II iiliiiiiilili iilili illiili III III III 1 REFERENCE

nmr

PUBUCATIONS

I NIST Measurement Services:

Measurement Assurance Program

for the Spectral Density of Relative

Intensity Noise of Optical Fiber

Sources near 1550 nm

Gregory E. Obarski

Jolene D. Splett

X

100

lis?

' ' lal Institute of Standards and Technology

NO. 250-57 OQy Administration, U.S. Departnnent of Commerce

2000
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NIST Special Publication 250-57

NIST MEASUREMENT SERVICES:

Measurement Assurance Program for the

Spectral Density of Relative Intensity Noise

of Optical Fiber Sources near 1550 nm

Gregory E. Obarski

Optoelectronics Division

Electronics and Electrical Engineering Laboratory

Jolene D. Splett

Statistical Engineering Division

Information Technology Laboratory

National Institute of Standards and Technology

Boulder, CO 80305-3328

September 2000

U.S. Department of Commerce

Norman Y. Mineta, Secretary of Commerce

Technology Administration

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

National Institute of Standards and Technology

Raymond G. Kammer, Director
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 250-57

Natl. Inst. Stand. Technol. Spec. Publ. 250-57, 96 pages (September 2000)

C0DEN:NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2000

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

1. Introduction 2

2. Background 4

2. 1 Definition of the RIN of an Optical Source 6

2.2 Application of Laser RIN to Noise Figure of Optical Amplifiers; Electrical Methods . . 7

2 .3 Measurement of RIN 9

3. A RIN Standard Based on Two Different Methods 10

3.1 Form of the RIN Standard or Primary Method 10

3 .2 Source RIN of the Secondary Method 11

4. Theory of the Spectral Density of the RIN 11

4. 1 Complete Derivation of the Spectral Density of the RIN fi-om the Optical Field

Correlations and the Semiclassical Theory of the Photodetection of Light 12

4.2 Numerical Formulation of RIN in the Wavelength Representation 18

5. Accurate Determination of RIN Requires Precise Calibration of Optical Spectrum

Analyzer Parameters 21

5.1 Measurement of Resolution Bandwidth and Its Uncertainty 21

5.2 Measurement of Wavelength Error and Distortion 22

5.3 Nonlinearity of the Optical Power Spectral Density Scale 23

6. Some Properties of the RIN Standard 24

6.1 Polarization 24

6.2 Absence of Ripple 24

6.3 RIN of Various Filters of Exact Mathematical Shape; Dependence on Filter

Bandwidth and Shape 25

6.4 Measured RIN of Three Different Filters When Linked to the Same EDFA 26

6.5 Use of Connectors and the Effect of Losses 27

6.6 Combined Effects of Attenuation, Pump Current, and Power Spectral Density Levels 27

7. Total Uncertainty in the RIN Standard 30

7. 1 Repeatability Error 30

7.2 Measurement Error From the OSA Parameters 31

7.3 Combined Standard Uncertainty 34

8. Achieving the Poisson Limit 35

8 .1 The DFB Laser of the Secondary Method Has Nearly Poisson-Limited RIN 36

9. RIN System Calibration Using the Standard and the Laser 37

9.1 Derivation of the Calibration Equations For the Standard and Secondary Methods . 38

iii
9.2 Equivalence of the Calibration Functions 39

10. Two Methods Applied to the NIST RIN System Give Similar Results .40

10. 1 Quantitative Comparison of Calibration Results from the Two Methods 40

10.2 Relative Stability of Two Different EDFAs With Respect to the Poisson Laser 45

10.3 Methods Compare Favorably Under Use of Variance Analysis 45

10.4 F-ratio Test Yields Similarity in the Variability of the Calibration Functions 46

1 1 . Maintaining a Measurement Assurance Program 48

11.1 Maintaining the RIN Standard 48

11.2 Substitution of Components 48

12. References 50

Appendix A. Calibration of the Electrical Spectrum Analyzer; Scale Fidelity Correction 53

Appendix B. Addition of RIN 54

Appendix C. Information for Applying the RIN Standard 54

Appendix D. Sample MAP Certificate 55

Appendix E. Calibration Service 62

Appendix F. Sample Calibration Certificate 63

Appendix G. Shipping Instructions 70

Figures 71

iv
Measurement Assurance Program for the Spectral Density of Relative

Intensity Noise of Optical Fiber Sources near 1550 nm

Gregory E. Obarski and Jolene D. Splett

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303

This paper provides the documentation to establish a measurement assurance

program (MAP) for the spectral density of relative intensity noise (RIN) of optical

sources. A standard is made available to industry for high-precision calibration of

RIN measurement systems. The device is an erbium-doped fiber amplifier (EDFA)

to which is coupled a linear polarizer followed by a narrow pass-band optical filter.

Measurements show that the spectral density of the RIN is invariant under

attenuation and pump current, and constant fi^om zero to many tens of gigahertz.

These properties render it suitable as a standard for the calibration of high-speed

systems. We characterize the device for use as a standard in the 1550 nm

wavelength range over a radio-frequency (rf) baseband of 0. 1 to 1 . 1 GHz. For the

typical device studied in depth, the magnitude of the RIN is - 109.9 dB/Hz with

uncertainty <0. 12 dB over the entire bandwidth. Since the behavior of the REST

standard can be determined from physical theory, we give a thorough derivation of

the spectral density of RIN in the frequency representation. This derivation has

been absent from the literature We use this derivation to formulate the needed

numerical RIN equations in spatial wavelength coordinates that are used to

determine the RJN from optical power spectral density measurements made with a

calibrated optical spectrum analyzer. The standard is then applied to calibrate a NIST RIN measurement system. To fijrther validate the standard we develop a

second calibration method based on a distributed-feedback (DFB) laser having

Poisson-limited RIN. We apply each method to determine the frequency1
dependent calibration function (Kappa) of our RIN system and derive the equation

that relates them. A comparison of the calibration functions obtained from

measurements using the two methods agrees well with the theory developed. The

relative uncertainty in their difference is similar to the relative uncertainty in the

RESf of the standard. Application of a statistical F-ratio test demonstrates that the

variability in Kappa of the two methods is similar. Thus we establish a RIN

standard that compares favorably with a second independent method (Poissonlimited laser) based on rigorous physical theory, high-precision measurements, and

thorough statistical analyses.

Key words: calibration; measurement assurance; optical fiber sources; Poissonlimited laser; relative intensity noise; spectral density; transfer standard

1. Introduction

Increasing demand for greater bandwidth in optical communications systems has brought to

fruition laser transmitters and optical fiber amplifiers with very-low relative intensity noise (RIN)

and noise figure, respectively. In this report we present a method for high-precision calibration of

RIN measurement systems (where RIN means the spectral density of the relative intensity noise).

A standard is made available to industry in the form of an erbium-doped fiber amplifier (EDFA)

whose output is coupled to a linear polarizer followed by a narrow-band filter. We characterize a

typical device for use as a standard in the 1550 nm wavelength range over an rf frequency

baseband of 0. 1 GHz to 1 . 1 GHz. However, the spectral density of the RIN is very nearly

constant from zero to many tens of gigahertz, rendering it suitable for calibration of systems of

greater bandwidth. Thus, depending on future requirements of industry, we will be able to certify

the RIN standard at higher bandwidths by using a higher bandwidth pre-amplifier in the RIN

system and applying identical calibration techniques.

The RIN of a typical device studied has a magnitude - 109 .9 dB/Hz, which can be decreased

by using a filter of greater bandwidth. The combined standard uncertainty in the RIN, over the

2
entire bandwidth, ranges from 0.036 dB/Hz to 0. 12 dB/Hz, depending on the fiher used. The

EDFA's built-in optical isolator, along with the property of invariance of the RIN under

attenuation, allows for the convenient use of fiber connectors. We chose a good-quality FC/PC

connector, with all components pigtailed to standard single-mode fiber. The invariance under

attenuation allows the user to achieve noise power levels on their electrical spectrum analyzer

(ESA) to match the values expected when measuring unknown devices.

Accurate specification of the RIN requires that we develop the underlying physical theory

from fundamental principles, then apply it to formulate a numerical representation for the RIN.

We then developed the metrology to describe the interaction of a potential standard device with a RIN measurement system. This yielded a frequency-dependent calibration function specific to the

RIN system under calibration. To validate the device as a standard, we developed a second

calibration method based on a distributed-feedback (DFB) laser whose RIN is specified by the

manufacturer to be less than - 1 72 dB/Hz. We demonstrated that under sufficient attenuation, the

RIN ofthis source becomes Poisson limited. Using this method to calibrate our RIN system also

yielded a similar calibration function (Kappa). By applying the RIN equations for each method to

calibrate the RIN system, we derived an exact expression that equates their calibration functions

and use it to compare the methods. A typical value for the difference between the functions

obtained from each method, as averaged over the 601 frequency points in a span, falls in the range

from 0.04 dB to 0.2 dB. Such values are comparable to the relative uncertainty in the RIN of the

standard (0 .12 dB). Application of a statistical F-ratio test demonstrates that the variability in

Kappa of the two methods is similar. Thus the RIN standard compares favorably with the

Poisson-limited laser. We selected the EDFA method for the standard because it is the most

stable, robust, and portable of the two RIN sources. However, in principle either method could

be used for the standard, in that either method would produce nearly equivalent results if applied

to similar RIN measurement systems.

A calibrated RIN system has two immediate applications that illustrate the need for a measurement assurance program. First, it is needed for precise measurement of the RIN of lasers

used in optical communications systems. This demand is of increasing importance as efforts are

broadened to create lasers with RIN approaching the standard quantum limit. Second, it is useful

3
in determining the noise figure of optical amplifiers. In the future we plan to develop a standard

(also based on a MAP) specifically for noise figure of optical amplifiers. This latter device will be

used to calibrate optical noise figure measurement systems based on electrical spectrum analyzers.

We will attempt to establish the MAP so that future changes can be made to the various

components that compose the standard and the measurement apparatus with little or no additional

documentation. These might include the EDFA, polarizer, and filter that compose a standard, the

optical spectrum analyzer, and RIN system components such as the pre-amplifier, photodetector,

bias-tee, electrical spectrum analyzer, and voltmeter.

Herein we refer to the EDFA-based standard as the primary method and the Poisson-limited

laser as the secondary method. To distinguish between the use of two different EDFAs and three

filters as components of the standard we use the notation EDFAl, EDFA2, and Fl, F2, F3,

respectively. The bulk of our measurements and analysis was performed on results using EDFA2

with Fl . Thus the standard has implicit in its definition the use of EDFA2 and Fl . For brevity,

instead of denoting the standard by EDFA + P + F, we omit the polarizer, P, and write EDFA +

F, keeping in mind that the polarizer is present unless otherwise specified. Finally, a brief

discussion of RESf expressed in logarithmic units is given in Appendix B for the reader unfamiliar

with this subject.

2. Background

REST is a concept that is often associated with optical data transmission using diode lasers as

the transmitters. However, the basic ideas of RESf are applicable to all classes of lasers as well as

almost all optical sources. In analog communications, such as cable television, total RIN within

the system bandwidth can limit the signal-to-noise ratio. In high-speed digital systems, RIN can

Umit the bit-error-rate (BER) and system performance under certain conditions. A laser's highfrequency RIN spectrum often contains a well-defined peak at the relaxation oscillation frequency;

for many classes of lasers this peak can be used to deduce the maximum intrinsic modulation

frequency for a specific laser. Knowledge of RIN can be applied to the design of new lasers to

give improved performance for specific applications. Very low-RIN lasers are used to detennine

4
the noise figure of the optical fiber amplifiers that are essential for building faster and more

efficient optical communications systems. The demand for better techniques to calibrate a RJN

measurement system's response and sensitivity is also increasing with the appearance of

commercial distributed-feedback lasers and diode-pumped Nd: YAG lasers having very low RIN.

Typical values of RIN range fi^om - 110 dB/Hz to - 130 dB/Hz for inexpensive multimode edge

emitting diode lasers, and less than - 170 dB/Hz for high quality DFB diode lasers. The RIN of an optical source can arise from a variety of variables and atomic parameters. In

this report, we are interested mainly in the RIN of semiconductor lasers and thermal light sources.

For semiconductor lasers, the most important parameters are frequency, source output power,

temperature, modulation frequency, time delay and magnitude of optical feedback, mode

suppression ratio, and relaxation oscillation frequency [1]. For certain kinds of multimode lasers,

RIN can be greatly affected by system components which have polarization or wavelengthselective properties [2]. The predominant source of RIN, however, is usually spontaneous

emission. Thus the low-frequency RIN of a laser is a maximum just above threshold, diminishing

with increasing output power. But it can be greatly increased by optical feedback, even at high

output power. For semiconductor lasers such as the DFB laser used for the secondary method of

this MAP, the RIN can be formulated by inclusion of Langevin noise sources in the differential

rate equations for the photon and carrier densities [3, 4]. Semiconductor laser RIN has important

applications in optical communications systems [5]. The source RIN of the standard or primary

method, however, will be shown to arise from the amplified spontaneous emission (ASE) of an EDFA. Such fluctuations, which are described by Bose-Einstein statistics, can be approximated

by thermal light [6, 7].

Other calibration sources that might apply to calibration of RIN measurement systems are

fast-pulse lasers, broadband sources such as light-emitting diodes, and a heterodyne method in

which the beat frequency oftwo tunable lasers is used to determine the frequency response of

ultra-high speed photoreceivers. We note that the filtered EDFA method developed herein

contains the information for performing such a frequency-response calibration.

5
2.1 Definition of the REV of an Optical Source

RIN [1, 3, 8] can be precisely calculated from the autocorrelation integral of optical power

fluctuations divided by total power squared. These temporal fluctuations can also be expressed in

terms of their spectral density via the Fourier transform of the autocorrelation integral. An optical

source of output power P(t) and fluctuation 8P(t) has a total RIN, RIN^, given by the ratio of the

mean square of the fluctuation to the square of the average power.

<P{t)>^

(2.1.1)

where the time average <6P(t)^> arises from the autocorrelation function A(t) = <6P(t)6P(t + t)

> evaluated at time x = 0. The total RIN, which is dimensionless, can be represented in the

frequency domain by defining a RIN spectral density, which we simply refer to as the RIN. Then

RINy is also the integral of the RIN, R(v), over all frequencies.

RIN^ = jR(v)dv , (2.1.2)

where v is linear optical frequency. This equation holds also for angular frequency units in which

0) = 2Tuf, since jR(v)dv = jR(o))do). The spectral density of the RIN, R(v), is derived by

application of the Wiener-Khintchine theorem [8] to X(t). By equating the right hand sides of eqs

(2. 1 . 1) and (2.

.2), one can show that this spectral density is

R{v) -2j A(T)e'^-MT , (2.1.3)

6
here X(x) = <AI(t)AI(t + x)>/ <I>^ is the intensity autocorrelation function ( section 4. 1 .4). Thus we define the "RIN" of an optical source to be the RIN spectral density, R(v), and the

integral of the RIN to be the "total RIN."

Our approach is to treat the RIN as consisting of two parts: a Poisson or shot noise

component, and a component we call "excess RIN." The excess RIN propagates unchanged

through the system while the Poisson RIN depends on system losses. The 'Toisson RIN" is the

minimum RIN that can be achieved for classical hght. It is ofl;en called the standard quantum limit.

Classical light obeys an uncertainty relation for which each conjugate field variable is greater than

or equal to its minimum value. (The perfectly coherent state is defined as the state when both

conjugates are equal and at their minimum.) The excess RIN is non-negative for classical light,

whereas it is zero for Poisson light. RIN is specified in units of 1/Hz, or in logarithmic form as

decibels per hertz. The total RIN is the sum of the spectral integrals of excess RIN and Poisson

RIN [9]; thus, it is dimensionless. To develop a MAP for RIN we characterized two different

kinds of sources; a RIN standard (EDFA + F) having nearly excess-limited RIN, and a laser

having nearly Poisson-limited RIN.

For light obeying a Poisson distribution, the variance in the photon number is proportional to

the photon number. Thus the square of the optical power fluctuations is proportional to the

optical power. When represented by a single-sided noise spectrum (positive fi-equencies only) the

Poisson RIN is 2hv/Po, where h is Planck's constant, v is photon fi^equency, and Pq is optical

power. In electrical units it is 2q/i, where q is electron charge, i = riqP(/hv is photocurrent, and rj

is photodetector quantum efficiency. Thus the Poisson RIN in a real detection circuit increases as

1/t|, so an ideal photodetector (t| = 1) would detect the laser's true RIN.

2.2 Application of Laser RIN to Noise Figure of Optical Amplifiers; Electrical Methods

Accurate measurement of EDFA noise figure is required for the design and development of

optical communications systems that rely on amplification to achieve high bandv^ddths. There is

significant interest in applying optical methods to the measurement of the noise figure because

they can be quickly applied to the amplifiers as they emerge fi-om the production line. Optical

methods, however, are incapable of measuring multipath interference effects which may arise fi"om

7
reflections within the amplifier, or between it and the span [10]. Recent reports demonstrate

accurate determination of noise figure using electrical methods. Electrical measurement methods

are becoming increasingly important because they include multipath interference effects, which,

however small, are necessary for the higher-speed analog systems.

There are at least two relevant electrical methods for determining optical amplifier noise

figure. The first of these, known as the RIN Subtraction Method [11, 12], requires a laser of low

RIN, such as a DFB laser with RIN spectral density <- 160 dB/Hz. The RIN is measured with a

calibrated RIN system such as the one used in the development of this RIN standard. This method

yields the fi^equency-resolved noise figure referenced to baseband fi^equencies, "f" It is of special

interest here because the RIN expUcitly appears in the noise-figure equation. The RIN of the laser

is measured before and afl;er transmission through the amplifier. If RlCQ is the RIN of the laser

(assuming Poisson-limited RIN) and R(f) the RIN of the amplified signal, then the noise figure is

N/J) -/?,(/)) A.G-\ (2.2.1)

where Pq is optical power, ^ is laser fi-equency, h is Planck's constant, and G is amplifier gain.

This method requires that the RIN of the amplifier be greater than the signal source's RIN and

detector's thermal RIN, and also that the signal source's RIN be greater than the detector's

thermal RIN.

A second electrical method reports lower RIN uncertainty than the RIN Subtraction

Method, and has been shown to agree well with the polarization nulling (optical) method [13, 14].

An attenuator is used to equalize the power levels on a photodetector with and without the

amplifier present. This results in equal amounts of shot, thermal, and excess REN levels, all of

which vanish fi^om the noise figure equation upon subtraction of the signals. The net result is a

simplified determination of the noise figure. Both methods are of paramount importance because

each includes contributions to the noise figure of multiple path interference.

8
2.3 Measurement of REV

We measure RIN in the electrical domain by direct detection, although it can be determined

using optical correlation techniques. A general RIN measurement system with losses is shown in

Figure 2.3.1. The beam passes through a loss medium, such as an attenuator, and is collected by

the photodetector. The RIN, R(v), is to be determined at reference plane A, before any losses.

The Poisson component of the RIN is increased at plane B due to losses, and again at plane C due

to inefficiency in the photodetection process. System efficiency can be combined into one factor = r)(l - L), where L is the fractional loss before the detector. The excess RIN, however,

propagates unchanged through the system. If Rc(v) is the measured RIN at plane C (which

includes Poisson RIN), then the laser RIN

is

= i?c(v)-^(l-Ti,) . (2.3.1)

The excess RIN, Rex(^)? is determined by subtracting the measured Poisson or shot-noise RIN,

2q/i, from Rc(v), giving

^Jv) = R^{v) - ^ . (2.3.2)

This last equation is equivalent to subtracting the Poisson RIN from the RIN at plane A,

(2.3.3)

where ^ and Pq are the laser frequency and power (at plane A), respectively.

To measure RIN in the electrical domain, a bias tee sends the dc photocurrent produced in a

photodetector by a test laser to an ammeter, while the ac noise is amplified and then displayed on

a radio-frequency (rf) spectrum analyzer. In the electrical domain we weight the noise power per

9
unit bandwidth,6Pg(f), measured on an rf spectrum analyzer, with a linear frequency-dependent

calibration function K(f) for the detection system, and divide by electrical dc power P^. We note

that K(f) is proportional to the frequency response of the system, and contains the noise added by

the amplifier. If the excess RIN is much greater than the Poisson RIN, or if we avoid system

losses, the RIN is

K(/)6P(/)

^00 = , (2.3.4)

e

where bVJif) is the noise after subtracting the thermal noise floor of the ESA. K(f), can be

obtained from a broadband, flat source of known RIN.

In the electrical domam, the total RIN is also the integral of the RIN over all frequencies, or

over the system bandwidth, BW,

BW

RIN^ = lR{/)df, (2.3.5)

0

Total RIN can be measured with an electrical filter and an rf power meter in place of the spectrum

analyzer.

3. A RIN Standard Based on Two Different Methods

3.1 Form of the RIN Standard or Primary Method

The form of the RIN standard is shown in Figure 3.1.1. The ASE from an erbium-doped

fiber amplifier (EDFA) is fed through a linejir polarizer followed by a narrow band optical filter (1

nm to 3 nm) centered in the 1550 nm range [15,16]. The wavelength spectrum of the ASE from

one of the amplifiers used in this study, EDFAl, is shown in Figure 3 . 1 .2. The EDFA has a builtin optical isolator and was chosen for its ruggedness. To simplify operation for the customer, we

arranged for a simplified front panel display with only an on/off power switch. The linear polarizer

eliminates the potential for a polarization imbalance between orthogonally polarized modes which

10
might occur due to fiber bending. The excess RIN of this device is much greater than its Poisson

RIN, so that the total RIN can be considered excess RIN. The shape and bandwidth of the filter

determine the RIN.

Figure 3.1.3 shows the setup for measurement ofthe standard's power spectral density

(OPSD) using a diffraction grating-type optical spectrum analyzer. For a single measurement, the

OSA is set to average four sweeps on high sensitivity v^th the resolution bandwidth set at the

minimum of 0.05 nm. High-quality FC/PC connectors and single-mode fiber are used. Points 1, 2,

3, and 4 represent locations where connectors were routinely disconnected to change

components. We later show that this procedure can change the power loss through the fiber

transmission line, but has no significant effect on the RIN which is invariant under attenuation.

Also, we v^U show that the EDFA's optical isolator sufficiently shields it fi^om backreflections due

to the connector's small but finite return loss, and prevents ripple on the output signal of the RIN

standard.

3.2 Source REV of the Secondary Method

To establish a MAP, a secondary method was used to calibrate our RIN measurement

system. Results were compared with those obtained fi"om the standard (or primary method).

The secondary method was a DFB laser having very low excess RIN, specified by the

manufacturer to be < - 172 dB/Hz at the recommended operating power of 28 mW. In section 6.6

we will show that attenuation of the light to a fi"action of a milliwatt results in practically Poissonlimited RIN. This result follows because under attenuation the excess RIN is invariant but the

Poisson RIN increases. Thus, the RIN of the standard is described by the excess RIN of filtered

ASE, and the RIN of the laser is described by Poisson RIN.

4. Theory of the Spectral Density of the RIN

The spectral density of the RIN of the standard used in this MAP, as approximated by thermal

light, must be derived fi"om physical theory, as the RIN cannot be directly verified through

experimental means. In practice, our theory must yield the RIN fi-om knowledge of the OPSD as

11
measured by an optical spectrum analyzer (OSA). Much of the fundamental theory is greatly

developed by Mandel and Wolf [17]. However, it is sketchy in places, and not formulated in

terms of RIN explicitly. It also contains an acknowledged error of a factor of two in one of the

key results [18]. Thus we need to give a complete and accurate derivation of the RIN spectrum in

the frequency and spatial wavelength representations. Although the amplitude fluctuations can be

described by distributions of photon number density with respect to time, this method need not be

applied to the filtered ASE of the EDFA (RIN standard) or the Poisson light of the laser. To

develop a useful formalism we applied the theory of fluctuations to the conversion of optical noise

on the source to electronic noise within the RIN measurement system. The correlation between

the amplitude fluctuations of partially or totally coherent hght and those of the associated

photocurrent are well known [17]. In formulating the RIN in terms of the spatial representation,

we note that a fluctuation of the intensity in time gives rise to a frequency component. Such

Fourier frequency components manifest themselves as a spatial wavelength distribution in the

grating-type optical spectrum analyzer used to measure the power spectral density. Thus we seek

to represent the temporal Fourier transform of the amplitude noise as fluctuations in either

frequency or wavelength. Any contribution from the Poisson or standard quantum limit will be

considered negligible compared to the filtered ASE of the EDFA. Since our derivation follows

that of Mandel and Wolf, we use their notation to minimize any confusion that may arise.

4.1 Complete Derivation of the Spectral Density of the RIN From the Optical Field

Correlations and the Semiclassical Theory of the Photodetection of Light

From the general form for the autocorrelation of the photocurrent fluctuations ([17], section

8 .4 . 1, eq (9 .8 . 10)), we derive the spectral density of the current fluctuations in terms of

measurable quantities ([17], eq (9.8.24)) which is omitted from the text. We then apply the

properties of the degree of coherence of the light field ([17], section 8 .4.1) to express the RIN as

an autocorrelation of a power spectral density function. For completeness we give the results for

both polarized and unpolarized hght, although we use only polarized light for the standard.

Unless specified, all integrals in both the time and frequency representations are double-sided;

thus their limits run from minus to plus infinity.

12
To relate the fluctuations in photoelectric current Aj(t) that arise from the intensity

fluctuations of the light field AI(t), we define the following quantities; j(t) is the total

photoelectric current in the photodetector circuit at time t, k the distribution of current pulses,

and T] the quantum efficiency of the detection system. Then the autocorrelation of the current

<Aj(t)Aj(t + t)> at delay or correlation time t is related to the autocorrelation of the intensity

fluctuations by

where t' and t" are just dummy integration variables and the first term represents the shot noise of

the photocurrent ([17], eq (9.8. 10)). To later arrive at a flmctional form for the RIN, we define

some quantities connecting the time and frequency domains. Recall that the spectral density of

the current fluctuations x(g)) is the Fourier transform of the photocurrent autocorrelation

function.

To represent the frequency response of the RIN system, we define the Fourier transform of k(t) as

00

(4.1.1)

(4.1.2)

K(o)):

(4.1.3)

13
To represent the intensity fluctuations in the time domain, we define X{z) as the autocorrelation in

time of the light intensity fluctuations divided by the square of the average intensity:

^^^^ ^ <A/(OA/(/+T)>

</>2

(4.1.4)

Then the Fourier transform of A(t) is the spectral density, which we denote by For

unpolarized thermal hght

(4.1.5)

which is proportional to the RIN.

We now proceed to derive eq (9.8.24) ofMandel and Wolf [17]. Substituting the above

relations into eq (4. 1 .2) above yields for x(^\

X(a)) - I

e'^^'dT [r]<I>l k{t')k{t'+'z)dt'

oo oo + Ti^ I I

k{t')k{t")<M{t)M{t^t' -t" + x))>dt'dt"]

— 00 — oo

= T1</>|^C0)|2

(4.1.6)

CO CO

-oo —CO

= T1</>|^(W)|2 + U{(x>).

If we define a fiinction G(t) as

14
CO CO G(T) = / /

K>")k(l')<Mi>m<^t'-,"*r)> j^,^^„^

-CO —CO <I>'

(4.1.7)

then we observe that U(a)) is the Fourier Transform of G(x),

f/(a)) = rfO^j G(t) e'"VT

—oo

= ti2</>2^G(t)}

k{t")k{t')<M{t)M{t + t' -t" ^x)>

= rf<I>^f

CO CO

—oo —oo <I>'

(4.1.8)

Since G is a function only of t, we can apply the shifting property of Fourier transforms to the

dummy variables t', and t" in A I(t + 1' - t" + x) before integrating. If .^represents the Fourier

Transform, then the result is

(4.1.9)

so that

-CO — oo —CO

CO CO oo (4.1.10)

15
U{(x)) = Ti2</>2^(a))A:(a))*i(r(a))

= Tf<I>^\K(0})\^\^{0)).

(4.1.11)

With these substitutions, x(^) becomes

X(a)) = Ti</>|A:(a))|2(l -f Ti</>i|;(co)) . (4.1.12)

Thus the spectral density of the electric current fluctuations arises directly from i|r(o)), which is

proportional to the RIN spectral density of the light. For applications regarding this MAP, K(a))

is referenced to the baseband frequency, and is proportional to the calibration fiinction to be

obtained for the RIN measurement system by application of the standard.

All equations up to this point hold for any kind of light. However, the amplified spontaneous

emission of the REST standard is represented well by treating it as thermal Ught. As such it is

governed by Gaussian statistics, for which all space-time correlation fiinctions of the field can be

represented by ones of lower-order ([17], section 8.4.1; see also 1.6.3 and 8.5.3 on Gaussian

moment theorem). An important result is that the second-order complex degree of coherence

Y(t), from which A(t) is derived, can be found from the first-order space-time correlation

fiinction. Thus the normalized intensity correlations for unpolarized thermal light at a single point

in space ( [17], eqs (8.4.10) and (8.4.24)) can be derived from the degree of coherence:

</>

2

.2 <A/(OA/(? + t)> = |Y(T)|' - (4.1.13)

Whereas for polarized thermal light.

16
<A/(/)A/(/ + t)> = </>2|y(t)P . (4.1.14)

Returning to unpolarized thermal light, the autocorrelation of the intensity fluctuations in the time

domain is

^ n ^— • (4.1.15)

</>2 2

Now the autocorrelation function of a stationary random process and the spectral density of the

process form a Fourier-transform pair (Wiener-Khintchine theorem). Thus there exists a Fourier

transform of y{z) in the frequency domain that is the normalized spectral density of the optical

iSeld [19],

oo

(t)(v) = j

Y(T)e-2'^'^^JT . (4.1.16)

Since (})(v) is single-sided, the inverse relation is

Y(t) = |(l)(v)e2--VT . (4.1.17)

From eqs (2. 1 .3) and (4.1.1 5), the RIN is

R{v) = j\y{T)\^e^^^''dx = f

(l)(^)(j)(^+v)^/n . (4.1. 18)

17
If S(v) is the power spectral density as measured by the OSA, and P is the total power in the

spectrum, then (t)(v) = S(v)/P, and the RIN for unpolarized thermal light is

0

^(v)^(v ^fjciv

(4.1.19)

For polarized thermal light we need only introduce the same factor of two as appears in eq

(4 .1.14) for the autocorrelation of the intensity fluctuations.

This derivation estabhshes the RIN equation of the standard from physical theory. The

magnitude and uncertainty of the RIN will be determined from measurement of the optical power

spectral density of the RIN standard with a well-calibrated OSA. The calibration properties of the

RIN measurement system, which to some extent are arbitrary, will be determined from

measurement and theory by application of the standard and the secondary method (Poissonlimited laser). The results of the two methods will be compared to verify the equivalence of their

calibration properties. The theory of the Poisson laser is historically known and proven by key

experiments that relate classical and non-classical states of light.

4.2 Numerical Formulation of the RIN in the Wavelength Representation

Having formulated a precise theory for the RIN of the standard, we now develop a

numerical representation that accurately treats the experimental data. This can be done in either

the frequency or the wavelength representation. As the data are recorded with a grating-type

OSA, we seek approximate numerical expressions that will yield the OPSD and the RIN from a

finite basis of data points in the wavelength representation specified by the OSA. In the previous

section, we showed that the RIN in the frequency representation is the autocorrelation of OPSD

0

(4.1.20)

18
divided by the power squared. If 6pj(Aj) is the optical power measured at wavelength Aj where

resolution bandvvddth is Bj(Aj), then the optical power spectral density Sj{X-) at is

(4.2.1)

Then in the wavelength representation

z

0

(4.2.2)

where P is total optical power, X is wavelength, Z is measurement span, and A is the shifting

parameter in units of wavelength. The integral is not exact since X and v are inversely

proportional {Xv = c, from which it follows that AA/Av = - A^/c). Thus a 1 Hz bandwidth will give

a bandwidth in wavelength units of AA = AVc. This can result in a considerable error in the RIN

when the optical power is significant over 5 nm or more of the wavelength span. Thus we first

convert from wavelength to frequency units before calculating the RIN.

The total power is obtained from the sum over the incremental power elements in each

resolution bandwidth. The OSA used in these developments measures total power according to

the relation

where AA is the wavelength interval defined by dividing the span by the number of data points

minus one. Rewriting both the autocorrelation of the power spectral density and the optical

power as sums, the RIN evaluated at some arbitrary shift A^ is

(4.2.3)

19
RIN{A) = 2E

J

I (4.2.4)

This is the most general expression, and accounts for errors in the RIN due to variation in the

wavelength scale (absolute wavelength and wavelength distortion) and resolution bandwidth, as

determined over the entire wavelength span. The shifting parameter does not appear explicitly,

but is defined to exist at the arbitrary shifting value of K-^ Because the RIN of the standard

is very nearly constant from zero shift to many tens of gigahertz, we can simplify this expression

by setting = 0, which implies i = 0. This gives

which is the most general form for the RIN with zero shifting.

Next we consider the shifting equation for the RIN (eq (4.2.4) when the wavelength

distortion is negligible and the resolution bandwidth is constant. Under these conditions,

AAj = AA and Bj (Aj ) = Bj.,j(Aj+j) = B for all i and j. Thus the resolution bandwidth is of no

consequence while a AA remains in the denominator. The RIN becomes

RIN{A=0) =

2 (4.2.5)

RIN. =

I J (4.2.6)

20
At zero shifting this simplifies to

2 E SP/X/

= —ft xT (4.2.7)

In section 7, we apply the propagation-of-errors formula to these equations to estimate the total

uncertainty in the RIN.

5. Accurate Determination of RIN Requires Precise Calibration of Optical Spectrum

Analyzer Parameters

Since the RIN of the optically filtered EDFA noise is proportional to the autocorrelation of

the optical power spectral density, the optical spectrum must be precisely measured by a wellcalibrated OSA. From the numerical equations for the RIN, the OSA parameters to be evaluated

for uncertainty are resolution bandwidth, wavelength, and power spectral density. The power

spectral density is not a true fiinction because the resolution bandwidth can never be zero. This

condition is acceptable since we can account for all errors in the measurement parameters at each

point numerically. We convert fi^om wavelength to fi"equency units since we need to reference

the RIN spectrum to the rf-baseband fi^equency.

5.1 Measurement of Resolution Bandwidth and Its Uncertainty

We determined resolution bandv^dth over a wide wavelength range by two distinct methods

using several narrow-linewidth lasers (linewidth « instrument resolution bandwidth). Among

these were a tunable laser (linewidth < 1 MHz) in the 1540 nm to 1580 nm range with wavelength

established by a high-accuracy wavemeter (1 ppm), a 1523 nm HeNe laser (linewidth < 50 MHz,

and previously developed as a secondary wavelength standard), and a 1310 nm YAG laser for

good measure. In the first method, the response of the OSA to the narrow linewidth laser (or

delta fiinction input) is read directly fi^om the OSA. The single-wavelength input is broadened by

the monochrometer, and the resolution bandwidth is equated to the 3 dB bandwidth as read

21
directly from the OSA. We refer to the broadened curve as the slit function. Figure 5.1.1 shows

that the slit function for our OSA is fairly smooth from the peak value down to about 25 dB

below peak value, below which it becomes quite irregular. The 1 nm span is centered at 1551 nm,

the resolution bandwidth is set at 0.05 nm, and the tunable laser is set at 3 mW optical power. In

the second method, the noise-equivalent bandwidth (denoted herein by P) is calculated and used

as the definition of resolution bandwidth. If Aq is the center wavelength of an arbitrary-shaped slit

function T(A) of peak value T{Xq), then

where integration is performed over the entire slit function with the background noise subtracted

out. For a perfectly rectangular slit, either method gives the exact answer, while for a distorted

sUt, P is more accurate because it accounts for the exact slit geometry.

For each method, the tunable laser was set at predetermined wavelengths and the slit

function displayed on the OSA. The two methods agree as shown in Figure 5.1.2. For either

method, the resolution bandwidth is practically constant over the wavelength range shown. For

the 3 dB method, the average resolution bandwidth is 0.041 nm, with standard deviation of 0.001

nm. For the noise equivalent bandwidth, the average is 0.045 nm, with the same standard

deviation. We use the latter resuh because our slit function is irregular. Note that the measured

values for the resolution bandwidth are actually smaller than the OSA setting.

5.2 Measurement of Wavelength Error and Distortion

The OSA wavelength scale (horizontal axis) undergoes distortion that manifests itself as a

nonuniform distribution of data points. The absolute error and distortion in the wavelength scale

was determined by comparing the wavelength from a narrow linewidth tunable laser as read by the

OSA with the known wavelength as read by a precision wavemeter. OSA data were averaged

over four sweeps. For example, a wavelength setting of the tunable laser at 1560 nm yielded a

1 (5.1.1)

22
value of 1559.975 nm when read by the wavemeter. The corresponding OSA wavelength

reading was 1559.94 nm. This gives an uncertainty of 0.035 nm (fractional uncertainty of 22-

lO"^), which falls well within the manufacturer's specifications for wavelength (±0.5 nm over the

350 nm to 1750 nm range). Wavelength error was measured for many points around both 1548

nm to 1560 nm. For the 21 points shown in Figures 5.2. 1 and 5.2.2, the standard deviation is

0.042 nm. This agrees with calibration results obtained by the manufacturer at specific

wavelengths. For example, application of a HeNe laser of wavelength at 1523 . 1 nm (in air)

yielded a wavelength reading of 1 523. 13 nm on the OSA. This is an error of 0.03 nm, and in

agreement with our average uncertainty of 0.042 nm. Although the error appears to be small,

application of the propagation-of-errors formula will later show that it contributes significantly to

the total uncertainty in the RIN (section 7.2).

5.3 Nonlinearity of the Optical Power Spectral Density Scale

Since the thermal RIN is a ratio of powers squared (eq 4 .2.4), and as such is invariant

under attenuation, absolute power measurements are not required. This simplifies calibration of

the OSA specifically for thermal RIN measurements. However, the potential effect on the

numerical RIN of a nonlinear power spectral density across the wavelength span of the OSA must

be considered. Also, if a sUght attenuation effect existed because of wavelength dispersion fi^om

some optical component or connector in the fiber transmission Une of the standard, it would

couple with the nonlinearity ofthe spectral responsivity of the OSA. Thus we determine the effect

on the RIN of spectral responsivity and attenuation in aggregate, and do not attempt to separate

potential contributions that may arise from the two variables. In the simplified eq (4.2.7) for the

RIN, a constant linear scaling error, say e, would cancel if uniformly applied at every noise

power, 6Pj(Aj), over the entire wavelength span. This follows by substituting e6Pj(Aj) for each

term. In general, we expect i|x to arise mainly fi^om the nonlinear spectral responsivity of the

OSA's photodetector and any wavelength dispersing components. As such, it is a measure of the

total wavelength or fi^equency response of the OSA. Thus, on some level of fineness, we expect €j = ej(Aj), so that the uncertainty in noise power will not cancel. In section 6.6, we determine that

il/j is a small quantity and devise a measurement scheme in which it need not be determined

23
explicitly. The error due to noise power measurement will be determined by attenuating the input

RIN signal from the standard to fall at predetermined levels on the OSA screen. In addition, RIN

measurements under varying conditions of attenuation and EDFA pump current adjusted to yield

equal values of power density on the screen will also determine that the nonlinearity in the spectral

responsivity is small. Measurements will show that the combined effect is indeed small.

6. Some Properties of the RIN Standard

6.1 Polarization

In section 4. 1, we showed that the RIN of the standard was a factor of 2 greater for linearly

polarized than for unpolarized thermal light. Thus for unpolarized light fiber bending could

imbalance the power transmitted between orthogonally polarized modes and change the RIN by a

finite amount. We attempted to measured this effect by changing the curvature of the fiber that

links the various components, but found it to be nearly negligible. Nonetheless, we add the

polarizer to eHminate potential effects which might arise under varying conditions.

We tested the theoretical relationships derived for the RIN for unpolarized and polarized

light. A linearly polarizing isolator determined the polarization behavior of the RIN standard.

Measurement of the RIN with and without the polarizing isolator gave a difference of 3.003 dB in

the noise power measured on the electrical spectrum analyzer (ESA). This compares well with

the 3.0103 dB difference predicted by theory. We note that the RIN system need not be

calibrated to perform this measurement because the calibration fianction cancels in the equations

that define the difference in the RIN of the two states; it is only necessary that the measurement

be performed at the same ESA settings.

6.2 Absence of Ripple

Low-amplitude ripple for frequencies in the tens of megahertz region was previously

observed in EDFAs and attributed to multiple path interference [20]. To test for ripple on the

RIN standard we visually inspected the RIN spectrum on the ESA at different frequency spans.

Figure 6.2.1 shows the amplitude noise over the total frequency range of interest, 0. 1 GHz to 1.

GHz, with no apparent ripple. Data points are spaced about 1.67 MHZ apart. Resolution and

24
video bandwidths are 300 kHz and 300 Hz, respectively. Figure 6.2.2 shows the frequency band

from 700 MHz to 850 MHz devoid of ripple. Data are spread over 0.25 MHZ and video

bandwidth has been reduced to 100 Hz. Finally, Figure 6.2.3 shows a ripple-free noise spectrum

from 500 MHz to 600 MHZ. Data points are spaced every 0. 166 MHZ, and video bandwidth is

30 Hz. Sampling other frequency intervals, such as 100 MHz to 250 MHz, and 400 MHz to 550

MHz (neither shown), also yielded no apparent ripple.

To insure that the RTN standard is indeed free of ripple, we compared the calibration

fiinction obtained by applying it to the RIN system with that obtained from a ripple-free

independent source (the Poisson laser of method two, see sections 9. 1, 9.2, and 10. 1). The

calibration functions from the two RIN sources are nearly identical, demonstrating that the RIN

standard is ripple-free. The absence of a ripple effect indicates that the built-in optical isolator

effectively shields the EDFA from feedback.

6.3 RIN of Various Filters of Exact Mathematical Shape; Dependence on Filter

Bandwidth and Shape

To understand the behavior and properties of the RIN standard, we can solve the exact RIN

equation for filters whose transmittance curves have exact mathematical shapes. Column 2 of

Table 1 shows the results for a Gaussian, a Lorentzian, and a rectangular-shaped transmittance

filter, v^th A the triangle function, the C's constants, f the baseband frequency, and B the filter

bandwidth. In all three cases, the RIN is proportional to the product of the the inverse of the

filter bandwidth and a bandwidth-dependent function [16]. It is practically constant to tens or

even hundreds of gigahertz, as expected for frequencies that are small compared to the optical

bandwidth as shown. From the form of the underlying fianctions, the magnitude of the RIN can be

increased significantly by decreasing the bandwidth.

25
Table 1 . RIN of optical filters whose transmittance curves have exact mathematical shapes.

Spectral density shape RIN = R Lim{6R/R} asf ^0

Rectangle (1/B)A (f/B)

(Ci /B)exp{-C2 (f/B) 2}

(1/B) ( 1 + (f/B)'

}

6B/B

Gaussian 6B/B

Lorentzian 6B/B

In the third column, we list the calculated limit of the variation in the RIN divided by the

RIN as the frequency tends toward zero. For all three cases, the result equals the variation in the

bandwidth divided by bandv^dth. Thus a uniform frequency increment, such as provided by an OSA with a constant-resolution bandwidth, should yield a very precise RIN. RIN calculations

give similar results for intermediate shaped filters. However, the RIN of a filter with an

asymmetric-transmittance shape may behave differently.

6.4 Measured REV of Three Different Filters When Linked to the Same EDFA

Figure 6.4. 1 shows the optical power spectral density from the OSA for the three filters Fl,

F2, and F3 used with EDFA2 (each combination a potential RIN standard). Very similar results

are also obtained using EDFAl . Filter Fl is quite rectangular in shape and has 3 dB bandwidth of

1.37 nm. Filter F2 is somewhat rectangular, but spreads more quickly toward the wings; it has

bandwidth 3 .42 nm. Although filter F3 spreads very quickly toward the wings, it has a 3 dB

bandwidth of 1 .32 nm. Figure 6.4.2 shows that the RIN obtained using all three filters is constant

out to tens of gigahertz. The rectangular shaped filter Fl falls off the fastest, since the RIN is an

autocorrelation fiinction. Increasing the bandwidth (BW) from 1.37 nm to 3.42 nm decreases the

RIN. This agrees with the results of Table 1 in which the RIN behaves according to the inverse

of the bandwidth. For filter F3, however, much ofthe power density exists far beyond the 3 dB

points, so that the contribution to the RIN of the filter shape outweighs the BW'^ dependence.

The RIN of two additional filters (not shown) having well-behaved, symmetrical shapes also

followed a BW'^ dependence.

Figure 6.4.3 compares the RINs obtained from filter Fl when connected to EDFAl or to

EDFA2. For both combinations the RIN is very nearly constant to tens of gigahertz. The

26
difference in RIN of about 0.012 dB is very small. This demonstrates that filter shape alone does

not determine the RIN. The similar shape of the curves occurs because each arises fi"om the same

filter. The filter bandwidth is probably narrow enough to compensate for a potentially non-zero

slope of the spectral density of a typical EDFA that might occur over a wavelength interval of

several nanometers around the center wavelength of the filter. If such an effect were significant,

the RIN would not be constant.

6.5 Use of Connectors and the Effect of Losses

The net effect of disconnecting and reconnecting the RIN standard will cause a sUght

variation in the total optical power transmitted dovm the transmission line. Connections can be

made by use of either fijsion splicing or fiber connectors. Since in principle the RIN is invariant

under attenuation, the effect of using connectors will turn out to be very small. Thus, for

convenience, we chose standard, high-quality FC/PC connectors to mate all of the fiber

components composing a standard. The error due to connector mating is included in the

repeatability error (section 7.1).

6.6 Combined Effects of Attenuation, Pump Current, and Power Spectral Density Levels

If the spectral responsivity of the OSA is nonlinear, an error will occur in measuring

different OPSD levels at the same wavelength. In principle, however, the total variation in the

RIN with respect to power per bandwidth will result from the combination of a nonlinear spectral

responsivity at each sampled wavelength, and any potential effect of attenuation on the RIN itself,

however small. We must consider attenuation because the transmission of the optical spectrum

through connectors and down the fiber transmission line of the standard may be subject to some

wavelength dispersion that could, in principle, alter the RIN spectrum. Such effects should vanish

to first order, but might contribute a small but finite uncertainty to the total RIN. To determine

this error, we devised a scheme in which the RIN standard is attenuated over a wide range of

values at various pump currents. In Figure 6.6. 1, the RIN is shown over a range of attenuations

fi-om 0 db to 10 dB. The average RIN is 1.0296 • 10'^^ Hz^ (-109.87 dB/Hz) with standard

deviation of 0.0008 10''^ Hz ' (0.003 dB/Hz). To first order, this resuh determines that the RIN is

27
nearly invariant under practical attenuation strengths that may arise from component and

connector losses.

However, we must determine any potential effects of attenuation and nonlinear spectral

responsivity in aggregate. The combined uncertainty wall be assigned to represent an upper bound

for the uncertainty due to a nonlinear spectral responsivity. Thus we determined the RIM for a

variety of pump currents, attenuation levels, and intensity levels as shown in Table 2. For

example, the effect of a variable attenuation could be studied with the spectral intensity held

constant on the OSA screen by compensating the pump current. For other measurements the

intensity level was allowed to vary. Column 3 of the Table shows the intensity relative to the

maximum, which occurs at zero attenuation and maximum pump current (214 mA). Thus the

maximum intensity is represented by 0 dB, while 4 dB below the maximum appears as -4 dB.

Such varied conditions, again give nearly the same average value for the RIN, 1.0297 • 10"" Hz

(- 109.87 dB/Hz) with a standard deviation of 0.002 • 10"" Hz "^ (0.008 dB/Hz), as when the

intensity levels were allowed to vary. Figure 6.6.2 shows the variation in RIN with pump current

at zero attenuation. The average RIN is 1.0291 • 10"" Hz "^ (- 109.87 dB/Hz) and the standard

deviation is 0.0005 • 10"" Hz "' (0.002 dB/Hz). Thus the uncertainty in the RIN due to the

combined uncertainties in spectral responsivity and attenuation in aggregate is indeed small.

28
Table 2. RIN for different values of pump current, attenuation, and intensity. To determine the

efifect of a nonlinear spectral responsivity, some combinations of pump current and attenuation

were adjusted to give equal values of intensity on the OSA screen.

Pump current (mA) Attenuation (dB) Intensity relative to

maximum, (dB)

RIN (10-^2 Hz -i)

214 0 0 10.296

214 0 0 10.286

187 0 -1 10.294

148 0 -3 10.288

137 0 -4 10.298

100.5 0 -10 10.286

214 1 -1 10.286

214 3 -3 10.304

214 4 -4 10.294

214 10 -10 10.308

187 3 -4 10.308

149 1 - 4 10.288

113 3 -10 10.298

185 10 -11 10.306

186 10 -11 10.31

29
7. Total Uncertainty in REV Standard

We determined the total uncertainty in the RIN standard from the random error or

repeatability of measurements, and the contributions of the OSA parameters to the OPSD

measurement. To determine the OSA's contribution to the total uncertainty we apply the

propagation of errors formula to the numerical RIN formulas of the preceding section. The OSA

parameters that contribute significant errors are resolution bandwidth, wavelength distortion

(absolute wavelength and wavelength interval), and nonlinear spectral responsivity.

7.1 Repeatability Error

To determine the repeatability uncertainty, five measurements were repeated on several

distinct measurement occasions over the course of several weeks. (EDFA2 with Fl was

measured on eight occasions and EDFA2 with F2 was measured on four occasions.) On each

occasion, the five repeated measurements were taken within a short period of time so that the

measurements would be similar within the measurement occasion. On each occasion, the four

connectors shown in Figure 3 .1.3 were disconnected and reconnected between each of the five

measurements. The repeatability uncertainty was computed as outlined in the ISO Guide to the

Expression of Uncertainty [21]. The average RIN for the five measurements on a given day is

<RIN,> = (7.1.1)

For a series of days, the average RIN is

<RIN> = ^"til^N . (7.1.2)

d-5 i=i ,=1

where d is the number of measurement occasions or days. Thus the repeatability uncertainty is

30
^ {<RIN>-<RIN>f

(7.1.3)

REP \U did -I)

Figure 7.1.1 shows that the variance of the RIN with connector mating over the three week

period is indeed very small. It is 0.002 dB and 0.005 dB for EDFA2 with filters Fl and F2,

respectively.

7.2 Measurement Error From the OSA Parameters

In section 6.6 we showed that the combined errors which may arise from nonlinearity in the

spectral responsivity, and any potential effects of attenuation, could be grouped into a single error

representing an upper bound for the responsivity alone. To determine this upper bound, we

varied the attenuation under constant pump current so that the spectral density level on the OSA

screen varied in direct proportion to the attenuation. We computed the standard deviation of the

RIN values obtained at the six attenuation levels, 0 dB, 3 dB, 6 dB, 9 dB, 1 1 dB, and 1 5 dB, from

the following formula.

without disconnecting or reconnecting any of the fiber components. For filters Fl and F2, the

uncertainties are 0.005 dB and 0.008 dB, respectively. For example, for Fl the uncertainty in the

RIN due to a nonlinear spectral responsivity has an upper bound of 0.005 dB, which will be used

to estimate the total uncertainty in the RIN.

The uncertainty in RIN due to wavelength distortion was determined by applying the

propagation-of-errors formula to eq (4.2.7) with AA = (Ajooi - Ai)/1000 and average wavelength

error of 0.042 nm as determined from the 21 data points of Figures 5.2.1 and 5.2.2. The

6 (RIN-<RIN>f

(7.1.4)

31
resulting uncertainty is

J 4008004

, (^1001 ~

-^i)"

(7.1.5)

where ( )^ioo\) = (Aj) = (0.042 nm)^, and j = 1,2,.... n, where n is the number of data points.

Since U;^ is different for each RIN measurement, the U;,^ used to compute the combined

uncertainty is based on the maximum U;^^ computed for the RIN measurements for a given filter. The resulting uncertainties are 0.051 dB and 0.017 dB for filters Fl and F2, respectively.

The uncertainty due to variation in resolution bandwidth, U^^, was computed by applying

the propagation of errors to eq (4.2.5). The propagation-of-errors formula takes the form

RBW

\

^ dRIN ^ dRIN ^ + +^ dRIN Y

dB a )

var(B„(XJ)

(7.1.6)

But since var(Bj (XJ) - = var(Bj,(AJ = var(B(A)) , we have

RBW

dRIN

dB{X)

var{B{X)) (7.1.7)

Performing the differentiation gives

32
U^^ = \jAB -^[B^C-2BDE^D^ F) var(B{X)) , (7.1.8)

where

A =

B =

C =

F =

4-2^

(AA)2

J w

y^ /

(7.1.9)

Resolution bandwidth was shown to be very nearly constant within the wavelength range of

interest, so that the computations were performed at each wavelength using Bj(Aj) = 0.045 nm,

with var(B(A)) = 0.001 nm as determined from the noise-equivalent bandwidth. The value of

Urbw used to compute the combined uncertainty is the worst-case value of Urb^ calculated

among the RIN measurements for a given filter. These uncertainties are 0.002 dB and 0.006 dB

for filters Fl and F2, respectively. The specific and combined standard uncertainties are shown in

Table 3 for each filter.

33
7.3 Combined Standard Uncertainty

The RTN of the standard is the average of all RIN measurements used to compute U^. For

filter Fl with 40 observations <RIN> = 1.0325 -10 ''* Hz'\ To compute the combined standard

uncertainty of the average RIN, u^, the four uncertainty estimates described in sections 7. 1 and

7.2, Ur£p, Ulin, U;,^, and U^^ff, are added in quadrature. Since all four sources of uncertainty use

measured data to compute their values (as opposed to manufacturer's specifications, for

example), they are all considered Type A uncertainties. (There are no significant Type B

uncertainties.) Although different amplifiers were used to quantify Urep and 11^^, this should not

influence the uncertainty estimates.

The expanded uncertainty, U, is twice the combined standard uncertainty (U = 2uX which

represents an approximate 95 % confidence interval for the average RIN [22]. The combined

standard uncertainty and expanded uncertainty for filters Fl and F2 are shown in Table 3. For Fl,

the combined standard uncertainty ( 0.014475 • 10"*^ Hz"^) is 1.4 % of the average RIN (1.0325 •

10'^' Hz"'). The average RIN for filter F2, <RIN> = 6.3712 • 10 ''^ Hz -\ was based on 20

observations used to compute Urep- The combined standard uncertainty (0.053564 • 10"^^ Hz"') is

0.84 % of the average RIN.

34
Table 3: Combined standard uncertainty in the RIN of the standard (EDFA2 with filters Fl and

F2).

EDFA2 + Fl Uncertainty Standard uncertainty Standard uncertainty

type (A or B) in 1/Hz in dB

Urep A 0.000561 • 10"'^ 0.002

A 0.001180 • 10-'' 0.005

A 0.012315 • 10-" 0.051

TT A 0 00041 Q • 1 0"^^ 0 00?

Combined, 0.014475 • 10"" 0.06

Expanded, U 0.029 • 10 0.12

EDFA2 + F2

UrFP A 0.0068325 • 10-^2 0.005

A 0.011804 • 10"^^ 0.008

A 0.025354 • 10-'- 0.017

A 0.009581 • 10-^2 0.006

Combined, u,. 0.053564 • 10-^2 0.036

Expanded, U 0.10713 • 10"'^ 0.072

8. Achieving the Poisson Limit

For an optical field at wavelength X and optical power the Poisson RIN is

^pi^) ^ ^ " constant , (g j)

where c is the speed of Ught and h is Planck's constant. To achieve the Poisson limit we recall that

any optical source can be rendered Poisson-limited by sufficient attenuation [23]. This occurs

because the Poisson RIN increases with attenuation while the excess RIN remains invariant. Thus

for applications of low-power lasers, the Poisson limit may be usefijl if the excess RIN is very

small and there is sufficient optical power available after attenuation to meet the power

requirements. However, the true Poisson limit is reached when the ratio of excess to Poisson RIN

35
approaches zero. A Poisson-limited source oflfers two distinct advantages over that of a low-excess-RIN

source. First, the Poisson RTN is manifest in the electrical detection circuit as the simple quantity

2q/i. Second, the calibration of a RIN system can be performed w^ith a Poisson-limited laser

without knowing the RIN explicitly, as will be shown in the following section. To establish a RIN

standard, we need not achieve the true Poisson limit, but require only that the ratio of excess to

Poisson RIN be small. Through attenuation we constrain this ratio to fall within some fixed value,

and thus limit the error it contributes to a RIN system calibration.

8.1 The DFB Laser of the Secondary Method Has Nearly Poisson-Limited REV

In this section we apply eq (8 . 1) to a series of RIN measurements under attenuation to show

that the RIN of our laser is nearly Poisson-limited, and contributes only a very small error in the

calibration of our RIN measurement system. Calibration of the RIN system yields a fi^equencydependent calibration flinction that we call Kappa. Kappa is a dimensionless quantity (precisely

defined in section 9) whose magnitude is not required for the present analysis. To proceed, we

first compare graphs of Kappa obtained fi^om measurements using the DFB laser at several

attenuation levels for which optical power ranged fi-om one half mW to 7 mW. Figures 8.1.1 and

8. 1 .2 show the fi^equency dependence of Kappa for the various attenuation levels. In Figure 8.1.1

the levels are 10, 12, and 15 dB based on a single sweep of the ESA. In Figure 8.1.2 the levels

are 10, 13, and 16 dB, with each curve obtained fi-om an average of nine sweeps. This gives a

smaller spread in the data. The data overlap for aU but the 10 dB curve in Figure 8. 1 .2, which sits

sUghtly below its neighbors. Thus the overlap of the 15 and 12 dB levels, and the 16 and 13 dB

levels, indicates that the RIN should be very close to the Poisson limit over the entire bandwidth.

At 10 dB, however, the optical power is considerably greater, the Poisson RIN smaller, so that

the ratio of excess to Poisson RIN may be too large to have achieved the Poisson hmit Since all

calibrations made with the laser are at 17 dB attenuation, this result for the Poisson limit should

still hold.

Figure 8.1.3 shows the rf-noise power (in arbitrary units) at 400 MHZ plotted versus dc

voltage. Since Poisson noise power manifests in the electrical detection circuit as 2qV (where q is

36
electron charge and V is voltage), the data should yield a straight line [24]. (The noise power is 2qVAB, which is 2qV in a IHz bandwidth.) The voltage values range from 9.39 to 23.66 mV,

with corresponding attenuations from 18 to 14 dB. The first curve is a second-order polynomial

fitted to all data points. The second curve is a linear fit of all points except V = 23 .66 mV (which

corresponds to only 12 dB attenuation). The two curves rapidly converge to a straight line with

increasing attenuation (decreasing voltage). At a voltage of 1 1 .82 mV, where the attenuation is

17 dB, the curves are straight lines. This is the normal operating regime for this standard. A

second-order polynomial fit of all points except V = 23 .66 mV yields a coefficient of very nearly

zero (slightly negative) for the second-order term. Thus the excess RIN component is too small

to resolve.

A simple argument can be given that further supports our results, and is based on the

manufacturer's specification of the excess RIN (<- 172 dB/Hz at the operating current of 169.44

mA, where power output is 27.82 mW). At this current and 17 dB attenuation, accounting for all

losses, the optical power incident on the detector is 0.275 mW. Since the Poisson RIN in the

photodetector circuit increases by l/r|, where r| = 0.77 is the detector quantum efiSciency, the

equivalent Poisson RIN at an optical power of 0.212 mW from eq (8.1) is - 149.2 dB/Hz. Since

the excess RIN remains < - 172 dB/Hz, the ratio of excess to Poisson RIN would be < 0.005

(<0.022 dB).

9. RIN System Calibration Using the Standard and the Laser

To validate the RIN standard and associated MAP, we developed two distinct methods, each

of which uses a precision RIN source, to separately calibrate our RIN measurement system. We

evaluate both methods by comparing calibration results. Because the photon number distributions

differ for the two methods, so too will their calibration functions. By formulating the optical RIN

of each source before it enters the RIN system and the electrical RIN measurement inside, we

derive an equation that relates the response of the system to the two sources. First, we note a

pair of simplifying distinctions between the methods. For the standard, we can consider the

amplitude fluctuations to be of purely second order, that is, devoid of Poisson light, as this

37
component is much smaller than the EDFA's amplified spontaneous emission. For the DFB laser,

the RJN can be considered purely Poisson, as shown previously. Figure 9. 1 demonstrates how

each method is applied separately to the RIN measurement system.

9.1 Derivation of the Calibration Equations For the Standard and Secondary Methods

In this section we derive the calibration equations (Kappas, or fi^equency-dependent

calibration fianctions) that govern the response of our RIN system to the input RIN of the

standard and the Poisson laser. Let 6P3 and 6Pp be the rf noise measured on the ESA fi^om the

EDFA + F and the laser, and P^ ,P„ the corresponding electrical dc powers, respectively. Let R3

be the RIN calculated fi-om the optical spectrum of the EDFA + F as measured on the OSA, and

K3(a)) and Kp(a)) the system calibration fiinctions fi-om the EDFA + F and the laser, respectively.

Then for the EDFA + F we must have

constant . (9.1.1)

Solving for gives

(9.1.2)

For the laser.

R - K (co)

p

' constant , (9.1.3) P IP

P o

so that

38
, . 2hc Pp

o P

where Ihc/XP^ is the Poisson RIN of the laser.

9.2 Equivalence of the Calibration Functions

To derive an exact expression equating the calibration fiinctions we note that the Poisson RIN

of the laser increases in the electrical detection circuit by an amount l/rj. Therefore an equivalent

optical RIN for the laser that would yield a Kappa equivalent to that for the standard, with all

other conditions kept constant, is

R 6P (w)

-^ = K/a))-— (9.2.1)

I n

where now = Kp Solving for Kp gives

R -P

= ' / ,

• (9.2.2)

The photocurrent in the electrical circuit is i = pP^ ^ r|qP/hv, where h is Planck's constant, q is

the electron charge, and p and r| are the responsivity and quantum efficiency of the photodetector,

respectively. The dc voltage is V = ir, where r is resistance. Substituting these expressions for

current and eq (9. 1.3) for the Poisson RIN, the quantum efficiency cancels and we obtain

, X 2qV

K (w) = —-— . 7

39
Therefore,

, . ^a'^a 2qV

where we dropped the subscripts on Kappa. From this analysis it is clear that Kp can be

determined without knowledge of the laser RIN or the quantum efficiency of the photodetector

(measured at 0.77 at the operating wavelength of 1555.9 nm). Note that the variation of Kappa

with frequency for either method is directly proportion to the frequency response of the RIN

system. As such, either method might be used to measure the frequency response of high-speed

photoreceivers. In the next section we use these results to compare the calibration functions

obtained fi"om actual calibrations of our RIN measurement system.

10. Two Methods Applied to the NIST RIN System Give Similar Results

To evaluate the accuracy of the RIN standard we used it to calibrate our rf (electrical) RIN

measurement system, and compared the results v^th those obtained using the laser. Such a

comparison should help determine the validity of the RIN standard with respect to the secondary

method, in that each method, when applied separately to the RIN system, should yield similar

results. From this we can predict how a typical RIN system will respond to the RIN standard, and

how well the results agree with any conclusions dravm about either method separately. It should

also provide a framework for comparing the statistical uncertainties obtained from each method.

10.1 Quantitative Comparison of Calibration Results from the Two Methods

Since we seek to establish a MAP that allows replacement of various components composing

the standard and the RIN system, we performed calibrations using a variety of components for the

standard, and compared results. Among these are the six combinations that arise from the two

EDFAs and the three filters discussed previously (section 6.4). Use of a single Poisson-Umited

laser for the secondary method is justified because the theory and measurement of Poisson light

40
are well established, so that we need only determine that the laser's RIN obeys Poisson statistics. To compare the standard with the laser we used eq (9.24), which equates their cahbration

functions.

First we obtained Kappa for the three filters of different shape and bandwidth using EDFA2.

The results are shown in Figure 10. 1 . 1 for bandwidths of 1 .32, 1.37, and 3.42 nm. The shape and

overlap of the three curves confirms that our calculation of the RIN scales with filter bandwidth

and shape as expected from theory. The similarity in all three Kappas indicates that calibration of

the RIN system is independent of the magnitude of the RIN and the shape of the filter. Next we

compared the laser with filter F2 using both EDFAl and EDFA2. The resuhs shown in Figure

10.1.2 are again similar. Note that measurements were taken sequentially in the shortest time

reasonable to duplicate experimental conditions. When a set of calibrations was performed using

different EDFAs, a matching set was performed with the laser, reinforcing the comparison of the

two methods.

To quantify the calibration results as a comparison of methods between the laser and

combinations of different components intended to compose a valid standard, we determined the

simple average of the difference between Kappas recorded at each frequency over the spectrum.

Let and Kp j represent Kappa of the standard and the laser at the ith fi^equency ^, respectively,

and is the difference between Kappas, Dj = K^j - Kp^ . Then the average difference, Z, is

obtained by summing over the 601 points in a spectrum.

Figure 10.1.3 shows a typical distribution of differences obtained for the standard (EDFAl + F2)

and the laser. The differences range fi"om - 1 to +1 dB, with an average difference of 0.058 dB.

The standard deviation of the differences is 0.3 dB, which illustrates the rather large fluctuations

that are characteristic of such rf noise spectra.

In Table 4 we compare calibration results from the laser with various combinations of

(10.1.1)

601 601

41
components that could form a valid standard. The sources compared are listed in column 1 along

with the date of the experiment. The first and second numbers in column 2 represent the average

difference of the Kappas without and with the ESA scale fidelity correction (SFC), respectively

(see Appendix A). Column 3 shows the standard deviation ofthe average differences of column

2, again, without and with the scale fidelity correction. We list some of the comparisons and their

meanings. Kappa from each of the two amplifiers was determined using all three filters, Fl, F2,

and F3, and compared with Kappa from the laser on different days. Thus we might compare

Kappa of EDFA 1+ Fl with Kappa of DFB (experiment of April 27). We also compare Kappa

among various combinations of EDFAs and filters. Thus we compare EDFAl + F2 with EDFA2

+ F2 (experiment of April 20), EDFAl + Fl with EDFAl + F2 (April 29) , and the laser at two

different times: DFB(2) with DFB(3) (experiment of April 13). The behavior for all comparisons

is very similar, with the smallest variation occurring for two different EDFAs using the same filter

(April 23), or the laser with itself (April 23).

We performed a number of comparisons using EDFAl and EDFA2 with all three filters

in which we calculated the average of the average difference of the two Kappas compared. For

example, we compared each EDFA + filter with the other EDFA using the same filter. We also

compared the laser with different combinations of EDFAs and filters. The results show good

agreement at all frequencies when averaged. The average differences between single data sets, as shown in Table 4, are quite small.

42
Table 4. Comparison of the standard with the Poisson laser; other similar comparisons.

Combinations of sources and filters compared

Z(eq 10.1.1), in dB

without, with SCF

Standard deviations of the

differences, D, in dB.

without, with SCF

jiilyy, rZ only

EDFAl + F2 with EDFA2 + F2 0.077, 0.049 0.337, 0.355

EDFAl + F2 with DFB 0.091, 0.108 0.301, 0.311

EDFA2 + F2 with DFB 0.013, 0.082 0.343, 0.359

4/29/99; Fl and F2

EDFAl + F2 with EDFA2 + F2 -0.041, -0.107 0.356, 0.372

EDFAl + F2 with DFB(2) 0.143, 0.161 0.305, 0.316

EDFA2 + F2 with DFB(2) 0.184, 0.268 0.34, 0.358

EDFAl + Fl with EDFA2 + Fl -0.043, -0.054 0.212, 0.215

EDFAl +F1 with DFB(l) 0.142, 0.064 0.246, 0.249

J_(JL/r/Tu6 ~ r 1 Willi LJrDx^l J 0.185, 0.118 0.251, 0.254

EDFAl + Fl with EDFAl + F2 0.11 0.279

EDFA2 + Fl with EDFA2 + F2 0.112 0.314

DFB(l) and DFB(2) 0.112 0.295

4/z //yy, r 1 only

EDFAl + Fl with EDFA2 + Fl 0.088, 0.079 0.211, 0.214

EDFAl + Fl with DFB 0.12, 0.042 0.255, 0.258

EDFA2 + Fl with DFB 0.033, -0.036 0.246, 0.25

4/23/99; Fl and F3

EDFAl + F3 with EDFA2 + F3 - 0.0066, -0.036 0.292, 0.30

EDFAl + F3 with DFB(3) n 1 AQ u.zy 1, EDFA2 + F3 with DFB(3) 0.115, 0.13 0.301, 0.311

EDFAl + Fl with EDFA2 + Fl 0.041, 0.041 0.195, 0.198

EDFAl +F1 withDFB(l) 0.188, 0.113 0.245, 0.248

EDFA2 + Fl with DFB(l) 0.146, 0.071 0.246, 0.249

EDFAl + Fl with EDFAl + F3 0.074 0.232

EDFA2 + Fl with EDFA2 + F3 0.025 0.252

DFB(l)and DFB(3) 0.0061 0.285

43
Combinations of sources and filters compared

Z(eq 10.1.1), in dB

without, with SCF

Standard deviations of the

differences, D, in dB.

without, with SCF

zl/9n/QQ- F9 r»nK7 EDFAl + F2 with EDFA2 + F2 -0.095, -0.202 0.31, 0.327

EDFAl + F2 with DFB -0.111, -0.147 0.286, 0.292

EDFA2 + F2 with DFB W.W ID, \) .\)\) It- 0U. '\A'\J, \J.JJJ

T'/ lyi yy, rj uiiiy

EDFAl + F3 with EDFA2 + F3 -0.015, -0.049 0.263, 0.21

EDFAl + F3 with DFB 0.132, 0.103 0.263, 0.269

EDFA2 + F3 with DFB A 1 Al U.l4/, n 1 ^9 A 97 A 97Q

H/ 1 D/ yy, jc 1 oiuy

EDFAl + Fl with EDFA2 + Fl 0.012, -0.108 0.157, 0.164

EDFAl +F1 with DFB 0.08, -0.001328 0.186, 0.188

EDFA2 + F1 with DFB 0.068 0.000864 0.188, 0.191

H/ 1 j/yy, rz, diiu vj

FFiFAl CyUrrxl +^ F9rz, -nnth Willi FFiFA? HUrrW. +~ F9rZ. -0.028, -0.074 0.331, 0.349

Fr»F A 1 + F9 -vx/itVi riFR/'9^ 0.053, 0.058 0.293, 0.302

FDFA9 curr\uL +< F9r jL with Willi urnFR/'9^ oyi.

)

0.08, 0.143 0.334, 0.35

FFIFAI + F'? An/itli Fr>F A9 + F'i iliiJr iW. ~ C J Willi CiJr r\A ~ T J -0.0042, -0.056 0.286, 0.295

FFiF A 1 4- F"? «7itli riFR/"?\ 0.103, 0.076 0.265, 0.271

FDFA9 + F^ wnth DFR/"^^ 0.099, 0.131 0.29, 0.301

EDFAl + F2 with EDFAl + F3 0.105 0.268 0.333

EDFA2 + F2 with EDFA2 + F3 0.073 0.28

DFB(2) and DFB(3) 0.051

44
Table 5. Relative stability of EDFAl and EDFA2 with respect to the Poisson laser.

Average of the Z's (dB) Average of standard

deviations (dB)

EDFAl + with DFB

EDFA2 + F^ with DFB

0.088

0.103

0.046

0.077

10.2 Relative Stability of Two Different EDFAs With Respect to the Poisson Laser

From the data in Table 4, we can compare the accuracy and relative stability of EDFAl and

EDFA2 with respect to the Poisson laser. The averages for each EDFA were made over all

comparisons with the laser. Specifically, we found the average of the average difference of

Kappas for a specific EDFA with any of the three filters as compared with the corresponding

Kappa fi^om the DFB laser. A comparison of EDFAl with laser will have the following entries

fi-om Table 4 - column 2, for computing this average; EDFAl + F2 with DFB (5/3, 4/29, 4/20),

EDFAl + Fl with DFB (4/29, 4/27, 4/23), EDFAl + F3 with (4/23, 4/19, 4/13). Similar entries

occur for comparisons of EDFA2 with the laser. We used the second set of numbers in column 2,

which accounts for the ESA scale fidelity correction. The results are shown in Table 5, where F^

represents filters Fl, F2, and F3. EDFAl is slightly more stable, with an average of 0.088 dB,

while EDFA2 (the standard) has an average of 0. 103 dB. These averages disagree by 0.015 dB,

which is quite small. Recall that we chose EDFA2 for the standard because of its semi-ruggedness

and ease of use. We note that in determining Kappa the ESA's noise floor is subtracted. This is an arbitrary

procedure because the noise floor, which is averaged in the measurement process, is the same for

both the standard and the laser. Of importance is that we be consistent in how we define the RIN

system's response to the standard and the laser.

10.3 Methods Compare Favorably Under Use of Variance Analysis

As was shown in section 9.2 above. Kappa fi^om the laser can be precisely determined without

explicit knowledge of the laser's RIN. Thus we can compare calibration results from the standard

45
and the laser by measuring their calibration functions. Our main objective in this section is to

verify that the variations in their calibration functions are similar. Again, all calibrations are

performed using the NIST RIN measurement system.

During a one-day period, we determined Kappa using both the standard and the laser as a pair

of sequential measurement sets taken in the least time possible (~2 min); this is the time needed

to store the data for the standard, disconnect the standard, connect the laser, and collect the new

data. This insures nearly identical environmental conditions (such as temperature and background

rf fields) for the two methods. Stray rf signals can appear unpredictably in a data spectrum, for

example from mobile telephone sources, and their magnitude may vary during the time of a

measurement. They must be averaged out by manual inspection of the data. (The ESA data are

averaged from nine sweeps, which takes about 20 s).

Figures 10.3.1, 10.3.2, and 10.3.3 show the data from four different days for Kappa of

EDFAl + Fl, EDFA2 + Fl, and the laser, respectively. The different symbols represent the four

measurement occasions. The distribution of Kappa with frequency is fairly repeatable within each

method, and follows a similar pattern when comparing methods. Figure 10.3.4 compares the

average value of Kappa for EDFAl + Fl with that of the laser, where the Kappas at each

frequency are the calculated averages of the same four data points from Figures 10.3. 1 and

10.3.3. Figure 10.3.5 compares the average value of Kappa for EDFA2 + F1 with that of the

laser, where the Kappas at each frequency are the calculated averages of the same four data points

from Figures 10.3.2 and 10.3.3. Kappa for the laser is slightly lower than that of either EDFA

using Fl.

To assess the variation in Kappa for both methods, we calculated the normalized standard

deviation of the four observations at each frequency. Scatter plots of the data are shown in

Figures 10.3.6 and 10.3 .7 for the laser compared with EDFAl + Fl and EDFA2 + Fl,

respectively. The data indicate that the two independent methods give similar standard deviations

over the entire frequency range, indicating that they are comparable.

10.4 F-ratio Test Yields Similarity in the Variability of the Calibration Functions

We performed a statistical F-test to compare the variability in Kappa between the two

46
methods. This test computes the ratio of the variances for the two methods and compares this

ratio to critical values from an F-table [25]. To apply the test we define the ratio

(10.4.1)

where Sl"^ and S^^ are the sample variances for Kappa of the laser and standard, respectively. If

the variances obtained from the two methods are very similar, then F wiU not be too large or too

small. Specifically, if F is greater than the 100( 1- a/2)* percentile of the F distribution, or less

than the 100(a/2)''' percentile, the variances will be considered significantly different. The value,

"a," is the probability of incorrectly concluding that the variation in Kappa for the two methods is

different. Usually "a" is a small number since we want the probability of making an error to be

small. The critical values from the F table are Fj . ^ / j: 3. 3 and F^ / 2: 3, 3, where the values 3 and 3 are

the respective degrees of freedom for Sl"^ and S^^. If a = 0.05, then the critical values are Fq 975.

= 15.44 and Fo.25:3,3 = 0.07.

To compare methods, we apply the F-ratio test at each frequency. Because the sample sizes

are identical for each method, the critical values are the same for each test. Figure 10.4.1 shows

the distribution of F-ratios with frequency by comparing the laser with EDFAl + Fl . The two

horizontal reference lines on the plot represent the critical values for the F test when a = 0.05.

The majority of the F ratios lie within the critical values, indicating that the two variances are not

statistically different. The F tests at each frequency confirm that the variation in Kappa is similar

for the two methods studied.

We repeated the F-test using EDFA 2 + Fl . The results shown in Figure 10.4.2 are

equivalent to those obtained for EDFAl, again confirming that the variation in Kappa is similar

for the two methods. We expect such good agreement because the RIN of both the laser and the

standard (using either EDFA) are both known and constant over the entire frequency band, and

the relationship between their Kappas was precisely determined from physical laws.

47
11. Maintaining a Measurement Assurance Program

11.1 Maintaining the RIN Standard

To insure the accuracy and stability of the RIN standard with time, the RIN will be determined

before it is sent to a customer, and again when it is returned. The customer will need only to

connect and disconnect the component chain at a single connector. However, because the

standard must be accurate and valid under substitution of different components, we will perform

any necessary measurements to account for disconnection and reconnection of the components as deemed relevant for its upkeep. Thus a reference database will be kept to evaluate the long-term

accuracy and stability ofthe standard.

For example, we began this database by performing a study using EDFA2 with filters Fl and

F2. Eight sets of RIN measurements were taken on seven different days over the course of

several weeks, each set composed of five repeated measurements. Filter Fl was measured on

eight occasions, while filter F2 was measured on four occasions. The five repeated measurements

were taken within a short period of time so that they would be similar within the measurement

occasion. On each occasion the four connectors shown in Figure 3.1.3 were disconnected and

reconnected between each of the five measurements. This relatively small data set, shown in

Figure 7. 1. 1, fails to indicate the presence of a long-term trend. However, the variability within a

day's measurements appears to be decreasing. Additional measurements will be required to

monitor the performance of the standard, and validate its long term stability.

11.2 Substitution of Components

Since components composing the standard and the NIST RIN measurement system, such as

the EDFA or the ESA, respectively, can fail and need replacement, it is our intention that this

MAP be vaUdated to account for such changes. We believe that the net effect of any required

changes in components has been accounted for based on our thorough development of the theory

and the precision with which the measurements were performed. Because both the RIN of the

standard as well as the Poisson-limited laser are constant in ft^equency out to tens of gigahertz,

this MAP should be extendable to such higher fi-equencies with little or no additional certification.

48
Also, since the intensity noise of the Poisson-limited laser is predictable and stable, and its RIN is

well known and historically accurate, it too can be considered a RIN standard. However,

because it is not as field employable, it is most usefiil as a laboratory standard

We are especially grateful to Wayne Itano for carefully verifying the mathematical expressions

for the RIN of thermal light. We thank the Electronics and Electrical Engineering (EEEL)

Measurement Committee, Richard Jones (chairman), John Kitching, and Wayne Itano for

evaluating various scientific and technical aspects of the manuscript. The first author thanks Paul

Hale for many stimulating discussions related to this work, and for his general interest in the

subject matter. Jack Dupre of Agilent Technologies provided insight on calibration methods for

optical spectrum analyzers. Jack Wang discussed statistical tests for comparing two independent

methods.

49
12. References

[1] Agrawal, G.P.; Dutta, N.K. Semiconductor Lasers. New York: Van Nostrand Reinhold; pp.

258-269; 1993. y

[2] Obarski, G.E.; Jones, R.D. Relative Intensity Noise Correlates with Beam Profile in an LPl 1 Mode Vertical-Cavity Surface-Emitting Laser, in Conference on Lasers and Electro-Optics, Vol.

1 1, 1997 OSA Technical Digest Series, Washington, D.C.: Optical Society of America, pp. 228-

229, 1997.

[3] Coldren, L.A.; Corzine, S.W. Diode Lasers and Photonic Integrated Circuits. New York:

John Wiley; pp. 221-236; 1995.

[4] Petermann, K. Laser Diode Modulation and Noise. Norwell, Massachusetts: Kluwer

Academic PubUshers; pp. 157-160; 1991.

[5] Agrawal, G.P. Fiber-Optic Communication Systems. New York: John Wiley; pp. 217, 306;

1992.

[6] Saleh, BE.A.; Teich, M.C. Fundamentals ofPhotonics. New York: John Wiley; pp. 405,

489; 1991.

[7] Goodman, J.W. Statistical Optics. New York: John Wiley; pp. 472-477; 1985.

[8] Yariv, A. Optical Electronics in Modem Communications. New York: Oxford University

Press; pp. 449-454, 703-722; 1997.

[9] Obarski, G.E.; Hale, P.D. How to Measure Relative Intensity Noise in Lasers. Laser Focus

World, pp. 273-277; May 1999.

50
[10] Becker, PC; Olsson, N.A.; Simpson, J R. Erbium-Doped Fiber Amplifiers—Fundamentals

and Technology. New York; Academic Press, pp. 258-263, 1999.

[11] Willems, F.W.; Van der Plaats, J.C. Optical Amplifier Noise Figure Determination by Signal

RIN Subtraction, in Technical Digest—Symposium on Optical Fiber Measurements, Day, G.W.;

Franzen, D.L.; Hickemell, R.K., eds. NIST Special Publication 864, pp. 7-9, Sept 1994.

[12] Willems, F.W.; Van der Plaats, J.C. Experimental Demonstration of Noise Figure Reduction

Caused by Nonlinear Photon Statistics of Saturated EDFAs. IEEE Photonics Technology

Letters, Vol. 7, No. 5, pp. 488-490, May 1995.

[13] Movassaghi, M.; Jackson, M.K.; Smith, V.M.; Hallum, W.J. Noise Figure of ErbiumDoped Fiber Amplifiers in Saturated Operation. Journal ofLightwave Technology, Vol. 16, No.

5, pp. 812-817, May 1998.

[14] Movassaghi, M.; Jackson, M.K.; Smith, V.M.; Young, J.F.; Hallum, W.J. Accurate

Frequency Resolved Measurement of EDFA Noise Figure. Optical Amplifier Conference Digest;

British Coulumbia; paper # TuDl-1; pp. 130-133; July 1997.

[15] Baney, D.M.; Sorin, W.V.; Newton, S.A. High-Frequency Photodiode Characterization

Using a Filtered Intensity Noise Technique. IEEE Photonics Technology Letters, Vol. 6, No. 10,

p. 1258; October 1994.

[16] Baney, D.; Sorin, W. Broadband Frequency Characterization of Optical Receivers Using

Intensity Noise. Hewlett-Packard Journal, pp. 6-12, February 1995.

[17] Mandel, L.; Wolf, E. Optical Coherence and Quantum Optics. New York: Cambridge

University Press; 1995.

51
[18] Private discussions with L. Mandel; June, 1999. Mandel acknowledges an error of a factor

of two in eq (9.8 .26) oftheir text; see reference 17. The factor of Vz in front of the middle

integral should be removed.

[19] Mandel, L. Fluctuations of Light Beams. Progress in Optics, Vol. 2, Wolf, E., ed. New

York: North-Holland Publishing Company—Amsterdam; p. 200; 1963.

[20] Private conversation with A. Girard. EXFO Fiber Optic Test Equipment Corp.; January

1999.

[21] Guide to the Expression of Uncertainty in Measurement. Section H-5: Analysis of Variance;

International Organization for Standardization, pp. 85-87; 1993.

[22] Taylor B.N.; Kuyatt, C.E. Guidelinesfor Evaluating and Expressing the Uncertainty of

NISTMeasurement Results. NIST Technical Note 1297; 1994.

[23] Machida, S .; Yamamoto, Y. Quantum-Limited Operation of Balanced Mixer Homodyne and

Heterodyne Receivers. IEEE Journal ofQuantum Electronics, Vol. QE-22, No. 5, p. 617-624;

May 1986.

[24] Cox, M.C.; Copener, N.J.; Williams, B. High sensitivity precision relative intensity noise

calibration standard using low noise reference laser source. lEE Proceedings, Science cmd

Measurement Technology, Vol. 145, No. 4, pp. 163-165, July 1998.

[25] Box, G.E.P.; Hunter, W.G.; Hunter, J.S. Statisticsfor Experimenters. New York: John

Wiley; pp. 117-123; 1978.

52
Appendix A. Calibration of the Electrical Spectrum Analyzer; Scale Fidelity Correction

A complete calibration of the rf spectrum analyzer is not necessary because all but one

fimction setting that contributes to a measurement is included in Kappa. Not included, however,

is a scale fidelity factor that accounts for the vertical position of the noise signal on the screen of

the ESA. RIN measurements made for which the rf amplitude noise has different magnitudes

must account for this factor. Like Kappa, this factor also has a frequency dependence.

We computed the scale fidelity factor for our ESA using the procedure illustrated in Figure

Al . An rf signal generator was set at a predetermined power level with oscillation frequency of

500 MHZ. The power was precisely measured with an rf power meter. A 10 dB attenuator was

then inserted into the transmission line and the power recorded, yielding a magnitude of 10 dB for

the attenuation. This procedure of measuring the power with and v^thout the attenuator was then

applied to the electrical spectrum analyzer. Connector losses were carefijUy accounted for, and

control settings were the same as for the RIN measurements, including the position of the signal

on the screen. The vertical scale was set at 5 dB per vertical division. Measurement of the rf

signal vsath and without the 10 dB attenuator occurred at a vertical separation of 9.67 dBm on the

screen. Thus for one division on the screen, the uncertainty in noise power due to the scale

fidelity was (10 - 9.1)12 = 0. 15 dB. (The manufacturer's specification for the ESA is that the

amplitude error can be no greater than 0.7 dB over the 10 divisions that compose the screen.)

Note that the uncertainty in ESA resolution bandwidth (RBW) is included in the calibration

fiinction; thus it need not be determined separately. Ofprime importance, however, is that a

calibration holds true only for a given group of ESA sweep control settings, such as RBW, sweep

time, internal attenuation, etc. Our calibration method neglects only error due to the vertical scale

reading, or scale fidelity factor. A number of calibrations performed at different settings of RBW

or sweep time etc. would give calibration curves of slightly different magnitude, but similar shape

at each setting.

We now determine a scale fidelity correction for comparing signals of varying magnitude,

such as occurs for Kappa from the amplifier compared with Kappa from the laser (see section 9.2

and eq (10. 1 . 1)). The direction of this correction, which is applied at each frequency separately,

is to expand the difference between the two noise powers on the screen. If the difference

between noise powers is 6Pi - 8P2 (at the same frequency) and S is the correction, then

^1 - bP^ +0.03-(6Pj- 5P2)

(Al)

53
The corrected Kappa at each frequency is

K

l.un 1

I.cor 6Pj +0.03-(6Pj-

(A.2)

where the subscripts cor and un represent the corrected and uncorrected Kappas, respectively.

This is a most general formula, in which SPj can be greater or less than 5P2. If it is greater, the

corrected Kappa increases. If it is less, the corrected Kappa decreases.

Appendix B. Addition of REV

Although RIN is often represented in logarithmic units, it must be added directly in linear

units. A good example is the subtraction of Poisson RIN from total RIN to yield excess RIN. If

these quantities are specified in logarithmic units, each must be converted to linear numbers, then

the subtraction performed. The resulting real number can be converted back to logarithmic form.

Recall that the RIN is defined as the sum of the Poisson and the excess RIN (sections 2. 1, 2.3).

Then a laser emitting 0.5 mW optical power (which has Poisson RIN of - 153 dB/Hz) and having

a RIN of - 152.2 dB/Hz) will have an excess RIN of - 160 dB/Hz. But 10 mW of optical power

(- 166 dB/Hz of Poisson RIN) with the same excess RIN will have a RIN of - 159 dB/Hz.

Appendix C. Information for Applying the RIN Standard

A calibration should be performed with the user's electrical spectrum analyzer in a fixed state of fijnction settings. If a setting is changed to accommodate a noise spectrum of different

magnitude, a new calibration curve must be obtained for the appropriate conditions.

As an example, we give some information on the ESA used in the NIST RIN system. Scale

fidelity can add an uncertainty of 0.075 dB per vertical division, and which requires that we shift the calibration curve down by this amount. Thus measuring the RIN of two lasers of noise spectra

three divisions apart on the screen, would result in an uncertainty in their calibration curves that

would shift them apart by up to 0.225 dB. But changing reference levels so that the second

spectra would fall at the same vertical position on the screen would add an even greater

uncertainty of 1 dB for our ESA. Changing RBW settings would add an error of 0.5 dB.

54
Appendix D: Sample MAP Certificate

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

ELECTRONICS AND ELECTRICAL ENGINEERING

LABORATORY

Boulder, Colorado 80303

MEASUREMENT ASSURANCE PROGRAM (MAP)

for

Spectral Density of Relative Intensity Noise

for

Customer

AaBbCc Corp.

Address

Calibration Summary

This report summarizes the measurement results for the spectral density of Relative Intensity Noise

(RIN) of the NIST transfer standard. The standard is cahbrated over the 0. 1 GHz to 1 . 1 GHz frequency

range. Hov^^ever, the spectral density of the RIN (from now on called simply the RIN) is practically constant up to several tens of gigahertz. The transfer standard is an erbium-doped fiber amplifer

(EDFA) to which is coupled a linear polarizer (P) followed by a narrowband filter (F) (represented as EDFA + P + F in Figure Dl). The EDFA has a built-in optical isolator to ensure that the amplifiedspontaneous emission (ASE) that it emits is free from potential multiple interference effects such as

ripple. High-quality FC/PC connectors and single-mode fiber are used throughout.

Folder No. and NIST ID: xx and yy

Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 55
The RIN of the standard is determined from measurements of the optical power spectral density

(OPSD) it emits as measured by a high resolution, grating-type, optical spectrum analyzer (OSA). The

RIN is proportional to the autocorrelation of the measured OPSD. Thus the uncertainties that contribute

to the RIN are the repeatability and those that arise from the OSA parameters involved in the

measurement.

The reported results are the average of the NIST calibration measurements made before and after shipment to the participant, and are summarized in Table I in linear as well as logarithmic units.

Table Dl. RIN of the transfer standard (based on 40 RIN measurements).

Frequency range ION (EDFA + P + F) Expanded uncertainty

0.1-1.1 GHz 1/Hz dB/Hz 1/Hz dB/Hz

1.0325 10" -109.9 0.029- 10" 0.12

RIN standard Customer's RIN measurement system

EDFA + P + F

spectrum

analyzer

Figure Dl. NIST RIN standard apphed to customer's RIN measurement system.

Folder No. and NIST ID: xx and yy

Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 56
Application of the transfer standard to a REV measurement system

When RIN is measured in the electrical domain, a bias tee sends the dc photocurrent from the

photodetector to an ammeter while the ac noise is amplified, then displayed on a radio-frequency (rf) spectrum analyzer (Figure 1). The RIN is the noise power per unit bandwidth, 6Pe(f), weighted with the

frequency-dependent cahbration frinction K(f) of the detection system (herein referred to as Kappa),

and divided by the electrical dc power P^. Thus

RIN - = constant , (D 1) Pe

where 6Pe(f) is the noise after subtracting the thermal noise floor.

To calibrate a RIN measurement system, the customer connects the RIN standard using a quality

FC/PC connector with standard single mode fiber. The h^JS) is measured on the rf spectrum analyzer; measure Pe(f) with a high accuracy voltmeter connected across a 50 Q resister. Substitute the value for

the RIN of the standard to obtain Kappa. Solution of eq (1) for K(f) gives

RIN-P if)

To determine the RIN of an unknovm source, the customer applies eq (2) witii the values ofKappa

obtained from the standard. Figure 2D is a sample graph of Kappa of the NIST RIN system using the

standard.

Folder No. and NIST ID: xx and yy

Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 57
-88 o

o

Frequency (GHz)

Figure D2. Graph of the frequency-dependent calibration function. Kappa, obtained for the NIST

RIN measurement system by apphcation of the RIN standard.

Uncertainty Assessment

Estimates of uncertainty for the NIST RIN standard are determined from the repeatability error and the

contributions of the optical spectrum analyzer parameters. All uncertainties related to the standard are TYPE A evaluations of standard uncertainty, in that each is obtained from measurements. There are no

significant Type B errors [1].

The uncertainties are listed in Table D2. The RIN of the standard is the average of all RIN

measurements used to calculate the repeatability error, Urep The uncertainties arising from the optical

spectrum analyzer parameters are nonlinearity spectral responsivity Ulin, wavelength distortion U^, and

resolution bandwidth Urrw

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Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 58
Table D2. Summary of typical measurement uncertainties contnbuting to the total uncertainty in the

RIN of the standard.

EDFA2 + Fl Uncertainty evaluation

Type (A or B)

Standard

uncertainty (1/Hz)

Standard

uncertainty (dB/Hz)

Urep A 0.000561 10" 0.002

A 0.001 180 10" 0.005

A 0.01231510-" 0.051

UrbW A 0.000419-10-" 0.002

Expanded, U 0.029-10-" 0.12

Combined, 0.014475-10-" 0.060

The repeatability error is calculated from the basic standard-deviation formula The uncertainties for

Ihe OSA parameters are determined by application of the standard propagation of errors formula The

combined standard uncertamty u^ of the average RIN is determined by combining the Type A

uncertainties (Urep Urbw) in quadrature. The expanded uncertainty, U, is twice the combined

standard uncertainty. The values used to calculate the NIST expanded uncertainties appear in Table 2.

Folder No. and NIST ID: xx and yy

Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 59
Useful Information for Calibrating the User's Electrical Spectrum Analyzer

for Scale Fidelity Correction

This section refers to Appendix A of the main document. Application of the RIN transfer standard to calibrate a RIN measurement system holds true for the rf electrical spectrum analyzer (ESA) set at a

distinct group of function settings, such as sweep time, resolution and video bandwidth, intemal

attenuation, etc. Changing a function setting to accomodate a signal requires a new calibration, since

the Kappa then obtained may differ slightly from the original. In addition, each ESA has a unique scale

fidelity factor that accounts for the vertical position of the noise signal on the screen. RIN

measurements for which the rf amplitude noise differs must be weighted with this factor, which like Kappa, is frequency dependent. The scale fidelity factor can be obtained using an rf signal generator, an

attenuator, the ESA, and an rf power meter. Connector losses should be included and control settings

kept the same as for a RESf measurement. The rf power is recorded at two different positions on the

ESA with and without the attenuator. The scale fidelity correction for signals of varying magnitude can be expressed as a correction to Kappa at each frequency separately.

Below is an example of how we calibrate the NIST ESA. The attenuation of a 10 dB attenuator is measured as shown in the top part of Figure A. I with the signal generator set at 600 MHZ and power

output at -50 dBm. Using the rf power meter the attenuation is measured to be 10.0 dB. With the

signal generator set at 600 MHZ and -70 dBm, the signal is positioned on the ESA screen as would

occur for an actual noise measurement. The result is recorded with and without the attenuator. When

our ESA is set at 5 dB per vertical division, the scale fidelity, S, is found to increase the difference

between the two readings by 0. 15 dB per division. Also, the manufacturer specifies that the amplitude

error must be <0.7 dB over the ten divisions that compose the screen. If the difference between noise

powers at different vertical positions on the screen is 6P, - 6P2 (at the same frequency), then the scale

fidelity correction is

6P

(A.1)

6Pj +0.03-(6Pj - 6P2)

Application of eq (A.l) to Kappa at each frequency (sections 9.1 and 9.2) gives

Folder No. and NIST ID: xx and yy

Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 60
KI,cor (A.2)

6Pj - 0.03 -(aPj- 6/^2)

'

where the subscripts cor and un represent the corrected and uncorrected Kappas, respectively. This is a most general formula in which 6P, can be greater or less than SP,. If it is greater, the corrected

Kappa increases at the set cahbration frequency. If it is less, the corrected Kappa decreases.

[1] B.N. Taylor and C.E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of NIST

Measurement Results, NIST Technical Note 1297, 1994 Edition.

For the Director, Report Prepared/Cahbrated By:

NIST

Gordon Day, Chief

Optoelectronics Division

Gregory E. Obarski

Physicist

Sources and Detectors Group

Folder No. and NIST ID: xx and yy

Date of Report: March 1, 2000

Reference: P.O. No. Mmm, 2/3/00 61
Appendix E. Calibration Service

As appropriate, the customer may benefit more fi-om a calibration service (CALSV) than a measurement assurance program (MAP). To use a CALSV, customers send their ovm devices to NIST

for calibration instead of renting the NIST standard through the MAP. We refer to the customer's

calibrated RIN device as a company standard. Although customers purchase their own components,

NIST would be available for consultation on which components to purchase (but as a matter of policy

does not recommend specific brands).

Calibration and traceability of the company standard to NIST would occur as a two step process.

Periodically, perhaps once per year, the customer would send NIST his or her company standard for

calibration. NIST calibrates the NIST RIN measurement system using the NIST standard, and then

within a few minutes this calibrated system is used to calibrate the customer's RIN device. NIST will

supply the customer with a calibration report, and make any recommendations needed for the customer

to continue possessing a quality RIN standard. This procedure will increase the uncertainty in the RIN

by about 0.03 dB over that of the MAP, which uses the NIST standard to calibrate the customer's RIN

device directly. The increased uncertainty occurs because, in addition to the uncertainty in the NIST

standard, the uncertainty inherent in the NIST RIN system is also transferred to the customer's

company standard. However, If the RIN of the source can be approximated by thermal light, such as the NIST RIN standard, the combined uncertainty is reduced by determining the RIN fi-om the same

method used for the NIST RIN standard. In this method, the theory ofthe RIN of thermal light is applied to the optical power spectral density of the device as measured by the NIST optical spectrum

analyzer, which is precisely calibrated as a standard. The latter method will be used at the customer's

discretion.

62
Appendix F: Sample Calibration Certificate

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

ELECTRONICS AND ELECTRICAL ENGINEERING LABORATORY

Boulder, Colorado 80303

REPORT OF CALIBRATION BY NIST

for

Spectral Density of Relative Intensity Noise

Submitted to: ABODE Corp.

Address

Calibration Summary

This report summarizes the measurement results for the spectral density of relative intensity noise

(RIN) of the customer's noise source. The source is calibrated over the 0. 1 GHz to 1 . 1 GHz

frequency range. The measurements were performed in two steps. First, the NIST RESF

measurement system was calibrated with the NIST RIN standard. Next, the RIN of the

customer's device was measured with the calibrated RIN system. The NIST RIN standard is an erbium-doped fiber amplifer (EDFA) to which is coupled a linear polarizer (P) followed by a narrowband filter (F). Thus, it is represented by EDFA + P + F as shovm in Figure Fl . The EDFA

has a built-in optical isolator to ensure that the amplified-spontaneous emission (ASE) that it emits is fi"ee from potential multiple interference effects such as ripple. High-quality FC/PC

connectors and single-mode fiber are used throughout.

The RIN of the NIST standard was determined from measurements of its optical power spectral

density (OPSD) as measured by a high resolution, grating-type, optical spectrum analyzer (OSA).

The RIN is proportional to the autocorrelation of the measured OPSD, and is constant out to

several tens of gigahertz. The uncertainties that contribute to the RIN are the repeatability in RIN

Folder No: bbbb

Date of Report: March 16, 2000

Reference: P.O. No. Tttt ee/yy/nn 63
Table Fl. RIN of customer's device and uncertainty of RIN expressed in linear and logarithmic

units.

Frequency range RIN of customer's device Expanded uncertainty

0.1-1 GHz 1/Hz dB/Hz 1/Hz dB/Hz

aaa bbb ccc ddd

measurements as well as the uncertainties that arise from the OSA parameters involved in the

measurement. Calibrations are performed after all equipment is warmed to steady-state thermal

stability (several hours). The results of the RIN measurements on the customer's device are summarized in Table Fl, where the expanded uncertainty reported is defined in the section on

uncertainty assessment.

NIST RIN standard

EDFA + P + F

or

EDFA + P + F

o

o

Customer's RIN device

SI

NIST RIN measurement system

Bias tee Ammeter

Photo

detector O

Pre amp

Electrical spectrum

analyzer

Figure Fl. Calibration of the customer's RIN device using the NIST RIN measurement system

as cahbrated by the RIN standard

Folder No: bbbb

Date of Report: March 16, 2000

Reference: P.O. No. Tttt ee/yy/mi 64
Application of the transfer standard to a RIN measurement system

When the RIN of the customer's device is measured, we first calibrate the NIST RIN system with

the NIST RIN standard. To measure RIN in the electrical domain, we use a bias tee to send the dc

photocurrent to an arrmieter, while the ac noise is amplified and displayed on a radio-fi'equency

(rf) spectrum analyzer (Figure Fl). The dc power is determined with a voltmeter connected across

a 50 Q resister instead of the ammeter. If i is the current, v the voltage, and R the resistance, the

dc power is = Ri^ = v^/R. The RIN is the noise power per unit bandwidth, 6Pe(f), weighted

with the fi"equency-dependent calibration function K(f) of the detection system (herein referred to as Kappa), and divided by the electrical dc power P^. Thus,

K(f)-6P(f)

RIN = — = constant , (F.l) ^e

where 6Pe(f) is the noise afl:er subtracting the thermal noise floor.

To calibrate the NIST RIN measurement system we apply the RIN standard and measure 6Pe(f)

and VJ^i). If R^ is the RIN of the standard, then fi-om eq (Fl) Kappa is

The RIN of an unknown source is determined by connecting the source to the NIST RIN

measurement system and then measuring 6Pe(f) and Pe(f). By substituting Kappa into eq (Fl), the

RIN is

P hP if)

RJN(f) = —• ——' R,(f) . (F 3)

ex ev /

Folder No: bbbb

Date of Report: March 16, 2000

Reference: P.O. No. Tttt ee/yy/nn 65
-88 o

o

Frequency (GHz)

Figure F2. Graph of the frequency-dependent calibration function. Kappa, obtained for the

NIST RIN measurement system by application of the RIN standard.

Uncertainty Assessment

The uncertainty in calibrating the REST of the customer's device will depend on whether it is a broadband source modelled after the NIST standard, or whether it is a laser. For a laser the total

uncertainty is due to the NIST RIN standard plus the uncertainty contributed by the NIST RIN

measurement system. The latter is the uncertainty in the calibration fimction (Kappa) and is determined at the time the calibration is performed. If the RIN of the source can be approximated

by thermal light, such as the NIST RIN standard, however, the combined uncertainty is reduced

by determining the RIN from the same method used for the NIST RIN standard. In this method

the theory of the RIN of thermal light is applied to the optical power spectral density of the device

as measured by the NIST optical spectrum analyzer, which has been accurately calibrated.

The uncertainty estimates for the NIST RIN standard are determined from the repeatability error

Folder No: bbbb

Date of Report: March 16, 2000

Reference: P.O. No. Tttt ee/yy/nn 66
Table F2. Summary of measurement uncertainties.

iLDr A2 + rl Uncertainty evaluation

Type (A or B)

Standard

uncertainty (1/Hz)

Standard

uncertainty (dB/Hz)

Urep A 0.000561 • 10-^^ 0.002

Ulin A 0.001180 • 10"^^ 0.005

T T AA A A1 '^'7 1 C 1 0.012315 • 10 A AC 1 0.051

UrBW A 0.000419 • 10"^^ 0.002

Combined, 0.014475 • 10"" 0.06

Expanded, U 0.029 • 10-^' 0.12

and the contributions of the optical spectrum analyzer parameters. All uncertainties related to the

standard are TYPE A evaluations of standard uncertainty, in that each is obtained from

measurements. There are no significant Type B errors [1].

The uncertainties are listed in Table F2. The RIN of the standard is the average of all RIN

measurements used to calculate the repeatability error, Urep . The uncertainties arising from the

optical spectrum analyzer parameters are nonlinearity spectral responsivity Uun, wavelength

distortion U;,^, and resolution bandwidth Urb^ •

The repeatability error is calculated from the basic standard-deviation formula. The uncertainties

for the OSA parameters are determined by application of the standard propagation of errors formula. The combined standard uncertainty u^ of the average RIN is determined by combining

the Type A uncertainties (Urep, Ulin, U;^, Urbw ) in quadrature. The expanded uncertainty, U, is twice the combined standard uncertainty. The values used to calculate the NIST expanded

uncertainties are Usted in Table F2.

Folder No: bbbb

Date of Report: March 16, 2000

Reference: P.O. No. Tttt ee/yy/nn 67
Useful Information for Calibrating the User's Electrical Spectrum Analyzer for Scale

Fidelity Correction

This section refers to Appendix A of the main document. Application of the RIN transfer

standard to calibrate a RIN measurement system holds true for the rf electrical spectrum analyzer

(ESA) set at a distinct group of function settings, such as sweep time, resolution and video

bandwidth, internal attenuation, etc. Changing a function setting to accomodate a signal requires a new calibration, since the Kappa then obtained may differ slightly from the original. In addition,

each ESA has a unique scale fidelity factor that accounts for the vertical position of the noise

signal on the screen. RIN measurements for which the rf amplitude noise differs must be weighted

with this factor, which like Kappa, is frequency dependent. The scale fidelity factor can be

obtained using an rf signal generator, an attenuator, the ESA, and an rf power meter. Connector

losses should be included and control settings kept the same as for a RIN measurement. The rf

power is recorded at two different positions on the ESA with and without the attenuator. The

scale fidelity correction for signals of varying magnitude can be expressed as a correction to

Kappa at each frequency separately.

Below is an example of how we calibrate the NIST ESA. The attenuation of a 10 dB attenuator

is measured as shown in part "a" of Figure A. 1 with the signal generator set at 600 MHZ and

power output at -50 dBm. Using the rf power meter, the attenuation is measured to be 10.0 dB.

With the signal generator set at 600 MHZ and - 70 dBm, the signal is positioned on the ESA

screen as would occur for an actual noise measurement. The result is recorded with and without

the attenuator. When our ESA is set at 5 dB per vertical division, the scale fidelity, S, is found to

increase the difference between the two readings by 0. 15 dB per division. Also, the manufacturer

specifies that the amplitude error must be <0.7 dB over the 10 divisions that compose the screen.

If the difference between noise powers at different vertical positions on the screen is 6?^ - 8P2

(at the same frequency), then the scale fidelity correction is

^1 = 6Pj +0.03-(6Pj- 6P2)

(A.1)

Folder No: bbbb

Date of Report: March 16, 2000

Reference: P.O. No. Tttt ee/yy/nn 68
Application of eq (A.l) to Kappa at each frequency (sections 9. 1, 9.2) gives

KIxor 6Pj +0.03-(6Pi-6/'2)

' (A-2)

where the subscripts cor and un represent the corrected and uncorrected Kappas, respectively.

This is a most general formula, in which 6Pi can be either greater or less than 6P2 . If it is greater, the corrected Kappa increases at the set calibration frequency. If it is less, the corrected

Kappa decreases.

[1] B.N. Taylor and C.E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of

NIST Measurement Resuhs, NIST Technical Note 1297, 1994 Edition.

For the Director, Report Prepared/Calibrated By:

NIST

G. W. Day, Chief

Optoelectronics Division

Gregory E. Obarski

Physicist

Sources and Detectors Group

Folder No: bbbb

Date of Pveport: March 16, 2000

Reference: P.O. No. Tttt ee/yy/nn 69
Appendix G: Shipping Instructions

The instrument to be shipped should be placed in a padded box with sufficient foam to protect it from mechanical shock, vibration, and other environmental hazards. The operating manual for the

optical fiber amplifier should be included, as well as specifications for the filter and polarizer. If

appropriate, the customer should specify the operating value of the pump current for the EDFA if it is adjustable. All cables and connectors needed to calibrate the equipment should be included. All parts

belonging to the instrument will be returned by NIST.

70
B

Laser

transmitter O

Lossy medium

such as attenuator

Reference plane that

defines total laser RIN

Photo

detector

Poisson RIN

increases due

to losses

Bias tee Ammeter

Detector adds

shot noise RIN

•O

V

Pre amp

Electrical sfjectrum

analyzer

Figure 2.3. 1 Basic RIN measurement system.

EDFA

(with built-in optical isolator)

Linear polarizer

Nanometer

bandwidth filter

Output

Figure 3.1.1. Form of the RIN standard.

71
Figure 3.1.2 Wavelength spectrum of the amplified spontaneous emission fi^om an EDFA.

EDFA OSA

Figure 3.1.3. Arrangement for measuring the optical power spectral density of the RIN standard

using a calibrated OSA.

72
I

^ I^

\

'

\ '

I '

\

'

I 1550>t 1550.6 1550.8 1551.0 1551.2 1551>* 1551.6 Wavelength (nm)

Figure 5.1.1. Response of the OSA to a narrow linewidth laser, or delta-function input. We refer to the

spatial wavelength spreading by the OSA's monochrometer of the single wavelength input as the sUt

function.

0.050

0.048

0.046

0.044

0.042

0.040

0.038

0.036

Arrowheads represent equiv noise bw; mean = 0.045 nm; solid line; std dev = 0.001

Circles represent 3 dB resolution bw; mean = 0.041 nm; dotted line; std dev = 0.001

^

o

o

- -(S - €) 0- ^Sc.

lDo

I

'

1

' 1

1500 1 510 1 520 1530 1540 1550

Wavelength (nm)

1560

^ V

V

o o

o o

o

o

1570 1580

Figure 5. 1 .2. Measurement of OSA resolution bandwidth versus wavelength as determined from the 3

dB bandwidth and the noise-equivalent bandwidth using a narrow-linewidth, tunable laser.

73
1548.6 —

1547.4 1547.6 1547.8 1548.0 1548.2 1548.4 1548.6 True wavelength (nm)

Figure 5.2. 1 . Comparison of wavelengths measured by the OSA with the true wavelength in the 1548

nm region.

1560.6 —I

1559.4 1559.6 1559.8 1560.0 1560.2 1560.4 1560.6 True wavelength (nm)

Figure 5.2.2. Comparison of wavelengths measured by the OSA with the true wavelength in the 1560

nm region.

74
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Frequency (GHz)

Figures 6.2. 1 . Absence of ripple on the rf noise from the RIN standard over the frequency band of

0.1 GHz through 1.1 GHz.

-67.5 —

0.70 0.72 0.74 0.76 O 78 0.80 0.82 0.84 0.86 Frequency (GHz)

Figure 6.2.2. Absence of ripple on the rf noise from the RIN standard over the frequency band of 0.7

GHz through 0.85 GHz.

75
0.50 0.52 0.54 0.56 0.58 0.60 Frequency (GHz)

Figure 6.2.3. Absence of ripple on the if noise from the RIN standard over the frequency bands of

0.5 GHz through 0.6 GHz.

76
1545 1548 1551 1554 1557 1560 Wavelength (nm)

Figure 6.4.1. Optical power spectral density of the three filters Fl, F2, and F3 used in this study.

-105 —I

-110 —

Frequency (GHz)

Figure 6.4.2. RIN of Fl, F2, and F3 fi-om near zero to 1000 GHz using EDFA2.

77
-109.84 —

-109.86 —

-109.88 m

D

±z -109.90 a:

-109.92

-109.94

EDFA1 + F1 EDFA2 + F1

T 1 r~i—I I I I T

1 1 1—I I I I T

10

Frequency (GHz)

Figure 6.4.3. Comparison of the RIN from Fl using EDFAl and EFDA2.

78
1.0314 —

1 .0308 —

•r^ 1.0302 —I

LjjX

sT 1.0296 I

1.0290 —

1.0284 —

1.0278 —

Average RIN = 1.0296

Std Dev = 0.0008 = 0.0036 dB

1

\—\—\—I—

2 3 4 5 6 7 Attenuation (dB)

10 11

Figure 6.6.1. RIN of EDFAl + Fl vs. attenuation. Any apparent trend is of no practical significance.

1 .0308 —

1 .0304 —

1 .0300 —

111 1 .0295 —

NX

IT

1.0292 —

1 .0288 —

1.0284 —

1.0280 —

1.0276

Average RIN = 1.0291 Std Dev = 0.0005 = 0.002 dB

~^—\—'—\—'—

100 120 140 150 Pump current (mA)

'—

180 200 220

Figure 6.6.2. RIN of EDFAl + Fl vs. pump current of the EDFA.

79
10.36-

10.35

10.34-

CMg 10.33 i

-| 1 1 r

1 1—I 1 r 06MAY99 16MAY99

]—1—I—I—I—I—1—I—I—I—

p

26MAY99 05JUN99

Measurement date

Figure 7.1.1. RIN of the standard over a three-week period. Circles represent second set of five

measurements taken on May 5, 1999.

80
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Frequency (GHz)

Figure 8.1.1. Calibration function of the laser versus frequency for various attenuation levels.

-88 —

0.1 0.2 0.3 0.4 0.5 06 0.7 0.8 0.9 1.0 1.1 Frequency (GHz)

Figure 8. 1 .2. Calibration ftinction of the laser versus frequency for similar but different attenuation

levels.

81
W> 13 —

CD ^ 11 — ^

10 —

N

Z 9-^

O 8 —

CO 7 —

O

Q.

0)

(OO

c

0)CO

CD

5 —

4 —

linear fit excluding v = 23.66 mV

— — 2nd order polynomial using all data O data points

1 \ I \ I I r

8 10 12 14 16 18 20

dc voltage (mV)

22 24

I 26

Figure 8.1.3. Electrical noise power of laser at 400 MHz versus dc voltage.

EDFA + P + F

RESf system to be calibrated

Photo

detector

or

Poisson limited DFB laser

Bias tee Ammeter

Pre amp

Electrical spectrum

analvzer

Figure 9. 1 . Calibration of the RIN system using the standard and the laser.

82
-88 —I

0.1 0.2 0.3 0.4 0 5 0 6 0 7 0 8 0 9 1.0 1.1 Frequency (GHz)

Figure 10. 1 . 1 . Comparison of Kappas using EDFA2 with filters Fl, ¥2, or F3.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Frequency (GHz)

Figure 10. 1.2. Comparison of Kappas from two different EDFAs + F2 with the laser.

83
1.5 —

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Frequency (GHz)

Figiire 10. 1 .3 . Difference between Kappas from the laser and EDFAl + F2. The data range from

to +1 dB. The average difference is 0.056 dB.

84
E

a.

a. 1 -

0.5 0.6 0.7

Frequency (GHz)

Figure 10.3.1. Kappa determined on four different days from EDFAl + Fl.

Figure 10.3.2. Kappa determined on four different days from EDFA2 + Fl.

85
m

u

J

E

g

COQ.

Q.

0.5 0.6 0.7 Frequency (GHz)

I

1.1

Figure 10.3.3. Kappa determined on four different days from the laser.

86
95 H

1 \ 1 1 1 1 1 1 \

1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Frequency (GHz)

Figure 10.3.4. Comparison of Kappa from EDFAl + Fl and the laser. Data were averaged over the four

days shown in Figures 10.3.1 (EDFAl + Fl) and 10.3.3 (laser).

— 95H 1 1 1 1 \ 1 1 \ 1 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

Frequency (GHz)

Figure 10.3.5. Comparison of Kappa from EDFA2 + Fl and the laser. Data were averaged over the four

days shown in Figures 10.3.2 (EDFA2 + Fl) and 10.3.3 (laser).

87
CO

T3L

E

c

o

••s

1T3C

Frequency (GHz)

Figure 10.3.6. Comparison of the frequency dependence of the normalized standard deviation of the four

data sets for Kappa from EDFAl + Fl (Kappa values shown in Figure 10.3.1) and the corresponding four

data sets from the laser (Kappa values shown in Figure 10.3.3).

73,

c

(0E

c

o

1

1

0.5

0.4

0.3

0:2 -y^

0.1

0.0

ate * *

o'

EDFA2 + R

Laser

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Frequency (GHz)

cP^ o° * * S

* o o

Figure 10.3.7. Comparison of the frequency dependence of the normalized standard deviation of the four

data sets for Kappa from EDFA2 + Fl (Kappa values shown in Figure 10.3.2) and the corresponding four

data sets from the laser (Kappa values shown in Figure 10.3.3).

88
o

1

I

180

160

140 H

120

100

80

60 -\

40

20

0

+

+

+

+ +

+

+

1 1 1 "1 1 1 1 1 1 -I

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Frequency (GHz)1.0 1.1

Figure 10.4.1. F-ratio versus frequency. The F-ratio shown is the variance of each Kappa from the laser divided by the variance of the Kappa from the EDFAl + Fl at each frequency. The two reference lines represent the critical values for the F-test at the 0.05 level of significance.

o

1

I

200-

180-

160

140 H 120

100-1 80

60

40

20-1

+

+

+

0.1 0.5 0.6 0.7

Frequency (GHz)

4-

Figure 10.4.2. F-ratio versus frequency. The F-ratio shown is the variance of each Kappa from the laser divided by the variance of the Kappa from the EDFA2 -i- Fl at each frequency. The two reference lines represent the critical values for the F-test at the 0.05 level of significance. An F-ratio of 428.863 at 1 .08 GHz is not shown.

89
rf signal generator rf power meter

Attenuator

—

Electrical

spectrum analyzer

Figure Al . Measurement of the scale fidelity of the electrical spectrum analyzer

using rf signal generator and attenuator, with output power traceable to rf power meter.

90
THE SP 250 SERIES ON NIST MEASUREMENT SERVICES*

SP 250-1 Spectral Radiance Calibrations PB871 79883

SP 250-2 Far Ultraviolet Detector Standards PB87227609

SP 250-3 Radiometric Standards in the Vacuum Ultraviolet PB87227625

SP 250-4 Fricke Dosimetry in High-Energy Electron Beams

PB881 10374

SP 250-5 Alpha-Particle Calibrations PB881 68620

SP 250-6 Regular Spectral Transmittance PB881 08550

SP 250-7 Radiance Temperature Calibrations PB881 23674

SP 250-8 Spectral Reflectance PB881 09905

SP 250-9 Calibration of Beta-Particle-Emitting Ophthalmic

Applicators

PB881 08535

SP 250-1 0 Radioactivity Calibrations with the "4u" Gamma

Ionization Chamber and Other Radioactivity

Calibration Capabilities

PB881 23708

SP 250-1 1 Dosimetry for High Dose Applications

PB88201587

SP 250-12 Neutron Personnel Dosimetry

PB87227617

SP 250-13 Activation Foil Irradiation with Californium

Fission Sources PB88217443

SP 250-14 Activation Foil Irradiation by Reactor Cavity

Fission Sources PB88217435

SP 250-15 Photometric Calibrations PB881 53747

SP 250-16 Calibration of X-Ray and Gamma-Ray

Measuring Instruments PB88211826

SP 250-1 7 The NBS Photodetector Spectral Response

Calibration Transfer Program

PB88201595

SP 250-1 8 Neutron Source Strength Calibrations PB88211818

SP 250-19 Calibration of Gamma-Ray-Emitting

Brachytherapy Sources PB891 93858

SP 250-20 Spectral Irradiance Calibrations PB881 23781 SP 250-21 Calibration of Beta-Particle Radiation

Instrumentation PB88201579

SP 250-22 Platinum Resistance Thermometer Calibrations PB881 38367

SP 250-23 Liquid-in-Glass Thermometer Calibration Service PB891 28888

SP 250-24 Standard Cell Calibrations PB881 23690

SP 250-25 Calibration Service for Inductive Voltage Dividers SP 250-26 NBS Phase Angle Calibration Services PB88225636

SP 250-27 AC-DC Difference Calibrations PB892222616

SP 250-28 Solid-state DC Voltage Standard Calibrations PB881 68703

SP 250-29 Traceable Frequency Calibrations PB881 68364

SP 250-30 GOES Satellite Time Code Dissemination:

Description and Operation

PB88 168760

SP 250-31 Mass Calibrations PB891 53894

SP 250-32 A Calibration Service for 30 MHz Attenuation and Phase Shift PB88238324

SP 250-33 A Calibration Service for Voltage Transformers and High-Voltage Capacitors

PB882252903

SP 250-34 High Vacuum Standard and Its Use PB89 193841 SP 250-35 The Calibration of Thermocouples

and Thermocouple Materials PB89209340 A Calibration Service for Current Transformers PB91216770

Photometric Calibrations PB97 148472 NIST Leak Calibration Service PB921 49772

NIST Pressure Calibration Service PB941 64043

SP 250-36

SP 250-37

SP 250-38

SP 250-39

SP 250-40 Absorbed-Dose Calibration of Ionization Chambers

in a "Co Gamma-Ray Beam

No PB number

SP 250-41 Spectroradiometric Detector Measurements:

Part I - Ultraviolet Detectors and

Part II - Visible to Near-Infrared Detectors PB98-1 49073

SP 250-42 Sprectroradiometric Detector Measurements:

Part III—Infrared Detectors PB99-1 34371 SP 250-43 Radiance Temperature Calibrations PB98-141047

SP 250-44 Radiation Processing Dosimetry Calibration Services and Measurement Assurance Program

PB98-1 40973

* Entries containing a stock number (SN003-003-) 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 or 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.
THE SP 250 SERIES ON NIST MEASUREMENT SERVICES* - Continued

SP 250-45 Radiation Processing Dosimetry Calibration Services: Manual of Calibration Procedures

PB98-1 40981 SP 250-46 NIST Multifunction Calibration System

PB98-131279

SP 250-47 NIST Calibration Service for Capacitance

Standards at Low Frequencies PB98-1 44687

SP 250-48 Spectral Reflectance PB98-149016

SP 250-49

SP 250-51

SP 250-52

SP 250-53

SP 250-54 Optical Fiber Power Meter Calibrations at NIST

SN003-003-03652-8, PB2000-1 06986

SP 250-56 Optical Fiber Power Meter Nonlinearity Calibrations

at NIST

SN003-003-03653-6, PB2000-1 06987

SP 250-57 Measurement Assurance Program for the Spectral

Density of Relative Intensity Noise of Optical Fiber Sources Near 1 550 nm

* Entries containing a stock number (SN003-003-) 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 or 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.
Technical Publications

Periodical

Journal of Research of the National Institute of Standards and Technology—Reports NIST research and

development in those disciplines of the physical and engineering sciences in which the Institute is active. These include physics, chemistry, engineering, mathematics, and computer sciences. Papers cover a broad

range of subjects, with major emphasis on measurement methodology and the basic technology underlying

standardization. Also included from time to time are survey articles on topics closely related to the Institute's technical and scientific programs. Issued six times a year.

Nonperiodicals

Monographs—Major contributions to the technical literature on various subjects related to the Institute's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed

in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications—Include proceedings of conferences sponsored by NIST, NIST annual reports, and

other special publications appropriate to this grouping such as wall charts, pocket cards, and bibliographies.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical

properties of materials, compiled from the world's literature and critically evaluated. Developed under a

worldwide program coordinated by NIST under the authority of the National Standard Data Act (Public Law

90-396). NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is published bi-monthly for NIST by the American Chemical Society (ACS) and the American Institute of Physics (AlP). Subscriptions,

reprints, and supplements are available from ACS, 1155 Sixteenth St., NW, Washington, DC 20056.

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materials, components, systems, and whole structures. The series presents research results, test methods,

and performance criteria related to the structural and environmental functions and the durability and safety

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Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a

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Voluntary Product Standards—Developed under procedures published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations. The standards establish nationally recognized

requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NIST administers this program in support of the efforts of private-sector

standardizing organizations.

Order the following NIST publications—FIPS and NISTIRs—from the National Technical

Information Sen/ice, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the official source

of information in the Federal Government regarding standards issued by NIST pursuant to the Federal Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR

(Code of Federal Regulations).

NIST Interagency Reports (NISTIR)—A special series of interim or final reports on work performed by NIST

for outside sponsors (both government and nongovernment). In general, initial distribution is handled by the sponsor; putilic distribution is by the National Technical Information Service, Springfield, VA 22161, in paper

copy or microfiche form.
w

g

03c

T3

W

5'

CD </) CCO

(D </* Uoo C CJl Q.

CD

OO ^ 2.

CO ^ ouI wCO

ro00

m2 C. a: CO O •

3-

5. 3

CD (0 O 3 -h r* w o

ST

"** l|H