Speckle Imaging with IMAGIN A M ulti A perture Imaging Simulation - - PowerPoint PPT Presentation

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Speckle Imaging with IMAGIN A M ulti A perture Imaging Simulation - - PowerPoint PPT Presentation

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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 :

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Speckle Imaging with IMAGIN

A Multi Aperture Imaging Simulation

“A good idea is worth more than a large telescope “

Arun Surya

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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
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Two Approaches of Dealing with Turbulence Online Approach Offline Approach Adaptive Optics Speckle Techniques

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Imaging Equation

Transfer Function Cutoff D/λ Spatial Frequency 1 MTF Cutoff r0/λ

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a

Ideal P.S.F

Long exposure Short Exposure Atmospheric Turbulence Cutoff Frequency limited by D Cutoff Frequency limited by r0 r0

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  • A.Labeyrie 1970 : Speckle Interferometry

Attainment of Diffraction Limited resolution in Large Telescopes by Fourier Analyzing Speckle patterns in Star Images, A&A

Object Autocorrelation Power Spectrum Object Fourier Amplitude Object Fourier Phase

Speckle Interferometry Transfer Function : >0 up to diffraction limit

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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

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  • G.Weigelt 1977 : Speckle Masking

Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications

Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase

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  • G.Weigelt 1977 : Speckle Masking

Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications

Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase

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Bispectrum of 1D Signals

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  • G.Weigelt

1977 : Speckle Masking

Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications

Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase

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  • G.Weigelt 1977 : Speckle Masking

Modified astronomical speckle interferometry 'speckle masking' ,Optics Communications

Image Triple Correlation Image Bispectrum Object Fourier Amplitude Object Fourier Phase

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Object Phase from Bispectrum

Object Bispectrum Phase Object phase

Recursion Formulae

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“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

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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

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Phase 2

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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
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Single Aperture Telescopes

R0 =5 cm D=1m R0 =30 cm D=1m

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Multi Aperture Systems

Based on Simple Algorithm using the correlation function

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Fizeau Imaging Interferometers

ψ1 ψ2 ψ4 ψ5 ψ3 ψ6 ψ4 ψ7 ψ8 ψ9 ψ10

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mirror

Fizeau Mode Imaging

  • 20 mirror aperture
  • Randomly arranged over 10 m disc
  • Individual aperture size of 1 m

Largest Baseline Smallest Baseline

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Fizeau Mode Imaging

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. A.Labeyrie 1996

  • Fizeau Interferometer
  • +
  • Pupil Densification
  • =
  • HyperTelescope

Resolved imaging of extra-solar planets with future 10-100km optical interferometric arrays.

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Hypertelescope

Fizeau Hypertelescope

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Aperture Configuration

20 mirror Aperture 50 mirror Aperture After Densification Aperture Rotation Through Night ..

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Parameters

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Objects

Binary Star Six Star Group Extended Object

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Binary Star Speckle

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Binary Star Six Star Group Extended Object With Photon Noise

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Speckle Interferometry : Binary Star

20 Mirror Aperture

Snapshot

50 Mirror Aperture

Snapshot

20 Mirror Aperture

With Aperture rotation through night

50 Mirror Aperture

With Aperture rotation through night

Autocorrelations

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Six Star Group

50 Mirror Aperture (With Rotation) 50 Mirror Aperture 20 Mirror Aperture (With Rotation) 20 Mirror Aperture

15 000 photon events !

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Extended Object

Object Speckle Recovered

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20 Aperture 20 Aperture (With rotation) 50 Aperture 50 Aperture (With Rotation) Object

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Conclusions

  • Speckle Masking Code
  • Multi Aperture Imaging Simulation
  • Speckle Imaging with Hypertelescopes
  • Real Data
  • Photometric Accuracy and Strehl Ratio

Measurement

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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