Table 5. Example of nonlinearity measurement uncertainties for a Ge optical
fiber power meter at 1300 nm.*

Source Standard uncertainty (type)
(%)
Laser stability
@ 1300 nm 0.03 (B)
Polynomial truncation 0.002 (B)
Test meter spectral responsivity
@ 1300 nm (Ge) 0.004 (B)
Equation approximation** 0.003 (B)
Polarization 0.014 (B)
Repeatability (N = 3) 0.07 (A)
Combined uncertainty 0.053
Expanded uncertainty (k = 2) 0.11

* For other wavelengths, use the appropriate uncertainty arising from a test meter spectral
responsivity (Table 3).

** This uncertainty depends on the nonlinearity value for each particular case.

15


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The data are acquired using the triplet superposition method. The measurements are performed
by taking three power readings from the OFPM: (1) when the shutter 1 is open (1 s) and shutter 2
is closed, (2) when both shutters are open (1 s), and (3) when the shutter 1 is closed and shutter 2
is open (1 s). These three power measurements are called a triplet. Shutters are controlled by the
computer, which sends a TTL signal to the shutter controller. This sequence is then repeated at
different powers. The OFPM response is linear when the sum of the two individual power
readings is equal to the combined-power reading. We usually divide each power range of an
OFPM into 10 parts or sets spaced equally in the logarithmic scale. Each set is a triplet
measurement taken three times and averaged. Each single measurement in a triplet is taken three
times as well, and the result is averaged. Thus, there are 27 single measurements for each set.
Generally, there are total of 270 single measurements per single power range. If an OFPM has six
ranges, the computer will take 1,620 single measurements for one run. The computer takes three
runs to calculate the final results. Thus, to measure an OFPM nonlinearity, the computer will
collect nearly 5,000 single measurements. For each measurement run, the averaged data, grouped
in three columns are saved on the hard drive of the computer. Each row of the data represents a
measurement set of a triplet.

To measure the range discontinuity (offsets between ranges or scales), readings are taken at the
lower-power end of each range and compared to the readings on the higher-power end of the next
lower range at the same input power. Generally, three sets of measurements for each range are
taken to calculate the range discontinuity. When shutter 1 is closed and shutter 2 is open, five
single measurements are taken (and averaged) for two neighboring ranges. Then, three values of
the range discontinuity (for each range except the lowest one) is stored in the data file. The
background or offset of each range is measured and the value is subtracted from the signal.

Using the system shown in Figure 4, the nonlinearity of an OFPM is characterized over the power
between 1.5 nW and 3.5 mW at a wavelength of 1314 nm. Sample results obtained on a NIST
OFPM are presented in Table 1 and shown graphically in Figure 5, in which a symbol represents a
power range of an OFPM. The correction factors result from meter nonlinearity within each
range, combined with the range discontinuity. Most OFPMs use power ranges in decibels/meter
units. Note: decibel/meter is not an SI unit, but is related to a power of 1 mW as 10 log (x),
where x is an unknown power in milliwatts. Each correction value listed in the Table 1 is the
average of six correction factors (except the 10 dBm or 10 mW range, which is represented by
only three points due to a limited laser power) found throughout that range. If the nonlinearity of
an OFPM is not negligible, it is necessary to provide correction factors at each power, as for the
highest power range in Figure 5, and avoid averaging correction factors.as it is done for ranges
with small nonlinearities. The flow chart of the measurement is shown in Appendix B.

To correct for nonlinearity and range discontinuity, the OFPM readings should by divided by the
appropriate correction factors. The standard deviation of the correction factors for each range in
Table 1 was calculated using three data runs. A sample copy of a calibration report is provided in
Appendix C.


Appendix B. Measurement Flow Chart

INITIALIZE
SYSTEM COMMON.
MAIN VARIABLES

¥

INITIALIZE
GPIB AND PIO-12 CARDS

t

SELECT TEST METER

¥

SELECT WAVELENGTH

START-UP PROCEDURE:

WARM UP LASERCS) FOR 30 MIN
CHECK ALL OPTICAL AND
ELECTRICAL CONNECTIONS

COLLECT AND SAVE DATA

ANALYZE DATA AND
CREATE 3 DATA FILES

PROCESS 3 ANALYZED DATA
FILES AND DETERMINE by,

USING CALIBRATION AT 100 uw
QO, ARE DETERMINED

PRINT DATA SHEET
FOR CALIBRATION REPORT

ee)

19


Contents

1. Introduction

2. Measurement of Nonlinearity and Range Discontinuity
2.1 Definition and Basic Expressions
2.2 Polynomial Expression for Conversion Function
2.2.1 Triplet Superposition Method

2.3 Correction Factor for Nonlinearity and Range Discontinuity

3. Nonlinearity Measurement System

4. Uncertainty Assessment

5. References

Appendix A. Laser Diode Optical Spectra
Appendix B. Measurement Flow Chart

Appendix C. Sample of a Calibration Report

iti

ll

17

18

19

20


SP 250-1

SP 250-2

‘SP 250-3

SP 250-4

SP 250-5

SP 250-6

SP 250-7

SP 250-8

SP 250-9

SP 250-10

SP 250-11

SP 250-12

SP 250-13

SP 250-14

SP 250-15

SP 250-16

SP 250-17

SP 250-18

SP 250-19

SP 250-20

SP 250-21

SP 250-22

SP 250-23

THE SP 250 SERIES ON NIST MEASUREMENT SERVICES*

Spectral Radiance Calibrations
PB87179883

Far Ultraviolet Detector Standards
PB87227609

Radiometric Standards in the Vacuum Ultraviolet
PB87227625

Fricke Dosimetry in High-Energy Electron Beams
PB8B1 10374

Alpha-Particle Calibrations
PB88168620

Regular Spectral Transmittance
PBB8108550

Radiance Temperature Calibrations
PB88123674

Spectral Reflectance
B88109905

Calibration of Beta-Particle-Emitting Ophthalmic
Applicators
PB88108535

Radioactivity Calibrations with the “4x” Gamma
lonization Chamber and Other Radioactivity
Calibration Capabilities

PB88123708

Dosimetry for High Dose Applications
PB88201587

Neutron Personnel Dosimetry
PB87227617

Activation Foil Irradiation with Californium
Fission Sources
PB88217443

Activation Foil Irradiation by Reactor Cavity
Fission Sources
PB88217435

Photometric Calibrations
PB88153747

Calibration of X-Ray and Gamma-Ray
Measuring Instruments
PBBB211826

‘The NBS Photodetector Spectral Response
Calibration Transfer Program
PB88201595

Neutron Source Strength Calibrations
PB88211818

Calibration of Gamima-Ray-Emitting
Brachytherapy Sources

PB89193858

Spectral Irradiance Calibrations
PB88123781

Calibration of Beta-Particle Radiation
Instrumentation
PB88201579

Platinum Resistance Thermometer Calibrations
PB88138367

Liquid-in-Glass Thermometer Calibration Service
PB89 128888

‘SP 250-24

SP 250-25

‘SP 250-26

SP 250-27

SP 250-28

SP 250-29

SP 250-30

SP 250-31

SP 250-32

SP 250-33

SP 250-34

SP 250-35

SP 250-36

SP 250-37

SP 250-38

SP 250-39

SP 250-40

SP 250-41

SP 250-42

SP 250-43

SP 25044

Standard Ceil Calibrations
PB88123690

Calibration Service for Inductive
Voltage Dividers

NBS Phase Angle Calibration Services
PB88225636

AC-DC Difference Calibrations
PB892222616

Solid-State DC Voltage Standard Calibrations
PB88168703

Traceable Frequency Calibrations
PBEB168364

GOES Satellite Time Code Dissemination:
Description and Operation
PB8B168760

Mass Calibrations
PB89153894

A Calibration Service for 30 MHz Attenuation
and Phase Shift
PB88238324

A Calibration Service for Voltage Transformers
and High-Voltage Capacitors
PB882252903

High Vacuum Standard and Its Use
PB89193841

The Calibration of Thermocouples
and Thermocouple Materials
PB89209340

A Calibration Service for Current Transformers
PBQ1216770

Photometric Calibrations
PB97148472

NIST Leak Calibration Service
PB92149772

NIST Pressure Calibration Service
PB94164043

Absorbed-Dose Calibration of lonization Chambers
in a Co Gamma-Ray Beam
‘SNO03-003-03034-1 $2.00

Spectroradiometric Detector Measurements:
Part | — Ultraviolet Detectors and

Part il— Visible to Near-Infrared Detectors
SN003-003-03550-5 $9.50

Sprectroradiometric Detector Measurements:
Part Ill—Infrared Detectors
SNO03-003-03582-3 $5.25

Radiance Temperature Calibrations
‘SNO03-003-03511-4 $10.00

Radiation Processing Dosimetry Calibration
Services and Measurement Assurance Program
SN003-003-035 13-1

* Entries containing a stock number (SN003-003-} and price can be purchased from the Superintendent of Documents, U.S. Government
Printing Office, Washington, DC 20402-9325. GPO will accept checks, money orders, VISA, and MasterCard. For more infomation, or to place
an order, call (202) 512-800. Be sure to cite the stock number on all orders,

Entries containing PB numbers can be purchased from the National Technical Information Service, Springfield, VA 22161. NTIS will accept
American Express in addition to the payment methods listed for GPO. For more information call (703)487-4650; to place an order call
(800) 553-6487. Fax: (703) 321-8547. Be sure to cite the PB number on all orders.

Entries without stock or PB numbers are in preparation.


Table 6. Example of nonlinearity measurement uncertainties for a InGaAs
optical fiber power meter at 1550 nm.*

Source Standard uncertainty (type)
(%)
Laser stability 0.01 (B)
@ 1550 nm
Polynomial truncation 0.002 (B)
Test meter spectral responsivity
@ 1550 nm (InGaAs) 0.0014 (B)
Equation approximation** 0.012 (B)
Polarization 0.014 (B)
Repeatability (N = 3) 0.03 (A)
Combined uncertainty 0.039
Expanded uncertainty (k = 2) 0.08

* For other wavelengths, use the appropriate uncertainty arising from a test meter spectral
responsivity (Table 3).

** This uncertainty depends on the nonlinearity value for each particular case.

This work was supported in part by the Calibration Coordination Group (CCG) of the
Department of Defense; the lead agency for this project is the U.S. Naval Warfare Assessment
Division, Corona, California and NIST’s Calibration Services Development Fund. Kent
Rochford, Steven Mechels, Rex Craig, and Jack Wang of NIST reviewed the manuscript; the
authors thank them for their valuable comments.

16


OPTICAL POWER METER
Meter’s Manufacturer
Model Number, Serial Number

with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Table 2. Nonlinearity correction factors (CF) at 860 nm for optical fiber power meter, Model
Number Y, Serial Number 2.

Meter/scale Output CF Standard Expanded
Tange current deviation for 3 uncertainty of
runs (%) CF (%)
600 pA 1.014 0.02 0.08
3 200 pA 1.006 0.01 0.08
150 pA 1,004 0.01 0.08
200 pA 1.005 0.02 0.08
4 100 pA 1.002 0.00 0.07
20 pA 0.9979 0.01 0.08
20 pA 0.9969 0,04 0.09
5 10 pA 0.9963 0.03 0.08
2pA 0.9954 0.05 0.09
6 150-2000 nA. 0.9948 0.03 0.08
7 15-200 nA 0.9941 0.02 0.08
8 15-20 nA 0.9941 0.05 0.09
9 150-2000 pA 0.9932 0.08 0.12
1.0150 =
: 1.0100
Z 1.0050
& 1.0000 A
; 0.9950 ee
Oe 1E3 1E-2 1E-1 1E0 1E1 1E2 1E3
CURRENT (A)

Figure 3. Correction factor versus output current at 860 nm for optical fiber power meter, Model
Number Y, Serial Number 2.

Folder No. & NISTID:

Date of Report:
Reference:

26000 & 81300
April 30, 2000
P.O. No. 2121 04/15/00

22

3 of 10


Appendix A. Laser Diode Optical Spectra

=

00

ao
oO

o
o

hb
oO

nN
oO

Relative intensity (%)

0 aal \ | L,

1530 1535 1540 1545 1550 1555 1560
Wavelength (nm)

Figure A-1. Optical spectra of a typical laser diode used in the linearity calibration system.

18


THE SP 250 SERIES ON NIST MEASUREMENT SERVICES* — Continued

SP 250-45 Radiation Processing Dosimetry Calibration
Services: Manual of Calibration Procedures
SN003-003-03514-9 $4.00

SP 250-46 NIST Multifunction Calibration System
SNO03-003-03515-7 $2.75

SP 250-47 NIST Calibration Service for Capacitance
Standards at Low Frequencies
SNO03-003-03549-1 $7.00

SP 250-48 Spectral Reflectance
SNO03-003-03545-9 $14.00

SP 250-49 NIST Calibration Services for Gas Flow
Meters: Piston Prover and Bell Prover
Gas Flow Facilities
SN003-003-03560-2 $6.00

SP 250-51 Calibration Service of Optoelectronic
Frequency Response at 1319 nm for
Combined Photodiode/rt Power Sensor
Transter Standards
SNO003-003-03623-4

SP 250-52 Error Analysis and Calibration Uncertainty of
Capacitance Standards at NIST

SP 250-53 Calibration Service for Spectral Responsivity of
Laser and Optical-Fiber Power Meters at
Wavelengths Between 0.4 xm and 1.8 pm
SN003-003-03624-2

SP 250-54 Optical Fiber Power Meter Calibrations at NIST

SP 250-56 Optical Fiber Power Meter Nonlinearity Calibrations
at NIST

* Entries containing a stock number (SNO03~003-) and price can be purchased from the Superintendent of Documents, U.S. Government
Printing Office, Washington, DC 20402-9325. GPO will accept checks, money orders, VISA, and MasterCard. For more infomation, or to place
an order, call (202) 512-1800. Be sure to cite the stock number on all orders.

Entries containing PB numbers can be purchased from the National Technical Information Service, Springfield, VA 22161. NTIS will accept
American Express in addition to the payment methods listed for GPO. For more information call (703)487-4650; to place an order call
(800) 553-6487. Fax: (703) 321-8547. Be sure to cite the PB number on all orders.

Entries without stock or PB numbers are in preparation.


Table 3. Standard uncertainty (%) for spectral responsivity for
Si, Ge, and InGaAs detectors.

Diode Type Wavelength (nm)
850 1300 1550
Si 0.004 NA NA
Ge 0.014 0.004 0.027
InGaAs 0.015 0.003 0.001

Table 3 presents the standard uncertainty values for Si, Ge, and InGaAs detectors. The standard
uncertainty due to this wavelength effect is equal to the appropriate value from Table 2 multiplied
by 0.1 nm and divided by 2V3.

d. Equation approximation: This uncertainty is due to the approximation defined by eq (7). The
uncertainty is of second-order in magnitude, i.e., if the nonlinearity is 1 %, then the uncertainty is
(0.01 or 10%. This uncertainty depends on the value for the nonlinearity in each case. The
maximum uncertainty will be divided by (2V°3).

e. Polarization: This uncertainty is due to effects caused by changes in polarization of the incident
power during each triplet measurement set. This uncertainty is related to polarization dependent
loss (PDL) of the nonlinearity system. Polarization uncertainty of the nonlinearity system is
assumed to be small because we take a large number of measurements (810 measurements per
one power range) and because measurement time scales are short compared to changes in the
system polarization state. The PDL of the nonlinearity system was measured using a random-
polarization generator. The maximum value of the system PDL is 0.002 dB or 0.05 %. The
standard uncertainty is 0.05/(2V'3) = 0.014 %.

Tables 4 through 6 list typical measurement uncertainties for calibrations of OFPMs which use Si,
Ge, and InGaAs detectors, respectively. The exact values of these various components change
for the particular measurement conditions at the time of the measurement.

13


The output responses of the commonly used photodiodes, Si, Ge, or InGaAs, are exponential (see
conversion function in Figure 3) with respect to the input power. However, they are often used in
nearly short-circuited or reverse-biased configurations to achieve a linear response. As a result,
their responses can be approximated as polynomials produced by the Taylor-series expansion of
the form shown in eq (6), where the zero-order term is not included because we always measure
the dark signal and later subtract it from the output of an OFPM. With the assumption of

A
y* viel cc,
k=2 a,

the nonlinearity Ay, of eq (5) can be approximated by (for the nonlinearity of less than 1 %, the
approximation error is less than 0.01 %)

Ay (ViV) = Eve! - VE. M
=2 Ay

If we divide all the coefficients a, in eq (6) by the first coefficient a,, the polynomial thus obtained
is called the normalized conversion function, denoted by p(V) and expressed as

p(v) = V + yay’ (8)

where b, = a,/a,. The coefficients b, correspond to an uncalibrated conversion function described
in reference [1]. Typically, n is equal to 3.

The nonlinearity can be expressed as

AWVV,) * x bveT - ve’). (9)

2.2.1 Triplet Superposition Method

In the triplet superposition method, a group of three power measurements is made, two for

individual powers from each beam and one for the combination of the two. For the i* group of
measurements, we have a set of three equations:


OPTICAL POWER METER
Meter’s Manufacturer

Model Number, Serial Number
with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Table 5. Typical nonlinearity measurement uncertainties.

Source Standard uncertainty (type)
(%)

Laser stability

@ 850 nm 0.06 (B)

@ 1300 & 1550 nm 0.03 (B)

Polynomial truncation 0.002 (B)

Test meter spectral responsivity

@ 850 nm (Si) 0.004 (B)

@ 850 nm (Ge) 0.014 B)

@ 850 nm (InGaAs) 0.015 (B)

@ 1300 nm (Ge) 0.004 (B)

@ 1300 nm (InGaAs) 0.003 (B)

@ 1550 nm (Ge) 0.027 (B)

@ 1550 nm (InGaAs) 0.001 (B)

Polarization 0.014 @)

Equation approximation 0.003 (B)

Repeatability (N = 3) See Tables 1 through 4 (A)

Typical combined uncertainty 0.05

‘Typical expanded uncertainty (k = 2) 0.10

Folder No. & NISTID: 26000 & 81300

Date of Report: April 30, 2000

Reference: P.O. No. 2121 04/15/00

28

9 of 10


OPTICAL POWER METER
Meter’s Manufacturer

Model Number, Serial Number
with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Correction Factor for Nonlinearity and Range Discontinuity

‘The nonlinearity of the OFPM and associated correction factors were found using the following guidelines. As mentioned
earlier in the report, the outputs corresponding to the two individual beams and their combination are measured at different
powers in each measurement range of the OFPM. Range discontinuity is also measured at several overlapping powers
between two neighboring ranges.

The relationship between the incident power P and its corresponding reading V of the OFPM on any range, m is expressed
as:

P= alm + Shims, ro)

where n is the order of the polynomial, n = 3, and m indicates the measurement range. b,{m] are determined from the
measured nonlinearity by means of the least squares curve fitting. The range discontinuity between two neighboring ranges,
mand m + 1, is found from a,[m]/a,[m + 1].

When the OFPM is calibrated at power P, which produces power meter reading, V, in range [cl], the calibration factor F, is

determined by F.=V/P,. ‘The correction factor CF[m] due to both nonlinearity and range discontinuity at any power reading
V in any range [m] can be calculated by:

1+ Yofave?
_ Alcl 2 .

CF[m] = —_—.— Q)
we) Domve
ke2
where
alc] s a{cl x me x a{m=1] for m > c,
a,[m] a[c+l] a,[m] (3)
or
a,c] 1
7 for
. a,[m] atm) oy ale“) re > @
a,[m+1] a,[c]
The incident power P{m] is obtained from the power meter reading V by for any given range m by
v
Pim) = Crimi" 6)

Tables 1 through 4 list CF values for each measurement range. These CF values represent an average of the individual CF
values found at various power levels within the range (except the ranges from 3 through 5 described in Table 2).

Folder No. & NISTID: 26000 & 81300
Date of Report: April 30, 2000
Reference: P.O. No. 2121 04/15/00 6 of 10

25


1000R¢
100R¢
"! Wr
[Wy
FEEDBACK
RESISTOR Ry
+
‘OPERATIONAL
‘AMPLIFIER
DETECTOR +

Figure 1. Simplified schematic of a typical optical power meter.

The NIST nonlinearity system is capable of measuring the nonlinearity of OFPMs over a dynamic
range of more than 60 dB at the three nominal telecommunication wavelengths: 850, 1300, and
1550 nm. This system uses optical fiber components and is designed to accommodate commonly
used OFPMs and other optical detectors. The system also measures the range discontinuity
between neighboring power ranges or scale settings of the OFPM. Measurements with this
system yield a correction factor for each power range of an OFPM. Note: for a bare detector, the
ranges may be the electrical voltage or current ranges of the output electronics.

2.1 Definition and Basic Expressions

The nonlinearity of an OFPM is defined as the relative difference between the responsivity at an
arbitrary power and the responsivity at the calibration power (i.e., the power at which the meter
was calibrated). This definition can be expressed as

R®) - RP, )

Ay @:P, ) = RP.)

> Q)

where R(P) = V/P is the responsivity of the OFPM at incident optical power P; the subscript c
indicates the calibration point, and V is the OFPM output, which can be electrical current,


Optical Fiber Power Meter Nonlinearity Calibrations at NIST

Igor Vayshenker, Shao Yang*, Xiaoyu Li, Thomas R. Scott, and Christopher L. Cromer
National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80303
*Biostar, 6655 Lookout Rd, Boulder, CO 80301

We describe a system for measuring the response nonlinearity of optical fiber
power meters and detectors over a wide power dynamic range at
telecommunication wavelengths. The system uses optical fiber components and is
designed to accommodate commonly used optical fiber power meters. The system
also measures the range discontinuities between neighboring power ranges or scale
settings of the optical fiber power meter. Measurements with this system yield
correction factors for all power ranges of the meter. The measurement system is
capable of producing results which have standard deviations as low as 0.01 %.
The measurement uncertainties associated with the system are described.

Key words: calibration; detector; linearity; measurement service; nonlinearity;
optical fiber power meter; optical power; range discontinuity; uncertainty.

1. Introduction

There are several methods currently used for the measurement of optical fiber power meter
(OFPM) or detector nonlinearity: differential, attenuation, and superposition. These methods
were compared analytically using a unified mathematical expression for nonlinearity [1-3]. Based
on these results, we developed a system, which uses a superposition method known as the triplet
method. This method relies on the principle that for a linear OFPM, the sum of the OFPM
outputs corresponding to inputs from two individual beams should equal the output when the two
beams are combined and incident on the OFPM at the same time. The triplet method does not
require a standard; a measurement system based on the triplet method is the standard by itself.

2. Measurement of Nonlinearity and Range Discontinuity

Generally, an OFPM has a dynamic range of more than 60 dB with many meters exceeding 90 dB.
To achieve these dynamic ranges, an OFPM is designed to switch ranges during optical power
measurements. The power ranges have their own gains or amplifications, which often differ by a
factor of 10. When the meter switches from one range to another, it is critical that two
neighboring ranges indicate the same power. If the power readings at these two ranges are not
the same, then the OFPM has a range discontinuity (assuming the power has remained constant).
A simplified schematic of a typical OFPM is depicted in Figure 1.


Table 4. Example of nonlinearity measurement uncertainties for a Si optical
fiber power meter at 850 nm.

Source Standard uncertainty (type)
(*)
Laser stability 0.06 (B)
@ 850 nm
Polynomial truncation 0.002 (B)
Test meter spectral responsivity
@ 850 nm (Si) 0.004 (B)
Equation approximation* 0.026 (B)
Polarization 0.014 (B)
Repeatability (N = 3) 0.05 (A)
Combined uncertainty 0.073
Expanded uncertainty (k = 2) 0.15

* This uncertainty depends on the nonlinearity value for each particular case.

14


p [uu -.--.-- teeteereeeeeey P(VV/V,

INPUT POWER

Vv
OUTPUT

Figure 3. A conversion function.

In practice, it is often more convenient to use the conversion function rather than the response
function. We can define the nonlinearity in terms of the output V as

PV, V |

AVS, ) = PWV,

(5)

2.2 Polynomial Expression for Conversion Function

When the nonlinearity is small, a polynomial can represent the conversion function well [4,5];
that is

PV) = day , ©

where n is the order of the polynomial and a, are the coefficients of the polynomial. The
coefficients a, correspond to a calibrated conversion function [1].


Appendix C. Sample of a Calibration Report

U.S. DEPARTMENT OF COMMERCE
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

ELECTRONICS & ELECTRICAL ENGINEERING LABORATORY
Boulder, Colorado 80303

REPORT OF NONLINEARITY CALIBRATION for

OPTICAL POWER METER
Meter’s Manufacturer
Model Number
with Sensors
Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Submitted by:

Company name
Address

Nonlinearity Measurement Summary

Using the system shown in Figure 1, the nonlinearity of the optical fiber power meter (OFPM) was characterized over the
following ranges: (1) 150 pA to 600 pA at a wavelength of 860 nm for Model X with S/N 1 (Si), and (2) 150 pA to 600 pA
at 860 nm, 150 pA to 2.0 mA at 1314 nm and 1542 nm for Model Y with S/N 2. The data were acquired and analyzed
using the triplet superposition method in which measurements were performed by taking sets of three power readings from
the test meter with: (1) shutter 1 open, shutter 2 closed, (2) both shutters open, and (3) shutter 1 closed, shutter 2 open. This
sequence was then repeated at different powers. In principle, the detector is considered linear when the sum of the two
individual power readings is equal to the combined power reading. The actual equations used to characterize the degree of
nonlinearity and resulting correction factors are discussed in the next section of this report. To measure range discontinuity
(ie, offsets between range or scale settings), readings were taken at the lower power end of each range and compared to the
readings on the higher power region of the next lower range (if available) at a constant power.

Test
Meter

[oir |
_ i

Figure 1. The nonlincarity measurement system.

Folder No. & NISTID: 26000 & 81300
Date of Report: April 30, 2000
Reference: P.O. No. 2121 04/15/00 lof 10


NIST Measurement Services:

Optical Fiber Power Meter NIST
i i i H pecia
Nonlinearity Calibrations at NIST Publication
250-56
Igor Vayshenker
Shao Yang
Xiaoyu Li

Thomas R. Scott
Christopher L. Cromer

|

NIST CENTENNIAL®

INUUSST wretione! Institute of Standards and Technology * Technology Administration « U.S. Department of Commerce


P.

ae] = ————_. ay
v.+> bc] VE
k=2
The true input power P is obtained from the OFPM reading V for any given range m by
Vv
P= ——_.,
F-CF[m] (13)

where F,= V_/P, is the calibration factor described in reference [6] and CF[m] is a correction
factor for nonlinearity over the entire range m and range discontinuity in any range (except the
range that corresponds to the lowest power used in a nonlinearity calibration). This correction
factor can be calculated by:

. k-1
af), 14 bale

<= , a4)
1+> b,[m]v*
k=2

where the discontinuity coefficients a,[m] outside range [c] are determined using eqs (15) and

(16):

a,[c] - a,[e] K ue x a,[m-1] for m>c. (15)
afm] —a,f[c+1] a,[m] °
or
ale) = u forc > m.
a,[m] a,[m] Ke xX a,[c-1] (16)
a,[m+1] a,[c]

The coefficients of the noncalibrated conversion function b,[m] in eq (14), are determined from
the measured nonlinearity by means of a least squares curve fitting. The ratio of a, between two
neighboring ranges a,[m]/a,[m + 1] is determined by the measured range discontinuity. Typically,
we use a third-order polynomial (n = 3) to calculate the correction factor in eq (14). Each range
of an OFPM has its own correction factor.


a
Pi = Vii * Devi

k=

‘ k
Pai = Vai + By oeVai- (10)

‘ k
Pyi * Pai = Vi * Dos.

where the p; are arbitrary unknowns and the V, are measured output values. A new equation
is formed by subtracting the first and second equations from the third equation while eliminating
the unknown p; in the group of the three equations in eq (10):

(V5, - Vai ~ Vad + Lvs - Vii - Va) = 0. ql)

The coefficients b, can be obtained by linear least-squares fitting of the measured data. The three
measurement runs are usually made in immediate succession, which helps reduce the uncertainty
that might occur due to drift of the laser source output. The details of the measurements are
described in Section 3.

2.3 Correction Factor for Nonlinearity and Range Discontinuity

While calibration gives the true relationship between the input power and the OFPM reading
(output) at the calibration point, the measurement of nonlinearity and range discontinuity,
together with calibration, provides this input-output relation at any power over the whole dynamic
range of the OFPM. It is, therefore, convenient to express the measured nonlinearity, Ay (V;V.)
in terms of the conversion function P = P(V), which relates the input power P to the output V,
referred to the calibration output V,.

We denote the range setting of the OFPM with brackets; [m] denotes some range m (m = 1, 2,
3,...), and [c] is the range where the reference power is used. Calibration determines a, in range
[c] where the calibration reference point is selected; P, is the calibration power at a reference
power of approximately 100 pW and V, is the calibration output as shown below:


OPTICAL POWER METER,
Meter’s Manufacturer

Model Number, Serial Number
with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

measurements are taken. The low power (when an individual shutter is open) is measured before and after the high power
(when both shutters are open). The value for laser stability is found by measuring the drift for each laser source. The slope
of the drift (percent per second) is then multiplied by the interval that the three shutters are open (3 s) during an actual
nonlinearity calibration. The maximum measured value of the power drift is 0.21 % at 850 nm, and 0.09 % at 1300 nm and
1550 nm. The standard uncertainty for laser stability is 0.21/(2¥'3) = 0.06 % at 850 nm, and 0.09/(2¥3) = 0.03 % at 1300
nm and 1550 nm.

b. Polynomial truncation: The conversion function of an OFPM is a least-squares fit to a third-order polynomial. The
uncertainty is due to truncation of the polynomial of higher orders. The maximum value of the error is equal to 0.007 %.
The standard uncertainty is 0.007/(2¥°3) = 0.002 %.

c. Test meter spectral responsivity: This uncertainty is caused by drift of the source wavelength and a drift of the optical
spectrum analyzer during each triplet measurement. The size of the uncertainty depends on the absorbing material of the
power meter detector. The value is estimated based on the spectral responsivity curves for Si, Ge, and InGaAs detectors.
We assume a combined variation for the lasers wavelengths and accuracy of the optical spectrum analyzer of 0.1 nm.

d, Equation approximation: This uncertainty is due to the approximation in the nonlinearity equation. The uncertainty is
of second-order in magnitude, i.e., if the nonlinearity is 1 %, then the uncertainty is (0.01)? or 10“. This uncertainty
depends on the value for the nonlinearity in each case. The maximum uncertainty will be divided by (2773).

e. Polarization: This uncertainty is due to effects caused by changes in polarization of the incident power during each
triplet measurement set. This uncertainty is related to polarization dependent loss (PDL) of the nonlinearity system.
Polarization uncertainty of the nonlinearity system is assumed to be small because we take a large number of measurements
(810 measurements per one power range) and because measurement time scales are short compared to changes in the
system polarization state. The PDL of the nonlinearity system was measured using a random-polarization generator. The
maximum value of the system PDL is 0.002 dB or 0.05 %, The standard uncertainty is 0.05/(2¥'3) = 0.014 %.

Table 5 lists typical measurement uncertainties associated with the nonlinearity calibration of an OFPM. The exact value of
these various components can change depending on the particular measurement conditions.

Folder No. & NISTID: 26000 & 81300
Date of Report: April 30, 2000
Reference: P.O. No. 2121 04/15/00 8 of 10

27


OPTICAL POWER METER
Meter’s Manufacturer

Model Number, Serial Number
with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Uncertainty Assessment

The uncertainty estimates in Tables 1 through 4 for the NIST linearity measurements are described and combined using the
guidelines of NIST Technical Note 1297. To establish the uncertainty limits, the uncertainty sources are separated into Type
A, whose magnitudes are obtained statistically from a series of measurements, and Type B, whose magnitudes are
determined by subjective judgement.

The Type A uncertainty components are assumed to be independent and, consequently, the standard deviation, S,, for each
component is

(6)

where the x; values represent the individual measurements and N is the number of x, values used for a particular Type A
component. The standard deviation of the mean is S,/N*, and the total standard deviation of the mean is [¥.(S2/N)]*, where
the summation is carried out for all Type A components.

All the Type B components are assumed to be independent and have rectangular or uniform distributions (that is, each has

an equal probability of being within the region, +5,, and zero probability of being outside that region). If the distribution is
rectangular, the standard deviation, o,, for each Type B component is equal to 6,/3” and the total ‘standard deviation’ is

(Zo,2)*, where the summation is performed over all Type B components.

The combined uncertainty is determined by combining the Type A and Type B standard deviations in quadrature; the
expanded uncertainty is obtained by multiplying this result by a coverage factor of 2. The expanded uncertainty, U, is then

0)

The values used to calculate the NIST expanded uncertainty (shown in Tables 1 through 4) are listed in Table 5. The
number of decimal places used in reporting the mean values of the correction factor were determined by expressing the
expanded NIST uncertainty to two significant digits.

Type A
Repeatability: This is an uncertainty due to the scatter of data points around the measurement average obtained from three
calibration runs on the OFPM being calibrated.

Type B
a. Laser power stability: During the nonlinearity calibration of an OFPM, changes in optical power such as drift or
fluctuations can cause a possible error. The power stability is measured during the time interval in which the three

Folder No. & NISTID: 26000 & 81300
Date of Report: April 30, 2000
Reference: P.O. No. 2121 04/15/00 7 of 10

26


voltage, or the display reading from the OFPM. A function that describes the relationship
between the incident optical power P and an OFPM or detector output is called the response
function and is expressed as:

Vv = V(). (2)

The response function is depicted in Figure 2. We can express the nonlinearity of eq (1) in terms
of the response function:

- 1. GB)

The inverse function (when the dependent and independent axes are switched) of the response
function is called the conversion function and is depicted in Figure 3. This conversion function
converts the output V to the input power P and is expressed as

P = PY). 4)

The response function and the conversion function represent the same physical quantity in
inverted variables. Consequently, the nonlinearity can equivalently be expressed and calculated in
terms of the response function and input power P.

102)

OUTPUT

PP, P

m G

INPUT POWER

Figure 2. A response function.


5. References

[1] Yang, S.; Vayshenker, I; Li, X.; Zander M.; Scott, T.R. Optical detector nonlinearity:
Simulation. Natl. Inst. Stand. Technol. Technical Note 1376; May 19, 1995.

[2] Yang, S.; Vayshenker, I.; Li, X.; Scott, T.R. Optical detector nonlinearity: a comparison of
five methods, Digest, Conf. Precision Electromagnetic Measurements: 455-456; June-July
1994,

[3] Yang, S.; Vayshenker, I; Li, X.; Scott, T.R. Accurate measurement of optical detector
nonlinearity. Proc., Natl. Conf. Standards Laboratories Workshop & Symposium, Session
5A: 353-362; July-August, 1994.

[4] Vayshenker, I; Yang, S.; Li, X.; Scott, T.R. Automated measurement of nonlinearity of
optical fiber power meters. Proc. Int. Symp. IMEKO, Vol. 2550, San Diego, CA; July 11-12;
1995.

[5] Vayshenker, I; Yang, S.; Li, X.; Scott, T.R. Nonlinearity of optical power meters. Natl. Inst.
Stand. Technol. Spec. Publ. 905: 101-104; 1996.

[6] Vayshenker, I.; Li, X.; Livigni, D.J.; Scott, T.R.; Cromer, C.L. Optical fiber power meter
calibration at NIST. To be published as Natl. Inst. Stand. Technol. Spec. Publ. 250-54, 2000.

[7] Taylor, B.N.; Kuyatt, C.E. Guidelines for evaluating and expressing the uncertainty of NIST
measurement results. Natl. Inst. Stand. Technol. Tech. Note 1297; January 1993.

17


OPTICAL POWER METER

Meter’s Manufacturer

Model Number, Serial Number

with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Table 3. Nonlinearity correction factors at 1314 nm for optical fiber power meter, Model
Number Y, Serial Number 2.

Meter/scale Output CF Standard Expanded
range current deviation for 3 uncertainty of
Tuns (%) CF (%)
3 0.15-2 mA 0.9999 0.05 0.07
4 15-200 pA 1.000 0.03 0.05
5 15-20 pA 0.9998 0.03 0.05
6 0.15-2 pA 0.9995 0.04 0.06
7 15-200 nA 0.9992 0.03 0.05
8 1.5-20 nA 0.9993 0.02 0.04
9 150-2000 pA 0.9984 0.08 0.10
1.0005
1.0000 =
&
2 0.9995 \ — Ne
Zz
co}
S 0.9990
1°}
3 0.9985
8 Zk
0.9980 4
0.9975
1E4 1E-3 1E-2 1E-1 1E0 1E1 1E2 1E3
CURRENT (1A)

Figure 4. Correction factor versus output current at 1314 nm for optical fiber power meter, Model Number Y,

Serial Number 2.

Folder No. & NISTID:
Date of Report:
Reference:

26000 & 81300
April 30, 2000
P.O. No. 2121 04/15/00

23

4 of 10


Certain commercial entities, equipment, or materials may be identified in this document in order to
describe an experimental procedure or concept adequately. Such identification is not intended to imply
recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended
to imply that the entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 250-56
Natl. Inst. Stand. Technol. Spec. Publ. 250-56, 34 pages (August 2000)
CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 2000

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325


Table 1. Nonlinearity and range discontinuity correction factors.

Meter Output Mean Standard

range [m} power correction deviation
(dBm)* factor (%)
1: 10 1,5-3,5 mW 1,007 0.30
2: 0 015-2 mW 0.9995 0.06
3: 10 [c] 15-200 pW 1.000 0.01
4: -20 1.5-20 pW 0.9993 0.02
5 -30 0.15-2 pW 1.003 0.04
6: -40 15-200 nW 1.002 0.06
7. -50 1,5-20 nW 1.003 0.06

* dBm is not an SI unit, but is related to a power of 1 mW as 10 log (x), where x is an
unknown power in milliwatts.

'

1E-3 1E-2 1E-1 1E0 1El 1E2 1E3 TE4 pte
OUTPUT POWER (uW) -50 dBm

Figure 5. Correction factor versus output power.

10


Type A
Repeatability: This is an uncertainty due to the scatter of data points around the measurement
average obtained from three calibration runs on the OFPM being calibrated.

Type B

a. Laser power stability: During the nonlinearity calibration of an OFPM, changes in optical
power such as drift or fluctuations can cause a possible error. The power stability is measured
during the time interval in which the three measurements are taken. The low power (when an
individual shutter is open) is measured before and after the high power (when both shutters are
open). The value for laser stability is found by measuring the drift for each laser source. The
slope of the drift (percent per second) is then multiplied by the interval that the three shutters are
open (3 s) during an actual nonlinearity calibration. The maximum measured value of the power
drift is 0.21 % at 850 nm, and 0.09 % at i300 nm and 1550 nm. The standard uncertainty for
laser stability is 0.21/(2V'3) = 0.06 % at 850 nm, and 0.09/(2¥°3) = 0.03 % at 1300 nm and 1550
nm.

b. Polynomial truncation: The conversion function of an OFPM is a least-squares fit to a third-
order polynomial. The uncertainty is due to truncation of the polynomial of higher orders. The
maximum value of the error can be found from Figure 9 of reference [1] and is equal to 0.007 %.
The standard uncertainty is 0.007/(2V'3) = 0.002 %.

c. Test meter spectral responsivity: This uncertainty is caused by drift of the source wavelength
and a drift of the optical spectrum analyzer during each triplet measurement. The size of the
uncertainty depends on the absorbing material of the power meter detector. The value is
estimated based on the spectral responsivity curves for Si, Ge, and InGaAs detectors. We assume
a combined variation for the lasers wavelengths and accuracy of the optical spectrum analyzer of
0.1 nm.

Table 2 lists typical spectral responsivity slopes (percent per nanometer) for Si, Ge, and InGaAs
detectors used in most OFPMs.

Table 2. Spectral responsivity slope (percent per nanometer) for Si,
Ge, and InGaAs detectors.

Diode type Wavelength (nm)
850 1300 1550
Si 0.14 NA NA
Ge 0.48 0.14 0.92
InGaAs 0.53 0.09 0.05



NIST Special Publication 250-56

NIST MEASUREMENT SERVICES:
Optical Fiber Power Meter Calibrations at NIST

Igor Vayshenker

Shao Yang*

Xiaoyu Li

Thomas R. Scott
Christopher L. Cromer

Optoelectronics Division

Electronics and Electrical Engineering Laboratory
National Institute of Standards and Technology
Boulder, CO 80303

*Biostar

6655 Lookout Road
Boulder, CO 80301

August 2000

U.S. Department of Commerce
Norman Y. Mineta, Secretary

Technology Administration
Dr. Cheryl L. Shavers, Under Secretary of Commerce for Technology

National Institute of Standards and Technology
Raymond G. Kammer, Director


OPTICAL POWER METER
Meter’s Manufacturer

Model Number, Serial Number
with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

The results of these measurements are presented in Tables 1 through 4 and shown graphically in Figures 2 through 5. To
correct for nonlinearity and range discontinuity, the OFPM readings should by divided by the appropriate correction factors
in Tables 1 through 4. The correction factors result from meter/detector nonlinearity within each range combined with the
range discontinuity (i.e., offsets between ranges). Except for the third, fourth, and fifth ranges for Model Y, S/N 2 detector
at 860 nm, each correction value listed in the table is the average of six correction factors found throughout that particular
range. Because of the observed nonlinearity, the correction factors for these ranges at 860 nm are for individual powers
rather than for the entire range. The uncertainty values listed in Table 1 through 4. The laboratory temperature during
these measurements was 22 °C (£2 °C) and the relative humidity was 11 % (+4 %).

Table 1. Nonlinearity correction factors (CF) at 860 nm for optical fiber power meter, Model

Number X, Serial Number 1.
Meter/scale Output CF Standard Expanded
range current deviation for 3 uncertainty of
Tuns (%) CF (%)
3 150-600 pA 1.000 0.08 0.12
4 15-200 pA 1.001 0.04 0.08
5 1,5-20 pA 1.000 0.02 0.07
6 150-2000 nA. 0.9998 0.03 0.08
7 15-200 nA 0.9993 0.03 0.08
8 15-20 nA 0.9995 0.05 0.09
9 150-2000 pA 0.9988 0.03 0.08

1.0010 <=
&% 1.0005
5 sh
<
= 1.0000 <<
9 0.9995 NS
2
5
S 0.9990 —

0.9985

1E4 1E3 1E-2 1E-1 1E0 1El 1E2 1E3
CURRENT (A)

Figure 2. Correction factor versus output current at 860 nm for optical fiber power meter, Model Number X,
Serial Number 1.

Folder No. & NISTID: 26000 & 81300
Date of Report: April 30, 2000
Reference: P.O. No. 2121 04/15/00 2 of 10

21


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OPTICAL POWER METER
Meter’s Manufacturer

Model Number, Serial Number
with Sensors

Model Number X, Serial Number 1
Model Number Y, Serial Number 2

For the Director,
National Institute of Standards
and Technology

Gordon W. Day, Division Chief
Optoelectronics Division

Report Reviewed By

Christopher L. Cromer, Project Leader
Sources and Detectors Group
Optoelectronics Division

Folder No. & NISTID: 26000 & 81300

Date of Report: April 30, 2000

Reference: P.O. No. 2121 04/15/00

29

Report Reviewed By:

Thomas R. Scott, Group Leader
Sources and Detectors Group
Optoelectronics Division

Report Prepared/Calibrated By:

Igor Vayshenker, Electronics Engineer
Sources and Detectors Group
Optoelectronics Division

10 of 10


OPTICAL POWER METER
Meter’s Manufacturer
Model Number, Serial Number
with Sensors
Model Number X, Serial Number 1
Model Number Y, Serial Number 2

Table 4. Nonlinearity correction factors (CF) at 1542 nm for optical fiber power meter,
Model Number Y, Serial Number 2.

Meter/scale Output CF Standard Expanded
range current deviation for 3 uncertainty of
runs (%) CF (%)
3 0.15-2 mA 1.001 0.06 0.08
4 15-200 pA 1.000 0.04 0.06
5 15-20 pA 0.9997 0.03 0.05
6 0.15-2 pA 0.9991 0.04 0.06
7 15-200 nA 0.9987 0.03 0.05
8 15-20 nA 0.9985 0.05 0.07
9 150-2000 pA 0.9990 0.17 0.20
1.0010
we 1.0005
© 1.0000 \ “
gh
© 0.9905 [|e
é Ten ‘.
2 0.9990
& 0.9985
is)
0.9980
0.9975
1E4 1E-3 1E-2 1E-1 1E0 1E1 1E2 1E3
CURRENT (uA)

1E4

Figure 5. Correction factor versus output current at 1542 nm for optical fiber power meter, Model Number Y, Serial
Number 2.

Folder No. & NISTID:
Date of Report:

Reference:

26000 & 81300
April 30, 2000
P.O. No. 2121 04/15/00

5 of 10


3. Nonlinearity Measurement System

The NIST OFPM nonlincarity system is depicted in Figure 4. The system is fully automated.
After the measurements are completed (typically in 3 h), the computer program analyzes the data
and prints the calibration data in a table form. We use high-power, single-mode, fiber-pigtailed
lasers whose powers are stabilized. All the lasers are temperature controlled for power and
wavelength stability. An external optical attenuator with a dynamic range of more than 60 dB
provides variable optical power. The output of the attenuator is divided into two approximately
equal parts by using a fiber splitter; one of the splitter arms has an additional length of fiber
(approximately 100 m, compared to the coherence length of the laser of only a few centimeters)
to avoid interference. A computer-controlled shutter is inserted into a collimated beam in each
arm. Both signals are combined in a fiber coupler which has an FC/APC connector at the output
to decrease reflections back to the laser and other components of the measurement system. We
use single-mode fiber components (e.g., splitters and couplers) throughout the system. Loose
system fibers are wrapped on spools 5 cm in diameter to minimize transient microbend losses.
Also, in this regard, all fibers are securely fixed so that they cannot move during the
measurements. All the lasers are of Fabry-Perot type and have several longitudinal (spectral)
modes (see Appendix A).

Driver

GPIB

GPIB —

Figure 4. The nonlinearity measurement system.


4. Uncertainty Assessment

In this section we assess the associated uncertainty of the OFPM nonlinearity measurements. The
uncertainty estimates for the NIST OFPM nonlinearity measurements are described and combined
using the referenced guidelines [7]. To establish the uncertainty limits, the uncertainty sources are
separated into Type A, whose magnitudes are obtained statistically from a series of
measurements, and Type B, whose magnitudes are determined by subjective judgement.

The Type A uncertainty components are assumed to be independent and, consequently, the
standard deviation, S,, for each component is

(17)

where the x, values represent the individual measurements and N is the number of x, values used
for a particular Type A component. The standard deviation of the mean is S/N“, and the total
standard deviation of the mean is [(S,?/N)]*, where the summation is carried out for all Type A
components.

All the Type B components are assumed to be independent and have rectangular or uniform
distributions (that is, each has‘an equal probability of being within the region, +5,, and zero
probability of being outside that region). If the distribution is rectangular, the standard deviation,
o,, for each Type B component is equal to 5,/3% and the total ‘standard deviation’ is (Y.o,”)",
where the summation is performed over all Type B components.

The combined uncertainty is determined by combining the Type A and Type B standard deviations

in quadrature; the expanded uncertainty is obtained by multiplying this result by a coverage factor
of 2. The expanded uncertainty, U, is then

. (18)

2|4,

v-2\De+¥

The number of decimal places used in reporting the mean values of the calibration factor are
determined by expressing the expanded NIST uncertainty in percentage to two significant digits.
In Table 2, we describe the nonlinearity of an OFPM calibration uncertainty using Type A and
Type B components as follows:

ll