NBS

PUBLICATIONS

U.S. DEPART

National Bureau of Standards

NBS Special Publication 692

Transmittance

MAP Service

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1^

Kenneth L. Eckerle, Jack J. Hsia, and Victor R. Weidner

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1985

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M he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

Jy Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

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The Bureau's technical work is performed by the National Measurement Laboratory, the National

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Science.

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Conducts research and provides measurements, data, standards, reference

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Gaithersburg, MD 20899. ^Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
KATIONAI, BUREAU OF STAI^DARDB LIBRARy

NBS Special Publication 692

Transmittance MAPService

Kenneth L. Eckerle Jack J. Hsia

I Victor R. Weidner

I Center for Radiation Research

National Measurement Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

|i

i|

1 March 1985

I U.S. Departmoit of Commerce

I Malcolm Baldrige, Secretary National Bureau of Standards

i Ernest Ambler, Director
Library of Congress U.S. Government Printing Office Catalog Card Number: 85-600513 Washington: 1985 National Bureau of Standards

Special Publication 692

Natl. Bur. Stand. (U.S.), Spec. Publ. 692 50 pages (Mar. 1985)

CODEN: XNBSAV

For sale by the Superintendent

of Documents,

U.S. Government Printing Office,

Washington, DC 20402
TABLE OF CONTENTS

PAGE

I. Introduction 1

II. MAP Package 2

III. Instructions for the Care of the MAP Standards 2

IV. Instructions for Data Acquisition 3

V. Pilot Run 5

VI. Recommendation for Participation 6

VII. NBS Research Results 6

VIII. Summary 7

References 16

Illustration 1 17

Illustration 2 18

Appendix A 19

Appendix B 32
LIST OF FIGURES

FIGURE NO.

Bl . Wavelength calibration curve for

B2. Wavelength calibration curve for

B3. Wavelength calibration curve for

B4. Wavelength calibration curve for

B5. Wavelength calibration curve for

PAGE

Instrument 1 .... 40

Instrument 2 . . . . 41

Instrument 3 . . . . 42

Instrument 4 .... 43

Instrument 5 . . . . 44

\;

' 1

'J f I

i V
LIST OF TABLES

TABLE NO. PAGE

1. Transmi ttance MAP Package 8

2. Map of Uniformity for Filter 1 9

3. Map of Uniformity for Filter 2 10

4. Map of Uniformity for Filter 3 11

5. Map of Uniformity for Filter 4 12

6. Map of Uniformity for Filter 5 13

7. Map of Uniformity for Filter 6 14

8. Map of Uniformity for Filter 7 15

APPENDIX B

1. Transmi ttance Results for the Indicated Instrument . . 35

2. Transmi ttance Results for the Indicated Instrument . . 36

3. Transmi ttance Results for the Indicated Instrument . . 37

4. Transmi ttance Results for the Indicated Instrument . . 38

5. Measurements by participant of Aj^j^ and A^j^p with

difference between NBS and the participating

laboratory, AA = ^nBS"^PARTICIPANT'

^"^^ expressed in nanometers 39

V

TRANSMITTANCE MAP SERVICE

Kenneth L. Eckerle, Jack J. Hsia, and Victor R. Weidner

An introduction to the Transmi ttance Measurement Assurance

Program (MAP) service is given. Documentation for the service is

provided through a comprehensive list of references. The results

of a pilot run for the MAP service are given in a sample calibration report.

Key Words: didymium filters; bandpass; glass filters; measurement

assurance program; neutral density filters; reference spectrophotometer; transmittance; transmi ttance MAP service; uncertainty

estimation; wavelength calibration

I. Introduction

The transmittance Measurement Assurance Program (MAP) [1]* provides

a means for a laboratory to assess the accuracy of its spectral transmittance measurement capabilities. A laboratory which participates in

this program will be sent a package of transmittance filters which have

been measured at NBS. These are to be measured by the laboratory on its

spectrophotometer(s) and returned, together with the measurement results,

to NBS. NBS will then remeasure the filters and send a final analysis

of the result to the participating laboratory. The range of filter

measurements provided in the MAP package permits an evaluation of the

accuracy of a laboratory's spectral transmission measurements and will

often reveal the cause of systematic errors if any exist. This publication describes the contents and use of this MAP package.

*Figures in brackets indicate the literature references on page 16.

1
II. MAP Package

The contents of the MAP package are itemized in Table 1 [2]. They

include seven neutral density filters with nominal transmi ttances

ranging from 0.92 to 0.001. Schott glass had previously been shown to

be useful [2,3], and the filters were all constructed of this glass except the clear filter whicn is made of NBS crown glass. The filters are

available in the three sizes given in Table 1. A participating laboratory

should specify the size desired. These filters are calibrated by NBS

using the method described in reference [4] (Included in Appendix A) at

548.5 nm for spectral passbands from 1.5 to 10.5 nm. The long term stability of a master set calibrated over 2 years showed that the transmittance of the clear glass filter decreased slightly while the other

filters in creased slightly. The relative changes over two years for

the seven filters in the master set were -0.12, 0.13, 0.15, 0.21, 0.36,

0.64, and 0.99 percent. In addition, each package contains one didymium

glass filter which is to be used for wavelength scale calibration: ji,

several wavelengths of transmi ttance minima and points of inflection , ,:

have been measured by NBS for these filters. [5] These wavelengths have

been shown [6] to be stable over long periods of time; therefore these

didymium filters are not normally remeasured by NBS with every use of

the MAP package. .,

III. Instructions for the Care of the MAP Standards io

Upon receipt of the MAP package the participating laboratory should

open the shipping container and the flat metal box containing the filters,

saving all the containers and packing material for use when returning

the package to NBS. The flat metal box is opened by removing the six

knob screws and should be used for storing the filters when they are not

in use. Each neutral density filter is mounted in an aluminum frame
with a Teflon cover. The filters must not be removed from these frames

nor should they be cleaned except to remove surface dust or lint by

light stroking with a clean camel-hair brush. In the unlikely event

that a filter becomes contaminated or damaged NBS should be notified by

telephone so that a procedure can be developed jointly which will minimize

the loss of time and data.

IV. Instructions for Data Acquisition

Illustration 1 shows a form for reporting the participating laboratory's measurements of the neutral density filters. The filters

should be measured as near their centers as possible (See appendix A and

Section VII below for additional information on uniformity) and at a

wavelength of 548.5 nm. This wavelength setting, as well as the wavelengths reported in the didymium glass filter measurements described

below should be based upon the normal wavelength scale associated with

the spectrophotometer being measured. Usually this will simply be the

reading of a counter on the instrument but if such readings are normally

corrected by an error correction curve then these corrections should be

applied in these measurements too. The final report from NBS will, of

course, refer any wavelength errors to this same scale. At least four

transmittance measurements should be made of each neutral density filter

(preferably on two successive mornings and afternoons) and the arithmetic

mean and a standard deviation for the four measurements be computed.

Illustration 2 shows a form for reporting the measurements of the

didymium glass filter. This filter is to be used in two experiments to

test the accuracy of the wavelength scale of the instrument. For certain

instruments a third experiment may be performed to diagnose causes of

any anomalies observed in experiments 1 and 2.

3
Experiment 1. The transmi ttance minima are determined directly '

from the instrument or a graph by inspection using transmi ttance versus

wavelength curves. (See ref. [5], pp. 4-9 and Appendix B).

Experiment 2. In addition to the transmi ttance minima, points of

inflection are determined. Included in the MAP package will be a table

of the nominal calibration wavelengths and corresponding inflection

point transmi ttance values required. The instrument wavelength must be

adjusted until the tabulated transmi ttance is observed, and the corresponding wavelength is recorded. Since this is sometimes cumbersome, it

is satisfactory to take measurements of the transmi ttance on either side

of the tabulated transmi ttance and to perform a linear interpolation to

find the wavelength corresponding to the given transmi ttance. (See ref.

[5] p. 23 and Appendix B.)

Experiment 3. This experiment applies only to single beam instruments or to double beam instruments which can be configured like a

single beam instrument. Most modern spectrophotometers are double beam

instruments which automatically measure simultaneously both a 100% -

'

transmitting reference standard and the unknown sample, and this experiment may not be feasible for such an instrument. A single beam spectrophotometer is one which requires the operator to insert the 100% transmitting reference into the beam alternately with the sample to be measured. Usually the instrument gain is adjusted to read 100% while the

reference is in the beam and then when the sample is in the beam the

instrument reads directly the sample transmi ttance. For such a single

beam instrument a further improvement in the wavelength scale accuracy

can be obtained by consideration of the instrument sensitivity function

(sometimes called the responsivity factor). Therefore for this experi4
ment a graph is required of the signal versus wavelength, obtained

sipply by scanning the instrument over the visible spectrum with no

samplin the instrument. In spectral regions where this signal changes

rapidly with wavelength, the didymium glass spectral features will

appear shifted. Although a calibration with the didymium glass filter

calibrates the instrument completely with respect to the centroid of the

passband (including the effects of the instrument sensitivity function),

data from this experiment could increase the accuracy of a wavelength

correction curve by correcting or identifying outliers in the wavelength

measurements. The instrument sensitivity function could help NBS to

distinguish between valid variations due to the instrument sensitivity

function itself or other causes such as offset in the wavelength due to

the sine bar or lead screw.

V. Pilot Run

After the MAP package and results of the participating laboratory's

measurements have been received by NBS, the neutral density filters will

be remeasured and a report will be prepared and returned to the laboratory.

An example of such a report stemming from a pilot test of this MAP procedure is shown in Appendix B. In this case the laboratory possessed

six spectrophotometers with varying passbands as indicated in the report.

The report is self-explanatory. In particular, it gives the NBS beforeand-after average values of the filter transmi ttances and the discrepancy

between the laboratory's measurements and these values. It also gives

an upper bound to the uncertainty in the NBS values. This uncertainty is

based upon the arithmetic sum of a systematic error [7], three times the

standard error based on four measurements, and the possible change in

the filter between the 'before' and 'after' measurements. Finally it

5
presents a table of wavelength errors based upon the didymium glass

filter measurements and a graphical presentation of this data. In the

example in Appendix B tlie results show that this laboratory's instrument

#1 requires a wavelength adjustment.

VI. Recommendation for Participation

It is strongly recommended that any laboratory which participates

in this MAP program acquire a set of filters as check standards which

are similar to those supplied in this MAP package and that these be

measured along with the MAP package filters. These filters will then

serve as an inhouse reference which should be remeasured periodically

and whenever any change in equipment, technique, or operator has taken

place. A plot of such measurements against time can be used to establish

a control chart in order to verify the continuing accuracy of a measurement

process. The user should strive to obtain at least 15 such data points.

More detail on control charts can be found in ref. [1] and examples in

ref. [3].

VII. NBS Research Results.

The MAP package filters are measured using a reference spectrophotometer developed at NBS. [7,8,9] A statistical analysis showed measurement at 5 wavelengths [4] to be sufficient to specify the transmi ttance

at bandpasses between 1.5 and 10.5 nm. Scattering, polarization, and

uniformity were also checked. The linearity of the spectrophotometer

was checked using the double aperture method [10]. Other systematic

errors are discussed in reference [11], and their effect is published in

reference [7j. These transmi ttance filters are calibrated for specular

or "regular" transmi ttance with no inter-reflections between sample and

optics or sample and detector. The uncertainty of the neutral filters

varies with the transmi ttance. The NBS uncertainty of transmittance

6
values (U) is estimated to be the arithmetic sum of a systematic error

of approximately 0.0001 to 0.000003 transmittance units for transmi ttances

from 0.92 to 0.001, respectively [7] plus 3 times the standard error

based on four measurements. Since these measurements are for specular

(or regular) transmittance, the effect of scattering by the filters on

transmittance is negligible [4]. Polarization was also found to be

statistically insignificant [4]. Non-uniformity of the filters was

found to be statistically significant, so NBS would prefer the transmittance measurements to be made near the center of the filters, however, this is not always possible. Further, non-uniformity of small

cuvette size filters can be large due to a possible wedge effect [12].

Consequently, the uniformity of one set of cuvette sized MAP filters

were carefully measured for uniformity. The results are shown in

Tables 2 through 8. Based on these data, NBS requests participants to

specify spot size and location of the beam on the filter. The NBS

uncertainty for the wavelength calibration using the didymium glass is

approximately 0.3 nm or less [5].

VIII. Summary

The MAP service provides a means of checking linearity and wavelength of spectrophotometers with an accuracy which was not previously

available. A user guide for participating in the MAP service is presented along with references documenting the method.

Acknowledgements . This project is supported by the Office of Physical

Measurement Services (W. P. Reed, Acting Chief). We would like to thank

R. K. Kirby, formerly with the Office of Physical Measurement Services.

The authors wish to acknowledge J. B. Shumaker for his critical review

and constructive suggestions. Thanks are due S. T. Chang for his help.

7
The Calibration Advisory Group subcommittee on the Transmi ttance MAP

Service was composed of T. Vorburger, M. C. Croarkin, and R. W. Burke.

TABLE 1

Transmi ttance MAP Package

1. Neutral Density Filters : Calibrated at 548.5 nm only

Filter Nominal Remarks

No. Transmi ttance (%)

1 92 Borosilicate crown glass

2 70 Schott NG-11

3 50 NG-11

4 25 NG-4

5 10 NG-4

6 1 NG-9

7 0.1 NG-9

Filter Filter

Size Holder Aperture

Large 51 x 51 mm 38 mm dia

Medium 51 x 38 mm 25 mm dia

Small Cuvette 30 x 8 mm

2 . Didymium Glass Filters for Wavelength :

Calibrated between approximately 400 to 750 nm for wavelength

for triangular bandwidths between 1.5 and 10.5 nm.

Size Remarks

Large 51 x 51 mm Corning

Small Cuvette Corning
TABLE l

Map of Uniformity of Filter 1 of a set of cuvette sized filters. The

spotsize illuminating the filters is 2 by 6 mm with the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, t, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-1,6) (0,+6) (+l,+6)

T = 0. 91 688±0. 00010 T = 0.91722±0. 00039 T = 0.91731±0. 00039

[0.00022] [0.00056] [0.00065]

(-1,0) (0,0) (+1,0)

T = 0. 91 675±0. 00033 T = 0.91666±0. 00017 T = 0.91603±0. 00027

[0.00009] [0] [-0.00063]

(-1,-6)

T = 0.91662±0. 00024

[-0.00004]

(0,-6)

T = 0.91632±0. 00021

[-0.00034]

(+1,-6)

T = 0.91624±0. 00018

[-0.00042]
TABLE 3

Map of Uniformity of Filter 2 of a set of cuvette sized filters. The

spotsize illuminating the filters is 2 by 5 mm with the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, t, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-1,6) (0,+6) (+l,+6)

T = 0.69053±0. 00015 t = 0. 68983±0. 00030 t = 0. 69006±0. 00018

[-0.00144] [-0.00214] [-0.00191]

(-1,0) (0,0) (+1,0)

T = 0.69148±0. 00021 t = 0. 691 97±0. 00020 t = 0. 691 90±0. 00021

[-0.00049] [0] [-0.00007]

(-1,-6) (0,-6) (+1,-6)

T = 0.6913310.00016 t = 0.6913U0. 00018 t = 0.69150±0. 00016

[-0.00064] [-0.00066] [-0.00047]

10
TABLE 4

Map of Uniformity of Filter 3 of a set of cuvette sized filters. The

spotsize illuminating the filters is 2 by 6 mm with the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, i, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-1,6) (0,+6) (+l,+6)

T = 0.b2054±0. 00010 T = 0.52038±0. 00031 x - 0. 52053±0.0001

[0.00015] [-0.00001] [0.00014]

(-1,0) (0,0) (+1,0)

T = 0.52049±0. 00014 x = 0. 52039±0. 0001 5 x = 0. 52029±0. 0001

[0.00010] [0] [-0.00010]

(-1,-6) (0,-6) (+1,-6)

X = 0.52049±0. 00020 x = 0. 52020±0. 00020 x = 0. 52028±0. 0001

[0.00010] [-0.00019] [-0.00011]

11
TABLE 5

Map of Uniformity of Filter 4 of a set of cuvette sized filters. The

spotsize illuminating the filters is 2 by 6 mm with the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, i, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-l,+6)

T = 0.23625±0. 00007

[0.00022]

(0,+6)

T = 0.23603±0. 00012

[0]

(+l,+6)

T = 0.23595±0. 00006

[-0.00008]

(-1,0)

T = 0.23623±0. 00008

[0.00020]

(0,0)

T = 0.23603±0. 00012

[0]

(+1,0)

T = 0.23588±0. 00007

[-0.00015]

(-1,-6) (0,-6) (+1,-6)

T = 0.23638±0. 00013

[0.00035]

T = 0.23623±0. 00011

[0.00020]

T = 0.23585±0. 00008

[-0.00018]

12
TABLE 6

Map of Uniformity of Filter 5 of a set of cuvette sized filters. The

spotsize illuminating the filters is 2 by 6 mm with the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, i, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-l,+6) (0,+6) (+l,+6)

T = 0.096705±0. 000093 x = 0. 096746±0. 000047

[-0.000103] [-0.000062]

T = 0.096532±0. 000089

[-0.000276]

(-1,0)

T = 0.096726±0. 000079

[-0.000082]

(0,0)

T = 0.096808±0. 000039

[0]

T

=

(+1,0)

0.096538±0. 000031

[-0.000270]

(-1,-6)

T = 0.096629±0. 000041

[-0.000179]

(0,-6)

0.096661±0. 000038

[-0.000147]

(+1,-6)

T = 0.096709±0. 000073

[-0.000099]
TABLE 7

Map of Uniformity of Filter 6 of a set of cuvette sized filters. The

spotsize illuminating the filters i s 2 by 6 mm v;ith the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, t, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-l,+6)

T = 0.0091033±0. 0000265 t

= [-0.0000343]

(-1,0)

T = 0. 0091 043±0. 00001 58 t

= [-0.0000333]

(-1,-6)

T = 0.0091 103±0. 0000076 x

= [-0.0000273]

(0,+6)

0.0091233±0. 000189

[-0.0000143]

(0,-6)

0.0091242±0. 0000157

[-0.0000134]

(+l,+6)

T = 0.0091324±0. 0000188

[-0.0000052]

(+1,0)

0.0091332±0. 0000128

[-0.0000044]

(+1,-6)

'

T = 0.0091483±0. 0000207

[+0.0000107]

(0,0)

0.0091376±0. 0000100 t

=

[0]

14
TABLE 8

Map of Uniformity of Filter 7 of a set of cuvette sized filters. The

spotsize illuminating the filters is 2 by 6 mm with the long dimension

vertical. The values in parentheses are the coordinates in mm of the

center of the area on the filter with respect to the center of the

filter which is illuminated when facing the detector. The transmittances, i, are listed along with plus/minus three times the standard

error based on four measurements. The values in square brackets

are the deviations in transmi ttance units from the value of transmittance at the center position.

(-l,+6) (0,+6)

T = 0.0009277±0. 0000054 t = 0. 0009236±0. 0000030

[-0.0000020] [-0.0000061]

(+l,+6)

0.0009248±0. 0000032

[-0.0000049]

(-1,0)

0.0009280±0. 0000065 t [-0.0000017]

(0,0)

0.0009297±0.U000042 t

[0]

(+1,0)

0.0009260±0. 0000040

[-0.0000037]

T

=

(-1,-6)

0.0009305±0. 0000044 i

[+0.0000008]

(0,-6)

0.0009309±0. 0000020

[+0.0000010]

(+1,-6)

T = 0.0009304±0. 0000044

[+0.0000007]

15
Croarkin, C. , "Measurement Assurance Programs Part II: Development

and Implementation", NBS (U.S.) Special Publication 676-11, (April

1984).

Certain commercial items are identified by manufacturer only to

define the procedure. It implies in no way endorsement or evaluation

by the National Bureau of Standards or that the item is best for

the procedure.

Mavrodineanu, R. and Baldwin, J. R. , "Glass Filters as a Standard

Reference Material for Spectrophotometers - Selection, Preparation,

Certification, Use SRM 930", NBS Special Publication 260-51

(November, 1975).

Eckerle, K. L., Weidner, V. R. , Hsia, J. J., and Kafadar, K.

,

"Measurement Assurance Program Transmi ttance Standards for Spectrophotometric Linearity Testing: Preparation and Calibration",

J. of Res. of the NBS, 88, 1 (Jan. -Feb., 1983).

Venable, W. H., and Eckerle, K. L., "Didymium Glass Filters for

Calibrating the Wavelength Scale of Spectrophotometers - SRM 2009,

2010, 2013, and 2014", NBS Special Publication 260-66, (Oct. 1979).

Eckerle, K. L., Chang, S., and Hsia, J. J., "Calibration in 1976

and 1983 of Didymium Glass Filters Issued as NBS Standard Reference

Materials", accepted for publication in COLOR research and

appl ication .

Mielenz, K. D., Eckerle, K. L., Madden, R. P., and Reader, J.,

"New Reference Spectrophotometer", Appl. Opt. 12^ (7), 1630 (July

1973).

Mielenz, K. D. , and Eckerle, K. L. , "Design, Construction, and

Testing of a New High Accuracy Spectrophotometer", NBS Technical

Note 729 (June 1972).

Eckerle, K. L. , "Modification of an NBS Reference Spectrophotometer",

NBS Technical Note 913 (July 1976).

Mielenz, K. D., and Eckerle, K. L., "Spectrophotometer Linearity

Testing Using the Double Aperture Method", Appl. Opt. U_ (10)

(Oct. 1972).

Mielenz, K. D., "Physical Parameters in High-Accuracy Spectrophotometry"

NBS Special Publication 378, (May 1973).

Burke, R. W., Center for Analytical Chemistry, (NBS), private

communication.

16
ILLUSTRATION 1

Regular Transnn" ttance , T

(Measured or interpolated at 548.5 nm)

Date of Measurement:

Filter Set No.

:

Type of Instrument:

HALF HEIGHT BANDWIDTH:

Sample Beam (Collimated or Convergent):

Detector System (with or without averaging sphere):

Other Information:

Filter No. T Standard Deviation No. of Measurements

-1

-2

-3

.4 „ - . '\

-5

-5

-7

17
ILLUSTRATION 2

WAVELENGTHS AT MINIMUM TRANSMITTANCE AND INFLECTION

^^MIN' ^INF^

Date of Measurement:

TYPE OF INSTRUMENT:

HALF HEIGHT BANDWIDTH:

Didymium glass filter:

EXPERIMENT 1 . (FINDING TRANSMISSION MINIMA)

No. Nominal ^^-^^ (nm) Measured '>^^-^^ (nm)

1 440

2 478

3 529

4 585

5 684

6 740

EXPERIMENT 2 . (FINDING INFLECTION POINTS)

Nominal Trans- Measured Nominal Trans- Measured

Aji^p(nm) mittance, T A-j.|,^p(nm) Ajj^p(nm) mittance, T Xj|^p(nm)

406 568

429 600

450 733

485 756

537

EXPERIMENT 3 . (Include curve of instrument sensitivity function.)

18
APPENDIX A

JOURNAL OF RESEARCH of the National Bureau of Standards

Vol. 88, No. 1, January-February 1983 Measurement Assurance Program Transmittance Standards

for Spectrophotometrk Linearity Testing:*

Preparation and Calibration

Kenneth L. Eckerle,** Victor R. Weidner,** Jack J. Hsia,** and Karen Kafadarf

National Bureau of Standards, Washington, DC 20234

August 26, 1982

A Measnrement Assurance Program for spiectrophotometry is being established in order to assist laboratories involved in spectrophotonietric calibrations. This paper deals with the preparation and calibration of neutral density glass filters for checking the linearity of photometric response, as applied to s()ectral transmittance measurements. Several sets of filters were prepared from suitable neutral glass to provide nominal transmit- tances of 92, 70, 50, 25, 10, 1, and 0.1% at a wavelength of 54S.5 nm. These filter sets will be available

in three sizes: these are, 38 mm diameter ap>erttu-e in 51 x 51 mm holder, 25 mm diameter aperture in 51 X 28 mm holder, and 30 x 8 mm aperture in a cuvette holder. The filters were calibrated for spectral transmittance on the NBS Reference S[)ectrophotometer for high accuracy transmittance measurements. Measurements were made with a 1.5 nm passband collimated sample beam. The filters were checked for uniformity and measurements were made to determine the effects of sample beam polarization. The transmit- tance data for the wavelength range of interest were analyzed by statistical methods to determine the ef- fects of passband for a range of 1 .5 nm to 10.5 nm passband. Ttie results of these measurements are presented

in tabular and graphical detail for the master filter set.

Key words: experimental design; filter uniformity; linearity testing; measurement assurance program; neutral

density glass; passband effects; polarization effects; polynomial fitting; sf>ectrophotometry; statistics; transmit- tance standards.

1. Introduction

This paper deals with the preparation and calibration

of neutral density glass filters for cheeking the linearity of photometric response, as applied to spectra! transmit- tance measurements.

The application of absolute techniques, such as the

double-aperture method [1],' for checking the linearity of a spectrophotometer's response, is difficult to realize on many instruments because of problems involving sample and reference beam geometry or detector configurations. The other approach to checking linearity is through

the use of a set of transmittance standards. Several sets of glass filters have been prepared and calibrated for this purpose. A Measiu-ement Assurance Program (MAP) is being established through which these sets of transmit- tance standards will be used for the purpose of improving the accuracy of spectrophotometer measurements in laboratories participating in the program.

*Thi8 project is supported by the Office of Measurement Services (Dr. B. C.

Belanger, Chiefl and coordinated by Dr. L. J. Kieffer. **Center for Radiation Research, National Measurement Laboratory. tCenter for Applied Mathematics, National Engineering Laboratory.

'Figures in brackets indicate literatiu-e references at the end of this paper.

2. Selection and Preparotion

of the Standards

Some of the factors to be considered in selecting suitable

filters for transmittance standards are: available range of transmittances, light scattering properties, imiformity,

stability, passband sensitivity, and wavelength sensitivity. Schott^ neutral density glass types NG-4, NG-9, and

NG-11 were selected on the basis of these characteristics and properties as well as previous experiences with Schott

glass by NBS in the preparation of Standard Reference

Material (SRM) 930 [2].^ Two levels of transmittance were prepared from each of the glass types as follows:

^Certain commercial materials are identified in this paper in order to adequately

specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Bureau of Standards nor does it imply

that the materials identified are necessarily the best available for the purpose. 'SRM 930 consists of three filters with nominal transmittances of 10%, 20%,

and 30% calibrated at several wavelengths. Originally these SRM filters were

designed for use by clinical chemists and are sold by the set. Our goal with the present filters was to provide a larger dynamic range so that the filters could be

used to measure linearity in applications when other methods are difficult if not

impossible. Also, these filters are not for sale, but are to be retained by NBS and

issued only temporarily as part of a MAP measurement service.

19
Equivalent

Glass Type Nominal Transmittance Transmission Density

NG-11 70% 0.15

NG-11 50% 0.3

NG-4 25% 0.6

NG-4 10% 1.0

NG-9 1% 2.0

NG-»^ 0.1% ,3.0

An additional filter of borosilicate crown glass having a nominal transmittance of 92% (transmission density

0.036) is included in the set. The filter sets were prepared in three sizes in order to accommodate different instruments. The largest filters are mounted in 51 x 51 mm holders with a filter aperture of 38 mm diameter. The intermediate size filters are mounted

in 51 X 38 mm holders with a filter aperture of 25 mm.

The smallest filters are mounted in cuvette holders and

provide a filter aperture of 30 x 8 mm.

The preparation of the filters from the stock glass was

done in the NBS Optical Shop. The tolerances on

parallelism of the two faces of the filters was maintained

at approximately 0.01°. They were polished to a flatness of 3 fringes or better. Calculations of the required thicknesses were made

from internal transmittance data supplied by the

manufactm-er. The internal transmittance of 1 mm path

length for the three glass types is as follows:

Glass Type 1 mm path

NG-4 0.32 NG-9 0.035 NG-11 0.78

The values of transmittance for a wavelength of 500 nm

were computed from these internal transmittance values. These transmittance values were converted to equivalent

transmission density. Since the transmission density is linear with thickness, it is possible to determine, by

graphical techniques, the required thickness for a desired transmittance value. Figure 1 shows the relation- ship of transmission density to thickness for the glass

types NG-4, NG-9, and NG-1 1. The degree of accuracy

in determining the required thickness for a given

transmittance value by this graphical technique is dependent on the initial accuracy of the internal

transmittance values used to determine the transmit- tance of 1 mm and 2 mm thicknesses. The actual

transmittance values achieved by this technique closely

approximated the desired nominal transmittance values

for the filter set.

TRANSMISSION DENSITY (-logT) — _ r\3 ro w w

TRANSMISSION a)

Fig L RE 1. Transmission density versus thickness of Schott NG-4,

NG-9, and NG-11 neutral glasses as derived from internal transmission data for 1 mm and 2 mm thicknesses.

3. Transmission Analysis

3.1 Light Scattering

Scattering of a collimated sample beam transmitted

through the neutral filters was quantitatively assessed by

the ASTM recommended method [3] for measiu-ing haze

percentage. The measurements were made on the reference hazemeter [4] using the ASTM recommended

geometry and methods. This instrument has a well col- limated circular incident beam having a color temperature of approximately 6800 K. A visual response

filter at the detector modifies its response to give the hazemeter a peak sensitivity at approximately 550 nm. The instrument measures total forward scattering

relative to the total transmission within the definition of

this response and for the ASTM recommended

geometry. The haze percentage determined for a set of

filters was found to be as follows:

20
ERRATA

"Measurement Assurance Program Transmi ttance Standards for Spectrophotometric Linearity Testing: Preparation and Calibration"

by Kenneth L. Eckerle, Victor R. Weidner,

Jack J. Hsia, and Karen Kafador

PAGE COLUMN LINE NOW READS IN PART SHOULD READ

20 2 Fig. 1 Rotated 90° clockwise Should rotate 90° countercl ockwi se

24 1 Table 2 2,P

2. P

3, p

2,P

2, s

3, s

24 1 & 2 Table 3 lino R "in L 1 1 Ic O III Table 3

97cl L c c

T {X ) = 1 ° h ('A)f(A-A )dA/

o' 1 , ' ^ 0

A -uj 0

Si. J A^ 0)

X +w

T (A ) =\"° h (A)f(A-> )dA

0 1, W ' 0 J\ -w

0

27 2 25 - A +UJ

J A -w

0 ;

h^(A)dA-i

27 2 27 V^o) = h^(A)f(A-A^)dA

J A " (i) 0 ^w(^o)=V VA)f(A-A„)d

0 ^

28 1 14 equal distances ±26 equal distances ±6, and

at approximately +26

28 2 17 |A~x-j jx^x^l |X"*X-J |*|a~x2|

28

2 19 1 = 0 ^0

=

29 2 6 h (w+A ) o'

29

1 13 0' Q

'./

21
r liter 1 laze Percentage TVT * 1 Trflnsmittance

1-1 0.05% 92%

1-2 0.02% 70%,

1-3 0.05% 50%

1-4 0.06% 25%,

1-5 0.04%, 10%

1-6 * 1%

1-7 * 0.1%

* The 1 and 0. 1% transmitting filters were too low in trainsinittance for analysis by the hazemeter. It was concluded from these results that the fihers scattered less than 0.1%, of the transroitted saanple beam.

3.2 Survey Transmiffance Measurements

The purpose of a survey study of the neutral filter transmittance was to assess their over-all spectral properties in the visible spectrum and select a specific

wavelength for detailed analysis and calibration. Since

the filters are not perfectly neutral, it was desirable that a wavelength be selected for calibration, at which the

transmittance values of the filters would be least sensitive to variation in passband and wavelength scale errors associated with various spectrophotometers.

With the exception of the borosilicate crown glass

filter, the filters in the set are of a similar type glass with

a common dye in three different concentrations for the

NG-4, NG-9, and NG-11 glass types. The spectral

transmission density curves of these filters in the spectral

range between approximately 440 nm and 620 nm shows

that the absorptions appear at the same wavelengths for the different concentrations associated with these glass

types. Figiu-es 2 through 8 illustrate the results of a 1-nm

interval survey of the spectral transmittance of the filters between 440 and 620 nm. These measurements were made with a commercial spectrophotometer. The slit- width was maintained at approximately 0.1 mm (0.37

nm passband). Further measurements were made of the

10% filter with slit-widths of 1.0, 2.0, and 3.0 mm.

These slit-widths correspond to passbands of 3.7, 7.4,

and 11.1 nm, respectively.

There are four wavelengths within the wavelength

range 440 to 620 nm corresponding to peaks and valleys

that could be used for the purpose of establishing a calibrated set of photometric scale standards. However,

only one wavelength is needed and the absorption peak

at approximately 548.5 nm was selected as being the most suitable. The spectral peak at approximately 464

nm and the absorption valleys at approximately 510 and

591 nm do not show a significant change in transmit- tance for the range of passbands used in this survey. A

photometric resolution of approximately ±0.01% is re- quired in order to detect the effect of passband on the

spectral transmittance measured at these wavelengths.

1.00

hi^ .95

CO<

.90

.85

FILTER l-l

1 1 1 400 450 500 550

WAVELENGTH (nmj

600 650

FiGL RE 2. Spectral transmittajice of Master Filter 1-1.

400 450 500 550

WAVELENGTH (nm)

600 650

Figure 3. Spectral transmittance of Master Filter 1-2.

400 450 500 550 600

WAVELENGTH (nm)

FRiURF, 4. Spectral transmittance of Master Filter 1-3.

650

22
400 450 500 550 600

WAVELENGTH (nm)

650

Figure 5. Spectral transmittance of Master Filter 1-4.

.105

.100- o

.095

<

.090-

.085

400 450 500 550 600

WAVELENGTH (nm)

650

Figure 6. Spectral transmittance of Master Filter 1-5.

.0105r

.0080

400 450 500 550 600

WAVELENGTH (nm)

650

,OOilOT

.O0I05

.OOJOOenz

<

a: .0O095 -

.00090-

00085

400 450 500 550

WAVELENGTH (nm)

600 650

Figure 7. Spectral transmittance of Master Filter 1-6.

Figure 8. Spectral Transmittance of Master Filter 1-7.

3.3 High Accuracy Transmittance Measurements

Calibration of the spectral transmittance of the master

set of filters and three other sets was done on the NBS

Reference Spectrophotometer [5,6,7] for measuring high

accuracy transmittance. The measurements were made

with a passband of 1.5 nm and a beam diameter of 10

mm. Measurements were made for perpendicularly (s) and horizontally (p) polarized incident sample beams at 1.5 nm intervals from 545.5 to 557.5 nm. Each filter was

scanned for uniformity at 547 nm. The uniformity

measurements were made at three locations; center, 2 mm horizontally from center, and 2 mm below center. Transmittances for master set #1 filters are listed in table

1 . The results of the uniformity scan at 547 nm are listed in table 2. The transmittance values listed in table 1 are an average of the two polarizations. The values for both

polarizations are listed for the uniformity measurements

made at 547 nm. The instrumental uncertainties in the values listed in tables 1 and 2 are estimated to be

±0.04% for filter 1-1 to ±0.0005% for filter 1-7. A

complete description of the measurement sequence and

data reduction for the high accuracy measiu-ements and

an analysis of the errors associated with such

measurements is given in refs. [5-7].

4. Statistical Analysis

A statistical analysis of the data obtained on the spectral transmittance of the neutral filters was used to deter- mine the magnitude of change in transmittance values

due to changes in passband and also the magnitude of

23
Table 1. Spectral Transmittance of Master Set No. 1 for a Passband of 1.5 nm.

WaveFiller Filter Filter Filter Filter Filter Filter

1-1 1-2 1-3 1-4 1-5 1-6 1-7

536.5 0.9164 0.6902 0.5177 0.2339 0.0955 0.00919 0.000915

.538.0 .9165 .6905 .5181 .2.345 .09,59 .00922 .000922

.539.5 .9165 .6908 .5185 .23.50 .0%2 .00926 .000925

541.0 .91()5 .6910 .5187 .23.53 .09(>4 .00928 .000929

-VIOO . 0 1 vu ._oo i .uvoo .lfV/V.> 1 .UUUVo

J

,544.0 .9166 .6913 .5192 .2,360 .0969 .00932 .000935

.545.5 .9166 .6913 .5192 .2362 .0<)70 .00933 .000936

.547.0 .9166 .6914 .5194 .2,363 .0971 .00934 .000938

,54«.5 .9168 .6913 .5193 .2363 .0971 .00934 .000938

5.50.0 .9167 .6912 .5191 .2363 .00934 .000940

551.5 .9167 .6912 .5190 .2362 .W71 .00933 .000937

553.0 .9167 .6911 .5190 .2.361 .0970 .(K»931 .000934

554.5 .9166 .6908 .5187 .23.58 .0*)68 .00930 .000934

556.0 .9168 .6908 .5184 .23,55 .09()6 .00928 .000929

557.5 .9168 .6904 .5180 .2351 .0964 .(XW24 .000923

Table 2. Transmittance Uniformity of Master Set No. I at 547 nm.

Location,

Polarization

Filter

1-1

Filter

1-2

Filter 1-3Filter 1-4Filter 1-5Filter 1-6

Filter 1-7

1- P 0.9166 0.6913 0.5193 0.2362 0.0971 0.00934 0.000939

1, s .9166 .6913 .5193 .2362 .0971 .00935 .000940

2- P .9166 .6914 .5193 .2361 .0971 .00934 .000937

2, p .9167 .6914 .5193 .2362 .0971 .00934 .000938

3, p .9164 .6913 .5192 .2362 .0971 .00934 .000938

3. p .9165 .6913 .5192 .2362 .0971 .00933 .000939

change due to location of the sample beam (filter uniformity).

Preliminary data from the commercial instrument in- dicated that the central wavelength of interest was at ap- proximately 547 nm. However, a further analysis of the data from the high accuracy instrument indicated that 548.5 nm was a better choice.

Data are presented in table 3 to illustrate the effect of passband on the transmittance at the central wavelength

for the master set #1 filters. These values are based on

calculation for a triangular passband, using continuous

integration. Figures 9 through 15 show these results plot- ted with the standard error limits. The data listed in table 4 illustrate the magnitude of change due to position

location for the master set of filters. Remeasurement of the spectral transmittances of the neutral filters was made one year after initial calibrations. The results of this second calibration for master

set #1 are compared with the original calibration and

listed in table 5 for wavelength 548.5 nm. Differences in spectral transmittances of the filters shown in table 5 are

too small to be clearly interpreted as changes with the

possible exception of filter 1-1. Here the apparent

change in transmittance was -0.0009. Further

measurements at longer time intervals will be required to confirm any real changes in spectral transmittance due

to aging.

Additional details of the statistical analysis are given

in appendix A.

Table 3. Transmittance of Master Set No. 1 at 548.5 nm as a Function of Passband for a Triangu lar Passband.

Passband Filter Filter Filter Filter Filter Filter Filter (nml 1-1 1-2 1-3 1-4 1-5 1-6 1-7

1.5 0.91665 0.69133 0.51928 0.23632 0.09713 0.009342 0.000939

( 3) ( 2) ( 2) ( 2) ( 11 ( 2) ( 4)

3.0 .91665 .69132 .51927 .23632 .09711 .009341 .000939

( 3) ( 2) ( 21 ( 2) ( 1) ( 2) ( 4)

4.5 .91665 .69130 .51924 .23628 .9709 .009338 .000938

( 3) ( 2) ( 2) ( 2) ( 1) ( 2) « 4)

6.0 .91665 .69128 .51921 .23624 .09706 .009335 .000938

( 3) ( 2) ( 2) ( 21 ( 1) 2) { 4)

7.5 .91665 .69125 .51916 .23618 .09703 .009332 .000937

( 31 ( 21 ( 2) ( 21 ( 11 2) ( 4)

9.0 .91665 .69121 .51911 .23616 .09698 .009327 .000937

( 3) ( 2) ( 2) ( 2) ( 11 2) ( 4)

10.5 .91665 .69117 .51905 .23604 .09693 .009321 .000936

( 3) ( 2) ( 2) ( 21 ( 1) 2) ( 4)

Note: uncertain ies (one standard deviation) are in parentheses

24
0.91S68

e.91S62

0.336^

BflNDPClSS UIDTH

SET 1 SHOUN UITH LiniTS OF 1 STANDARD ERROR

0.5363

0.3361

.2360 -

Bf>NDPflSS 'JIDTH SET 1 SHOUN UITrl LiniTS OF 2 STANDARD ERRORS

Figure 9. Spectral transmittance at 548.5 run versus bandpass for FIGURE 12. Spectral transmittance at 548.5 nm versus bandpass for Master Filter 1-1. Master Filter 1-4.

0.69140

e. 69135 -

0.69130

0.59LB5

0.G9115 -

0.S9119

BANDPASS L'IDTH SET ! SHOUN UITH LiriTS 0^ ^ qTANDARD ERRORS Figure 10. Spectral transmittance at 548.5 nm versus bandpass for Master Filter 1-2. , - .

C.5913

8.5910

BANDPASS UIDTH

SET 1 SHOUM UITH LiniTS OF 2 STANDARD ERRORS Figure 11. Spectral transmittance at 548.5 nm versus bandpass for Master Filter 1-3.

BANDPASS UIDTH

SET 1 SHOUN UITH LiniTS OF 2 STANDARD ERRORS Figure 13. Spectral transmittance at 548.5 nm versus bandpass for Master Filter 1-5. ,-2

BANDPASS UIDTH

SET 1 SHOUN UITH LiniTS OF 2 STANDARD ERRORS Figure 14. Spectral transmittance at 548.5 nm versus bandpass for Master Filter 1-6.

25
BANDPASS UIDTH

SET 1 5H0UN UITH LIMITS OF S STANDARD ERRORS

Figure 15. Spectral transmittance at 548.5 nm versus bandpass for Master Filter 1-7.

Tabi.k 4. Magnitude of Filter Nonuniformity

Filter No. Location

Transmittance

at 548.5 nm

Location

Difference

I-l 1 0.91658 (1H2) -0.00008

1-1 2 .91666 (2M3) .00018

1-1 3 .91648 (1M3) .00010

1-2 1 .69132 (1M2) ~ .00006

1-2 2 .69138 (2M3t .00007

1-2 3 .69131 (1M3) .(MKX)!

1-3 1 .51926 (1M2) - .00002

1-3 2 .51928 (2M3) .mm

1-3 3 .51919 (1M3) .(MKX)7

1-t 1 .23624 (1)-(2| .00009 1^ 2 .23615 (2M3I - .00004

1-4 3 .23619 (1H3I .00005

1-5 1 .09709 (1M2I .0(HX)1 1-5 2 .09708 (2M3) .00000

1-5 3 .09708 (1M3) .00001

1-6 1 .009.341 (1M2) - .000001

1-6 2 .009342 (2H3I .000011

1-6 3 .009331 <1M3) .000010

1-7 1 .000939 (1M2) .000001

1-7 2 .0009.38 (2H3) .000001

1-7 3 .000937 (1M3) .000002

5. Summary

One master set and three working sets of neutral density glass filters have been calibrated for use as spectral

transmittance standards for checking the photometric

scale linearity of spectrophotometers. Each set consists of seven filters ranging in transmittance from 0.1 to

92%. These filters will be used in a Measurement

Assurance Program (MAP). The purpose of this pro- gram will be to assist laboratories wishing to maintain a high level of confidence in the accuracy of their spec- trophotometric measurements.

Data are presented that show the spectral transmit- tances of these filters at 548.5 nm to be relatively insensitive to variations in passband and slight errors in in- strument wavelength setting. The filters are of sufficient uniformity for use as transmittance standards.

Table 5. Spectral Transmittance of Master Set No. I for a Passband of 1.5 nm at 548.5 nm.

Filter No.

(Apparent changes in transmittance)

Apparen*

change

First Calibration

(Oct. 1980)

Second Calibration

(Oct. 1981)

1-1 0.9168 0.9159 -0.0009

1-2 .6913 .6914 .0001

1-3 .5193 .51% .0003

1-4 .2363 .2365 .0002

1-5 .09712 .09722 .00010

1-6 .009337 .0093,50 .000013

1-7 .0009376 .0009395 .0000019

6. References

[1| Mielenz, K. D. and Eckerle, K. L. Spectrophotometer Linearity

Testing Using the Double-Aperture Method, Appl. Opt. 11

(10), 2294 (Oct. 1972).

[2] Mavrodineanu, R. and Baldwin, J. K. Glass Filters as a Standard Reference Material for Spectrophotometer—Selection, Preparation, Certification, Use SRM 930. NBS Special Publication 260-51 (November 19751.

(3| ASTM D1003, Haze and Luminous Transmittance of Transparent

Plastics. ASTM Subcommittee D20, 40 on Optical Properties

of Plastics,

[4| Weidner, V. R. and Hsia, J. J. NBS reference hazemeter: its development and testing. Appl. Opt. 18 (10) 1619 (May 15, 1979).

[5] Mielenz, K. D. and Eckerle, K. L. Design, Construction, and

Testing of a New High Acciu'acy Spectrophotometer. Natl. Bur. Stand. (U.S.) Tech. Note 729; June 1972. 55 p.

[6] Eckerle, K. L. Modification of an NBS Reference Spectrophotometer. Natl. Bur. Stand. (U.S.) Tech. Note 913; July

1976, 39 p.

[7] Mielenz, K. D., Eckerle, K. L. Madden, R. P., and Reader J. New Reference Spectrophotometer. Appl. Opt. 12 (7), 1630

(July 1973).

[8] Davis, Philip J., Interpolation and Approximation. New York:

Biaisdell; 1%5.

(9] Federov, V.V., Theory of Optimal Experiments. New York: Academic Press; 1972.

(10) Keifer, J. and Studden, W. J. Optimal designs for large degree

polynominal regression, Ann. Statist. 4, 1113-23 (1976).

[11] Karlin, Samuel and Studden, William. Optimal experimental

designs. Ann. Math. Statist. 37, 783-815 (1966).

26
Appendix

Statistical Design and Analysis for Calibrating the

Transmittance of Filters for Spectrophotometer

Linearity Testing

For four sets of filters, each set containing seven filter types of various transmittances, an assigned transmit- tance value needed to be determined when a triangular

passband of given width is superimposed. Additionally,

the polarization and location of the spot size on the filter had an unknown influence on the transmittance value. Although a commercial instrument can scan the entire

spectrum at little cost, the measurements are an order of

magnitude less accurate than those obtained using the

high accuracy instrument. For this reason, a design was

developed to determine: :

, , ; . . ,

, .

(1) The values to be measured for purposes of

calibration, and

(2) The existence of a possible effect due to polarity or the effect of location on the filter.

The motivation behind the choice of design is discussed

in section A below. In the event of (2 1, the calibration

must be reconsidered. On the basis of these extremely

precise measurements, an effect due to location was

statistically significant. This suggests that either:

(1) The calibrated values can be used only for the

central location on each filter; or

(2) Additional measurements will be required to determine the magnitude of changes in transmit- tance due to spot location.

Since the observed differences are small (<0.2%; see table 4), the location effect may not interfere with practical usage of these filters. However, measurement as near to the central location on each filter as possible is recommended. The conclusions regarding location and

polarity effects are presented in section B, and the

estimation of the transmittance curve leading to the

calibration values is shown in sections C and D. The

method of extension for general passbands is given in section E.

A. The Design

Most organizations using these filters will have

triangular passbands on their measuring equipment.

Therefore, adequate determination of the transmittance

using this passband is essential. However, other pass- band shapes may be used, and for these, a more general

approach is taken. The problem then becomes one of estimating the transmittance curve with high precision.

Since the measurements on the high accuracy instrument

are time-consiuning, a design was chosen so as to permit

adequate curve estimation with relatively few points.

1. Preliminary analysis: Choice of Wavelength.

The choice for a wavelength to be calibrated required

consideration of:

{i\ Varying passband widths, and

in) The potential for imprecise wavelength specification. We consider neighborhoods of 21 nanonijeters, since the

widest passband that is most commonly used weights

frequencies within a range of this length. The chosen

wavelength is:

A„ = 548-5 nm.

This subsection explains this choice in li^t of considerations (i^ and (ii). For a passband having width w and functional form

h„{X), the transmittance at wavelength is given by the

convolution integral

A„ +aj A. +a» tJxj = ; hjk\f{X-X)dx I f hjxm,

where /(A| is the spectrum (transmittance curve). If the

passband is normalized so that

X^ +OJ J hJX)dX = 1, A^—CO then this simplifies to

rJXJ = Y''hJX)f{X-XJdX. (1)

A^-o) In all that follows, we will assume that the passband /i„ has been normalized in this way.

In order for this average value to be relatively insensitive to wavelength specification, /(A) needs to be a smooth, slowly-varying function. In mathematical

terms, we search for a neighborhood where the first two

derivatives of the spectrum are fairly small. This suggests a region where /(A) is nearly constant, or, at worst, a quadratic having very small degree of curvature. A

locally linear spectrum with a noticeably nonlinear slope

would yield a seriously biased estimate, whereas a locally

quadratic spectrum, centered at a peak or trough, would

have a negligible linear term and therefore a bias which

depends primarily on the second-order term (hopefully

27
small). Preliminary readouts on a commercial instru- ment suggested a central wavelength of 547.0 nm for most filters. On the basis of the first set of measurements

on the high accuracy instrument, however, this was later amended to A„ = 548.5 nm.

2. Number of Points

Assiuning that the spectrum is locally quadratic and

has a maximum around A,, = 548.5 nm, our goal is to estimate the three parameters a, fi, y in the approximation:

/U) = a + pk + Y^-- (2)

In order to estimate o, ft, and y, by a, (i, y, the proposed

design specifies a total of five points, one at the central wavelength, and one each at equal distances ±26 from

the central wavelength.

Let X = X - 548.5, so as to center the relation at the

origin. A minimum of three points is required to specify

the parameters. This leaves no room for the assessment

of error. With more points, the variance of (1) will be a

linear combination of the variances and covariances of the parameters, and will be dominated primarily by the

variance of the constant term. If our chosen points are symmetrically placed about 0, it can be shown that:

Var {&) =o'/{n-cye), ' (3)

where

c = I X,' = 21 x,^

e = I X* = 21 X,*. Xi >0

As (Ix.*) < (Ijc.^P (x, > 0), the smallest value of cVe is 2

(all points at the origin except for the two at ±1). A

lower bound on (3) is therefore:

Var (a) = oV(n-2). (3 'I

If we concern ourselves with only the first term, then,

relative to o^, eq (3') gives the reduction in the overall variance that we may hope to gain in our variance of the

transmittance value. With n = 3, there is no reduction;

with 71 = 5, the variance is already reduced to 33% of its value. An extra two points provides only an extra 13%

improvement. Thus, the design specifies a minimum of two points on either side of the central wavelength.

3. Location of Points

We consider two criteria in selecting the four

wavelengths (two symmetrically placed on either side of the central wavelength):

(i) Small error in quadratic interpolation of the

transmittance curve;

(ii) Small variance in the transmittance estimate

given by (1).

On the basis of these two criteria, the proposed design

specifies measurements to be taken at:

A„, A„ ± 6 nm, A„ ± 9 nm.

The reasoning behind this choice is explained by considering (i) and (ii) separately.

(i) Error is quadratic interpolation. A bound for the

estimate of error in polynominal interpolation of degree

n at the points a ^ Xi, X2, ... < 6 is

|£(A)| < max |f<n + lNA)| \X-xAK-X2\ |A-x„,,|

a<A<b

(see, e.g., [8]). The first part of this error depends upon

the transmittance curve and led to the choice of /„ =

548.5 in subsection 1 above. Now we concentrate on

selecting Xi, ... , so that the error is as small as possible. The answer to this problem is given by the zeroes of the Chebyshev polynomials, namely

X, = (10.5nm) cos I(2y£-l)/(2n+2)], k = I, n + 1. (4)

For the problem at hand, n + 1 = 5; thus:

Xi = -X5 = 9.986 nm from A„ X2 = -Xi = 6.172 nm from A„ X3 = 0 nm from A„ .

As most passbands are in multiples of 1.5 nm, the closest multiples to these points are ±6 nm and either ±9 nm or ±10.5 nm. However, the nature of the triangular pass- band which is frequently used in practice would assign zero weight to the values ±10.5 nm. Since a primary

goal is the estimation of the transmittance using this passband, we choose ±9 nm.

28
(ii) Minimum variance of transmittance estimate. If we estimate the transmittance curve using a quadratic

function, viz.

fix) = a +iix + yx^ (5)

then the transmittance using passband of width w is

iJXJ = f hJw+XJ (a +Px +yx^)dx.

Let ' -

= XI hjx) dx

Then

tJAJ =ac„ + ftci + yc2 = c '0

where

C

' - (C„, Cud)

0' = (a,^, y).

Then minimizing the variance of c '0 is equivalent to

min Var(c'0) = min c' Var(©) c.

A design which minimizes the variance-covariance

matrix Var(0l of the parameter estimates is given in

[9]. The design would place the two observations each at

A„ + 10.5 nm in addition to the one at If oiu- function

is truly quadratic, such a design would be optimal.

For many reasons, however, we modify the optimal

design which permits more flexibility in our choice of model. Such a design is suggested in [10]. The design

recommends two different values rather than repeating

them at the endpoints.

Closely related to this design is the one which

minimizes the maximum variance of the best linear unbiased estimate of the function f(x) given by eq (5). Reference [11] shows that the five points should be

placed at the zeros of the polynomial

10.5 (1 -x^) P,'(x) ,

where ' is the derivative of the fovulh degree Legendre polynomial

PAx) = 17.5x^ - 1.5x .

Hence, the five points are 0, ±7.1, ±10.5 nm from A,. Again, since our passband applies decreasing weight to

f(x) as X is fluther from the origin, we choose to make

these points in towards 0, to ±6 and ±9 nm.

4. Tests for Polarity and Spot Location

Additional measurements at the central wavelength

are needed to provide tests for difference in polarization

and spot location. In addition to the measurement at the

central wavelength with polarity 1 (point 1 at location

(0,01), measiu-ements were taken at

Point 2: Spot location (2,0), Polarity 1 Point 3: Spot location (0,2), Polarity 2 Point 4: Spot location (0,2), Polarity 1.

This permits a check for a difference due to polarity by

comparing the third and fourth points, and check for location differences by comparing points 1 and 4 (or 1 and 2 or 2 and 4). A more extensive check based on a full 2X3 factorial combination was made on the master set #1.

6. Results: Polarity and Location

The reported results are based on measiu-ements taken on four sets of filters. A complete series of 15

measurements across the 21-nm range at 1.5 nm spacing was taken on the master set, as a check for the adequacy

of the five-point design used on the other three sets. In

addition, polarity and location were tested on each filter in all sets. The results of these tests are reported in this section; transmittance calculations are reported in sec- tion C. For set 1, six measiurements were taken at A = 547.0,

at both polarity 1 and 2 at the center of the filter (0,0)

and at placements of two units to the right (2,0) and

above (0,2) the center. This permits a 3 X 2 factorial analysis for detecting differences due to location and

polarity.

For sets 2, 3, and 4, f-tests on location and polarity were calculated. The test on location was deemed signifi- cant if the comparison of either (0,0) and (0,2) or (0,2)

and (2,0) indicated a chance of less than 1% under the hypothesis of no effect. None of the tests of polarity was significant at the 0.01

level. (One filter from one set gave significance of 0.025. Out of 28 such tests, the chance of obtaining one or more

spu_rious significances is more than 50% , so this is hardly

surprising.) For location, however, the following sets showed a significant difference (level given in parentheses):

29
Filter Set (level of significance)

2 3 (0.00041 3 2 (0.0131. 3 (0.002), 4(<0.0001) 4 2 (0.0013), 3 (0.0003), 4 (0.01) 5 3 (0.01), 4 (0.0003) 6 1 (0.006), 4 (0.0013) [3 (0.02)] 7 1 (0.0002), 4 (0.0025)

Out of 28 tests of significance, the chance of 13 or more

coming up significant at the 0.01 level when in fact location is irrelevant is

28

and the chance that at least 2 of the 4 sets would show

significance on a given filter type is

4

I if] (0.01 )* (0.99r* = 0.0006.

k=2

For 7 types of filters, the overall level of significance is approximately 0.004. These tests of significance suggest that it is highly

imlikely that location on the filter in measiu^ing transmit- tance is irrelevant. However, all tests were based on the

internal standard errors of the foiu- measurements made

within the twenty-minute measiuement period. This

standard error reflects only the error of the foiu- internal

readings but does not reflect the measurement-tomeasurement variation caused by apparatus set-up,

filter placement in the wheel or polarity switches. As

such, the actual error in taking successive measurements

may in fact be larger than the reported standard error. However, measurements on these filters as near to the

central location as possible is recommended. The

transmittance values using triangular passbands have

been calculated assuming location is irrelevant (thereby

using all data in the estimation of the transmittance

curve) and assuming location has a significant effect on

the transmittance value (using only the data at the center

(0,0) spot). Only the latter are given for the master Set #1

in table 3 of the main report.

C. Estimation of Transmittance Curve

As there are four sets which contain all filter types, it will be helpful to use all filters having the same nominal

transmittance in estimating the transmittance curve. We

fit quadratic functions of the form in eq (5).

Consider one filter type from each set having a nominal transmittance (say, 69% ). The average value of transmittance, given by the parameter a, is likely to be

specific to each filter in the different sets. However, the

curvatiu-e parameters ft and y are likely to be common to

all 4 filters having a given nominal transmittance. Thus

we use all these observations to fit a relation of the form

fix^j) = aj + (i-x„ + yxl , (7)

I = 1, Oy ( = # of measurements in jth set) / = 1, 4 (= # of sets).

Note that

n, = 21,

{xn} = {-12., -10.5, . . ., 7.5, 9, -1.5 -1.5} ,

since set 1 has the full 15 measiu-ements and 6 additional

measm-ements for polarity and location, and

nj = 8, {x,j} = {-9, -6, 0, 6, 9, 0, 0, 0}

for sets 2, 3 and 4. Note also that the average level, ay, is specific to the filter in the set, as the level may reflect the amount of dye that is contained in the filter. However,

the parameters (i and y are likely to be influenced by the

properties of the dye contained in this glass and are thus

common to the filters with the same nominal transmit- tance from all four sets. This joint estimation permits the more acciu-ate calcidation of [} and y in sets 2, 3, and 4, where the number of observations is only eight.

Since transmittance may depend on location (section

B), we also estimate a, (i, y, for each of the 7 filter types,

using only those observations at location (0,0). In this case,

n, = 17, {xn} = {-12, -10.5 . . ., 7.5, 9, -1.5, -1.5}

nj = 5, {x,} = {-9, -6, 0, 6, 9}, / = 2, 3, 4.

These parameters were not found to differ from those

using all the data by more than two standard errors. In

light of potential location differences, however, table Al

provides these estimates of the parameters a, (i and y for the master set #1 filters.

D. Estimation of Transmittance Values Using

Triangular Passband

As indicated in eq (1 ), when the transmittance ctu-ve is superimposed with a normalized passband centered at

A„, the observed transmittance can be expressed as a convolution integral. Using a triangular passband of width

30
w, symmetric about A„, the result is a weighted average

of all transmittances around the central wavelength.

This weighted average may be computed either as a

discrete sum:

Twi^o^ ^u.(A.,)y, y, = transmittance at wavelength A,; =1 hJx^+XJy„ X, - A, - A„, (8)

where

hjx) = u; '[1 - signix] X/w], -w < x < m;, (9)

or as an integral as in eq (1). The first approach, based on eq (8), is a discrete computation based on the observed values y,. The second approach, eq (1), uses the

values y, to estimate fix) {eq (5)) and integrates directly.

For sets 2, 3, and 4 where data inside ±6 nm exists only

at the central wavelength, eq (1 ) is clearly the method of

choice. Furthermore, the estimation oifix) uses all of the

data in its estimation (section C), and is therefore likely to remove much of the variability in the values y,. The standard error of t^, can be computed using the

reported standard errors (s,) associated with each

measurement:

SE { tj = nK{x^f s,\

Using the triangular passband of width w {eq (9)) and

the fitted relation (7), we have that the transmittance of a filter from the /th set is A

+"' rJX ) = / hJX) [h, + p{X-XJ + y{X-XJY dX

= 'qj + (u;V6) • Y UO)

for which

SEirJ =[Var(<J,) + (M;V36)Var(y) + (t^V3)Cov(a„y)]y2 = SE {&,);

TabI.K A1. Coefficients for Estimation of Transmittance Curve for Set #1 (includes data from center location only).

f(x| = 'a +Px + yx^ X = wavelength -54^.5

Table gives constant term; aII standard errors given in parentheses

a ji X 10-' y X 10^

Filter 1 .9166525 l.(>493 -0.002562

( 2001 ( .1877) ( .032669)

2 .6913352 -2.0067 -0.91372

( 1171

3 .5192856 -2.7205 -1.2973

( 135) ( .1151) { .0200)

4 .2363304 + 1.1966 -1..5858

( 147) ( .0923) { .0161)

5 .0971290 +0.8657 -1.0699

( 068) ( .0736) { .0128)

6 .00934226 -.05959 -0.11355

( 115) 1.00979) ( .00170)

7 .000939014 -0.008245 -0.017568

( 266) ( .002893) { .000504)

since the variance of the curvature parameter y and the

covariance term are typically two orders of magnitude

smaller than the variance of the fitted constant term.

E. Other Passbands

Table 3 of the main report gives transmittances for the

master set #1 filters for a triangular passband. For

passbands other than those listed in table 3, the

transmittance may be calculated directly via eq <10), us- ing the estimated coefficients Qi,fi, and y listed in table Al.

31
«) APPENDIX B

U.S. DEPARTMENT OF COMMERCE

NATIONAU BUREAU OF STANDARDS

Gaithersburg, MD 20899

REPORT OF CALIBRATION

for

Pilot Transmi ttance MAP

vn'th Participant:

Laboratory A.

^ (Please see your purchase order number xyz dated July 23, 1984.)

1

.

Purpose

The purpose of this test is to determine the spectrophotometric

accuracy of Participant's instrumentation via a MAP package.

2. Material

The MAP package consists of a set of seven neutral filters (Set 4)

and a didymium filter (D-41) of type SRM 2010.

3. Measurements

The measurements on the neutral filters were made by NBS, then by

Participant, and again by NBS. The didymium wavelength values are known

not to change and were only measured by Participant. The instrument

used by NBS was a high accuracy reference spectrophotometer. The instruments used by Participant were 6 commercial instruments identified

as Instruments 1 through 6.

4. Results

'

A. Transmittance , ,

The results for the MAP procedure are listed in Tables 1 through

4 for the indicated instruments. The symbols and quantities in these

tables are defined as follows:

T - Transmittance measured by NBS before (B) the participating

laboratory at bandpass denoted by x.

Transmittance measured by the participating laboratory at

the bandpass x.

/\ T Transmittance measured by NBS after (A) the participating

laboratory at bandpass denoted by x.

32
APPENDIX B

REPORT OF CALIBRATION

Pilot Transmittance MAP

with Participant: Laboratory A Page 2

j^^^ = {-i^+T^)/2 The average of the before and after measurement.

X XX

B A

(t -t )/2 Denotes the error due to a possible change in the filter

^ ^ between the before and after measurements at bandpass x. AVE

U The uncertainty in the average value t accounting for systematic

and random errors.

B A

I (t -t )/2|+U An upper bound combining the NBS uncertainty and possible

^ ^ change in the filter.

^AVE_^p

ji^g difference between the average NBS value and the value of

^ ^ Participant at bandpass denoted by x.

If 1 t^^^-t'^ I > I (t^-t''^)/2 I +U, then there is a bias in the measurements due

X X

to a systematic error since the Participant stated the random error as zero. In comparing these two quantities for the different instruments

and for each filter, we do not see any serious discrepancies. However,

in most cases, there exists a bias. The method for obtaining the standard values for NBS are described in one of the enclosed publications.

B. Wavelength Calibration

Table 5 contains the measured deviations from the standard values

for the transmittance minima and the points of inflection for SRM type

2010. (A sample certificate is enclosed.) The wavelengths of the

minimum transmi ttances of the absorption bands are designated ^^-^^^ and

the wavelengths of the inflection points as Ajj^p. A curve may be fitted

to these data and an additive correction obtained. However, we attempted

to go one step further, and accounted for systematic errors in bandwidth

and transmittance using the method described in Section 2.3.3 of Special

Publication 260-66 (A copy is enclosed.). Some of the experimental data

have a relatively large random component as evidenced by the large

standard deviations of the coefficients. The corrected data are shown

in Figures Bl through B5 for the indicated instruments. The final

figures Bl through B5 are not plots of the data shown in Appendix B

- Table 5. The plots are derived from the data evaluation according to

Equation 8 page 30 in reference [5] using the error terms and the

corresponding bandwidth and transmittance corrections. We had some difficulty in estimating systematic errors for Instrument 1 supporting

the view of Participant that this instrument needs recal ibration. Also,

there is one outlier which we cannot explain. The additive corrections

indicated in the figures are the "best values" based on the information

we have.

33
APPENDIX B

REPORT OF CALIBRATION

Pilot Transmi ttance MAP

with Participant: Laboratory A Page 3

5. Comments

A water mark was detected on filter 4-1. It is unknown when thi

spot, which decreased the transmi ttance, was acquired.

For the Director,

Radiometric Physics Division

Center for Radiation Research

Enclosures

1 Report of Test

6 Tables

5 Figures

34
Fi Iter

APPENDIX B Table 1

Transmi ttance Results for the Indicated Instruments

R ^10 .0 (NRS)

I nst rument

1 Instrument2

10 .0 (NRS)

-AVE

^-1

4-2

4-3

4-4

4-5

4-6

4-7

0.91615

0.69058

0.51947

0.23528

0.096580

0.0092677

0.0009405

0.9179

0.6907

0.5191

0.2356

0.0967

0.0095

0.0011

0.919

0.691

0.520

0.236

0.097

0.0095

0.0015

0.91474

0.69014

0.51889

0.23559

0.096404

0.0092576

0.0009353

0.91545

0.69036

0.51918

0.23544

0.096492

0.0092627

0.0009379

B A B A

+11 ^AVE-^p

Instrument

1

^AVE -^p

I nst rument

9

4-1 0.00071 0.00062 0.00133 -0.00246 -0.00356

4-2 0.00022 0.00043 0.00065 -0.00034 -0.00064

4-3 0.00029 0.00036 0.00065 0.00008 -0.00082

4-4 -0.00016 0.00016 ' 0.00032 -0.00017 -0.00057

4-5 0.000088 0.000135 0.000223 -0.000208 -0.000510

4-6 0.0000051 0.0000282 0.0000333 -0.0002374 -0.0002400

4-7 0.0000026 0.0000127 0.0000154 -0.0001620 -0.0005600

35
Fi Iter

4-1

^-^

4-3

4-4

4-5

4-6

4-7

APPENDIX B Table 2

Transmittance Results for the Indicated Instruments

^8.0

(NBS)

0.91615

0.69064

0.51955

0.23538

0.096632

0.0092747

0.0009416

fx -T ^ ) /?

tP

I nst rument

3

0.920

0.692

0.522

0.239

0.097

0.0089

0.0009

IJ

Instrument

4

0.919

0.693

0.522

0.236

0.096

0.0088

0.0008

^8.0

(NBS)

0.91474

0.69020

0.51897

0.23569

0.096456

0.0092646

0.0009364

^AVE

0.91545

0.69042

0.51926

0.23554

0.096544

0.009270

0.000939

.AVE -tP .AVE -tP

Instrument Instrument

4-1 0.00071 0.00062 0.00133 -0.00456 -0.00356

4-2 0.00022 0.00043 0.00065 -0.00158 -0.00258

4-3 0.00029 0.00036 0.00065 -0.00274 -0.00274

4-4 -0.00016 0.00016 0.00032 -0.00346 -0.00047

4-5 0.000088 0.000135 0.000223 -0.004560 0.000544

4-6 0.0000051 0.0000282 0.00003327 0.00036960 0.00047000

4-7 0.0000026 0.0000128 0.00001538 0.00003900 0.00013900

36
APPENDIX B Table 3

Transmi t-tance Results for the Indicated Instrument

Fi Iter

tP

Inst rument

5

4-1 0.91615 0.919 0.91474

4-2 0.69073 -.^ 0.690 0.69029

4-3 0.51969 : 0.515 0.51911

4-4 0.23554 0.236 0.23585

4-5 0.096734 0.096 0.096558

4-6 0.0092867 0.0088 0.0092766

4-7 0.0009436 0.0006 0.0009382

(X R -T ^ )/2

Zon, U Zon, U (t ^ -T ^ )/2|+n

o n o n Z , U Z , U

4-1 0.00071 0.00062 0.00133

4-2 0.00022 0.00043 0.00065

4-3 0.00029 0.00036 0.00065

4-4 -0.00016 0.00016 0.00032

4-5 0.000088 0.00014

' 0.00023

4-6 0.0000051 0.000028 0.0000333

4-7 0.0000027 0.000013 0.0000155

0.91545

0.69051

0.51940

0.23570

0.096646

0.0092816

0.0009409

Inst rument

5

-0.00356

0.00051

0.00440

-0.00031

-0.00065

0.0004810

0.0003410

37
APPENDIX B Table 4 Transmi ttance Results for the Indicated Instrument

i 1 ter

p

^ / MDC \ tP

Instrument

6

A AVE

4-1 0.91615 0.919 0.91474 0.91545 0.00071

4-2 0.69073 0.694 0.69030 0.690525 0.00022

4-3 0.51970 0.524 0.51913 0.51942 0.00029

4-4 0.23556 0.239 0.23587 0.23572 -0.00016

4-5 0.096737 0.096 0.096561 0.096649 0.000088

)/2

6

AVE

4-6

4-7

4-1

4-2

4-3

4-4

4-5

0.0092867

0.0009436

U

0.00062

0.00043

0.00036

0.00016

0.000135

IJ

0.0093

0.0008

0.0092766

0.0009382

R A

T -T 0.1 0.1 +U

0.00133

0.00064

0.00065

0.00032

0.000223

R A

T -T 2.0 2.0

2

+11

0.0092817

0.0009409

0.0000051

0.0000027

AVE p

T -T Inst rumen

t

6

-0.00356

-0.00349

-0.00459

-0.00329

0.000649

AVE p

T -T Instrument

6

4-6

4-7

0.0000282

0.0000128

0.0000333

0.0000155

-0.0000184

0.0001409

38
APPENDIX B

i Table 5

Measurements hy participant of \m and Ajj^p with difference between NBS and

the participating laboratory, AA = ^[\|R5-^p/\R-[jf ip/\[\jj. All are expressed in

nanometers

.

Nominal Instrument 1 Instrument 2 Instriiment 3 Instrument 4 Instrument 5

A A AA A AA A AA A AA A AA

MIN MIN MIN MIN MIN MIN MIN MIN MIN MIN MIN

440 439.

q

1.65 441.1 0.45 441.5 0.77 441.8 0.47 445.7 -0.26

478 474.7 1.23 475.7 0.23 476.3 0.77 476.6 0.47 478.9 0.14

52Q 527.5 1.46 528.6 0.36 529.1 0.12 529.1 0.12 529.6 0.13

5H5 583.5 1.23 584.9 -0.17 585.3 0.48 586.0 -0.22 585.6 -0.19

684 685.2 -0.59 684.5 0.11 684.0 0.69 684.0 0.69 684.8 -0.13

740 742.9 0.52 740.1 -0.21

Nominal

A A AA A AA A AA A AA A AA

INF INF INF INF INF INF INF INF INF INF INF

406 404.4 2.04 405.6 0.84 405.6 0.84

429 427.6 1.83 429.3 0.13 429.3 0.13

450 448.6 0.89 449.1 0.39 449.5 -0.01

485 483.1 1.74 484.9 -0.06 484.9 -0.06

537 534.7 1.80 536.3 0.20 536.8 -0.30

568 566.0 2.15 567.6 0.55 568.2 -0.05

600 597.1 1.95 598.7 0.35 599.6 -0.55

733

756

39
o

1.5

1.0

0

0.5

O Corrections derived from minima

• Corrections derived from

points of inflection

I I Q_

400 500 600 700

A (nm) -»

Figure Bl . Wavelength calibration curve for Instrument 1 40
1.0

Figure B2, Wavelength calibration curve for Instrument 2

41
1.0 - O Corrections derived from minima

• Corrections derived from

points of inflection

0.5

0

o

o

1 I

400 500 600

A (nm)

700

Figure B3. Wavelength calibration curve for Instrument 3

42
1.0

O Corrections derived from minima

• Corrections derived from

points of inflection

-0.5

1 i

400 500 600

A (nm)

^

Figure B4. Wavelength calibration curve for Instrument 4

700

43
I

0.5

t 0

<3

6

-0.5

O Corrections derived from minima

i i

400 500 600

A (nm)

700

Figure B5. Wavelength calibration curve for Instrument 5

44
NBS-114A IREV. 2-ec) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publ Icatlon Date BIBLIOGRAPHIC DATA REPORT NO. SHEET (See instructions) NBS/SP-692 March 1985

4. TITLE AND SUBTITLE

Transmi ttance MAP Service

5. AUTHOR(S)

Kenneth L. Eckerle, Jack J. Hsia, and Victor R. Weidner

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No.

National Bureau of Standards

8. Type of Report & Period Covered Department of Commerce

Gaithersburg, MD 20899 Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State. ZIP)

Same as item 6.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 85-600513

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificant

bi bliography or literature survey, mention it here)

An introduction to the Transmittance Measurement Assurance Program

(MAP) service is given. Documentation for the service is provided

through a comprehensive list of references. The results of a pilot run for the MAP service are given in a sample calibration report.

12. KEY WORDS (Six to twelve entries; alphabet! cal order; capitalize only proper names; and separate key words by semicolons)

bandpass ;didymi urn filters; glass filters; measurement assurance program; neutral

density filters; reference spectrophotometer; transmittance; transmittance MAP

service; uncertainty estimation; wavelength calibration

13. AVAILABILITY

Unl imi ted For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO, OF

PRINTED PAGES

50

15. Price

USCOMM-DC 6043-P60
I

I

.- J

I
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