Exoplanet detection with simultaneous spectral differential imaging: effects of out-of-pupil-plane optical aberrations Page: 4 of 13
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--Puj
Upii
102 03 04
Figure 1. Simulation schematic. Aberrated surfaces are located at 01, 02, 03 and 04 (respectively at the pupil and
at 10%, 50% and 90% of the focal length) in between the pupil and focal planes. Corresponding conjugated plane in the
collimated beam are found in front of the pupil (position C1, C2, C3 and C4).
radian) are scaled by the ratio of the wavelength to produce the chromatic PSF. Such approach is optimistic
since all wavefronts at different wavelengths are perfectly aligned and all aberrations are located in the pupil
plane.
In this paper, we analyze how out-of-pupil-plane phase aberrations affect SSDI performances by using a
Talbot wavefront propagation software. Simulations include a typical differential atmospheric refraction effects
and a coronagraph case is also studied. Results are confirmed using a fast Fourier transform-based code. Such
analysis is fundamental for current high-contrast imaging projects, like the Gemini Planet Imager (GPI) and the
VLT Planet Finder (VLTPF) as well as for future high-contrast space observatories.
2. OUT-OF-PUPIL-PLANE OPTICAL ABERRATIONS
For simplicity, we consider a simple optical system containing a collimated beam, a pupil, an aberrated optical
surface and a focal plane. Aberrated optics are located in between the pupil and focal planes. PSFs are obtained
by first finding the corresponding conjugate plane of the aberrated optic in the collimated beam above the pupil,
by propagating the aberrated wavefront to the pupil plane and by Fourier transform of the complex pupil. As
the aberrated optic gets closer to the focal plane, the corresponding conjugated plane in the collimated beam
above the pupil goes to infinity (see Fig. 1).
Conjugated wavefronts are propagated to the pupil by using Talbot imaging. Such an approach, though not exact
for finite optics, is useful to get physical insight into wavefront propagation problems. Results obtained with
this technique are of the same order of magnitude as the one obtained from a fast Fourier transform-based code
for our simulated cases (see Sect. 3). Talbot imaging stipulates that when a wavefront propagates by a certain
length, an initial phase aberration will oscillate between being a pure phase and a pure amplitude aberration.
The length for a complete cycle is called the Talbot length TL." Propagating a phase aberration of a specific
frequency by a quarter of its Talbot length will result in a pure amplitude aberration, while propagating by
half the Talbot length will result in a pure phase aberration that has the opposite sign as the original phase
aberration. Since the Talbot length is chromatic, the ratio of aberration in phase and amplitude space is not
the same in two adjacent wavelengths, the two PSFs will be partially decorrelated and the SSDI speckle noise
attenuation performance will not be as good as expected. The Talbot length is proportional to twice the ratio
of the aberration spatial period A squared over the wavelength A
2A2
TL 2 -2 (I)
If the wavefront propagates by a length S to reach the pupil plane, the total number of Talbot lengths traveled
NTL is simply the ratio of S over TL
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Marois, C; Phillion, D W & Macintosh, B. Exoplanet detection with simultaneous spectral differential imaging: effects of out-of-pupil-plane optical aberrations, article, May 2, 2006; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc879681/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.