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Astron. Astrophys. 346, 181-189 (1999)

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3. Instrumental results

Results are given for the nights of April 2 and April 3 1998, and are consistent with each other.

3.1. Background characterization

In this section we estimate the amount of thermal background received by the detector, and quantify its estimated uncertainty at the time of stellar observations.

3.1.1. Intensity

As described above, the interferometric beam is seen by the detector with a beam etendue of roughly 10 [FORMULA]. Assuming an overall emissivity of the warm optics of 1 and a transmission of the cold optics of 1, we find a maximum thermal background Noise Equivalent Power (N.E.P.) of 1.6 [FORMULA]. For comparison the N.E.P. of the detector (measured around 300 Hz) is [FORMULA], i.e. six times larger, so our observations in the L band are presently limited by the detectors. Table 1 compares the amount of thermal background expected in the K, L, M and N photometric bands. Note that the detector's N.E.P. only depends on the fringe apparent frequency. As long as this frequency is set around a few hundred Hz in each spectral band, the detector's N.E.P. is then considered here as a constant versus wavelength in a first approximation.


Table 1. Theoretical intensity of the thermal background in various standard photometric bands. The overall emissivity of warm optics is taken to be unity. Fluxes are computed for a 300 K source seen in one coherence etendue, i.e. a beam etendue of [FORMULA], where [FORMULA] is the mean wavelength of the spectral band. The ratio of thermal to detector noises assumes a detector Noise Equivalent Power of [FORMULA] as expected with our current photometer for frequencies of a few hundred Hz. Last two lines give theoretical point source limiting magnitudes using single mode fibers on IOTA in the L, M and N bands. Assumptions are: telescope diameter of 45 cm, overall emissivity of 1, beam etendue seen by the detector of 10 [FORMULA], overall transmission (optics and detector) per arm of 1%, interferometric efficiency of 50%, and fringe frequencies of 200 to 500 Hz.

3.1.2. Resulting sensitivity

The theoretical limiting magnitudes for observations of a point source with the TISIS experiment on IOTA can be estimated in the various spectral bands as presented in Table 1. These values are derived from the FLUOR detection and reduction strategy (Coudé du Foresto 1997), taking a signal to noise ratio of 5 on each single measurement of the visibility squared modulus, assuming a beam etendue seen by the detector of 10 [FORMULA], an overall transmission (optics and detector) per arm of 1%, and an interferometric efficiency of 50%. With the Noise Equivalent Power of our photometer ([FORMULA] for frequencies in the range of 200 to 500 Hz), we expect a theoretical limiting magnitude of -2.5 in the L band.

With a Noise Equivalent Power of [FORMULA] the detector noise dominates in L and M. With a detector of 10 times lower N.E.P. we should reach the thermal regime in the M band. In the N band, the thermal background is of course always dominant, and the sensitivity of the 45 cm siderostats is very low. The only candidates for observations in the N band have weak visible counterparts so that an infrared star tracker would be required.

A search for fringes on SW Vir, whose L magnitude is -2, was unsuccessful. [FORMULA] Her and Arcturus have respective magnitude -3.7 and -3.1 in L, so that the observed limiting magnitude is about -3 at the moment, which is in good agreement with theoretical expectations. Sensitivity can be improved using a fully transparent coupler in the L band, and detecting fringes on two complementary interferometric outputs. Less noisy detectors would also be very helpful, as Table 1 clearly shows.

3.1.3. Temporal fluctuations

  • A slow parallel drift of the shutter and sky signals is observed, probably due to a slow drift of the detector inner temperature (Fig. 4a). The shutter signal effectively needs to be taken as a reference if one wants to estimate the background signal at the time of stellar observations.

  • The difference between the sky and shutter signals is averaged over each scan ([FORMULA]s long), and ultimately over each consecutive batch of 100 scans. Fig. 4b shows the average level computed on such batches and the related error bars. In all cases the variation of the "sky-shutter" level between two consecutive batches bracketing stellar observations is small enough to estimate the average background level at the time of stellar interferometric observations within 1 mV. This error has to be compared with a stellar signal of typically 100 to 200 mV. We can then conclude that background fluctuations are correctly sampled and do not constitute a major source of uncertainty on visibility measurements, as discussed in Sect. 4.2.

  • For each scan on the sky (250 ms long with an analog filter frequency of 1000 Hz) a Fourier transform is computed, and its average value (on 600 independent scans) is plotted in Fig. 4d. It provides the high frequency part of the sky signal between 4 and 500Hz.

    The low frequency part of the spectrum corresponds to the time evolution of the average of the scan signal, computed every 4 seconds, on 100 scans. This gives access to the frequencies between 2.5 mHz and 125 mHz (Fig. 4c).

    The analysis of these curves shows a rather sharp increase of the amplitude spectrum of the sky signal for frequencies lower than 15 mHz, which probably reflects the slow variations of the thermal background. The slowly decreasing and reasonably flat noise found for higher frequencies appears compatible with the hypothesis of a dominant detector noise. In any case chopping on the sky at reasonable rates (about 1Hz) should remove most of the observed fluctuations.

[FIGURE] Fig. 4. a  Temporal evolution of the shutter signal (upper points) and of the sky signal (lower points). Each point represents an average level over 250 ms. b  Temporal evolution of the difference between the shutter and sky signals. Each point represents an average level over a batch of 100 scans. Error bars represent the standard deviation of the averaged scan level. c  Amplitude spectrum of the low frequency part of the signal obtained from sky observations. d  average amplitude spectrum of the high frequency part of the sky signal (same units as plot a ). Note that the noise is reasonably flat for frequencies higher than 100 mHz, showing no peaks that might be confused with the fringe signal around 400 Hz.

3.2. Coupling efficiency

For a diffraction limited image formed at the focus of a telescope, the spatial distribution of the electric field scales proportionately with the wavelength, keeping the same profile (the Airy pattern, in a first approximation). Close enough to the cutoff wavelength (Neumann 1988) the fundamental mode of a single-mode fiber is described by a gaussian-like profile with its radius also roughly proportional to the wavelength. The theoretical coupling efficiency into the fiber is then achromatic in the absence of turbulence. With our fibers optimized for the K band, the fundamental mode is not strictly gaussian in L, and the theoretical coupling efficiency is about 10% less in L than in K.

In presence of a turbulent atmosphere, the coupling efficiency is, to a first approximation, proportional to the Strehl ratio of the incoming wavefront. The former theoretical discrepancy of the coupling efficiency is then compensated by the improved seeing of the L band. More accurate calculations (Shaklan & Roddier 1988; Ruilier 1998) show that the injection efficiency should be roughly the same for the two wavelength domains, but that its time stability should be about 3 times better in the L band than in K.

On TISIS we can measure the stability of the injection into the fiber. A typical "interferometric" signal is given on Fig. 3a. Since there is no independent photometric measurement of the signals injected into each fiber, we use the incoherent addition of the two signals, as seen outside of the fringe packet, in order to probe the coupling efficiency of the starlight and its temporal evolution. The rms value of the fluctuations is 8% of the mean signal (the background has been subtracted). Assuming uncorrelated fluctuations of equal intensity at the two telescopes, we then estimate the relative variations of the coupling efficiency at the focus of each telescope to be about 6%, which is indeed much better than what we usually get in the K band.

From these temporal fluctuations of the coupling efficiency, and depending on the number of turbulent modes corrected, we can theoretically (Shaklan & Roddier 1988; Ruilier 1998) estimate the turbulence strength, i.e. the Fried's parameter [FORMULA] at the wavelength of observation. Assuming a perfect tip-tilt correction on a telescope of diameter D, we find D/[FORMULA] =1.3, and D/[FORMULA] =0.3 for uncorrected turbulence. Observations on IOTA are carried out in an intermediate regime with a partial tip-tilt correction, and then most probably at D/[FORMULA] in the L band. This leads to a minimum value of 4 cm for the Fried's parameter at 0.5 µm.

3.3. Characterization of the single mode coupler

3.3.1. Transmission

The transmission of the 2 m long single-mode X coupler is measured to be about 10% from one input to the single usable output, and 20% from the other input. Thus the split ratio of the coupler is 2 to 1, and it absorbs 85% of the energy over the whole spectral range of the L band. Since the chemical composition of the fiber and the geometry of the coupler were optimized for operation in the K band, this stronger attenuation in the L band was expected.

3.3.2. Dispersion

The ideal (zero dispersion) number of fringes expected with our L band filter ([FORMULA]m, and [FORMULA]m) is about 13. Dispersion is quite low as indicated by the interferograms obtained on [FORMULA] (Fig. 5), numerically filtered at the fringe frequency, i.e. between 360 and 440 Hz, that shows roughly 16 fringes. Although the coupler used was optimized to exhibit very low dispersive effects in the K band, this property appears to hold in L.

[FIGURE] Fig. 5. Coherent addition of the signals injected by the two telescopes into the single mode coupler: a typical single-scan interferogram obtained on [FORMULA], filtered at the optical bandpass. Resolution is limited on the temporal axis by the finite sampling rate (2092 Hz), and in the detected signals by the dynamic of the data acquisition board (2.4 mV of resolution).

3.3.3. Interferometric efficiency

When single mode fibers are used for interferometric combination, visibility measurements can be corrected for atmospheric effects using either photometric derivations (so that further degradation of the interferometric efficiency is solely due to the instrumental transfer function, as in FLUOR), or the low frequency - photometric - part of the interferograms. This latter method is used for TISIS and leads to visibility measurements which are independent of atmospheric con ditions to a good approximation (Coude du Foresto et al. 1997). In what follows we then consider that interferometric efficiency and instrumental transfer function ([FORMULA]) are strictly equivalent and can be determined by observing a calibrator i.e. either an unresolved source, or a source of known diameter.

For our observations, the derivation of [FORMULA] comes from the interferometric data obtained on Arcturus. The model used to compute its theoretical visibility, the reduction method and effective wavelength determination are detailed in Sect. 4.2.

The three measurements of the transfer function on April 2 are steady within a 4% wide band, and all are above 50%. The first value, corresponding to the following night is consistent with this number of 50% (Fig. 6).

[FIGURE] Fig. 6. Temporal evolution of the instrumental transfer function. First point is for the night of April 3, the other three points are for April 2 1998.

Considering that the individual components of the interferometer were not optimized for operation in the L band, and that no active polarization control was applied by macrobending of the fibers, this value of the interferometric efficiency is very encouraging. For comparison the typical value of [FORMULA] obtained in the K band with FLUOR is 70%.

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© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999