A boostrap algorithm for temporal signal reconstruction in the presence of noise from its fractional Fourier transformed intensity spectra

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A bootstrap algorithm for reconstructing the temporal signal from four of its fractional Fourier intensity spectra in the presence of noise is described. An optical arrangement is proposed which realises the bootstrap method for the measurement of ultrashort laser pulses. The measurement of short laser pulses which are less than 1 ps is an ongoing challenge in optical physics. One reason is that no oscilloscope exists today which can directly measure the time structure of these pulses and so it becomes necessary to invent other techniques which indirectly provide the necessary information for temporal pulse reconstruction. One method called FROG ... continued below

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128 pages

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Tan, Cheng-Yang February 1, 2011.

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A bootstrap algorithm for reconstructing the temporal signal from four of its fractional Fourier intensity spectra in the presence of noise is described. An optical arrangement is proposed which realises the bootstrap method for the measurement of ultrashort laser pulses. The measurement of short laser pulses which are less than 1 ps is an ongoing challenge in optical physics. One reason is that no oscilloscope exists today which can directly measure the time structure of these pulses and so it becomes necessary to invent other techniques which indirectly provide the necessary information for temporal pulse reconstruction. One method called FROG (frequency resolved optical gating) has been in use since 19911 and is one of the popular methods for recovering these types of short pulses. The idea behind FROG is the use of multiple time-correlated pulse measurements in the frequency domain for the reconstruction. Multiple data sets are required because only intensity information is recorded and not phase, and thus by collecting multiple data sets, there is enough redundant measurements to yield the original time structure, but not necessarily uniquely (or even up to an arbitrary constant phase offset). The objective of this paper is to describe another method which is simpler than FROG. Instead of collecting many auto-correlated data sets, only two spectral intensity measurements of the temporal signal are needed in the absence of noise. The first can be from the intensity components of its usual Fourier transform and the second from its FrFT (fractional Fourier transform). In the presence of noise, a minimum of four measurements are required with the same FrFT order but with two different apertures. Armed with these two or four measurements, a unique solution up to a constant phase offset can be constructed.

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128 pages

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  • Report No.: FERMILAB-TM-2486-AD
  • Grant Number: AC02-07CH11359
  • DOI: 10.2172/1009591 | External Link
  • Office of Scientific & Technical Information Report Number: 1009591
  • Archival Resource Key: ark:/67531/metadc845019

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • February 1, 2011

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Aug. 30, 2016, 3:50 p.m.

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Tan, Cheng-Yang. A boostrap algorithm for temporal signal reconstruction in the presence of noise from its fractional Fourier transformed intensity spectra, report, February 1, 2011; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc845019/: accessed December 10, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.