## Non-invasive characterization of microstructured optical fibers using Fourier domain optical coherence tomography

Optics Express, Vol. 13, Issue 4, pp. 1228-1233 (2005)

http://dx.doi.org/10.1364/OPEX.13.001228

Acrobat PDF (353 KB)

### Abstract

Fourier domain optical coherence tomography (FDOCT) is used to non-invasively measure properties of the hole pattern in microstructured fibers. Features in the FDOCT data are interpreted and related to the hole diameter and spacing. Measurement examples are demonstrated for three different fibers with one hole, three holes at the vertices of an equilateral triangle, and a full triangular lattice. These studies provide the first path to real time monitoring of microstructured fibers during their draw.

© 2005 Optical Society of America

## 1. Introduction

2. J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, “Group-Velocity Dispersion Measurements in a Photonic Bandgap Fiber,” J. Opt. Soc. Am. B **20**, 1611–1615 (2003). [CrossRef]

3. C. J. Voyce, A. D. Fitt, and T. M. Monroe, “Mathematical Model of the Spinning of Microstructured Fibres,” Opt. Express **12**, 5810–5820 (2004). [CrossRef] [PubMed]

4. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical Coherence Tomography - Principles and Applications,” Rep. Prog. Phys. **66**, 239–303 (2003). [CrossRef]

5. J. Jasapara, E. Monberg, F. DiMarcello, and J. W. Nicholson, “Accurate Noncontact Optical Fiber Diameter Measurement with Spectral Interferometry,” Opt. Lett. **28**, 601–603 (2003). [CrossRef] [PubMed]

6. J. Jasapara and S. Wielandy, “Characterization of Coated Optical Fibers Using Fourier Domain Optical Coherence Tomography,” Opt. Lett. (accepted for publication). [PubMed]

## 2. Theory and experimental setup

6. J. Jasapara and S. Wielandy, “Characterization of Coated Optical Fibers Using Fourier Domain Optical Coherence Tomography,” Opt. Lett. (accepted for publication). [PubMed]

*I(ν)*is described mathematically by,

*I*is the spectral intensity reflected by the reference arm mirror,

_{r}*I*is the spectral intensity reflected by the

_{i}*i*interface in the fiber that is an

^{th}*optical*distance

*d*from the reference,

_{i}*ν*is the frequency and

*c*is the velocity of light in space. The third term is the interference of the reference with each interface of the fiber. The fourth term is the interference between various fiber interfaces and constitutes the autocorrelation of the fiber structure. The Fourier transform of

*I(ν)*contains peaks at 2

*d*/

_{i}*c*and 2(

*d*-

_{i}*d*)/

_{j}*c*, corresponding to the optical separation between the various reflecting surfaces. Hence the location of various interfaces of the object can be determined from the FFT and the object cross section can be reconstructed.

*F*=5.5

_{R}*µ*m which implies a resolution of ~4.0

*µ*m in glass of index

*n*=1.444. By peak fitting the FFT, the reflecting surfaces could be located with a~1

*µ*m accuracy.

## 4. Fiber with three holes arranged in a concentric equilateral triangle

*M*orientation (cf. Fig. 3(a)), for light that scatters off just one surface, the round trip optical distance of surfaces from plane

*A*are

*AB*=2

*d*=16

*µ*m,

*AC*=2

*n*Λ√3/2=40

*µ*m, and

*AD*=2[

*n*Λ√3/2+

*d*]=56

*µ*m. The measured distances of

*AB*=16.2

*µ*m (⇒

*d*=8.1

*µ*m),

*AC*=37.4

*µ*m (⇒Λ=15

*µ*m), and

*AD*=54.8

*µ*m compare well with these expected values.

*θ*=sin

_{c}^{-1}(1/

*n*)=43.85°. This totally reflected light can suffer retro reflection at another hole if it is incident along its diagonal. For our studies we assume that the light recorded in the spectrogram has scattered off a maximum of two holes and the two holes involved are the nearest neighbors. Path

*X*(shown in the inset of Fig. 3(a)) represents such a two hole scattered ray. The round trip optical path difference of

*X*with respect to the ray reflected at surface

*A*is,

*AX*=28.2µm agrees well with the calculated value of

*T*=30.6

*µ*m for such a ray that is scattered off two holes.

*K*orientation arrived at by rotating the fiber by thirty degrees from orientation

*M*. The round-trip optical distance of the various surfaces from surface

*A*are,

*AB*=2

*d*=16

*µ*m,

*AC*=2[

*n*Λ/2]=23

*µ*m,

*AD*=2[

*n*Λ/2+

*d*]=39

*µ*m,

*AE*=4[

*n*Λ/2]=46

*µ*m, and

*AF*=4[

*n*Λ/2]+2

*d*=62

*µ*m. From the measured peaks we get

*AC*=20.3

*µ*m

*AD*=34.6

*µ*m,

*AE*=45.7

*µ*m, and

*AF*=58.9

*µ*m. Except for

*AD*, the error in the

*one way geometrical*distance between the reflecting planes lies within the 1

*µ*m accuracy of the system. The surfaces

*B&C*, and

*D&E*have round trip optical separations of 7

*µ*mfrom each other which is less than the FWHM, 2

*F*, of the FFT peaks. Hence peak

_{R}*B*is not resolved, and the error in peak

*D*is higher than the stated 1

*µ*m accuracy.

## 5. Fiber with concentric triangular lattice of holes

*D*=245µm, with six rings of holes of diameter

*d*=5.5±0.5

*µ*m, and pitch Λ=10.8

*µ*m surrounding a core formed by the absence of a single hole at the center. Figure 4(a) shows the FFT recorded for orientation

*M*(light incident perpendicular to a side of the hexagonal hole pattern where the holes are oriented as shown in inset of Fig. 3(a) with respect to the incident beam) with the reference arm blocked. The FFT (which, with the reference arm blocked, is an autocorrelation of the fiber cross section) shows very distinct peaks. The spectrogram (shown in inset of (a)) consists of slow modulations due to interference amongst the holes (resulting in peaks at short distances in the FFT), and fast modulations due to the interference of holes with the fiber surfaces (resulting in peaks at larger distances in the FFT). The early peaks therefore contain direct information about the lattice structure. However, in an autocorrelation the origin of the FFT peaks can be ambiguous and more complicated to associate with real crystal features and therefore we will stick to examining the cross correlation of the crystal features with the reference arm.

*M*, and

*K*(light incident on vertex of hexagonal hole pattern where the holes are oriented as shown in inset of Fig. 3(b) with respect to the incident beam) respectively. The distances 2

*nX*and 2

_{1}*nX*(for orientations

_{2}*K*and

*M*respectively; see Figs. 4(b) and (c)) between peak

*S*(due to the fiber surface) and the first peak from the hole pattern

*A*, give the round trip distance of the first hole surface from the fiber surface. If the crystal pattern is uniform and concentric with the fiber surface (as with our fiber), then the hole pitch Λ can be derived from measurements along

*K*and

*M*directions as Λ=(

*X*

_{2}-

*X*

_{1})/

*N*(1-√3/2) where

*N*(

*N*=6 in our case) is the number of lattice periods from the center of the fiber to the center of the hole in the outermost ring. From the FFTs we get

*X*

_{1}=55.8

*µ*m, and

*X*

_{2}=64.5

*µ*m, which gives Λ=10.8

*µ*m in agreement with measurements under the microscope.

*M*direction, light sees the three hole structure of Fig. 3(a) repeated several times. The round trip optical distance of hole surfaces from the first reflecting hole surface

*A*are given by

*U*=2

_{m}*m*(

*n*Λ√3/2), and

*V*=

_{m}*U*+2

_{m}*d*(

*m*=0,1,2, …). Figure 4(d) shows that in Fig. 4(b) the distance of most measured peaks from peak

*A*lie within 3

*µ*m of the predicted

*U*, and

_{m}*V*values. The average hole diameter

_{m}*d*=(

*V*-

_{m}*U*)/2 from the measured FFT is 5.9

_{m}*µ*m which agrees well with microscope measurements. In addition, we observe a peak at 18.8

*µ*m from peak

*A*which agrees well with the expected value of 20.5

*µ*m for a ray that suffers total reflection at one hole surface and is retro reflected by another hole (like

*X*in Fig. 3(a)).

*K*orientation (Fig. 3(b)), the peak distances from peak

*A*in Fig. 4(c) are

*P*=2

_{m}*m*(

*n*Λ/2), and

*Q*=

_{m}*P*+2

_{m}*d*. The peaks are closer in the

*K*orientation than the

*M*orientation and are therefore more difficult to resolve. With a limited resolution system, the error due to overlapping of peaks is therefore larger in the

*K*orientation.

7. B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer Axial Resolution Optical Coherence Tomography,” Opt. Lett. **27**, 1800–1802 (2002). [CrossRef]

8. S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-Speed Spectral-Domain Optical Coherence Tomography at 1.3 *µ*mWavelength,” Opt. Express **11**, 3598–3604 (2003). [CrossRef] [PubMed]

*K*orientation is identified unambiguously when one device measures the shortest distance between the fiber surface peak

*S*and the first peak from the hole structure

*A*- the second device then records data for the

*M*orientation. From these measurements Λ can be retrieved. In addition, if

*F*≤

_{R}*d*, the

*M*orientation can be analyzed to retrieve

*d*.

## Acknowledgments

## References and links

1. | J. C. Knight, T. A. Birks, and P. S. J. Russell, |

2. | J. Jasapara, T. H. Her, R. Bise, R. Windeler, and D. J. DiGiovanni, “Group-Velocity Dispersion Measurements in a Photonic Bandgap Fiber,” J. Opt. Soc. Am. B |

3. | C. J. Voyce, A. D. Fitt, and T. M. Monroe, “Mathematical Model of the Spinning of Microstructured Fibres,” Opt. Express |

4. | A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical Coherence Tomography - Principles and Applications,” Rep. Prog. Phys. |

5. | J. Jasapara, E. Monberg, F. DiMarcello, and J. W. Nicholson, “Accurate Noncontact Optical Fiber Diameter Measurement with Spectral Interferometry,” Opt. Lett. |

6. | J. Jasapara and S. Wielandy, “Characterization of Coated Optical Fibers Using Fourier Domain Optical Coherence Tomography,” Opt. Lett. (accepted for publication). [PubMed] |

7. | B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer Axial Resolution Optical Coherence Tomography,” Opt. Lett. |

8. | S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-Speed Spectral-Domain Optical Coherence Tomography at 1.3 |

**OCIS Codes**

(060.2270) Fiber optics and optical communications : Fiber characterization

(170.4500) Medical optics and biotechnology : Optical coherence tomography

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 11, 2005

Revised Manuscript: January 10, 2005

Published: February 21, 2005

**Citation**

J. C. Jasapara, "Non-invasive characterization of microstructured optical fibers using Fourier domain optical coherence tomography," Opt. Express **13**, 1228-1233 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-4-1228

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### References

- J. C. Knight, T. A. Birks, and P. S. J. Russell, Optics of Nanostructured Materials, chap. Holey Silica Fibers, pp. 39–71 (John Wiley Sons, Inc., 2001).
- J. Jasapara, T. H. Her, R. Bise, R.Windeler, and D. J. DiGiovanni, “Group-Velocity Dispersion Measurements in a Photonic Bandgap Fiber,” J. Opt. Soc. Am. B 20, 1611–1615 (2003). [CrossRef]
- C. J. Voyce, A. D. Fitt, and T. M. Monroe, “Mathematical Model of the Spinning of Microstructured Fibres,” Opt. Express 12, 5810–5820 (2004). [CrossRef] [PubMed]
- A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical Coherence Tomography - Principles and Applications,” Rep. Prog. Phys. 66, 239–303 (2003). [CrossRef]
- J. Jasapara, E. Monberg, F. DiMarcello, and J. W. Nicholson, “Accurate Noncontact Optical Fiber Diameter Measurement with Spectral Interferometry,” Opt. Lett. 28, 601–603 (2003). [CrossRef] [PubMed]
- J. Jasapara and S. Wielandy, “Characterization of Coated Optical Fibers Using Fourier Domain Optical Coherence Tomography,” Opt. Lett. (accepted for publication). [PubMed]
- B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J.Wadsworth, J. C. Knight, P. S. J. Russell, M. Vetterlein, and E. Scherzer, “Submicrometer Axial Resolution Optical Coherence Tomography,” Opt. Lett. 27, 1800–1802 (2002). [CrossRef]
- S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, “High-Speed Spectral-Domain Optical Coherence Tomography at 1.3 µm Wavelength,” Opt. Express 11, 3598–3604 (2003). [CrossRef] [PubMed]

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