Sensitivity analysis of phase diversity technique for high resolution earth observing telescopes

Transcription

1 Sensitivity analysis of phase diversity technique for high resolution earth observing telescopes C. Latry a, J.-M. Delvit a, C. Thiebaut a a CNES (French Space Agency) ICSO 2016 Biarritz, France October

2 OUTLINE Active optics for high resolution earth remote sensing systems Principles of phase diversity technique Solving algorithm Benchmark presentation Conclusions and perspectives ICSO 2016 Biarritz, France October

3 OUTLINE Active optics for high resolution earth remote sensing systems Principles of phase Diversity technique Solving algorithm Benchmark presentation Conclusions and perspectives ICSO 2016 Biarritz, France October

4 Optics and image resolution Ground resolution earth of observing systems has constantly improved from the 80 s SPOT1-SPOT4 : 10m SPOT5 : 3,4m (quincunx supermode sampling) Pleiades : 0,7m Next generation < 30cm Resolution is now limited by telescope diameter S/B may be achieved thanks to TDI detector (and not only with the telescope diameter) Cut off frequency : f c = D λ in rad-1 unit (diffraction limit) Increases linearly with the telescope diameter Maximum use of telescope potential when R=f Nyquist /f c ~1 Minimizing optical aberrations allows to increase R ratio ICSO 2016 Biarritz, France October

5 f nyquist /f c and telescope diameter historical evolution Increasing f nyquist /f c is of utmost importance for large diameter values MTF optics has to be maximized (diffraction telescope) Active optics to correct evolving aberrations ICSO 2016 Biarritz, France October

6 OUTLINE Active optics for high resolution earth remote sensing systems Principles of phase Diversity technique Solving algorithm Benchmark presentation Conclusions and perspectives ICSO 2016 Biarritz, France October

7 Phase diversity principle on unknown extended landscapes Primary image Secondary defocused image Two simultaneous acquisitions of the same landscape with a differential known defocus. Theory : secondary defocused image is mandatory to identify the sign of symmetrical WFE component. Practically : It helps to get rid of unknown landscape between the observation equations 11 ICSO 2016 Biarritz, France October

8 OUTLINE Active optics for high resolution earth remote sensing systems Principles of phase Diversity technique Solving algorithm Benchmark presentation Conclusions and perspectives ICSO 2016 Biarritz, France October

9 Phase diversity : an inverse problem Each acquisition is described by formation model in the Fourier domain landscape convolution with PSF becomes multiplicative product with the MTF MTF is decomposed as a multiplicative product of MTF detector and OTF OTF is mathematically linked to WFE FT landscape MTF detector OTF WFE + FT noise 1 = FT image 1 FT landscape MTF detector OTF WFE + α 4 Z 4 + FT noise 2 = FT image 2 WFE is decomposed as the sum of an a priori knowledge and a finite combination of Zernike polynomials a i weight factors are the searched aberration coefficients WFE = WFE a priori + α i Z i i I 13 ICSO 2016 Biarritz, France October

10 Solving the phase diversity problem α i i I should minimize the following functional quantity : F WFE = νx ν y, H ν x, ν y 2 dνx dν y = x,y TF 1 H 2 dxdy with H ν x, ν y = FT image 1 OTF WFE + α 4 Z 4 FT image 2 OTF WFE 2 2σ bruit OTF WFE 2 + OTF WFE + α 4 Z σ bruit =mean noise variance (computed from a noise model) Interpretation : If true WFE is found, TF 1 H unity variance is a noise image whith Solved with iterative Levenberg-Marquardt algorithm 14 ICSO 2016 Biarritz, France October

11 OUTLINE Active optics for high resolution earth remote sensing systems Principles of phase Diversity technique CNES solving algorithm Benchmark presentation Conclusions and perspectives ICSO 2016 Biarritz, France October

12 Phase diversity benchmark overview Goal : sensitivity analysis of phase diversity retrieval to key parameters WFE 6 WFEs representative of post launch or routine WFEs Post launch WFEs have much higher RMS value Number of searched aberrations Z4, Z4-Z13 and Z4-Z36 WFE a priori knowledge Binary : full knowledge/ no kwowledge of unsearched Zi Differential defocus Da 4 50nm, 190nm, 300nm Landscapes 400 (128x128 pixels) phase diversity couples 400x6x3x2x3=43200 aberration estimation runs 16 ICSO 2016 Biarritz, France October

13 Instrumental hypothesis and simulations WFS hypothesis: 128x128 pixels images with 30cm sampling grid SNR : Low values due to beamsplitter and reduced spectral bandwidth L1 L2/2 L2 Radiances (Wm -2 Str -1 mm -1) SNR Fully representative simulations from airborne 10cm images with L2/2 mean radiance 17 ICSO 2016 Biarritz, France October

14 WFEs and landscapes WFE1 WFE2 WFE3 WFE4 WFE6 WFE7 Amiens Cannes La Crau Marseille Each airborne image produces 100 Phase diversity 128x128 couples couples 18 ICSO 2016 Biarritz, France October

15 Major results of sensitivity analysis WFE Post launch WFE6 and WFE7 large aberrations are difficult to assess, unless limiting the estimation to Z4 only Routine WFEs leads to accurate estimation with better behaviour with non structured high order aberrations WFE a priori knowledge More significant with structured high order aberrations Number of searched aberrations Accuracy decreases when trying to assess more aberrations 19 ICSO 2016 Biarritz, France October

16 Major results of sensitivity analysis Differential defocus Each of the three tested defocus values (even 50nm) give accurate results when assessing only defocus When estimating more aberrations, large defocus values (190nm and 300nm) are to be preferred Landscape type Urban areas with high frequency content (Amiens) give the best results Algorithm may fail in quasi uniform zones such (water in Cannes) Phase diversity algorithm succeeds even with sparse frequency content 20 ICSO 2016 Biarritz, France October

17 Quantitative results Sensitivity to landscapes Landscape AMIENS CANNES LA_CRAU MARSEILLE Searched aberrations % of results better than 20nm Sensitivity to searched aberrations number WFE Searched aberrations % of results better than 20nm Sensitivity to WFE a priori knowledge. Percentage of estimation better than 20nm with differential defocus=190nm WFE a priori knowledge : True WFE1 WFE2 WFE3 WFE4 Z4 seul Z4-Z Z4-Z WFE a priori knowledge : False Z4 seul Z4-Z Z4-Z Sensitivity to differential defocus for Z4-Z36 estimation WFE Defocus % better than 20nm ICSO 2016 Biarritz, France October

18 OUTLINE Active optics for high resolution earth remote sensing systems Principles of phase Diversity technique Solving algorithm Benchmark presentation Conclusions and perspectives ICSO 2016 Biarritz, France October

19 Conclusions and perspectives Active optics is currently studied by CNES for its future high resolution earth observing systems Phase diversity is a good candidate as Wave Front sensor with 20nm RMS performance easily achievable Next step will consist in reducing the algorithm complexity in order to make its on board implementation easier. 23 ICSO 2016 Biarritz, France October

20 Thank you for your attention! 24 ICSO 2016 Biarritz, France October