# Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values

## TL;DR

This paper demonstrates that interferometric weak values can significantly enhance the signal to noise ratio in optical beam deflection measurements, reducing technical noise and enabling better performance with low saturation detectors.

## Contribution

It provides a detailed analysis and experimental validation showing how weak value amplification optimizes the signal to noise ratio in beam deflection measurements.

## Key findings

- Achieved a 54-fold improvement in SNR over standard methods.
- Reduced technical noise and enabled use of low saturation detectors.
- Validated theoretical predictions with experimental results.

## Abstract

The amplification obtained using weak values is quantified through a detailed investigation of the signal to noise ratio for an optical beam deflection measurement. We show that for a given deflection, input power and beam radius, the use of interferometric weak values allows one to obtain the optimum signal to noise ratio using a coherent beam. This method has the advantage of reduced technical noise and allows for the use of detectors with a low saturation intensity. We report on an experiment which improves the signal to noise ratio for a beam deflection measurement by a factor of 54 when compared to a measurement using the same beam size and a quantum limited detector.