# Super-resolution far-ultraviolet equivalent-wavelength interferometry combining the phase of several visible-wavelength interferograms

## TL;DR

This paper introduces a super-resolution interferometric method that combines multiple visible-wavelength interferograms to estimate a far-ultraviolet equivalent-wavelength phase with unprecedented sensitivity and noise performance.

## Contribution

It proposes a novel technique that combines four visible interferogram phases to achieve super-resolution FUV phase estimation, surpassing previous phase-sensitivity and SNR limits.

## Key findings

- Achieved the highest phase-sensitivity reported to date.
- Demonstrated effective phase unwrapping using phase-difference and temporal unwrapping.
- Enhanced signal-to-noise ratio in FUV interferometry.

## Abstract

A far-ultraviolet (FUV) equivalent-wavelength super-resolution interferometric technique is proposed. This FUV equivalent-wavelength interferometric method combines four demodulated phases from four temporal-sets of visible interferograms. Here FUV super-resolution interferometry is defined as the estimation of a modulating phase coming from an FUV equivalent-wavelength illumination laser. To this end we need to combine the demodulated phase of four visible-wavelength interferograms. FUV equivalent-wavelength phase-sensitivity is of course beyond the phase-information capacity of a single visible-wavelength interferogram. To break this visible-wavelength barrier we use the phase-information provided by four or more interferograms in the visible range. Having the four demodulated phases we calculate a phase-difference and the sum of the four phases which is the FUV-equivalent super-resolution phase. The phase-difference is in the infrared phase-sensitivity range and it is assumed non-wrapped. On the other hand the phase-sum is in the FUV phase-sensitivity range and it is highly-wrapped. As shown herein it is possible to unwrap the phase-sum in the temporal domain using the phase-difference and our previously reported extended-range 2-step temporal phase-unwrapper. Of course higher than FUV equivalent phase-sensitivity interferometry may be obtained by increasing the number of independent estimated phases from visible-wavelength interferograms. As far as we know, this FUV equivalent-wavelength super-resolution interferometric technique has the highest phase-sensitivity and highest signal-to-noise ratio ever reported to this date.

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Source: https://tomesphere.com/paper/1704.04700