Theoretical performance of solar coronagraphs using sharp-edged or apodized circular external occulters

Aime, Claude

doi:10.1051/0004-6361/201322304

Cited by 22 publications

(26 citation statements)

References 20 publications

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“…Radially apodized external occulters have already been analytically proved by Aime (2013) to be more efficient than the sharp-edged disc, in the context of solar coronagraphy. In an experimental approach, Bout et al (2000) and Landini et al (2010) investigated 3D-shaped occulters which deviate from a simple radial apodization.…”

Section: Discussionmentioning

confidence: 99%

“…(4)) remains a delicate operation, as described by Lemoine (1994). We chose to use NIntegrate in Mathematica (Wolfram 2012), since it has been proved to give sufficient numerical precision (Aime 2013). An analytic expression using the Lommel series can alternatively be used.…”

Section: Fresnel Diffraction By the External Occultermentioning

confidence: 99%

“…Sensitive analysis of this particular stray light is rather complex as it includes an extended light source -the Sun -which makes such a work much more difficult than considering one single point source, as is done in the particular domain of exoplanet coronagraphy where numerous analytic studies have been done -see for instance (Cash 2006;Vanderbei et al 2007;Flamary et al 2014). In solar coronagraphy, only a few numerical and analytical studies of rejection performance have been published (Lenskii 1981;Aime et al 2002;Aime 2007Aime , 2013. We also note that the purely analytical studies of Ferrari (2007) and Ferrari et al (2010) come with the drawback that the Lyot stop must equal the entrance pupil and cannot be reduced.…”

Section: Introductionmentioning

confidence: 99%

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Performance of the hybrid externally occultedLyotsolar coronagraph

Rougeot

Flamary

Galano

et al. 2017

A&A

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Context. High-contrast hybrid coronagraphs, which combine an external occulter and a Lyot-style coronagraph became a reality in recent years, despite the lack of analytic and numerical end-to-end performance studies. The solar coronagraph ASPIICS which will fly on the future ESA Formation Flying mission Proba-3 is a good example of such a hybrid coronograph. Aims. We aim to provide a numerical model to compute theoretical performance of the hybrid externally occulted Lyot-style coronagraph, which we then aim to compare to the performance of the classical Lyot coronagraph and the externally occulted solar coronagraph. We will provide the level and intensity distribution of the stray light, when the Sun is considered as an extended source. We also investigate the effect of different sizes for the internal occulter and Lyot stop. Methods. First, we have built on a recently published approach, to express the diffracted wave front from Fresnel diffraction produced by an external occulter at the entrance aperture of the coronagraph. Second, we computed the coherent propagation of the wave front coming from a given point of the Sun through the instrument. This is performed in three steps: from the aperture to the image of the external occulter, where the internal occulter is set, from this plane to the image of the entrance aperture, where the Lyot stop is set, and from there to the final image plane. Making use of the axis-symmetry, we considered wave fronts originating from one radius of the Sun and we circularly average the intensities. Our numerical computation used the parameters of ASPIICS. Results. The hybrid externally occulted Lyot coronagraph rejects sunlight below 10 −8 B from 1.3 R -in the particular configuration of ASPIICS. The Lyot coronagraph effectively complements the external occultation. We show that reducing the Lyot stop allows a clear gain in rejection, being even better than oversizing the internal occulter, that tends to exclude observations very close to the solar limb. As an illustration, we provide a graph that allows us to estimate performance as a function of the internal occulter and Lyot stop sizes. Conclusions. Our work consists of a methodological approach to compute the end-to-end performance for solar coronagraph.

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Section: Discussionmentioning

confidence: 99%

Section: Fresnel Diffraction By the External Occultermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Performance of the hybrid externally occultedLyotsolar coronagraph

Rougeot

Flamary

Galano

et al. 2017

A&A

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“…The range 1.08 − 3 R ⊙ is expected for the direct corona recording [ Renotte et al ., ]. An extensive study of the umbral pattern in an externally occulted coronagraph was recently presented by Aime []. He numerically demonstrated the large superiority of apodized circular occulters with respect to the sharped‐edge circular ones.…”

Section: Total Solar Eclipse As An Approachmentioning

confidence: 99%

Imaging the structure of the low K‐corona

et al. 2017

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The first 2‐D distributions of the polarization angle and of the relative color index for the K‐corona of 29 March 2006 are presented. The distributions illustrate the efficiency of the total solar eclipse approach for high‐precision measurements of the K‐corona continuum in the range < 1.4 R⊙. Natural ground and space total solar eclipses caused by external occulting the bright solar‐disk light by the Moon or Earth group planets are discussed. Calculations of the eclipse magnitude m are carried out to show ideal conditions for total solar eclipse observations in space from Lagrange point L2 for Mars (m ≈ 1.025). The illumination in Mars' shadow is estimated to equal 5.6 × 10−11 for the wavelength of 550 nm. No internal or external occulting coronagraphs are needed. Partial solar eclipses with m > 0.91 can be observed from Lagrange points L2 for Mercury, Venus, and Earth.

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“…Appendix A: Quality test of the numerical computation using an analytical expression for a sharp-edged circular occulter Aime (2013) has shown, using an approach similar to Born & Wolf (1999), that an analytic expression using Lommel series could be derived for the Fresnel diffraction of a sharp circular occulter of the form f (r) = f • (r, Ω) = Π(r/Ω), defining here Π(r) as the function equal to 1 for |r| ≤ 1 and 0 otherwise. At the wavelength λ, the complex amplitude ψ • (r, Ω) of the wave at the distance z for (i) inside the geometrical umbra (r < Ω) and, (ii) outside (r > Ω), can be written using two series:…”

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confidence: 99%

Optimization of starshades: focal plane versus pupil plane

Flamary

Aime

2014

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We search for the best possible transmission for an external occulter coronagraph that is dedicated to the direct observation of terrestrial exoplanets. We show that better observation conditions are obtained when the flux in the focal plane is minimized in the zone in which the exoplanet is observed, instead of for the total flux received by the telescope. We describe the transmission of the occulter as a sum of basis functions. For each element of the basis, we numerically computed the Fresnel diffraction at the aperture of the telescope and the complex amplitude at its focus. The basis functions are circular disks that are linearly apodized over a few centimeters (truncated cones). We complemented the numerical calculation of the Fresnel diffraction for these functions by a comparison with pure circular disks (cylinder) for which an analytical expression, based on a decomposition in Lommel series, is available. The technique of deriving the optimal transmission for a given spectral bandwidth is a classical regularized quadratic minimization of intensities, but linear optimizations can be used as well. Minimizing the integrated intensity on the aperture of the telescope or for selected regions of the focal plane leads to slightly different transmissions for the occulter. For the focal plane optimization, the resulting residual intensity is concentrated behind the geometrical image of the occulter, in a blind region for the observation of an exoplanet, and the level of background residual starlight becomes very low outside this image. Finally, we provide a tolerance analysis for the alignment of the occulter to the telescope, which also favors the focal plane optimization. This means that telescope offsets of a few decimeters do not strongly reduce the efficiency of the occulter.

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Theoretical performance of solar coronagraphs using sharp-edged or apodized circular external occulters

Cited by 22 publications

References 20 publications

Performance of the hybrid externally occultedLyotsolar coronagraph

Performance of the hybrid externally occultedLyotsolar coronagraph

Imaging the structure of the low K‐corona

Optimization of starshades: focal plane versus pupil plane

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