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arXiv:1807.03622 · Journal of the Optical Society of America A

Interferometry-based modal analysis with finite aperture effects

Davood Mardani, Ayman F. Abouraddy, George Atia

Published Oct 22, 2018• 1 citation
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Abstract

We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary bases using generalized interferometry. We develop a scheme for modal reconstruction from interferometric measurements that accounts for the ensuing clipping effects. Clipping-cognizant reconstruction is shown to yield significant performance gains over traditional schemes that overlook such effects that do arise in practice.

DOI
10.1364/josaa.35.001880

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We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary bases using generalized interferometry. We develop a scheme for modal reconstruction from interferometric measurements that accounts for the ensuing clipping effects. Clipping-cognizant reconstruction is shown to yield significant performance gains over traditional schemes that overlook such effects that do arise in practice.
We generalize the traditional concept of temporal optical interferometry to any degree of freedom of a coherent optical field. By identifying the structure of a unitary optical transformation that we designate the generalized phase operator, we enable optical interferometry to be carried out in any modal basis describing a degree of freedom. The structure of the generalized phase operator is that of a fractional optical transform, thus establishing the connection between fractional transforms, optical interferometry, and modal analysis.
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Optical precision measurement is evolving from conventional intensity and phase readout toward a paradigm centered on mode selection, statistical estimation, and information extraction. Conventional intensity- and phase-based schemes can achieve high sensitivity, but their performance is often constrained by finite-aperture diffraction, reference stability, optical path control, and environmental perturbations in systems. Quantum estimation theory provides a physical framework for optical resolution and measurement precision by optimizing the measurement basis. Inspired by spatial mode demultiplexing, this paper extends quantum parameter estimation from incoherent point-source resolution to small-displacement measurement. Metasurface enabled mode control converts displacement induced optical-field variations into measurable changes in orthogonal modal coefficients, providing a route for extracting sub-diffraction-scale displacement information. This paper introduces Rayleigh’s curse, Fisher information, and spatial mode projection, discusses their applications in one-dimensional displacement measurement and two-dimensional super-resolution imaging, and outlines future directions in digital optics, Engineering Optics 2.0, mode-basis optimization, two-dimensional information reconstruction, and intelligent optical measurement systems for engineering applications.