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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 10 — May. 11, 2009
  • pp: 8370–8381
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Full Stokes polarimeter for characterization of fiber optic gyroscope coils

Arthur Lompado, John C. Reinhardt, L. Chris Heaton, Jeff L. Williams, and Paul B. Ruffin  »View Author Affiliations


Optics Express, Vol. 17, Issue 10, pp. 8370-8381 (2009)
http://dx.doi.org/10.1364/OE.17.008370


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Abstract

We describe the design, construction, calibration, and validation of a Stokes vector polarimeter for investigating the polarization characteristics of fiber optic gyroscope coils. The device measures the complete Stokes vector, and reports conventional polarization properties including the Degree of Polarization (DoP), the orientation and Degree of Linear Polarization (DoLP), and the handedness and Degree of Circular Polarization (DoCP). The sensor operates at 1550 nm and employs a division of aperture optical architecture to acquire full Stokes vectors at 8 kHz while calculating polarization properties at a rate of 200 Hz. Preliminary measurements performed on both traditionally and unconventionally wound gyroscope coils are also presented.

© 2009 OSA

1. Introduction

Knowledge of the polarization properties of an optical fiber is important in fiber based applications where the emitted polarization state directly affects subsequent optical components, detection schemes, and data processing algorithms [1

1. A. David, Krohn, Fiber Optic Sensors- 2nd Ed., (ISA, Research Triangle Park, NC, 1992).

,2

2. S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors - 2nd Ed., (CRC Press, New York, NY, 2008).

]. The fields of telecommunications, medicine, and many military applications all employ fiber based components and instruments which rely on polarization to perform accurately. Certain applications use relatively expensive polarization maintaining (PM) and, more recently, photonic crystal PM fiber to insure control over the emitted polarization state [3

3. H. L. W. Chan, K. S. Chiang, and J. L. Gardner, ““Polarimetric optical fiber sensor for ultrasonic power measurement,” Ultrasonics Symposium,” Proc. IEEE 1, 599–602 (1988).

,4

4. H. Y. Fu, H. Y. Tam, L.-Y. Shao, X. Dong, P. K. A. Wai, C. Lu, and S. K. Khijwania, “Pressure sensor realized with polarization-maintaining photonic crystal fiber-based Sagnac interferometer,” Appl. Opt. 47(15), 2835–2839 (2008). [CrossRef] [PubMed]

]. Recent investigations into the use of spirally coiled single mode (SM) fiber in a so-called depolarized fiber optic gyroscope (FOG) architecture [5

5. K. Böhm, P. Marten, K. Petermann, E. Weidel, and R. Ulrich, “Low-Drift Fibre Gyro Using a Superluminescent Diode,” Electron. Lett. 17(10), 352–353 (1981). [CrossRef]

] has shown that SM fiber can be an effective and inexpensive PM fiber surrogate. These investigations led to the development of a polarimeter to fully characterize these and more general fiber components [6

6. A. Lompado, M. S. Kranz, J. S. Baeder, L. C. Heaton, and P. B. Ruffin, “Geometrical and polarization analyses of crossover-free fiber optic gyroscope sensor coils,” Proc SPIE 6314, 63140E.1 - 63140E.12 (2006).

].

The most thorough way to characterize the polarization properties of a fiber component is to measure the exiting light’s Stokes vector [7

7. W. A. Shurcliff, and S. S. Ballard, Polarized Light, (Van Nostrand, Princeton, NJ, 1969), Chap. 2.

]. The Stokes vector has been well described and contains four elements obtained by making (at least) four measurements of the emitted light after passing it through unique polarizing filters. The data set may be acquired serially by changing the polarizing filter between measurements, or simultaneously using multiple filters and detectors. Regardless of the chosen technique, all of the light’s polarization properties may be extracted from the Stokes vector including the total Degree of Polarization (DOP), the magnitude and orientation of the linear component (DoLP and θ, respectively), and the magnitude and handedness of the circular component (DoCP and its sign, respectively). The described polarimeter measures the Stokes vector components and computes the derived polarization properties for any fiber based component operating at 1550 nm. These properties may then be analyzed to assess the applicability of the component under test for a polarization sensitive application. An example investigated here is the polarimetric characterization of spirally wound FOG coils designed to mimic the behavior of PM fiber based coils.

Section 2 presents a review of the design and construction of the fiber optic polarimeter. Section 3 describes the requisite radiometric and polarimetric calibration procedures. Section 4 highlights validation measurements aimed at ascertaining the device sensitivity to polarization metrics. Section 5 reports on preliminary FOG coil measurements and Section 6 presents a summary of the work.

2. Polarimeter Design and Construction

The polarimeter was designed to characterize fiber based components with standard FC termination operating at a wavelength of 1550 nm. The target application required a polarimetric sampling rate of 200 Hz which is well suited to a multiple channel, simultaneous acquisition design. The so called division of aperture (DoAp) optical architecture was chosen because it easily configurable to the known light input parameters such as the wavelength, mode field diameter, and numerical aperture [8

8. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45(22), 5453–5469 (2006). [CrossRef] [PubMed]

,9

9. D. B. Chenault, A. Lompado, E. R. Cabot, and M. P. Fetrow, “Handheld polarimeter for phenomenology studies,” Proc. SPIE 6619, 145–154 (2004). [CrossRef]

]. In this approach, the optical pupil plane is sub-sectioned using an array of mini-lenses to create four discrete optical channels for processing. Three of the four channels contain linear polarizers oriented at 0°, 60°, and 120° with respect to the positive horizontal direction when looking toward the source. Channel four contains a ¼ wave retarder followed by a linear polarizer whose transmission axis is oriented 45° relative to the retarder’s fast axis. Taken together, these components form a circular polarizer although here they are operated in “reverse” with the retarder preceding the polarizer. In this way, a circular analyzer is formed which measures the circular polarization component of the incident light. Figure 1(a)
Fig 1 Top: Optical ray trace of fiber optic polarimeter. Bottom: Opto-mechanical details of the polarization filters, array lenses, and detectors.
shows a schematic of the sensor’s optical layout, which includes the light source and a (pseudo)collimating lens that produces a very slowly converging beam. This slow convergence permits the creation of an accessible pupil plane for the array lenses, assuring each channel detector “sees” the entire fiber output face. The figure only shows three of the four channels since, in this view, the middle channel actually lies “outside” the page toward the reader and obscures the fourth channel which lies “inside” the page. Figure 1(b) shows an isometric cross section of the back end of the system including the polarization filters, array lenses, and detectors along with their mechanical mounting components. The optical design parameters may be easily reconfigured for other wavelengths or fiber output specifications as needed.

The optical system design was first laid out paraxially and then optimized using Zemax. The collimating and mini-lenses are plano-convex and, due to the slow nature of the optical layout, are capable of producing near diffraction limited imagery at the detector plane. All four channel polarizers are near infrared (NIR) dichroic sheet and the retarder is a zero order quartz plate whose fast axis alignment to its companion polarizer was confirmed to within 3° during the calibration procedure described below. The detectors are low noise InGaAs photodiodes operating in photoconductive mode. Each detector current is transimpedence amplified, digitized (16 bits) at 100 kHz, and fed to a single board computer (SBC) containing four digital input channels. The SBC, housed within the polarimeter enclosure, averages 256 samples per channel and transmits the results via Ethernet to a control laptop computer running the polarization data reduction software. This software has been described [9

9. D. B. Chenault, A. Lompado, E. R. Cabot, and M. P. Fetrow, “Handheld polarimeter for phenomenology studies,” Proc. SPIE 6619, 145–154 (2004). [CrossRef]

] and, in brief, applies the polarimetric data reduction matrix obtained during calibration to the four measured averages to yield the current Stokes vector. From the Stokes vector, the DoP, DoLP and θ, and DoCP are reported at a user selectable rate of up to 200 Hz. The software also reports raw channel voltages (in counts) and the normalized Stokes vector elements which are helpful during alignment, testing, calibration, and validation of the sensor. All parameters are available numerically and graphically using a set of four configurable virtual strip charts. Additionally, polarization information may be viewed graphically via an available Poincarè sphere [10

10. E. Collett and B. Schaefer, “Visualization and calculation of polarized light. I. The polarization ellipse, the Poincaré sphere and the hybrid polarization sphere,” Appl. Opt. 47(22), 4009–4016 (2008). [CrossRef] [PubMed]

] animation, although this added rendering reduces the polarimetric refresh rate to a maximum of 70 Hz. Automatic file logging at user specified intervals is also available.

3. Calibration

The data of Fig. 2 can be used to obtain the so-called polarimetric data reduction matrix, which is applied to all subsequent measurements to calculate the input light’s Stokes vector. A number of ways to do so have been reported and a technique based on nonlinear regression has been used here [12

12. R. A. Chipman, “Polarimetry,” in Handbook of Optics – Volume II, M. Bass ed. (McGraw-Hill, New York, NY., 1995), Chap. 22.

,13

13. J. C. Ramella-Roman and D. Duncan, “A new approach to Mueller matrix reconstruction of skin cancer lesions using a dual rotating retarder polarimeter,” Proc. SPIE 6080, 60800M (2006). [CrossRef]

]. In this approach, the calibration modulation curves are fit using the Levenberg-Marquardt technique with the Stokes-Muller algebra providing the model function for fitting [14

14. D. M. Bates, and D. G. Watts, Nonlinear Regression and Its Applications, (Wiley, New York, NY, 1988).

]. Concentrating first on the linear channels, the measured power on any particular channel is a function of the Stokes vector of the incident light and the employed polarizers’ principle transmittances and orientations and may be written as
P=(M(q,r,θi)·Mcal(q,r,θcal)·Sin)[[1]]   i=1,2,3
(1)
where M(q, r, θi) is the Mueller matrix of a linear polarizer with principal transmittances q and r, oriented at θi. M cal(q, r, θcal)) is the calibration polarizer’s Mueller matrix and, since the same material was used for the calibration polarizer as the channel polarizers, q and r are the same as for M. S in is the unpolarized input Stokes vector and the [[1]] notation indicates the first element of the vector obtained on the right hand side. The Mueller matrices and Stokes vector of Eq. (1) are well known and have been described elsewhere [15

15. Dennis Goldstein, Polarized Light-2nd Ed., (Marcel-Dekker, New York, NY, 2003).

]. A similar approach can be performed on the circular channel in which case the model function takes the form

P=(M(q,r,θi)·Mret(δ,θret)·Mcal(q,r,θcal)·Sin)[[1]]
(2)

Here, M ret(δ, θret) is the Mueller matrix of a linear retarder with retardance δ whose fast axis is oriented along θret. Performing the algebra leads to the following model equations for the 3 linear channels;
Pi=12((q+r)2+(qr)2cos(2(θiθcal))
(3)
where i = {1,2,3} and {θ1 = 0°, θ2 = 60°, θ3 = 120°}. The model function for the circular channel is given by;

P4=12((q+r)2+(qr)2(cos(δ)sin(2(θ4θret))sin(2(θcalθret))+       cos(2(θ4θret))cos(2(θcalθret))))
(4)

The data of Fig. 2 are fit to the models of Eqs. (3) and (4) using q, r, θi, δ, and θret as the fit parameters. The numerical nature of the fitting procedure requires seed values for the parameters, which were obtained from component specification sheets and/or the measured component properties (e.g., principal transmittances and orientations). For the linear channels, seed values of q = 0.86, r = 0.006, and θi = 0°, 60°, 120°, were used and the extra circular channel parameters were seeded using δ = 90° and θret = -45° (i.e., 135°). Table 1

Table 1. Regressed parameter values after data fitting

table-icon
View This Table
contains the regressed parameter values, obtained separately for each channel. Ideally, the regressed q and r values would be constant across all channels and consecutive linear channel orientations would be spaced by 60°. As well, the regressed retardance and fast axis orientation in channel 4 should be 90° and 135° respectively, based on manufacturer’s specifications. Table 1 shows that all of the regressed values are quite close to the seed values and it was found that the fitting procedure was relatively insensitive to the seed values, consistently converging to the same set of regressed parameter values. Importantly, q and r are practically constant over the linear channels and the slight deviations of the regressed values from the seed values represent the inherent polarimetric signature which the calibration procedure strives to correct.

Note that the fitting procedure is performed across the entire 60 element data set so that regressing only 5 parameters results in an overspecified system of equations. Indeed only 5 power measurements are sufficient to obtain the regression values but the overspecification technique has been found to improve the general accuracy of the sensor. Analysis has shown that using the minimum number of required calibration states to obtain the data reduction matrix subsequently yields very accurate Stokes vector measurements of input states corresponding to those used during the calibration but measurements of intermediate (i.e., non-calibration) states exhibited reduced accuracy. Employing the entire calibration data set in the regression has the effect of only slightly reducing the measurement accuracy of the states used during calibration, while greatly improving it for arbitrary inputs.

Once the regressed values are known, they are plugged into the model equations and θcal is allowed to range from 0° to 360°. These modulation curves are shown in Fig. 3
Fig. 3 The data of Fig. 2 (symbols) overlain with the fits of Eq. (3) using the regressed polarization parameters of Table 1 (curves).
along with the calibration data of Fig. 2. It is seen that the fit curves quite accurately match the data and thus the regressed parameter values can be relied upon to generate an accurate data reduction matrix (DRM) for the sensor.

As an interim step to obtaining the system data reduction matrix, the so-called calibration matrix is obtained by modeling each channel using only the Mueller matrices of the polarization element(s) contained therein, with the regressed parameter values plugged in as required. The first rows of each of the 4 resulting matrices, called the analyzer vectors, are extracted and concatenated into the 4x4 calibration matrix. It can be shown that each channel’s analyzer vector is simply the Stokes vector of the eigenpolarization of that channel. Figure 4
Fig. 4 Measured (left) and ideal calibration matrices.
shows the measured normalized calibration matrix as well as the ideal normalized calibration matrix (assuming perfect polarizing elements) for the channel arrangements described. There is an overall good agreement between the two with slight deviations that are attributable to the slight rotational misalignments of the channel polarization elements, measurement noise, and/or numerical round off errors that propagate through the polarimetric calculations.

As a final step, the calibration matrix is inverted to yield the DRM which will inherently correct for the channel polarization signatures. The DRM is subsequently multiplied by the radiometrically normalized four element measurement vector (P1, P2, P3, P4) to yield the input light’s Stokes vector, where † indicates transpose.

4. Validation and Testing

Two measurements were performed to assess the instrument’s validity, one aimed at quantifying its accuracy while the other was designed to determine its repeatability. In the first case, a measurement that mimicked the calibration measurement was performed. Again, 60 linear states oriented in 5° increments were introduced and the DRM obtained from the calibration procedure was applied to the measurement vectors. The resulting Stokes vectors were then processed into the polarization products including the degree of polarization (DoP), degree of linear polarization (DoLP), degree of circular polarization (DoCP), and the orientation of the linear component (θ). Using the conventional Stokes vector notation, S = (s0, s1, s2, s3), these polarization products have been described extensively [12

12. R. A. Chipman, “Polarimetry,” in Handbook of Optics – Volume II, M. Bass ed. (McGraw-Hill, New York, NY., 1995), Chap. 22.

] and are given by

DoP=s12+s22+s32s0DoLP=s12+s22s0DoP=s3s0θ=tan1(s2s1)
(5)

Based on these definitions, the measured polarization products as the input polarizer is rotated 360° are shown in Fig. 5
Fig. 5 Measured polarization properties for a rotating linearly polarized input. Top: DoP and DoLP. Bottom: DoCP and orientation residuals.
. For such a measurement, the DoP and DoLP are ideally 100% while the DoCP should be 0% and the orientation of the linear component should vary linearly throughout the 360° rotation. The first three properties are found in Fig. 5 to behave as expected to within 2.5% with the largest error observed in the DoCP. Averaging over the entire data set yields mean DoP, DoLP, and DoCP values of 99.6%, 99.59%, and 0.7% respectively. To better reveal the orientation accuracy, the figure shows the orientation residuals, defined as the measured orientation minus the known orientation and represented as Δθ. The polarizer was mounted in a high resolution rotation stage (specified accuracy of 0.001°) which provided the known value. The figure shows orientation residuals within an envelope of ±0.325° across the entire measurement with the average residual of 0.18°. The slight deviations between the polarization products and the ideal results are primarily attributable to measurement noise, since this is the only signal contribution that differs from the calibration measurement used to derive the DRM.

Repeatability testing consisted of performing multiple measurements of the same input which is again due to a rotating linear polarizer in the beam. Three measurements were made consecutively within a 20 minute time period and the Stokes vector and polarization product means and standard deviations (SDs) calculated. Figure 6
Fig. 6 Polarization products' accuracy and repeatability. Accuracy over 3 identical measurements is similar to that of Fig. 5, with excellent repeatability (typically < ±0.15%).
shows the polarization products’ mean values across the measurements, with error bars defined as ± 1 SD. The figure shows accuracies similar to those of Fig. 5 with very small error bars, indicating high repeatability.

Fig. 7 Polarization products of a linear polarizer followed by a rotating 95.3° waveplate. Note the sign of the DoCP indicates polarization handedness.

5. Fiber optic gyroscope coil measurements

Figure 8
Fig. 8 FOG coil polarimetric testing setup.
is a schematic of the test arrangement showing a fiber pigtailed 1550 nm amplified spontaneous emission source with an 80 nm wide bandwidth whose output goes through a free space coupler containing a linear polarizer that could be rotated about the beam axis. The polarized output is injected into the coil under test and the output is monitored as the polarizer is rotated at a constant angular velocity.

Figure 9
Fig. 9 Time evolution of the polarization properties of a traditionally wound FOG coil. From top to bottom are the DoLP, DoCP, DoP, and θ measured as the input polarizer was rotated 500° (≈1.5 cycles).
displays the polarization properties of the light exiting the traditional coil. The coil is seen to marginally retain the DoP, reaching maxima of about 52% and 48% when its eigenpolarizations are injected. The DoCP oscillates about 0% with a range of approximately ± 40% while the DoLP ranges from 30% - 50%. These behaviors imply the presence of both retardance and depolarization in the coil, presumably arising from the multiple crossover points. These points create localized but uncorrelated stress induced retardance and scattering centers. The former have arbitrarily aligned fast axes resulting in an overall arbitrary retardance magnitude while the latter tend to reduce the DoP. The orientation of the linear component is expected to vary linearly with the input polarizer’s orientation except in the special case when the retardance is one quarter wave (± n 2π for integral n) as described below. A pseudo-linear variation is observed in the bottom panel of the Fig. 9 implying that the overall induced coil retardance is not close to λ/4 ± n 2π.

Figure 10
Fig. 10 Polarimetric properties of 8 (top) and 24 (bottom) layer CF coils.
shows the 8 and 24 layer CF coil performances. These coils display much better polarization maintenance, reaching DoP maxima close to 100% for input eigenpolarizations. This is presumably due to the absence of crossover points with their associated scattering and depolarization. The 8 layer coil exhibits reduced symmetry in its response, an offset in the DoCP of 22.5% and the linear orientation is seen to follow the injected orientation. It can be shown that this behavior, coupled with the appearance of a nonzero circular component ranging from -25°-60° and a DoLP range of about 65%- 95%, implies that the coil is acting to first order as a linear wave plate with retardance approximately equal to 132° [12

12. R. A. Chipman, “Polarimetry,” in Handbook of Optics – Volume II, M. Bass ed. (McGraw-Hill, New York, NY., 1995), Chap. 22.

]. The 24 layer coil response was more symmetric and shows almost complete conversion of the output state from linear to circular as the input state is rotated. This time however, the orientation is seen to exhibit a binary type behavior, rapidly transitioning from one orientation to another (offset by 90°) as the output passes through the completely circular state. This behavior is indicative of a ¼ wave linear retarder [12

12. R. A. Chipman, “Polarimetry,” in Handbook of Optics – Volume II, M. Bass ed. (McGraw-Hill, New York, NY., 1995), Chap. 22.

]. Using the Mueller algebra, these data have been fit to a first order model of the system comprising a single linear retarder and yield an overall coil retardance magnitude of ≈ 96°.

For comparison sake, Fig. 11
Fig. 11 Polarimetric properties of a 2 m long PM patch cord.
shows the measured response of a 2 m long PM patch cord. The patch cord behaves somewhat like the CF coils (particularly the 24 layer coil) in that high DoP and DoLP values are obtained for input eigenpolarizations. This is to be expected since again there are no crossovers to confound the polarization degrees. An offset in the DoCP is observed as with the 8 layer CF coil although the overall magnitude and modulation envelope are relatively small. The orientation evolution is similar to that of the 24 layer coil showing a binary response with a 90° envelope, this time centered at about 100°. In this case, the DoCP never approaches 100% so the fiber is not acting simply as a ¼ wave plate even though the orientation behavior is binary. This behavior is typical of a number of tested PM fibers and is currently being further investigated. In short however, the polarimetric properties of the CF coils are found to better approximate the behavior of a PM device than the traditionally wound coil, supporting the premise that the CF design can potentially serve as a FOG coil. These results are preliminary and more thorough testing is planned to better understand the details of coil winding parameters and the measured results.

6. Summary

In summary, a fiber optic polarimeter capable of analyzing the polarimetric properties of light emitted from optical fibers and its application to the measurement of FOG coils has been presented. The sensor design, construction, and calibration approaches have been detailed along with validation measurements to assess system accuracy and repeatability. The polarization evolution, as the input to a number of FOG coils is varied, is given as an example of the sensor utility for characterizing polarization sensitive fiber components. Initial measurements indicate that SM coils wound in the crossover-free configuration behave similarly to PM fiber and may serve as an inexpensive alternative to PM based coils.

Acknowledgements

This work was supported by the Defense Advanced Research Projects Agency under contract number W31P4Q-07-C-0191. Information contained herein has been approved for public release, distribution unlimited.

References and links

1.

A. David, Krohn, Fiber Optic Sensors- 2nd Ed., (ISA, Research Triangle Park, NC, 1992).

2.

S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors - 2nd Ed., (CRC Press, New York, NY, 2008).

3.

H. L. W. Chan, K. S. Chiang, and J. L. Gardner, ““Polarimetric optical fiber sensor for ultrasonic power measurement,” Ultrasonics Symposium,” Proc. IEEE 1, 599–602 (1988).

4.

H. Y. Fu, H. Y. Tam, L.-Y. Shao, X. Dong, P. K. A. Wai, C. Lu, and S. K. Khijwania, “Pressure sensor realized with polarization-maintaining photonic crystal fiber-based Sagnac interferometer,” Appl. Opt. 47(15), 2835–2839 (2008). [CrossRef] [PubMed]

5.

K. Böhm, P. Marten, K. Petermann, E. Weidel, and R. Ulrich, “Low-Drift Fibre Gyro Using a Superluminescent Diode,” Electron. Lett. 17(10), 352–353 (1981). [CrossRef]

6.

A. Lompado, M. S. Kranz, J. S. Baeder, L. C. Heaton, and P. B. Ruffin, “Geometrical and polarization analyses of crossover-free fiber optic gyroscope sensor coils,” Proc SPIE 6314, 63140E.1 - 63140E.12 (2006).

7.

W. A. Shurcliff, and S. S. Ballard, Polarized Light, (Van Nostrand, Princeton, NJ, 1969), Chap. 2.

8.

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45(22), 5453–5469 (2006). [CrossRef] [PubMed]

9.

D. B. Chenault, A. Lompado, E. R. Cabot, and M. P. Fetrow, “Handheld polarimeter for phenomenology studies,” Proc. SPIE 6619, 145–154 (2004). [CrossRef]

10.

E. Collett and B. Schaefer, “Visualization and calculation of polarized light. I. The polarization ellipse, the Poincaré sphere and the hybrid polarization sphere,” Appl. Opt. 47(22), 4009–4016 (2008). [CrossRef] [PubMed]

11.

G. R. Bird and M. Parrish Jr., “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. 50(9), 886–891 (1960). [CrossRef]

12.

R. A. Chipman, “Polarimetry,” in Handbook of Optics – Volume II, M. Bass ed. (McGraw-Hill, New York, NY., 1995), Chap. 22.

13.

J. C. Ramella-Roman and D. Duncan, “A new approach to Mueller matrix reconstruction of skin cancer lesions using a dual rotating retarder polarimeter,” Proc. SPIE 6080, 60800M (2006). [CrossRef]

14.

D. M. Bates, and D. G. Watts, Nonlinear Regression and Its Applications, (Wiley, New York, NY, 1988).

15.

Dennis Goldstein, Polarized Light-2nd Ed., (Marcel-Dekker, New York, NY, 2003).

16.

J. H. Shields and J. W. Ellis, “Dispersion of Birefringence of Quartz in the Near Infrared,” J. Opt. Soc. Am. 46(4), 263–265 (1956). [CrossRef]

17.

J. Williams, P. Ruffin, A. Lompado, J. Reinhardt, and C. Heaton, “Polarization and Drift Analysis of Thermally Symmetric Double Sided Crossover Free SM Fiber Coils,” Proc. SPIE 7056, 70560Z (2008). [CrossRef]

18.

Edward Collett, Polarized Light in Fiber Optics, (The PolaWave Group, Lincroft, NJ, 2003).

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(060.2800) Fiber optics and optical communications : Gyroscopes
(120.5410) Instrumentation, measurement, and metrology : Polarimetry

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: March 6, 2009
Revised Manuscript: April 27, 2009
Manuscript Accepted: April 29, 2009
Published: May 1, 2009

Citation
Arthur Lompado, John C. Reinhardt, L. Chris Heaton, Jeff L. Williams, and Paul B. Ruffin, "Full Stokes polarimeter for characterization of fiber optic gyroscope coils," Opt. Express 17, 8370-8381 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8370


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References

  1. A. David, Krohn, Fiber Optic Sensors- 2nd Ed., (ISA, Research Triangle Park, NC, 1992).
  2. S. Yin, P. B. Ruffin, and F. T. S. Yu, eds., Fiber Optic Sensors - 2nd Ed., (CRC Press, New York, NY, 2008).
  3. H. L. W. Chan, K. S. Chiang, and J. L. Gardner, ““Polarimetric optical fiber sensor for ultrasonic power measurement,” Ultrasonics Symposium,” Proc. IEEE 1, 599–602 (1988).
  4. H. Y. Fu, H. Y. Tam, L.-Y. Shao, X. Dong, P. K. A. Wai, C. Lu, and S. K. Khijwania, “Pressure sensor realized with polarization-maintaining photonic crystal fiber-based Sagnac interferometer,” Appl. Opt. 47(15), 2835–2839 (2008). [CrossRef] [PubMed]
  5. K. Böhm, P. Marten, K. Petermann, E. Weidel, and R. Ulrich, “Low-Drift Fibre Gyro Using a Superluminescent Diode,” Electron. Lett. 17(10), 352–353 (1981). [CrossRef]
  6. A. Lompado, M. S. Kranz, J. S. Baeder, L. C. Heaton, and P. B. Ruffin, “Geometrical and polarization analyses of crossover-free fiber optic gyroscope sensor coils,” Proc SPIE 6314, 63140E.1 - 63140E.12 (2006).
  7. W. A. Shurcliff, and S. S. Ballard, Polarized Light, (Van Nostrand, Princeton, NJ, 1969), Chap. 2.
  8. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45(22), 5453–5469 (2006). [CrossRef] [PubMed]
  9. D. B. Chenault, A. Lompado, E. R. Cabot, and M. P. Fetrow, “Handheld polarimeter for phenomenology studies,” Proc. SPIE 6619, 145–154 (2004). [CrossRef]
  10. E. Collett and B. Schaefer, “Visualization and calculation of polarized light. I. The polarization ellipse, the Poincaré sphere and the hybrid polarization sphere,” Appl. Opt. 47(22), 4009–4016 (2008). [CrossRef] [PubMed]
  11. G. R. Bird and M. Parrish., “The wire grid as a near-infrared polarizer,” J. Opt. Soc. Am. 50(9), 886–891 (1960). [CrossRef]
  12. R. A. Chipman, “Polarimetry,” in Handbook of Optics – Volume II, M. Bass ed. (McGraw-Hill, New York, NY., 1995), Chap. 22.
  13. J. C. Ramella-Roman and D. Duncan, “A new approach to Mueller matrix reconstruction of skin cancer lesions using a dual rotating retarder polarimeter,” Proc. SPIE 6080, 60800M (2006). [CrossRef]
  14. D. M. Bates, and D. G. Watts, Nonlinear Regression and Its Applications, (Wiley, New York, NY, 1988).
  15. Dennis Goldstein, Polarized Light-2nd Ed., (Marcel-Dekker, New York, NY, 2003).
  16. J. H. Shields and J. W. Ellis, “Dispersion of Birefringence of Quartz in the Near Infrared,” J. Opt. Soc. Am. 46(4), 263–265 (1956). [CrossRef]
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