No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms

Rent:

Rent this article for

USD

10.1063/1.3603452

### Abstract

Phase retrieval techniques are widely used in optics, imaging and electronics. Originating in signal theory, they were introduced to interferometry around 1970. Over the years, many robust phase-stepping techniques have been developed that minimize specific experimental influence quantities such as phase step errors or higher harmonic components of the signal. However, optimizing a technique for a specific influence quantity can compromise its performance with regard to others. We present a consistent quantitative analysis of phase measurement uncertainty for the generalized linear phase stepping algorithm with nominally equal phase stepping angles thereby reviewing and generalizing several results that have been reported in literature. All influence quantities are treated on equal footing, and correlations between them are described in a consistent way. For the special case of classical *N*-bucket algorithms, we present analytical formulae that describe the combined variance as a function of the phase angle values. For the general Arctan algorithms, we derive expressions for the measurement uncertainty averaged over the full 2π-range of phase angles. We also give an upper bound for the measurement uncertainty which can be expressed as being proportional to an algorithm specific factor. Tabular compilations help the reader to quickly assess the uncertainties that are involved with his or her technique.

© 2011 American Institute of Physics

Received 01 February 2011
Accepted 19 May 2011
Published online 29 June 2011

Article outline:

I. INTRODUCTION

II. PHASE STEPPING ALGORITHMS OF A GENERAL ARCTAN FORM

III. PHASE MEASUREMENT UNCERTAINTY FOR THE GENERAL ARCTAN ALGORITHM

A. Uncertainty analysis

B. Uncertainty for the classical *N*-bucket algorithm and Fourier method

IV. CONTRIBUTIONS TO THE MEASUREMENT UNCERTAINTY

A. Uncorrelated, phase-independent contributions

B. Uncorrelated contributions involving the phase angle

1. Illumination instability and camera gain fluctuations

2. Phase step jitter

3. Poisson count statistics

C. Correlated contributions

1. Linear phase step miscalibration

2. General phase step miscalibration

3. Detector nonlinearity

4. Higher harmonics

5. Drift of background irradiance

6. Drift of source irradiance

V. COMBINED PHASE MEASUREMENT UNCERTAINTY

VI. CONCLUSIONS

/content/aip/journal/rsi/82/6/10.1063/1.3603452

http://aip.metastore.ingenta.com/content/aip/journal/rsi/82/6/10.1063/1.3603452

Article metrics loading...

/content/aip/journal/rsi/82/6/10.1063/1.3603452

2011-06-29

2014-04-23

Full text loading...

### Most read this month

Article

content/aip/journal/rsi

Journal

5

3

Commenting has been disabled for this content