In-line holography for the characterization of ultrafast laser filamentation in transparent media

Abstract

A powerful experimental method, based on holographic microscopy, is used to retrieve the spatiotemporal distribution of small (<10−3) refractive index perturbations induced by ultrafast laser pulses in transparent media. A numerical iterative wavefront propagation approach is used to accurately reconstruct both the phase and the amplitude of the perturbed probe beam wavefront, while Abel inversion recovers the exact three dimensional distribution of the perturbation. For demonstration, a laser filament induced plasma string in air is fully characterized.

Application of inverse Abel techniques in in-line holographic microscopy

“…r P x R r z dx x r p ¥ ¶ ¶ = -ò (2) Practically, the numerical implementation of equation (2) is difficult due to the singularity point at the lower limit of integral and because the derivative of the projection ( ) P x ¶ ¶ tends to enhance the noisecorruption of the experimental data. Moreover, the projection function ( , ) P x z , cannot be treated as a continuous function, as its value is known only in certain discrete points [9].…”

“…This approach is widely applied in tomographic imaging applications where the object under study is somewhat static. On the other hand, it is quite difficult to retrieve the large number of projections required in the case of dynamical objects encountered in ultrafast pump-probe experiments [1][2][3][4][5][6]. In this case the objects under study are laser induced perturbations in the refractive index of a transparent medium with micron sized spatial dimensions.…”

“…Up to now, the commonly applied method for calculating the inverse Abel transform in problems of laser induced perturbations is the Fourier-Hankel technique (F-H) [2,6,9]. More specifically, this method is based on a representation of the inverse Abel transform (eq.…”

“…Furthermore, these structures dynamically change with time at time scales well below 1 ps. All the above mentioned problems make the retrieval from multiple M. I. Apostolopoulos, M. I. Taroudakis and D. G. Papazoglou projections impractical, leading to the utilization of a single projection and an implementation of the Abel transform for the retrieval of the refractive index distribution [2,6].…”

“…In the field of holographic microscopy [1][2][3][4][5][6], the treatment of inverse problems, as for instance, that of recovering the volume of the three-dimensional distribution of the refractive index, is based on the application of various techniques of Abel transform. The Abel transform [7][8][9] is actually a solution of the inverse mathematical problem of retrieving the three-dimensional distribution of a physical property such as the refractive index or absorption on the basis of the knowledge of a single projection.…”