© Fraunhofer IOSB 1 New physical constraints for multi-frame blind deconvolution Roberto Baena Gallé Real Academia de Artes y Ciencias de Barcelona Szymon Gładysz Fraunhofer Institute of Optronics, System Technologies and Image Exploitation Laurent Mugnier ONERA - The French Aerospace Lab Rao Gudimetla, Robert L. Johnson and Lee Kann Air Force Research Laboratory

© Fraunhofer IOSB 2 Motivation Speckle imaging and multi-frame blind deconvolution work well only for very short integration times and very narrow bandwidths. Adaptive optics (AO) at visible wavelengths is very hard. Attainment of diffraction-limited resolution is only possible in conjunction with deconvolution. Objectives Develop a new theory of statistics of images blurred by turbulence. Test if inclusion of this theory in deconvolution removes the need for human intervention. Motivation and objectives No AO With AO With AO + deconv.

© Fraunhofer IOSB 3 Likelihood when noise is Gaussian Prior on the PSFs P(h) can be formulated in: spatial domain (focal-plane intensity statistics). Fourier domain (statistics of the optical transfer function, OTF). Bayesian framework i : dataset o : object h : PSF

© Fraunhofer IOSB 4 Likelihood when noise is Gaussian Prior on the PSFs, assuming intensity is gamma-distributed Bayesian framework (Goodman 2006) i : dataset o : object h : PSF

© Fraunhofer IOSB 5 ■ Fried’s parameter r 0 can be estimated directly from the data: (Spectral ratio. von der Lühe 1984) (Fourier contrast. Gladysz et al. 2012) Estimation of r 0

© Fraunhofer IOSB 6 single stars observed with the 3.5 m telescope at AFRL’s SOR Fourier contrast maps Size of the “black hole” is ~ 2 r 0 (where r 0 = Fried’s parameter). Estimation of r 0

© Fraunhofer IOSB 7 Estimation of r 0 isoplanatic simulation of satellite observation with a 50-cm telescope wavelength = 500 nm, bandwidth = 100 nm 100 short-exposure images per trial Gaussian noise added to images In our tests this method achieves accuracy of around 10%

© Fraunhofer IOSB 8 Focal-plane constraint. Average PSF D = diameter of the telescope z = focal length of the telescope = (mean) wavelength of the observations FFT h(x) : PSF H(u) : OTF

© Fraunhofer IOSB 9 Focal-plane or image constraint (Goodman 2006) Focal-plane constraint. PSF statistics

© Fraunhofer IOSB 10 Parameter M is related to the ratio of speckle size to pixel size. (Skipetrov et al. 2010) Focal-plane constraint. Integration parameter M

© Fraunhofer IOSB 11 Focal-plane constraint. Integration parameter M small M large M pixel sizeexposure time spectral bandwidth small pixels short exposure narrow bandwidth large pixels long exposure wide bandwidth

© Fraunhofer IOSB 12 Focal-plane constraint. Integration parameter M Luckily, for the gamma PDF parameter M has a very simple relation to first-order statistics:  - spatial integration - spectral integration  - temporal integration

© Fraunhofer IOSB 13 For large D/r 0 real and imaginary parts of the OTF are Gaussian random variables. Models are needed for means and variances of real and imaginary parts of the OTF. Focal-plane constraint in the Fourier domain

© Fraunhofer IOSB 14 Implementation I

© Fraunhofer IOSB 15 one frameshift-and-add reconstruction original Results SNR = 100 SNR = 20

© Fraunhofer IOSB 16 OriginalNo priorSpatial constraint prior Fourier constraint prior Results

© Fraunhofer IOSB 17 Built self-referencing, autonomous multi-frame blind deconvolution based on new statistical description of turbulent quantities (“PSF prior”) The approach leads to a user-independent, controllable deconvolution without noise amplification input data with PSF prior without prior Results Experimental turbulence measurements at Starfire Optical Range (AFRL)

© Fraunhofer IOSB 18 Implementation II. Estimation of PSFs using the true object

© Fraunhofer IOSB 19 Results for simulated speckles at r 0 = 10 cm

© Fraunhofer IOSB 20 Results for simulated speckles at r 0 = 10 cm

© Fraunhofer IOSB 21 TruthReconstructions Results for simulated speckles at r 0 = 4 cm & 16 cm

© Fraunhofer IOSB 22 Results using wrong r 0 (SNR = 100)

© Fraunhofer IOSB 23 Results using wrong r 0 (SNR = 20)

© Fraunhofer IOSB 24 Estimation of integration parameter M The correcting factor for τ has been calculated as F=5 μ – spatial integration can be calculated given pixel size ν – spectral integration can be calculated given filter bandwidth τ – for temporal integration one must know exposure time and turbulence-weighted wind speed

© Fraunhofer IOSB 25 Results for real SOR observations

© Fraunhofer IOSB 26 Results for real SOR observations

© Fraunhofer IOSB 27 Summary We are developing a new framework for deconvolution of images of space-based objects for the Air Force Research Lab. The algorithms must be autonomous. Average PSF is derived directly from the data. No hyperparameters are needed. Priors on the PSFs are derived from physics of the imaging process. Spatial-, and Fourier-frequency-based priors delay the onset of noise amplification. Objects and PSFs are reconstructed correctly.

© Fraunhofer IOSB 28 New physical constraints for multi-frame blind deconvolution Effort sponsored by U.S. Air Force Office of Scientific Research, Air Force Materiel Command, under grant FA