Iterative Phase Retrieval for Bunch Profile Reconstruction Tanaji

Iterative Phase Retrieval for Bunch Profile Reconstruction Tanaji Sen ASTA Meeting Feb 21, 2014

Topics • • Kramers-Kronig method Phase retrieval method Retrieval algorithm, ambiguities & removal Test Profiles: KK and iterative method Profiles of A 0 bunches: KK and iterative Benefits and Limits of the iterative method Application to ASTA T. Sen Iterative bunch profile reconstruction 2

Kramers-Kronig issues T. Sen Iterative bunch profile reconstruction 3

Iterative Phase Retrieval - 1 • Origin: Gerchberg & Saxton (1972), Fienup (1982) • Applied to astronomy since 1980 s, e. g. used to improve Hubble images. • Routinely used in X-ray crystallography, in coherent diffractive imaging (CDI) for noncrystalline objects, ptychographic imaging • Greater ambiguity in applying this method in 1 D than in 2 D/3 D T. Sen Iterative bunch profile reconstruction 4

Iterative Phase Retrieval – 2 T. Sen Iterative bunch profile reconstruction 5

Real Space Constraints S. Marchesini, Rev. Sci. Instrum. 78, 011301 (2007) T. Sen Iterative bunch profile reconstruction 6

Iterative Algorithm T. Sen Iterative bunch profile reconstruction 7

Post selection with cross-correlations T. Sen Iterative bunch profile reconstruction 8

Known Input profiles - 1 Gaussian + noise T. Sen Lorentzian + noise Iterative bunch profile reconstruction 9

Known Input Profiles – Lorentzian + Gaussian Sep. = 40 Sep. = 100 T. Sen Sep. = 200 + noise Iterative bunch profile reconstruction 10

A 0 bunch profiles No chirp May 9, 2011 Aug 24, 2011 FWHM Iter= 1. 2 ps KK= 1. 2 ps FWHM Iter= 1. 1 ps KK= 0. 8 ps Courtesy: Randy Thurman-Keup Aug 25, 2011 T. Sen FWHM Iter= 0. 8 ps KK= 0. 6 ps Oct 5, 2011 Iterative bunch profile reconstruction FWHM Iter= 1. 2 ps KK= 0. 6 ps 11

A 0 profiles w/wo chirp Auto-correlation function FWHM (no chirp)= 1. 3 ps FWHM(chirp)= 0. 6 ps Bunch compressed with chirp 17 o off-crest in 9 cell cavity July 1, 2011 Courtesy: Charles Thangaraj Compressed with chirp T. Sen FWHM Iter= 0. 5 ps KK= 0. 8 ps No chirp Iterative bunch profile reconstruction FWHM Iter= 1. 5 ps KK= 1. 4 ps 12

Iterative method Advantages • Appears to be more robust against noise than KK • More realistic at the head of the pulse • Better suited for non-Gaussian profiles with long tails Limitations • Accuracy determined by interferometer & detector • No unique solution but post selection with cross-correlations • Iterative method takes longer (~5 secs) than the KK method Extensions • Several algorithms are on the market, we’ve used the most tested and developed one. Other extensions in the works T. Sen Iterative bunch profile reconstruction 13

Applications to ASTA • Bunch profile measurement with coherent COTR/CODR spectrum from MP interferometer or alternatives • Limit on short bunch resolution ~ 0. 4 ps (from MP interferometer) • 2 D/3 D iterative phase retrieval is needed for lensless imaging with X-rays: coherent diffractive imaging (CDI) and ptychographic imaging. X-rays generated via channeling, PXR, ICS • CDI can be used for electron transverse bunch size measurement; e. g as done at NLCTA using the COTR generated by a laser induced microbunching. T. Sen Iterative bunch profile reconstruction 14