# Using a Complex Optical Orbital-Angular-Momentum Spectrum to Measure Object Parameters: A Spatial Domain Approach

## TL;DR

This paper introduces a spatial domain method using complex optical orbital angular momentum spectra to accurately measure object parameters, such as opening angle, with high signal-to-noise ratio and robustness against orientation variations.

## Contribution

The study presents a novel approach utilizing complex OAM spectra for spatial spectrum analysis to extract object parameters more reliably than traditional methods.

## Key findings

- Achieved over 15 dB signal-to-noise ratio in measurements.
- Dip positions in OAM intensity spectrum depend on opening angle.
- Phase spectrum slope depends on object orientation.

## Abstract

Light beams can be characterized by their complex spatial profiles in both intensity and phase. Analogous to time signals, which can be decomposed into multiple orthogonal frequency functions, a light beam can also be decomposed into a set of spatial modes that are taken from an orthogonal basis. Such a decomposition can provide a tool for spatial spectrum analysis, which may allow the stable, accurate and robust extraction of physical object information that may not be readily achievable using traditional approaches. As an example, we measure the opening angle of an object using the complex spectrum of orbital angular momentum (OAM) modes as the basis, achieving a more than 15 dB signal-to-noise ratio. We find that the dip (i.e., notch) positions of the OAM intensity spectrum are dependent on an object's opening angle but independent of the object opening's angular orientation, whereas the slope of the OAM phase spectrum is dependent on the object opening's orientation but independent on the opening angle.

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Source: https://tomesphere.com/paper/1705.09051