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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Phasorial analysis of detuning error in temporal phase shifting algorithms.

J F Mosiño¹, M Servin, J C Estrada

¹Centro de Investigaciones en Optica, Loma del Bosque 115, León, México. jfmosino@cio.mx

|April 1, 2009

Summary

This summary is machine-generated.

This study presents an exact analytical method for analyzing phase error in Temporal Phase Shifting (TPS) algorithms caused by frequency detuning, improving upon previous numerical approaches.

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Area of Science:

Optics and Photonics
Signal Processing

Background:

Temporal Phase Shifting (TPS) algorithms are crucial for phase measurement.
Frequency detuning in TPS algorithms has historically been analyzed solely through numerical simulations.
Accurate phase error analysis is essential for reliable optical metrology.

Purpose of the Study:

To derive an exact analytical expression for phase error in TPS algorithms due to frequency detuning.
To introduce a novel method based on the spectral TPS response and phasorial representation.
To demonstrate the method's applicability to common TPS algorithms.

Main Methods:

Utilizing the spectral Temporal Phase Shifting (TPS) response.
Employing the phasorial representation of the TPS quadrature filter output.
Reducing the detuning problem to a ratio of spectral responses at the detuned frequency.

Main Results:

An exact analytical expression for phase error caused by frequency detuning in TPS algorithms has been derived.
The proposed method simplifies detuning analysis to a ratio of quadrature filter spectral responses.
The method's effectiveness is validated through the analysis of popular TPS algorithms.

Conclusions:

The developed analytical method offers a precise and efficient way to assess phase errors in TPS algorithms.
This spectral approach provides valuable insights into the impact of frequency detuning.
The findings are applicable to various TPS techniques, enhancing their practical implementation.