Speckle Imaging with IMAGIN A M ulti A perture Imaging Simulation Arun Surya “ A good idea is worth more than a large telescope “
Contents a. Atmosphere, Phase and Speckles b. Speckle Interferometry and Speckle masking c. IMAGIN : Simulations of Speckle imaging with Multi Apertures d. Hypertelescopes e. Reconstruction Results f. Conclusion
Two Approaches of Dealing with Turbulence Online Approach Offline Approach Adaptive Optics Speckle Techniques
Imaging Equation Transfer Function 1 MTF Cutoff r 0 / λ Cutoff D/ λ 0 Spatial Frequency
Atmospheric Turbulence r 0 a Short Exposure Ideal P.S.F Long exposure Cutoff Frequency limited by D Cutoff Frequency limited by r 0
• A.Labeyrie 1970 : Speckle Interferometry Attainment of Diffraction Limited resolution in Large Telescopes by Fourier Analyzing Speckle patterns in Star Images, A&A Speckle Interferometry Transfer Function : >0 up to diffraction limit Object Autocorrelation Power Spectrum Object Fourier Amplitude Object Fourier Phase
The curious case of phase dominance .. • Alan V Oppenheim 1981 “Importence of phase in signals” • Many of the important features of the signal are preserved if only phase is retained • Under variety of conditions phase information is alone sufficient to reconstruct the signal
• G.Weigelt 1977 : Speckle Masking Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase
• G.Weigelt 1977 : Speckle Masking Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase
Bispectrum of 1D Signals
• G.Weigelt 1977 : Speckle Masking Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase
• G.Weigelt 1977 : Speckle Masking Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase
Object Phase from Bispectrum Object Bispectrum Phase Object phase Recursion Formulae
“The Code” 1. Get the Short exposure frames 2. Do frame by frame fourier transform 3. Get Object Magnitude by Speckle Interferometry 4. Do frame by frame fourier transform 5. Compute average Bispectrum 6. Use Recursion Formulae to retrieve phase 7. Averaging phasor over many iterations 8. Combining Phase and Amplitude to get signal back
Specs and Issues • Written in IDL(Interactive Data Language) • Bispectrum for a 2D signal is 4D • Memmory issues • Currently Code can process 200x200 pixel data • Code is computationaly very expensive • 8hrs for processing 500 frames of 200x200 in Core 2 duo ,4 GB system Computationally efficient Radon Transform versions gave poor reconstruction
Phase 2
Speckle Imaging Simulation Package : IMAGIN a) Single and Multi Aperture Telescopes b) Fizeau Type Imaging Inteferometers c) Hypertelescopes Written in MATLAB • Any Mirror Dimensions , Baselines • Night time rotation • Photon Limited Interferograms • Different Plate Scales, wavelength
Single Aperture Telescopes R0 =5 cm D=1m R0 =30 cm D=1m
Multi Aperture Systems Based on Simple Algorithm using the correlation function
Fizeau Imaging Interferometers ψ2 ψ3 ψ1 ψ4 ψ8 ψ9 ψ4 ψ10 ψ6 ψ5 ψ7
Fizeau Mode Imaging • 20 mirror aperture • Randomly arranged over 10 m disc • Individual aperture size of 1 m mirror Largest Baseline Smallest Baseline
Fizeau Mode Imaging
. A.Labeyrie 1996 Resolved imaging of extra-solar planets with future 10-100km optical interferometric arrays . • Fizeau Interferometer + • Pupil Densification • = • HyperTelescope •
Hypertelescope Fizeau Hypertelescope
Aperture Configuration 20 mirror Aperture 50 mirror Aperture After Densification Aperture Rotation Through Night ..
Parameters
Objects Binary Star Six Star Group Extended Object
Binary Star Speckle
Binary Star Six Star Group Extended Object With Photon Noise
Speckle Interferometry : Binary Star Autocorrelations 20 Mirror 20 Mirror Aperture Aperture Snapshot With Aperture rotation through night 50 Mirror Aperture 50 Mirror With Aperture Aperture rotation through Snapshot night
Six Star Group 20 Mirror Aperture 20 Mirror 15 000 Aperture photon (With Rotation) events ! 50 Mirror Aperture 50 Mirror Aperture (With Rotation)
Extended Object Object Recovered Speckle
20 Aperture 20 Aperture (With rotation) 50 Aperture Object 50 Aperture (With Rotation )
Conclusions • Speckle Masking Code • Multi Aperture Imaging Simulation • Speckle Imaging with Hypertelescopes • Real Data • Photometric Accuracy and Strehl Ratio Measurement
Thank you Reference A.Labeyrie 2006 “Optical Stellar Interferometry ” Weigelt, Lohman 1983 “Speckle Masking in astronomy” Swapan K Saha 2007 “Diffraction Limited Imaging with Large and Moderate telescopes “ Alan V Openheim 1981 “Importance of Phase in signals” Lohmann ,Wirnitzer 1985 “Triple Correlations” A good idea is worth more than a large telescope : R.O.Redman
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