Simulation and results

 

j R_max R 0 ph. 0 ph. (star SNR

(star) +planet)

15000 136796 110377 71.4

80 440000 150000 87672 85546 7.2

360000 82340 80625 5.9

144 790000 560000 111044 107946 9.3

950000 155959 150017 4.0

To assess the dark-speckle method we did a laboratory simulation using a single-pixel photon-counting detector, in the form of an avalanche photodiode. The star and planet were simulated by two He-Ne lasers, with adjustable attenuators. A Lyot-type coronagraph permitted to remove the star's Airy peak and rings, thus decreasing the local halo intensity 10 to 15 times. Artificial ``seeing'' was generated with a moving scatterer, selected to provide a Strehl ratio approaching that typical of current adaptive optical systems. The equivalent peak/halo gain was G=3.4.10³. The flux of the central star was 44.10⁶ photons/s. Calculating an histogram of the detected photon events, we determined the SNR by comparing the number of zero-photon events with the planet turned on and off. As listed in Table 1, the results strongly depend on the sampling parameter j. They are consistent with Eq.(7) which gives the maximum brightness ratio (R_max) theoretically reachable. In these laboratory tests, the dark-speckle analysis outperforms the long exposure when the sampling exceeds 144 pixels/speckle area.

 

Figure: Laboratory simulation of stellar companion detection with the dark speckle method. The artificial companion, 966 times fainter than the star, is at the center of the dark map, emerging from the halo. A coronagraphic mask, which hides the star's central peak is visible in the lower right corner. The blob seen in the upper right part of the field is a ``static speckle'' caused by permanent aberrations and removable with a reference star.

In this experiment the short exposure time ($100\mu s$) is about 100 times shorter than the speckle lifetime (10ms). Available photon counting camera do not yet allow quite as short exposure.

 

Figure: Cleaned image, generated through dark-speckle analysis, of the multiple star HD144217($\beta$ Sco). A companion ($\beta$ Sco B) appears near the masked star image. (mask diameter=0.5'', F/D=1200)

We also used the CP40 photon-counting camera developed by Foy and Blazit ([Blazit 1986]). It has pixels of $50\mu m$ and a rather low saturation level of 50000 photons/s. Each pixel has a lower dark noise than an avalanche photodiode, but a much slower response. We used the algorithm described in Labeyrie (1995), generating a ``dark map'' by counting, in each pixel, the number of 20ms exposures which contribute zero photon. As contributions from successive 20ms exposures are accumulated in the dark map, a planet's Airy peak is expected to emerge as a black dot among background noise. To obtain the cleaned image, results are displayed in positive form using, for example, an inverse square law.
The CP40 discriminates between events featuring zero photoelectron and those featuring one or more photoelectron/pixel/exposure. Adding all exposures generates an image which brings out faint companions better than would a similarly long exposure on a CC D detector.
The flux of the central star was 5.3.10⁶ photons/s, and the gain of the adaptive optics was about 1556. The optical system operated at $\lambda =0.67\mu m$, F/D=3200, and the mask diameter was 0.34", i.e. it covered the central 2 rings of the Airy pattern. The planet was located near the fifth ring of the diffraction pattern.
Figure 2 shows that a companion 966 times fainter is well detected in 116 seconds. The SNR measured on a speckle size region ($37\times 37$ pixels) is 799, while the dark-speckle model predict an SNR of 1008. This model does not take into account the halo shape which can explain the $20\%$ discrepancy. These initial results, where the companion is brighter than the halo, are very modest with respect to the performance expected at a later stage, but have provided useful insight for improving the instrument.
Currently, as seen in Figs 2 and 3, the detection sensitivity is limited by the presence of spurious blobs in the cleaned image. These are caused by static aberrations and coronagraphic mask effects. These residual blobs may be substracted from data obtained on a reference star.
Finally, dark-speckle data have been recorded at the 152cm telescope of Haute-Provence, using, during a single night, the BOA adaptive optics system ([Madec 1997]) developped by the Office National d'Etudes et de Recherches Aérospatiales (ONERA).

 

Figure: Same image enhanced with unsharp mask and high pass filter to emphasize the contrast and median filter to smooth the image at the speckle scale.

This system, optimized for visible light, reaches a Strehl ratio of about 0.4 at $0.6\mu m$ in long exposures and higher in short exposures. 30 minutes of observation, with an interference filter centered at $0.67\mu m$ ($\Delta\lambda=100 \mbox{\AA}$), evidenced the faint component of the spectroscopic binary HD144217 ($\alpha=16h05'26''$,$\delta=-19^{\circ}48'18''$, V=2.62). On the detector, the flux from the primary was only 11860 photons/s. The angular separation is about 0.45" with an uncertainty due to the mask offset. Owing to the low elevation of the star, the adaptive optics gain was only 12. The SNR measured on $16\times 16$ pixels is 168 and allows to derive from Eq.(10) a brightness ratio of 88, corresponding to a 4.8 magnitude difference. On the long exposure synthesized from the same data (1 photon-events analysis) the SNR is very similar, but a direct imaging should give a SNR of 42 according to Eq.(11). However, a recent measurement of lunar-occultation ([Evans 1983]) gives $\Delta m=3.3$. In this case, dark-speckle analysis should provide a very good detection with a SNR of 756 instead of 168. Unfortunately, the Hipparcos mission failed to detect the companion, probably because the Hipparcos satellite is unable to achieve $\Delta m\gt 4$ with small angular separation, which is consistent with our data. More observations are needed to verify the companion magnitude.
A continuing observing program is initiated.