AlllOS M78T11 PUBLICATIONS

NIST SPECIAL PUBLICATION 260-135

U.S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

Standard Reference Materials.

Film Step Tablet Standards of Diffuse Visual

Transmission Density — SRM 1001 and SRM 1008

Edward A. Early, Thomas R. O'Brian,

Robert D. Saunders and Albert C. Parr

c00 —— —

57

260-135
rhc National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . . . needed to improve product quality, to modernize manufacturing processes,

to ensure product reliability . . . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One

of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and

applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. Major technical operating units and their principal activities are listed below. For more information contact the Publications and Program Inquiries Desk, 301-975-3058. Office of the Director

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'At Boulder, CO 80303.

2 Some elements at Boulder, CO.
NIST Special Publication 260-135

Standard Reference Materials:

Film Step Tablet Standards of Diffuse Visual

Transmission Density — SRM 1001 and SRM 1008

Edward A. Early Thomas R. O' Brian Robert D. Saunders

Albert C. PanPhysics Laboratory

Optical Technology Division National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

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

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Under Secretary for Technology NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director Issued July 1998
National Institute of Standards and Technology Special Publication 260-135

Natl. Inst. Stand. Technol. Spec. Publ. 260-135, 55 pages (July 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) as defined by the National Institute of Standards and

Technology (NIST) are well-characterized materials, produced in quantity and certified for one or more physical or chemical properties. They are used to assure the accuracy and compatibility of measurements throughout the Nation. SRMs are widely used as primary standards in many

diverse fields in science, industry, and technology, both within the United States and throughout

the world. They are also used extensively in the fields of environmental and clinical analysis. In many applications, traceability of quality control and measurement processes to the national measurement system is carried out through the mechanism and use of SRMs. For many of the

Nation's scientists and technologists, it is therefore of more than passing interest to know the

details of the measurements made at NIST in arriving at the certified values of the SRMs

produced. The NIST Special Publication 260 Series is a series of papers reserved for this purpose. The 260 Series is dedicated to the dissemination of information on different phases of the

preparation, measurement, certification, and use of NIST SRMs. In general, much more detail

will be found in these papers than is generally allowed, or desirable, in scientific journal articles. This enables the user to assess the validity and accuracy of the measurement processes

employed, to judge the statistical analysis, and to learn details of techniques and methods

utilized for work entailing greatest care and accuracy. These papers also should provide

sufficient additional information so SRMs can be utilized in new applications in diverse fields not foreseen at the time the SRM was originally issued.

Inquiries concerning the technical content of this paper should be directed to the author(s). Other questions concerned with the availability, delivery, price, and so forth, will receive prompt

attention from: Standard Reference Materials Program

Bldg. 202, Rm. 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

iii
OTHER NIST PUBLICATIONS IN THIS SERIES

Trahey,N.M., ed., NIST Standard Reference

Materials Catalog 1998-99, NIST Spec.Publ. 260 (1998 Ed.). PB95-232518/AS

Michaelis, R.E., and Wyman, L.L., Standard Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards, NBS Misc.

Publ. 260-1 (June 1964). COM74-1 1061**

Michaelis, R.E., Wyman, L.L., and Flitsch, R., Standard Reference Materials: Preparation of NBS Copper-Base Spectrochemical Standards, NBS Misc. Publ. 260-2 (October 1964). COM74-11063**

Michaelis, R.E., Yakowitz, H., and Moore, G.A., Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric LowAlloy Steel Standard, NBS Misc. Publ. 260-3

(October 1964). COM74-1 1060**

Hague, J.L., Mears, T.W., and Michaelis, R.E., Standard Reference Materials: Sources of

Information, Publ. 260-4 (February 1965). COM74-11059**

Alvarez, R., and Flitsch, R., Standard Reference

Materials: Accuracy of Solution X-Ray

Spectrometric Analysis of Copper -Base Alloys, NBS Misc. Publ. 260-5 (February 1965). PB168068**

Shultz, J. I., Standard Reference Materials: Methods

for the Chemical Analysis of White Cast Iron Standards, NBS Misc. Publ. 260-6 (July 1965). COM74-11068**

Bell, R.K., Standard Reference Materials: Methods

for the Chemical Analysis of NBS Copper -Base

Spectrochemical Standards, NBS Misc. Publ. 260-7 (October 1965). COM74-1 1067** Richmond, M.S., Standard Reference Materials: Analysis of Uranium Concentrates at the National Bureau of Standards, NBS Misc. Publ. 260-8 (December 1965). COM74-1 1066**

Anspach, S.C., Cavallo, L.M., Garfinkel, S.B., et al., Standard Reference Materials: Half Lives of

Materials Used in the Preparation of Standard Reference Materials of Nineteen Radioactive Nuclides Issued by the National Bureau of

Standards, NBS Misc. Publ. 260-9 (November

1965). COM74-11065**

Yakowitz, H., Vieth, D.L., Heinrich, K.F.J., et al., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards II: Cartridge Brass and Low Alloy

Steel, NBS Misc. Publ. 260-10 (December

1965). COM74-11064**

Napolitano, A., and Hawkins, E.G., Standard Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-1 1** (November 1966). Yakowitz, H., Vieth, D.L., and Michaelis, R.E., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards III: White Cast Iron and Stainless Steel Powder Compact, NBS Misc. Publ. 260-12 (September 1966). Spijkerman, J.J., Snediker, D.K., Ruegg, F.C., et al., Standard Reference Materials :Mossbauer

Spectroscopy Standard for the Chemical Shift of

Iron Compounds, NBS Misc. Publ. 260-13**

(July 1967). Menis, O., and Sterling, J.T., Standard Reference

Materials: Determination of Oxygen in Ferrous

Materials (SRMs 1090, 1091, 1092), NBS Misc.

Publ. 260-14** (September 1966).

Passaglia, E. and Shouse, P.J., Standard Reference

Materials: Recommended Method of Use of

Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Testiles for Colorfastness to Light, NBS Spec.Publ. 260-15

(July 1967). Superseded by SP 260-41. Yakowitz, H., Michaelis, R.E., and Vieth, D.L., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe

Characterization of W-20%Mo Alloy Fabricated by Powder Metallurgical Methods, NBS Spec.

Publ. 260-16 (January 1969). COM74-1 1062**

Catanzaro, E.J., Champion, C.E., Garner, E.L., et al., Standard Reference Materials: Boric Acid;

Isotopic, and Assay Standard Reference

Materials, NBS Spec.Publ. 260-17 (February

1970). PB189457**

iv
Geller, S.B., Mantek, P.A., and Cleveland, N.G.,

Calibration of NBS Secondary Standards Magnetic Tape Computer Amplitude Reference Amplitude Measurement "Process A" NBS

Spec. Publ. 260-18 (November 1969). Superseded by SP 260-29.

Paule, R.C., and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold

(Certification of SRM 745). NBS Spec.Publ. 260-19 (January 1970). PB 190071**

260-20: Unassigned

Paule, R.C., and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and Silver, NBS Spec.Publ. 260-21

(January 1971). COM74-1 1359**

Yakowitz, H., Fiori, C.E., and Michaelis, R.E., Standard Reference Materials: Homogeneity

Characterization of Fe-3Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357**

Napolitano, A., and Hawkins, E.G., Standard Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec.Publ. 260-23 (December 1970). COM71-00157**

Sappenfield, K.M., Marinenko, G., and Hague, J.L., Standard Reference Materials: Comparison of Redox Standards, NBS Spec. Publ. 260-24

(January 1972). COM72-50058**

Hicho, G.E., Yakowitz, H., Rasberry, S.D., et al., Standard Reference Materials: A Standard Reference Material Containing Nominally Four

Percent Austenite, NBS Spec. Publ. 260-25

(February 1971). COM74-1 1356**

Martin, J.F., Standard Reference Materials: NBS-U.S. Steel Corp. Joint Program for Determining Oxygen and Nitrogen in Steel, NBS

Spec. Publ. 260-26 (February 1971). PB

81176620**

Garner, E.L., Machlan, L.A., and Shields, W.R.,

Standard Reference Materials: Uranium Isotopic Standard Reference Materials, NBS Spec.Publ. 260-27 (April 1971). COM74-1 1358**

Heinrich, K.F.J., Myklebust, R.L., Rasberry, S.D., et

al., Standard Reference Materials: Preparation and Evaluation of SRMs 481 and 482 GoldSilver and Gold -Copper Alloys for Microanalysis, NBS Spec.Publ. 260-28 (August

1971). COM71-50365**

Geller, S.B., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape Amplitude Measurement "Process A -Model 2," NBS Spec.

Publ. 260-29 (June 1971). COM7 1-50282**

Supersedes Measurement System in SP 260-18. Gorozhanina, R.S., Freedman, A.Y., and Shaievitch, A.B., (translated by M.C. Selby), Standard Reference Materials: Standard Samples Issued in the USSR (A Translation from the Russian), NBS Spec. Publ. 260-30 (June 1971). COM71-

50283**

Hust, J.G., and Sparks, L.L., Standard Reference

Materials: Thermal Conductivity of Electrolytic Iron SRM 734 from 4 to 300 K, NBS Spec. Publ. 260-31 (November 1971). COM7 1-50563** Mavrodineanu, R., andLazar, J.W., Standard Reference Materials: Standard Quartz Cuvettes

for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). COM74-

50018**

Wagner, H.L., Standard Reference Materials: Comparison of Original and Supplemental SRM

705, Narrow Molecular Weight Distribution Polystyrene, NBS Spec.Publ. 260-33 (May

1972). COM72-50526**

Sparks, L.L., and Hust, J.G., Standard Reference

Material: Thermoelectric Voltage of Silver-28 Atomic Percent Gold Thermocouple Wire, SRM

733, Verses Common Thermocouple Materials (Between Liquid Helium and Ice Fixed Points), NBS Spec. Publ. 260-34 (April 1972). COM72-

50371**

Sparks, L.L., and Hust, J.G., Standard Reference

Materials: Thermal Conductivity of Austenitic

Stainless Steel, SRM 735 from 5 to 280 K, NBS

Spec. Publ. 260-35 (April 1972). COM72-

50368**

v
Cali, J. P., Mandel, J., Moore, L.J., et al., Standard Reference Materials: A Reference Method for the Determination of Calcium in Serum NBS

SRM 915, NBS Spec. Publ. 260-36 (May 1972). COM72-50527**

Shultz, J.I., Bell, R.K., Rains, T.C., et al., Standard Reference Materials: Methods of Analysis of NBS Clay Standards, NBS Spec. Publ. 260-37

(June 1972). COM72-50692**

Richard, J.C., and Hsia, J.J., Standard Reference

Materials: Preparation and Calibration of

Standards of Spectral Specular Reflectance, NBS

Spec. Publ. 260-38 (May 1972). COM72-

50528**

Clark, A.F., Denson, V.A., Hust, J.G., et al., Standard Reference Materials: The Eddy Current Decay Method for Resistivity Characterization of

High-Purity Metals, NBS Spec. Publ. 260-39 (May 1972). COM72-50529**

McAdie, H.G., Garn, P.D., and Menis, O., Standard Reference Materials: Selection of Differential Thermal Analysis Temperature Standards Through a Cooperative Study (SRMs 758, 759,

760), NBS Spec. Publ. 260-40 (August 1972) COM72-50776**

Wood. L.A., and Shouse, P.J., Standard Reference

Materials: Use of Standard Light-Sensitive Paper

for Calibrating Carbon Arcs Used in Testing

Textiles forColorfastness to Light, NBS Spec.

Publ. 260-41 (August 1972). COM72-50775**

Wagner, H.L., and Verdier, P.H., eds., Standard Reference Materials: The Characterization of

Linear Polyethylene, SRM 1475, NBS Spec.

Publ. 260-42 (September 1972). COM72-

50944**

Yakowitz, H., Ruff, A.W., andMichaelis,R.E.,

Standard Reference Materials: Preparation and Homogeneity Characterization of an Austenitic Iron-Chromium-Nickel Alloy, NBS Spec. Publ. 260-43 (November 1972). COM73-50760**

Schooley, J.F., Soulen, R.J., Jr., and Evans, G.A.,

Jr., Standard Reference Materials: Preparation and Use of Superconductive Fixed Point Devices, SRM 767, NBS Spec. Publ. 260-44 (December 1972). COM73-50037**

Greifer, B., Maienthal, E.J., Rains, T.C., et al., Standard Reference Materials: Development of NBS SRM 1579 Powdered Lead -Based Paint, NBS Spec. Publ. 260-45 (March 1973). COM73-

50226**

Hust, J.G., and Giarratano, P.J., Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRMs 735 and 798, from 4 to 1200 K, NBS Spec. Publ. 260-46 (March 1975). COM75-10339**

Hust, J.G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and

Austenitic Stainless Steel, SRM 798, from 5 to 280 K, NBS Spec. Publ. 260-47 (February

1974). COM74-50176** Mangum, B.W., and Wise, J.A., Standard Reference

Materials: Description and Use of Precision Thermometers for the Clinical Laboratory, SRM

933 and SRM 934, NBS Spec. Publ. 260-48 (May 1974). Superseded by NIST Spec.Publ. 260-113. COM74-50533**

Carpenter, B.S., and Reimer, G.M., Standard Reference Materials: Calibrated Glass Standards

for Fission Track Use, NBS Spec.Publ. 260-49 (November 1974). COM74-51 185**

Hust, J.G., and Giarratano, P.J., Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRMs 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975). COM75-10698**

Mavrodineanu, R., and Baldwin, J.R., Standard Reference Materials: Glass Filters As a SRM for Spectrophotometry-Selection, Preparation,

Certification, and Use-SRM 930 NBS Spec.

Publ. 260-51 (November 1975). COM75-

10339**

Hust, J.G., and Giarratano, P.J., Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity SRMs 730 and 799, from 4 to 3000

K, NBS Spec. Publ. 260-52 (September 1975). COM75-11193**

Durst, R.A., Standard Reference Materials: Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1978). Superseded by SP 260-53 Rev. 1988 Edition. PB88217427**

vi
Burke, R.W., and Mavrodineanu, R., Standard Reference Materials: Certification and Use of

Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard, NBS Spec.

Publ. 260-54 (August 1977). PB272168**

Ditmars, D.A., Cezairliyan, A., Ishihara, S., et al., Standard Reference Materials: Enthalpy and

Heat Capacity; Molybdenum SRM 781, from

273 to 2800 K, NBS Spec. Publ. 260-55 (September 1977). PB272127**

Powell, R.L., Sparks, L.L., andHust, J.G., Standard Reference Materials: Standard Thermocouple

Material, Pt-67: SRM 1967, NBS Spec. Publ. 260-56 (February 1978). PB277172**

Cali, J. P., and Plebanski, T., Standard Reference

Materials: Guide to United States Reference

Materials, NBS Spec. Publ. 260-57 (February

1978). PB277173**

Barnes, J.D., and Martin, G.M., Standard Reference

Materials: Polyester Film for Oxygen Gas

Transmission Measurements SRM 1470, NBS

Spec. Publ. 260-58 (June 1979). PB297098**

Chang, T., and Kahn, A.H., Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard: SRM 2601; Description and

Use, NBS Spec. Publ. 260-59 (August 1978). PB292097**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al., Standard Reference Materials: A Reference Method for the Determination of Sodium in Serum, NBS Spec. Publ. 260-60 (August 1978). PB286944**

Verdier, P.H., and Wagner, H.L., Standard Reference Materials: The Characterization of

Linear Polyethylene (SRMs 1482, 1483, 1484), NBS Spec. Publ. 260-61 (December 1978). PB289899**

Soulen, R.J., and Dove, R.B., Standard Reference

Materials: Temperature Reference Standard for Use Below 0.5 K (SRM 768), NBS Spec. Publ. 260-62 (April 1979). PB294245**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al, Standard Reference Materials: A Reference Method for the Determination of Potassium in Serum, NBS Spec. Publ. 260-63 (May 1979). PB297207**

Velapoldi, R.A., andMielenz, K.D., Standard Reference Materials: A Fluorescence SRM

Quinine Sulfate Dihydrate (SRM 936), NBS

Spec. Publ. 260-64 (January 1980). PB80132046**

Marinenko, R.B., Heinrich, K.F.J., andRuegg, F.C., Standard Reference Materials: Micro- Homogeneity Studies of NBS SRM, NBS

Research Materials, and Other Related Samples, NBS Spec. Publ. 260-65 (September 1979). PB3 00461**

Venable, W.H., Jr., andEckerle, K.L., Standard Reference Materials: Didymium Glass Filters for Calibrating the Wavelength Scale of Spectrophotometers (SRMs 2009, 2010, 2013,

2014). NBS Spec. Publ. 260-66 (October 1979). PB80104961**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al., Standard Reference Materials: A Reference Method for the Determination of Chloride in Serum, NBS Spec. Publ. 260-67 (November

1979). PB801 101 17** Mavrodineanu, R., and Baldwin, J.R., Standard Reference Materials: Metal -On-Quartz Filters as a SRM for Spectrophotometry SRM 203 1, NBS

Spec. Publ. 260-68 (April 1980). PB80197486**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al., Standard Reference Materials: A Reference Method for the Determination of Lithium in Serum, NBS Spec. Publ. 260-69 (July 1980). PB80209117**

Marinenko, R.B., Biancaniello, F.,Boyer, P.A., et

al., Standard Reference Materials: Preparation and Characterization of an Iron-ChromiumNickel Alloy for Microanalysis: SRM 479a, NBS

Spec. Publ. 260-70 (May 1981). SN003-003-

02328-1*

Seward, R.W., and Mavrodineanu, R., Standard Reference Materials: Summary of the Clinical Laboratory Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-71 (November 1981). PB82135161**

Reeder, D.J., Coxon, B., Enagonio, D., et al., Standard Reference Materials: SRM 900, Anti- epilepsy Drug Level Assay Standard, NBS Spec.

Publ. 260-72 (June 1981). PB81220758

vii
Interrante, C.G., and Hicho, G.E., Standard Reference Materials: A Standard Reference

Material Containing Nominally Fifteen Percent

Austenite (SRM 486), NBS Spec.Publ. 260-73

(January 1982). PB82215559**

Marinenko, R.B., Standard Reference Materials: Preparation and Characterization of K-4 1 1 and K-412 Mineral Glasses for Microanalysis: SRM

470, NBS Spec. Publ. 260-74 (April 1982). PB82221300**

Weidner, V.R., andHsia, J. J., Standard Reference

Materials: Preparation and Calibration of First Surface Aluminum Mirror Specular Reflectance Standards (SRM 2003a), NBS Spec.Publ. 260-

75 (May 1982). PB82221367**

Hicho, G.E., and Eaton, E.E., Standard Reference

Materials: A Standard Reference Material Containing Nominally Five PercentAustenite (SRM 485a), NBS Spec. Publ. 260-76 (August

1982). PB83 115568**

Furukawa, G.T., Riddle, J.L.,Bigge, W.G., et al., Standard Reference Materials: Application of Some Metal SRMs as Thermometric Fixed

Points, NBS Spec. Publ. 260-77 (August 1982). PB831 17325**

Hicho, G.E., and Eaton, E.E., Standard Reference

Materials: Standard Reference Material Containing Nominally Thirty Percent Austenite (SRM 487), NBS Spec. Publ. 260-78 (September

1982). PB83 115576** Richmond, J.C., Hsia, J.J., Weidner, V.R., et al., Standard Reference Materials: Second Surface Mirror Standards ofSpecular Spectral Reflectance (SRMs 2023, 2024, 2025), NBS

Spec. Publ. 260-79 (October 1982). PB84203447**

Schaffer, R., Mandel, J., Sun, T., et al., Standard Reference Materials: Evaluation by an ID/MS

Method of the AACC Reference Method for Serum Glucose, NBS Spec. Publ. 260-80

(October 1982). PB84216894**

Burke, R.W., and Mavrodineanu, R., Standard Reference Materials: Accuracy in Analytical Spectrophotometry, NBS Spec.Publ. 260-81

(April 1983). PB83214536**

Weidner, V.R., Standard Reference Materials: White

Opal Glass Diffuse Spectral Reflectance Standards for the Visible Spectrum <SRMs 2015

and 2016), NBS Spec. Publ. 260-82 (April

1983). PB83220723**

Bowers, G.N., Jr., Alvarez, R., Cali, J.P., et al., Standard Reference Materials: The Measurement

of the Catalytic (Activity) Concentration of Seven Enzymes in NBS Human Serum (SRM

909), NBS Spec. Publ. 260-83 (June 1983). PB83239509**

Gills, T.E., Seward, R.W., Collins, R.J., et al., Standard Reference Materials: Sampling,

Materials Handling, Processing, and Packaging

of NBS Sulfur in Coal SRMs 2682, 2683, 2684, and 2685, NBS Spec. Publ. 260-84 (August

1983). PB84109552**

Swyt, D.A., Standard Reference Materials: A Look

at Techniques for the Dimensional Calibration of

Standard Microscopic Particles, NBS Spec.Publ. 260-85 (September 1983). PB841 12648**

Hicho, G.E., and Eaton, E.E., Standard Reference

Materials: A SRM Containing Two and OneHalf Percent Austenite, SRM 488, NBS Spec.

Publ. 260-86 (December 1983). PB84143296** Mangum, B.W., Standard Reference Materials: SRM

1969: Rubidium Triple-Point - A Temperature

Reference Standard Near 39.30 0 C, NBS Spec.

Publ. 260-87 (December 1983). PB84149996**

Gladney, E.S., Burns, C.E., Perrin, D.R., et al., Standard Reference Materials: 1982 Compilation of Elemental Concentration Data for NBS

Biological, Geological, and Environmental

Standard Reference Materials, NBS Spec.Publ. 260-88 (March 1984). PB842 18338**

Hust, J.G., Standard Reference Materials: A Fine- Grained, Isotropic Graphite for Use as NBS

Thermophysical Property RMs from 5 to 2500 K, NBS Spec. Publ. 260-89 (September 1984). PB851 12886**

Hust, J.G., and Lankford, A.B., Standard Reference

Materials: Update of Thermal Conductivity and

Electrical Resistivity of Electrolytic Iron, Tungsten, and Stainless Steel, NBS Spec.Publ. 260-90 (September 1984). PB851 15814**

viii
Goodrich, L.F., Vecchia, D.F., Pittman, E.S., et al., Standard Reference Materials: Critical Current Measurements on anNbTi Superconducting Wire SRM, NBS Spec. Publ. 260-91 (September

1984). PB85118594**

Carpenter, B.S., Standard Reference Materials: Calibrated Glass Standards for Fission Track Use

(Supplement to NBS Spec. Publ. 260-49), NBS

Spec. Publ. 260-92 (September 1984). PB851 13025**

Ehrstein, J.R., Standard Reference Materials: Preparation and Certification of SRM for Calibration of Spreading Resistance Probes, NBS Spec. Publ. 260-93 (January 1985). PB85177921**

Gills, T.E., Koch, W.F., Stolz, J.W., et al., Standard Reference Materials: Methods and Procedures Used at the National Bureau of Standards to Certify Sulfur in CoalSRMs for Sulfur Content,

Calorific Value, Ash Content, NBS Spec.Publ. 260-94 (December 1984). PB85 165900**

Mulholland, G.W., Hartman, A.W., Hembree, G.G.,

et al., Standard Reference Materials: Development of a 1mm Diameter Particle Size Standard, SRM 1690, NBS Spec.Publ. 260-95 (May 1985). PB95-232518/AS**

Carpenter, B.S., Gramlich, J.W., Greenberg, R.R., et

al., Standard Reference Materials: Uranium-235

Isotopic Abundance Standard Reference

Materials for Gamma Spectrometry Measurements, NBS Spec. Publ. 260-96

(September 1986). PB87 108544**

Mavrodineanu, R., and Gills, T.E., Standard Reference Materials: Summary of the Coal, Ore, Mineral, Rock, and Refactory Standards Issued by the National Bureau of Standards, NBS Spec.

Publ. 260-97 (September 1985). PB861 10830**

Hust, J.G., Standard Reference Materials: Glass

Fiberboard SRM for Thermal Resistance, NBS

Spec. Publ. 260-98 (August 1985). SN003-003-

02674-3*

Callanan, J.E., Sullivan, S.A., and Vecchia, D.F., Standard Reference Materials: Feasibility Study

for the Development of Standards Using

Differential Scanning Calorimetry, NBS Spec.

Publ. 260-99 (August 1985). PB86106747**

Taylor, J.K., Trahey, N.M., ed., Standard Reference

Materials: Handbook for SRM Users, NBS Spec.

Publ. 260-100 (February 1993). PB93183796** Mangum, B.W., Standard Reference Materials: SRM

1970, Succinonitrile Triple -Point Standard: A

Temperature Reference Standard Near 58.08°

C, NBS Spec. Publ. 260-101 (March 1986). PB86197100**

Weidner, V.R., Mavrodineanu, R., Mielenz, K.D., et

al., Standard Reference Materials: Holmium

Oxide Solution Wavelength Standard from 240

to 640 nm - SRM 2034, NBS Spec. Publ. 260-102 (July 1986). PB86245727**

Hust, J.G., Standard Reference Materials: Glass

Fiberblanket SRM for Thermal Resistance, NBS

Spec. Publ. 260-103 (September 1985). PB86109949**

Mavrodineanu, R., and Alvarez, R., Standard Reference Materials: Summary of the Biological and Botanical Standards Issued by the National Bureau of Standards, NBS Spec.Publ. 260-104 (November 1985). PB86155561**

Mavrodineanu, R., andRasberry, S.D., Standard Reference Materials: Summary of the Environmental Research, Analysis, and Control Standards Issued by the National Bureau of

Standards, NBS Spec. Publ. 260-105 (March

1986) . PB86204005**

Koch, W.F., ed., Standard Reference Materials: Methods and Procedures Used at the National Bureau of Standards to Prepare, Analyze, and

Certify SRM 2694, Simulated Rainwater, and Recommendations for Use, NBS Spec.Publ. 260-106 (July 1986). PB86247483**

Hartman, A.W., and McKenzie, R.L., Standard Reference Materials: SRM 1965, Microsphere

Slide (10 |im Polystyrene Spheres), NIST Spec.

Publ. 260-107 (November 1988). PB89153704**

Mavrodineanu, R., and Gills, TiE., Standard Reference Materials: Summary of Gas Cylinder and Permeation Tube Standard Reference

Materials Issued by the National Bureau of

Standards, NBS Spec. Publ. 260-108 (May

1987) . PB87209953**
Candela, G.A., Chandler, Horowitz, D.,Novotny,

D.B., et al., Standard Reference Materials: Preparation and Certification of an

Ellipsometrically Derived Thickness and

Refractive Index Standard of a Silicon Dioxide

Film (SRM 2530), NIST Spec. Publ. 260-109

(October 1988). PB89133573**

Kirby, R.K., andKanare, H.M., Standard Reference

Materials: Portland Cement Chemical

Composition Standards (Blending, Packaging, and Testing), NBS Spec. Publ. 260- 110

(February 1988). PB88193347**

Gladney, E.S., O'Malley, B.T., Roelandts, I., et al., Standard Reference Materials: Compilation of

Elemental Concentration Data for NBS Clinical, Biological, Geological, and Environmental

Standard Reference Materials, NBS Spec. Publ. 260-111 (November 1987). PB88156708**

Marinenko, R.B., Blackburn, D.H., and Bodkin,

J.B., Standard Reference Materials: Glasses for Microanalysis: SRMs 1871-1875, NIST Spec.

Publ. 260-1 12 (February 1990). PB90215807** Mangum, B.W., and Wise, J.A., Standard Reference

Materials: Description and Use of a Precision Thermometer for the Clinical Laboratory, SRM

934, NIST Spec. Publ. 260-1 13 (June 1990). PB90257643**

Vezzetti, C.F., Varner, R.N., and Potzick, J.E., Standard Reference Materials: Bright - Chromium Linewidth Standard, SRM 476, for Calibration of Optical MicroscopeLinewidth

Measuring Systems, NIST Spec. Publ. 260-1 14 (January 1 99 1 ). PB9 1 1 67 1 63 * * Williamson, M.P., Willman,N.E., and Grubb, D.S., Standard Reference Materials: Calibration of NIST SRM 3201 for 0.5 in. (12.65 mm) Serial Serpentine Magnetic Tape Cartridge, NIST Spec.

Publ. 260-1 15 (February 1991). PB91 187542**

Mavrodineanu, R., Burke, R.W., Baldwin, J.R., et

al., Standard Reference Materials: Glass Filters as a Standard Reference Material for Spectrophotometry-Selection, Preparation,

Certification and Use of SRM 930 and SRM

1930, NIST Spec. Publ. 260-1 16 (March 1994). PB94-188844/AS**

Vezzetti, C.F., Varner, R.N., and Potzick, J.E., Standard Reference Materials: Anti-reflecting- Chromium Linewidth Standard, SRM 475, for Calibration of Optical MicroscopeLinewidth

Measuring Systems, NIST Spec. Publ. 260-1 17 (January 1992). PB92- 149798**

Williamson, M.P., Standard Reference Materials: Calibration of NIST Standard Reference Material 3202 for 18-Track, Parallel, and 36 -Track,

Parallel Serpentine, 12.65 mm (0.5 in), 1491 cpmm (37871 cpi), Magnetic Tape Cartridge, NIST Spec. Publ. 260-1 18 (July 1992). PB92-

226281**

Vezzetti, C.F., Varner, R.N., and Potzick, Standard Reference Materials: Antireflecting-Chromium Linewidth Standard, SRM 473, for Calibration of

Optical MicroscopeLinewidth Measuring

System, NIST Spec. Publ. 260-1 19 (September

1992) Caskey, G.W., Philips, S.D., Borchardt., et al., Standard Reference Materials: A Users' Guide to NIST SRM 2084: CMM Probe Performance

Standard, NIST Spec. Publ. 260-120 (1994) Rennex, B.G., Standard Reference Materials:

Certification of a Standard Reference Material

for the Determination of Interstitial Oxygen

Concentration in Semiconductor Silicon by

Infrared Spectrophotometry, NIST Spec. Publ. 260-121 (1994) PB95-125076/AS

Gupta, D., Wang, L., Hanssen, L.M., Hsai, J.J., and

Datla, R.U., Polystyrene Films for Calibrating

the Wavelength Scale of Infrared Spectrophotometer (SRM 1921). NIST Spec.

Publ. 260-122 (1995) PB95-226866/AS

Development of Technology and the Manufacture of

Spectrometric SRMs for Naval Brasses (MC62

M63). NIST Spec. Publ. 260-123 (IN PREP).

Strouse, G.F., SRM 1744: Aluminum Freezing Point

Standard. NIST Spec. Publ. 260-124 (1995) SN003-003-03342-1

Schiller, S.B, Standard Reference Materials:

Statistical Aspects of the Certification of Chemical Batch SRMs. NIST Spec. Publ. 260-

125 (1996) PB96-210877/AS

x
Guenther, F.R., Dorko, W.D., Miller, W.R., et al., Standard Reference Materials: The NIST

Traceable Reference Material Program for Gas

Standards, NIST Spec. Publ. 260-126 (1996) PB96-210786/AS

Strouse, G.F., and Ahmet, A.T., Standard Reference

Material 1747: Tin Freezing-Point Cell and

Standard Reference Material 1748: Zinc

Freezing-Point Cell. NIST Spec. Publ. 260-127

SN003-003-03488-6.

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

Datla, R.U., Transmission Filters with Measured

Optical Density at 1064nm Wavelength-SRMs

2046, 2047, 2048, 2049, 2050, and 205 1 . SRM

Spec. Publ. 260-128 (IN PREP).

Potzick, J.E., Antireflecting-Chromium Linewidth

Standard, Standard Reference Material 473, for Calibration of Optical Microscope Linewidth Measuring Systems, NIST Spec. Publ. 260-129

(1997) SN003-003-03447-9.

Zarr, R.R., Standard Reference Materials: Glass

Fiberboard, Standard Reference Material 1450c,

for Thermal Resistance from 280K to 340K, NIST Spec. Publ. 260-130 (1997) PB97-

177166/AS.

Ehrstein, J.R., andCroarkin, M.C., The Certification of 100 mm Diameter Silicon Resistivity SRMs

2541 through 2547 Using Dual-Configuration

Four-Point Probe Measurements. NIST Spec.

Publ. 260-131.

Strouse, G.G., Standard Reference Material 1745: Indium Freezing Point Standard and Standard Reference Material 2232: Indium DSC Melting

Point Standard, NIST Spec. Publ. 260-132 (IN PREP).

Gilbert, S.L., and Swann, W.C., Acetylene 12 C2 H2 Absorption Reference for 15 10-1 540 nm

Wavelength Calibration - SRM 2517. NIST

Spec. Publ. 260-133 (1998) SN003-003-03 542-4

Ripple, D., et al., Standard Reference Material 1749: Gold vs. Platinum Thermocouple. NIST Spec.

Publ. 260-134 (IN PREP)

Send order with remittance to: Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325. Remittance from

foreign countries should include an additional one fourth of the purchase price for postage. **May be ordered from: National Technical

Information Services (NTIS), Springfield, VA

22161. For information phone (703-487-4650) To Place an Order with PB# phone (800-553- 6847)

xi
ABSTRACT

The instrument used to measure the diffuse visual transmission densities of both

x-ray (SRM 1001) and photographic (SRM 1008) film step tablets is described. It is fully automated to measure the transmission densities of the steps of many tablets in a single batch run. The instrument was designed and characterized to comply with the

international standards for measuring transmission density using the diffuse influx mode.

Transmission densities as great as four can be measured with an expanded uncertainty

(& = 3)of0.006.

Keywords: densitometer; diffuse transmission; standard reference materials; transmission density

xii
TABLE OF CONTENTS

Abstract ix

1. Introduction 1

2. Measurement Equations 1

3. Description of Instrument 9

4. Characterization of Instrument 17

5. Operation of Instrument 25

6. Uncertainties 27

7. Conclusions 31 Acknowledgments 31

References 33

xiii
LIST OF FIGURES

Figure 2.1 Important components of the diffuse transmittance densitometer 3

Figure 3.1 Cross-section of the source system 11

Figure 3.2 Top view of the film transport system 12

Figure 3.3 Cross-section of the film transport system 13

Figure 3.4 Cross-section of the detection system 14

Figure 3.5 Schematic of all the densitometer components and their connections 15

Figure 3.6 Electrical connections of the relays 16

Figure 4. 1 Relative flux distribution of the source as a function of wavelength 18

Figure 4.2 Reflectance of the opal as a function of wavelength 19

Figure 4.3 Relative flux distribution of the source as a function of angle 20

Figure 4.4 Relative responsivity of the detector as a function of wavelength 22

Figure 4.5 Linearity of the detector as a function of current 23

Figure 4.6 Reflectance and transmittance of the films as a function of wavelength .... 24

xiv
LIST OF TABLES

Table 2.1 Properties and symbols of components 4

Table 3.1 Components of the densitometer 10

Table 4. 1 Values of successive gain ratios 23

Table 5.1 Values of gain ratios for calculations 26

Table 6. 1 Transmission densities calculated for different opal reflectances 30

Table 6.2 Components of uncertainty and resulting standard uncertainties 32

xv
LIST OF APPENDICES

Appendix A Certificate, SRM 1001 Appendix B Certificate, SRM 1008

xvi
1. Introduction

Transmission density is an important physical property for exposed films in the

fields of medicine, non-destructive testing, photography, and graphic arts. Standards for transmission density are provided by the National Institute of Standards and Technology

(NIST) in the form of Standard Reference Materials (SRMs). These standards are film

step tablets, 254 mm long by 35 mm wide, with steps extending the width of each film and equally spaced along its length. A double emulsion x-ray film is used for SRJVI 1001, while a single emulsion photographic film is used for SRM 1008. The steps have

increasing transmission densities from approximately 0.1 to 4 from one end of the film to the other. SRM 1001 has 17 steps, while SRM 1008 has 23. The transmission densities of film step tablets for both SRM 1001 and 1008 are determined with an instrument using the diffuse influx mode. Diffuse illumination is achieved with a flash opal, while directional detection is accomplished with a lens system. The transmitted radiant flux is detected by a temperature-controlled silicon (Si) photodiode with amplifier electronics capable of measuring signals spanning seven orders of magnitude. The instrument is designed to automatically measure many films using

computerized data acquisition and control. The organization of this Special Publication is as follows. The measurement

equations relevant to the determination of transmission density using the diffuse influx mode are derived in section 2. The instrument used for measuring transmission density is described in section 3; its characterization, particularly in relation to the applicable

international standards for this measurement, is detailed in section 4; and its operation is discussed in section 5. Finally, the uncertainties in the measured transmission density

resulting from various components are derived in section 6.

2. Measurement Equations

The purpose of the measurement equations derived in this section is to obtain mathematical expressions of the transmission density as a function of different quantities. These quantities are the signals measured by the Si photodiode detector, the spectral properties of the influx and detected radiant flux, and the spatial properties of the radiant

flux. Therefore, three measurement equations are derived and are used both for calculating transmission densities from experimental results and for determining the uncertainty in these transmission densities. Two radiant fluxes are important for determining transmission density. Following

the nomenclature given in [1, 2], these fluxes are the aperture flux <Z> - the flux emerging from the sampling aperture in the directions and parts of the spectrum to be utilized in the measurement - and the transmitted flux 0X - the flux that passes through the specimen,

emerging from a surface other than that on which the incident flux falls, and then utilized in the measurement. In terms of these fluxes, the transmittance factor T is given by

1
(2.1) and the transmission density DT

is defined by

Z>r =-logio T (2.2)

To this point, neither the geometrical nor spectral properties of the fluxes have been specified. For diffuse transmission density, either the incident flux (influx) must be

diffuse or detection must include both the regular and diffuse components of the transmitted flux (efflux) [3]. Therefore, two equivalent experimental modes are possible

for measuring diffuse transmission density: the diffuse influx mode, in which the illumination is diffuse and the detection is directional, and the diffuse efflux mode, in which the illumination is directional and the detection is diffuse.

Likewise, the spectral properties of the fluxes are defined for diffuse transmission

density [4]. The relative spectral flux distribution of the incident flux is denoted by SH and is based on the spectral flux distribution of the CIE Standard Illuminant A modified

in the infrared region to protect the sample and optical elements from excessive heat. For

visual transmission density, the combined spectral response of the detector and the

spectral characteristics of the optical elements collecting the transmitted flux is denoted by VT

. The spectral product is obtained by multiplying, at each wavelength, the spectral power of the influx spectrum by the spectral response of the receiver. The spectral product is specified to be the same as the product of CIE Standard Illuminant A, SA, with

the spectral luminous efficiency function for photopic vision, Vx. Therefore, at each

wavelength,

In terms of the definitions and concepts presented in the previous paragraphs, the instrument measures diffuse visual transmission density using the diffuse influx mode. The important components of the instrument are shown in figure 2.1, as well as a

spherical coordinate system. The film step tablet is in contact with the opal, which

provides an influx with angles of incidence 6 from 0° to 90° and a relative spectral flux

distribution SH

. The efflux is collected within an acceptance cone having a half-angle k

less than 10° and with a spectral response VT. Therefore, using the functional notation

specified in [1, 2, 3], the measured transmission density is described by

The properties of the various components used in deriving the measurement

equations are given in table 2.1. The influx has radiance L^X), where A is the wavelength. The opal has reflectance p0(A) and diffusion coefficient d (defined below),

SH -VT = (2.3)

Z)x(90° opal^H^lO0 ;^). (2.4)

2
Amplifier

Si Photodiode

Focusing Lens

Photopic Filter

< Collimating Lens

Opal Film

Figure 2.1 Important components of the diffuse transmittance densitometer.

while the step being measured has transmittance rs {X) and reflectance ps {X). The efflux has radiance L^{X). As shown in section 3, the aperture stop of the optical system is the

collection lens. Therefore, to first order, the throughput is given by A Q where A is the area of the opal and Qis the solid angle, with half-angle k, from the center of the opal to the edges of the collection lens. Note that the opal is the aperture of the system defining

the aperture flux Q}

. The photopic filter has transmittance r^A), the photodiode has

spectral responsivity R(X), and the amplifier has gain G.

3
Table 2.1 Properties and symbols of components of transmission density instrument

Property Symbol

Influx radiance LfjL) Opal reflectance Opal diffusion coefficient d

Step transmittance Step reflectance Efflux radiance Acceptance cone half-angle K

Filter transmittance Til) Photodiode responsivity R(A)

Amplifier gain G

The differential radiant flux d0 from the opal or the step to the collecting lens is given by

d0(A,a,co) = L(A,a,o)).dadco , (2.5) where a is a point on the opal or step and co is a direction with angles 0 and Assume

that the radiance L(X, a, co) is constant within the acceptance cone. Then, by integrating eq (2.5) over the spatial variables the spectral flux 0(A) is given by

0(A) = ljd0(A,a,6))dadco

= L(A)-A-n

which is the spectral flux incident on the photopic filter. The photopic filter modifies this flux so that the spectral flux incident on the photodiode is given by

0(A) = L(A)-rf (A)-A-n . (2.7)

For the opal, the spectral radiance is

L(A) = Lj(A), (2.8)

while for the step the spectral radiance is

4
L(A) = Zt (A) rtf) , (2-9) LS {X)

showing that the radiance from the opal is modified by the transmittance of the step and by inter-reflections between the opal and the step. Combining eq (2.7) with eqs (2.8) and

(2.9) yields the spectral aperture and transmitted fluxes, respectively. Thus, the spectral aperture flux is 0} {X) = ZjOM)- Tf (A) A Q (2.10)

and the spectral differential transmitted flux is

g, (A) = L. (A, co) • T

'£\ a) —• rf (A) • A • Q . (2.11)

The spectral output current /(A) from the photodiode, for either the spectral aperture flux or the spectral transmitted flux, is given by

I{X) = $(X) R(X) . (2.12) The total current lis obtained by integrating eq (2.12) over wavelength, yielding

/= fd/(/l) (2.13)

From eq (2.13) and eqs (2.10) and (2.1 1), the current from the aperture flux /j is given by

7j = A n- JZj(A) • rf (A) • i?(A) dA (2.14)

and the current from the transmitted flux IT by

I = A-Q.- |z,j(A) • ^ —-rf (A)-i?(A)-dA . (2.15)

Note that the currents in eqs (2.14) and (2.15) are proportional to the radiant flux and

contain both the spectral and geometrical information specified by eq (2.4). In terms of

the nomenclature,

SH

oc Lj(A,ft>) (2.16)

5
and

Finally, the measured signal S, a voltage, is given by

SS = IS GS

for the aperture flux and by

ST = /T -GT

for the transmitted flux.

(2.17)

(2.18)

(2.19)

Re-expressing eq (2.2) in terms of the aperture and transmitted fluxes, the transmission density is

£>T =log, 0

(2.20)

The first two measurement equations derived below depend upon the currents being

proportional to the fluxes, so that eq (2.20) is equivalent to

£>T =log] (2.21)

For transmission density as a function of the measured signals, the first measurement equation is obtained by substituting eqs (2.18) and (2.19) into eq (2.21) to yield

Z)T =logl S. G.

(2.22)

The second measurement equation expresses the transmission density as a function of the

spectral variables. Using eqs (2.14) and (2.15) and considering only the wavelength

dependence of the variables, eq (2.21) becomes

Z>r = log10 JZj(A)Tf (A)/g(A)-dA

r

f (A)/?(A)dA

(2.23)

6
The transmission density as a function of the spatial variables is given by the third measurement equation. The derivation which follows is adapted from [5]. Considering

only the spatial variables, the radiant flux incident on the photodiode is a fraction of the

total efflux. Integrating eq (2.5) over the spatial variables and ignoring the wavelength

yields a flux of 0 = jjL(a,Q))-da-dco . (2.24)

Assuming that the radiance L(a, co) is constant over the area of the opal and over all azimuthal angles (f>, eq (2.24) becomes 0 = 27t-A- Jz,(0).cos0sin0 d0 . (2.25)

For the measured aperture and transmitted fluxes (Z> and 0X , respectively, the limits of

integration in eq (2.25) are 0 to k, while for the total aperture and transmitted fluxes 0TJ and 0T x , respectively, the limits are 0 to n/2. The ratios of these fluxes are given by

0: 1^(0 • cos esme-diO

JL (2.26) jZj(#)-cos6>sin6>-d<9

o and

0. \LT (0)- cos 6 sin 0d0

. (2.27) jZr (0) • cos 6> sin <9-d<9

Substituting eqs (2.26) and (2.27) into the definition of transmission density given by

eq (2.20) yields

7
DT = log,

Jz,j(0)-cos0sin0-d0

T,J n/1^.(0)- cos 0 sin 0-d0

Jzr (0) • cos 0 sin 0-d0

j4(0)-cos0sin0-d0

(2.28)

Assuming that the opal is Lambertian for 0 < 6 < k, L}{0) is constant for these angles. Furthermore, assume that the scattering properties of the step make it Lambertian for 0 < 6< n/2. Therefore, eq (2.28) reduces to

Z)T =logl

'A Otj • Jcos0sin0-d0

/2

( L,{0) 0Tt • M cos0sin0-d0

(2.29)

where LfQ) is the radiance from the opal at 0= 0. Defining the diffusion coefficient d to be — cos0sin0-d0 =

o mYijcos0sin#'• d6

o

(2.30)

eq (2.29) becomes

DT = log, ^

0 (2.31)

The three measurement equations are given by eqs (2.22), (2.23), and (2.31). The

first is the method for calculating DT from the measured signals and the gains, while the second relates DT to the spectral properties of the influx, opal, step, photopic filter, and

photodiode. The third measurement equation expresses the dependence of DT on the

8
spatial properties of the aperture flux, accounting for the non-Lambertian quality of the

opal.

3. Description of Instrument The instrument was designed and built to automatically measure the diffuse visual transmission density of film step tablets using the diffuse influx mode. The major optical and electronic components are those shown in figure 2.1. A computer controls the entire measurement sequence. This section provides a detailed description of the instrument, which is conveniently divided into three systems: the source, the film transport, and the

detector. A list of all the components of the instrument is given in table 3.1 . f The source system provides a diffuse illumination to the film step tablet with the

correct spectral flux distribution. The system consists of a lamp and housing, an infrared

filter assembly, a shutter, and an opal assembly. A cross section of the source system is shown in figure 3.1. Starting from the bottom of the figure, a 100 W quartz-tungsten- halogen lamp is contained in a lamp housing. The lamp is burned in at 8.0 A for 24 h and

then at 7.8 A for an additional 48 h prior to being used for measurements. An elliptical reflector focuses the light from this lamp at approximately the position of the opal. The

lamp housing is cooled with distilled water at a temperature of 25 °C pumped through a

chiller, and a constant dc current is run through the lamp from a power supply. If the flow of water is interrupted, the flow meter closes a switch, which in turn disables the power supply. This prevents the infrared filter assembly, described next, from

overheating. The infrared filter assembly consists of aluminum plates for mounting to the lamp

housing and the shutter and an infrared filter. Infrared filtering is accomplished with a combination of water and an optical filter. Distilled water is circulated, using the same

chiller as for the lamp housing, through the stainless steel water filter in the direction indicated in figure 3.1. This water absorbs most of the light at infrared wavelengths, as well as cooling the plates which seal, with rubber gaskets, the top and bottom of the water

filter. The bottom plate is simply a piece of BK-7 glass with a diameter of 1 00 mm and a

thickness of 4 mm. The top plate is an optical filter, Hoya LP-1 5, with the same diameter and thickness as the glass plate. The optical filter was chosen so that its transmittance would modify the spectral flux distribution from the lamp to one approximating SH

. When the shutter is closed, it blocks all light from reaching the opal so that a background

signal can be measured. A controller operates the shutter and is interfaced to the computer.

f Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately

the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

9
Table 3.1 Components of diffuse transmission densitometer

Component Description Manufacturer Model

Lamp 100 W quartz- tungsten-halogen

Oriel 6333 Lamp Housing

Shell Oriel 60100

Reflector Ellipsoidal, f/2 Oriel 60112 Lamp Power Supply 20 V, 10 A Hewlett-Packard 6642A

Optical Filter Infrared cut-off Hoya LP- 15 Water Chiller Lytron MCS10G01

Flow Meter Proteus G203C24

Shutter Vincent Assoc. VS35

Shutter Controller JML Optical

Industries SDS 16555 Motion Controller Aerotech DR 500 with three DS 16020

Horizontal Stage Aerotech ATS70090-U-TB

Vertical Stage Aerotech ATS02010-U-40L

Solenoid Valve Atkomatic S240-4-V-N

Electro-mechanical Relay

National

Instruments ER-16

Collecting Lens Biconvex, BK-7,

75.6 mm focal length

Newport KBX048AR.14

Collimating Lens, Focusing Lens

Biconvex, BK-7,

38.1 mm focal length

Newport KBX139AR.14

Photopic Filter Graseby

Photodiode ricullcuIlcUoU 1997-1 01 ORO

Photodiode

Amplifier

Reyer Corp. S10/3-RC

Temperature

Controller ILX LDT-5412

Digital Voltmeter Hewlett-Packard 3457A

10
Lamp Housing

Figure 3.1 Cross-section of the source system for providing a diffuse influx.

The opal assembly consists of a plate for mounting to the shutter, two large pieces —one for holding the opal and mounting to the film plate and the other to provide

a vacuum for bringing the film step tablet in contact with the opal (described below) —

and several smaller pieces for mounting the opal. All the pieces are aluminum, and the vacuum plate is black-anodized. A flash opal with a diameter of 3 mm and a thickness of

1.5 mm is the source of diffuse illumination. The opal is fit partially into the black- anodized sleeve and held in place with black tape. The depth of the opal in the sleeve and

the height of the spacer are adjusted so that the top of the opal is aligned with the vacuum

plate when the opal assembly is complete. Black enamel paint is used so that all the light incident on the film step tablet originates from the top of the opal, which defines the sampling aperture for the influx. This paint is applied to the sides of the opal and between the opal and the sleeve. The sleeve and spacer are inserted in the opal plate and

a mounting plate attached to the opal plate holds the sleeve in place. The film transport system picks up a film from a tray, positions the film to measure the transmission density of each step on the film, and drops the film in another

tray. A top view of this system is shown in figure 3.2, while a cross section of the film holder and opal assembly is shown in figure 3.3. The film trays consist of flat aluminum

11
Film Holder Film Plate Optical Table Film Tray Vacuum Plate Film Tray

Vertical —

Translation Stage

Horizontal Translation Stage

Figure 3.2 Top view of the film transport system.

plates with vertical posts to hold the films in the proper position. The film tray on the left side in figure 3.2 holds the films to be measured, while the one on the right side holds

those that have been measured. The film holder, made of black-anodized aluminum, is attached to a vertical spring-loaded stage on a vertical translation stage, which in turn is attached to a horizontal translation stage. Both translation stages have absolute encoders. The film holder and translation stages move the films to the appropriate location; the sequence is described in section 5. The film plate is black-anodized aluminum and

supports the part of the film that is not on the vacuum plate. A vacuum both holds the film on the film holder and brings the film into direct contact with the opal. The vacuum is applied through solenoids controlled by the computer. The film holder has a groove along its outer edge, as shown in figure 3.3. When the film holder is in contact with a film and a vacuum is applied to this groove, the film is attached to the film holder and can be moved vertically and horizontally with the

translation stages. There are small holes in the vacuum plate of the opal assembly, shown

in cross-section in figure 3.3 and with a pattern indicated in figure 3.2. When a film is on

the vacuum plate and a vacuum is applied between the opal and vacuum plates, the film is pulled down onto the opal. The detector system collects the efflux within an acceptance cone and focuses this radiant flux onto the Si photodiode for detection. A cross section of this system is shown

in figure 3.4, along with the marginal and chief rays. All the lenses have diameters of

5 cm and are made of BK-7 glass. The lenses perform the functions indicated by their designations: collecting the light within the acceptance cone, collimating it through the photopic filter, and focusing it onto the detector. A baffle with a diameter of 10 mm

reduces scattered light in the detector system. The spectral transmittance of the photopic

filter is such that, in combination with the spectral response of the Si photodiode, the

spectral response of the detector system closely approximates the photopic spectral luminous efficiency function. The photopic filter is slightly tilted so that the light

12
Film Holder Vacuum Plate

Solenoid Valves

Vacuum

Figure 3.3 Cross-section of the film holder and opal assembly of the film transport system.

reflected from it does not travel back down to the opal. The lenses, baffle, and filter are housed in a black-anodized aluminum cylinder. The 4 mm by 4 mm Si photodiode is contained in a package that provides both thermoelectric temperature control at 25 °C and

current-to-voltage conversion with a gain that can be selected either manually or

automatically. Light reflected from the Si photodiode back onto the opal has no

measurable effect on the values of visual transmission density. The aperture stop of the optical system is the collecting lens, which defines an

acceptance cone with a half-angle k= 9.5° between it and the opal. If the opal is included

in the optical system, it is the field stop. However, the step of a film diffuses the transmitted light, making the area from which light exits the film ill-defined. Therefore,

if the opal is not included in the optical system, the photodiode is the field stop. The field of view has a diameter of 10 mm at the position of the opal, which is large enough to capture the entire area from which light exits the film. The systems of the instrument described above - source, transport, and detection -

are located on an optical table. The horizontal translation stage and film trays are attached directly to the table, as is a vertical post of 80/20 aluminum to which the lamp

housing, film plate, and optic housing attach. The mounting plate of the source attaches

to the film plate, as shown in figure 3.1, and the photodiode package attaches to the optic housing, as shown in figure 3.4. The solenoids that control the vacuum are also attached

13
Amplifier

Si Photodiode

Focusing Lens

Photopic Filter

Collimating Lens

Baffle

/ *r~~" Collecting Lens T^— — Opal Figure 3.4 Cross-section of the detection system, including the marginal and chief rays.

to the vertical post. The electronics used with the instrument are located in a rack

adjacent to the optical table. A schematic diagram showing all the components of the instrument and their connections is shown in figure 3.5. A computer performs all the data acquisition and

control, using a program written in Visual Basic. The GPIB interface communicates with

the lamp power supply and the digital voltmeter. Separate, custom cards control the electro-mechanical relays and the motion controller.

14
Signal +5V±15 VDC

Digital Voltmeter GPIB

Electro- mechanical

Relays

Gain

AC

Relays To Vacuum JL

To Air

PC

Computer

Figure 3.5 Schematic diagram of all the components of the diffuse transmittance densitometer and their connections.

15
Most of the automatic experimental control is achieved with the electro- mechanical relays, which are powered from an external voltage supply. One relay provides signals to the shutter controller, which in turn opens or closes the shutter. The

two solenoids on the vacuum lines are also opened and closed using ac relays controlled by signals from the electro-mechanical relays. The gain on the photodiode amplifier is set using the signals from three relays. The remainder of the automatic experimental

control is achieved by the linear translation stages, which are operated by the motion

controller. A diagram of the electrical connections is shown in figure 3.6.

To Shutter Controller COM

NO NC

To Amplifier Gain Control GND CLK G3 G2 Gl

Relays 8-15

Relays 0-7

o o 6 o 6 o o

NC

poo ood ooo ooo ooo ooo oop ooo

NO COM

GND

Power

Supply +5 VDC

To Computer

66 66 66 66 66 66

0 0 o b~ o 5 o J o

NC NO

To Solenoids

Electro- mechanical

Relays

AC Relays

AC

GND

Figure 3.6 Electrical connections for the electro-mechanical relays and the AC relays.

16
Separate power supplies provide the dc voltages needed by the photodiode

amplifier and the electro-mechanical relays, while a temperature controller maintains the photodiode at a constant temperature. A digital voltmeter measures the signal from the photodiode amplifier.

4. Characterization of Instrument The instrument was thoroughly characterized not only to ensure proper operation

but also to verify compliance with the applicable standards for measuring transmission

density [2,3,4]. These standards specify both the geometrical and spectral conditions for

this measurement. The characterization is detailed for the source and detector systems and for the step tablet films. The relative spectral flux distribution of the source, denoted by SH, is specified in

[4]. This distribution depends upon the opal, infrared optical filter, and current through

the lamp. With the type of opal, lamp, and filter fixed, as well as the thickness of the

filter, the only adjustable parameter is the current. Therefore, the optimal current to achieve a close approximation of SH was determined experimentally. The relative spectral flux distribution of the source at different lamp currents was

measured by a spectroradiometer in the Low-Level Radiance facility [6]. The source system was placed on its side so that the opal was imaged onto the entrance slit of the monochromator. The spectral radiant flux emerging from the exit slit of the monochromator was measured with a Si photodiode. The spectral radiance responsivity of the spectroradiometer - imaging optics, monochromator, and photodiode - was

determined by measuring the signal S£A) when the output port of an integrating sphere with known radiance LS (X) was imaged onto the monochromator entrance slit. The signal from the opal S0(X) was then measured for different lamp currents. The radiance of the opal L0{X) was calculated using

(4' 1}

and normalized to have a value of 100 at 560 nm to compare with Su

. The best agreement between Sn and the measured relative spectral flux

distribution was obtained with a lamp current of 7.8 A. These two distributions are shown as a function of wavelength in figure 4.1, with the distribution of the instrument denoted by Sv This distribution was relatively insensitive to changes in lamp current of

0.1 A. For greater changes in current, the measured distribution at wavelengths less than 600 nm was either obviously greater or less than <SH

for increased or decreased currents, respectively. Since the lamp power supply maintains a constant current to within 1 mA,

the distribution Sl is not expected to change during measurements of step tablet films.

17
500 600

Wavelength [nm]

Figure 4.1 Relative flux distribution specified by the standards, SH, and achieved by

the instrument at a lamp current of 7.8 A, Sb as a function of wavelength.

The spectral reflectance p0{X) is specified to be 0.55 ± 0.05 [4]. The 6° - hemispherical reflectance of flash opals of the same type used in the instrument was

measured in the Spectral Tri-function Automated Reference Reflectometer facility [7]. A

flash opal with a diameter of 6 mm was mounted in the vacuum plate of the source

system, which was then placed at the sample port of the integrating sphere of the

reflectometer. A converging lens reduced the monochromatic incident beam diameter to approximately 4 mm. Since this diameter was larger than the 3 mm diameter of the opal used in the instrument, a 6 mm diameter opal was measured instead. The angle of

incidence of the beam on the opal was 6°, and both the specular and diffuse components

of reflection were included in the integrating sphere. The radiant flux at the detector port of the integrating sphere was measured with a Si photodiode. At each wavelength of the incident beam, the signal from reflection from the opal S0{%) and the signal from

reflection from the integrating sphere wall SW(A) were measured. Since the spectral reflectance of the wall pw(/l) is known, the spectral reflectance of the opal p0(X) is calculated from

(A) (4.2)

The reflectance of a flash opal as a function of wavelength is shown in figure 4.2. The reflectance of all three 6 mm diameter opals cut from the same large piece were the same, and this reflectance is expected to apply to the 3 mm diameter opal used in the

18
0.65

0.50 1 1 1 1 1 300 400 500 600 700 800 Wavelength [nm]

Figure 4.2 6° - hemispherical reflectance of the opal as a function of wavelength.

instrument. The reflectance decreases monotonically with wavelength and is within the values specified by the standard for wavelengths longer than 490 nm. The effect of this discrepancy between the actual opal reflectance and the standard reflectance is discussed

in section 6. The diffusion coefficient d of the opal is specified to be greater than or equal to 0.9 [4]. The radiant flux from the opal was measured as a function of polar angle fusing

the bi-directional reflectance goniometer of the Spectral Tri-function Automated

Reference Reflectometer facility [7]. The entire source system was placed on its side so

that the opal was centered in the sample holder of the goniometer and the face of the opal was on the axis of rotation of the detector arm. The lamp was operated at a current of 7.8 A and water was circulated through the lamp housing and water filter. A green filter was

placed in front of the Si photodiode on the detector arm to simulate the spectral conditions of the transmission density instrument detector system. The signal S(0) was measured at polar angles of the detector from -80° to +80° in 5° steps. The signals were normalized by the signal at 0°, S(0), to yield s(9). These U6)

normalized signals are proportional to the factor —— cos# in eq (2.30). The

Lj(U) normalized signal, divided by cos 0, as a function of polar angle is shown in figure 4.3. For an ideal, Lambertian diffuser, this ratio is one at all angles. The decrease of this ratio

19
1.1

Angle [deg]

Figure 4.3 Normalized signal of the efflux from the opal divided by the cosing of the angle as a function of angle.

as the angle increases indicates that the opal is not an ideal diffuser. There are two

methods for calculating the diffusion coefficient. The first is given in [4],

^ = ^4, (4.3) 2^ cos 6?

where the summation is over all the angles at which signals were measured. The second method is adapted from eq (2.30), which was originally derived in [5], and is given by

d= £ p p

- (4 - 4)

The diffusion coefficient calculated using eq (4.3) is d = 0.95, while using eq (4.4) d = 0.91 . Both of these values are greater than 0.90. The spectral response of the detector system VT

is specified in [4] and is given by

eq (2.3), namely

(4.5)

20
Here, SA

is the relative spectral flux distribution of Illuminant A, Vx is the photopic

spectral luminous efficiency function, and SH

is the relative spectral flux distribution specified in [4]. The spectral response of the detector system is the product of the

spectral responsivity of the photodiode and the transmittance of the filter, as indicated in eq (2.17). The transmittance of the lenses is not included since it is constant with wavelength in the visible spectral region for BK-7 glass. The spectral responsivity of the Si photodiode was measured in the Spectral Comparator Facility [8]. Monochromatic, collimated light was incident on a calibrated detector with spectral responsivity RC{X) yielding a signal SC (X). This light was then

incident on the photodiode, yielding a signal S{X). Assuming the same incident spectral radiant flux, the spectral responsivity of the photodiode R(X) is given by

W= 777;-W • (4-6)

The transmittance of the filter was measured in the Regular Spectral Transmittance

facility [9]. The signals of a Si photodiode from a collimated, monochromatic beam with and without the photopic filter present in the beam are S£A) and S(A), respectively. The

transmittance t^A) of the photopic filter is then •xa-fg. (4.7)

The spectral response of the detector system, normalized by its value at 550 nm

and denoted by Vbis shown as a function of wavelength in figure 4.4, along with the

specified spectral response VT. There is an obvious discrepancy between the two spectral responses for wavelengths longer than 570 nm. However, Vl closely approximates Vx, which is expected since the filter was designed so that the spectral response obtained in combination with the Si photodiode is Vx

. Because the photopic spectral luminous

efficiency function is widely used, and because no filter could be readily found to modify

Vl to VT, no attempt was made to obtain VT

. The effect of the discrepancy between VT and Vx is discussed in section 6. To use eq (2.22) to calculate transmission density from the signals and gains, the

linearity of the photodiode and the ratio of gains GT / G} must be determined accurately. The linearity of the photodiode-amplifier combination was measured in the Beamconjoiner facility [10]. This facility uses the beam addition method with sets of

filters on each beam path to automatically vary the radiant flux on the detector by three decades. The source system of the transmission density instrument provided the input

flux. The linearity was determined at each gain setting of the amplifier, the maximum

radiant flux incident on the detector being controlled by the lamp current and neutral- density filters in front of the photodiode. The relative responsivity, defined as the ratio of

the measured signal to the incident radiant flux as a function of current from the photodiode is shown in figure 4.5 at several gain settings. A relative responsivity of one

21
1.2

1.0 - I 0.8 -

>

0.0

0.2 -

350 450 550

Wavelength [nm]

650 75

Figure 4.4 Relative responsivity specified by the standard, VT, and achieved by the photopic filter and photodiode of the instrument, Vh

as a function of

wavelength.

corresponds to ideal linearity. The relative responsivity of the photodiode - amplifier combination is very close to one for gain settings 5 to 8. Deviations from one occur at gain setting 9, mostly due to the small currents at this gain setting. The gain setting of the amplifier is the nominal power of ten by which the current from the photodiode is multiplied to convert it to an output voltage. For example, at a

gain setting of 7 the gain is 107 V/A. From eq (2.22), the ratios of gains are required, not

the actual gains. These were determined using a constant current source in place of the photodiode as the input to the amplifier and a voltmeter to measure the output signal. At

each gain setting, the current was set to obtain a 10 V signal and then reduced in ten steps

to obtain 1 V and then by another ten steps to obtain 0.1 V. The output signal was

measured at each current. Since this procedure yielded currents that were common for successive gain settings, the average of the ratio of the signals at the same currents was

the gain ratio. For example, currents from 0. 1 uA to 1 uA yielded voltages from 1 V to 10 V at a gain setting of 7, while the same currents resulted in voltages from 0.1 V to 1 V

at a gain setting of 6. The measured gain ratios for successive gain settings are given in table 4.1, where the gain settings are denoted by subscripts on the gain G. Note that the gain ratios are not exactly ten. The spectral transmittance and reflectance of the film step tablets are parameters

in eq (2.23). These properties were therefore measured for both the SRM 1001 and 1008

22
1.015

1.010 :

0.980

* 1 1 0.0001 0.001 0.01 0.1 1 10 100 100

Current [uA]

Figure 4.5 Relative responsivity (measured signal divided by actual flux) of the photodiode and amplifier as a function of current at the indicated gain

settings.

step tablets at the step with the lowest transmission density. This is the step that is not exposed during processing and so is representative of the properties of the base film. The

regular transmittance and directional - hemispherical reflectance were measured using a commercial Varian-Cary 5E spectrophotometer. The transmittance and reflectance as a

function of wavelength are shown in figure 4.6 for both the SRM 1001 x-ray film step

tablets and the SRM 1008 photographic film step tablets. There is spectral structure in these properties for the x-ray film, giving it a blue tint, while the neutral photographic

Table 4.1 Values of successive gain ratios

Gain Ratio Value Relative Standard Uncertainty

G 5 /G 4 10.00032 4.13 x

10"* G 6 /G 5 10.00493 6.31 xlO"5 G 7 /G 6 10.00311 4.62 xlO"5 G 8 /G 7 10.00098 5.29 xlO 5 G 9 /G 8 9.97574 1.09 xlO"5 G 10 / G 9 10.01515 2.36 xlO"4

23
300 400 500 600 700 800

Wavelength [nm]

Figure 4.6 Reflectance and transmittance of the indicated films as a function of

wavelength.

film has no such spectral structure.

Several other geometrical conditions are specified by [3] in addition to the

diffusion coefficient of the opal. The half-angle of the acceptance cone must be less than

24
10°. From the description of the lens system in the previous section, the half-angle of the instrument is 9.5°. The film must be in contact with the opal when the efflux is measured, which is achieved by pulling the film onto the opal with a vacuum. The transmission density is to be measured at the center of each step. Centering

the steps on the opal is accomplished by optical means in the transverse direction of the

steps and by mechanical means in the longitudinal direction. Note that the transverse

direction of a step corresponds to the longitudinal direction of the film step tablet. The

step widths are equal for each type of film and the position along the longitudinal

direction of the film in continuously adjustable with the horizontal translation stage. Therefore, all that is required to center the opal in the transverse direction of each step is to determine the location of a reference position on each film. This is done by measuring

the signal from the opal as the film is moved in the longitudinal direction in increments of

0.08 mm from the first to the second step. The signal decreases at the boundary between

the steps; the location at which the signal has decreased by 5 % from its value in the first step is the reference position. Knowing this position sets the locations of the centers of

each step along their transverse direction. The center along the longitudinal direction is set mechanically. The positions of the horizontal translation stage and the film holder are adjusted so that the film holder is centered on the opal over its entire length. This fixes the positions of the stage and holder. The posts on the film tray are then adjusted to give

the minimum possible clearance between them and the film holder. This centers the films

in the tray and thereby the longitudinal direction of the steps. The instrument was designed to measure diffuse visual transmission density

according to spectral and geometrical conditions specified by the applicable standards. The conditions are satisfied by the instrument, with the exception of the opal reflectance and the spectral response. The effects of these discrepancies between the standards and

the instrument are detailed in section 6.

5. Operation of Instrument The instrument automatically measures the transmission density of each step of a batch of step tablet films. The setup for the measurements is fairly simple. The films are loaded into the film holder in the order in which they are to be measured, with the serial numbers face-down so that the correct side of the film will be in contact with the opal. The serial numbers of the films are entered in a separate text file, which is used by the program during the measurements to keep track of the films. The digital voltmeter is setup to auto-zero and to use ten power line cycles for each reading. The lamp is operated at 7.8 A for a 30 minute warm-up period, the room lights are turned off, and the measurements are begun. For each film, the film holder is moved horizontally over the film tray and then

vertically until the holder is in contact with a film. The vertical spring-loaded stage allows the film holder to remain stationary and in contact with the film while the vertical translation stage continues to move downward, preventing unnecessary torques on the

holder. The vacuum is applied, attaching the film to the holder. The signal from the

25
aperture flux is measured at a gain setting of 5 by closing the shutter, recording five readings from the voltmeter, opening the shutter, and recording five more readings. The

signals measured with the shutter closed are referred to as dark signals. The holder is then translated vertically and horizontally until the first step of the film is 1 .6 mm above

the opal. The signal is measured to verify that a film is attached to the film holder; if not, the process is repeated until a film is attached. The boundary between the first and

second steps is found, as described in the previous section. This sets the location of the horizontal translation stage so that the centers of the steps are measured. To measure the signal from the transmitted flux of a step, the film is moved

horizontally to center the step on the opal, the film is lowered until it is on top of the opal, and a vacuum is applied with the vacuum plate while the vacuum on the film holder is released. This pulls the film into close contact with the opal, and five readings from the voltmeter are recorded. A vacuum is applied to the film holder while it is released from

the vacuum plate, which attaches the film to the holder. The holder is then raised and the process is repeated for the next step. If the signal from a step is less than 1 .3 V, the gain

setting for the next step is increased by one and a dark signal is measured prior to measuring the signal from the transmitted flux. After the last step is measured, the film is moved over the other film tray, the vacuum on the film holder is released and air is introduced into the line, and the film falls onto the tray. The signal from the aperture flux

is then measured as before. The transmission density is calculated from the signals and ratios of the gain

settings. Each set of five signal readings are averaged, and the dark signals at each gain

setting are subtracted from those signals obtained at that setting to yield the net signals. The two net signals for the aperture flux are averaged to yield the final aperture signal Sy For each step, the transmission density is calculated using eq (2.22),

where ST is the net signal from the transmitted flux at each step and GT / G} is the gain

ratio. The signal from the aperture flux is approximately 1.5 V on gain setting 5. For Dt= 4, this corresponds to a signal of 1.5 V at gain setting 9. Therefore, only gain

Table 5.1 Values of the gain ratios used to calculate transmission density

(5.1)

Gain Ratio Value Relative Standard Uncertainty

G 6 /G 5 G 7 /G 5 GJG 5 G 9 /G 51.000 493x 10* 1.000 804 x 102 1.000 903 xlO3 0.998 475 xlO4

6.31x10"

7.82x10-'

9.44 x 10" 9.50x101-5

26
settings 5 to 9 are used for calibrating the SRMs. The gain ratios, relative to gain setting

5, are listed in table 5.1, along with the relative standard uncertainties. A batch of films is measured on three separate occasions in both ascending and

descending serial number order. The average of the three determinations is reported on

the calibration certificate as the transmission density of a step. The standard deviation of

the three determinations must be less than the expanded uncertainty due to random

effects, detailed in the next section. Sample calibration certificates are given in Appendices A and B. Proper operation of the instrument is verified by including in each

batch several check standard films that were measured previously. These check standard

films were randomly chosen from each lot of films received from the manufacturer.

6. Uncertainties Each measurement of transmission density has an uncertainty associated with it. This section details the components of uncertainty, their evaluation, and the resulting uncertainty in transmission density. This uncertainty analysis follows the guidelines

given in [11].

In general, the purpose of a measurement is to determine the value of a measurand

y, which is obtained from n other quantities Xj through the functional relationship/ given

by

y=J[xx ,x2 ,...,Xj,...,xn). (6.1) The standard uncertainty of an input quantity Xj is the estimated standard deviation

associated with this quantity and is denoted by u(xf). The relative standard uncertainty is given by u(xi) / Xj. The standard uncertainties may be classified either by the effect of

their source or by their method of evaluation. The effects are either random or

systematic, the former arising from stochastic temporal or spatial variations in the measurement and the later from recognized effects on a measurement. The method of

evaluation is either Type A, which is based on statistical analysis, or Type B, which is based on other means. To first order, the estimated standard uncertainty u(y) in the measurand due to a

standard uncertainty w(jc/) is

u(y) = ^-u(Xi), (6.2)

where df I dxi is the sensitivity coefficient. The combined standard uncertainty uc(y) in the measurand is the root-sum-square of the standard uncertainties associated with each

quantity x/, assuming that these standard uncertainties are uncorrelated. The expanded

uncertainty U is given by k-uc(y), where k is the coverage factor and is chosen on the basis of the desired level of confidence to be associated with the interval defined by U. For

27
these SRMs, k = 3, which defines an interval having a level of confidence of

approximately 99.73 %. While a coverage factor k = 2 is customary for the expanded

uncertainty [1 1], the larger coverage factor maintains consistency with previous SRMs of

these types and is accepted by users because of the use of the SRMs in the areas of health and safety. The components of uncertainty for transmission density are conveniently divided

into those arising from the signal measurements, the uniformity of each step, and

agreement with the appropriate standards [3,4]. In the first case, the appropriate measurement equation is eq (2.22), while for the last case eqs (2.23) and (2.31) are

applicable. Expressing eq (2.22) as

Z>T = log 10(x) (6.3) where x can be a signal or the gain ratio, the sensitivity coefficient is ^= 0.434- i. (6.4) 3c x

Therefore, the standard uncertainty u(DT) due to the standard uncertainty u{x) is

W(Z>r) = 0.434 . (6.5) x Note that the standard uncertainty of DT

is proportional to the relative standard

uncertainty of x. There are several components of uncertainty associated with calculating transmission density from eq (2.22), which assumes that the signals are directly proportional to the fluxes. In addition, the same influx is assumed when measuring S} and Sx

. These components are the accuracy of the digital voltmeter, signal noise, lamp

stability, detector linearity, and the gain ratio. The uncertainty arising from the accuracy of the digital voltmeter is a systematic

effect with a Type B evaluation and assuming a normal probability distribution. Using

the manufacturer's specifications, the relative standard uncertainty of 5j is 23 x 10"6

, while the maximum relative standard uncertainty of is 77 x 10

-6

. The combined

relative standard uncertainty of S} I ST is therefore 80 x lO^

6 which, using eq (6.5), results in a standard uncertainty u(DT) «0.001

Signal noise and lamp stability result in uncertainties from random effects with Type A evaluations. A typical relative standard deviation of the signal calculated from

measurements of ten different films is 0.002, which results in a standard uncertainty

u(DT)= 0.001. Likewise, a typical relative standard deviation of the signal from the aperture flux monitored over a period of 15 min is 0.002.

28
The uncertainties arising from the detector linearity and the gain ratio are systematic effects with Type A evaluations. The signals are always between 0.1 V and

12 V at each gain setting, except for gain setting 9, for which the minimum signal is 1 V. The maximum relative standard deviation of the relative responsivity of the photodiode - amplifier combination, subject to the ranges of the signals, is 0.0028, resulting in a

standard uncertainty u(DT) = 0.001. The relative standard uncertainties for the gain ratios are given in table 5.1, resulting in a standard uncertainty u(DT) < 0.001. The transmission density is supposed to be determined at the center of each step. However, if the transmission density of a step is not uniform, an uncertainty in centering

the opal results in an uncertainty in the measured transmission density. The standard

uncertainty in centering the opal along the transverse direction of a step depends upon

finding the boundary between the first and second steps of a film and knowing the spacing between the centers of the steps, and is 0.5 mm. The standard uncertainty for the longitudinal direction depends upon the mechanical adjustments of the film holder and

the posts on the film tray so that the transverse direction of the film is centered on the opal along the entire length of the film. The standard uncertainty in centering in this dimension is 1 mm.

The uniformity of the transmission densities of the steps of five representative films of each type of SRM was determined by measuring the transmission density every

0.17 mm along three lines running the length of each film. One line was centered along

the width of the films, the other two were displaced by -1.5 mm and +1.5 mm from the center line. All the transmission densities varied by much less than 0.001 within 0.5 mm

of the center in the transverse direction of the steps and by approximately 0.001 within

1 mm of the center in the longitudinal direction. Therefore, the standard uncertainty

u{DT) due to the uniformity of the steps is 0.001

As mentioned in section 4, neither the opal reflectance nor the spectral product are

in agreement with the standards specified in [4]. The uncertainties arising from these two

components are systematic effects evaluated using Type B methods and a normal

probability distribution. The standard uncertainties are estimated from eq (2.23) using

the measured transmittance rs(A) and reflectance ps {X) of the films and separating the

effects of the two components by assuming either an ideal spectral product or opal

reflectance. The diffusion coefficient <i = 0.91 is within the range of values specified in [3]. Therefore, the standard uncertainty arising from this component is less than 0.001. However, instruments using opals with different diffusion coefficients could measure

significantly different transmission densities. Using eq (2.31), the difference in transmission density ADT due to different diffusion coefficients is

(6.6)

29
where d0 is the diffusion coefficient of the opal used in this instrument and d is the

diffusion coefficient of another instrument. From [3], the minimum acceptable value of d

is 0.9, while from [5] the physically maximum value is 0.95. Therefore, from eq (6.6) ADT can range from +0.005 to -0.019. As shown in figure 4.2, the opal reflectance p0(X) is greater than the acceptable

maximum of 0.6 [4] for wavelengths shorter than 490 nm. The standard uncertainty

u(DT) is estimated from eq (2.23) by calculating DT for different values of p0 (X) using

Dy = log, TAX)

p0 (X)-ps (X) VT (X)-dX

(6.7)

Values of DT for different opal reflectances and both types of films are given in table 6.1. Since the transmission densities calculated using the actual opal reflectance are within the ranges obtained from the acceptable opal reflectances, the standard uncertainty u(DT) associated with the opal reflectance is less than 0.001.

Table 6.1 Calculated values of transmission density for both types of step tablet films at various opal reflectances

Opal Reflectance

Step Tablet Film X-Ray (SRM 1001) Photographic (SRM 1008)

0.50 0.173 0.121

0.55 0.172 0.118

0.60 0.171 0.117

actual 0.171 0.118

Finally, the spectral product of the instrument Sx Vl is not Su

• VT, but approximately SH Vx since the spectral response of the detector is nearly the photopic spectral luminous efficiency function. The standard uncertainty u(Dr) is estimated from eq (2.33) by calculating the transmission densities obtained with the ideal and actual spectral products, using the ideal opal reflectance p0(X) = 0.55. The difference in transmission

density ADXis given by

30
ADy = log10 J^(A)-F!(A)-dA

1- 0.55 -ps (A) J

(6.8)

-logio

J^(A)-FT (A)-dA

1-0.55-^(1)

•FT (^)-dA

Using eq (6.8), AZ)T = 0.000 282 and 0.000 002 for the x-ray and photographic films, respectively. This results in a standard uncertainty u(DT) < 0.001 for both types of films. Since the reflectance and transmittance of the photographic films are relatively constant over the wavelength range for which the spectral product is appreciable, AZ)T

is expected

to be nearly zero for these films. The standard uncertainty u{DT) resulting from each component of uncertainty is given in table 6.2, along with the combined and expanded uncertainties for each SRM.

The only components that contribute to the combined uncertainty are the signal noise, lamp stability, detector linearity, and step uniformity, all of which except the detector

linearity are caused by random effects. The expanded uncertainty from these random

effects is 0.005. Therefore, as mentioned at the end of the previous section, the standard

deviation of the three determinations of the transmission densities of a step must be less than 0.005 to accept the average as the reported transmission density of the step. Otherwise, the instrument is assumed to have malfunctioned in some manner during one

of the runs and the film is measured again. Note that even though the opal reflectance and the spectral product do not comply with those specified in the standards [4], the

resulting standard uncertainty in transmission density is less than 0.001 in both cases.

6. Conclusions The instrument detailed in this Special Publication measures the diffuse visual transmission density of both x-ray film (SRM 1001) and photographic film (SRM 1008)

step tablets using the diffuse influx mode. It is fully automated so that many films can be measured in one batch run. Comprehensive characterizations of the instrument were

performed to ensure that it complies with the relevant international standards for these measurements. The expanded uncertainty (k = 3) for transmission density is 0.006. Acknowledgments

Funding for the diffuse transmission densitometer was provided by the Standard Reference Materials Program under the direction of Nancy Trahey. Design, construction, and characterization of the diffuse transmission densitometer benefited from the efforts of

Daniel Dummer, Christopher Cromer, and Xiaxiong Xiong, all of the Optical Technology

31
Division, and from discussions with Michael Goodwin and Philip Wychorski of the Eastman Kodak Co.

Table 6.2 Components of uncertainty and the resulting standard uncertainties in transmission density

Component of

Uncertainty Effecta) Typeb) Standard

Uncertainty u(DT) Voltmeter Accuracy

Signal Noise Lamp Stability Detector Linearity

Gain Ratio Step Uniformity

X-Ray Film

Photographic Film

Diffusion Coefficient Opal Reflectance X-Ray Film

Photographic Film

Spectral Product X-Ray Film

Photographic Film

«0.001 0.001

0.001

0.001 «0.001

0.001

0.001 < 0.001

< 0.001 < 0.001

< 0.001 « 0.001

Combined Uncertainty uc(Dr) X-Ray Film (SRM 1001)

Photographic Film (SRM 1008) Expanded Uncertainty U (k = 3) X-Ray Film (SRM 1001)

Photographic Film (SRM 1008)

0.002 0.002

0.006

0.006

a) R = random, S = systematic

b) A = Type A evaluation, B = Type B evaluation

32
References

[I] C. S. McCamy, " Concepts, Terminology, and Notation for Optical Modulation,"

Photogr. Sci. Eng. 10, 314 (1966).

[2] ISO 5-1 : Photography - Density Measurements - Part 1 : Terms, Symbols, and

Notations (1984).

[3] ISO 5-2: Photography - Density Measurements - Part 2: Geometric Conditions for Transmission Density (1991).

[4] ISO 5-3 : Photography - Density Measurements - Part 3 : Spectral Conditions

(1984).

[5] E. Buhr, D. Hoeshen, and D. Bergmann, "The Measurement of Diffuse Optical

Densities. Part I: The Diffusion Coefficient," J. Imag. Sci. and Technol. 39, 453

(1995).

[6] James H. Walker and Ambler Thompson, " Spectral Radiance of a Large-Area

Integrating Sphere Source," J. Res. Natl. Inst. Stand. Technol. 100, 37 (1995).

[7] P. Yvonne Barnes, Edward A. Early, and Albert C. Parr, "NIST Measurement

Services: Spectral Reflectance," Natl. Inst. Stand. Technol., Spec. Publ. 250-48

(1998).

[8] Thomas C. Larason, Sally S. Bruce, and Albert C. Parr, "NIST Measurement

Services: Spectroradiometric Detector Measurements: Parts I and II - Ultraviolet and Visible to Near Infrared Detectors," Natl. Inst. Stand. Technol., Spec. Publ. 250-41 (1997).

[9] Kenneth L. Eckerle, Jack J. Hsia, Klaus D. Mielenz, and Victor R. Weidner,

"Regular Spectral Transmittance," Natl. Bur. Stand. (U.S.), Spec. Publ. 250-6

(1986).

[10] Ambler Thompson and How-More Chen, "Beamcon III, a Linearity Measurement

Instrument for Optical Detectors," J. Res. Natl. Inst. Stand. Technol. 99, 751

(1994).

[I I] Barry N. Taylor and Chris E. Kuyatt, " Guidelines for Evaluating and Expressing

the Uncertainty of NIST Measurement Results," Natl. Inst. Stand. Technol., Tech. Note 1297 (1994).

33

Appendix A

Certificate

Standard Reference Material® 1001

X-Ray Film Step Tablet

This Standard Reference Material (SRM) is intended for use in the calibration of optical densitometers and similar equipment used in the photographic, graphic arts, and x-ray fields. SRM 1001 is a double emulsion x-ray film step

tablet 25.4 cm (10 in) long by 3.5 cm (1.375 in) wide. The tablet has 17 steps 1.3 cm (0.5 in) wide perpendicular to the long edge of the film with certified transmission densities ranging from less than 0.200 to greater than 4.000. The

serial number is located at one end of the step tablet. Determination of Certified Transmission Density: The transmission density of each step of the tablet was measured

using the NIST Diffuse Transmittance Densitometer [1]. The instrument and measurements conform to the conditions specified for American National Standard Diffuse Visual Transmission Density, Dr (90° Opal; SH

: ^ 10°; Vr), in [2,3]. The certified transmission densities listed in Table 2 were measured on a 3 mm diameter circle at the center of each step, and apply only to that area. When measured, the side of the tablet with the serial number was in contact with the diffuser of the densitometer.

Expiration of Certification: The certification of this SRM is deemed to be valid, within the uncertainties specified,

for a period of two years from the calibration date given in Table 2, provided the SRM is stored and handled in accordance with the Instructions for Use and Storage and Handling sections of this certificate. However, certification

will be nullified if the SRM is damaged or contaminated.

Discussion of Uncertainties: Uncertainties were calculated according to the procedures outlined in [4]. Measured

(Type A) uncertainties were assumed to be Gaussian-distributed, and were calculated from the standard deviations. Estimated or inferred (Type B) uncertainties were also assumed to be Gaussian-distributed, and were calculated from

the measurement equation. The uncertainties were combined by adding their variances in quadrature. Table 1 is a

list of all identifiable sources of uncertainty. The measured standard deviations are listed in (a), the inferred standard

deviations are listed in (b).

Instructions for Use: Remove the film from its protective sleeve and place the center of a step on the diffuser of the densitometer to be calibrated, with the side of the step tablet with the serial number in contact with the diffuser. Calibrate the densitometer using the transmission density of that step, and repeat this procedure with other steps of the step tablet. Film step tablets were produced by the Bayer Corporation, AGFA division, Ridgefield Park, NJ. The technical direction and physical measurements leading to certification were provided by E.A. Early with

assistance from C.L. Cromer, D. Dummer, T.R. O'Brian, X. Xiong, and R.D. Saunders of the NIST Optical Technology Division and P.F. Wychorski of the Eastman Kodak Co. The support aspects involved in the preparation, certification, and issuance of this SRM were coordinated through the Standard Reference Materials Program by N.M. Trahey and R.J. Gettings.

Gaithersburg, MD 20899 Thomas E. Gills, Chief

Certificate Issue Date: 14 October 1997 Standard Reference Materials Program

SRM 1001 Page 1 of 3
Storage and Handling: The densities of this x-ray film step tablet may change with time. To minimize such

changes, the film should be stored in a cool, dry place, where it will not be exposed to light, or other radiant energy, or to chemical fumes, or to dust in the air. Scratches, abrasion marks, or foreign matter on the film can change the density. Fingerprints are a common source of contamination. Fingerprints on the film surfaces can be avoided by

handling the step tablet only by the edges and by wearing clean cloth gloves available from photographic film dealers

for this purpose. Any attempt to clean a film step tablet, other than to remove dust with a soft camel-hair brush, is not recommended as it is likely to alter the certified values.

Table 1 . Tabulation of Uncertainties Source of Uncertainty Uncertainty in Transmission Density

(a) Measured (Type A) Uncertainties Source Stability ± 0.001

Signal Noise ± 0.001

Amplifier Gain < < 0.001

Detector Linearity ± 0.001

Step Uniformity ± 0.001

(b) Inferred (Type B) Uncertainties Voltmeter Accuracy < < 0.001

Diffusion Coefficient < 0.001 Opal Reflectance < 0.001

Spectral Product < 0.001

Combined Uncertainty (la) ± 0.002 Expanded Uncertainty (3a) ± 0.006 REFERENCES

[1] Early, E.A., O'Brian, T.R., and Saunders, R.D., "Diffuse Transmission Densitometer," SP 260-xxx, In Press.

[2] ANSI/ISO 5.2-1991, Photography - Density Measurements - Part 2: Geometric Conditions for Transmission Density.

[3] ANSI/ISO 5.3-1995, Photography - Density Measurements - Part 3: Spectral Conditions.

[4] Guide to the Expression of Uncertainty in Measurement, ISBN 92-67-10188-9, 1st Ed. ISO, Geneva,

Switzerland, (1993): see also 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).

It is the responsibility of users of this SRM to assure that the certificate in their possession is current. This can be accomplished by contacting the SRM Program at: Phone: (301) 975-6776 (select Certificates), Fax: (301) 926-

4751, e-mail: srminfo@nist.gov, or WWW: http://ts.nist.gov/srm.

SRM 1001 Page 2 of 3
Table 2. Transmission Densities of SRM 1001

Serial No.: 9701000 Calibration Date: 13 June 1998

Step Number Transmission Density

a)

1 0.136 2 0.236

3 0.476 4 0.714

5 0.953

6 1.199

7 1.429

8 1.681 9 1.920

10 2.155

11 2.401

12 2.683

13 2.914

14 3.170

15 3.428

16 3.686

17 3.979

a)Expanded uncertainty (k = 3) of the transmission density of each step is ± 0.006

(see Table 1).

SRM 1001 Page 3 of 3

Appendix B

(Ezxtxiitzctt

Standard Reference Material® 1008

Photographic Film Step Tablet

This Standard Reference Material (SRM) is intended for use in the calibration of optical densitometers and similar equipment used in the photographic, graphic arts, and x-ray fields. SRM 1008 is a photographic silver density film

step tablet 25.4 cm (10 in) long by 3.5 cm (1.375 in) wide. The tablet has 23 steps 1.0 cm (0.39 in) wide

perpendicular to the long edge of the film with certified transmission densities ranging from less than 0.200 to greater than 4.000. The serial number is located at one end of the step tablet. Determination of Certified Transmission Density: The transmission density of each step of the tablet was

measured using the NIST Diffuse Transmirtance Densitometer [1]. The instrument and measurements conform to the conditions specified for American National Standard Diffuse Visual Transmission Density, Dr (90° Opal; SH: < 10°; Vr), in References [2,3]. The certified transmission densities listed in Table 2 were measured on a 3 mm diameter

circle at the center of each step, and apply only to that area. When measured, the side of the tablet with the serial number was in contact with the diffuser of the densitometer. Expiration of Certification: The certification of this SRM is deemed to be valid, within the uncertainties specified,

for a period of two years from the calibration date given in Table 2, provided the SRM is stored and handled in accordance with the Instructions for Use and Storage and Handling sections of this certificate. However, certification will be nullified if the SRM is damaged or contaminated.

Discussion of Uncertainties: Uncertainties were calculated according to the procedures outlined in [4] . Measured

(Type A) uncertainties were assumed to be Gaussian-distributed, and were calculated from the standard deviations. Estimated or inferred (Type B) uncertainties were also assumed to be Gaussian-distributed, and were calculated from

the measurement equation. The uncertainties were combined by adding their variances in quadrature. Table 1 is a

list of all identifiable sources of uncertainty. The measured standard deviations are listed in (a), the inferred standard

deviations are listed in (b).

Instructions for Use: Remove the film from its protective sleeve and place the center of a step on the diffuser of the densitometer to be calibrated, with the side of the step tablet with the serial number in contact with the diffuser. Calibrate the densitometer using the transmission density of that step, and repeat this procedure with other steps of the

step tablet. Film step tablets were produced by the Bayer Corporation, AGFA division, Ridgefield Park, NJ. The technical direction and physical measurements leading to certification were provided by E.A. Early with

assistance from C.L. Cromer, D. Dummer, T.R. O'Brian, X. Xiong, and R.D. Saunders of the NIST Optical Technology Division and P.F. Wychorski of the Eastman Kodak Co. The support aspects involved in the preparation, certification, and issuance of this SRM were coordinated through the Standard Reference Materials Program by N.M. Trahey and R.J. Gettings.

Gaithersburg, MD 20899 Thomas E. Gills, Chief

Certificate Issue Date: 27 February 1998 Standard Reference Materials Program

SRM 1008 Page 1 of 3
Storage and Handling: The densities of this photographic film step tablet may change with time. To minimize such

changes, the film should be stored in a cool, dry place, where it will not be exposed to light, or other radiant energy, or to chemical fumes, or to dust in the air. Scratches, abrasion marks, or foreign matter on the film can change the density. Fingerprints are a common source of contamination. Fingerprints on the film surfaces can be avoided by

handling the step tablet only by the edges and by wearing clean cloth gloves available from photographic film dealers

for this purpose. Any attempt to clean a film step tablet, other than to remove dust with a soft camel-hair brush, is not recommended as it is likely to change the densities.

Table 1 . Tabulation of Uncertainties Source of Uncertainty Uncertainty in Transmission Density

(a) Measured (Type A) Uncertainties Source Stability ± 0.001

Signal Noise ± 0.001

Amplifier Gain < < 0.001

Detector Linearity ± 0.001

Step Uniformity ± 0.001

(b) Inferred (Type B) Uncertainties Voltmeter Accuracy < < 0.001

Diffusion Coefficient < 0.001 Opal Reflectance < 0.001

Spectral Product < < 0.001

Combined Uncertainty (la) ± 0.002 Expanded Uncertainty (3a) ± 0.006 REFERENCES

[1] Early, E.A., O'Brian, T.R., and Saunders, R.D., "Diffuse Transmission Densitometer," SP 260-xxx, In Press.

[2] ANSI/ISO 5.2-1991, Photography - Density Measurements - Part 2: Geometric Conditions for Transmission

Density.

[3] ANSI/ISO 5.3-1995, Photography - Density Measurements - Part 3: Spectral Conditions.

[4] Guide to the Expression of Uncertainty in Measurement, ISBN 92-67-10188-9, 1st Ed. ISO, Geneva,

Switzerland, (1993): see also 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).

It is the responsibility of users of this SRM to assure that the certificate in their possession is current. This can be

accomplished by contacting the SRM Program at: Phone (301) 975-6776 (select "Certificates"), Fax (301) 926-4751,

e-mail srminfo@nist.gov, or via the Internet http://ts.nist.gov/srm. SRM 1008 Page 2 of 3
Table 2. Transmission Densities of SRM 1008

Serial No.: 9708000 Calibration Date: 13 June 1998

Step Number Transmission Density

a)

1 0.057 2 0.191

3 0.394 4 0.600

5 0.793

6 0.996

7 1.201 8 1.403 9 1.601 10 1.793

11 2.018

12 2.215

13 2.419

14 2.610

15 2.818

16 3.020

17 3.213

18 3.405 19 3.616 20 3.824

21 4.031 22 4.205 23 4.346

a)Expanded uncertainty (k = 3) of the transmission density of each step is ± 0.006

(see Table 1).

SRM 1008 Page 3 of 3

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