6 Limitations regarding detection capability

6.1 Nature of the various limitations

In order to improve the performance of AIC one wants to know the relative weights of the various limitations. Far from the star the main limitation comes from the camera noise but close to the star it is the residual energy from the star which decreases the detectivity. This latter limitation is the most annoying since it tends to cancel a specific advantage of AIC (close sensing capability) and since AO correction is particularly efficient close to AIC axis (Paper I). This residual energy comes from the corruption of the wavefront by optical aberrations. These aberrations can be divided into the optical aberrations before the AIC (residual turbulence through the AO, fixed aberrations in the wavefront sensor unit or in the optical set-up after the AO beamsplitter), the optical aberrations inside AIC, and the OPD variations (which could be also included into the aberrations inside AIC).

   
6.2 OPD variations

From laboratory tests, we know that the contributions of the various aberrations inside AIC amount to less than 0.5% of the integrated energy without AIC. Besides, we have already said that OPD residual fluctuations were exceedingly large, as a result of the unexpected vibrations of the building structure and of numerous acoustic perturbations (rms variation about $\frac{\lambda}{15}$ in IR).

In Appendix A: we show that the main contribution to the residual energy of AIC comes from these OPD variations. The mean intensity in the output image plane takes the form:

$$I(\vec{\rho}) \approx RT \left[<\vert 2\sum_{\mathrm{odd},i=J... ...rho})}\vert^2>+<d^2\vert\hat{Z}_{1}(\vec{\rho})\vert^2>\right]$$

with

$$\hat{Z}_{i}(\vec{\rho})=\pi\sqrt{n+1}(-1)^{(n-k)/2} i^{-k}\frac{2J_{n+1}(2\pi\rho)}{2\pi\rho}\exp(ik\theta).$$

As explained in Paper I, and as appearing in the formulae, the summation in the first term applies only on Zernike polynomials with odd radial degree. Since $J_{n}(\rho)/\rho=0$ for $\rho=0$ for n>1, the summation in the first term is null for small $\rho$, and there is no contribution from the first term on the axis of AIC. The observed radial profile of the residual energy coming out of AIC shows a central peak (see Fig. 5). The second term explains this a priori unexpected shape, and is much likely to be the major cause yielding the central peak, eventhough the finite pixel size contribute to this central peak (see Sect. 5.2). In other words when RT.<d²> is not null the central pixel is not utterly dark. Taking this into account we calculate the coefficient RT.<d²> that is a weighting factor to apply to the theoretical diffraction pattern without coronagraph. The coefficient RT.<d²> for our data exhibits a mean value of 2.5% and varies between 1.5% to 3% from one star to another one. This is consistent with the variation of $\frac{\lambda}{15}$ rms in IR observed during the run. One must keep in mind that about 0.5% of the integrated energy comes from the AIC aberrations but for such small aberrations the contribution on the axis is negligible.