Open AccessMulti-filter transport of intensity equation solver with equalized noise sensitivity
Author(s) -
Juan Martínez-Carranza,
Konstantinos Falaggis,
Tomasz Kozacki
Publication year - 2015
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.23.023092
Subject(s) - phase retrieval , robustness (evolution) , a priori and a posteriori , solver , sensitivity (control systems) , optics , phase (matter) , filter (signal processing) , frequency domain , algorithm , noise (video) , computer science , physics , fourier transform , mathematics , mathematical analysis , artificial intelligence , computer vision , electronic engineering , biochemistry , chemistry , philosophy , epistemology , quantum mechanics , engineering , image (mathematics) , gene , programming language
Phase retrieval based on the Transport of Intensity Equation (TIE) has shown to be a powerful tool to obtain the phase of complex fields. Recently, it has been proven that the performance of TIE techniques can be improved when using unequally spaced measurement planes. In this paper, an algorithm is presented that recovers accurately the phase of a complex objects from a set of intensity measurements obtained at unequal plane separations. This technique employs multiple band-pass filters in the frequency domain of the axial derivative and uses these specific frequency bands for the calculation of the final phase. This provides highest accuracy for TIE based phase recovery giving minimal phase error for a given set of measurement planes. Moreover, because each of these band-pass filters has a distinct sensitivity to noise, a new plane selection strategy is derived that equalizes the error contribution of all frequency bands. It is shown that this new separation strategy allows controlling the final error of the retrieved phase without using a priori information of the object. This is an advantage compared to previous optimum phase retrieval techniques. In order to show the stability and robustness of this new technique, we present the numerical simulations.