Abstract
The study of the optical transmission matrix (TM) of a sample reveals important statistics of light transport through it. The accuracy of the statistics depends strongly on the orthogonality and completeness of the basis in which the TM is measured. While conventional experimental methods suffer from sampling effects and optical aberrations, we use a basis of Bessel modes of the first kind to faithfully recover the singular values, eigenvalues and eigenmodes of light propagation through a finite thickness of air.
Highlights
The optical transmission response of a linear medium is described by the transmission operator (TO), which links all input modes to the transmitted output modes [1,2,3,4]
We find that when the transmission matrix (TM) is measured straightforwardly in a basis of diffraction limited Airy spots [6], the propagation eigenvectors are strongly affected by system aberrations
We demonstrated a procedure for simultaneous resampling and aberration correction of a measured transmission matrix, and tested the procedure on transmission measurements of the simplest possible sample, empty space
Summary
The optical transmission response of a linear medium is described by the transmission operator (TO), which links all input modes to the transmitted output modes [1,2,3,4]. Our choice for resampling the light fields is to use a basis of Bessel functions of the first kind, which is complete and orthogonal on an infinite 2D-plane and on a disk since the modes are solutions of the circular infinite square well [42] and of a cylindrical waveguide [43], as well as being eigenfunctions of the circular well in quantum mechanics [44]. The advantage of such Bessel modes is that they are propagation invariant, up to terms at the edge of the field of view. After the aberration-correcting resampling procedure the eigenvectors of the TM are no longer IGM but correspond to the true modes of the system
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