NIST SPECIAL PUBLICATION 260-146

U. S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

Standard Reference Materials

Carbon Monoxide Absorption References

for 1560 nm to 1630 nm Wavelength Calibration ó

SRM 2514 (12C16O) and SRM 2515 (13C16O)

S. L. Gilbert and W. C. Swann
NIST Special Publication 260-146

Standard Reference Materials

Carbon Monoxide Absorption References

for 1560 nm to 1630 nm Wavelength Calibration ó

SRM 2514 (12C16O) and SRM 2515 (13C16O)

S. L. Gilbert and W. C. Swann

Optoelectronics Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, CO 80305-3328

U.S. DEPARTMENT OF COMMERCE, Donald L. Evans, Secretary

TECHNOLOGY ADMINISTRATION, Phillip J. Bond, Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Arden L. Bement, Jr., Director

Issued October 2002
Certain commercial equipment, instruments, or materials are identified in this paper in

order to specify the experimental procedure 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 materials or equipment identified are

necessarily the best available for the purpose.

National Institute of Standards and Technology Special Publication 260-146

Natl. Inst. Stand. Technol. Spec. Publ. 260-146, 40 pages (October 2002)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2002

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov ó Phone: (202) 512-1800 ó Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
Contents

Abstract......................................................................................................................................... iv

1. Introduction ............................................................................................................................... 1

2. Pressure Shift Adjustment........................................................................................................ 2

3. Sensitivity to Other Environmental Conditions ..................................................................... 3

4. NIST Certification Procedure .................................................................................................. 4

5. Summary .................................................................................................................................... 4

6. References .................................................................................................................................. 4

Table 1. Pressure Shift of 12C16O Lines....................................................................................... 6

Table 2. Pressure Shift of 13C16O Lines....................................................................................... 7

Table 3. Certified Wavelengths for SRM 2514 (12C16O)............................................................ 8

Table 4. Certified Wavelengths for SRM 2515 (13C16O)............................................................ 9

Figure 1. Carbon Monoxide 3ν Rotational-Vibrational Spectra ............................................ 10

Figure 2. Schematic Diagram of the Fiber-Pigtailed SRM Cell Holder................................. 11

Figure 3. 12C16O Pressure Shift Measurements ........................................................................ 12

Figure 4. 13C16O Pressure Shift Measurements ........................................................................ 12

Appendixes................................................................................................................................... 13

Appendix A. Certificate of Analysis, SRM 2514

Appendix B. Certificate of Analysis, SRM 2515

Appendix C. ìPressure-induced shift and broadening of 1560ñ1630 nm carbon

monoxide wavelength-calibration lines,î W.C. Swann and S.L. Gilbert

[J. Opt. Soc. Am. B 19, 2461-2467 (2002)]

iii
iv

NIST Special Publication 260-146

Standard Reference Materials:

Carbon Monoxide Absorption References for 1560 nm to 1630 nm Wavelength Calibration

– SRM 2514 (12C

16O) and SRM 2515 (13C16O)

Sarah L. Gilbert and William C. Swann

Optoelectronics Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, CO 80305-3328

Abstract

Standard Reference Materials (SRMs) 2514 and 2515 are optical-fiber-coupled wavelength

references based on the fundamental absorption lines of carbon monoxide 12C

16O and 13C16O in

the 1560 nm to 1630 nm region. The center wavelengths of 41 lines of the 3ν rotationalvibrational band of carbon monoxide 12C

16O are certified for SRM 2514, and the center

wavelengths of 41 lines in the corresponding band of 13C

16O are certified for SRM 2515. These

lines are certified with expanded uncertainties (2σ) ranging from 0.4 to 0.7 pm. This document

describes SRMs 2514 and 2515 and details the uncertainty analysis.

Keywords: absorption; carbon monoxide; CO; molecular spectroscopy; optical fiber

communications; pressure broadening; pressure shift; Standard Reference Material; wavelength

calibration; wavelength division multiplexing; wavelength reference; wavelength standards; WDM
1

1. Introduction

Wavelength division multiplexing (WDM) in optical fiber communication systems increases

bandwidth by using many wavelength channels. Current WDM systems typically employ 50 or

100 GHz channel spacing (0.4 or 0.8 nm, respectively) in the 1530–1560 nm WDM C-band, and

WDM is expanding into the L-band region (approximately 1565–1625 nm). Wavelength

references are needed in these regions to calibrate instruments that are used to characterize

components and monitor the wavelengths of the channels. To complement our wavelength

calibration references for the WDM C-band (Standard Reference Materials SRM 2517a and

SRM 2519) [1,2], we have developed SRMs 2514 and 2515, carbon monoxide 12C

16O and

13C16O, respectively. SRM 2514 is for use as a wavelength reference in the 1560–1595 nm

region and SRM 2515 is for use in the 1595–1630 nm region. This document describes SRMs

2514 and 2515 and summarizes the results of our uncertainty analysis.

Fundamental atomic or molecular absorption lines provide wavelength references that are very

stable under changing environmental conditions, such as temperature and pressure variations or

the presence of electromagnetic fields. The carbon monoxide 12C

16O 3ν rotational-vibrational

combination band, shown in Fig. 1a, contains about 40 absorption lines between 1560 nm and

1595 nm. The 13C

16O isotopic species of carbon monoxide, shown in Fig 1b, has about 40

absorption lines between 1595 nm and 1630 nm

Standard Reference Material 2514 is intended for wavelength calibration in the spectral region

from 1560 nm to 1595 nm. The unit contains a 20 cm long borosilicate glass cell filled to a

pressure of 133 kPa (1000 Torr) with high purity (99.95 %) 12C

16O gas. The gas is contained in

the cell with all-glass seals at the windows and the fill port. Before filling, the cell window seals

are inspected and leak-tested by the manufacturer. To reduce optical loss and interference

fringes the cell windows are antireflection coated, wedged by about 1°, and fused to the cell body

at an angle of 5°. Light from a singlemode optical fiber is collimated into a free beam, and then

passes through the cell in a four-pass configuration, yielding an 80 cm path length. Figure 2

shows a schematic diagram of the fiber-pigtailed SRM cell holder. The cell holder is packaged

in a small instrument box (approximately 32 cm long × 12.5 cm wide × 9 cm high) with two

FC/PC fiber connectors for the input and output of a user-supplied light source. When measured

using a narrowband source, such as a tunable laser, the 80 cm path length provides lines with

depths ranging from a few percent to 18 % and widths of 0.04 nm to 0.06 nm. When measured

using an optical spectrum analyzer (OSA) set at 0.05 nm resolution bandwidth, the maximum

line depth is reduced to about 14 %; this depth is further reduced to about 9 % when measured

using an OSA set at 0.1 nm resolution bandwidth. The certificate for SRM 2514 is presented in

Appendix A. It includes the certified wavelength values, spectra, and instructions for use.

Standard Reference Material 2515 is intended for wavelength calibration in the spectral region

from 1595 nm to 1630 nm. The unit contains a 20 cm long borosilicate glass cell filled to a

pressure of 133 kPa (1000 Torr) with high purity (99%) 13C

16O gas. The optical packaging is

identical to that described above for SRM 2514 and provides similar line strengths and widths.

The certificate for SRM 2515 is presented in Appendix B.

The vacuum wavelengths of selected 12C

16O 3ν lines have been measured and tabulated for very

low pressure conditions with an uncertainty of about 8 x 10-6 nm [3]. The HITRAN database [4]
2

values for 12C

16O agree with those in Ref. [3] to within 0.02 pm. The predicted line centers of

13C16O 3ν lines are also reported in the HITRAN database [4]. Our measurements of 18 line

centers in the 13C

16O spectrum [5] show excellent agreement (within 0.14 pm) with the HITRAN

data. For a wavelength reference, the stability of the wavelength of each absorption line is a

critical characteristic. The largest potential source of line shift is energy level shifts caused by

the interaction of the molecules during elastic collisions [6]. Commonly called the pressure shift,

this shift depends linearly on the collision frequency. For wavelength calibration of instruments,

it is often desirable to use a moderate or high pressure sample in order to pressure-broaden the

lines and match the reference bandwidth to the instrumental resolution. This results in the

strongest signals for a given resolution bandwidth. To provide maximum sensitivity when used

with a 0.05 nm resolution instrument, such as an OSA, we chose a pressure of 133 kPa. Our

measurement of the pressure-induced shift and broadening for 14 lines in the 3ν rotationalvibrational band of carbon monoxide 12C

16O and 18 lines in the corresponding 13C16O band is

described in Ref. 5 (Appendix C of this document).

The dominant source of uncertainty for SRMs 2514 and 2515 is the pressure shift uncertainty.

Other potential sources of uncertainty are negligible at the level of uncertainty quoted for the line

centers. For example, a slope or variation in the background level can shift the apparent center

of a line. Nearby absorption lines, interference fringes due to reflected laser light, wavelength

dependence of the optical components, and variations in the optical source spectrum can cause

background variation. We found no evidence of nearby absorption lines in either spectrum. As

discussed above, interference fringes were minimized in the SRM design. Each SRM unit is

carefully aligned to reduce background slope. For higher accuracy applications, the instructions

for use in the SRM Certificate caution the user to divide the SRM output spectrum by the source

spectrum.

Section 2 gives the uncertainty analysis for the pressure shift adjustment. We summarize the

results in section 3.

2. Pressure Shift Adjustment

SRM 2514 uses carbon monoxide 12C

16O gas at a pressure of 133 ± 27 kPa (1000 ± 200 Torr).

We have accurately measured the pressure shift for 14 lines in the 3ν rotational-vibrational band

of 12C

16O [5]. For SRM 2514, we derive the line centers by adding each line’s pressure shift (at

133 kPa) to the low-pressure literature values [4]. SRM 2515 uses carbon monoxide 13C

16O gas

at a pressure of 133 ± 27 kPa. We have accurately measured the pressure shift for 18 lines in the

3ν rotational-vibrational band of 13C

16O [5] and derive the line centers for SRM 2515 by adding

each line’s pressure shift (at 133 kPa) to the low-pressure literature values [4].

The uncertainties quoted in this document are specified as either standard uncertainties (i.e., 1σ

values) or expanded uncertainties using a coverage factor of 2 (i.e., 2σ values). If no

specification is given, the uncertainties quoted are expanded uncertainties.

Figures 3 and 4 show the results of our pressure shift measurements. The pressure shift varies

with line number and is largest for lines far from the band center (transitions between states with

high rotational quantum number). The two isotopic species showed nearly identical shift
3

behavior, with a shift coefficient of about +0.01 pm/kPa (equivalently, +1.3×10-3 pm/Torr or

−0.16 MHz/Torr) near the band center, and about 0.02 pm/kPa (equivalently, +2.7×10-3 pm/Torr

or −0.31 MHz/Torr) for lines further from the band center. As discussed in Ref. [5], our shift

coefficient values for 12C

16O have lower uncertainty and are in good agreement with previous

measurements [3,7]. To our knowledge, there are no other measurements of the pressure shift of

13C16O absorption lines reported in the literature.

For the remainder of the lines in the band, we derive pressure shift coefficient values using linear

interpolation between the measured data points. Since we do not have a quantitative theoretical

model for the pressure shift of carbon monoxide, we assign a higher uncertainty to these

interpolated values. We assume that there is a 95 % probability that the shift coefficient values

for the intermediate lines lie between the values bounded by the upper and lower extents of the

expanded (2σ) uncertainties of the bracketing measured values. This yields an interpolation

standard uncertainty of a/2, where the range bounded by the expanded uncertainties of the

bracketing measured values is 2a [8]. We combine this (in quadrature) with the uncertainty of

the bracketing measured values to obtain the combined standard uncertainty of the pressure shift

coefficient for the interpolated values. In the case where the uncertainties for the bracketed

measured values are different, we use the larger uncertainty in this calculation. For example, we

measured the shift coefficients for lines R21 and R16 in 12C

16O (see Table 1). We assume that

there is a 95 % probability that the shift coefficients for intermediate lines lie between (0.0157 –

2 × 0.0009) and (0.0188 + 2 × 0.0010) pm/kPa, and assign an interpolation standard uncertainty

of [0.0188 + 2 × 0.0010 – (0.0157 – 2 × 0.0009)]/4 = 0.0017 pm/kPa. This is then combined in

quadrature with the larger of the bracketing measured value’s standard uncertainty

(0.0010 pm/kPa) to yield a shift coefficient standard uncertainty of 0.0020 pm/kPa for lines R17,

R18, R19, and R20. We compared our interpolated pressure shift coefficient values for 12C

16O

with previous measurements [3,7] and find that they agree within the quoted uncertainties.

There are two components of the pressure shift uncertainty for the SRMs: the component arising

from the pressure shift coefficient uncertainty (described above) and the component arising from

the uncertainty of the pressure within the absorption cell (P = 133 ± 27 kPa). We add these two

components in quadrature to obtain the pressure shift uncertainty for each certified line. The

pressure shift coefficient values, the pressure shift at the SRM pressure of 133 ± 27 kPa, and the

respective uncertainties are tabulated in Tables 1 and 2.

3. Sensitivity to Other Environmental Conditions

We evaluated molecular absorption line center sensitivity to temperature changes and

electromagnetic fields in Ref. [9] and concluded that these effects are small compared with the

pressure shift. Due to the fact that the pressure shift depends on the molecular collision rate,

there is a small dependence of the pressure shift on temperature:

m

m

T

T

Δl(T ) = Δl(T ) ,
4

where Δλ(T) is the pressure shift at temperature T, Δλ(Tm) is the pressure shift measured at

temperature Tm, and the temperatures T and Tm are in degrees Kelvin. From the above equation

it can be seen that a line center is fairly insensitive to temperature changes; a 50 °C increase from

room temperature would increase the pressure shift by only 8 %. This corresponds to a

maximum shift change of only 0.2 pm. To avoid thermal stress of the optical packaging, we

recommend that the SRM units be used and stored near ambient room temperature (22 ± 5 oC).

4. NIST Certification Procedure

The purpose of the SRM certification procedure is to verify that the unit (a) contains the correct

pressure of the appropriate isotopic species of carbon monoxide gas, (b) has no significant

contaminants, and (c) shows no evidence of cell leakage. Measurements of the spectral band,

similar to those shown in Figure 1 of the certificates (Appendices A and B), are made using a

broadband source and an optical spectrum analyzer. Higher resolution measurements are made

using a tunable diode laser (∼1 MHz linewidth) and a calibrated wavelength meter; spectra

similar to those shown in Figure 3 of the certificates are taken of each SRM unit, and one or

more lines are accurately fit to verify the line’s center and width using the procedure described in

Ref. [5]. To test for cell leakage, the higher resolution measurements described above are

repeated after a minimum waiting period of one month, and the results are compared to the

earlier data. Any differences between the two data sets, particularly the linewidth values, may

indicate cell leakage. This test is repeated on any suspicious unit, and the unit is rejected if it

continues to change or does not meet the line center specifications.

5. Summary

Tables 3 and 4 give the SRM certified wavelengths for 41 lines of the 3ν rotational-vibrational

band of 12C

16O (Table 3; SRM 2514) and 41 lines of the 3ν rotational-vibrational band of 13C16O

(Table 4; SRM 2515). The lines are certified with expanded uncertainties (2σ) ranging from

0.4 pm to 0.7 pm.

Sample certificates for SRMs 2514 and 2515 are presented in Appendices A and B. The

certificates include the certified wavelength values, spectra, and instructions for use. Appendix

C gives details of our pressure shift and pressure broadening measurements.

6. References

[1] S. L. Gilbert and W. C. Swann, “Acetylene 12C2H2 absorption reference for 1510 nm to

1540 nm wavelength calibration – SRM 2517a,” Natl. Inst. Stnd. Technol. Spec. Publ.

260-133 (2001 Edition).

[2] S. L. Gilbert, W. C. Swann, and C. M. Wang, “Hydrogen cyanide H13C

14N absorption

reference for 1530–1560 nm wavelength calibration – SRM 2519,” Natl. Inst. Stnd.

Technol. Spec. Publ. 260-137 (1998).

[3] N. Picque and G. Guelachvili, “Absolute wavenumbers and self-induced pressure lineshift

coefficents for the 3-0 vibration-rotation band of 12C

16O,” J. Mol. Spectrosc. 185, 244-248

(1997).
5

[4] L. S. Rothman et al., “The HITRAN molecular spectroscopic database and Hawks

(HITRAN atmospheric workstation): 1996 Edition,” J. Quant. Spectrosc. Rad. Transf. 60,

665-710 (1998).

[5] W. C. Swann and S. L. Gilbert, “Pressure-induced shift and broadening of 1560–1630-nm

carbon monoxide wavelength-calibration lines,” J. Opt. Soc. Am. B 19, 2461-2467 (2002)

[Appendix C of this document].

[6] W. Demtröder, Laser Spectroscopy, second edition, Springer-Verlag, New York (1996) pp.

67-82.

[7] J. Henningsen, H. Simonsen, T. Møgelberg, and E. Trudsø, “The 0→3 overtone band of

CO: precise linestrengths and broadening parameters,” J. Mol. Spectrosc. 193, 354-362

(1999).

[8] M. S. Levenson et al. “An approach to combining results from multiple methods motivated

by the ISO GUM,” J. Res. Natl. Inst. Stnd. Technol. 105, 571-579 (2000); B. N. Taylor

and C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST

measurement results,” Natl. Inst. Stand. Technol. Tech. Note 1297 (1994).

[9] W. C. Swann and S. L. Gilbert, “Pressure-induced shift and broadening of 1510–1540-nm

acetylene wavelength calibration lines,” J. Opt. Soc. Am. B 17, 1263-1270 (2000).
6

Table 1. Pressure Shift of 12C

16O Lines

Pressure shift coefficients and pressure shifts at SRM 2514 pressure of 133 ± 27 kPa for lines in

the 3ν band of 12C

16O. The lines measured at NIST [5] are indicated in bold. The other line

values are interpolated from the measured values. The pressure shift uncertainty is the

quadrature combination of the contribution from the pressure shift coefficient uncertainty and the

contribution from the cell pressure uncertainty.

line

pressure shift

coefficient

pm/kPa

coefficient standard

uncertainty (1σ)

pm/kPa

pressure shift

at 133 kPa

pm

shift expanded

uncertainty (2σ)

pm

R21 0.0188 0.0010 2.50 0.57

R20 0.0182 0.0020 2.42 0.72

R19 0.0176 0.0020 2.34 0.71

R18 0.0169 0.0020 2.25 0.70

R17 0.0163 0.0020 2.17 0.69

R16 0.0157 0.0009 2.09 0.48

R15 0.0156 0.0012 2.08 0.52

R14 0.0156 0.0012 2.07 0.52

R13 0.0155 0.0012 2.06 0.51

R12 0.0154 0.0004 2.05 0.42

R11 0.0153 0.0007 2.03 0.44

R10 0.0151 0.0007 2.01 0.44

R9 0.0150 0.0007 1.99 0.44

R8 0.0148 0.0007 1.97 0.43

R7 0.0147 0.0003 1.96 0.40

R6 0.0142 0.0009 1.88 0.45

R5 0.0136 0.0009 1.81 0.44

R4 0.0131 0.0005 1.74 0.37

R3 0.0124 0.0014 1.64 0.51

R2 0.0116 0.0014 1.55 0.49

R1 0.0109 0.0008 1.45 0.36

R0 0.0097 0.0010 1.29 0.37

P1 0.0112 0.0010 1.49 0.40

P2 0.0115 0.0009 1.53 0.39

P3 0.0127 0.0017 1.69 0.56

P4 0.0139 0.0007 1.85 0.41

P5 0.0146 0.0013 1.94 0.52

P6 0.0152 0.0013 2.03 0.53

P7 0.0159 0.0005 2.11 0.44

P8 0.0162 0.0012 2.16 0.53

P9 0.0166 0.0012 2.20 0.54

P10 0.0169 0.0012 2.24 0.54

P11 0.0172 0.0007 2.29 0.49

P12 0.0174 0.0014 2.32 0.59

P13 0.0177 0.0014 2.35 0.59

P14 0.0179 0.0014 2.38 0.60

P15 0.0181 0.0009 2.41 0.54

P16 0.0184 0.0016 2.44 0.64

P17 0.0186 0.0016 2.47 0.65

P18 0.0189 0.0016 2.51 0.65

P19 0.0191 0.0010 2.54 0.57
7

Table 2. Pressure Shift of 13C

16O Lines

Pressure shift coefficients and pressure shifts at SRM 2515 pressure of 133 ± 27 kPa for lines in

the 3ν band of 13C

16O. The lines measured at NIST [5] are indicated in bold. The other line

values are interpolated from the measured values. The pressure shift uncertainty is the

quadrature combination of the contribution from the pressure shift coefficient uncertainty and the

contribution from the cell pressure uncertainty.

line

pressure shift

coefficient

pm/kPa

coefficient standard

uncertainty (1σ)

pm/kPa

pressure shift at

133 kPa

pm

shift expanded

uncertainty (2σ)

pm

R21 0.0200 0.0010 2.66 0.59

R20 0.0196 0.0012 2.60 0.68

R19 0.0191 0.0012 2.54 0.67

R18 0.0187 0.0010 2.49 0.56

R17 0.0178 0.0017 2.37 0.69

R16 0.0169 0.0017 2.25 0.68

R15 0.0160 0.0009 2.13 0.49

R14 0.0160 0.0009 2.13 0.53

R13 0.0160 0.0009 2.13 0.53

R12 0.0160 0.0006 2.13 0.45

R11 0.0156 0.0007 2.07 0.49

R10 0.0152 0.0006 2.02 0.43

R9 0.0152 0.0006 2.02 0.45

R8 0.0152 0.0006 2.02 0.45

R7 0.0152 0.0004 2.02 0.42

R6 0.0146 0.0011 1.94 0.49

R5 0.0140 0.0011 1.86 0.48

R4 0.0134 0.0006 1.78 0.39

R3 0.0125 0.0015 1.66 0.58

R2 0.0115 0.0015 1.53 0.57

R1 0.0106 0.0010 1.41 0.39

R0 0.0101 0.0010 1.34 0.38

P1 0.0111 0.0010 1.48 0.40

P2 0.0118 0.0010 1.57 0.41

P3 0.0127 0.0013 1.69 0.56

P4 0.0136 0.0008 1.81 0.42

P5 0.0146 0.0017 1.95 0.60

P6 0.0157 0.0017 2.08 0.62

P7 0.0167 0.0007 2.22 0.48

P8 0.0169 0.0007 2.25 0.53

P9 0.0171 0.0007 2.27 0.49

P10 0.0178 0.0010 2.36 0.58

P11 0.0184 0.0007 2.45 0.52

P12 0.0180 0.0009 2.39 0.58

P13 0.0175 0.0008 2.33 0.51

P14 0.0180 0.0013 2.40 0.65

P15 0.0186 0.0013 2.47 0.66

P16 0.0191 0.0010 2.54 0.57

P17 0.0197 0.0013 2.62 0.70

P18 0.0203 0.0013 2.70 0.71

P19 0.0209 0.0010 2.78 0.62
8

Table 3. Certified Wavelengths for SRM 2514 (12C

16O)

Literature values from Ref. [4] adjusted for the pressure shift listed in Table 1 due to the 133 kPa

(1000 Torr) cell pressure. These vacuum wavelengths of the 3ν band of 12C

16O are certified with

the uncertainty indicated in parentheses for the last digits. The uncertainties quoted are the

expanded uncertainty using a coverage factor k = 2 (i.e., our quoted uncertainty is ±2σ).

R Branch Wavelength (nm) P Branch Wavelength (nm)

21 1560.5025(6) 1 1575.6498(4)

20 1560.8680(7) 2 1576.6311(4)

19 1561.2600(7) 3 1577.6397(6)

18 1561.6786(7) 4 1578.6758(4)

17 1562.1237(7) 5 1579.7392(5)

16 1562.5953(5) 6 1580.8300(5)

15 1563.0935(5) 7 1581.9485(4)

14 1563.6183(5) 8 1583.0945(5)

13 1564.1697(5) 9 1584.2683(5)

12 1564.7477(4) 10 1585.4698(5)

11 1565.3523(4) 11 1586.6993(5)

10 1565.9835(4) 12 1587.9567(6)

9 1566.6414(4) 13 1589.2422(6)

8 1567.3261(4) 14 1590.5559(6)

7 1568.0375(4) 15 1591.8978(5)

6 1568.7756(5) 16 1593.2681(6)

5 1569.5405(4) 17 1594.6669(6)

4 1570.3323(4) 18 1596.0942(7)

3 1571.1509(5) 19 1597.5502(6)

2 1571.9965(5)

1 1572.8691(4)

0 1573.7687(4)
9

Table 4. Certified Wavelengths for SRM 2515 (13C

16O)

Literature values from Ref. [4] adjusted for the pressure shift listed in Table 2 due to the 133 kPa

(1000 Torr) cell pressure. These vacuum wavelengths of the 3ν band of 13C

16O are certified with

the uncertainty indicated in parentheses for the last digits. The uncertainties quoted are the

expanded uncertainty using a coverage factor k = 2 (i.e., our quoted uncertainty is ±2σ).

R Branch Wavelength (nm) P Branch Wavelength (nm)

21 1595.3772(6) 1 1610.6596(4)

20 1595.7554(7) 2 1611.6393(4)

19 1596.1595(7) 3 1612.6457(6)

18 1596.5895(6) 4 1613.6788(4)

17 1597.0454(7) 5 1614.7388(6)

16 1597.5271(7) 6 1615.8255(6)

15 1598.0349(5) 7 1616.9392(5)

14 1598.5686(5) 8 1618.0797(5)

13 1599.1284(5) 9 1619.2473(5)

12 1599.7141(5) 10 1620.4420(6)

11 1600.3258(5) 11 1621.6641(5)

10 1600.9636(4) 12 1622.9132(6)

9 1601.6274(5) 13 1624.1898(5)

8 1602.3174(5) 14 1625.4940(6)

7 1603.0334(4) 15 1626.8257(7)

6 1603.7756(5) 16 1628.1851(6)

5 1604.5439(5) 17 1629.5723(7)

4 1605.3385(4) 18 1630.9873(7)

3 1606.1593(6) 19 1632.4303(6)

2 1607.0064(6)

1 1607.8799(4)

0 1608.7799(4)
10

 (a)

 (b)

Figure 1. Carbon monoxide 3ν rotational-vibrational spectra; (a) 12C

16O spectrum, (b) 13C16O spectrum.

Data were taken by passing LED light through an absorption cell and recording the spectrum of the

transmitted light using an optical spectrum analyzer set to a resolution bandwidth of 0.05 nm. The figure

shows the recorded spectrum divided by the LED spectrum. The CO gas pressure is 133 kPa (1000 Torr);

light makes four passes through the cell for a total optical path length of 80 cm.

1560 1565 1570 1575 1580 1585 1590 1595

0.80

0.85

0.90

0.95

1.00

R Branch P Branch

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

Normalized Transmittance

Wavelength (nm)

1595 1600 1605 1610 1615 1620 1625 1630

0.80

0.85

0.90

0.95

1.00

R Branch P Branch

19 18

17

16

15

14

13

12

11

10

9

8 7

6

5

4

3

2

1

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

Normalized Transmittance

Wavelength (nm)
Figure 2. Schematic diagram of the fiber-pigtailed SRM cell holder. The light beam path is shown in 

solid and dashed lines; the mirror on the left end directs the beam down to the lower beam path. The 

absorption cell length is 20 cm and the light makes four passes through the cell for a total optical beam 

path of 80 cm. 

11
12

Figure 3. 

12C16O pressure shift measurements: Plot of the pressure shift coefficient and pressure shift at

the SRM pressure of 133 kPa versus line number for the R and P branches of the 3ν band. Data are from

Ref. [5].

Figure 4. 

13C16O pressure shift measurements: Plot of the pressure shift coefficient and pressure shift at

the SRM pressure of 133 kPa versus line number for the R and P branches of the 3ν band. Data are from

Ref. [5].

R25 R20 R15 R10 R5 R0 P5 P10 P15 P20 P25

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

P19

1597.5 nm

R21

1560.5 nm

Pressure Shift Coefficient (pm/kPa)

Line

 Pressure Shift at 133 kPa (pm)

R25 R20 R15 R10 R5 R0 P5 P10 P15 P20 P25

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Pressure Shift Coefficient (pm/kPa)

Line

P19

1632.4 nm

R21

1595.4 nm

 Pressure Shift at 133 kPa (pm)
13

Appendix A

SRM 2514 Certificate

Appendix B

SRM 2515 Certificate

Appendix C

Journal Article:

W.C. Swann and S.L. Gilbert, “Pressure-induced shift and broadening of 1560–1630-nm

carbon monoxide wavelength-calibration lines,” J. Opt. Soc. Am. B 19, 2461-2467

(2002).
National Institute of Standards & Technology 

Certificate of Analysis 

Standard Reference Material® 2514 

Wavelength Calibration Reference for 1560 nm to 1595 nm 

(Carbon Monoxide 12C16O) 

Serial No.: 

This Standard Reference Material (SRM) is intended for wavelength calibration in the spectral region from 1560 nm

to 1595 nm. SRM 2514 is a single-mode optical-fiber-coupled absorption cell containing carbon monoxide (12C16O) 

gas at a pressure of 133 kPa (1000 Torr). The absorption path length is 80 cm and the absorption lines are about

50 pm wide. The cell is packaged in a small instrument box (approximately 32 cm long x 12.5 cm wide x 9 cm

high) with two FC/PC fiber connectors for the input and output of a user-supplied light source. This SRM can be 

used for calibrating a variety of wavelength-measuring instruments, such as optical spectrum analyzers, tunable 

lasers, and wavelength meters. Carbon monoxide 12C16O has about 40 accurately measured absorption lines in the 

1560 nm to 1595 nm wavelength region. 

Certified Wavelength Values: The vacuum wavelengths of absorption lines in the R and P branches of the 3ν

rotational-vibrational band of 12C16O have been determined previously to high accuracy and are tabulated in the 

HITRAN database [1]. These literature values for the vacuum wavelengths were adjusted for the pressure shift due

to the collisions between carbon monoxide molecules at the 133 kPa (1000 Torr) pressure within the SRM cell to 

obtain the certified wavelength values for this SRM. Details of the measurement procedure and data analysis for the 

determination of the pressure shift can be found in Reference 2, and the uncertainty analysis for the SRM is

documented in Reference 3. A spectrum of the absorption band is shown in Figure 1 and certified wavelength 

values are given in Table 1. Figure 2 shows an expanded scan near lines R6, R7, and R8. Figure 3 shows a high 

resolution scan of line R7. The center wavelengths of the lines listed in Table 1 are certified with uncertainties 

ranging from 0.4 pm to 0.7 pm. These uncertainties are the expanded uncertainties using a coverage factor k = 2, 

i.e., our quoted uncertainty is ± 2σ. 

Expiration of Certification: The certification of this SRM is valid indefinitely within the measurement 

uncertainties specified, provided the SRM is handled, stored, and used in accordance with the instructions given in 

this certificate (see Instructions for Use). The gas is contained in a glass cell with all-glass seals at the windows and 

the fill port. In the unlikely event of cell leakage, the linewidths and the small pressure shift of the line centers will 

change. Contact NIST if the linewidths or depths differ significantly from those shown in Figures 1 through 3, 

when measured using comparable resolution (see specific criteria in the section Suggested Procedure for HighAccuracy Requirements). 

Development of this SRM and supporting measurements were performed by W.C. Swann and S.L. Gilbert of the 

NIST Optoelectronics Division. 

Statistical consultation was provided by C.M. Wang of the NIST Statistical Engineering Division. 

The support aspects involved in the preparation, certification, and issuance of this SRM were coordinated through 

the NIST Standard Reference Materials Program by J.W.L. Thomas. 

Gordon W. Day, Chief 

Optoelectronics Division 

Gaithersburg, MD 20899 John Rumble, Jr., Acting Chief 

Certificate Issue Date: 17 May 2002 Standard Reference Materials Program

SRM 2514 Page 1 of 6 
Table 1. Certified Wavelengths for SRM 2514 

Literature values from Reference 1 adjusted for the pressure shift due to the 133 kPa (1000 Torr) cell pressure. 

These vacuum wavelengths of the 3ν band of 12C16O are certified with the uncertainty indicated in parenthesis for 

the last digits. The uncertainties quoted are the expanded uncertainty using a coverage factor k = 2, i.e., our quoted 

uncertainty is ± 2σ. 

R Branch Wavelength 

(nm)

P Branch Wavelength 

(nm)

21 1560.5025(6) 1 1575.6498(4)

20 1560.8680(7) 2 1576.6311(4)

19 1561.2600(7) 3 1577.6397(6)

18 1561.6786(7) 4 1578.6758(4)

17 1562.1237(7) 5 1579.7392(5)

16 1562.5953(5) 6 1580.8300(5)

15 1563.0935(5) 7 1581.9485(4)

14 1563.6183(5) 8 1583.0945(5)

13 1564.1697(5) 9 1584.2683(5)

12 1564.7477(4) 10 1585.4698(5)

11 1565.3523(4) 11 1586.6993(5)

10 1565.9835(4) 12 1587.9567(6)

9 1566.6414(4) 13 1589.2422(6)

8 1567.3261(4) 14 1590.5559(6)

7 1568.0375(4) 15 1591.8978(5)

6 1568.7756(5) 16 1593.2681(6)

5 1569.5405(4) 17 1594.6669(6)

4 1570.3323(4) 18 1596.0942(7)

3 1571.1509(5) 19 1597.5502(6)

2 1571.9965(5)

1 1572.8691(4)

0 1573.7687(4)

SRM 2514 Page 2 of 6 
Storage and Handling: The protective caps provided for the FC/PC fiber connectors should be replaced when the 

SRM is not in use. This SRM is intended to be used in a laboratory environment near ambient room temperature 

(22 °C ± 5 °C). The user should avoid exposing the unit to large temperature variations, temperature cycling, or 

mechanical shock, as these may cause the optical alignment to degrade. Such optical misalignment affects the 

throughput of the SRM but will not shift the centers of the absorption lines. 

Certification Measurement Conditions and Procedure: The long term stability of carbon monoxide and the use 

of fundamental molecular absorption lines render the SRM insensitive to changes in environmental conditions. The 

purpose of the certification procedure is to verify that the unit contains the correct pressure of 12C16O gas, has no 

significant contaminants, and shows no evidence of cell leakage. Measurements of the spectral band, similar to that 

shown in Figure 1, are made using a broadband source and an optical spectrum analyzer. Higher resolution 

measurements are made using a tunable diode laser (∼1 MHz linewidth) and a calibrated wavelength meter; spectra 

similar to that shown in Figure 3 are taken of each SRM unit and one or more lines are accurately fit to verify the 

line’s center and width using the procedure described in Reference 2. 

INSTRUCTIONS FOR USE 

General Considerations: The SRM can be used to calibrate a laser or wavelength measuring instrument in the 

1560 nm to 1595 nm region. The values in Table 1 are vacuum wavelengths; if the user requires the wavelength in

air, the appropriate correction for the index of refraction of air must be applied (see Reference 4). Depending on 

what type of instrument is being calibrated, a user-supplied broadband source or a tunable narrowband source may

be used. Typical optical connections are shown in Figure 4. The unit is bi-directional (has no preferred 

input/output port); connections to the unit should be made using single-mode optical fibers terminated with clean

FC/PC connectors. 

Use With a Broadband Source: A broadband source in the 1560 nm to 1595 nm region such as a light emitting 

diode, white light, or amplified spontaneous emission source is useful when calibrating an instrument, such as a 

diffraction grating based optical spectrum analyzer. A schematic for this type of calibration is shown in Figure 4(a). 

Light from the broadband source is coupled into the SRM and the output (transmission through the SRM) is

connected to the instrument that is being calibrated. The absorption lines of carbon monoxide appear as dips in the 

spectrum of the light source. 

Use With a Tunable Source: The SRM can be used to calibrate the wavelength scale of a tunable source in the 

1560 nm to 1595 nm region (such as a diode laser, a fiber laser, or a source filtered by a tunable filter). A 

schematic for this type of calibration is shown in Figure 4(b). The laser is tuned over one or more of the carbon 

monoxide absorption lines. The transmission through the SRM is monitored by a detector; the transmitted power 

passes through a minimum at the center of an absorption line. Alternatively, a tunable laser source and the SRM

can be used to check the calibration of a wavelength meter by measuring the wavelength of the laser (using the 

wavelength meter) as the laser is tuned through an absorption line. 

Suggested Procedure for Low-Accuracy Requirements; Calibration Uncertainty > 30 pm: If calibrating an 

instrument using a broadband source, use an instrument resolution of ≤ 0.1 nm. If using a tunable source, use a data

point density of at least one point every 0.005 nm (5 pm). After identifying a particular absorption line by comparing to

the spectrum in Figure 1, find the center or minimum point of the line. Calibrate the instrument to the center 

wavelength of this line (from Table 1) using the calibration procedure specified by the instrument manufacturer. The 

instrument’s linearity can be checked by repeating the procedure for a different absorption line and comparing it to the 

value listed in Table 1.

Suggested Procedure for Moderate-Accuracy Requirements; Calibration Uncertainty in the Approximate 

Range of 3 pm to 30 pm: If the source power varies significantly with wavelength, divide the SRM transmission 

spectrum by the source spectrum to obtain a normalized trace. After identifying a particular absorption line by 

comparing to the spectrum in Figure 1, make a high resolution scan of the line. If calibrating an instrument using a 

broadband source, use an instrument resolution of ≤ 0.05 nm. If using a tunable source, use a data point density of at

least one point every 0.002 nm (2 pm). Find the wavelength readings on both sides of the line where the absorption is

50 % of the maximum; the line center is half-way between these two wavelength readings. For higher accuracy results, 

repeat this procedure five times and take the average of the measurements. Alternatively, the line center can be

determined by fitting the central portion using a fourth order polynomial function. Calibrate the instrument to the 

center wavelength of this line (from Table 1) using the calibration procedure specified by the instrument manufacturer. 

The instrument’s linearity can be checked by repeating the procedure for a different absorption line and comparing it to

the value listed in Table 1.

SRM 2514 Page 3 of 6 
NOTE: Highly reproducible relative wavelength measurements can be made using the procedure described for 

moderate-accuracy requirements. However, the procedure described in the following section is recommended to 

achieve high-accuracy absolute wavelength calibration. 

Suggested Procedure for High-Accuracy Requirements; Calibration Uncertainty < 3 pm: Connect a 

narrowband tunable light source (source bandwidth ≤ 1 pm) to one of the fiber connectors on the SRM unit.

After identifying a particular absorption line by comparing to the spectrum in Figure 1, make a high resolution scan 

of the line. Use a data point density of at least one point every 1 pm and divide the SRM transmission spectrum

by the source spectrum to obtain a normalized trace. Using a fitting technique such as the least squares 

technique, fit the absorption data to a Lorentzian or Voigt lineshape. Details of a line fitting procedure and

potential errors sources can be found in Reference 2, which is also included as an appendix in Reference 3. 

Calibrate the instrument to the center wavelength of this line (from Table 1) using the calibration procedure 

specified by the instrument manufacturer. The instrument’s linearity can be checked by repeating the procedure 

for a different absorption line and comparing it to the value listed in Table 1. Contact NIST if the width of line 

R7 differs by more than 25 % from the width shown in Figure 3. A large change in linewidth could indicate cell

leakage. 

1560 1565 1570 1575 1580 1585 1590 1595

0.80

0.85

0.90

0.95

1.00

R Branch P Branch

19

18

17

16

15

14

13

12

11

10

9 8 7 6

5

4

3

2

1

21

20

19

18

17

16

15

14

13

12

11

10

9 8 7

6

5

4

3

2

1

0

Nor

malized Transmittanc

e

Wavelength (nm)

Figure 1. Normalized spectrum of the 3ν band of 12C16O obtained by passing LED light through an SRM 2514 unit

and recording the spectrum of the transmitted light using an optical spectrum analyzer set to a resolution bandwidth

of 0.05 nm. The figure shows the recorded spectrum divided by the LED spectrum. The 12C16O gas pressure is 

133 kPa (1000 Torr); light makes four passes through a 20 cm long cell for a total optical path length of 80 cm. 

SRM 2514 Page 4 of 6 
1567.0 1567.5 1568.0 1568.5 1569.0

0.80

0.85

0.90

0.95

1.00

R6 R7 R8

Resolution BW 0.05 nm

Nor

m

alized Transmitta

n

c

e

Wavelength (nm)

Figure 2. Spectrum of the R6, R7, and R8 lines obtained by passing LED light through an SRM 2514 unit and

recording the spectrum using an optical spectrum analyzer set to a resolution bandwidth of 0.05 nm. 

1567.90 1567.95 1568.00 1568.05 1568.10 1568.15

0.80

0.85

0.90

0.95

1.00

Nor

malized Transmittanc

e

Wavelength (nm)

Figure 3. High resolution spectrum of line R7 obtained by passing tunable diode laser light through an SRM 2514 

unit and recording the transmittance as the laser is scanned.

SRM 2514 Page 5 of 6 
Figure 4. (a) Schematic of technique when using the SRM and a broadband source to calibrate an optical spectrum

analyzer. (b) Schematic of technique when using the SRM to calibrate a tunable source. A wavelength meter can be

calibrated by using a tunable laser in the configuration shown in (b) and measuring its wavelength using the

wavelength meter. 

REFERENCES 

[1] Rothman, L.S. et al.; The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN atmospheric 

workstation): 1996 Edition; J. Quant. Spectrosc. Rad. Transf. Vol. 60, pp. 665-710 (1998); available at

http://www.hitran.com/. 

[2] Swann, W.C.; Gilbert, S.L.; Pressure-Induced Shift and Broadening of 1560–1630 nm Carbon Monoxide 

Wavelength Calibration Lines; J. Opt. Soc. Am. B 19, pp. 2461-2467 (2002). Note: This paper is included as an appendix

in Reference 3 (below). 

[3] Gilbert, S.L.; Swann, W.C.; Carbon Monoxide Absorption References for 1560 nm to 1630 nm Wavelength 

Calibration – SRM 2514 (

12C16O) and SRM 2515 (13C16O); NIST Special Publication 260-146. 

[4] Edlen, B.; The Refractive Index of Air, Metrologia; Vol. 2, p. 12 (1966); CRC Handbook of Chemistry and 

Physics 77th Ed., pp. 10-266 (1996). 

Users of this SRM should ensure that the certificate in their possession is current. This can be accomplished by 

contacting the SRM Program at: telephone (301) 975-6776; fax (301) 926-4751; e-mail srminfo@nist.gov; or via 

the Internet http://www.nist.gov/srm.

SRM 2514 Page 6 of 6
National Institute of Standards & Technology 

Certificate of Analysis 

Standard Reference Material 2515 

Wavelength Calibration Reference for 1595 nm to 1630 nm 

(Carbon Monoxide 13C16O) 

Serial No.: 

This Standard Reference Material (SRM) is intended for wavelength calibration in the spectral region from 1595 nm

to 1630 nm. SRM 2515 is a single-mode optical-fiber-coupled absorption cell containing carbon monoxide (

13C16O) 

gas at a pressure of 133 kPa (1000 Torr). The absorption path length is 80 cm and the absorption lines are about 

50 pm wide. The cell is packaged in a small instrument box (approximately 32 cm long x 12.5 cm wide x 9 cm high) 

with two FC/PC fiber connectors for the input and output of a user-supplied light source. This SRM can be used for 

calibrating a variety of wavelength-measuring instruments, such as optical spectrum analyzers, tunable lasers, and 

wavelength meters. Carbon monoxide 13C16O has about 40 accurately measured absorption lines in the 1595 nm to 

1630 nm wavelength region. 

Certified Wavelength Values: The vacuum wavelengths of absorption lines in the R and P branches of the 3ν

rotational-vibrational band of 13C16O have been determined previously to high accuracy and are tabulated in the 

HITRAN database [1]. These literature values for the vacuum wavelengths were adjusted for the pressure shift due 

to the collisions between carbon monoxide molecules at the 133 kPa (1000 Torr) pressure within the SRM cell to 

obtain the certified wavelength values for this SRM. Details of the measurement procedure and data analysis for the 

determination of the pressure shift can be found in Reference 2, and the uncertainty analysis for the SRM is 

documented in Reference 3. A spectrum of the absorption band is shown in Figure 1 and certified wavelength 

values are given in Table 1. Figure 2 shows an expanded scan near lines R6, R7, and R8. Figure 3 shows a high 

resolution scan of line R7. The center wavelengths of the lines listed in Table 1 are certified with uncertainties 

ranging from 0.4 pm to 0.7 pm. These uncertainties are the expanded uncertainties using a coverage factor k = 2, 

i.e., our quoted uncertainty is ± 2σ. 

Expiration of Certification: The certification of this SRM is valid indefinitely within the measurement 

uncertainties specified, provided the SRM is handled, stored, and used in accordance with the instructions given in 

this certificate (see Instructions for Use). The gas is contained in a glass cell with all-glass seals at the windows and 

the fill port. In the unlikely event of cell leakage, the linewidths and the small pressure shift of the line centers will 

change. Contact NIST if the linewidths or depths differ significantly from those shown in Figures 1 through 3, when 

measured using comparable resolution (see specific criteria in the section Suggested Procedure for High-Accuracy

Requirements).

Development of this SRM and supporting measurements were performed by W.C. Swann and S.L. Gilbert of the 

NIST Optoelectronics Division. 

Statistical consultation was provided by C.M. Wang of the NIST Statistical Engineering Division. 

The support aspects involved in the preparation, certification, and issuance of this SRM were coordinated through 

the NIST Standard Reference Materials Program by J.W.L. Thomas. 

Gordon W. Day, Chief 

Optoelectronics Division 

Gaithersburg, MD 20899 John Rumble, Jr., Acting Chief 

Certificate Issue Date: 17 May 2002 Standard Reference Materials Program

SRM 2515 Page 1 of 6 
Table 1. Certified Wavelengths for SRM 2515 

Literature values from Reference 1 adjusted for the pressure shift due to the 133 kPa (1000 Torr) cell pressure. 

These vacuum wavelengths of the 3ν band of 13C16O are certified with the uncertainty indicated in parenthesis for 

the last digits. The uncertainties quoted are the expanded uncertainty using a coverage factor k = 2, i.e., our quoted 

uncertainty is ± 2σ. 

R Branch Wavelength 

(nm)

P Branch Wavelength 

(nm)

21 1595.3772(6) 1 1610.6596(4)

20 1595.7554(7) 2 1611.6393(4)

19 1596.1595(7) 3 1612.6457(6)

18 1596.5895(6) 4 1613.6788(4)

17 1597.0454(7) 5 1614.7388(6)

16 1597.5271(7) 6 1615.8255(6)

15 1598.0349(5) 7 1616.9392(5)

14 1598.5686(5) 8 1618.0797(5)

13 1599.1284(5) 9 1619.2473(5)

12 1599.7141(5) 10 1620.4420(6)

11 1600.3258(5) 11 1621.6641(5)

10 1600.9636(4) 12 1622.9132(6)

9 1601.6274(5) 13 1624.1898(5)

8 1602.3174(5) 14 1625.4940(6)

7 1603.0334(4) 15 1626.8257(7)

6 1603.7756(5) 16 1628.1851(6)

5 1604.5439(5) 17 1629.5723(7)

4 1605.3385(4) 18 1630.9873(7)

3 1606.1593(6) 19 1632.4303(6)

2 1607.0064(6)

1 1607.8799(4)

0 1608.7799(4)

SRM 2515 Page 2 of 6 
Storage and Handling: The protective caps provided for the FC/PC fiber connectors should be replaced when the 

SRM is not in use. This SRM is intended to be used in a laboratory environment near ambient room temperature 

(22 °C ± 5 °C). The user should avoid exposing the unit to large temperature variations, temperature cycling, or 

mechanical shock, as these may cause the optical alignment to degrade. Such optical misalignment affects the 

throughput of the SRM but will not shift the centers of the absorption lines. 

Certification Measurement Conditions and Procedure: The long term stability of carbon monoxide and the use 

of fundamental molecular absorption lines render the SRM insensitive to changes in environmental conditions. The 

purpose of the certification procedure is to verify that the unit contains the correct pressure of 13C16O gas, has no 

significant contaminants, and shows no evidence of cell leakage. Measurements of the spectral band, similar to that 

shown in Figure 1, are made using a broadband source and an optical spectrum analyzer. Higher resolution 

measurements are made using a tunable diode laser (∼1 MHz linewidth) and a calibrated wavelength meter; spectra 

similar to that shown in Figure 3 are taken of each SRM unit and one or more lines are accurately fit to verify the 

line’s center and width using the procedure described in Reference 2. 

INSTRUCTIONS FOR USE 

General Considerations: The SRM can be used to calibrate a laser or wavelength measuring instrument in the 

1595 nm to 1630 nm region. The values in Table 1 are vacuum wavelengths; if the user requires the wavelength in 

air, the appropriate correction for the index of refraction of air must be applied (see Reference 4). Depending on 

what type of instrument is being calibrated, a user-supplied broadband source or a tunable narrowband source may 

be used. Typical optical connections are shown in Figure 4. The unit is bi-directional (has no preferred input/output 

port); connections to the unit should be made using single-mode optical fibers terminated with clean FC/PC

connectors. 

Use With a Broadband Source: A broadband source in the 1595 nm to 1630 nm region, such as a light emitting 

diode, white light, or amplified spontaneous emission source is useful when calibrating an instrument, such as a 

diffraction grating based optical spectrum analyzer. A schematic for this type of calibration is shown in Figure 4(a). 

Light from the broadband source is coupled into the SRM and the output (transmission through the SRM) is 

connected to the instrument that is being calibrated. The absorption lines of carbon monoxide appear as dips in the 

spectrum of the light source. 

Use With a Tunable Source: The SRM can be used to calibrate the wavelength scale of a tunable source in the 

1595 nm to 1630 nm region (such as a diode laser, a fiber laser, or a source filtered by a tunable filter). A schematic 

for this type of calibration is shown in Figure 4(b). The laser is tuned over one or more of the carbon monoxide 

absorption lines. The transmission through the SRM is monitored by a detector; the transmitted power passes 

through a minimum at the center of an absorption line. Alternatively, a tunable laser source and the SRM can be 

used to check the calibration of a wavelength meter by measuring the wavelength of the laser (using the wavelength 

meter) as the laser is tuned through an absorption line. 

Suggested Procedure for Low-Accuracy Requirements; Calibration Uncertainty > 30 pm: If calibrating an 

instrument using a broadband source, use an instrument resolution of ≤ 0.1 nm. If using a tunable source, use a data 

point density of at least one point every 0.005 nm (5 pm). After identifying a particular absorption line by comparing to 

the spectrum in Figure 1, find the center or minimum point of the line. Calibrate the instrument to the center wavelength 

of this line (from Table 1) using the calibration procedure specified by the instrument manufacturer. The instrument’s 

linearity can be checked by repeating the procedure for a different absorption line and comparing it to the value listed in 

Table 1. 

Suggested Procedure for Moderate-Accuracy Requirements; Calibration Uncertainty in the Approximate Range 

of 3 pm to 30 pm: If the source power varies significantly with wavelength, divide the SRM transmission spectrum by 

the source spectrum to obtain a normalized trace. After identifying a particular absorption line by comparing to the 

spectrum in Figure 1, make a high resolution scan of the line. If calibrating an instrument using a broadband source, use 

an instrument resolution of ≤ 0.05 nm. If using a tunable source, use a data point density of at least one point every 

0.002 nm (2 pm). Find the wavelength readings on both sides of the line where the absorption is 50 % of the maximum;

the line center is half-way between these two wavelength readings. For higher accuracy results, repeat this procedure 

five times and take the average of the measurements. Alternatively, the line center can be determined by fitting the 

central portion using a fourth order polynomial function. Calibrate the instrument to the center wavelength of this line 

(from Table 1) using the calibration procedure specified by the instrument manufacturer. The instrument’s linearity can 

be checked by repeating the procedure for a different absorption line and comparing it to the value listed in Table 1. 

SRM 2515 Page 3 of 6 
NOTE: Highly reproducible relative wavelength measurements can be made using the procedure described for 

moderate-accuracy requirements. However, the procedure described in the following section is recommended to 

achieve high-accuracy absolute wavelength calibration. 

Suggested Procedure for High-Accuracy Requirements; Calibration Uncertainty < 3 pm: Connect a 

narrowband tunable light source (source bandwidth ≤ 1 pm) to one of the fiber connectors on the SRM unit. After

identifying a particular absorption line by comparing to the spectrum in Figure 1, make a high resolution scan of the 

line. Use a data point density of at least one point every 1 pm and divide the SRM transmission spectrum by the 

source spectrum to obtain a normalized trace. Using a fitting technique such as the least squares technique, fit 

the absorption data to a Lorentzian or Voigt lineshape. Details of a line fitting procedure and potential errors 

sources can be found in Reference 2, which is also included as an appendix in Reference 3. Calibrate the 

instrument to the center wavelength of this line (from Table 1) using the calibration procedure specified by the 

instrument manufacturer. The instrument’s linearity can be checked by repeating the procedure for a different 

absorption line and comparing it to the value listed in Table 1. Contact NIST if the width of line R7 differs by 

more than 25 % from the width shown in Figure 3. A large change in linewidth could indicate cell leakage. 

1595 1600 1605 1610 1615 1620 1625 1630

0.80

0.85

0.90

0.95

1.00

R Branch P Branch

19 18

17

16

15

14

13

12

11

10

9 8 7 6

5

4

3

2

1

21

20

19

18

17

16

15

14

13

12

11

10

9

8 7

6

5

4

3

2

1

0

Nor

malized Transmittance

Wavelength (nm)

Figure 1. Normalized spectrum of the 3ν band of 13C16O obtained by passing LED light through an SRM 2515 unit

and recording the spectrum of the transmitted light using an optical spectrum analyzer set to a resolution bandwidth

of 0.05 nm. The figure shows the recorded spectrum divided by the LED spectrum. The 13C16O gas pressure is 

133 kPa (1000 Torr); light makes four passes through a 20 cm long cell for a total optical path length of 80 cm. 

SRM 2515 Page 4 of 6 
1602.0 1602.5 1603.0 1603.5 1604.0

0.80

0.85

0.90

0.95

1.00

R6 R7 R8

Resolution BW 0.05 nm

Normalized Transmitta

n

c

e

Wavelength (nm)

Figure 2. Spectrum of the R6, R7, and R8 lines obtained by passing LED light through an SRM 2515 unit and

recording the spectrum using an optical spectrum analyzer set to a resolution bandwidth of 0.05 nm. 

1602.90 1602.95 1603.00 1603.05 1603.10 1603.15

0.80

0.85

0.90

0.95

1.00

Normalized Transmittance

Wavelength (nm)

Figure 3. High resolution spectrum of line R7 obtained by passing tunable diode laser light through an SRM 2515

unit and recording the transmittance as the laser is scanned. 

SRM 2515 Page 5 of 6 
Broadband

Source

Tunable

Source

SRM

Unit

SRM

Unit

Optical

Spectrum

Analyzer

(a)

(b)

Detector

Figure 4. (a) Schematic of technique when using the SRM and a broadband source to calibrate an optical spectrum

analyzer. (b) Schematic of technique when using the SRM to calibrate a tunable source. A wavelength meter can be

calibrated by using a tunable laser in the configuration shown in (b) and measuring its wavelength using the

wavelength meter. 

 REFERENCES 

[1] Rothman, L.S. et al.; The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN atmospheric 

workstation): 1996 Edition; J. Quant. Spectrosc. Rad. Transf. Vol. 60, pp. 665-710 (1998); available at 

http://www.hitran.com/. 

[2] Swann, W.C.; Gilbert, S.L.; Pressure-Induced Shift and Broadening of 1560–1630 nm Carbon Monoxide 

Wavelength Calibration Lines; J. Opt. Soc. Am. B 19, pp. 2461-2467 (2002). Note: This paper is included as an 

appendix in Reference 3 (below). 

[3] Gilbert, S.L.; Swann, W.C.; Carbon Monoxide Absorption References for 1560 nm to 1630 nm Wavelength 

Calibration – SRM 2514 (

12C16O) and SRM 2515 (13C16O); NIST Special Publication 260-146. 

[4] Edlen, B.; The Refractive Index of Air; Metrologia, Vol. 2, p. 12 (1966); CRC Handbook of Chemistry and 

Physics 77th Ed., pp. 10-266 (1996). 

Users of this SRM should ensure that the certificate in their possession is current. This can be accomplished by 

contacting the SRM Program at: telephone (301) 975-6776; fax (301) 926-4751; e-mail srminfo@nist.gov; or via 

the Internet http://www.nist.gov/srm.

SRM 2515 Page 6 of 6 
Pressure-induced shift and broadening of

1560–1630-nm carbon monoxide

wavelength-calibration lines

W. C. Swann and S. L. Gilbert

Optoelectronics Division, National Institute of Standards and Technology, Boulder, Colorado 80305

Received February 20, 2002; revised manuscript received May 6, 2002

We have measured the line centers and the pressure-induced shifts of 14 lines in the 3n rotational–vibrational

band of carbon monoxide, 12C16O, and 18 lines in the corresponding band of 13C16O. These lines can be used

as wavelength references in the optical fiber communication wavelength-division multiplexing L band (approximately 1565–1625 nm). The 12C16O spectrum has useful reference lines from 1560 to 1595 nm, and the 13C16O spectrum has lines from 1595 to 1630 nm. We observed that, except for a shift of 35 nm toward longer

wavelengths for the 13C16O spectrum, the behaviors of the two isotopic species are similar. We found that the

pressure shift varies with line number, from ;10.01 to 10.02 pm/kPa (;0.16 to 0.31 MHz/Torr). In addition,

we measured the pressure broadening of these lines; we found that it also varies with line number and is typically 0.3–0.4 pm/kPa (approximately 5–7 MHz/Torr).

OCIS codes: 020.3690, 060.2330, 120.3940, 120.4800, 300.0300, 300.6390.

1. INTRODUCTION

Wavelength-division multiplexing (WDM) in optical fiber

communication systems increases bandwidth by using

many wavelength channels. Current WDM systems

typically employ 50- or 100-GHz channel spacing (0.4 or

0.8 nm, respectively) in the 1540–1560 nm WDM C band.

WDM will expand into the L-band region (approximately

1565–1625 nm) in the near future, and WDM may be

implemented in shorter wavelength regions as well.

Wavelength references are needed in these regions for

calibration of instruments that are used to characterize

components and monitor the wavelengths of the channels.

Fundamental atomic or molecular absorptions provide

wavelength references that are stable under changing environmental conditions such as temperature and pressure

variations or the presence of electromagnetic fields. The

National Institute of Standards and Technology has developed wavelength calibration transfer standards for the

1510–1560-nm region based on acetylene and hydrogen

cyanide.1–3 We examined a number of molecules as potential references for the WDM L-band region. Hydrogen and deuterium halides generally have strong lines

and simple spectra, but of these only hydrogen iodide4 has

spectral lines in the L band. Unfortunately, hydrogen iodide has several drawbacks: the spectrum (lines from

1534 to 1595 nm) only partially covers the L band, some

of the lines have significant substructure owing to the

electric-quadrupole hyperfine interaction, and the gas is

difficult to work with because of its reactivity and tendency to decompose. We also investigated various hydrocarbons, halogenated hydrocarbons, and other gases containing one or more C—H bonds, because overtones of the

C—H bond’s fundamental vibrational frequency have

spectra near 1550 nm. Although some of the spectra

were in the correct location, we found that they either

were too weak or were highly convoluted, containing hundreds of overlapping lines. These are typically not

simple linear molecules, and off-axis vibrations cause

complicated spectra. The carbon monoxide 3n

rotational–vibrational band has a simple spectrum in this

region, but the absorption strength is small; at a pressure

of 133 kPa (1000 Torr), a path length of 80 cm produces an

absorption of ;15% for the stronger lines.

We decided to develop National Institute of Standards

and Technology Standard Reference Material (SRM)

transfer standards for the WDM L band based on the absorption lines of carbon monoxide (12C16O and 13C16O).

Figure 1 shows the spectra for these two isotopic species;

12C16O has ;40 lines from 1560 to 1595 nm, and 13C16O

has ;40 lines from 1595 to 1630 nm. The vacuum wavelengths of selected 12C16O line centers of the 3n band have

been measured and tabulated for low-pressure

conditions,5,6 with one author quoting an uncertainty of

8 3 1026 nm.5 Similarly accurate measurements of the

corresponding band of 13C16O have not been made, to our

knowledge. However, the predicted low-pressure line

centers for 13C16O, calculated by use of mass-independent

Dunham parameters, are reported in the HITRAN

database.7 For wavelength calibration of instruments it

is often desirable to use an intermediate- or high-pressure

sample to pressure broaden the lines and match the reference bandwidth to the instrument resolution. Doing so

results in the strongest signals for a given resolution

bandwidth. To provide maximum sensitivity when it is

used with a 0.05-nm resolution instrument, such as an

optical spectrum analyzer, the gas in the carbon monoxide

SRM will be at a pressure of ;133 kPa (1000 Torr). In

addition to broadening the lines, the higher pressure also

slightly shifts the line centers. This shift, which results

from energy-level shifts caused by the interaction of molW. C. Swann and S. L. Gilbert Vol. 19, No. 10/October 2002/J. Opt. Soc. Am. B 2461
ecules during collisions,8 increases linearly with pressure

and is often called the pressure shift. Inasmuch as our

goal is to certify the SRM references with an uncertainty

of less than 1 pm, we need an accurate measurement of

the pressure shift for both isotopic species. Picque and

Guelachvili5 measured the pressure shifts of a number

of 12C16O lines with an uncertainty of ;2.5

3 1023 pm/kPa, and Henningsen et al.6 measured the

pressure shift of many lines of the 12C16O R branch with

an uncertainty of ;1.4 3 1023 pm/kPa (Henningsen did

not report values for the P branch). To our knowledge

there are no measurements of the pressure shift of 13C16O

absorption lines reported in the literature.

We measured the line centers, pressure shifts, and

pressure broadening of 14 lines in the 12C16O spectrum

and of 18 lines in the 13C16O spectrum. As a check on our

measurement accuracy we also extrapolated these line

centers to zero pressure and compared those values with

the literature values. We describe our measurement procedure in Section 2 and summarize the results in Section

3. Conclusions are presented in Section 4.

2. MEASUREMENT DESCRIPTION AND

DATA ANALYSIS

A schematic diagram of our pressure-shift measurement

apparatus is shown in Fig. 2. Light from a tunable diode

laser is sent through two absorption cells simultaneously,

and the transmission through each cell is monitored by

detectors. One cell contained carbon monoxide gas (either 12C16O or 13C16O) at a relatively low pressure of ;27

kPa (;200 Torr), and the other contained the same isotopic species at a higher pressure of ;133 kPa (;1000

Torr). A third detector monitored the laser power, and a

wavelength meter measured the laser’s wavelength with

an uncertainty of 1 part in 107 (0.16 pm at 1600 nm). A

computer controlled the laser wavelength scan and recorded the readings of the three detectors and the wavelength meter.

Figure 3 shows spectra of line R7 of 13C16O obtained

with the low- and high-pressure cells. The pressure

broadening in the high-pressure spectrum is obvious.

We are interested primarily in the shift of the highpressure line center relative to the low-pressure line center. Fourteen lines in the 12C16O spectrum and eighteen

lines in the 13C16O spectrum were scanned with this technique. The measured quantity, transmitted power IT , is

related to absorption coefficient a and absorption path

length L by

IT 5 I0 exp~2aL!, (1)

where I0 is the incident power. We first divided the cell

transmission curves by the laser power monitor signal to Fig. 1. Carbon monoxide 3n rotational–vibrational spectra.

Top, the 12C16O spectrum; bottom, the 13C16O spectrum. We

took these data by passing LED light through an absorption cell

and recording the spectrum of the transmitted light with an optical spectrum analyzer with a 0.05-nm resolution bandwidth.

The recorded spectrum divided by the LED spectrum is shown.

The CO gas pressure was 133 kPa (1000 Torr); light made four

passes through the cell for a total optical path length of 80 cm.

The bottom spectrum is noisier because of lower power from the

LED.

Fig. 2. Diagram of pressure-shift measurement apparatus.

Fig. 3. Tunable diode laser scan of the 13C16O R7 line showing

transmittance through the low-pressure (26.7-kPa) and highpressure (133-kPa) cells.

2462 J. Opt. Soc. Am. B/Vol. 19, No. 10/October 2002 W. C. Swann and S. L. Gilbert
remove common-mode intensity variations and normalized the data. We then took the natural logarithm to obtain the absorbance, aL.

Individual lines were then fitted to Voigt profiles8 by

use of an orthogonal distance regression algorithm.9 The

orthogonal distance regression, called either error-invariables or total-least-squares regression, obtains the

model parameters by minimizing the sum of squares of

the orthogonal distances from the model to the data

points. The fitting program was able to account for a

background slope and uncertainties in both x (wavelength) and y (transmitted power). A Voigt profile is a

convolution of Lorentzian and Gaussian profiles; it results

when there is a combination of Gaussian broadening (resulting from Doppler broadening, for example) and

Lorentzian line shape (resulting from the natural linewidth or pressure broadening, for example). In our situation, the natural linewidth is small (typically ,2 MHz

for molecular absorption lines in this region10) compared

with the Gaussian Doppler broadening (;400 MHz) and

the Lorentzian pressure broadening. The pressurebroadened component of the linewidths ranged from 23

to 553 the Doppler-broadened component. We fixed the

Doppler linewidth at 3.65 pm (Ref. 8) and allowed other

fitting parameters to vary.

The fused-silica absorption cells are 20 cm long, with

windows attached to the cells by a glass frit method. To

prevent interference fringes in the transmitted signal the

windows are mounted at an angle of 11° and also are

wedged by ;2°. The cells were first evacuated and leak

checked and were then filled with isotopically pure gas

(99.95% 12C16O or 99% 13C16O). During the fill process

the pressure in the fill manifold (and hence in the cell)

was monitored with a capacitance manometer. Once

filled, the cells were closed off with a glass valve with

O-ring seals. To check a cell’s pressure after closing the

valve (which changes the cell’s pressure as the valve’s O

ring compresses), and to monitor a cell’s pressure over the

course of the measurements, we generated a plot of the

Lorentzian component of the linewidth (derived from the

Voigt line fit) versus pressure for line R7. This allowed

us to determine a cell’s pressure at any time by measuring the width of line R7 and comparing it with the plot.

To generate the plot we mounted a cell in our pressureshift measurement apparatus and attached it to our fill

manifold with a copper tube. In this way we monitored

the cell pressure by using the capacitance manometer

while we measured the linewidth and the line center. We

conducted these measurements on line R7 of both isotopic

species for several pressures from 13.3 kPa (100 Torr) to

133 kPa (1000 Torr). Figure 4(a) is a plot of the full

width at half-maximum (FWHM) of the Lorentzian component of the 13C16O line R7 versus pressure and a linear

least-squares fit to the data. As can be seen from the figure, the Lorentzian component of the width (pressure

broadening) has a linear dependence on pressure. Figure 4(b) shows the line-center wavelength versus pressure of the same line and the corresponding linear leastsquares fit; as can be seen from this figure, the pressure

shift is also linearly dependent on pressure. Based on

our calibration of linewidth versus pressure for line R7,

the pressures for the low- and high-pressure cell pairs

used in the subsequent shift measurements were 26.4

6 0.5 kPa (198 6 4 Torr) and 134.5 6 1.3 kPa (1009

6 10 Torr) for 12C16O, and 26.9 6 0.5 kPa (202

6 4 Torr) and 133.5 6 1.3 kPa (1001 6 10 Torr) for 13C16O. The pressure uncertainty quoted here is the expanded uncertainty that we obtained by applying a coverage factor k 5 2 (i.e., our quoted uncertainty is 62s).11

Inasmuch as the spectra for the low- and high-pressure

cells were measured simultaneously, the absolute accuracy of the wavelength meter was not of critical importance for measurement of the relative pressure shift.

However, the short-term statistical variation of the wavelength measurement did add noise to the data. To determine this statistical variation we repeatedly measured a

laser that was stabilized to a narrow rubidium line. The

statistical variation of repeated measurements yielded a

Gaussian distribution with a standard deviation of 0.1

Fig. 4. (a) FWHM of the Lorentzian component of the 13C16O R7

line versus pressure and the corresponding linear least-squares

fit to the data (error bars are smaller than the points). (b) Line

R7 center wavelength shift from the zero-pressure value versus

pressure and the corresponding linear least-squares fit to the

data; the error bars are 1 standard uncertainty (1s).

W. C. Swann and S. L. Gilbert Vol. 19, No. 10/October 2002/J. Opt. Soc. Am. B 2463
pm. Because of the band coverage of the two carbon

monoxide spectra, and the band limitations of our lasers,

we needed to use two different lasers through the course

of the measurement. We determined the experimental

uncertainty in the signal level by measuring the statistical variation of the data within a region of a line wing.

The standard deviation of the fluctuations was 3 parts in

105 and 8 parts in 106 of the transmitted power, depending on the laser used.

Each data point was assigned a standard uncertainty

of 0.1 pm for the wavelength and a fractional uncertainty

of 3 parts in 105 or 8 parts in 106, depending on which

laser we used, for the transmitted power. The fitting program determined the line centers and the Lorentzian

component of the linewidths, the corresponding uncertainties, and the reduced residual-sum-of-squares (x2)

value for the fit.

A. Background Variation

A slope or a variation in the background level can shift

the apparent center of a line, particularly for the wide

lines of the high-pressure cells. Nearby absorption lines,

interference fringes owing to reflected laser light, wavelength dependence of the optical components, beam pointing stability, and variations in the laser power can cause

background variation. We found no evidence of nearby

absorption lines in either spectrum. As mentioned

above, we removed common-mode laser power variations

by dividing the cell transmittance data by the power

monitor data. Owing to the wavelength dependence of

optical fiber couplers (splitters), we used free-space beam

splitters to send the laser light to the cells and the power

monitor. We minimized interference effects by using

wedged cell windows and beam splitters, windowless detectors, and two optical isolators.

Because the remaining background variations were not

purely statistical noise, they can potentially add uncertainty to our measurements. We modeled the effect of

these variations to determine their contribution to our

line-center and linewidth uncertainties. Two model Voigt

functions were generated to represent the strongest (R7)

and the weakest (P19) lines that we measured in 13C16O.

We obtained a sample baseline spectrum by scanning a

cell transmittance in a spectral region between two absorption lines. Sections of this baseline noise were then

added to the model lines, along with modeled wavelength

measurement noise. The resultant noisy modeled lines

were then fitted by the procedure described above. We

then repeated this process approximately 25 times, using

a different sample of baseline noise each time; this resulted in a set of fit parameters for the centers and widths

of both lines. For the weaker line we found that the standard deviations of the line-fitting parameters were considerably larger than the uncertainties returned by the

fitting program for a single line fit (0.09 versus 0.03 pm

for the line center and 0.6 versus 0.2 pm for the linewidth

of the high-pressure sample). For the stronger line, however, the standard deviations of the modeled line-fitting

parameters were approximately the same as the uncertainties returned by the fitting program for a single line

fit. This result is not surprising, because we would expect the background noise to have a larger effect for the

weaker line. To verify the results of the model we

scanned and fitted lines R7 and P19 eleven times. The

standard deviation of the fit parameters agreed with our

simulation results. To account for the effect of background variations on the other lines’ uncertainties, we interpolated the results that we obtained for lines P19 and

R7 to the other lines based on their line strength.

B. Wavelength Accuracy

Although the absolute accuracy of the wavelength measurement was not relevant to the pressure-shift measurement, extrapolating our line-center measurements to zero

pressure and comparing them with literature values

serves as a good verification of our measurements. To determine the line-center accuracy for our measurements

we first checked the accuracy of the wavelength meter

used in the measurements. We set up a high-accuracy

wavelength reference for this purpose.3 Diode laser light

at 1560.5 nm was amplified with an erbium-doped fiber

amplifier and was frequency doubled in a periodically

poled lithium niobate crystal. The resultant 780-nm

light was then used to conduct saturated absorption spectroscopy on the 5S1/2 → 5P3/2 transitions of rubidium

(85Rb and 87Rb). The line centers of the hyperfine components of these transitions have been measured with an

uncertainty of 60.4 MHz (Ref. 12); a subset of these lines

has been measured to higher accuracy.13 We stabilized

the laser to several different hyperfine components of the

87Rb transition and compared the wavelength meter reading (vacuum wavelength) with the literature values multiplied by 2. As the lines were very narrow (less than 10

MHz), the absolute stability of the laser was much better

than the quoted wavelength meter uncertainty of 1 part

in 107 (;20 MHz at 1600 nm). From measurements

taken before and after our pressure-shift scans we found

that the wavelength meter reading was offset by 20.07

6 0.07 pm (19 6 9 MHz). The uncertainty (2s) is derived from the standard deviation of multiple wavelength

meter calibration measurements made over the course of

the pressure-shift measurement. During this time the

wavelength meter’s offset varied from 10.03 pm to 20.13

pm.

3. PRESSURE SHIFT, LINE CENTER, AND

PRESSURE-BROADENING RESULTS

Tables 1 and 2 summarize our line-center, pressure-shift,

and pressure-broadening results. To obtain the unperturbed line-center values we adjusted the low- and highpressure line-center data for the wavelength meter’s offset and extrapolated the line centers to zero pressure by

use of a Monte Carlo fitting procedure. We also derived

the pressure-shift coefficient (change in line-center wavelength versus pressure) from this Monte Carlo fit. The

pressure-broadening coefficient for each line was determined by a Monte Carlo fit to the Lorentzian component

of the high- and low-pressure linewidths.

Temperature changes can slightly modify the pressure

shift and pressure broadening of a molecular line by

changing the collision frequency.8 For the measurements

reported here, the temperature was 22 6 2 °C. As discussed in Ref. 1, this temperature range would cause a

2464 J. Opt. Soc. Am. B/Vol. 19, No. 10/October 2002 W. C. Swann and S. L. Gilbert
60.3% change in the pressure shift and pressure broadening, which is negligible compared with our pressureshift and presure-broadening uncertainties.

Figure 5 shows the pressure shift versus line number

for 13C16O. In all cases the wavelength shift was positive

with increasing pressure. The R and P branches of both

isotopic species showed similar shift-versus-line number

behavior, with a shift of approximately 0.01 pm/kPa for

lines near the band center, rising to ;0.02 pm/kPa for

lines far from the band center (i.e., transitions between

states with high rotational quantum numbers).

As discussed above, pressure broadening is responsible

for the Lorentzian component of the Voigt line shape. We

found that the pressure broadening also varied with line

number (Fig. 6). In contrast to the pressure-shift dependence, however, the pressure broadening was largest for

lines near the band center (transitions between states

with low rotational quantum numbers). The pressureTable 1. 12C16O Line-Center, Pressure-Shift, and Pressure-Broadening Resultsa

Line Line Center Extrapolated to Zero Pressure (nm)

Shift Coefficient Broadening Coefficient

pm/kPa MHz/Torr pm/kPa MHz/Torr

R21 1560.50004(24) 0.0188(20) 20.309(32) 0.267(14) 4.38(22)

R16 1562.59327(20) 0.0157(18) 20.257(29) 0.273(12) 4.47(20)

R12 1564.74563(14) 0.0154(8) 20.251(13) 0.294(8) 4.80(14)

R7 1568.03555(10) 0.0147(6) 20.239(10) 0.315(6) 5.12(10)

R4 1570.33051(14) 0.0131(10) 20.212(16) 0.339(8) 5.49(12)

R1 1572.86770(20) 0.0109(16) 20.176(26) 0.388(12) 6.27(20)

R0 1573.76745(24) 0.0097(20) 20.157(32) 0.407(14) 6.57(22)

P1 1575.64836(24) 0.0112(20) 20.180(32) 0.413(14) 6.65(22)

P2 1576.62961(20) 0.0115(18) 20.185(29) 0.385(12) 6.19(20)

P4 1578.67400(16) 0.0139(14) 20.223(22) 0.359(12) 5.76(20)

P7 1581.94641(16) 0.0159(10) 20.254(16) 0.330(8) 5.27(12)

P11 1586.69708(16) 0.0172(14) 20.273(22) 0.312(8) 4.95(12)

P15 1591.89544(20) 0.0182(18) 20.285(28) 0.295(12) 4.65(18)

P19 1597.54775(24) 0.0191(20) 20.299(31) 0.279(14) 4.37(22)

aResults for the measured lines of the 3n band of carbon monoxide 12C16O at a temperature of 22 6 2 °C. Line-center vacuum wavelength results are

for low-pressure conditions; our measurements (column 2) are values obtained by extrapolation of the line center to zero pressure. The broadening coefficient is the pressure dependence of the FWHM of the Lorentzian component of the Voigt line profile. The uncertainties in the final digits of the values are

indicated in parentheses. The uncertainties quoted are the expanded uncertainties obtained by application of a coverage factor k 5 2 (i.e., our quoted

uncertainty is 62s).

Table 2. 13C16O Line-Center, Pressure-Shift, and Pressure-Broadening Resultsa

Line Line Center Extrapolated to Zero Pressure (nm)

Shift Coefficient Broadening Coefficient

pm/kPa MHz/Torr pm/kPa MHz/Torr

R21 1595.37446(20) 0.0200(20) 20.314(38) 0.253(16) 3.97(26)

R18 1596.58693(20) 0.0187(20) 20.293(34) 0.272(16) 4.27(25)

R15 1598.03287(18) 0.0160(18) 20.250(28) 0.287(12) 4.50(20)

R12 1599.71196(16) 0.0160(12) 20.250(20) 0.303(10) 4.74(15)

R10 1600.96157(16) 0.0152(12) 20.237(18) 0.313(8) 4.88(13)

R7 1603.03136(12) 0.0152(8) 20.237(14) 0.326(8) 5.07(12)

R4 1605.33673(16) 0.0134(12) 20.208(20) 0.345(10) 5.36(16)

R1 1607.87857(20) 0.0106(20) 20.164(32) 0.401(14) 6.20(22)

R0 1608.77849(20) 0.0101(20) 20.157(38) 0.419(16) 6.47(26)

P1 1610.65814(20) 0.0111(20) 20.171(36) 0.424(16) 6.54(24)

P2 1611.63775(20) 0.0118(20) 20.182(32) 0.410(14) 6.31(22)

P4 1613.67706(18) 0.0136(16) 20.209(26) 0.368(14) 5.65(21)

P7 1616.93687(16) 0.0167(14) 20.255(20) 0.342(10) 5.23(16)

P9 1619.24491(16) 0.0171(14) 20.261(22) 0.329(10) 5.02(16)

P11 1621.66151(18) 0.0184(14) 20.280(22) 0.320(10) 4.87(15)

P13 1624.18751(18) 0.0175(16) 20.265(24) 0.318(12) 4.82(18)

P16 1628.18261(20) 0.0191(20) 20.288(34) 0.300(16) 4.52(22)

P19 1632.42759(20) 0.0209(20) 20.314(36) 0.286(16) 4.29(24)

aResults for the measured lines of the 3n band of carbon monoxide 13C16O at a temperature of 22 6 2 °C. Line center-vacuum wavelength results are

for low-pressure conditions; our measurements (column 2) are values obtained by extrapolation of the line center to zero pressure. The broadening coefficient is the pressure dependence of the FWHM of the Lorentzian component of the Voigt line profile. The uncertainties in the final digits of the values are

indicated in parentheses. The uncertainties quoted are the expanded uncertainties obtained by application of a coverage factor k 5 2 (i.e., our quoted

uncertainty is 62s).

W. C. Swann and S. L. Gilbert Vol. 19, No. 10/October 2002/J. Opt. Soc. Am. B 2465
broadening data for 12C16O showed similar trends and

magnitudes. Our pressure-broadening analysis does not

include the small effect of collisional narrowing that is

due to velocity averaging. This effect is negligible at

higher pressures, where pressure broadening dominates,

but can cause the line shape to deviate from the expected

Voigt profile at low pressures.14 Since we do not observe

significant discrepancies between our data and the Voigt

function, we conclude that the line-shape modification

that is due to collisional narrowing is negligible at the

level of our quoted uncertainty.

Figure 7 compares our 12C16O pressure-shift results

with those of Picque and Guelachvili5 and Henningsen

et al.6 Our pressure-shift standard uncertainty (1s)

ranges from 3 3 1024 to 1 3 1023 pm/kPa; the uncertainty quoted in Ref. 5 is 2.5 3 1023 pm/kPa, and the uncertainty quoted in Ref. 6 is ;1.4 3 1023 pm/kPa. Our

shift values have lower uncertainty and are in good agreement with those of Refs. 5 and 6; the differences between

our values and those previous measurements are within

the quoted uncertainty for each line. Our pressurebroadening results also agree well with those reported in

Ref. 6 for the R branch of 12C16O (Ref. 6 does not report

values in the P branch). Figure 8 compares our determinations of the zero-pressure line-center values for 12C16O

with the more accurate values reported in Ref. 5, which

were also extrapolated to zero pressure. Our standard

uncertainty (1s) is typically near 0.1 pm, whereas the estimated uncertainty given in Ref. 5 is 3 3 1025 cm21

(0.008 pm). All our line-center values are in good agreement with those of Refs. 5 and 7; the differences between

the values are within our standard uncertainty for each

line center. To date, the only reference that we have

found that reports zero-pressure line-center values for

13C16O is the HITRAN database.7 To our knowledge,

there are no measurements of the pressure shift of 13C16O

absorption lines reported in the literature. Our zeropressure line-center values for 13C16O are in good agreement with the HITRAN values; the differences between

our values and the HITRAN values are less than 0.15 pm.

These comparisons with calculations and previous meaFig. 5. Pressure-shift coefficient versus line number for 13C16O.

Fig. 6. Pressure dependence of the Lorentzian component

(FWHM) of the linewidth versus line number for 13C16O.

Fig. 7. Comparison of 12C16O pressure-shift results. Plotted is

the difference between the results of this work, with 1s standard

uncertainty error bars, and the measurements of Picque and

Guelachvili.5 The difference between the results of Henningsen

et al.6 and Ref. 5 are also plotted.

Fig. 8. Comparison of 12C16O line-center results. Plotted is the

difference between the results of this work, with 1s standard uncertainty error bars, and the measurements of Picque and

Guelachvili.5 The HITRAN database values7 (not shown) are all

within 0.02 pm of the Picque–Guelachvili values.

2466 J. Opt. Soc. Am. B/Vol. 19, No. 10/October 2002 W. C. Swann and S. L. Gilbert
surements give us further confidence in our analysis of

the pressure-shift coefficient values and uncertainties for

the 12C16O and 13C16O measurements.

4. CONCLUSIONS

We have measured the pressure-shift coefficient for 14

lines of the 12C16O isotopic species and 18 lines of the 13C16O isotopic species of the 3n rotational–vibrational

band of carbon monoxide. The two isotopic species

showed nearly identical shift behavior, with a shift of

;10.01 pm/kPa (equivalently, 11.3 3 1023 pm/Torr or

20.16 MHz/Torr) near the band center and of ;0.02 pm/

kPa (equivalently, 12.7 3 1023 pm/Torr or 20.31 MHz/

Torr) for lines farther from the band center. We have

also measured the pressure broadening of these lines and

found that it also varies with line number, ranging from

0.25 pm/kPa (4 MHz/Torr) to 0.42 pm/kPa (6.5 MHz/Torr).

For a pressure of 133 kPa (;1000 Torr; the conditions of

the National Institute of Standards and Technology SRM)

the pressure shift is typically near 2 pm but can be as

large as 2.8 pm for lines far from the band center and as

low as 1.3 pm for lines near the band center. The Lorentzian component of the linewidths at this pressure varies

from 34 pm (;4 GHz) for lines far from the band center to

56 pm (;7 GHz) near the band center.

Although the pressure shift and the pressure broadening are both due to the interactions between molecules

during collisions, they depend on line number rather differently. The pressure shift is largest for lines far from

the band center (transitions between states with high rotational quantum number J ), whereas the pressure

broadening is largest for lines near the band center (transitions between states with low J ). One explanation for

the pressure-broadening line dependence is that rotational averaging of the potential during a collision causes

states with high rotational angular momentum (high J )

to be perturbed less than states with low J. The pressure

shift is more difficult to interpret; it represents the difference between the shift of the excited state and the shift of

the ground state. We would need to conduct a more extensive study before drawing any conclusions about the

shift of a particular state. Our measurements of pressure broadening and shift of acetylene lines1 show trends

that are similar to those observed in carbon monoxide.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the help of C. Wang

for discussions and suggestions on the uncertainty analysis.

S. L. Gilbert can be reached by e-mail at sgilbert

@boulder.nist.gov.

REFERENCES

1. W. C. Swann and S. L. Gilbert, ‘‘Pressure-induced shift and

broadening of 1510–1540-nm acetylene wavelength calibration lines,’’ J. Opt. Soc. Am. B 17, 1263–1270 (2000).

2. S. L. Gilbert and W. C. Swann, ‘‘Acetylene 12C2H2 absorption reference for 1510 nm to 1540 nm wavelength

calibration—SRM 2517a,’’ Natl. Inst. Stand. Technol. (US)

Spec. Publ. 260–133 (2001).

3. S. L. Gilbert, W. C. Swann, and C. M. Wang, ‘‘Hydrogen cyanide H13C14N absorption reference for 1530–1560 nm wavelength calibration—SRM 2519,’’ Natl. Inst. Stand. Technol.

(US) Spec. Publ. 260–137 (1998).

4. F. Bertinetto, P. Gambini, R. Lano, and M. Puleo, ‘‘Stabilization of the emission frequency of 1.54 mm DFB laser diodes to hydrogen iodide,’’ IEEE Photon. Technol. Lett. 4,

472–474 (1993).

5. N. Picque and G. Guelachvili, ‘‘Absolute wavenumbers and

self-induced pressure lineshift coefficients for the 3–0

vibration–rotation band of 12C16O,’’ J. Mol. Spectrosc. 185,

244–248 (1997).

6. J. Henningsen, H. Simonsen, T. Møgelberg, and E. Trudsø,

‘‘The 0 → 3 overtone band of CO: precise linestrengths

and broadening parameters,’’ J. Mol. Spectrosc. 193, 354–

362 (1999).

7. L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D.

P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V.

Dana, J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks,

L. R. Brown, V. Nemtchinov, and P. Varanasi, ‘‘The HITRAN

molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition,’’ J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998); http://

www.hitran.com

8. W. Demtro ̈der, Laser Spectroscopy, 2nd ed. (SpringerVerlag, Berlin, 1996), pp. 67–82.

9. P. A. Boggs, R. H. Byrd, J. E. Rogers, and R. B. Schnabel,

‘‘Users reference guide for ODRPAC version 2.01 software

for weighted orthogonal distance regression,’’ Natl. Inst.

Stand. Technol. (US) Interagency Rep. 4834 (1992).

10. K. Nakagawa, M. de Labachelerie, Y. Awaji, and M.

Kourogi, ‘‘Accurate optical frequency atlas of the 1.5-mm

bands of acetylene,’’ J. Opt. Soc. Am. B 13, 2708–2714

(1996).

11. B. N. Taylor and C. E. Kuyatt, ‘‘Guidelines for evaluating

and expressing the uncertainty of NIST measurement results,’’ Natl. Inst. Stand. Technol. (US) Tech. Note 1297

(1993).

12. G. P. Barwood, P. Gill, and W. R. C. Rowley, ‘‘Frequency

measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm,’’ Appl. Phys. B 53, 142–147

(1991).

13. J. Ye, S. Swartz, P. Jungner, and J. Hall, ‘‘Hyperfine structure and absolute frequency of the 87Rb 5P3/2 state,’’ Opt.

Lett. 21, 1280–1282 (1996).

14. P. L. Varghese and R. K. Hanson, ‘‘Collisional narrowing effects on spectral line shapes measured at high resolution,’’

Appl. Opt. 23, 2376–2385 (1984).

W. C. Swann and S. L. Gilbert Vol. 19, No. 10/October 2002/J. Opt. Soc. Am. B 2467