4 Sky results

The miniature hyper telescope was tested on the sky (Fig. 4). This image was obtained on the star Capella (a close binary which is completely unresolved here) by taking two separate exposures of 100 s in the Fizeau and densified-pupil mode of the hyper-telescope. It is of interest to calculate the intensification achieved in the densified-pupil case comparing the 2 images of Fig. 4. We start off calculating the theoretical intensity gain, in the central peak, for the 2 instrumental configurations. For an unresolved star the photon count in the central peak is $f=F_{\rm s}(d_{0}/D_{0})^{2}$, where $F_{\rm s}$ is the photon count from a single, unresolved star, d₀the output sub-pupil diameter and D₀ the output pupil diameter (Labeyrie 1996). In the case of our interferometer the value of d₀/D₀ is 1/70 with the micro-lenses removed (Fizeau) and 1/7 with the micro-lenses in place (densified pupil). Substituting these values in the previous equation and dividing the densified pupil photon count by the Fizeau photon count we find a value of $100 \times$ for the intensification.

Figure 4: Fizeau (bottom-left) and densified (bottom-right) surface plots of the star Capella. The top plot is an angularly averaged intensity profile from the bottom plots. The dashed line represents the intensity profile for the Fizeau image, which matches the diffraction pattern of a sub-aperture, represented by the dotted line fit. The solid line is the densified intensity profile. Both snapshot images were taken in a short succession with the same exposure time of 100 s. An intensity gain is noticeable by comparing the graphs. Ghost images (left and top of the surface plot), caused by a sub-pupil diffractive spill off of light outside of the facing micro lens are visible around the densified pupil image. The loss can be negligible with proper adjustments

Figure 5: White light image of the double star  Gemproduced by the miniature hyper-telescope. The central peak is seen to be double in accordance to the calculated position angle and separation of the binary star (sketched at top-right). Attenuated and dispersed side lobes are also visible around the central peak owing to the incomplete pupil densification and to a slight pointing offset of the telescope. The ghost images shown in Fig. 4 are outside the picture

We then calculate the intensification factor from the images used for generating the plots of Fig. 4. For the densified pupil image and the Fizeau image, the intensity f was measured by integrating the central peak. The measurements were repeated for the Fizeau and densified configuration, using several recorded images. The comparison of the obtained values showed an intensity gain of $9.2\pm 0.4\times$ of the densified with respect to the Fizeau configuration. When we take into account the stray light introduced in the measurement, caused by the instrument not being properly baffled we obtain a value of $24\pm 3\times$, closer to the theoretical value. The stray light produced a constant offset in both the Fizeau and densified pupil image. The value of this offset was calculated from the Fizeau image by fitting to the measured data an Airy function corresponding to the diffraction function of the $0.8~{\rm mm}$ entrance apertures (Fig. 4). After the first minimum at $220^{\prime \prime}$ the function is nearly constant and its corresponding value can be subtracted from the intensity calculation of the Fizeau and densified pupil images. We verified that the discrepancy between the Airy fit and the data, towards the end of the plot, was due to the detector response threshold at low light intensity levels. This effect was found in several other images. The data plot is also affected by photon and atmospheric noise. The remaining discrepancy between the theoretical and the measured intensification is probably caused by the residual optical path errors introduced by the micro-lenses unequal thickness, the atmosphere and the misalignment of the micro-lenses with respect to the Fizeau mask.

Given its miniature size, narrow field and modest collecting area ( $41~{\rm mm}^{2}$), comparable to that of a naked human eye, the hyper-telescope was tested on bright binary stars. Figure 5 shows the image obtained on $\alpha$ Gem the night of December the 3rd 1999 with a $30~{\rm s}$ exposure. This image is compared to the calculated position angle and separation of the system for ${\rm JD}\, 2451515.694$ in Fig. 5.

Figure 6: Numerical simulation of PSF for the instrument (left) with the pupil densifier removed (Fizeau mode), in densified-pupil mode on a dispersed order (centre) and the star $\alpha$ Gem (right). Comparing the star image to the numerically simulated PSF we deduced that pointing errors positioned the object outside the field of view of the interferometer. The result is a dispersed image of the double star

The orbital parameters of the star were obtained from the Washington Double Star catalog. The angular separation and the position angle were calculated using the peak pattern produced by the array. The period of the peaks is in fact equal to ; we found a value for the angular separation. The position angle measured on the photo centres of the double star image produced a value of . This values agree with the calculated separation and position angle