7. SUMMARY AND FINAL REMARKS

In summary, here are the main points treated in the present paper:
- A model of the occultation phenomenon is derived taking diffraction into account: This diffraction greatly broadens the size of the KBO shadow (section 3). The occultation rates computed with these diffracting models are much larger (section 4) than the ones computed only using the geometric shadow (section 2). We therefore expect the number of valid occultations (def. as a $4\sigma$ event) going from a few to several tens per night, if we obtain an r.m.s. signal fluctuation $\sigma \;\rlap{\lower 2.5pt \hbox{$\sim$}}\raise 1.5pt\hbox{$<$}\;1\%$ and observe stars in the ecliptic with angular radius $\;\rlap{\lower 2.5pt \hbox{$\sim$}}\raise 1.5pt\hbox{$<$}\;$ 0.01 mas.
- Occultation rates are computed for a differential size distribution $\propto \rho^{-q}$ with a constant index $q = 4$ (Table I) and with a double index differential size distribution, $q = 4$ for objects larger than 1 km and q for sub-kilometer objects, with q varying from 2.5 to 4.5 (Fig.4). The differences between the occultation rates for different sites, instruments or occulted stars show that, with several occultation data sets, it should be possible to provide a good estimation of q for the small KBOs.
- The main limitation of the photometric precision comes from the scintillation of the star, which remains about the same to a visual magnitude of $\sim 12$. The blue O5 stars are the best candidates for detecting KBOs since they have the smallest angular radius ($\sim$100m at 40 AU) for 12th magnitude.
- Stellar occultations by Solar System small objects involve very rapid fluctuations of the stellar flux ( $\;\rlap{\lower 2.5pt \hbox{$\sim$}}\raise 1.5pt\hbox{$>$}\;$1Hz) , so that rapid photometry must be used. Moreover, the occultation events are shorter but more numerous when observed in the antisolar direction, so we may optimize the detections of KBOs with a high speed photometer ( $\;\rlap{\lower 2.5pt \hbox{$\sim$}}\raise 1.5pt\hbox{$>$}\;20$Hz).
- In the near future, observations with the French space mission Corot will provide an excellent opportunity to explore the Kuiper Belt using this occultation research method.

We have shown here that stellar occultations can detect a population of very small objects, invisible by other observation methods and that these detections can be statistically exploited if the population has a sufficient surface density on the sky. In particular this is the only method for detecting the population of small (sub-kilometer-sized) KBOs which should contain most of the mass of the Kuiper Belt. Let us note however that such an observation of serendipitous occultations is not a discovery of each occulting object because the orbit of the object remain unknown. In otherwords, this method allow us to explore the population as a whole, but not the individual objects.

We foresee two ways to extend the present work: On one hand, the simultaneous observation of an occultation at two different wavelengths provides events of different depth, which could allow us to retrieve the Fresnel scale and then to determine the distance of the occulting object. On the other hand, if we could obtain both high speed and high precision photometric observations (on a telescope >5m, or from space), we could observe the diffraction fringes of each occultation event and identify individually, instead of statistically, the occulting objects. In this case, we could deduce the object size and location by fitting our occultation model to the precise light profile of the event. Then, occultation could also be used to explore other small bodies populations in the Solar System, a priori more rare in the sky than the KBOs, such as asteroids or comets in the Oort clouds, or small bodies possibly confined at nest of gravitational stability, as the Lagrangian points of the planets. It is currently very difficult to evaluate the probability of observing occultations by such objects but we think these points deserve further investigation.