A111QS 5b3257

T

PUBLICATIONS

NIST SPECIAL PUBLICATION 260-128

QC

100

U57

NO. 260-

128

1998

U.S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

Standard Reference Materials:

Transmission Filters With Measured

Optical Density at 1064 nm Wavelength

SRMs 2046, 2047, 2048, 2049, 2050, and 2051

Zhuomin M. Zhang, Thomas R. Gentile,

Alan L. Migdall and Raju U. Datla
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NIST Special Publication 260-128

Standard Reference Materials:

Transmission Filters With Measured

Optical Density at 1064 nm Wavelength

SRMs 2046, 2047, 2048, 2049, 2050, and 2051

Zhuomin M. Zhang

Department of Mechanical Engineering

University of Florida

Gainesville, FL 32611

and

Thomas R. Gentile

Alan L. Migdall

Raju U. Datla

Optical Technology Division

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director

Revised November 1998
National Institute of Standards and Technology Special Publication 260-128

Natl. Inst. Stand. Technol. Spec. Publ. 260-128, 32 pages (Nov. 1998)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

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

Standard Reference Materials (SRMs) are certified reference materials (CRMs) issued by

NIST that are well-characterized using state-of-the-art measurement methods and/or

techniques for chemical composition and physical properties. They are used to ensure the

accuracy and compatibility of measurement results in many diverse fields of science,

industry, and technology both within the United States and throughout the world. For

many of the nation's scientists and technologists, it is therefore of more than a passing

interest to know the details of the philosophy and procedures used at NIST to use, produce, and certify SRMs. The NIST Special Publication Series is a series of

publications used for this purpose and a list of these can be assessed through the Internet,

http://ts.nist.gov/srm.

This 260 publication is dedicated to the dissemination of information on the value

assignment and certification of SRMs 2046-205 1

, Transmission Filters with Measured

Optical Density at 1065 nm Wavelength. This publication explains the theory which

serves as the basis for the preparation, measurement values and uncertainties,

certification, and use of this series of SRMs. In general, much more detail will be found

in this publication than is generally allowed or desired in scientific journal articles. This

publication should provide sufficient additional information so these SRMs can be

utilized in new applications in diverse fields not foreseen at the time the SRMs were

originally issued.

Standard Reference Materials Program

Bldg 202 Room 204

National Institute of Standards and Technology

Gaithersburg, MD 20899

Telephone: (301)975-6776

FAX: (301)948-3730

e-mail: srminfo@nist.gov, or www:http ://ts .nist. gov/srm

Thomas E. Gills, Chief

Standard Reference Materials Program

TABLE OF CONTENTS

Page

Abstract 1

1. Introduction 2

2. Material Preparation and Instructions for Use 3

3. Theory of Transmittance and Optical Density 4

4. Measurement Techniques and Instrumentation 5

5. Effects of Temperature, Position, Interference, and

Wavelength 8

5.1 Temperature Effect 8

5.2 Spatial Nonuniformity 9

5.3 Interference Effects 10

5.4 Wavelength Dependence 11

6. Uncertainty Determination 12

7. Summary 13

8. Acknowledgments 13

9. References 14

Table 1 16

Figures 1-8 17-24

Appendix: Certificate of Analysis for SRMs 2046-2051 25

V
LIST OF TABLES Page

1. Thickness, optical density, filter temperature, and 16

uncertainty components for six typical filters.

LIST OF FIGURES

1. Schematic of the optical setup for transmittance 17

measurements at 1064 nm wavelength, where

M represents mirror; FD = feedback detector; MD = monitor detector; SD = signal detector.

2. Optical density of a filter (nominal OD = 4) measured 18

with different laser powers.

3. Outputs from the signal detector and the monitor 19

detector during measurements when the laser beam

passes through the reference. The laser power is more

stable in a) than in b).

4. Comparison of the optical density calculated with and 20

without normalization using the monitor detector

output.

5. Optical density versus filter temperature for two filters: 21

a) Nominal OD = 2; b) Nominal OD = 3.

6. Spatial variation of the optical density for two filters, 22

where the positions are measured from the center of the

filter: a) Nominal OD = 1, relatively poor spatial

uniformity; b) Nominal OD = 6, relatively good spatial

uniformity.

7. Interference effects on the transmittance: a) Predicted 23

OD vs. £ = 2nd/ X; b) Reduced optical density of an OD 1

filter as a function of temperature.

8. Transmittance in the region from 800 nm to 1400 nm of 24

two filters measured using a Fourier transform infrared

spectrometer.

vi
NIST SPECIAL PUBLICATION 260-128

Standard Reference Materials:

Transmission Filters with Measured Optical Density at 1064 nm

Wavelength — SRMs 2046, 2047, 2048, 2049, 2050, 2051

Zhuomin M. Zhang,* Thomas R. Gentile, Alan L. Migdall, and

Raju U. Datla

Optical Technology Division

Physics Laboratory

National Institute of Standards and Technology

Gaithersburg, Maryland 20899

ABSTRACT

Standard Reference Materials (SRMs) 2046-2051 are transmission

filters and may be used for calibrating transmittance measurements

made using lasers or infrared spectrophotometers, for attenuating the

optical power with an accurately known transmittance at a wavelength of

1064 nm, and for characterizing the nonlinearity of detection systems.

The external transmittance (which is expressed as optical density in this

publication) of these filters has been measured at a wavelength of

1064 nm using a Nd:YAG laser and silicon diode detectors. The

uncertainty associated with the measured optical density of each filter

has been individually determined. The filters are made of colored glass

with uncoated, polished surfaces. The filter plates are 51 mm x 51 mm,

with thicknesses ranging from 1 mm to 6.4 mm which correspond to

nominal optical densities from 1 to 6.

Keywords: Attenuation; infrared filter; Nd:YAG laser; optical density;

photodiode detector; transmittance; uncertainty.

* Department of Mechanical Engineering, University of Florida, Gainesville,

Florida 32611.

1
1. Introduction

For over 20 years, NIST has developed instrumentation and

produced standard reference materials for spectral transmittance

measurements at ultraviolet, visible, and near infrared wavelengths [1,2].

High-accuracy spectrophotometers are commonly used for these

measurements [3,4]. Recent advances in stable laser sources and

sensitive linear photodiode detectors have allowed accurate

measurements of infrared spectral transmittance for very low

transmittance materials [5-8]. Both direct and heterodyne detection

methods have been employed for measuring transmittance at

wavelengths of 633 nm (He-Ne line), 1064 nm (Nd:YAG line), as well as

10.2 |im and 10.6 |im (CO2 lines), for up to 10 decades of attenuation, as

reviewed in the work of Gentile et al. [9]. These developments allow NIST

to provide calibration services and calibrated neutral density filters over a

wide range of attenuation.

Standard Reference Materials (SRMs) 2046 (nominal OD 1,

thickness 1.0 mm), 2047 (nominal OD 2, thickness 2.2 mm), 2048

(nominal OD 3, thickness 3.2 mm), 2049 (nominal OD 4, thickness

4.2 mm), 2050 (nominal OD 5, thickness 5.4 mm), and 2051 (nominal

OD 6, thickness 6.4 mm) are transmission filters and are primarily

intended for use in calibrating transmittance measurements made with

lasers or spectrophotometers, accurately attenuating the optical power,

and characterizing detector nonlinearity. The optical density (OD) is

defined as -log10 T, where Tis the external transmittance. The filters in

this series are made of colored glass with polished (uncoated) surfaces.

The lateral dimensions are 51 mm x 51 mm. The OD of these filters has

been determined at a wavelength of 1064 nm. This special publication

discusses in detail the measurement theory and instrumentation,

material preparation, and uncertainty determination for the certification

of these standard reference materials.

2
2. Material Preparation and Instructions for Use

The transmission filters are fabricated and polished by Laser

Optics, Inc.,* using NG-9 ionically colored glass manufactured by Schott

of Mainz, Germany [10, 11]. The glass filters are uncoated and optically

smooth. Each surface is flat to within one tenth of the wavelength of a

He-Ne laser (633 nm) and the wedge angle is less than 5 |irad (1 arc s).

The filter plates are 51 mm x 51 mm, with thicknesses varying from

1 mm to 6.4 mm for different optical densities.

Each transmission filter is stored in a special container to

minimize the contamination of filter surfaces. The hard-foam insert

supports the filter by its edges and prevents any contact between the

middle portion of the filter surface and the walls of the container. The

filter may be held by the edges with soft plastic gloves or optical lens

tissue. A metallic mount may be used to hold the edge of the filter

(within 7 mm from the edge). The central portion of the filter should

never be touched by fingers or any hard objects. Dust may be removed

by blowing with clean, dry air.

Only the central 20 mm x 20 mm region should be used. It is

desirable to average the measured transmittance of the filter at several

positions around the center. The laser beam should be perpendicular

(within 2° or 0.035 rad) to the filter surface to avoid translating the beam

and increasing the path length within the filter. The laser power (flux) on

the filter should not exceed 20 mW (300 mW/cm2

) to avoid excessive

heating. Furthermore, the filter temperature should be between 21 °C

and 27 °C during measurements.

* The use of trade name or company name is for identification only and does not

imply endorsement by the National Institute of Standards and Technology, nor does

it imply that the material or product identified are necessarily the best available for

the purpose.

3
3. Theory of Transmittance and Optical Density

The refractive index, n, of the glass material used for these SRMs is

about 1.5 at visible and near-infrared wavelengths. At normal incidence,

2 2 the reflectivity at the air-filter interface is p = (n - 1) / (n + 1) ~ 0.04. The

filters attenuate radiation mainly by absorption. The external

transmittance Tis

T = (\-p)2 ead

(1)

for normal incidence, where a is the absorption coefficient and d is the

thickness of the filter. Multiple reflections between the two surfaces of

the filter have negligible effect on the transmittance if d > 2 mm because

of the strong absorption inside the filter and the weak reflection at the

surfaces. [2] This greatly reduces the difficulty of measuring the external

transmittance with a high accuracy. For filters with 10% transmittance

(d ~ 1 mm), however, interference between multiple reflections can cause

a large uncertainty and eq (1) needs to be modified to include

interference effects. [12, 13] The uncertainty caused by neglecting

multiple reflections is evaluated in section 5.3.

The optical density, defined by OD = -log 10 T, can be calculated

from eq (1), viz.

OD = odlog10 e - 21og10 (l - p) (2)

The change in the optical density is proportional to the change in the

thickness or the absorption coefficient. The second term in eq (2) is

about 0.035. The room-temperature absorption coefficient for the glass

materials used for these SRMs is about 2.16 mm-1 at 1064 nm.

Therefore, filters of 1 mm thickness exhibit an OD near 1 , filters of 2 mm

thickness exhibit an OD near 2, and so on. An absolute difference of

0.001 in OD corresponds to a relative difference AT/T of 0.23% in

transmittance.

4
4. Measurement Techniques and Instrumentation

The measurement setup is shown in figure 1 . The optical source is

a continuous-wave (CW), arc lamp pumped, Nd:YAG laser with an output

power of 3 W at 1064 nm. The laser beam is directed through a

collimator (which reduces the beam diameter to about 1 mm), a polarizer

and a power stabilizer, a lens, and then to a light-tight enclosure. A

wedged quartz beamsplitter is placed inside the enclosure to produce two

reflected beams (each with an optical power =4% of the incident beam).

The beam reflected from the first surface of the wedge goes to the

stabilizer's feedback detector (FD) to maintain a constant optical power.

The power is stabilized to better than 0.3 % rms fluctuation over several

hours of operation. The beam reflected from the second surface of the

wedge is sent to a monitor detector (MD) to normalize the input power,

which further reduces the effect of power fluctuation. The transmitted

beam passes through a shutter and the sample (or a reference), and is

then reflected by a mirror to the signal detector (SD). Attenuating filters

reduce the laser power so that the detectors are operated in their linear

ranges. A baffle located at the middle of the enclosure prevents stray

laser light from reaching the signal detector. A detector enclosure made

of anodized aluminum is required for measuring filters with OD > 9.

Transmittance measurements for OD =10 are discussed in a separate

publication [14].

The signal detector is a Hamamatsu SI 337 series silicon

photodiode, with an area of 10 mm x 10 mm. The detector responsivity

at 1064 nm is approximately 0.15 A/W. A built-in trans-impedance

amplifier is used with linearized gain factors from 2 kQ to 100 GQ.,

yielding an overall responsivity of 300 V/W to 15 GV/W. A six-and-half

digit voltmeter measures the dc voltage from the amplifier. The dynamic

range and linearity of the detector/ amplifier electronics were discussed

in [5] and [6]. Another voltmeter is used to simultaneously measure the

output voltage from the monitor detector/ amplifier.

5
The filter is mounted on a copper holder with a thermistor placed

on the holder to monitor the filter temperature during the measurement.

The temperature dependence of the optical density is discussed in

section 5.1. Two computer-controlled motors move the filter holder

horizontally and vertically so that the laser beam can be positioned at a

desired location of a sample or a reference. The reference is left blank for

measuring filters of OD 1 to 4, and an OD 3 filter is used as the reference

for measuring filters of OD 5 and 6. An automatic data acquisition

program controls the motion of the shutter and the motors, takes

readings from the voltmeters, and calculates the transmittance (and

optical density) for each measurement.

Six measured values are required to determine the relative

transmittance of the sample filter at a single position. The working

equation is

'relative

\ ( y y )/y 1 ^

W

y s\ y s0>' y m\reference

where Vis the output voltage, subscripts s and m indicate signal detector

and monitor detector, respectively, and subscripts 0 and 1 indicate

shutter closed and open, respectively. The signal when the shutter is

closed (Vso) is subtracted from the output signal (Vs i) to eliminate

background. The sample transmittance is the same as the relative

transmittance for filters of OD 1 to 4 since the reference is blank.

The gain setting cannot be changed during each measurement.

The signal-to-noise ratio is lower with higher OD filters since the

resolution of the voltmeter is 1 |liV. Therefore, a reference substitution

method is used to increase the dynamic range of the measurement.

Filters of OD ~ 5 and 6 were measured relative to a reference filter of

OD ~ 3. The transmittance of the reference filter was measured at a fixed

position with a lower gain setting. The transmittance of the high OD

filter relative to that of the reference filter was measured with a higher

gain setting. The transmittance of OD 5 or 6 filters is calculated from

6
T,sample = T,relative reference (4)

where Trefterence e is the transmittance of the reference filter measured at a

single fixed position. Eckerle et al. [2] used this "step-down" method for

measuring spectral transmittance down to OD = 4.

The linearity of the detector was tested by varying the power levels

on the detector using attenuation filters. The amplifier gain was

optimized to yield the best signal-to-noise ratio without saturating the dc

voltmeter. The optical density of an OD = 4 filter measured with different

incident laser powers is shown in figure 2. It can be seen that the

detector is linear at optical powers less than 1 mW. At an input optical

power of 1 nW, the power reaching the detector was =10- 13 W when the

beam passes through the OD 4 filter. The low signal-to-noise ratio

resulted in a large uncertainty for the OD measurement at the low power

end.

The output voltages from the monitor detector/ amplifier and the

signal detector/ amplifier during typical measurements are shown in

figure 3 to illustrate the power stability and the significance of the

monitor detector. Only the output when the laser beam passes through

the reference (blank) is shown. The background voltage of =40 (iV is

negligible compared to the signal voltage. The power stability varies from

measurement to measurement, with figures 3a and 3b representing the

best and worst cases, respectively. The relative standard deviations for

both Vs and Vm are less than 0.04 % in figure 3a. Due to the high

stability, the effect of normalization by the monitor detector, Vm in eq (3),

is insignificant.

The normalization by Vm becomes important when the laser power

variation is relatively large. In figure 3b, the relative standard deviations

of the output signals are =0.4%, i.e., about an order of magnitude

greater than those in figure 3a. The outputs from MD and SD exhibited

similar trends in figure 3b. In this case, the optical density of the sample

filter calculated with and without normalization by Vm is compared in

figure 4. The standard deviation in OD is significantly reduced when the

laser power is normalized by the monitor detector output.

7
5. Effects of Temperature, Position, Interference, and Wavelength

The laser beam incident on the filter was perpendicular to the

surface (angle of incidence < 2 °). This was checked by observing the

reflected beam spot using an infrared sensing card. The slight

translation of the beam through the filter (maximum 0.12 mm) has little

effect on the measurement because of the high degree of spatial

uniformity of the detector. The beam diameter at the filter was ~3 mm

full width at half maximum and the beam divergence is less than 2 mrad.

The detector was tilted about 1° so that the beam was not reflected back

on to the filter. The temperature and relative humidity of the laboratory

were between 22 °C and 24 °C and between 40 % and 60 %, respectively,

during the calibration measurements. Because there are no water

absorption lines near 1064 nm and the refractive index of air is

insensitive to humidity, the humidity level has negligible effect on the

measurements.

5.1 Temperature Effect

The temperature of the filter was varied to investigate the effect on

the optical density. The central air conditioner in the building was used

to vary the temperature in the laboratory from 23 °C to 27 °C. The filter

temperature was assumed to be the same as that of the copper holder.

The filter temperature was about 1 °C higher than room temperature due

to the heating of the positioning motors. To reduce the filter temperature

below 24 °C, cold N2 gas from a liquid-nitrogen tank was passed through

the enclosure. The enclosure was then closed, and the optical density

and filter temperature were monitored. The change of the filter

temperature (1 °C to 2 °C per hour) was slow enough for a correlation

between the OD and temperature to be obtained.

The measured OD versus temperature for two filters are shown in

figure 5. The OD increases linearly with the filter temperature. The

slight deviation at the low-temperature end is not surprising since the

8
temperatures of the filter and the holder may not have equilibrated for

the first few data points (each measurement takes about 100 s). A linear

fit shows that the OD increases 0.00052 /°C for the OD 2 filter and

0.0008 /°C for the OD 3 filter. This implies that the change in OD is

caused by a change in the absorption coefficient of the glass material.

Because the thermal expansion coefficient of the material is

=6.3 x 10~6 /°C [10], the change in thickness is negligibly small. For the

OD 3 filter, the correlation between OD and temperature was also

obtained as the temperature decreased with time (by reducing the

laboratory temperature). The results, shown by the circles in figure 5b,

agree well with those when the temperature is increased with time.

By substituting the measured OD and thickness values into eq (2),

we found the absorption coefficient of the glass material to be

=2.16 mm"1 at 25 °C with a temperature coefficient of =0.026 %/°C at a

wavelength of 1064 nm. Therefore, a correction in the measured OD may

be necessary for measurements at temperatures different from that

indicated in the certificate. The correction depends on the nominal OD

values. In the temperature range between 21 °C and 27 °C, the change

in OD per °C temperature change for SRMs 2046, 2047, 2048, 2049,

2050, and 2051 is 0.00026, 0.00054, 0.00078, 0.00103, 0.00133, and

0.00157, respectively.

5.2 Spatial Nonuniformity

The spatial variation of OD depends on the filter. Measurements

were performed either at 9 positions in a 3 x 3 matrix with 10 mm

spacing or at 25 positions in a 5 x 5 matrix with a 5 mm spacing around

the center of the filter. These measurements were repeated at least once

for all positions. The measured optical densities of two filters at 25

positions are shown in figure 6. The OD 1 filter possesses a much larger

spatial deviation in optical density than the OD 6 filter. Because the

filter surfaces are extremely flat and parallel, the spatial variation is

attributed to the inhomogeneity of the material with the exception for

9
OD 1 filters, where interference between multiple reflections may affect

the spatial uniformity. Measurement using a micrometer (resolution of

2.5 |j.m) could not detect any variations in the filter thickness. The

spatial nonuniformity is the major source of uncertainty for most filters.

5.3 Interference Effects

The transmittance of a plate with two parallel, optically smooth

surfaces for completely coherent radiation is [12]

T = d-P)2 *

(5)

l + p

2 T2 -2pTcos(27r£)

where r = e~

ad

is the internal transmittance and £ is a parameter defined

as £ = 2nd I X . The transmittance oscillates as | varies. The amplitude of

oscillation is estimated to be 0.8 % for OD 1 filters and 0.08 % for OD 2

filters. For OD 1 filters (d ~ 1.044 mm), a variation of either 0.18 |im in d

or 0.17 nm in A or 0.016 % in n would change the transmittance from a

maximum to a minimum. The large spatial variation for OD 1 filters is

caused by interference effects since the thickness variation is of the order

of 0.2 Jim. The spectral linewidth zlvof the laser is between 1 cm-1 and

5 cm-1 [15, 16]. Hence, the laser radiation is not completely coherent.

Using the expression for partially coherent radiation given by Zhang [13],

the transmittance can be calculated from

2 T= ^

l ~ P

} 9T

fl + 2pTcos(2^) sinc(27mdAv)

1-p T

L

+ 2p

2 r2 cos(4^) sinc(47mdAv) + H.O.T.] (6)

where the function sinc(x) = sin{x)/ x, Av is the laser spectral width, and

H.O.T. indicates higher-order terms. Because p

2 T2 <2xl0 , eq (6) can

be approximated as

7 = (l-p)2 T [l + 2prcos(2^) sinc(27m</Av)] (7)

10
Figure 7a shows the predicted transmittance of an OD 1 filter (using a =

2.16 mm-1 and d = 1.044 mm) for Av = 0, 1 cm" 1

, and for incoherent

radiation. The relative amplitude of oscillation is AT/ T ~ 2prsinc(27cndAv).

Using A v = 1 cm-1

, the standard uncertainty in OD caused by

interference effects {(Jinterji is estimated to be 0.0016 for OD 1 filters,

0.0001 for OD 2 filters, and negligible for filters of OD > 3. As shown in

figure 7b, variations in the range of ±0.0025 OD were observed for an

OD 1 filter after subtracting the effect of absorption coefficient change,

when the filter temperature was varied from 21 °C to 27 °C. This could

be caused by a slight temperature dependence of n. The OD variation is

less than 2ointerf, indicating that the calculated (Jinterf on the basis of

Av = cm-1 is still a conservative estimate.

5.4 Wavelength Dependence

A Fourier transform infrared (FT-IR) spectrometer (configured with

a halogen source, a quartz beamsplitter and a DTGS pyroelectric

detector) was used to determine the wavelength dependence of the

transmittance. The spectral transmittance for two filters is shown in

figure 8 for wavelengths from 800 nm to 1400 nm. The spectral

resolution was 8 cm-1 (-0.9 nm at 1064 nm). The beam exiting the

interferometer was focused at the filter with a =8 mm diameter spot size

and a maximum divergence angle of -7°. The optical power was

attenuated to improve the radiometric accuracy at the expense of a

reduction of the signal-to-noise ratio. No absorption lines were observed

and the transmittance spectra are relatively flat near 1064 nm. The

spectral width of the Nd:YAG laser is less than 0.5 nm at 1064 nm [15,

16]. Transmittance values obtained using the laser and the spectrometer

agree at the 1 % level, which is within the overall uncertainty of the two

different measurement techniques. Hence, these filters are appropriate

for use in calibrating infrared spectrometers at 1064 nm wavelength.

11
6. Uncertainty Determination

The standard uncertainty for measurement repeatability at the

same position on the filter is better than 0.00006 for OD 1 and 2 filters,

0.0002 for OD 3, 5 and 6 filters, and 0.00067 for OD 4 filters (because of

a lower signal-to-noise ratio). Table 1 lists the mean OD values averaged

over 9 or 25 positions, the average filter temperature during the

measurement, and all uncertainty components for six typical filters. The

thickness of each filter measured using a micrometer is also listed in

Table 1, with an expanded uncertainty (2oj of 2.5 \im.

The uncertainty given in Table 1 associated with the nonuniformity

{(^spatial) > which includes the repeatability component, is the standard

deviation of the measurements at different positions of the filter. The

standard uncertainty due to spatial nonuniformity {(JSpatiai) was as large

as 0.005 for some filters. Filters with (JSpatiai > 0.002 were excluded from

this certification. The reproducibility {(Jreprod) was determined from

various sets of measurements of OD 1, 2, and 3 filters, performed on

different dates when the samples had been unmounted and remounted.

The standard uncertainty associated with the detector nonlinearity

{Ononiin) was estimated to be 0.0002 for all filters. The standard

uncertainty (o>emp) caused by the temperature variation of ±0.5 °C was

calculated from the temperature dependence of the absorption

coefficient. The uncertainty due to the reference measurement (o>e/) for

filters with OD > 5 is a combination of the nonlinearity, reproducibility,

temperature effect, and the repeatability for measurements of the OD 3

reference filter at the fixed position. The combined standard uncertainty

was calculated as a prediction interval, i.e.,

^combined ~ (^spatial "spatial ^^reprod ®nonlin ®temp ®ref ®interf)

(8)

where N ( 9 or 25) is the number of measurement positions on the filter.

The prediction interval, which includes twice the reproducibility variance

12
and (1 + 1/N) times the spatial-nonuniformity variance, gives users a

basis to determine if a new measurement at any random position agrees

with the certified value [17]. The expanded uncertainty (95 % confidence)

is twice the combined standard uncertainty [18].

To determine the stability of the OD measurements, several filters

were measured over a one-year period. The agreement in OD is within

the expanded uncertainty of the measurements, indicating that these

filters have good long-term stability.

7. Summary

We have developed and utilized an apparatus to characterize the

optical density of colored glass filters (51 mm x 51 mm) at 1064 nm line

of a Nd:YAG laser. The optical density of these filters ranges from OD 1

to OD 6 depending on filter thickness. The expanded uncertainty for the

OD measurements is between 0.001 and 0.004 for all the certified filters,

with inhomogeneity of the material being a major source of uncertainty

for filters of OD > 1 . Interference between multiple reflections causes a

large uncertainty in the measurement of OD 1 filters. The effect of

temperature on the OD was determined from 21 °C to 27 °C. The

wavelength dependence and long-term stability were also investigated.

8. Acknowledgments

The authors gratefully acknowledge the contributions of George

Eppeldauer for help in the detector electronics, Anatoly Frenkel for

participation in the development of the instrumentation, Simon G.

Kaplan for the FT-IR transmittance measurement, C. Dawn Vaughn for

the thermistor calibration, M. Carroll Croarkin and Susannah B. Schiller

for consultation in the statistical analysis, and Jennifer C. Colbert for

support and coordination leading to the certification of these SRMs.

13
9. References

[1] R. Mavrodineanu and J.R. Baldwin, Glass Filters as a SRM for

Spectrophotometry - Selection, Preparation, Certification, and Use - SRM 930, NBS Special Publication 260-51, U.S. Government

Printing Office, Washington, DC (November 1975).

[2] K.L. Eckerle, J.J. Hsia, K.D. Mielenz, and V.R. Weidner, Regular

Spectral Transmittance, NBS Special Publication 250-6, U.S.

Government Printing Office, Washington, DC (July 1987).

[3] K.D. Mielenz and K.L. Eckerle, Design, Construction, and Testing of

a New High Accuracy Spectrophotometer, NBS Technical Note 729,

U.S. Government Printing Office, Washington, DC (June 1972).

[4] K.L. Eckerle, V.R. Weidner, J.J. Hsia, and Z.W. Chao, Extension of

a Reference Spectrophotometer into the Near Infrared, NBS

Technical Note 1175, U.S. Government Printing Office,

Washington, DC (April 1983).

[5] G. Eppeldauer and J. E. Hardis, "Fourteen-Decade Photocurrent

Measurements with Large-Area Silicon Photodiodes at Room

Temperature," Applied Optics 30, 3091-3099 (1991).

[6] A.L. Migdall and C. Winnewisser, "Linearity of a Silicon Photodiode

at 30 MHz and Its Effect on Heterodyne Measurements," Journal of

Research of the National Institute of Standards and Technology 96,

143-146 (1991).

[7] A.L. Migdall, B. Loop, and G.J. Xai, "Measuring Filter

Transmittance Using Heterodyne Detection," Metrologia 28,

217-220 (1991).

[8] A.L. Migdall, A. Frenkel, and D.E. Kelleher, "Filter Transmittance

Measurements in the Infrared," Journal of Research of the National

Institute of Standards and Technology 98, 691-697 (1993).

[9] T.R. Gentile, A. Frenkel, A.L. Migdall, and Z.M. Zhang, "Neutral

Density Filter Measurements at the National Institute of Standards

and Technology," in Spectrophotometry, Luminescence and Colour;

14
Science and Compliance, C. Burgess and D.G. Jones eds., Elsevier,

Amsterdam (1995), pp. 129-139.

Optical Glass Filters, Schott Glass Technologies, Inc., York Avenue,

Duryea, PA 18642 (1984).

C.R. Bamford, Colour Generation and Control in Glass, Elsevier,

New York (1977), Chap. 1.

Z.M. Zhang, "Reexamination of the Transmittance Formulae of a

Lamina," J. Heat Transfer 119, 645-647 (1997).

Z.M. Zhang, "Optical Properties of Layered Structures for Partially

Coherent Radiation," in Heat Transfer 1994 — Proceedings of the

Tenth Intl. Heat Transfer Conf, G. F. Hewitt ed. (Institution of

Chemical Engineers, Rugby, UK, 1994), Vol. 2, pp. 177-182.

Z.M. Zhang, T.R. Gentile, A.L. Migdall, and R.U. Datla,

"Transmittance Measurements for Filters of Optical Density from

One to Ten," to appear in Applied Optics.

A. A. Kaminskii, Laser Crystals, Springer-Verlag, New York (1981),

p. 332.

J. Hecht, The Laser Handbook, McGraw-Hill, New York (1992),

Chap. 22.

G.J. Hahn and W.Q. Meeker, Statistical Intervals: A Guide to

Practitioners, John Wiley & Sons, Inc., New York (1991).

B. N. Taylor and C.E. Kuyatt, Guidelines for Evaluating and

Expressing the Uncertainty of NIST Measurement Results, NIST

Technical Note 1297, U.S. Government Printing Office,

Washington, DC (1994).

15
Table 1 Thickness, optical density, filter temperature, and uncertainty

components for six typical filters

Filter Number 10-01 22-01 32-01 42-01 54-01 64-01

Corresponding

SRM Number

2046 2047 2048 2049 2050 2051

Thickness (mm) 1.044 2.177 3.157 4.194 5.410 6.391

Optical Density (OD) 1.0111 2.0785 2.9931 3.9679 5.1140 6.0325

Filter Temperature

(°C)

24.7 25.4 23.8 24.1 25.1 25.3

Nonuniformity

\Pspatial! 0.00129 0.00065 0.00021 0.00072 0.00026 0.00023

Reproducibility

{@reprodl

0.00035 0.00035 0.00035 0.00035 0.00035 0.00035

Detector Nonlinearity

i^nonlin)

0.0002 0.0002 0.0002 0.0002 0.0002 0.0002

Temperature

Variation

(0"femp)

0.00007 0.00015 0.00022 0.00030 0.00038 0.00045

N/A N/A N/A N/A 0.00050 0.00050

Interference

Effects

[Ginterfl 0.0016 0.0001 N/A N/A N/A N/A

Combined Standard

Uncertainty

(^combined)

0.00214 0.00087 0.00062 0.00097 0.00087 0.00089

Expanded

Uncertainty

0.0043 0.0017 0.0012 0.0019 0.0017 0.0018

16
Light-Tight Enclosure

Figure 1 . Schematic of the optical setup for transmittance

measurements at 1064 nm wavelength, where M represents

mirror; FD = feedback detector; MD = monitor detector;

SD = signal detector.

17
QO

>

H

CA

111

O

!=a.O

4.20

4.15

4.10

4.05

4.00

3.95

3.90

3.85

i i i iiiii —i i i iiiiii—i i 1 1 1hi—i i i iimii—i i i Mini—i i i miiii—i i i mm—i i i miiii—rm

ERROR BARS INDICATE THE STANDARD

DEVIATION FOR POWERS < 10"7 W

f\ THE STANDARD DEVIATION IS WITHIN

\ 0.002 FOR POWERS > 1 0'7 W

\

s 5- -o o o o- oA

\

FILTE:R Nc). 41-09

\

3.80 rill llllll I

I

I 'I i i I i i ' mill i ii I i '

i mill 10" 10 10"9 10" 8 10" 7 10"6 10"5 10"4 10 3 10

2 10" 1 LASER POWER (W)

Figure 2. Optical density of a filter (nominal OD = 4) measured with

different laser powers.

18
(a)

2.402

^

2.401

5 2.400

Q_

I-D

O 2.399

-l

<

Z

(D 2.398

2.397

TTT

:

1.328

1.327

P 1.326

o --MD OUTPUT

l_l I L—L,

H

o

O

H

:.. d...i£...^P.j| 1.325 2

1.324 3

1.323

0 500 1000 1500 2000 2500 3000

TIME (s)

(b)

CLH

O

1.48 ^

1.47

0 200 400 600 800 1000 1200 1400 1600

TIME (s)

Figure 3. Outputs from the signal detector and the monitor detector

during measurements when the laser beam passes through

the reference. The laser power is more stable in a) than in b).

19
QO

>-H

CO

z

m

Q

—J

<

O

H

O

3.002

3.000

2.998

2.996

2.994

2.992

2.990

2.988

o

I I I |

I I I | I I T

o— NOT NORMALIZED BY V

NORMALIZED BY V

p

FILTER No. 32-01

P-.

' o

J I I L. _1__J I I 1111 L_J I I I U 200 400 600 800 1000 1200 1400 1600

TIME (s)

Figure 4. Comparison of the optical density calculated with and without

normalization using the monitor detector output.

20
(a)

QO

z

LUQ

<

U

I-

£LO

(b)

QO

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(Ji z

UJQ

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2.081

2.080

2.079

2.078

2.077

2.076

2.075

2.074

.

1 1 1 1

-

-

1,11

FILTEER No.

1111

22-02

1111 1111 , , , , —i—i—i—i

-

:-

+ \

: V?

^ LINEAR F

OD = 2.0656 + 0

T: .000519 t

-_ ++

"

, , , , _l l l l i i i i i i i i

, , , , , , , , , , , , . , . ,

- 20 21 22 23 24 25 26 27

FILTER TEMPERATURE, t (°C)

28

21 22 23 24 25 26 27

FILTER TEMPERATURE, t (°C)

28

Figure 5. Optical density versus filter temperature for two filters:

a) Nominal OD = 2; b) Nominal OD = 3.

21
(a)

o

<

o

p

a.O

1.014

1.013

Z 1-012

HIQ

1.011

1.010

1.009

I I

1 1 1 1 1 r

VERTICAL POSITION: —o 10 mm

• v -5 mm

—x- 0 mm

- - - 5 mm

10mm

-i 1 1 1 1 1 1 1 r -• k

-5 0 5 10

HORIZONTAL POSITION (mm)

(b)

^

6.034

Q

O

> 6.033

H

uj 6.032

Q

_l

g 6.031

0lQ 6.030 -4

VERTICAL POSITION:

-10 mm

- V- - -5 mm —x- - 0 mm

— - 5 mm

- -- - 10 mm

10 -5 0 5 10

HORIZONTAL POSITION (mm)

Figure 6. Spatial variation of the optical density for two filters, where

the positions are measured from the center of the filter:

a) Nominal OD = 1, relatively poor spatial uniformity;

b) Nominal OD = 6, relatively good spatial uniformity.

22
(a)

1.020

QO_. 1.018

>

(/) 1.016

UJQ

<

(b)

QO

QO

Q

UJO

D

Q

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1.014

CL 1.012

1.010

1 1 —1

1 SPECTR

. . . ,

i AL WIDTH A1

,

vV =— 0\J

1 1 1 1

/ # - / / /'

ft

ft

%\

l\ ft

fa

1 *\

~

if

§ JI mi 1 w*-f- /

- w/o INTER

i i i i

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, , , , i

i Av = 1 cm"1 v, .

0 f \*

# / \ • - */ V*

1 1 1 1 I 1 1 1 1 0 0.5 1 1.5

PARAMETER, ^ = 2ndA

1.018

1.017

1.016 -

1.015 -

1.014 -

1.013

1.012

i—i—i—

OD

t—i—i—I—i—i—i—i—I—i—i—i—i—I—i—r—i—i—I—i—i—i—

= OD - 0.00025 (t/°C - 25)

reduced measured v '

FILTER No. 10-02 ++ *+

#

j j + + "Hi + ++++++

+ i + + V

+++ +

!

1 I I I I I I I I I I

I I L 21 22 23 24 25 26

FILTER TEMPERATURE, t (°C)

27

Figure 7. Interference effects on the transmittance: a) Predicted OD vs. % = 2nd/ X; b) Reduced optical density of an OD 1 filter as a

function of temperature.

23
800 900 1000 1100 1200 1300 1400

WAVELENGTH (nm)

Figure 8. Transmittance in the region from 800 nm to 1400 nm of two

filters measured using a Fourier transform infrared

spectrometer.

24
^National ^nstttute oi JStanimrfrs 8c tEecljrtnlngg

Standard Reference Materials® 2046, 2047, 2048,

2049, 2050, 2051

Transmission Filters with Measured Optical Density

at 1064 nm Wavelength

Serial No.

Standard Reference Materials (SRMs) 2046-2051 are a series of filters intended primarily for use in the calibration of transmittance measurements using lasers or infrared spectrophotometers; for attenuating the optical

power with an accurately known transmittance at a wavelength of 1064 nm; and for characterizing the nonlinearity

of detection systems. The filters are made of colored glass with uncoated, polished surfaces having dimensions of

51 mm x 51 mm. Each surface is flat to within one tenth of the helium-neon wavelength (633 nm), while the wedge angle is less than 5 urad (1 arc s). The optical density (OD) of each filter has been determined at a wavelength of 1064 nm using a Nd-YAG laser and silicon diode detectors. The nominal optical density and the corresponding thickness of each SRM are given in Table 1

.

Table 1 . Nominal Optical Density with Corresponding Thickness

SRM Nominal Thickness

Number Optical Density (mm)

2046 1 1.0 2047 2 2.2 2048 3 3.2 2049 4 4.2

2050 5 5.4 2051 6 6.4

Certified Values of the Optical Density: The certified optical density value and associated uncertainty for

this filter are given in Table 2. The source and magnitude of each uncertainty component and the average

temperature of the filter during the measurement are also listed in Table 2. The optical density is related to the transmittance, T, of the filter by OD = -log 10 T. An uncertainty of 0.001 in OD corresponds to a

relative uncertainty AT/T of 0.23 % in transmittance. The certified OD value is the average of the measured values over the central 20 mm x 20 mm area of the filter. The certified values are for normal

incidence (angle of incidence < 2°).

Expiration of Certification: The certification of the SRM is valid until 30 June 2003, within the measurement

uncertainties specified, provided the SRM is handled and stored in accordance with the instructions given in this certificate (see Instructions for Use). However, this certification is nullified if the SRM is damaged,

contaminated, or modified.

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

the Standard Reference Materials Program by J. W.L. Thomas and J.C. Colbert.

Gaithersburg, MD 20899 Thomas E. Gills, Chief

Certificate Issue Date: 9 July 1998 Standard Reference Materials Program

SRMs 2046, 2047, 2048, 2049, 2050, 2051 Page 1 of 5
Overall Uncertainty Determination: The nonlinearity of the detector system was checked by measuring

an OD 4 filter with different laser powers between 1 nW and 10 mW. The uncertainty associated with the detector nonlinearity was estimated to be 0.0002 for all filters. The reproducibility was determined from

multiple measurements of OD 1, 2, and 3 filters performed on different dates. The interference effects added additional uncertainty for OD 1 and OD 2 filters. An uncertainty due to reference measurement is included in the combined standard uncertainty for OD 5 and OD 6 filters. The combined standard

uncertainty was calculated as a prediction interval [1]. The uncertainty and its components for the given

filter are listed in Table 3 [2].

Maintenance of SRM Certification: NIST will monitor these SRMs over the period of their certification. If substantive technical changes occur that affect the certification before the expiration of certification, NIST will notify the purchaser. Return of the attached registration card will facilitate notification.

The development of the instrumentation and the measurements used to certify these SRMs were performed by

Z.M. Zhang, T.R. Gentile, and A.L. Migdall of the NIST Optical Technology Division.

The overall direction and coordination of the technical measurements leading to certification were performed

under the supervision of R.U. Datla of the NIST Optical Technology Division.

Statistical consultation was provided by M.C. Croarkin and S.B. Schiller of the NIST Statistical Engineering

Division.

Source of Material: The filters were fabricated and polished by Laser Optics, Inc., using the NG-9 glass materials manufactured by Schott of Mainz, Germany. 1

NOTICE AND WARNINGS TO USERS

Storage and Handling: The SRMs are stored in a wooden box, designed to minimize the contamination of the

filter surfaces. The air gap in the box prevents any contact between the middle portion of the surfaces and the walls of the storage container. The filter may be held by the edges with soft plastic, powder-free gloves, or

optical lens tissue. No filter mount is provided. A metallic mount may be used to hold the edge of the filter (within 7 mm from the edge). Care must be taken not to break the glass filter. The central portion of the

filter should never be touched by fingers or any hard objects. Dust may be removed by blowing with clean,

dry air.

Instructions for Use: Only the central 20 mm x 20 mm area of the filter should be used. It is desirable to integrate over several positions on the filter. The laser beam should be perpendicular (within 2° or 0.035 rad) to the filter surface since the filter attenuates the radiation through absorption. Because the optical density increases with increasing temperature at this wavelength, for filters with OD > 3, a correction may be necessary if the filter temperature in the actual application differs from the value indicated in Table 2 (see the section entitled Temperature Dependence). The laser power on the filter should not exceed 20 mW (or 300 mW/cm2 ) in order to avoid excessive heating.

CERTIFICATION ANALYSIS

Measurement Conditions: A continuous-wave (CW) Nd-YAG laser with an output wavelength of 1064 nm was

used. The beam spot was approximately 3 mm in diameter (full width at half maximum). The laser beam

incident on the filter was perpendicular to its surface. The temperature of the sample was monitored by a thermistor attached to the filter holder. The temperature and humidity in the measurement laboratory were

between 22 °C and 24 °C and between 40 % and 60 %, respectively.

Certain commercial materials and equipment are identified in order to adequately specify the experimental procedure. Such

identification does not imply a recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that

the materials or equipment are necessarily the best available for this purpose.

SRMs 2046, 2047, 2048, 2049, 2050, 2051 Page 2 of 5
Determination of the Optical Density: A Nd-YAG laser and three silicon diode detectors were used to measure

the normal transmittance of the filters at 1064 nm. The root-mean-square (rms) fluctuation of the laser power is less than 0.3 % over several hours of operation using a stabilizer. A wedged quartz beamsplitter was used. One

of the reflected beams goes to a feedback detector that controls the laser stabilizer. The other beam reflected by

the wedge is used to simultaneously monitor the laser power via the monitor detector. The transmitted beam

passes through a shutter and the sample filter (or a reference), and then to the signal detector. The relative transmittance is

Trelative 0 ) [(v„ - Vso)/ Vm 1 reference

where V is the output voltage from the dc voltmeter, subscripts s and m indicate signal detector and monitor

detector, respectively, and subscripts 0 and 1 indicate shutter closed and open, respectively. The detectors are placed inside a light-tight enclosure. The signal when the shutter is closed (V^) is subtracted from the output

signal Vjj to eliminate background. For filters with OD < 4, the reference is air (blank). Therefore, the sample

transmittance is equal to the relative transmittance given in Equation 1. A reference filter with OD near 3 was

used for filters with OD > 5. The transmittance of the reference filter, Treference , is measured at a fixed position.

The transmittance of OD > 5 filters is determined by

Tsample 1 relative ^ Treference

The dynamic range and linearity of the detector and amplifier electronics are discussed in References [3] and [4]

The temperature of the filter is monitored by measuring the resistance of a thermistor on the filter holder during

the data acquisition process. Detailed discussions of the theory and measurements are given in Reference [1].

Spatial Nonuniformity: The spatial variation in OD among different locations depends on the filter. Measurements were performed either on nine positions in a 3 x 3 matrix with 10 mm spacing or on 25 positions in a 5 x 5 matrix with a 5 mm spacing around the center of the filter. Because of the extremely flat and parallel surfaces of these filters, the spatial variation is attributed to the inhomogeneity of the material. For SRM 2046

OD 1 filters, interference between multiple reflections may also affect the spatial uniformity [3]. The

measurement repeatability at the same position is better than 0.000 06 for OD 1 and 2 filters; 0.0002 for OD 3, 5, and 6 filters; and 0.000 67 for OD 4 filters (due to a lower signal-to-noise ratio). The

uncertainty given in Table 3 associated with the nonuniformity (crspalial) is the standard deviation of the measurements on different positions of the filter, which includes the repeatability component.

Temperature Dependence: The OD increases slightly with temperature because of a change in the absorption

coefficient of the material. The absorption coefficient of the glass material is 2.16 mm"1 at 25 °C with a temperature coefficient of 0.026 %/°C at a wavelength of 1064 nm [3]. Therefore, a correction in the measured

OD may be necessary for measurements at temperatures different from that indicated in this certificate. The

correction depends on the nominal OD values. Table 4 lists the change in OD per 1 °C temperature change at temperatures between 21 °C and 27 °C for different OD filters. The standard uncertainty resulting from the temperature variation of + 0.5 °C is given in Table 3. The higher the OD of the filter is, the larger the standard

uncertainty due to temperature variation.

SRMs 2046, 2047, 2048, 2049, 2050, 2051 Page 3 of 5
REFERENCES

[1] Taylor, B.N. and Kuyatt, C.E., Guidelines for Evaluating and Expressing the Uncertainty of NIST

Measurement Results, NIST Technical Note 1297, U.S. Government Printing Office, Washington DC,

(1994).

[2] Zhang, Z.M., Gentile, T.R., Migdall, A.L., and Datla, R.U., Optical Density Measurements for Infrared

Filters at 1064 nm Wavelength, NIST Special Publication 260-128, (1997).

[3] Eppeldauer, G. and Hardis, J.E., "Fourteen-Decade Photocurrent Measurements with Large-Area Silicon Photodiodes at Room Temperature," Applied Optics 30, pp. 3091-3099, (1991).

[4] Migdall, A.L. and Winnewisser, C, "Linearity of a Silicon Photodiode at 30 MHz and Its Effect on

Heterodyne Measurements," Journal of Research of the NIST 96, pp. 143-146, (1991).

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 (select "Certificates"), Fax (301) 926-4751, e-mail

srminfo(a),nist.gov, or via the Internet http://ts. nist.gov/srm.

SRMs 2046, 2047, 2048, 2049, 2050, 2051 Page 4 of 5
Table 2. Certified Optical Density at 1064 nm, SRM 2046

Serial No. 10-04 at Filter Temperature 24.8 °Ca

Optical Density (OD): 1.0102

Expanded Uncertainty (2<r): 0.0035

aNominal Thickness (in mm): 1 .044

Table 3. Uncertainty Components, Serial No. 10-04

Spatial Nonuniformity (ospatial)'- 0.00045

Reproducibility (areprod)' 0.00035

Detector Nonlinearity (<rM0„/,„): 0.0002

Temperature Variation {(7temp): 0.00007

Reference (are/): 0

Interference Effects ( ainter/): 0.00 1

6

Combined Standard Uncertainty (<7COmbined)'- 0.00175

Expanded Uncertainty (2 <JCombined)'- 0.0035

Table 4. Change in OD for 1 °C Temperature Change

SRM No. 2046 2047 2048 2049 2050 2051

Nominal OD 1 2 3 4 5 6

AOD/°C 0.00026 0.00054 0.00078 0.00103 0.00133 0.00157

SRM 2046 Page 5 of 5

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