Technical Note. ODiSI-B Sensor Strain Gage Factor Uncertainty

Transcription

1 Technical Note EN-FY160 Revision November 30, 016 ODiSI-B Sensor Strain Gage Factor Uncertainty Abstract Lna has pdated or strain sensor calibration tool to spport NIST-traceable measrements, to compte both linear and qadratic gage factors, extended the calibration range from to microstrain (), and has pdated or gage factor ncertainty estimate. Lna measred linear and qadratic Strain Gage Factors of /GHz and -4.0x10-5 /GHz, and estimates a measrement ncertainty of ± /GHz in the linear term (0.16%) and ± 1.0x10-5 / GHz in the qadratic term. Contents Introdction... 1 Strain Calibration Procedre and Fixtre... 1 Strain Gage Factor Uncertainty... 4 Strain Gage Factor Variability... 7 Strain Gage Factor Smmary... 5 Appendix: Steel Rle Calibration Certificate Appendix: Translation Stage Calibration Certificate Appendix: Temperatre Monitor Calibration Certificate... 1 Prodct Spport Contact Information Introdction Lna s Optical Distribted Sensor Interrogator (ODiSI) instrments se sweptwavelength interferometry to prodce a high spatial resoltion map of the sensor Rayleigh scatter pattern. By comparing a sensor measrement Rayleigh scatter pattern to a reference pattern, the scatter pattern optical freqency shift as a fnction of sensor length can be determined and scaled to a strain or temperatre change. This Engineering Note details the method for determining the strain calibration coefficients (or strain gage factors), estimates the degree of ncertainty associated with the gage factor vales, and presents data on the variability of strain gage factor measrements within a single fiber spool. Since Lna originally pblished the first revision of this docment in 015 Lna has made sbstantial improvements to the calibration fixtre and has implemented a qadratic in place of a linear crve fit, reslting in redced strain gage factor ncertainties and improved measrement traceability. Strain Calibration Procedre and Fixtre The strain gage factors (linear and qadratic terms) of a particlar sensor may be calibrated in a straightforward manner by recording the optical freqency spectral shift for a known applied strain and compting the best qadratic crve fit the freqency response. A diagram of the fixtre sed to apply a known strain to a fiber segment is shown in Figre 1. A pictre of the fixtre Lna is shown in Figre. The fixtre 1 Riverside Circle, Site 400 Roanoke, VA 4016 soltions@lnainc.com

2 consists of a linear translation stage with micrometer actator at one end of a steel rail and another movable stage at the far end of the rail. The fixtre is monted in an alminm box with transparent lid that is closed dring operation to keep temperatre stable and shield the fiber from air crrents. Optical fiber clamps are positioned on both stages. The fiber is inserted into the clamps and the micrometer is sed to apply extensive strain to the fiber segment. The micrometer is then stepped throgh a series of displacements, with the optical freqency shift of the Rayleigh scatter for the sensor portion between the clamps recorded with an ODiSI-B nit for each step. The strain is calclated by dividing the displacement L by the initial gap between the clamps of L. A least sqares fit is performed to find a qadratic expression for strain as a fnction of optical freqency shift. Sample calibration data with fit reslts and a plot of the fit residals from Lna s strain calibration software tility is shown in Figre 3. L Clamp L Clamp Translation Stage Rail Sensor Fiber Figre 1. Diagram of optical fiber strain gage factor calibration fixtre. Figre. Pictre of optical fiber strain gage factor calibration fixtre. 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page of 13

3 Figre 3. Top graph: least sqares fit to optical freqency shift vs. strain data; Bottom graph: fit residals are typically 0.1% of the fll strain range. To improve qality of the calibration, the following best practices were established: The micrometer displacement L is cycled at least 5 times to a displacement at least 10% of the highest test level, so that if the fiber slipped position in the clamps de to the loading force indced by the displacement, sch slippage was likely to happen dring the cycling stage and not dring the gage factor measrement. The optical fiber segment is pre-strained by roghly 100 to insre that no measrements are taken while the fiber is ntensioned and the effects of gravity on the horizontal fiber orientation don t inflence the low-strain reslts. The test data was taken in a ramp p from low to high strain, then a ramp back down from high to low strain. If the fiber slips in the clamps, or if there is any other error that cases a nidirectional drift in the optical freqency shift readings, the error will be readily apparent in the fit residal plot as a difference in optical freqency shift residals between the ramp p and ramp down. In Figre 3 the difference between the start and end Freqency Shift vales was nder 3 for a excrsion, and the Root-Mean_Sqare of the strain residal to the crve fit was 7., less than 0.1% of the test range, representing a level of hysteresis that well below other sorces of gage factor ncertainty. Calibrations with strain fit residal RMS vales above 0.% of the test range are rejected. The temperatre of the rail was monitored with a thermistor and monitor nit with NIST-traceable calibration while acqiring measrements so that the error cased by thermal expansion of the rail is known. 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 3 of 13

4 The sampling spacing of L is set to be one fll revoltion of the micrometer dial to minimize errors associated with periodic deviations in the micrometer screw thread. NIST traceability for the strain comptation is achieved by sing a calibrated steel rle to measre L and a calibrated micrometer head to indce L; the calibration of both rle and micrometer is performed sing apparatses at the rle and micrometer manfactrers that are traceable to NIST standards. The steel rle and micrometer calibration certificates are presented in the Appendix of this docment. Frther, the ODiSI-B nit optical freqency is calibrated against a HCN gas cell reference with every scan. All ODiSI gas cell references are compared to a NIST standard gas cell to assre traceability of the optical freqency shift measrement. 3 Strain Gage Factor Uncertainty The primary sorces of ncertainty in the strain gage factors are the ncertainties in the measred vales L and L sed to calclate strain and in the spectral shift calclation. Strain is calclated by dividing the displacement L by the initial gap between the clamps of L: L. (1) L The Rayleigh scatter optical freqency shift of the sensor fiber is measred for the segment of fiber nder strain sing an ODiSI-B instrment. The strain gage factors, and are calclated by performing a qadratic least sqares fit of strain to optical freqency shift, expressed as:. () 0 1 While the zero-order term is sefl for fitting prposes, it generally does not exceed a few in practice; frther strain is a relative vale evalated between measred and reference states; for these reasons is not recorded. The third term in Eqation () is also qite small compared to the second; for a total strain range of 10,000 the qadratic component typically reaches a maximm vale of less than 100 in magnitde. The ncertainty of the strain gage factor as a fnction of the ncertainty of the components of the calclation above is expressed as: L L L. (3) L 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 4 of 13

5 In the above expression we have dropped terms associated with the ncertainty in or becase, as discssed above, the linear term in the right hand side of Eqation () dominates, so differences in the constant and qadratic terms have little effect on the slope. Also, we can simplify the final expression for the ncertainty in sing the approximation: L 1 (4) L Sbstitting the expressions in eqations (1), () and (4) into eqation (3) we find: L L 1 1 L L. (5) Ths if we estimate the ncertainties associated with the inpts L, L and we can se Eqation (5) to calclate the expected ncertainty in the strain gage factor. We can write a similar expression to define the ncertainty of strain gage factor : L L L L 1 1. (6) This time we need to inclde a term that incldes / becase a small change in the slope fit can case a large change in the estimated qadratic fit term. Sbstitting the expressions in eqations (1), () and (4) into eqation (6) we find: 1 L L 1 1 L L. (7) Ths the ncertainty of the qadratic gage factor can be easily calclated from the ncertainty of the linear gage factor. Next we will estimate the ncertainty of each component of the calclation. Displacement L Uncertainty: The ncertainty of L is dominated by the accracy of the micrometer actator for the linear stage, how accrately a certain position can be set by the test engineer, and by the change in rail length de to any temperatre change dring the measrement. The micrometer actator is manfactred by Mittoyo (model ), has 13 mm travel, with 0.5 mm per revoltion, and gradations of 10 m. The calibration certificate indicates measred errors were -1.8 to +0.9 m over the travel range, with a 1 m measrement ncertainty, so we will se a position accracy estimate of ±3 m over the range of travel. We estimate the set point accracy of the micrometer to also be ±3 m. The rail temperatre is monitored with a thermocople probe and monitor nit with 0.1 C resoltion and 1 C accracy (Thomas Scientific model nmber 16L99); the 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 5 of 13

6 largest temperatre change we have observed dring the min it takes to collect the data is 0.1 C. Given L = 1000 mm, a thermal expansion coefficient of 16.0 ppm/ C for 316 stainless steel, and a temperatre change ncertainty of 0.1 C, we calclate an ncertainty in the rail length of mm. The total ncertainty when setting the micrometer at two positions and measring a displacement L is: L mm mm. (8) We also considered compression of the rail in response to force eqal and opposite that applied to the fiber by the micrometer. Becase the rail has a mch larger cross sectional area compared to the fiber, we estimate the error in L to be less than 1% of the ncertainty estimated in eqation 5, so we will neglect this term. Strain Application Length L Uncertainty: The ncertainties in measring L are dominated by the error in determining where the clamps grip the fiber, and in the accracy of the steel rle sed to measre the gap. We estimate a ±1 mm ncertainty in the estimate of where the clamps grip the fiber, and ±0.5 mm accracy of the steel rle over its 1 m length. Ths, assming both error sorces apply to the position measrement of each clamp, we estimate the ncertainty in the measrement of L to be: L mm 1. 46mm. (9) Optical Freqency Shift Uncertainty: The ODiSI-B center wavelength and sweep range are set by calibrating to the onboard HCN gas absorption cell. The wavelength accracy is conservatively estimated at 1.5 pm ( GHz), and the wavelength scale accracy is similarly estimated at 0.005%. For the data set depicted in Figre 3, there is a maximm optical freqency shift of 1500 GHz, so the scale accracy limit wold imply a GHz ncertainty. The combined optical freqency shift ncertainty when measring the Rayleigh scatter spectral shift between a reference and test state is: GHz 0. 76GHz. (10) Next, we can se Eqations (5) and (7) to calclate the ncertainty of the linear and qadratic gage factors from the ncertainty of each component of the calclation. Total Linear Strain Gage Factor Uncertainty: Eqation (5) gives the expected ncertainty for the linear gage factor for a pair of measrements for two micrometer displacements. If we only consider the case in which we calclate the gage factor from the two points with the largest difference in displacement, the total strain gage factor ncertainty is estimated from Eqation (5) to be: 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 6 of 13

7 * (11) GHz GHz GHz Performing a least sqares linear regression with seven points (as shown in Figre 3) will lead to lower ncertainty than only sing the two points with the largest displacement, so Lna expects this ncertainty estimate to be conservative. The largest term in Eqation (11) relates to the gage length L ncertainty. Compared to the previos test fixtre, we are sing a steel rle with improved accracy to measre the gage length, and the new fixtre spports a longer gage length (690 mm previosly vs mm now). These improvements have reslted in a redction in the ncertainty of the linear strain gage factor from.7% to 1.6%. Total Qadratic Strain Gage Factor Uncertainty: Eqation (7) relates the ncertainty in the qadratic gage factor to the ncertainty in the linear gage factor. If we se the appropriate nmbers from or calibration station, we find: x10. (1) 1500 GHz GHz As with the linear gage factor ncertainty, Lna regards Eqation (1) to be a conservative estimate. 4 Strain Gage Factor Variability Lna s sensor fiber is delivered by the manfactrer on spools with length of typically several hndred to several thosand meters apiece. We set aside fiber segments (generally from the beginning and end of the spools, at a minimm) for the prpose of characterizing these fiber segments for strain and temperatre response. Testing is non-destrctive, and these spool segments are archived and are available for frther testing if warranted. Sensors manfactred from a given spool are assigned strain gage factors that are averaged over the test segments for that spool. For a spool delivered in the 3 rd qarter of 015 Lna set aside additional fiber segments from mltiple locations along the spool length as the spool was consmed. Strain gage factor calibration reslts from both the 015 and 016 fixtres, from 8 sensor fiber segments, are shown in Table 1. Becase we have changed the calibration fit from linear to qadratic and are calibrating over a broader strain range, the linear gage factors between the two measrements are not directly comparable. To compensate for these factors, we can calclate an eqivalent linear gage factor from the qadratic components as follows: 1, Eqivalent 1. (13) 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 7 of 13

8 Eqation (13) shold be calclated for the optical freqency shift vale at the middle of the calibration range of the 015 calibration (at 375 GHz); this reslt is tablated in the final colmn of Table 1. Table 1. Strain Gage Factor Measrements on Fiber Segments from a Single Spool 015 Fixtre 016 Fixtre Test Segment Designation Residal RMS Eqiv. 015 (/GHz) (/GHz) (/GHz^) Strain () (/GHz) OFD00076E_OtsideEnd E OFD00076E_ E OFD00076E_ E OFD00076E_ E OFD00076E_509m E OFD00076E_656m E OFD00076E_753m E OFD00076E_InsideEnd Broken Termination Mean E Standard Deviation E We observe a difference in the mean eqivalent vales for the linear gage factor from crrent fixtre verss the 015 fixtre vale of /GHz. This difference exceeds the 015 and 016 linear gage factor ncertainty estimates of ± and ± /GHz. The difference is likely de to mis-scaling of the 015 gage length L or displacement L measrements becase of a systematic error in the steel rle or micrometer we sed in the 015 fixtre. Since we have better docmentation of the steel rle and micrometer calibration for the 016, we are mch more confident in the new reslts. The standard deviation of the vales for the strain gage factors and noted in Table 1 are below the ncertainty estimates in Eqations (11) and (1), indicating that the strain gage factors are not likely to vary by more than their ncertainty estimates along a 1 km spool length. Also, the consistency of the strain gage factor reslts across the spool gives s some confidence that or ncertainty estimates are not too low. With the previos strain calibration fixtre, Lna completed mltiple strain gage factor measrements on fiber segments from 5 separate spools. This data showed that the linear strain gage factor reslts for the other 4 spools were within 0.% of spool OFD00076E1, shown in Table 1. Lna has not yet completed calibrating fiber segments from additional spools with the new test fixtre, bt we expect to find similar levels of variation, and we will pdate this Technical Note with additional test reslts when they become available. 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 8 of 13

9 5 Strain Gage Factor Smmary In this Technical Note we have described the new strain gage factor calibration fixtre and test procedre, estimated a measrement ncertainty, and have demonstrated variation in gage factor measrement spanning seven measrements over one spool from or fiber manfactrer that are generally within or ncertainty estimate. The strain gage factors for spool OFD00076E1 are of /GHz and -4.0x10-5 /GHz, and we estimate a measrement ncertainty of ± /GHz in the linear term (0.16%) and ± 1.0x10-5 / GHz in the qadratic term. Measrements with the previos strain calibration fixtre indicated that the reslts for the linear strain gage factor for this spool are within 0.% of 4 other spools. Until Lna compiles frther measrements, the vales above represent Lna s best estimate of the strain gage factors to se if the sensor sorce spool is nknown. Lna has established sensor manfactring procedres that associate the strain gage factors of a sensor with the measrements from its sorce spool; these vales are inclded in the sensor calibration file recorded on the USB drive shipped with each sensor. Measrements with the crrent strain calibration fixtre are made over a range, compared to the 0 to 5500 range of the previos fixtre. NIST-traceable calibration of the steel rle sed to measre the fixtre gage length, of the micrometer sed to measre the fixtre displacement, and of the absorption gas cell to measre freqency shift assres fll traceability of the strain calibration. Since measrement variation over the length of a single spool and over mltiple spools showed less variation than the ncertainty estimate, Lna is confident that the ncertainty estimate is conservative, and that sensor fiber manfactring variation rotinely yields sensors with a real gage factor variation within this ncertainty limit. Lna plans to contine to add to the strain gage factor measrement data base as we manfactre new sensors from new shipments from or fiber manfactrer, to track gage factors corresponding the spool each sensor was manfactred from, and to refine and pgrade the strain calibration test fixtre better accracy. 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 9 of 13

10 Appendix: Steel Rle Certification Letter 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 10 of 13

11 Appendix: Steel Rle Calibration Certificate 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 11 of 13

12 Appendix: Micrometer Calibration Certification 016 Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 1 of 13

13 Prodct Spport Contact Information Lightwave Division: 3155 State Street Blacksbrg, VA 4060 Main Phone: Toll-Free Spport: Fax: Website: Specifications of prodcts discssed in this docment are sbject to change withot notice. For the latest prodct specifications, visit Lna s website at Lna Innovations Incorporated. All rights reserved. Technical Note EN-FY Lna Innovations Incorporated. All rights reserved. EN-FY160 Page 13 of 13