All Figures

$\begin{figure} \par\includegraphics[width=8.8cm]{5648fig1.eps}\end{figure}$ Figure 1: Schematic of a possible optical layout for the UNI-PAC method (unbalanced nulling interferometer followed by a phase and amplitude correction adaptive optics). The various optical planes are those referred to in the text.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5648fig2.eps}\end{figure}$ Figure 2: Schematic of wavefront phase and amplitude magnification in the process of the UNI-PAC method, where only the real part is indicated for the amplitude. In planes A), B), B'), B'') solid and dashed lines show wavefront 1 and 2, respectively. In planes UNI and PAC the combined wavefront is shown.
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In the text

$\begin{figure} \par\includegraphics[width=6cm]{5648fig3.eps}\end{figure}$ Figure 3: Complex amplitude at a point (x,y) in the pupil plane under the processes of the UNI-PAC method. In each panel, an arrow from the origin indicates the unaberrated amplitude, E⁰, and the complex aberration component, $\varepsilon$ , is shown by other small arrow(s), where the distribution area of the complex amplitude is drawn by a dashed-lined ellipse. Traditional phase aberration, $\theta$ , is indicated by an arc. The upper four panels indicate the complex amplitude of beam A, beam B with ND filter before $\pi$ phase shift, UNI, and finally PAC planes respectively from top to bottom, in $E^0_{\rm A}$ units. The two lower panels are similar to the last two frames of the upper panel, except that the vectors have been normalized by the factor $g E^0_{\rm A}$ , where g=0.2. The normalized aberration is magnified by 1/g by the UNI (UNI output plane), and compensated by a factor h(x,y) at the PAC output plane.
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{5648fig4.eps}\end{figure}$ Figure 4: Wavefront aberration magnification by the unbalanced nulling interference. a) Complex amplitude of 400 points is simulated in a wavefront whose phase aberration rms is 0.0063 radian and amplitude aberration rms is 0.004. b) After the unbalanced nulling interference with a no-aberration wavefront with an amplitude ratio of 0.9, the phase aberration is easily seen as magnified, and c) the amplitude aberration magnification is also obvious when the complex numbers are normalized by the unaberrated wavefront electric field, which is 0.1E⁰ in this case if we represent the original unaberrated field as E⁰. The magnified aberrations seen in panel c) can be corrected again to the same quality as a) by an AO system in the next stage.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{5648fig5.eps}\end{figure}$ Figure 5: Results of a simplified numerical simulation showing the improvement of the dynamic range in the image plane by the UNI-PAC method. The curves show the central star (bold line) and its speckle halo noise (solid line) normalized by the planet peak intensity (dashed line). Initially ( left panel) the contrast between the star and the planet is assumed to be $5\times 10^{9}$ and the speckle halo lies $4\times 10^{2}$ above the planet, which is a result of the phase aberration of $\lambda$ /1000 rms and the amplitude aberration of 0.004 rms with a flat spectrum ( $30~\times~~30$ square grids in the pupil). After the UNI is applied with the factor g=0.1 ( middle panel), the central star intensity is reduced by g²/(2- 2g+g²)=0.0055 times. After the PAC process ( right panel), the aberration-magnified wavefront is compensated to the same aberration rms as the input. The speckle halo noise is then decreased k²=0.0055 times, that is, twice the planet peak intensity. The star profile is drawn as a point spread function of a non-modified pupil, which can be suppressed by a downstream coronagraph.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm]{5648fi6a.eps} \bigskip \mbox{\i... ...4cm]{5648fi6c.eps} } \par\includegraphics[width=8.8cm]{5648fi6d.eps}\end{figure}$ Figure 6: Simulation of the UNI-PAC resulting in a $\sim$ $\lambda$ /10 000 rms from input wavefronts quality of $\sim$ $\lambda$ /1000 rms. The top row shows the complex amplitude distribution in the complex plane for the input Beam A, Beam B (including the unbalance factor g=0.1), and for the unbalanced combined beam, i.e. at the UNI output plane. The middle row shows the amplitude (modulus) distribution of UNI output beam after the propagation between DM1 and DM2, before ( left), and after ( right) the Gerchberg-Saxton algorithm convergence. DM1 compensates for amplitude fluctuations only, while DM2 compensates for the phase. The bottom row shows the PAC output wavefront complex distribution. Note that the real and imaginary axes scale has been reduced by a factor of 1/10.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm]{5648fig7.eps}\end{figure}$ Figure 7: Azimuthally averaged profiles of focal plane images at different locations in the UNI-PAC system: a reference Airy profile (dotted), the profile at the UNI (dashed) and the PAC (solid) planes. The thick dotted profile corresponds to the speckled halo (aberration component) before the UNI stage. The two thick lines at the bottom of this plot are (thick black) the image profile by the virtually-corrected PAC output wavefront with the ideal coronagraph, and (thick grey) the image computed by the initial wavefront with the artificial enhancement (i.e. with the complex aberrations reduced by a factor of 1/10) combined with the ideal coronagraph.
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In the text

$\begin{figure}\par\includegraphics[width=7.5cm]{5648fig8.eps}\end{figure}$ Figure 8: Wavelength dependence of the magnified aberration. The wavefront shape aberration after the UNI, ${z _{\rm UNI}},$ is shown for the input wavefront shape aberration $z _{\rm A} = 1$ nm with zero amplitude aberration and g=0.1. In the wavelength band of 500 nm to 600 nm, the wavefront aberration is magnified about 9.96 times with a small wavefront difference of about 0.01 nm, i.e., $\lambda$ /50000 level.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm]{5648fig9.eps} \end{figure}$ Figure 9: Differential phase dependence of the magnified aberration. The wavefront shape aberration after the UNI, ${z_{\rm UNI}}$ , is shown as a function of the additional phase change where the input wavefront shape aberration $z _{\rm A} = 1$ nm with zero amplitude aberration under a condition of g=0.1, B = 0.2 m, and $\lambda =500$ nm. Within the phase change of $\pm$ 0.006 rad, the wavefront aberration is magnified about 9.95 times with a small wavefront difference of about $\pm$ 0.1 nm, $\lambda$ /5000 level.
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In the text

$\begin{figure} \par\includegraphics[width=5.3cm,clip]{5648figa.eps} \end{figure}$ Figure A.1: Correspondence of the electric field definitions.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm]{5648fig1.eps}\end{figure}$	Figure 1: Schematic of a possible optical layout for the UNI-PAC method (unbalanced nulling interferometer followed by a phase and amplitude correction adaptive optics). The various optical planes are those referred to in the text.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{5648fig2.eps}\end{figure}$	Figure 2: Schematic of wavefront phase and amplitude magnification in the process of the UNI-PAC method, where only the real part is indicated for the amplitude. In planes A), B), B'), B'') solid and dashed lines show wavefront 1 and 2, respectively. In planes UNI and PAC the combined wavefront is shown.
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$\begin{figure} \par\includegraphics[width=5.3cm,clip]{5648figa.eps} \end{figure}$	Figure A.1: Correspondence of the electric field definitions.
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