Optical Backscatter Reflectometer Length Measurement Accuracy
Short Summary
This technical note offers detailed discussion on how Luna’s Optical Backscatter Reflectometers (OBR) are capable of measuring fiber lengths to an unprecedented level of accuracy. The OBR product line offers a uniquely advantageous combination of reflection amplitude sensitivity, length range, resolution and accuracy. Assuming the group index of refraction is well known, length measurement accuracy for the OBR 4600 and 5T-50 is expected to be better than 0.0034% immediately after calibration. And with the OBR 4200, length accuracies are expected to be within 0.06%.
Link
www.lunainc.com 1 Riverside Circle, Suite 400 | Roanoke, VA 24016 solutions@lunainc.com 1.540.769.8400 Technical Note EN_FY1406 Revision 1 h November 6, 2014
Optical Backscatter Reflectometer Length Measurement
Accuracy
Contents 1 Introduction ……………………………………………………………………………………………………………………………………………….. 1
2 Length Measurement ………………………………………………………………………………………………………………………………… 1
3 Length Error Specifications …………………………………………………………………………………………………………………….. 4
OBR 4600 and OBR 5T-50 ……………………………………………………………………………………………………………………………. 4
OBR 4200 …………………………………………………………………………………………………………………………………………………………. 4
4 Measurement Example: OBR 4600 Repeatability ………………………………………………………………………………. 5
5 Summary……………………………………………………………………………………………………………………………………………………… 6
6 References …………………………………………………………………………………………………………………………………………………… 6
Product Support Contact Information ……………………………………………………………………………………………………………. 7
1 Introduction
Lunafs Optical Backscatter Reflectometers (OBRs) operate on a principle know as Optical
Frequency Domain Reflectometry (OFDR). In OFDR, a tunable laser is used as a source for an
interferometer formed by a reference arm internal to the instrument and a measurement arm that
is connected in line with the Device Under Test (DUT).
1 As the laser is swept through an optical
frequency range, interference fringe data is collected and analyzed. A Fourier Transform is applied
to the raw interferometer fringe data to produce a record of reflection events observed as a
function of the optical time delay which occurs when light propagates from the instrument to the
reflection event and back. This Fourier Transform relationship between the optical frequency
domain, in which the raw data is collected, and the optical time-of-flight domain, in which the
results are presented, is integral to the determination of the OBR length accuracy: length
measurement accuracy is primarily constrained by knowledge of the optical frequency range of the
acquisition scan.
2 Length Measurement
The time delay increment
between adjacent data points in the optical time delay domain is
simply given by the inverse of the optical frequency scan range
1 (1)
The optical time delay between two reflection events is computed by using cursors to measure the
x-axis index separation between the reflection amplitude peaks corresponding to each event and
multiplying index difference by
. Length is calculated in the same maner, but using a length
increment /O instead of
. The length increment /O between successive data points is found by
assuming a group index of refraction n and scaling the time delay to length.
2014 Luna Innovations Incorporated. All rights reserved. Page 2 of 7 EN_FY1406 ncl2 (2)
In the above equation, c is the vacuum speed of light, 2.998 x 10
8 m /s.
In all of Lunafs OFDR-based instruments, a laser monitor interferometer is used to sample the
measurement interferometer fringe data in equal units of optical frequency. The optical frequency
scan range
is the number of sample points S times the laser monitor frequency increment lm.
lmlmSS
2014 Luna Innovations Incorporated. All rights reserved. Page 3 of 7 EN_FY1406 values are small compared to the uncertainties of the measured (y-axis) values and can be
neglected, and that the uncertainty of each measured value is independent of each other, we can
propagate the uncertainty of the y values u
y,i to the uncertainty in the slope ub using the Kline-
McClintock relationship:
iiyibuybu2,2 (5)
If we further assume that the uncertainty magnitude of each measured gas cell line is the same,
applying equation (5) to the equation for b yields a compact result.
222xNxxxuuiiiiyb
2014 Luna Innovations Incorporated. All rights reserved. Page 4 of 7 EN_FY1406
3 Length Error Specifications
OBR 4600 and OBR 5T-50
The maximum expected time of flight measurement error
max_err is expected to be within the
bounds given by summing the effects of the gas cell fit uncertainty and the error due to the effects
of temperature drift.
Txxerr66max_102.91034 (9)
Since length measurements are scaled by the user determined group index of refraction, length
measurement error will also be subject to inaccuracies in n. For a given index of refraction error
n
err, the maximum length error lmax_err is thus expected to be within the bounds given by the
following expression.
2014 Luna Innovations Incorporated. All rights reserved. Page 5 of 7 EN_FY1406 4 Measurement Example: OBR 4600 Repeatability
Two spools of SMF28e placed in an insulated box were scanned using six OBR 4600s operating in
extended range mode immediately after calibration (Figure 1). Spool length measurements with
each instrument returned constant results to six significant figures after repeated calibrations, and
showed variations between instruments in the last of six significant figures as seen in Table 1
below. Over the test duration the spool temperatures were constant to within 0.1~C. The results
show that repeatability of the length measurement between multiple OBR 4600 instruments has a
standard deviation of 10 ppm or better. The theoretical estimate for length error due to the gas cell
fit uncertainty described in Section 2 of 34 ppm thus appears to be conservative; users will typically
observe much better performance.
Figure 1: OBR 4600 spool length measurement test setup
OBR Serial Number Short Spool Length (m) Long Spool Length (m) 14084279 163.808 2030.37 14094280 163.805 2030.36 14084278 163.806 2030.36
2014 Luna Innovations Incorporated. All rights reserved. Page 6 of 7 EN_FY1406
2014 Luna Innovations Incorporated. All rights reserved. Page 7 of 7 EN_FY1406 Product Support Contact Information
Headquarters: 3157 State Street
Blacksburg, VA 24060
Main Phone: 1.540.961.5190
Toll-Free Support: 1.866.586.2682
Fax: 1.540.961.5191
Email: solutions@lunainc.com
Website: www.lunainc.com Specifications of products discussed in this document are subject to change without notice. For the latest product specifications, visit Lunafs website at www.lunainc.com. 2014 Luna Innovations Incorporated. All rights reserved. Technical Note EN-FY1406