u,v) map, we use mathematics methods to take the inverse Fourier transform and obtain an approximation of the image of the object!
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