Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2880fig1.eps}\end{figure}$ Figure 1: Example of $T_{\rm C}(x, y)$ for a $k_{\rm max} = 30$ Fresnel zones, i.e. 7200 apertures orthogonal Fresnel array.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig2.eps}\end{figure}$ Figure 2: Computer generated point spread function (PSF) of a 100-zone (center to edge) 80 000-aperture Fresnel array. The intensity is displayed at the 1/2nd power, to enhance the low luminosity regions of the PSF.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig3.eps}\end{figure}$ Figure 3: evolution of the phase within an individual aperture, as seen from common focus.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig4.eps}\end{figure}$ Figure 4: Diagonal cut of the PSF, for non-apodized arrays having 125, 250, 500 and 1000 zones: respectively 1.25 105, 5.105, 2.106 and 8.106 apertures top to bottom curves. The PSF are computed by Fresnel transform with a wavefront sampling adjusted to 1/25th of the smallest aperture for each array.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig5.eps}\end{figure}$ Figure 5: Normalized PSF (diagonal cut) for a 600 zones $T_{\rm c}$ type array, non apodized (dashed line) compared to apodized with Apod $_{\cos^2}(x)$ (a₀ = 0, full line).
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig6.eps}\end{figure}$ Figure 6: Normalized PSF (diagonal cut) with apodization functions Apod $_{\cos^2}$ (a₀ = 0), Apod $_{\rm sqrt}$ (a₀ = 0), and Apod $_{\rm trig}(x)$ (a₀ = 0.1), respectively full, dashed and dotted lines.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig7.eps}\end{figure}$ Figure 7: Three-dimensional representation of the PSF resulting from Apod $_{\rm trig}$ . Vertical scale is in powers of 10.
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In the text

$\begin{figure} \par\includegraphics[width=55mm]{2880fig8a.eps} \includegraphics[width=55mm]{2880fig8b.eps}\end{figure}$ Figure 8: Top: contours of the PSF resulting from the above observing procedure. Shaded areas indicate where the rejection factor R is poor: $R > 6\times 10^{-6}$ , and white ones indicate where $R < 6\times 10^{-6}$ . The two circles mark 4.5 and 5.5 resels distances from the center of the PSF. Bottom: contours and limitations of the same PSF combination for a $R = 2\times 10^{-6}$ threshold (same scale as left figure). The two circles mark 5.5 and 8 resels from center.
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In the text

$\begin{figure} \par\includegraphics[width=88mm]{2880fig9.eps}\end{figure}$ Figure 9: Diagonal cut of the PSF of an array with "jigsaw'' perturbations on the element edges, corresponding to $\lambda /4$ PTV on the wavefront from the smallest (outer) elements. The PSF of a perfect array is drawn for comparison. These two curves closely overlap.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig10.eps}\end{figure}$ Figure 10: 2-D PSF of an array with a "parallelogram'' shear distortion. The square root of the PSF intensity is displayed. Distortion effects are clearly visible on the diffraction spikes. The Strelh ratio is $\simeq$ 71%.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig11.eps} \vskip 1 cm\end{figure}$ Figure 11: Diagonal cut PSF of an array with a "parallelogram'' shear distortion (dashed line) compared to the PSF of a perfect array (full line). The central part of the PSF might become unusable depending on the target, but the outer peaks are only slightly brighter for the disturbed PSF.
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In the text

$\begin{figure} \par\includegraphics[width=15cm,height=5cm,clip]{2880fig12.eps}\end{figure}$ Figure 12: Achromatizer setup: D_B is the distance from primary array L₁ to field lens L₂ placed in the primary focal plane, D_C is the distance from L₂ to the L₃ set, and D_D is the distance from L₃ set to final focal plane. Distance D_A, not shown on this scheme, is the distance from the target to the front lens.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig13.eps}\end{figure}$ Figure 13: Warm Jupiter at 1 AU from a solar-type star at 10 Pc, 6 m array, 10 min integration, wavelengths from 380 nm to 650 nm. Minimal S/N ratio is better than 4 at the shortest wavelengths.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig14.eps}\end{figure}$ Figure 14: Cold Jupiter at 5 AU, 6m array, 10 h integration, wavelengths from 380 nm to 3.2 $\mu$ m. S/N ratio is higher than 4 at $\simeq$ 900 nm.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig15.eps}\end{figure}$ Figure 15: Venus at 0.7 AU, 15 m array, 10 h integration, wavelengths from 380 nm to 1.1 $\mu$ m. S/N $\geq$ 3 throughout the observable wavelengths.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig16.eps}\end{figure}$ Figure 16: Earth at 1 AU, 40 m array, 10 hours integration, wavelengths from 380 nm to 4.3 $\mu$ m. S/N $\geq$ 3 at $\simeq$ 900 nm.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig17.eps}\end{figure}$ Figure 17: Cold Jupiter at 5 AU, 40 m array, 10 h integration, wavelengths from 380 nm to 21 $\mu$ m. The S/N in IR depends upon the grid temperature: 40 K to 70 K, top to bottom curves, but remains $\geq$ 3 out to 17 $\mu$ m below 60 K.
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In the text

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig18.eps}\end{figure}$ Figure 18: Earth at 1 AU, 120 m array, 10 h integration, wavelengths from 380 nm to 12.9 $\mu$ m.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2880fig1.eps}\end{figure}$	Figure 1: Example of $T_{\rm C}(x, y)$ for a $k_{\rm max} = 30$ Fresnel zones, i.e. 7200 apertures orthogonal Fresnel array.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig2.eps}\end{figure}$	Figure 2: Computer generated point spread function (PSF) of a 100-zone (center to edge) 80 000-aperture Fresnel array. The intensity is displayed at the 1/2nd power, to enhance the low luminosity regions of the PSF.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig3.eps}\end{figure}$	Figure 3: evolution of the phase within an individual aperture, as seen from common focus.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig4.eps}\end{figure}$	Figure 4: Diagonal cut of the PSF, for non-apodized arrays having 125, 250, 500 and 1000 zones: respectively 1.25 105, 5.105, 2.106 and 8.106 apertures top to bottom curves. The PSF are computed by Fresnel transform with a wavefront sampling adjusted to 1/25th of the smallest aperture for each array.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig5.eps}\end{figure}$	Figure 5: Normalized PSF (diagonal cut) for a 600 zones $T_{\rm c}$ type array, non apodized (dashed line) compared to apodized with Apod $_{\cos^2}(x)$ (a₀ = 0, full line).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig6.eps}\end{figure}$	Figure 6: Normalized PSF (diagonal cut) with apodization functions Apod $_{\cos^2}$ (a₀ = 0), Apod $_{\rm sqrt}$ (a₀ = 0), and Apod $_{\rm trig}(x)$ (a₀ = 0.1), respectively full, dashed and dotted lines.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig7.eps}\end{figure}$	Figure 7: Three-dimensional representation of the PSF resulting from Apod $_{\rm trig}$ . Vertical scale is in powers of 10.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm]{2880fig9.eps}\end{figure}$	Figure 9: Diagonal cut of the PSF of an array with "jigsaw'' perturbations on the element edges, corresponding to $\lambda /4$ PTV on the wavefront from the smallest (outer) elements. The PSF of a perfect array is drawn for comparison. These two curves closely overlap.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig10.eps}\end{figure}$	Figure 10: 2-D PSF of an array with a "parallelogram'' shear distortion. The square root of the PSF intensity is displayed. Distortion effects are clearly visible on the diffraction spikes. The Strelh ratio is $\simeq$ 71%.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig11.eps} \vskip 1 cm\end{figure}$	Figure 11: Diagonal cut PSF of an array with a "parallelogram'' shear distortion (dashed line) compared to the PSF of a perfect array (full line). The central part of the PSF might become unusable depending on the target, but the outer peaks are only slightly brighter for the disturbed PSF.
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$\begin{figure} \par\includegraphics[width=15cm,height=5cm,clip]{2880fig12.eps}\end{figure}$	Figure 12: Achromatizer setup: D_B is the distance from primary array L₁ to field lens L₂ placed in the primary focal plane, D_C is the distance from L₂ to the L₃ set, and D_D is the distance from L₃ set to final focal plane. Distance D_A, not shown on this scheme, is the distance from the target to the front lens.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig13.eps}\end{figure}$	Figure 13: Warm Jupiter at 1 AU from a solar-type star at 10 Pc, 6 m array, 10 min integration, wavelengths from 380 nm to 650 nm. Minimal S/N ratio is better than 4 at the shortest wavelengths.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig14.eps}\end{figure}$	Figure 14: Cold Jupiter at 5 AU, 6m array, 10 h integration, wavelengths from 380 nm to 3.2 $\mu$ m. S/N ratio is higher than 4 at $\simeq$ 900 nm.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig15.eps}\end{figure}$	Figure 15: Venus at 0.7 AU, 15 m array, 10 h integration, wavelengths from 380 nm to 1.1 $\mu$ m. S/N $\geq$ 3 throughout the observable wavelengths.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig16.eps}\end{figure}$	Figure 16: Earth at 1 AU, 40 m array, 10 hours integration, wavelengths from 380 nm to 4.3 $\mu$ m. S/N $\geq$ 3 at $\simeq$ 900 nm.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig17.eps}\end{figure}$	Figure 17: Cold Jupiter at 5 AU, 40 m array, 10 h integration, wavelengths from 380 nm to 21 $\mu$ m. The S/N in IR depends upon the grid temperature: 40 K to 70 K, top to bottom curves, but remains $\geq$ 3 out to 17 $\mu$ m below 60 K.
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$\begin{figure} \par\includegraphics[width=88mm,clip]{2880fig18.eps}\end{figure}$	Figure 18: Earth at 1 AU, 120 m array, 10 h integration, wavelengths from 380 nm to 12.9 $\mu$ m.
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