Introduction to MOMFBD

Transcription

1 Introduction to MOMFBD a short overview Mats Löfdahl Institute for Solar Physics Stockholm University 1st CASSDA-SOLARNET Workshop Freiburg February, 2014 Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

2 Multi-Object Multi-Frame Blind Deconvolution 1 What is MOMFBD? MOMFBD Deconvolution MOMFBD Blind Deconvolution MOMFBD Multiple Frames MOMFBD Phase Diversity MOMFBD Multiple Objects 2 History 3 Problems and solutions Alignment Truncated wavefront expansion Model mismatch Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

3 Multi-Object Multi-Frame Blind Deconvolution 1 What is MOMFBD? MOMFBD Deconvolution MOMFBD Blind Deconvolution MOMFBD Multiple Frames MOMFBD Phase Diversity MOMFBD Multiple Objects 2 History 3 Problems and solutions Alignment Truncated wavefront expansion Model mismatch Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

4 Multi-Object Multi-Frame Blind Deconvolution 1 What is MOMFBD? MOMFBD Deconvolution MOMFBD Blind Deconvolution MOMFBD Multiple Frames MOMFBD Phase Diversity MOMFBD Multiple Objects 2 History 3 Problems and solutions Alignment Truncated wavefront expansion Model mismatch Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

5 What is MOMFBD? Blurring and unblurring MOMFBD Deconvolution Convolution d = f s = Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

6 What is MOMFBD? Blurring and unblurring MOMFBD Deconvolution Convolution d = f s = Deconvolution f = d 1 s = 1 Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

7 What is MOMFBD? MOMFBD Blind Deconvolution BD: Joint estimation of object and aberrations Image: Image = mix of two unknown quantities How do they separate? Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

8 What is MOMFBD? MOMFBD Blind Deconvolution BD: Joint estimation of object and aberrations Object: PSF: Perfect optics and fuzzy object? Or... Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

9 What is MOMFBD? MOMFBD Blind Deconvolution BD: Joint estimation of object and aberrations Object: PSF: Stellar object and weird PSF? Or... Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

10 What is MOMFBD? MOMFBD Blind Deconvolution BD: Joint estimation of object and aberrations Object: PSF: Constrain the solution and find... A star and a proper PSF! Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

11 What is MOMFBD? MOMFBD Multiple Frames Data collection model: Multiple samples of seeing Extended target Turbulence Optics Filter Collected images:... Detector t = 1, 2, 3,... T Varying seeing, one object Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

12 What is MOMFBD? MOMFBD Multiple Frames Maths Image formation model d j = f s j + n j s j = F 1 {P j } 2 P j = A exp(iφ j ) φ j M m α mjψ m = ˆφ j Image PSF Pupil function Pupil phase Image = + Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

13 Maths What is MOMFBD? MOMFBD Multiple Frames Image formation model d j = f s j + n j s j = F 1 {P j } 2 P j = A exp(iφ j ) φ j M m α mjψ m = ˆφ j Image PSF Pupil function Pupil phase PSF and pupil function { ( = F 1 exp i )} 2 Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

14 What is MOMFBD? MOMFBD Multiple Frames Maths Image formation model d j = f s j + n j s j = F 1 {P j } 2 P j = A exp(iφ j ) φ j M m α mjψ m = ˆφ j Image PSF Pupil function Pupil phase Pupil phase α 4 + α 5 + α α M = Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

15 Maths What is MOMFBD? MOMFBD Multiple Frames Image formation model d j = f s j + n j s j = F 1 {P j } 2 P j = A exp(iφ j ) φ j M m α mjψ m = ˆφ j Pupil phase Image PSF Pupil function Pupil phase Model fitting Minimize difference between data and model data: minα j pixels d j ˆf ŝ j 2 α 4 + α 5 + α α M = Non-linear optimization methods, linear equality constraints Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

16 Maths What is MOMFBD? MOMFBD Multiple Frames Image formation model d j = f s j + n j s j = F 1 {P j } 2 P j = A exp(iφ j ) φ j M m α mjψ m = ˆφ j Pupil phase Image PSF Pupil function Pupil phase Model fitting Minimize difference between data and model data: minα j pixels d j ˆf ŝ j 2 α 4 + α 5 + α α M = Karhunen Loève functions statistically uncorrelated for atmosphere Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

17 What is MOMFBD? MOMFBD Phase Diversity Data collection model: Multiple samples of seeing Extended target Turbulence Optics Filter Collected images:... Detector t = 1, 2, 3,... T Varying seeing, one object Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

18 What is MOMFBD? MOMFBD Phase Diversity Data collection model: Multiple samples of seeing with PD Extended target Turbulence Optics Shutter Beam splitter Filter Collected images: d = 0: d = 1: Detector Two cameras w/ identical seeing, intentional focus difference t = 1, 2, 3,... T Varying seeing, one object Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

19 What is MOMFBD? MOMFBD Multiple Objects Data collection model: Multiple samples of seeing with MO Extended target Turbulence Optics Shutter Beam splitter Filter i = 1 Collected images: i = 1: i = 2: Filter i = 2 Detector Two cameras w/ identical seeing t = 1, 2, 3,... T Varying seeing, two objects Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

20 History MOMFBD time line Phase Diversity R.A. Gonsalves. Optical Engineering, 21(5): , R.G. Paxman, T.J. Schulz, and J.R. Fienup. JOSA A, 9(7): , 1992a. R.G. Paxman, T.J. Schulz, and J.R. Fienup. OSA Technical Digest Series, 11:5, 1992b. M.G. Löfdahl and G.B. Scharmer. A&A Suppl. Ser., 107:243, R.G. Paxman, J.H. Seldin, M.G. Löfdahl, G.B. Scharmer, and C.U. Keller. ApJ, 466:1087, MFBD and MOMFBD T.J. Schulz. JOSA A, 10: , M.G. Löfdahl. Proc. SPIE, 4792:146, M. van Noort, L. Rouppe van der Voort, and M.G. Löfdahl. Solar Physics, 228(1 2):191, M.J. van Noort and L.H.M. Rouppe van der Voort. ApJ, 489:429, R. Schnerr, J. de la Cruz Rodríguez, and M. van Noort. A&A, 534:A45, V.M.J. Henriques. A&A, 548:A114, Phase Diversity Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

21 History MOMFBD time line Phase Diversity R.A. Gonsalves. Optical Engineering, 21(5): , R.G. Paxman, T.J. Schulz, and J.R. Fienup. JOSA A, 9(7): , 1992a. R.G. Paxman, T.J. Schulz, and J.R. Fienup. OSA Technical Digest Series, 11:5, 1992b. M.G. Löfdahl and G.B. Scharmer. A&A Suppl. Ser., 107:243, R.G. Paxman, J.H. Seldin, M.G. Löfdahl, G.B. Scharmer, and C.U. Keller. ApJ, 466:1087, MFBD and MOMFBD T.J. Schulz. JOSA A, 10: , M.G. Löfdahl. Proc. SPIE, 4792:146, M. van Noort, L. Rouppe van der Voort, and M.G. Löfdahl. Solar Physics, 228(1 2):191, M.J. van Noort and L.H.M. Rouppe van der Voort. ApJ, 489:429, R. Schnerr, J. de la Cruz Rodríguez, and M. van Noort. A&A, 534:A45, V.M.J. Henriques. A&A, 548:A114, Phase Diversity, Solar Phase Diversity Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

22 History MOMFBD time line Phase Diversity R.A. Gonsalves. Optical Engineering, 21(5): , R.G. Paxman, T.J. Schulz, and J.R. Fienup. JOSA A, 9(7): , 1992a. R.G. Paxman, T.J. Schulz, and J.R. Fienup. OSA Technical Digest Series, 11:5, 1992b. M.G. Löfdahl and G.B. Scharmer. A&A Suppl. Ser., 107:243, R.G. Paxman, J.H. Seldin, M.G. Löfdahl, G.B. Scharmer, and C.U. Keller. ApJ, 466:1087, MFBD and MOMFBD T.J. Schulz. JOSA A, 10: , M.G. Löfdahl. Proc. SPIE, 4792:146, M. van Noort, L. Rouppe van der Voort, and M.G. Löfdahl. Solar Physics, 228(1 2):191, M.J. van Noort and L.H.M. Rouppe van der Voort. ApJ, 489:429, R. Schnerr, J. de la Cruz Rodríguez, and M. van Noort. A&A, 534:A45, V.M.J. Henriques. A&A, 548:A114, Phase Diversity, Solar Phase Diversity, MFBD & MOMFBD Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

23 History MOMFBD time line Phase Diversity R.A. Gonsalves. Optical Engineering, 21(5): , R.G. Paxman, T.J. Schulz, and J.R. Fienup. JOSA A, 9(7): , 1992a. R.G. Paxman, T.J. Schulz, and J.R. Fienup. OSA Technical Digest Series, 11:5, 1992b. M.G. Löfdahl and G.B. Scharmer. A&A Suppl. Ser., 107:243, R.G. Paxman, J.H. Seldin, M.G. Löfdahl, G.B. Scharmer, and C.U. Keller. ApJ, 466:1087, MFBD and MOMFBD T.J. Schulz. JOSA A, 10: , M.G. Löfdahl. Proc. SPIE, 4792:146, M. van Noort, L. Rouppe van der Voort, and M.G. Löfdahl. Solar Physics, 228(1 2):191, M.J. van Noort and L.H.M. Rouppe van der Voort. ApJ, 489:429, R. Schnerr, J. de la Cruz Rodríguez, and M. van Noort. A&A, 534:A45, V.M.J. Henriques. A&A, 548:A114, Phase Diversity, Solar Phase Diversity, MFBD & MOMFBD, MOMFBD strategies Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

24 Problems and solutions Alignment Pinhole calibrated camera alignment 10 arcseconds a b arcseconds 5 0 c 0 5 arcseconds d 0 5 arcseconds a. LCP; b. RCP; c. MOMFBD magnetogram; d. Traditional magnetogram; note artifacts Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

25 Problems and solutions Alignment Single WB object van Noort et al. (2005) Diversity k Fe Wide Object i Fe LCP Fe RCP Realization t All WB frames single restored image NB frames co-restored with some WB frames Different NB states aligned by the common WB image Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

26 Problems and solutions Alignment Single WB object van Noort et al. (2005) Extra WB objects Henriques (2012) Diversity k Fe Wide Object i Fe LCP Fe RCP Realization t All WB frames single restored image NB frames co-restored with some WB frames Different NB states aligned by the common WB image Allow for residual misalignment Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

27 Encirc cm Problems and solutions Truncated wavefront expansion A finite number r / 1" of wavefront r 0 / 1 cm modes Fig. 2: Encircled PSF energy for different r0 as indicated in the figure. Red: PSFs based on S ; Blue: PSFs based on Ŝ ; Black: diffraction limited PSF; Black dashed: 90% level. S Fig. 3: Strehl ratios as a function of r0. Solid line: Eq. (11); Plus (+) symbols: PSFs based on S ; Cross ( ) symbols: PSFs based on Ŝ u Perfect correction of 36 KL modes restores resolution, not contrast cm 5 cm Fig. 4: Power spectra (angular averages) of S (red) and Ŝ (blue) for r0 as indicated % 12.78% 11.83% 9.77% 7.23% 4.63% 14.52% 14.51% 14.51% 14.50% 14.48% 14.41% 14.29% Figure 6 shows RMS intensity errors of restored images using different techniques (MFBD, JPDS), number of aberration parameters (M=35, 50 and 100) without and with Ŝ compensa- Fig. 5: r 0 Images. = Far left: Original 25 cm image. Top: Low-pass 20 cm images degraded 15 cm by high-order aberrations, 10 cm i.e., by S 7, cm corresponding to 5 r0=25, cm 20, 15, 10, 7 and 5 cm, resp. (same layout as Fig. 1). Bottom: Degraded images compensated by use of the method described, i.e., by Ŝ. All images are scaled between min and max of the original image and low-pass filtered to 90% of the SST diffraction limit. The numbers above and below the image tiles are the RMS contrasts in percent of the mean intensity (100 RMS/mean). Solution Post-restoration correction based on atmospheric statistics. Not in pipeline yet. Scharmer & Löfdahl (2010) The synthetic images were processed with the MOMFBD program in various ways (MFBD or JPDS, different numbers of realizations, different subfield sizes (256 pixels = 15, 128 pixels = 7. 6, 80 pixels = 4. 7), different number of estimated wavefront parameters, without and with added noise). In this section we summarize the results of these simulations. Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13

28 Problems and solutions Model mismatch Model mismatch hurts the fit Pupils Non-common paths Telescope FL Field stop/pinholes CT DM TM RL NBR NBT PBSLCs LRE HRE Dual FPI CRISP Prefilter Shutter WB AO WFS Not used DC Blue path Other problems Optical parameters Finite exposures Flats: time-dependent, polarized, IR Symptoms Under-estimated wavefronts under-corrected images Small-scale image artifacts amplified by deconvolution Mats Löfdahl (Institute for Solar Physics) Introduction to MOMFBD Freiburg / 13