Femtosecond digital in-line holography with the fractional Fourier transform: application to phase-contrast metrology

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The possibility to analyze transparent phase objects using femtosecond digital in-line holography is demonstrated. We show that the diffraction patterns produced by the diffraction of 20-fs pulses by pure phase objects can be advantageously processed by using the fractional Fourier transform. The optimal fractional orders lead to the longitudinal location of the phase object while the analysis of the reconstructed patterns leads to its diameter and to the value of the phase shift. Simulations and experimental results are in good concordance. This work shows new important applications of these reconstruction techniques in the domain of digital phase-contrast metrology. We further show that the use of femtosecond pulses results in a significant reduction of coherent noise.