with IMAGIN A Multi Aperture Imaging Simulation Arun Surya

“A good idea is worth more than a large “ Contents a. Atmosphere, Phase and Speckles b. Speckle 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 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 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