### Abstract

Based on measuring one-dimensional small rotation angles by using a parallel interference pattern (PIP), a method for measuring two-dimensional (2D) small rotation angles by using two different PIP's that are orthogonal to each other is proposed. We simultaneously measure the 2D small rotation angles Δθ and Δφ by detecting the phases of the orthogonal PIP's reflected by an object at two detection points. A sensitivity of 4.9 mrad/arcsec and a spatial resolution of 1.5 × 1.5 mm^{2} are achieved in the measurement. Theoretical analysis and experimental results show that error ε_{1} in the measurement of Δφ is almost equal to -0.01Δθ and error ε_{2} in the measurement of Δθ is almost equal to -0.01Δφ For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant.

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

Pages (from-to) | 5657-5666 |

Number of pages | 10 |

Journal | Applied Optics |

Volume | 35 |

Issue number | 28 |

State | Published - Oct 1 1996 |

### Fingerprint

### Keywords

- Interferometry
- Orthogonal parallel interference patterns
- Two-dimensional small rotation angles

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Applied Optics*,

*35*(28), 5657-5666.

**Measurement of two-dimensional small rotation angles by using orthogonal parallel interference patterns.** / Dai, Xiaoli; Sasaki, Osami; Greivenkamp, John E; Suzuki, Takamasa.

Research output: Contribution to journal › Article

*Applied Optics*, vol. 35, no. 28, pp. 5657-5666.

}

TY - JOUR

T1 - Measurement of two-dimensional small rotation angles by using orthogonal parallel interference patterns

AU - Dai, Xiaoli

AU - Sasaki, Osami

AU - Greivenkamp, John E

AU - Suzuki, Takamasa

PY - 1996/10/1

Y1 - 1996/10/1

N2 - Based on measuring one-dimensional small rotation angles by using a parallel interference pattern (PIP), a method for measuring two-dimensional (2D) small rotation angles by using two different PIP's that are orthogonal to each other is proposed. We simultaneously measure the 2D small rotation angles Δθ and Δφ by detecting the phases of the orthogonal PIP's reflected by an object at two detection points. A sensitivity of 4.9 mrad/arcsec and a spatial resolution of 1.5 × 1.5 mm2 are achieved in the measurement. Theoretical analysis and experimental results show that error ε1 in the measurement of Δφ is almost equal to -0.01Δθ and error ε2 in the measurement of Δθ is almost equal to -0.01Δφ For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant.

AB - Based on measuring one-dimensional small rotation angles by using a parallel interference pattern (PIP), a method for measuring two-dimensional (2D) small rotation angles by using two different PIP's that are orthogonal to each other is proposed. We simultaneously measure the 2D small rotation angles Δθ and Δφ by detecting the phases of the orthogonal PIP's reflected by an object at two detection points. A sensitivity of 4.9 mrad/arcsec and a spatial resolution of 1.5 × 1.5 mm2 are achieved in the measurement. Theoretical analysis and experimental results show that error ε1 in the measurement of Δφ is almost equal to -0.01Δθ and error ε2 in the measurement of Δθ is almost equal to -0.01Δφ For small rotation angles of less than a few tens of arcseconds, the random errors whose standard deviations are 0.6 arcsec are dominant.

KW - Interferometry

KW - Orthogonal parallel interference patterns

KW - Two-dimensional small rotation angles

UR - http://www.scopus.com/inward/record.url?scp=0038807093&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038807093&partnerID=8YFLogxK

M3 - Article

C2 - 21127572

AN - SCOPUS:0038807093

VL - 35

SP - 5657

EP - 5666

JO - Applied Optics

JF - Applied Optics

SN - 1559-128X

IS - 28

ER -