II. C. The Fringe Sensor Unit
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I. Introduction A. The goals of PRIMA B. Interferometry Tutorial C. Atmospheric and physical Constraints   II. Description A. The STS B. The PRIMET C. The FSU D. The DDL E. PRIMA Software III. Applications   IV. The Team   V. The Partners   VI. References, links

Table of contents of the FSU part: 1) Objectives of the FSU 2) Technical requirements on the FSU 3) Principle 4) Next milestones 5) Publications about FSU   After the picking up of the stars, the PRIMA facility must be able to track the fringes of a bright guide star to give a reference to the fringe tracking on a fainter object. To realize it PRIMA will use the Fringe Sensor Unit that will be put in the laboratory of the VLTI. Concerning this subsystem, we have to see what are its objectives, the technical requirements it has to perform, its general principle of working and the next milestones. The FSU A and B are located in the laboratory of the VLTI, just after the DDL and before the OPD controller system, moreover they are linked to the PRIMET system (cf fig.1):   Warning! The Netscape and Mozilla navigators don't recognize the greek letters, that could disturb the good reading of this page.

Fig. 1: Link between the FSU and PRIMA

Objectives of the FSU

The Fringe Sensor Unit (FSU) shall perform the tasks of a general purpose fringe tracker and a dedicated astrometric camera: it has to allow accurate measurements of the fringe position and (re)centering of the fringe packages and measurements of the group delay. For astrometry, we need two FSU: one for fringe tracking (FSU B) and one as an astrometric camera (FSU A). They must be symmetrical. This symmetry will allow permuting the two observed stars in the astrometric mode between the feeds in order to calibrate for instrument biases not measured by the metrology. The FSU design shall also be integrated and optimised with the metrology injection optics in order to reduce the non-common optical paths to the minimum and to stabilize them in a controlled environment.

FSU B is in charge to track the fringes of a bright guide star very fast and measures the corresponding group delay. With the help of the Delay Lines, this FSU stabilizes the fringes around an arbitrary "zero" point.

FSU A will ensure the fringe tracking on fainter objects and the measurement of the group delay. In vacuum, the group delay of a polychromatic light (i.e. the maximum of the envelope function) corresponds exactly to the local maximum of the white fringe (as you can see on figure 2).

Fig. 2: Fringe package in vacuum, exact correspondance between the local maximum of the fringes and the group delay

But if the beams propagate in air filled delay lines, due to the Longitudinal Atmospheric Dispersion (LAD) , the local maximum of the white fringe is shifted compared to the maximum of the enveloppe function (this shift varies with the DL position), so the objective of the FSU is to measure the fringe phase and the position of the group delay.

Requirements on the FSU

In a general way, performances specified for the FSU are required for the following conditions: the celestial object effective temperature is comprised between 3500 and 25000 K, and the celestial zenital angle is comprised between 0.5 and 60 degrees.

a) Fringe tracking:

The FSU has to combine the beams and to observe interferences. First, in order to realize it, the FSU must detect the local maximum of the fringe pattern on bright stars with a high measurement speed (at a frequency of ~ 8kHz).

Secondly, the FSU has to realize a group delay measurement with the same resolution on faint stars or slowlier on bright stars to check if fringes locked in fringe track are still centered on the group delay. This measurement has a slowlier frequency , typically f < 100 Hz.

b) Sensivity:

The FSU has to track fringes with low residuals on bright stars (typically K<10 for the ATs, and K<13 for the UTs) and allow an accurate fringe detection and measurements on fainter stars (K<16 for the ATs and K<19 for the UTs), typically the wanted resolution has to reach the nanometer level. Required fringe tracking accuracy is given in Table 1.

c) Observing band:

Initially, a fringe sensor already exists in the VLTI: FINITO, that works in H band.The FSU needed for PRIMA must allow observations in K band (with wavelengths from 2.0 to 2.4 µm). It will complement FINITO and the fringe measurement accuracy is better in K band (thanks to higher photon flux, higher visibility, lower LAD, larger wavelength, despite higher background noise).

Finally we can resume the main performances required by PRIMA concerning the FSU in the following table:

Table 1: Required performances on the FSU

Principle of the FSU

a) FSU modes:

Both FSUs can work in two modes:

Phase tracking mode: This mode is very fast (a frequency of 8 kHz) and is used for finding the local maximum of the fringes, we verify that it is the global maximum thanks to

Group Delay Tracking mode: This mode is slower and is used to find the group delay (typically a frequency inferior to 100 Hz). Indeed the signal detected (the envelope function due to the polychromaticity) is less contrasted, the signal to noise ratio is lower and we must integrate a longer time to reach the same precision.

b) ABCD Algorithm:

To reconstitute the phase delay, the FSU of PRIMA will use the ABCD Algorithm.

For the moment, let's consider what would happen if we would work in vacuum (without the problem of shift between the group delay and the local fringe maximum).For a monochromatic source the equation of the fringes is the following: (cf the interferometry tutorial)

(cf the sinusoid form on the fig. 3)

where V is the visibility and f the phase delay that we have to measure. Technically, only these two parameters are necessary to characterize the curve. With only two measurement points and the equation, we can fit the fringes. If we want to take more points to improve the precision, there will be less photons decreasing the sensitivity.

Two points could be enough (for example A and B shifted by p) but because of an incertitude on the sign of f we would have a choice between two curves (cf fig.3):

Fig . 3: Intersections of two sinusoides shifted

To avoid this uncertainty the classical ABCD algorithm has been prefered for PRIMA. The ABCD algorithm consists in taking 4 points each shifted by a phase of p/2 (cf fig. 4).

Fig. 4: The ABCD points separated by a phase of p/2

c) Realization of the phase shifts:

But this technique led to the essential following question: How to introduce the p/2 shifts?

One possibility is to scan the fringes with an OPD depending, but this mixes the variability of the signal due to the atmospheric turbulence with the OPD scan, reducing the accuracy and the sensitivity of the measurement. To avoid this problem, we need to have our 4 points without such a scan: we introduce simultaneously 4 different OPD shifted by p/2 (discret phase jump):

To realize it, one solution is to separate the light into 4 beams and to introduce a different achormatic OPD on each. This is done by using the phenomenon of total reflection which is weakly dependent on the wavelength.

d) FSU Principle:

To separate the main beam into 4 secondary beams and introduce between them the wanted phase, we will use the polarisation properties of the light. After the obtention of the wanted phases for these beams, the cube separates each beam into two beams that will interfere with their counterpart of the other telescope. But between the transmitted and reflected combined beams, a phase of p is introduced by the cube beam splitter (Cf fig. 5).

Fig. 5: Principle's scheme of the FSU

Finally at the exit of the final beams, we put 4 optical fibres whose core diameter corresponds exactly to the diameter of the Airy's disk (the image of the star).

e) The influence of the group delay:

This would be very simple if there was no group delay. To measure this one we keep the same principle and we send the beams into a dispersive Prism.The 4 optical fibers are sending a polychromatic beam on a convergent lens before a dispersive prism that deviates the different wavelength of the beam, each collimated by an another convergent lens to image the fibers on an IR detector (cf fig.6).

Fig. 6: The dispersive prism of the FSU

Instead of having a traditionnal disk (case 1 on the fig.5) as image we will have an elongated disk in the direction of the dispersive prism (case 2 on the fig.7).

The elongated (dispersed) image of each beam is sent to an IR detector and detected on a certain number (To be determined, TBD) of pixels (e.g. 3 pixels on the fig.8), each corresponding to a different wavelength.

We apply the ABCD Algorithm on each of the separated wavelengths. Taking into account the atmospheric dispersion, having the phase delay at each wavelength and the phase delay of the white fringe, we can reconstruct the group delay which was our objective.

Next milestones

The FSU has passed with success its first milestone, the Preliminary Design Review. The next milestones are given in the following table:

I. Introduction A. The goals of PRIMA B. Interferometry Tutorial C. Atmospheric and physical Constraints   II. Description A. The STS B. The PRIMET C. The FSU D. The DDL E. PRIMA Software III. Applications   IV. The Team   V. The Partners   VI. References, links

More informations about FSU "PRIMA Technical Description and Implementation", F.Derie, F.Delplancke,A.Glindeman,S.Leveque, S.Menardi,F.Paresce,R.Wilhelm,K.Wirenstrand,Workshop "Hunting for Planets ", Lorentz center, Leiden University, 3-6 June 2002. Slides of the presentation. “Optimized fringe tracker for the VLTI/PRIMA instrument” F. Cassaing, C. Coudrain, B. Fleury, P. Madec, A. Glindemann, S.Leveque, SPIE conference: "Astronomical Telescope and Instrumentation 2000", Munich (Germany), 25-31 March 2000, [4006-17] For the other publications, see the part: References and links.

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