## Multi-turn all-reflective optical gyroscope

Optics Express, Vol. 7, Issue 8, pp. 285-291 (2000)

http://dx.doi.org/10.1364/OE.7.000285

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### Abstract

We use calculation and simulation to characterize an all-reflective monolithic gyroscopic structure that supports 3 sets of orthogonal, spatially dense and continuous helical optical paths. This gyroscope differs from current fiber optic and ring laser gyroscopes primarily in the free space multi-turn nature of the optical path. The design also creates opportunities for introducing gain while minimizing spontaneous emission noise from those gain regions. The achievable angular measurement precision for each axis, given ideal components and no gain, is calculated to be ~0.001°/hr for a structure of ~6.5 cm diameter, ~1 watt average optical power, and a wavelength of 0.5 µm. For fixed power, the uncertainty scales as the reciprocal cube of the diameter of the structure. While the fabrication and implementation requirements are challenging, the needed reflectivities and optical surface quality have been demonstrated in more conventional optics. In particular, the low mass, compact character, and all reflective optics offer advantages for applications in space.

© Optical Society of America

## 1. Introduction

### 1.1 The Sagnac interferometer as the sensing element

### 1.2 Objective

3. A.F. Stewart, S. Lu, M. Tehrani, and C. Volk, “Ion beam Sputtering of Optical Coatings,” SPIE **2114**, 662–677 (1994). [CrossRef]

## 2. Measurement precision

*δ*Ω for an optical gyroscope given an optical pathlength

*L*, light at wavelength

*λ*

_{o}in microns, a photon flux of

*n*

_{ph}photons/second at the detector, a detector quantum efficiency of

*η*, and an integration time

*τ*is

## 3. Open multi-turn configuration for implementing an optical gyroscope

## 4. Limiting precision for a given characteristic dimension

*D*≅4.6√2·

*ω*

_{i}[2]. Here

*ω*

_{i}is the radius of the beam waist for the i

^{th}path segment. The relationship between pathlength

*2Z*

_{i}, beam waist

*ω*

_{i}, and wavelength

*λ*

_{o}is 2

*Z*

_{i}=2

*λ*[2].

*R*, the length of a single side of a cube inscribed in that sphere is

*a*=2

*R*√3. The worst case confocal parameter is 2Z

_{i}=2R. Substituting this into the above equations using a wavelength of

*λ*=0.5µm yields

*ω*

_{o}=18.8µm. Here

*Ω*

_{o}is the upper limit on beam radius. A worst case estimate of the diameter of a sphere that supports this 21-turn-per-row configuration is small, i.e., 2

*R*=2

*Z*

_{o}=2

*λ*=0.446

*cm*.

*A*

_{TOTAL}=

*NA*, in equation 1. Our Advanced Systems Analysis Program (ASAP) simulation gives this area as 0.00192 m

^{2}. For photon flux we take

*n*

_{ph}=3×10

^{18}photons/sec which corresponds to 1 Watt. This is a higher flux than typically used for fiber. We regard this as accessible given the use of free space optics. Using

*η*=0.5 and

*τ*=1 sec, Eq. (1) yields

*δ*Ω=7.99×10

^{-6}

*rad*/sec=1.65°/

*hr*. This is a modest precision, however, the diameter of the gyroscope, <5 mm, is small compared to most conventional gyroscopes offering this degree of precision. Scattering from the multiple surfaces must be addressed as a potential source of error. See Sections 8 and 9 below.

*2R*=6.5 cm, has an average enclosed area

*A*

_{TOTAL}=3.36 m

^{2}. For this total area with all other values the same, the limiting angular resolution is

*δΩ*=0.001°/hr. This number is an order of magnitude better precision than the typical fiber gyro for a structure 2/3 the size. We note that the reduction in uncertainty is due in significant part to the higher photon flux.

^{2}. This yields an uncertainty of

*δΩ*=0.00005°/hr. There is thus reason to believe that precision beyond the values now characteristic of current optical gyroscopes might be realized.

## 5. Routing of beams in the open multi-turn gyroscope

*a*=2

*R*/√3. Fig. 1a and the associated animation illustrate one family of mirror facets and a portion of the beam path produced by the mirror facet array

*p*polarized beam through our gyroscope with R=1cm, or 377 turns, the resulting beam is 95.6% polarized. Polarizing elements can be introduced to maintain the polarization closer to 100%.

## 6. Effects of paraboloidal optics on a Gaussian beam

## 7. Acceptable reflection losses

3. A.F. Stewart, S. Lu, M. Tehrani, and C. Volk, “Ion beam Sputtering of Optical Coatings,” SPIE **2114**, 662–677 (1994). [CrossRef]

## 8. Detection

## 9. Noise

*ω*

_{o}[2] for the separation between the active reflecting regions of ~2

*R*, the fraction of the spontaneous emission that is collected at the next optical element is ~10

*R*

^{2}. For our approximately confocal geometry this is ~

*πλ/R*, or for our representative example where

*R*=3.25 cm, the fraction of spontaneous emission coupled into the propagating beam is ~5×10

^{-5}.

## 10. Conclusions

## 11. Acknowledgments

## References and links

1. | William K. Burns, |

2. | Anthony E. Siegman, |

3. | A.F. Stewart, S. Lu, M. Tehrani, and C. Volk, “Ion beam Sputtering of Optical Coatings,” SPIE |

4. | Richard L. Fork, Spencer T. Cole, Lisa J. Gamble, William M. Diffey, and Andrew S. Keys, “Optical amplifier for space applications,” Optics Express |

5. | A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable Concept for Diode-Pumped High- Power Solid-State Lasers,” Applied Physics B |

**OCIS Codes**

(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments

(130.6010) Integrated optics : Sensors

**ToC Category:**

Research Papers

**History**

Original Manuscript: August 31, 2000

Published: October 9, 2000

**Citation**

Spencer Cole, Richard L. Fork, David Lamb, and Patrick Reardon, "Multi-turn all-reflective optical gyroscope," Opt. Express **7**, 285-291 (2000)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-8-285

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### References

- William K. Burns, Optical Fiber Rotation Sensing, (Academic Press, Inc., New York 1994).
- Anthony E. Siegman, Lasers, (University Science Books., Mill Valley, CA 1986).
- A.F. Stewart, S. Lu, M. Tehrani, and C. Volk, "Ion beam Sputtering of Optical Coatings," SPIE 2114, 662- 677 (1994). [CrossRef]
- Richard L. Fork, Spencer T. Cole, Lisa J. Gamble, William M. Diffey, and Andrew S. Keys, "Optical amplifier for space applications," Optics Express 5, 292-301 (1999). http://www.opticsexpress.org/oearchive/source/14181.htm. [CrossRef] [PubMed]
- A. Giesen, H. H�gel, A. Voss, K. Wittig, U. Brauch, H. Opower, "Scalable Concept for Diode-Pumped High- Power Solid-State Lasers," Applied Physics B 58, 365-372 (1994). [CrossRef]

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