NIST Special Publication 250-87

Shao Yang

Calibration Service for Instruments

that Measure Laser Beam Diameter

National Institute of Standards and Technology

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NIST Special Publication 250-87

Calibration Service for Instruments

that Measure Laser Beam Diameter

Shao Yang

Optoelectronics Division

National Institute of Standards and Technology

325 Broadway

Boulder, CO 80305-3337

July 2010

U.S. DEPARTMENT OF COMMERCE

Gary Locke, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

Patrick D. Gallagher, Director
For sale by the Superintendent of Documents, U.S. Government Printing Office

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

Mail Stop SSOP, Washington, DC 20402-0001

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2010

Certain commercial entities, equipment, or materials may be indentified in this document in order to describe an

experimental procedural or concept adequatetly. Such identification is not intended to imply recommention 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 Technical Note

Natl. Inst. Stand. Technol. Spec. Publ. 250-87, 20 pages (July 2010)

CODEN:NTNOEF
CONTENTS

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

2. Calibration Service Summary .......................................................... 1

3. Theory of Measurement .................................................................. 2

3.1 System Basics and Measurement Principle ................................... 2 

3.2 Measurement Equations ........................................................ 4 

3.3 Data Analysis .................................................................... 7 

4. Measurement System ....................................................................... 7 

4.1 Test Beam ......................................................................... 7 

4.2 Scanning Slit Measurement System ........................................... 8 

4.3 Data Acquisition ................................................................ 8 

5. Standard operating Procedure .......................................................... 8 

5.1 System Startup ................................................................... 8 

5.2 Optical Alignment .............................................................. 8 

5.3 Data Acquisition ................................................................... 8 

5.4 Data Analysis .................................................................... 9 

6. Uncertainty Evaluation .................................................................. 9

6.1 Test Beam Uncertainties ....................................................... 10 

6.1.1 Laser Power Stability (Type A) ....................................... 10 

6.1.2 Interference Pattern (Type A) ......................................... 11 

6.1.3 Wavelength Stability (Type B) ....................................... 11 

6.2 Measurement System Uncertainties ........................................... 11 

6.2.1 Detection Noise (Type A) ............................................. 11 

6.2.2 Measurement Area (Type B) .......................................... 11 

6.2.3 Optical Axis Tilt (Type B) ............................................. 11 

6.2.4 Positioning of the Measurement Plane (Type B) ................... 11 

6.2.5 Detector Nonlinearity (Type B) ....................................... 12 

6.2.6 Slit Tilt (Type B) ........................................................ 12 

6.2.7 Off-Centroid Slit Scan (Type B) .......................................12 

7 Quality Control ......................................................................... 13

8 Summary ................................................................................. 14

9 References ............................................................................... 15

1 

Calibration Service for Instruments that Measure Laser Beam 

Diameter 

Shao Yang 

National Institute of Standards and technology 

Optoelectronics Division 

325 Broadway 

Boulder, CO 80305 

This document describes the calibration service for instruments that measure laser beam 

diameter. An overview of the measurement procedures, measurement system, and 

uncertainty analysis is presented. A sample measurement report is included in this 

document that is similar to what is provided to the customer. The measurement report 

contains an absolute correction factor and a summary of the uncertainty assessment for 

the device under test. 

Key words: laser beam diameter; laser beam diameter measurement; laser beam profile; 

slit scan measurement; 

1. Introduction 

This measurement service compares laser beam diameter measurements made with the 

NIST beam diameter measurement system with those made by a test meter (or device 

under test, DUT) (usually a laser beam profiler). The measured beam diameter is the 

second-order moment (or 4σ) beam diameter defined by the International Organization 

for Standardization (ISO) [1 – 3]. A test laser beam, generated with a single-mode optical 

fiber and an optical fiber collimator at a wavelength of 830 nm, is used as a stable source 

for laser beam diameter measurements. The nominal measured beam diameter is 2.2 mm 

with a typical expanded (k=2) uncertainty of 0.3 %. The service identification (ID) for the 

measurement service in this document is 42220C. 

2. Calibration Service Summary 

The provision of calibration services (or measurement services in this document) is an 

essential element of the work of the Sources, Detectors, and Displays Group (as part of 

the Electronics and Electrical Engineering Laboratory). In the conduct of this work, as in 

all its efforts, the group is committed to excellence that is characteristic of a global leader 

in measurements and standards. Our goal is to provide measurement services that meet 

the needs of our customers and, through continuous improvement, to anticipate their 

needs, exceed their expectations, and deliver outstanding value to the nation. 

This calibration service is performed under conditions determined by the system setup 

and the test beam generated therewith. For these measurements, the customer’s meter, or 

device under test (DUT), is sent to NIST, where it is used to measure the test beam 

diameter. The test beam diameter has been characterized by the NIST beam diameter 

measurement setup. The DUT should be able to measure the second-order moment (or 
2 

4σ) beam diameter defined by ISO, but may use different measurement methods other 

than the NIST measurement. At the completion of the calibration measurements, the 

DUT and a calibration report are sent to the customer. The calibration report summarizes 

the results of the measurements and provides a list of the associated measurement 

uncertainties. (See Table 6.1.) The NIST beam diameter measurement system for this 

calibration service was designed and built at NIST. 

More information can be found in NIST Optoelectronics Division Quality Manual (QMII) for descriptions of NIST, the NIST Optoelectronics Division, and their quality 

systems. 

3. Theory of Measurement 

3.1 System Basics and Measurement Principle 

This service involves a direct comparison between measurements of the beam diameter of 

a test laser beam made with the DUT and those of the NIST beam diameter measurement 

system. The test beam is generated with a semiconductor diode laser, coupled into a 

single-mode fiber and expanded with a fiber collimator (as shown in Figure 3.1). The 

laser beam is stable in profile, power, and wavelength. The test beam profile is 

determined by the fiber-collimator, constant over a wide power range controlled with a 

fiber attenuator to meet the measurement power requirements for different test meters. 

Because the beam diameter varies along the propagation axis, the DUT and NIST 

measurements are made at the same position with reasonable tolerance. The NIST 

measurement system employs the slit scan method, where a narrow slit with a finite 

length scans across the beam in two orthogonal directions. The slit length and the scan 

distance are selected according to conditions stipulated in the ISO standard [1 – 3] for 

laser beam diameter measurements. The circularity of the test beam is sufficiently good 

that the identification of the major and minor axes of the test beam is not necessary 

within our quoted uncertainties. 
3 

Figure 3.1. Schematic diagram of the NIST beam diameter measurement system. The gray box is the test 

beam source. The fiber-coupled 830 nm laser diode (LD) is mounted on a temperature-controlled platform. 

All the fiber components are single-mode at 830 nm and linked with FC/PC connectors. The single-mode 

fiber (dotted line) and the collimator determine the diameter of the test beam. The slit and detector are 

placed on a rotation indexing mount and moved together during the scan. The DUT and the slit are in the 

same measurement plane from the collimator.

Slit & detector 

NIST beam diameter 

measurement system 

Detection plane 

FC/PC 

connectors 

Fiber splitter 

FC/PC 

connectors 

LD mount 

Test beam 

DUT 

Variable fiber 

attenuator 

Collimator 

Monitor 

detector 

LD 

Current source 

& TE controller 
4 

3.2 Measurement Equations 

ISO defines laser beam diameter by use of the second order moments of the beam power 

density distribution I(x, y) [1 - 3]: 

 

  













  

I x y dxdy

x x I x y dxdy

x

( , )

( ) ( , ) 2

2  , 3.1 

and 

 

  













  

I x y dxdy

y y I x y dxdy

y

( , )

( ) ( , ) 2

2  . 3.2 

x and y are the centroid coordinates of the power density distribution: 

 

 















 

I x y dxdy

xI x y dxdy

x

( , )

( , )

, 3.3 

 

 















 

I x y dxdy

yI x y dxdy

y

( , )

( , )

. 3.4 

The generalized beam diameter, used to represent the beam width and also called the 4σ

beam diameter, is defined as 



 

4

2

4

2 2

   x y d . 3.5 

This expression defines the beam diameter uniquely for all laser beam power 

distributions. For beams with a perfectly Gaussian profile, the 4σ beam diameter is 

exactly the width between the two 1/e

2

 points of the peak of the profile. 

The integrations in Equations 3.1 to 3.4, 





 P(x)  I(x, y)dy , 3.6 

and 





 Q( y)  I(x, y)dx , 3.7 

are power intensities of the beam along the x and y directions and represent powers in an 

infinitely long and narrow slit, P(x) and Q(y), at positions x and y, respectively. We may 

rewrite Equations 3.1 to 3.4 as 



 





  

P x dx

x x P x dx

x

( )

( ) ( ) 2

2  , 3.8 



 





  

Q y dy

y y Q y dy

y

( )

( ) ( ) 2

2  , 3.9 
5 











 

P x dx

xP x dx

x

( )

( )

, 3.10 











 

Q y dy

yQ y dy

y

( )

( )

. 3.11 

Equations 3.5 through 3.11 are the basis of slit scan measurement of the 4σ laser beam 

diameter. The integration limits in Equations 3.1 to 3.4 and 3.6 to 3.11 are from negative 

to positive infinity. This is impossible to realize in practice. Finite integration limits must 

be used in all practical measurements. The ISO standard stipulates that a square 

integration area whose width is three times the beam diameter in both the major and 

minor axes for a general elliptical beam be used for the evaluation of beam diameter. This 

uniquely defines the beam diameter for almost all practical beam profiles as shown in 

Figure 3.2 for an ideal Gaussian beam and the test beam in this measurement system. The 

ideal Gaussian beam has a theoretical beam diameter of 2.19 mm, and the measured test 

beam diameter is 2.194 mm. (For an ideal Gaussian beam, its measured beam diameter 

within this area differs from the true diameter by less than 5 millionth of a percent.) It is 

also impractical in many real measurements to limit the widths of measurement area to 

exactly three times the beam diameter. A reasonable deviation must be tolerated. Figure 

3.3 shows the percentage deviation of the measured beam diameter with different 

integration areas from that measured with the exact integration area stipulated in ISO 

standard for the NIST test beam. The integration limits of the NIST slit scan 

measurement are from 0 mm to 7 mm. This measurement area is within the range of 

integration area for the 0.1 % uncertainty limit for the test beam, as shown in Figure 3.3. 

For test beam profilers, the measurement areas are always finite but may be different, 

depending on the measurement principle and the design of the meter. 
6 

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10

Width of Integration Area W a (mm )

Width of Measured Beam 

Db (mm )

Gaussian

Test Beam

W a = 3D b

Figure 3.2 An integration area with a width of three times the beam diameter defines measured beam 

diameter for the test beam and the best fit Gaussian beam. The solid and dotted curves show the measured 

beam diameter, Db, of the test beam and the Gaussian beam as a function of the width of the integration 

area, Wa. The dashed straight line is Wa=3×Db. The intersecting point defines the beam diameter and the 

corresponding width of the measurement area. The theoretical beam diameter of the Gaussian beam is 2.19 

mm. The measured test beam diameter is 2.194 mm. 

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

456789

Width of Integration Area W a (mm )

Deviation (%)

Figure 3.3: Percentage deviation of the test beam diameter measured within an area of width Wa from that 

measured within the ISO defined area. The solid vertical line indicates the ISO defined measurement area. 

The two dashed vertical lines define the allowed range of measurement area that keeps the related Type B 

uncertainty contribution of measured beam diameter below 0.1 %. Due to a small side lope peaked at the 

position of about 8 mm, the curve does not level off as expected for a more well-behaved beam profile. 
7 

3.3 Data Analysis 

In the NIST slit scan measurement system, the width of the slit is 10 μm and the length is 

7 mm. For one single complete measurement, the slit scans in both the horizontal (x) and 

vertical (y) directions at steps of 25 μm for a range of 8 mm. Using iterations in the data 

processing software, the centroid and a 7 mm range around it in each direction are found 

and used in the calculation. The integration area is a square of 7 mm × 7 mm. The data 

analysis of the DUT is performed with the software provided by the customer. The final 

result is displayed in the meter and recorded.

4. Measurement System 

The NIST calibration service for instruments that measure laser beam diameter consists of a 

system to create a stable laser beam with a nominal diameter of 2.2 mm, referred to as the 

test beam, and a system characterizing the test beam by use of the slit scan method. A 

schematic of the beam creation-characterization system is shown in Figure 3.1. 

4.1 Test Beam 

A laser diode operating at a nominal wavelength of 830 nm and driven in constant current 

mode, and mounted on a temperature controlled platform serves as the source for the test 

beam. The laser is pigtailed with a single-mode fiber connected to a variable fiber 

attenuator. The fiber attenuator can be used to adjust the test beam intensity for different 

measurement conditions. The far end of the attenuator is connected to a 98/2 fiber 

splitter. The minor leg of the fiber splitter is coupled to a monitor detector, providing the 

means to correct for power drifts of the laser. The main leg of the fiber splitter is 

connected to a two-meter long fiber coupled to a beam collimator. The nominal focal 

length of the collimator is 11 mm. 

The test beam exiting the collimator serves as the working beam diameter standard for 

the measurements. The laser beam has a nearly Gaussian profile with a long tail. The 

beam has an ellipticity ratio better than 0.995, as based on results of two-dimensional 

pinhole scan, slit-scan, and camera-based measurements. The beam width should ideally 

be measured at the beam waist, which is the conjugate point of the fiber end face from the 

collimator lens (the back focal point) for an ideal Gaussian beam with perfect alignment 

of the collimator. However, the actual test beam waist is at a distance much longer than 

this theoretical position, due to the non-ideal Gaussian beam and imperfect alignment of 

the collimator. A series of beam width measurements shows that at convenient working 

distances between 50 mm and 100 mm from the collimator, the beam width changes by 

approximately 1 μm for a path length change of 5 mm, corresponding to a full converging 

angle of 0.01°, allowing for a large positioning tolerance with very low uncertainty. The 

beam width varies slightly as a function of the laser wavelength [4, 5]. We have observed 

that the laser wavelength varies by as much as 0.11 nm or 0.011 % during a four-hour 

period (typical duration of an entire beam width calibration), which leads to a change in 

beam width of 0.24 μm. The beam width also varies slightly as a function of the 

temperature of the fiber [4, 5]. For example, a change of 2 °C in temperature results in a 
8 

change of 0.002 % in the fiber mode field diameter, or a change of 0.05 μm in the test 

beam width. 

4.2 Scanning Slit Measurement System 

For the characterization of the test beam diameter, the NIST measurement system uses 

the scanning slit method. The width of the slit is 10 μm (±1 μm) and the length is 7 mm 

(±25 μm). The long axis of the slit is perpendicular to the scan axis. For one complete 

measurement, the slit is scanned in both the horizontal (x) and vertical (y) directions at 

incremental steps of 25 μm, for a full range of 8 mm. The resolution of the scanning 

linear stages is 0.05 μm. The slit is mounted on an indexed rotation stage in order to 

change the orientation of the slit for the horizontal and vertical scan measurements. 

4.3 Data Acquisition 

The data acquisition of DUT measurements follows the instructions of the DUT. For each 

data point of the NIST slit scan measurement, the slit integrated beam power intensity is 

acquired simultaneously with a reading of the monitor detector. The scan data are 

corrected for the laser power drift by applying a normalization factor using the monitor 

readings and recorded in the scan data file. 

5. Standard Operating Procedures 

5.1 System Startup 

All electronics and other support systems are powered up at least one hour prior to the 

start of the measurement. All test equipment is allowed to equilibrate with room 

temperature. The laser is powered at the pre-selected drive current for at least one hour 

before the measurement in order to allow for the output power to stabilize. 

5.2 Optical Alignment 

The DUT measurement plane and the NIST scanning slit are aligned in positions at the 

same distance from the collimator surface within a tolerance of 5 mm. The beam pointing 

direction is aligned perpendicular to the measurement surface within a tolerance of 2.5°, 

which is determined from the shift of the centroid of the scanned data at two different 

distances of the scan position from the collimator. For NIST measurement, the beam is 

centered within the system scan range with enough scan distance on each side from the 

center. For DUT measurement, the beam is aligned according to the instructions of the 

DUT. 

5.3 Data Acquisition 

Data acquisition consists of several alternations of NIST measurement runs and DUT 

measurement runs. The number and order of alternations depends on measurement 
9 

specifics of the DUT. Each measurement run may also consist of several measurements. 

Each NIST measurement includes one scan in each of the x and y directions. The scan 

takes 25 μm in each step and covers a range of 8 mm. Each scan datum is acquired 

simultaneously with a monitor detector reading, which is used to correct the slow drift of 

the test beam power. Before the first NIST measurement, in the middle of the entire 

measurement, and after the last NIST measurement, the system baseline is scanned with 

the beam blocked. All the scans are performed with the collimator-scanning-detector 

covered in a black box to shield off the stray light from the environment. 

Other measurement conditions recorded include test beam wavelength, environment 

temperature, distance of measurement plane from the collimator, DUT model, serial 

number, and NIST ID number. 

5.4 Data Analysis 

For the NIST measurement, the average of the system baseline is obtained first from the 

baseline measurement data. For each scan in each direction (x or y), a software algorithm 

determines the centroid, a 7 mm integration area around the centroid, and the secondorder moment from the corrected scan data with baseline subtraction. The beam diameter 

is obtained for every two consecutive scan results in the two, x and y, directions for each 

NIST measurement. The average of all the measured beam diameters is the NIST 

measurement result. 

The DUT measurement result is obtained according to the instrument instructions. The 

average of all the DUT measurements is the DUT measurement result. 

The ratio of DUT measurement result to the NIST measurement result is the correction 

factor supplied to the customer. 

6. Uncertainty Evaluation 

The uncertainty estimates for the NIST laser beam diameter measurements are assessed 

following guidelines given in NIST Technical Note 1297 [6]. To establish the uncertainty 

limits, the error sources are separated into Type B errors, whose magnitudes are 

determined by subjective judgment or other non-statistical methods, and Type A errors, 

whose magnitudes are obtained statistically from a series of measurements. 

All Type B error components are assumed independent and to have rectangular or 

uniform distributions (that is, each has an equal probability of being within the region, 

±δi, and zero probability of being outside that region). If the distribution is rectangular, 

the standard deviation, σs, for each Type B error component is equal to δi/31⁄2 and the total 

standard uncertainty is (Σσs

2

)

 1⁄2, where the summation is performed over all Type B error 

components. 

Type A errors are assumed to be independent and normally distributed and, consequently, 

the standard deviation, Sr, for each component is 
10 

 N 1

N

( x )

x

S = 

2

2

r



  

, 6.1 

where the x values represent the individual measurements and N is the number of x values 

used for a particular Type A error component. The standard deviation of the mean is 

Sr/N1⁄2, and the total standard uncertainty of the mean is [Σ(Sr

2

/N)] 1⁄2, where the 

summation is carried out for all the Type A error components. 

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

uncertainties in quadrature (the combined uncertainty) and multiplying this result by an 

expansion factor of 2. The expanded uncertainty, U, is then 

N

S U = 2 +

2

2 r  s  . 6.2 

The number of decimal places used in reporting the mean value of the calibration factor 

listed in the calibration report is determined by expressing the expanded uncertainty to 

two significant digits. 

Sources of uncertainties are identified and their contributions to the beam width 

measurement result are determined by test, or theoretical calculation, or computer 

simulation, or a combination of these methods. Generalized beam diameter, d, defined in 

Equation 3.5 is a function of the second order moment diameters 4σx and 4σy measured 

independently in the slit scan method. The uncertainty contributions u(σx) and u(σy) of σx

and σy to the uncertainty u(d) of d follow the law of propagation of uncertainty. Some 

uncertainty sources, especially the Type A uncertainties, affect σx and σy independently, 

and the uncertainties u(σx) and u(σy) are uncorrelated. Because the test beam has very 

good circularity, and these uncertainty sources affect the measurements equally in the 

two measurement directions, we have 4 and  x  4 y  4  d

u(4 ) u(4 ) u(4 ) x  y  , and therefore 

2

(4 ) ( ) u 

u d  . Some Type B uncertainty 

sources directly impact the measured beam diameter d, so their influences on u(4σx) and 

u(4σy) are completely correlated, resulting in u(d)  u(4 ). Some other Type B sources 

also have a direct impact on beam width d, but their effect on u(4σx) and u(4σy) are 

neither completely correlated nor completely uncorrelated. Because it is difficult to 

estimate the degree of correlation, we use the worst-case estimate in their evaluations, 

that is, assuming they are completely correlated. In the following description of the major 

uncertainty sources, the values of uncertainties are all their final contributions to the 

uncertainty of u(d). 

6.1 Test Beam Uncertainties 

6.1.1 Laser Power Stability (Type A)

Laser power output exhibited fast fluctuations and slow drift. The combined standard 

deviation of laser power in four hours was 1 %. The standard deviation of the measured 

laser power was reduced to 0.1 % by applying a power drift correction using input from 
11 

the monitor detector. Simulation results indicated that this resulted in an uncertainty of 

0.1 μm in the beam width measurement. 

 

 6.1.2 Interference Pattern (Type A) 

Because of the narrow spectral width of the laser beam, interference due to reflections 

between the fiber end face and the collimator lens resulted in fluctuations in the scanned 

beam profile. From the raw data, it was estimated that this effect caused a RMS 

fluctuation of about 0.5 % in the measured signal, resulting in a standard uncertainty of 

0.4 μm in the final result, according to simulations. 

 

 6.1.3 Wavelength Stability (Type B) 

The single-mode fiber beam width is dependent on the laser beam wavelength. 

Measurements showed that the laser beam wavelength exhibited fast fluctuation and slow 

drift. Fast fluctuation will cause noise-like effects on the measurement. However, the 

magnitude of wavelength fast fluctuation is less than 0.003 %, which caused a similar 

change in beam width magnitude that can be ignored. The slow drift of the wavelength 

will cause a difference between results of NIST and DUT measurements and a difference 

between NIST measurements before and after the test meter measurements due to the 

time difference of the measurements. Test results showed that wavelength drift could be 

as high as 0.01 % when the laser is operated in constant current mode, which converts to 

an estimated standard uncertainty in beam width measurement of 0.07 μm, or 0.003 %, 

which can be ignored. 

6.2 Measurement System Uncertainties 

 

 6.2.1 Detection Noise (Type A) 

Detection noise is the combined result of detector noise (dark current noise, shot noise, 

etc.) and the readout electronics noise. The detection signal to noise ratio was 5×105

, 

resulting in a standard uncertainty of 0.2 μm in the beam width. 

 6.2.2 Measurement Area (Type B) 

The uncertainty limit of the measured beam width due to the difference between the 

actual measurement area and the ISO defined area is 0.1 %, as described earlier. The 

standard uncertainty is then 0.06 %.

 

 6.2.3 Optical Axis Tilt (Type B) 

Results of multiple realignments and measurements showed that the tilt angle between 

the optical axis of the beam and the beam profile plane can be controlled within 2.5°. The 

standard uncertainty of the measured beam width due to this tilt is 0.05 %. 

 

 6.2.4 Positioning of the Measurement Plane (Type B) 

For a maximum possible difference of 5 mm in the relative longitudinal positions of slitscan and DUT measurements, a standard uncertainty of 0.6 μm, or 0.03 %, is incurred in 

the measured beam width. 
12 

 6.2.5 Detector Nonlinearity (Type B) 

Nonlinearity measurement of the NIST detector showed a positive response nonlinearity 

of up to 2 % occurred at the lower end of the measurement range. Simulations indicated 

that this results in a standard uncertainty of 0.4 μm or 0.02 % in the beam width. 

 6.2.6 Slit Tilt (Type B) 

The tilt of the slit can be kept within 1° relative to the scan axis. Simulation indicated that 

this results in a standard uncertainty of 0.4 μm or 0.02 %.

6.2.7 Off-Centroid Slit Scan (Type B) 

The scanning slit should ideally be centered at the centroid in the direction orthogonal to 

the scanning direction. Because the slit cannot be perfectly positioned at the center of the 

rotation stage, the slit may not be centered at the centroid during the scans. Test results 

showed that a maximum position error of 200 μm off-center may occur, which may result 

in a standard uncertainty of 0.6 μm or 0.03 % uncertainty in the measured beam diameter. 

Type A uncertainties discussed in 6.1.1, 6.1.2, and 6.2.1 cannot be separately estimated in 

each and every particular measurement. However, their combined effect contributes to 

the measurement standard deviation of the NIST and DUT measurements, which are 

listed in the test report. Other sources of uncertainty we have considered include the finite 

slit width, scan resolution, effect of ellipticity, and motion accuracy. Their contributions 

to the overall uncertainty of the beam width measurement are all less than 0.1 μm and 

deemed negligible. Major uncertainty contributions are listed in Table 6.1. 

Source Uncertainty 

Type A Standard 

Deviation (%)

N 

NIST measurement 0.02 6 

DUT measurement 0.06 30 

Type B Standard Uncertainty (%) 

Measurement area 0.06 

Optical axis (z direction) tilt 0.05 

Relative positioning of detection plane 0.03 

Detector linearity 0.02 

Slit tilt 0.02 

 Slit off-centroid 0.03 

Combined standard uncertainty uc 0.09 

Expanded uncertainty (k=2) U=k uc 0.19 

Table 6.1 Example summary of measurement uncertainties associated with NIST and DUT measurements. 
13 

7. Quality Control 

The measurement services of the Optoelectronic Division make use of quality assurance 

practices to ensure the validity of measurement results and their uncertainties. Such 

practices include: 

 Repeated measurements/calibrations compared over many time intervals 

 Comparison of previous results obtained using multiple measurement methods, if 

available. 

 Routine, periodic measurements with different methods. 

For this service, we periodically measure the test beam diameter using three different 

methods, slit scan, two-dimensional pin-hole scan, and camera-based beam profiling. 

Figure 7.2 shows the history of the test beam measurements during the period from June 

2008 to April 2009. 

2.190

2.192

2.194

2.196

2.198

2.200

6/20/2008

6/30/2008

7/1/20088/5/20088/6/20088/7/2008

12/4/2008

12/5/2008

12/22/2008

12/29/2008

2/18/2009

2/19/20092/20/20092/24/2009

4/2/2009

4/10/2009

Date

D (mm)

Slit

Camera

Pinhole

Slit average

Camera average

Pinhole average

Figure 7.1. Test beam measurements using three different methods, slit scan, two-dimensional pinhole 

scan, and camera-based beam profiling from June 2008 to April 2009. The average and standard deviation 

of these measurements are 2.1949 ± 0.0015 mm for slit scan, 2.1951 ± 0.0021 mm for camera beam 

profiling, and 2.1948 ± 0.0020 mm for pinhole scan.

In the Optoelectronics Division, all calibration, MAP, and remote measurement (RM) 

services maintain check standards and control charts for periodic test of the measurement 
14 

service. When available, historic data from previous measurements of the test beam shall 

be placed into the test folder by the Measurement Services Coordinator after the 

preparation of the calibration report. The Calibration Leader and the Group Leader shall 

review this data before signing the calibration reports. If a significant variance from 

previous results is observed, the Group Leader may require another measurement of the 

calibration item as a test of measurement system conformance. 

8. Summary 

NIST provides a calibration service for instruments that measure laser beam diameters. In 

this document, we have summarized the basic measurement equations, the measurement 

procedure, and described the quantities that contribute to the relative standard 

uncertainty. 
15 

References 

[1] ISO 11146-1:2005, “Lasers and laser-related equipment – Test methods for laser 

beam widths, divergence angles and beam propagation ratios – Part 1: Stigmatic 

and simple astigmatic beams,” 2005. 

[2] ISO 11146-2:2005, “Lasers and laser-related equipment – Test methods for laser 

beam widths, divergence angles and beam propagation ratios – Part 2: General 

astigmatic beams,” 2005. 

[3] ISO/TR 11146-3:2004, “Lasers and laser-related equipment – Test methods for 

laser beam widths, divergence angles and beam propagation ratios – Part 3: 

Intrinsic and geometrical laser beam classification, propagation and details of test 

methods,” 2004. 

[4] “Single-Mode Fiber Optics: Principles and Applications,” Luc B. Jeunhomme, 2nd

Edition, Marcel Dekker, Inc., New York, 1990. 

[5] “Single-Mode Fibers: Fundamentals,” Ernst-Georg Neumann, Springer-Verlag 

Berlin Heidelberg, 1988. 

[6] “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results,” NIST Technical Note 1297, Barry N. Taylor and Chris E. Kuyatt, 1993. 

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