### Abstract

An innovative iterative search method called the synthetic phaseshifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.

Original language | English (US) |
---|---|

Pages (from-to) | 26398-26417 |

Number of pages | 20 |

Journal | Optics Express |

Volume | 21 |

Issue number | 22 |

DOIs | |

State | Published - Nov 4 2013 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Optics Express*,

*21*(22), 26398-26417. https://doi.org/10.1364/OE.21.026398

**Synthetic phase-shifting for optical testing : Point-diffraction interferometry without null optics or phase shifters.** / Park, Ryeojin; Kim, Dae Wook; Barrett, Harrison H.

Research output: Contribution to journal › Article

*Optics Express*, vol. 21, no. 22, pp. 26398-26417. https://doi.org/10.1364/OE.21.026398

}

TY - JOUR

T1 - Synthetic phase-shifting for optical testing

T2 - Point-diffraction interferometry without null optics or phase shifters

AU - Park, Ryeojin

AU - Kim, Dae Wook

AU - Barrett, Harrison H

PY - 2013/11/4

Y1 - 2013/11/4

N2 - An innovative iterative search method called the synthetic phaseshifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.

AB - An innovative iterative search method called the synthetic phaseshifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.

UR - http://www.scopus.com/inward/record.url?scp=84887438350&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887438350&partnerID=8YFLogxK

U2 - 10.1364/OE.21.026398

DO - 10.1364/OE.21.026398

M3 - Article

C2 - 24216862

AN - SCOPUS:84887438350

VL - 21

SP - 26398

EP - 26417

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 22

ER -