Diffraction model for the external occulter of the solar coronagraph ASPIICS

Transcription

1 Diffraction model for the external occulter of the solar coronagraph ASPIICS Raphaël Rougeot OCA, Nice 14/05/ /05/2018 R.Rougeot 1

2 Outline 1) Proba-3 mission and ASPIICS 2) Diffraction from external occulters a) How to compute diffraction b) Diffraction patterns for several occulters 3) Penumbra profile 4) Conclusion 14/05/2018 R.Rougeot 2

3 Proba-3 mission and ASPIICS 14/05/2018 R.Rougeot 3

4 ESA Proba-3 mission In-orbit demonstration of precise Formation Flying Two spacecraft flying 150m apart, controlled with a millimeter accuracy Occulter Spacecraft Coronagraph Spacecraft 14/05/2018 R.Rougeot 4

5 ESA Proba-3 mission In-orbit demonstration of precise Formation Flying Two spacecraft flying 150m apart, controlled with a millimeter accuracy The formation will be co-aligned with the Sun during the 6-hours apogee phase 14/05/2018 R.Rougeot 5

6 Solar coronagraph ASPIICS Associtation de Satellites Pour l Imagerie et l Interférométrie de la Couronne Solaire A 1,42m diameter occulting disk carried by the Occulter Spacecraft A 5cm Lyot-style coronagraph on the Coronagraph Spacecraft Observation of the K-corona - Findings on the heating process - Alven s waves, dynamics of the plasma - Coronal Mass Ejections Lamy, 2010 Renotte, 2015 ASPIICS in a nutshell White light [540nm ; 570nm] 2,8 arcsec/pixel High cadence 14/05/2018 R.Rougeot 6

7 Coronagraphy and diffraction The corona of the sun is much fainter than the solar disk itself Observation in white light requires perfect eclipse conditions B corona ~10 6 to 10 9 B sun Allen, 1997 Cox, /05/2018 R.Rougeot 7

8 Coronagraphy and diffraction The hybrid externally occulted Lyot solar coronagraph ASPIICS External occulter Pupil L1 Focal plane Internal Occulter L2 Lyot stop L3 Focal plane O A B O C D 14/05/2018 R.Rougeot 8

9 Coronagraphy and diffraction The hybrid externally occulted Lyot solar coronagraph ASPIICS External occulter Pupil L1 Focal plane Internal Occulter L2 Lyot stop L3 Focal plane O A B O C D 14/05/2018 R.Rougeot 9

10 Coronagraphy and diffraction The hybrid externally occulted Lyot solar coronagraph ASPIICS External occulter Pupil L1 Focal plane Internal Occulter L2 Lyot stop L3 Focal plane O A B O C D 14/05/2018 R.Rougeot 10

11 Coronagraphy and diffraction The hybrid externally occulted Lyot solar coronagraph ASPIICS External occulter Pupil L1 Focal plane Internal Occulter L2 Lyot stop L3 Focal plane O A B O C D 14/05/2018 R.Rougeot 11

12 Diffraction by an external occulter 14/05/2018 R.Rougeot 12

13 Diffraction by an external occulter Point source at External occulter Plane of the entrance aperture N f = R2 λz 6400 Propagation z=144,348m λ=550nm R=710mm 1 Ψ 0 (x, y) Ψ z (x, y) 14/05/2018 R.Rougeot 13

14 Diffraction by an external occulter Major issue in solar coronagraphy: the Sun is an extended light source R sun =16,2 z=144,348m Umbra of 38mm The diffraction pattern must be known over a large spatial extent stellar coronagraphy 14/05/2018 R.Rougeot 14

15 How to compute diffraction? Apodisation No Axis-symmetry Brute force 2D FFT Analytical Hankel transform X Vanderbei et al. Approach O (periodicity) Lommel series X X Rougeot & Aime, 2018 Aime, 2013 Vanderbei, 2003 Aime, 2013 Maggi-Rubinowicz representation Boundary diffraction integral X Cady, 2012 Born & Wolf 14/05/2018 R.Rougeot 15

16 How to compute diffraction Brute force 2D FFT The occulter is padded in a 2D arrays Size K Occulter Fresnel filter Condition from the Fresnel filter: σ > Consequence: K of very large size Kz λ Sampling σ In Rougeot & Aime 2018, we tried x , not sufficient for petalized shape 14/05/2018 R.Rougeot 16

17 How to compute diffraction Maggi-Rubinowicz representation Requires a binary mask (1 or 0) Ψ z x, y = Ψ d z x, y in the geometrical shadow Ψ z x, y = Ψ 0 (x, y) Ψ d z x, y otherwise W(x, y; l) Ψ z d (x, y) Boundary diffraction integral Ψ z d = 1 4π W dl Sampling of the occulter edge must be carefully chosen Cady, 2012 Born & Wolf Rougeot & Aime, /05/2018 R.Rougeot 17

18 Diffraction by an external occulter The sharp-edged occulting disk R=710mm Occulting ratio of 1,05 solar radius at z=144m 14/05/2018 R.Rougeot 18

19 Diffraction by an external occulter The sharp-edged occulting disk The bright spot of Arago (or Poisson demonstrated by Fresnel) Geometrical umbra 14/05/2018 R.Rougeot 19

20 Diffraction by an external occulter The sharp-edged occulting disk Bright spot of Arago Transition shadow/light 710mm 14/05/2018 R.Rougeot 20

21 Diffraction by an external occulter The apodized occulting disk Variable radial transmission R=710mm Δ Δ 14/05/2018 R.Rougeot 21

22 Diffraction by an external occulter The apodized occulting disk Δ = 20mm 14/05/2018 R.Rougeot 22

23 Diffraction by an external occulter The serrated (or petalized) occulter In stellar coronagraphy, the reasonning starts from the ideal apodized occulter τ apod r = τ petal r, θ dθ The petalized occulter is the discrete substitute Cady, 2006 Vanderbei et al., /05/2018 R.Rougeot 23

24 Diffraction by an external occulter The serrated (or saw-toothed) occulter In solar coronagraphy, the reasonning is well different! The diffraction occurs perpendicularly to the edge A toothed disc rejects the light outside the central region Boivin (1978) predicted the radius of the dark inner region of the diffraction pattern based on geometrical considerations Boivin s radius Koutchmy, /05/2018 R.Rougeot 24

25 Diffraction by an external occulter The serrated (or saw-toothed) occulter N t teeth N t = 1024 ; Δ=20mm Δ R=710mm 14/05/2018 R.Rougeot 25

26 Diffraction by an external occulter The serrated (or saw-toothed) occulter Occulter: 512-teeth, 10mm Modulus Ψ z x,y Phase Ψ z x,y 14/05/2018 R.Rougeot 26

27 Diffraction by an external occulter The serrated (or saw-toothed) occulter 14/05/2018 R.Rougeot 27

28 Diffraction by an external occulter The serrated (or saw-toothed) occulter A Dark inner region A 14/05/2018 R.Rougeot 28

29 Diffraction by an external occulter The serrated (or saw-toothed) occulter A Dark inner region A B B Intermediate region 14/05/2018 R.Rougeot 29

30 Diffraction by an external occulter The serrated (or saw-toothed) occulter C A Dark inner region A B B Intermediate region C Fully illuminated region 14/05/2018 R.Rougeot 30

31 Diffraction by an external occulter We numerically verified the geometrial predictions of Boivin (1978) Size of teeth Rougeot & Aime, /05/2018 R.Rougeot 31

32 Diffraction by an external occulter The serrated (or saw-toothed) occulter 14/05/2018 R.Rougeot 32

33 Penumbra profile 14/05/2018 R.Rougeot 33

34 Penumbra profiles R sun =16,2 z=144,348m Umbra of 38mm Convolution of the diffraction pattern Ψ z x, y 2 with the solar disk Centre-to-limb darkening function 14/05/2018 R.Rougeot 34

35 Penumbra profiles The sharp-edged occulting disk Diffraction Purely geometrical I z (r = 0) 10 4 I sun 14/05/2018 R.Rougeot 35

36 Penumbra profiles The serrated (or saw-toothed ) occulter Δ=20mm N t =464 N t increases Δ increases 14/05/2018 R.Rougeot 36

37 Penumbra profiles The serrated (or saw-toothed ) occulter Integrated illumination over the pupil, normalized to the sharp-edged disk cas pupil I serrated ds pupil I sharp ds Boivin radius N t, Δ > r sun =671mm 14/05/2018 R.Rougeot 37

38 Conclusion 14/05/2018 R.Rougeot 38

39 Conclusion Model of diffraction for external occulters in solar coronagraphy - Limits of Fresnel diffraction integrals using 2D FFT - Maggi-Rubinowicz representation Assessement of the theoretical performance of serrated occulters References - Aime C. 2013, A&A, 558, A138 - Rougeot R., Flamary R., Galano D., Aime C. 2017, A&A, 599, A2 - Rougeot R., Aime C. 2018, A&A, 612, A80 14/05/2018 R.Rougeot 39

40 Other works Propagation of the diffracted wavefronts inside the Lyot-style coronagraph - end-to-end performance in straylight rejection - impacts of the size of the internal occulter and the Lyot stop - PSF in the vignetting zone On-going/future works: - optical aberrations of the optics - effects of surface roughness scattering 14/05/2018 R.Rougeot 40

41 Questions? Thank you for your attention! 14/05/2018 R.Rougeot 41

42 Propagation inside the coronagraph 14/05/2018 R.Rougeot 42

43 Propagation inside the coronagraph The hybrid externally occulted Lyot solar coronagraph ASPIICS External occulter Pupil L1 Focal plane Internal Occulter L2 Lyot stop L3 Focal plane O A B O C D 14/05/2018 R.Rougeot 43

44 Propagation inside the coronagraph Propagation of the diffracted wavefront from one plane to the next one: - Fourier optics formalism - ideal optics - perfect axis-symetric geometry Numerical implementation: successive FFT with arrays of large size Objective: - estimate the level and spatial distribution of the residual diffracted sunlight - address the rejection performance of the coronagraph 14/05/2018 R.Rougeot 44

45 Propagation inside the coronagraph Intensity in plane O, where the internal occulter is set Without external occulter With external occulter 14/05/2018 R.Rougeot 45

46 Propagation inside the coronagraph Intensity in plane O, where the internal occulter is set With external occulter Without external occulter Solar disk image (out-of-focused) Rougeot et al., /05/2018 R.Rougeot 46

47 Propagation inside the coronagraph Intensity in plane O, where the internal occulter is set Internal occulter With external occulter Without external occulter Solar disk image (out-of-focused) 14/05/2018 R.Rougeot 47

48 Propagation inside the coronagraph Intensity in plane C, where the Lyot stop is set Without external occulter With external occulter 14/05/2018 R.Rougeot 48

49 Propagation inside the coronagraph Intensity in plane C, where the Lyot stop is set With external occulter Without external occulter (Lyot coronagraph) 14/05/2018 R.Rougeot 49

50 Propagation inside the coronagraph Intensity in plane C, where the Lyot stop is set Lyot stop With external occulter Without external occulter (Lyot coronagraph) 14/05/2018 R.Rougeot 50

51 Propagation inside the coronagraph Intensity in plane D, final focal plane with the detector With external occulter 14/05/2018 R.Rougeot 51

52 Propagation inside the coronagraph Intensity in plane D, final focal plane with the detector No occulter and stop Solar disk image Just the external occulter No internal occulter No Lyot stop Without external occulter (Lyot coronagraph) With external/internal occulters and Lyot stop 14/05/2018 R.Rougeot 52

53 Propagation inside the coronagraph Impact of sizing the internal occulter and the Lyot stop Intensity on plane D, the final focal plane Fixed Lyot stop Fixed internal occulter 14/05/2018 R.Rougeot 53

54 Propagation inside the coronagraph Impact of sizing the internal occulter and the Lyot stop Residual diffracted 1.3R Better rejection Closer to solar edge 14/05/2018 R.Rougeot 54

55 Propagation inside the coronagraph PSF in the vignetted zone 14/05/2018 R.Rougeot 55

56 Annex on diffraction formulations 14/05/2018 R.Rougeot 56

57 2D FFT technique The Fresnel filter exp iπλzu 2 has its phase varying as u 2 At the edge of the array, u c = 1/2σ We impose that the (maximum) phase variation at the edge of the array is <π σ > λz K Consequence: σ K 14/05/2018 R.Rougeot 57

58 2D FFT technique Very sensitive to numerical sampling: impact of the size of the array 2D FFT computation Reference curve (Hankel) K 14/05/2018 R.Rougeot 58

59 2D FFT technique Very sensitive to numerical sampling: impact of sampling Sampling too small regarding Fresnel filter s condition Sampling meeting the condition Sampling too large to correctly sample the occulter 14/05/2018 R.Rougeot 59

60 The Hankel transformation Fourier wave optics formalism Fresnel free-space propagation Axis-symmetric (apodized) occulter Ψ z x, y = 1 f r 1 iλz exp iπ λz x2 + y 2 Diffraction at z Radial function Ψ z r = φ R z r iλz න 2πρ f ρ exp iπρ2 0 λz J 0 2πρr λz Radial apodization dρ Lommel series decomposition into series (Aime, 2013) 12/02/2018 R.Rougeot 60

61 The Hankel transformation Fresnel free-space propagation Axis-symmetric (apodized) occulter Ψ z x, y = 1 f r 1 iλz exp Radial apodization iπ λz x2 + y 2 Ψ z r = φ R z r iλz න 2πρ f ρ exp iπρ2 0 λz J 0 2πρr λz dρ Lommel series: decomposition into series (Aime, 2013) 12/02/2018 R.Rougeot 61

62 Vanderbei et al. approah Based on Fresnel diffraction theory For serrated or petal-shaped occulter, i.e. a periodic pattern by rotation Ψ z r, θ = Ψ z apod r + j=1 f 1 j, N t R+Δ 2πrρ න f 2 j, ρ J jnt 0 λz ρdρ In stellar coronagraphy: N t 20, and very small working angles: j=1 dominates In solar coronagraphy: N t , and large region (671mm): the computation is very heavy 14/05/2018 R.Rougeot 62

63 Penumbra and Boivin radii 14/05/2018 R.Rougeot 63

64 Penumbra for serrated occulters Convolution of the diffraction intensity Ψ z x, y 2 with the solar stenope image Includes limb darkening function R sun =16,2 r sun =671mm Solar image Penumbra: Diffraction x Solar image 14/05/2018 R.Rougeot 64

65 Penumbra for serrated occulters Diffraction pattern Solar image I x = 0 14/05/2018 R.Rougeot 65

66 Penumbra for serrated occulters Diffraction pattern Solar image I x 1 I(0) 14/05/2018 R.Rougeot 66

67 Penumbra for serrated occulters Diffraction pattern Solar image I x 2 > I(0) 14/05/2018 R.Rougeot 67

68 Penumbra for serrated occulters Diffraction pattern Solar image I x = 0 14/05/2018 R.Rougeot 68

69 Penumbra for serrated occulters We can predict the penumbra depth for serrated occulters: The deepest umbra is achieved when: r sun Boivin radius N t, Δ > r sun The second parameter is the intensity level of the diffraction pattern Large number of teeth preferred! 14/05/2018 R.Rougeot 69