Multi-frame blind deconvolution and phase diversity with statistical inclusion of uncorrected high-order modes

Context. Images collected with ground-based telescopes suffer blurring and distortions from turbulence in the Earth’s atmosphere. Adaptive optics (AO) can only partially compensate for these effects. Neither multi-frame blind deconvolution (MFBD) methods nor speckle techniques perfectly restore AO-compensated images to the correct power spectrum and contrast. MFBD methods can only estimate and compensate for a finite number of low-order aberrations, leaving a tail of uncorrected high-order modes. Restoration of AO-corrected data with speckle interferometry depends on calibrations of the AO corrections together with assumptions regarding the height distribution of atmospheric turbulence. Aims. We seek to develop an improvement to MFBD image restoration that combines the use of turbulence statistics to account for high-order modes in speckle interferometry with the ability of MFBD methods to sense low-order modes that can be partially corrected by AO and/or include fixed or slowly changing instrumental aberrations. Methods. We modify the MFBD image-formation model by supplementing the fitted low-order wavefront aberrations with tails of random high-order aberrations. These tails follow Kolmogorov statistics scaled to estimated or measured values of Fried’s parameter, r0, that characterize the strength of the seeing at the moment of data collection. We refer to this as statistical diversity (SD). We test the implementation of MFBD with SD with noise-free synthetic data, simulating many different values of r0 and numbers of modes corrected with AO. Results. Statistical diversity improves the contrasts and power spectra of restored images, both in accuracy and in consistency with varying r0, without penalty in processing time. Together with focus diversity (FD, or traditional phase diversity), the results are almost perfect. SD also reduces errors in the fitted wavefront parameters. MFBD with SD and FD seems to be resistant to errors of several percentage in the assumed r0 values. Conclusions. The addition of SD to MFBD methods shows great promise for improving contrasts and power spectra in restored images. Further studies with real data are merited