Speckle Imaging with IMAGIN A Multi Aperture 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 r0/λ Cutoff D/λ 0 Spatial Frequency Atmospheric Turbulence
r0
a Short Exposure
Ideal P.S.F Long exposure
Cutoff Frequency limited by D Cutoff Frequency limited by r0 • 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 50 Mirror Aperture Aperture With Aperture Snapshot rotation through 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