# Proper scaling for triangular aperture in OAM measurement

## TL;DR

This paper demonstrates that dynamically scaling the triangular aperture according to the OAM beam's radius improves measurement accuracy, revealing a minimum aperture size necessary for precise OAM detection.

## Contribution

It introduces a method to programmatically adjust the aperture size for accurate OAM measurement, establishing a bound based on diffraction pattern analysis.

## Key findings

- A minimum aperture size R is necessary for accurate OAM measurement.
- The aperture radius R scales with the beam's rms radius as reported in literature.
- Larger apertures cause smearing effects that hinder fringe analysis.

## Abstract

A standard triangular aperture for measuring the orbital angular momentum (OAM) of light by diffraction usually has a fixed and limited radius R. This possesses a crucial issue since for an increasing topological charge m of an OAM beam, the radius r of the beam also increases. Here, we prove experimentally our supposition. We use a dynamic triangular aperture that can be programmed to have different characteristic R to diffract beams of various OAM values. By analysing the diffraction patterns with 2d-correlation, we find a minimum bound for R. For a constant initial waist w in the spatial light modulator and a constant position z of the aperture system, we find that the radius of the aperture is unique for each m value. Interestingly, this R scales according to the literature-reported beam's rms radius. We also show that with larger aperture, a smearing effect can be seen in the diffraction patterns which becomes a setback on discerning fringes for the measurement of the topological charge value and thus of the OAM of light. Employing this limit is required if a precise measurement of the OAM of light is needed.