NBSIR 75-682

Basic Considerations of Densitometer

Adjustment and Calibration

Richard E. Swing

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 3, 1975

Interim Report

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 75-682

BASIC CONSIDERATIONS OF DENSITOMETER

ADJUSTMENT AND CALIBRATION

Richard E. Swing

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 3, 1975

Interim Report

U. S. DEPARTMENT OF COMMERCE, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

This document has been prepared as part of the program to upgrade

and improve the density-measurement capability at NBS through research

in the Optics and Mlcrometrology Section of the Optical Physics

Division. It is the first of several that will be released In this

subject-area, and will occasionally undergo revision and expansion as

the program develops. At the end of the program, a complete NBS

report on Densitometry and related matters will be prepared and

published.
SCOPE

The considerations of this note are limited to instruments which

measure large-area, or macro-density (as opposed to microdensity) and

to those devices in which the geometry of illumination and lightcollection are permanently fixed within the system. Further, we shall

restrict our discussion to transmission density (although many of the

principles of adjustment and calibration will apply to reflection

density measurement), and limit the type of density measured to that

known as diffuse (or singly diffuse).

V

; '

J r>

, STANDARDS

There are two types of standards that must be considered.

Documentary standards are written procedures or methods which define

the quantities to be measured, specify the conditions under which

measurements will be valid and useful, and provide guidance in the

interpretation of results. Physical measurement standards provide a means for transferring measurements of the same quantity from a "standard" instrument to an "operational" instrument. The physical

measurement standard is used to provide an absolute measurement of a quantity that is repeatable, conforms to an accepted documentary

standard and whose precision of measurement is certifiable. The

physical measurement standard is then used to bring an instrument's

response into conformity with another's. This guarantees that the

instrument output is identical (in the mathematical sense), or

related, to that which was in effect when the physical measurement

standard was calibrated. Thus, the instrument response is such that

when measurements are subsequently made on other materials, the

results are said to be "traceable" to the calibrating source, and in

principle, can be reproduced on the source's measurement instrument.

In the case of transmission density, the documentary standard is

ANSI Standard PH2. 19-1959, "American Standard Diffuse Transmission

Density," and the physical measurement standard is a step tablet

calibrated at the National Bureau of Standards.

NBS TRANSMISSION DENSITY PHYSICAL STANDARDS

Diffuse density and its measurement are governed by the cited ANSI

documentary standard. This standard is currently under revision by

ANSI Subcommittee PH2.28. The two techniques used at NBS for

calibration of physical measurement standards for optical density are

in full conformance with the provisions of the documentary standard.

Primary density standard calibrations are achieved through an inversesquare technique. This method provides density measurements with a certifiable precision of 0.005 density units or 1/2-percent, whichever

-2-
is larger. The calibration of a secondary, less-precise physical

measurement standard is accomplished with a densitometer that itself

has been calibrated with a NBS primary density standard, and used with

a geometry and procedure equivalent to those specified for ANSI

measurements of diffuse density. This method provides density

measurements with a certifiable precision of 0.01 density units or 1-

percent, whichever is larger. All densities measured at NBS are characterized as diffuse (visual) density, a spectral type of diffuse

density that relates to the average normal husian eye adapted to

photopic vision,

NBS routinely provides calibrated step tablets (21 steps, on a 3.5

X 25 cm tablet) through the Office of Standard Reference Materials.

SRM-1009 has a density range of 0 to 3.0, while SRM-1008 increases the

upper limit to 4.0. The precision in both cases is 0,01 density units

or 1 percent, whichever is larger. These tablets are also suitable

for primary standards, but must be calibrated on the inverse-square

instrument to the cited precision. Primary standards are only

provided on request, because the need is less and because they are more than ten times as costly as the secondary standards

Occasionally, NBS will calibrate user-submitted step tablets.

However, when these are soiled, scratched, fingerprinted or otherwise

blemished, or contain non-uniform densities within the various steps

NBS will return them uncalibrated, NBS prefers to provide the basic

tablet for calibration. This results from an important concern of

diffuse density measurement. When the densitometer is configured in

conformance with ANSI Standard PH2, 19-1959, density so measured is

independent of the material comprising the step tablet. Scattering or other density-varying attributes of materials do not enter into this

measurement. However, densitometers that do not conform to the

standard configuration will give varying responses with different

materials, and NBS strongly suggests that instrtments be brought into

conformity to eliminate this difficulty.

PRACTICAL DENSITOMETER ADJUSTMENT

The purpose of the calibrated step tablets ^ consistent with the

role of physical measurement standards, is th© calibration of normal

operational instrument response in terms of diffuse (visual) density.

This is necessary for several reasons.

Each densitometer, no matter the manufacturer, design,

configuration or mode of operation, obtains an indication of

illuminance in the aperture of his detector system that results from

the passage of light through the sample. The mode of indication

varies. In some instruments, it is a meter-needle read against a scale; in others it may be digitized. Whatever it is, the

"3-
manufacturer, to provide means whereby the instrument can be reset to

obtain reproducible results, supplies an adjustment procedure .

This adjustment procedure commonly adjusts the needle reading (or

other output indication) at a density value of zero and at one other

density value much higher on the scale. Having done this, it is not

uncommon to check a third point, although it is not necessary. It is

only necessary to be able to reproduce this adjustment, at the two

values, whenever it is required.

At this instrument setting, the densitometer has a response

determined by the photometric measurement system. It may be linear,

it may not be. In a meter-needle/density scale system the system

response is assumed to follow the scale markings; when they are equally-spaced, the response is assumed to be linear. The logarithmic

amplifiers in the device are usually of high quality, and the output

is generally linear over a reasonable range. But straight-line

response from the origin to densities in excess of 3.0 depends on having a logarithmic converter that reads accurately over an input

voltage range of 1000:1. This is difficult to do without correcting

adjustments. It is particularly true of instruments fabricated on a production basis. The dial (or other readout device) and electronic

circuits are designed and installed according to nominal

specifications, but like the "average man," are not expected to exist

as exactly specified for all instruments, for all time. But perfect

straight-line response is not really necessary; variability can be

compensated by the simple procedure of calibration .

PRACTICAL DENSITOMETER CALIBRATION

Calibration of the instrument against a physical measurement

standard modifies the assumed (or indicated) response so that the

instrument produces correct values of diffuse density. Calibration is

effected by first adjusting the densitometer according to the

procedure discussed previously. After adjustment, the physical

measurement standard is then inserted into the measuring system and

each step read and recorded.* This gives a set of values of

instrument reading corresponding to the set of diffuse density values

on the standard. The calibration is summarized in the form of a plotted curve of Instrument Reading vs. Diffuse Density, or in a Calibration Table (discussed in the next Section) . If the instrument

As with all such measurements, these are repeated as often as necessary to establish a good statistical base, so that the user has

sufficient confidence in the results to subject them to subsequent

analysis and use.
conforms to ANSI standard geometry and Illumination, and the step

tablet used to calibrate it has values of diffuse density (measured in

the manner directed by the documentary standard) , then all readings

subsequently made with the instrument are characterized as diffuse

density (using the calibration curve or table) , within the precision

of the step tablet used for the calibration and the measurement

tolerances of the instrximent data readout.

Thus, in principle, the need for building the "perfect" or "nearperfect" densitometer does not exist. Any reasonable response can be

compensated through calibration. Practically, it is convenient not to

have to use a curve or table to correct instrument readings; the

saving in time alone is often sufficient to repay the added cost for

accuracy in density measurement. But even the best instruments

require calibration: it checks system response, determines error

bounds, and provides a "traceability" in the measurement procedure.

Calibration of densitometers is particularly essential in

instruments that are not strictly configured to measure diffuse

density. A prime example of this is the microdensitometer which

measures a specular density that varies with the numerical apertures

of the optics. Macrodensitometers that do not meet ANSI

specifications for diffuse density must also undergo thorough and

repeated calibration to reduce readings to diffuse density values.

The frequency of calibration and the precision of the standard used

depend to a great extent on the purpose of the instrument. In many

instances, commercial interests do not require calibration curves or

tablets, but merely insist that the instrument read to within some specified density range for each step on the calibration tablet. A

typical value is +0.05 density linits. When a periodic check against

the physical measurement standard indicates departure of density

values beyond these error bounds, the instrument is serviced. For

inspection, acceptance-testing or sorting operations, the application

of such error bounds is adequate. However, for precision use (where

subsequent calculations will be based on the characteristic curve of

the material, for example) calibration curves or tables are a necessity.

CALIBRATION DISPLAY AND USE

Calibration displays should reflect the precision of measurement,

be accurately drawn or summarized and be convenient to use. Ordinarily, most densitometers can read to 0.02 density units (scale

divisions); some can visually interpolate to 0.01 density units quite

accurately. Most digital displays have a least-count of 0.01. Thus,

if the operator is going to read density to the nearest 0.01 unit, his

calibration display should reflect that precision. If he chooses to

-5-
plot his calibration, he should not be required to interpolate between

lines to obtain his corrections. This stems from the problem of eye

fatigue and loss of time in tracking between lines from the abscissa

up to the curve - then over to the ordinate value. For densities on

the physical standard up to, say 4.0, 400 separate and distinct lines

on his graph paper are required, in both dimensions. For nearly all

cases, this requires a sheet of paper that is prohibitively large,

although by halving (and using the spaces between lines, with its

attendant interpolation problem), the paper size can sometimes be

reduced to manageability. Accuracy will be affected by the ability to use a draftsman's spline (French Curve) in connecting the points to

make a smooth curve. Unless a great deal of care is exercised, the

precision inherent both in the calibration and the physical

measurement standard will disappear, and the precision implied by the

abscissa and ordinate graduations will be illusory.

Probably the most accurate way of displaying calibration

information is in a Calibration Table. This is a listing of

Instrument Reading versus Diffuse Density for the entire range of the

instrument calibration. The values of Instrument Reading should

reflect the smallest value (precision) the operator intends to measure. If he will read to 0.01 density units, then the table should

increment Instrument Reading by that unit. In use, it is a simple

matter to look up the Instrument Reading in the listing and its

corresponding value of Diffuse Density. There is no problem of lines

to follow, and the contiguous pairing of the two numbers simplifies

use. The major problem lies in the preparation of the table.

Ordinarily, 22 points are available from the calibration

(including the point 0,0). The remainder of the values, those inbetween the calibration points must be calculated. The calculation of

400 of more points, using any of the various algorithms provided in

classical texts on numerical analysis will be prohibitive in time

unless carried out on a digital computer. However, once reduced to a program for the computer, the computation and printing of the table is

vastly simplified, and gives the calibration quickly and efficiently.

Futheirmore, as the instrument changes its performance (as it "wearsin"), new calibration tables can be computed and printed with very

little additional expenditure of time and effort. Updating the

calibration ceases to be a major undertaking.

COMPUTER PROGRAM FOR CALIBRATION TABLES

A computer program has been prepared for use at NBS by the Optics

and Micrometrology Section, for the express purpose of calculating

densitometer calibration tables. This program as shown in the listing

of the Appendix will handle densities up to 6.0 (with an expansion of

-6-
two arrays, this limit can be extended). The program name Is DENCAL;

a typical print-out is shown in the Appendix, following the listing.

DENCAL calculates the density values between calibration points

through a technique of spline-fitting, a method completely analogous

to using a French Curve to smooth points into a continuous curve on a graph. Details of general spline-fitting can be found in Ralph H.

Pennington, Introductory Computer Methods and Numerical Analysis , 2d

Ed., (The MacMillan Company, Toronto, Canada, 1970), pp. A45-452.

Every calibration point lies on the "curve," and it is as accurate as any of the standard interpolation formulas.

The program is written in BASIC language, and used at NBS through

a teletype unit with a commercial time-sharing computer. BASIC, in

form and content, is equivalent to elementary FORTRAN and can quickly

be converted to that language if a user so requires. The Print and

Format statements for setting up the tables have purposely been

written with conversion to FORTRAN in mind.

Data Input for DENCAL:

The following procedure should be used for entering data in

DENCAL

1) On line 900, enter the number of pairs of points to be used

in the calibration, and which will listed in lines following

that entry.

2) Following line 900, enter data in the form of pairs of points

(paired as INSTRUMENT READING, DIFFUSE DENSITY), in

increasing order. Including the lower instrument adjustement

end-point, 0,0. See lines 910 and subsequent in the listing

of the Appendix for a specific example.

3) DENCAL will increment the Instrument Reading column of the

table by whatever value the user specifies. In the cited

listing, it is specified as 0.01, and this should be used for

those Instruments with a real or implied precision of 0.01.

Enter the desired value on line 920, or do not patch-in if

the one already there is correct.

Output from DENCAL:

The program prints two column-pairs per page; the columns contain

50 pairs of values each. Sufficient spacing Is provided in the

program's print-outs so that each page can be trimmed to an 8-1/2 x 11

inch size for insertion into standard-size notebooks. The input

-7-
(calibration) data are not printed-out in a separate group. However,

the actual points can be checked against the table after preparation;

the spline-fit procedure will always have the basic calibration points

in the table.

*****************************************

A punched tape containing DENCAL is available from the Optics and

Micrometrology Section for loan to those interested in using the

program. Direct requests for this tape or for additional information

to: R. E. Swing, A-123 Metrology Building, National Bureau of

Standards, Washington, D. C,^ 20234.
APPENDIX

DENCAL

A Computer Program for Preparing Densitometer

Calibration Tables

001 * KICHAKD E. SWING* PR0GKAM: DtiMCAL

002 * 003 * THIS PKaGRAM PKEPAKES A CALIBhATI^N TABLE THAT RELATES

004 INSTRUMENT READINGS Tk) A CALIBRATED PHYSICAL STANDARD.

005 * THE TABLE STEPS INSTRUMENT READING ACC^dRDlNG T0 THE VALUE

006 dN LINE 920. CHANGE F0RMAT STATEMENTS ^N LINES b02* 506

007 * 525* 528* 541 > 543> 547* 560 AND 570 AS REQUIRED F^R THE SPECIFIC

008 INSTRUMENT* AND PATCH-IN THE APPRkJPRlATE DATA kJN LINES

009 * 9 10 AND SUBSEQUENT. CHANGE DATA LINE 900 TwJ REFLECT THE

010 * NUMBER PAIRS 0F PwJlNTS. DATA MUST BE LISTED IN INCREAS"

011 * IN6 0RDER* IN PAIRS* INSTRUMENT READING URST IN EACH PAIR.

012

013 DIM A(30* 3)*C(4* 30)

01 4 DIM G< 601 )*H( 601

)

015 DIM X(30)*Y(30)*i(30)*B(30)*D(30)*E(30)*P(39)

0 1 6 f 0R J = 1 T0 10

0 17 PRINT

018 NEXT J

020 G0SUB 540 'PRINT TABLE HEADING*

024 READ M

026 h3H I = i Ta M 'INPUT THE DATA*

027 READ X( I )*y (I ) 028 NEXT I 029 READ C

030 B = (X(M) -X( 1 ) ) /C

031 I P B > 601 G0 Tk3 601

032 Ml = M-1 'CALCULATE M T - C0E h F I C 1 ENTS ' 034 F0R K = 1 T0 Ml

036 D(K) = X(K+ 1 )-X<K)

038 P(K) = D(K)/6

040 E(K) = <y (K+ 1 )-Y(K) )/D(K)

042 NEXT K

044 F0R K = 2 T0 Ml

046 B(K ) = E(K ) - E<K- 1

)

0 48 NEXT K

050 A(l*2) = - 1 .0-D( 1 )/D(2)

052 A( 1 * 3) = D< 1 )/DC2)

054 AC2*3) = P(2)-P( 1 )*A( 1* 3)

056 A(2*2) = 2*(P( 1 )+P(2) )-P( 1 )*A( 1*2)

058 A(2*3) = A(2* 3) /A(2* 2)

060 B(2) = B(2)/A<2*2)

062 F0R K = 3 Ti3 Ml

064 A(K*2) = 2*(P(K- 1 )*P<K) )-P(K- 1 )*A(K- 1 * 3)

066 B(K) = B(K ) -P(K- 1 )*B(K- 1

)

068 A(K*3) = P(K)/A(K*2)

070 B(K) = B<K)/A(K*2)

072 NEXT K

074 Q = D(M-2)/D(M- 1

)

076 A(M*1) = 1 Q A(M-2*3)

078 A(M*2) = -Q - ACM* 1 )*A(M- 1* 3)

080 BCM) = B(M-2)-A(M* 1 )*B(M- 1

)

082 Z(M) = B<M)/A(M*2)

084 M2 = M-2

08 6 F0R I = 1 T0 M2

088 K = M-I

090 Z(K) = B(K)-A<K* 3)*Z(K+ 1

)

092 NEXT I
094 Z(l) = -A( 1*2)*Z(2)-A( 1,3)*Z(3)

09 6 F0R K = 1 T0 Ml

098 Q = 1/<6*D(K))

100 C( 1*K) = Z(K)*Q

102 C(2*K) = Z (K+ 1 )*Q

104 C(3*K) = (y (K)/D(K))-<Z(K)*H(K)

106 CC4*K) - (Y(K+1 )/D(K) )-(Z(K*l )*P(K)

108 NEXT K

114 F0R J = 1 B+1 'CALCULATE TABLE*

1 1 6 G( J ) = X( 1 ) ( J- 1 )*C

122 IF (G<J)-X( 1 ) )> 146# 124* 128

124 H(J) = Y( 1 ) 126 G0 T0 148

1 28 K = 1 130 IF (G(J)-X(K+ 1 ) )* 1 40* 132* 136

1 32 H(J ) = y <K+ 1 ) 134 G0 T0 1 48

136K=K+1

138 IF (G(J)-X(M) ), 130* 1 46* 1 46

140 H(J) = (X(K+ 1 )-G< J ) )*(C( 1 *K )( <X(K+ 1 )-G( J ) )**2)+C< 3*K)

142 H(J) = H(J)+CG(J)-X(K))*<C<2*K)«<<G(J)-X(K) )**2)+C<4*K))

1 43 G0 T0 1 48

1 46 H(J) s y(M)

1 48 NEXT J

1 49 PRI NT

150 PRINT 'PRINT-i^UT HEADINGS AND kJPTIiJNS'

151 K = 0

152 IF (B+1) < 100 Gd Ti3 216

153 G0SUB 500

154 F0R J = C(2*K*50)*1) TvJ ( < 50* ( 2*K 1 ) ) 1 ) 160 PRI NT* 560* G( J )* H( J) * G< J+50) *H( J+50)

170 NEXT J

180 F0R J = 1 T3 10

182 PRINT

183 NEXT J

190 IF < ( 50*<2*K*3)+51 )-(B* 1 ) )* 195* 195* 205

195K=K+1

200 G0 T0 I 53

205 IF (B+1) > ( 50*(2*K<»- 1 ) + 51 ) G0 T0 220

210 F0R J = 1 T0 10

212 PRINT

214 NEXT J

215 G0 T0 999

21 6 K = - 1 217 IF (B+1) < 50 G0 T0 250

218 G0 T0 222

220 IF (B+1) < ( lOO+CK* 1 )+51 ) G0 T0 250

222 G0SUB 500

224 F0R J = (2*(K+ 1 )*50+l ) T0 ((B+l)-50)

226 PRINT* 560*G(J)*H(J)*G<J*50)*H(J+50>

230 NEXT J

232 F0R J = (B+l)-49 T0 ( 50* ( 2*K + 3 ) 1

234 PRINT* 570*G<J)*H<J)

23 6 NEXT J
2 40 F0R J = 1 T'3 10

242 PRINT

244 Nf.XT J

245 Gk) T0 999

2 50 G.ISUB 522

252 K)K J = (2*(K+ 1 )*50-»- 1 ) TkJ ( B* 1 ) 254 PRI iMT* 570* G( J ) * H( J)

25f NEXT J

260 F^K J = 1 T0 ( 60+2*(K* I )*50-B) 'EXTRA SPACES* LAST PAGE'

2 62 PRINT

2 64 NEXT J

2 65 G0 T0 999

bOO PRINT* 502 'TW^-C^LWN HEADING SUBK0UTINE'

5 02 h^iT X5* •'INSTRUM"*X5* "Dl h hUSE"*X 1 5* "INSTRUM"* X b* "Dl f- USE"

504 PKINT*506

50 6 MT X5* ••READING"*X5*"DENSI TY'SX 1 5* "KEADI NG"* X 5* "UENSI TV"

508 PRINT

509 RETURN

522 PRINT* 525 ' SI N6L E- COLUMN HEADING SUBkJUTINE'

525 FMT X5* ••INSTRUM"*X5#"DI ff-USE"

527 PRINT* 528

528 hi^T X5* "READING"*X5* "DENSI TY"

529 PRINT

530 kETURN

540 PRINT. 541 'TABLE-HEADING SUBROUTINE*

541 FMT "DENSITOMETER CALIBRATION TABLE"

542 PRINT* 543

543 FMT "XYZ COMPANY LABORATORY* INSTRUMENT *7"

545 PRINT "DATEt "I

546 PRINT* 547* TIM( 1 )* TIM( 2)* TIM(3)

547 FMT I 3* "/", I 3, "/", I 3

548 PRINT

549 PRINT

550 RETURN

555 FORMAT STATEMENTS

560 FMT X3* F8 .2*X4* F8 .2*X I 4* F8 . 2*X4» FB . 2

570 FMT X3* F8 .2*X4* F8 .2

600 * WARNING STATEMENT ABOUT ARRAY SldE

601 PRINT "THE CALCULATIONS WILL REUUlKE MORE AHRAY CAPACITY.

602 PRINT "INCREASE THE DIMENSIONS OF G( ) AND H( )*"

603 PRI NT* 604* I NT( B+ 1 ) 604 FMT "ON LINE 014* TO"* 1 5* "* "* " AND RUN AGAIN."

606 PRINT . , 607 GO TO 999

899 DATA SECTIOi>J

900 DATA 20

910 DATA 0*0*0.04*0.055*0.21*0.23*0.42*0.43*0.64*0.64

912 DATA 0.83*0.84* 1 .04*1.05* 1 .23*1.25* 1 .45* 1 .45* 1 . 65*1.65

914 DATA 1 .8 6*1.8 6*2.04*2.05*2.22*2.25*2.43*2.465*2.65*2. 68

916 DATA 2.8 6*2.88* 3.05*3.045*3.22*3.245

918 DATA 3.42*3.365*3.64*3. 68

920 DATA 0.01

999 END
DEiMSI IOMETER CALIBKATlidN TABLE

XYZ C0MPANy LABt3RATaRy* INSTRUMENT #7

DATEJ 2/ 25/ 7b

INSTRUM DIFFUSE

READING DENSITY

00 .00

01 .01

02 .03

03 .04

OA .05

0 5 .07

0 6 .08 V 07 .09

08 .10

09 .11

1 0 .12

I 1 .13

12 .14

1 3 .15

1 A .16

1 5 . 1 7

1 6 .18

1 7 .19

18 . 20

19 .21

20 .22

21 .23

22 . 24 /

23 .2b

24 .26

25 .27

26 .28

27 .29

28 . 30

29 .31

30 •32

31 .32

32 . 33

33 .34

34 .3b

35 .36

3 6 . 37

37 .38

38 . 39

39 . 40

40 .41

41 .42

42 .43

43 .44

44 .4b

45 .46

46 . 47

47 . 48

48 . 49

49 . bO

50 . 50

INSTRUM DIFFUSE

READING DENSITY

. 50 . 50

. 51 • 51

. 52 . 52

.53 . 53

. 54 . 54

. 55 . 55

. 56 . 56

. 57 . 57

. 58 . 58

. 59 . 59

. 60 • 60

. 61 • 61

. 62 • 62

. 63 . 63

. 64 . 64

. 65 . 65

. 66 . 66

. 67 . 67

. 68 . 68

. 69 . 69

. 70 .70

.71 .71

. 72 .72

.73 .73

.74 .75

.75 . 76

.76 . 77

.77 . 78

. 78 . 79

. 79 .80

.80 .8 1 .8 1 .82

.82 .83

.83 • 84

.84 .85

.85 .86

.86 .87

.87 • 88

.88 .89

.89 .90

.90 .91

.9 1 .92

.92 .93

.93 .94

.94 .95

.95 .96

.96 .97

.97 .98

.98 .99

.99 1 .00

1 .00 1 .01
I iM STRUM

READING 1 .00

1.01 1 .02 1 .03 1 .04 1 .05

1.06 1 .07 1 .08 1 .09

1.10

1.11

1.12

1.13 1 . M

1.15

1.16

1.17

1.18 1 . 19 1 .20

1.21 1 . 22 1 .23 1 .24 1 .25 1 .26 1 .27 1 .28 1 .29 1 .30

1.31 1 .32 1 . 33 1 . 34 1 .35

1.36 1 . 37 1 . 38 1 . 39 1 . 40 1 . 41 1 . 42 1 . 43 1 . 44 1 . 45 1 . 46 1 . 47 1 . 48 1 . 49 1 . 50

DI FhUSE

DENSI Tr 1 .01 1 .02 1 .03 1 .04 1 .05 1 .06 1 .07 1 .08 - 1 .09

1.10

1.11

1.12

1*14

1.15

1.16

1.17 1 . 18 1 . 19 1 .20

1.21 1 .22 1 .23 1 .24 1 .25 1 .26 1 .27 1 .28 1 .29 1 .30 1 .31 1 .32 1 .32 1 . 33 I .34 1 .35 1 .36 1 .37 1 . 38 1 . 39 1 . 40 1 . 40 1 . 41 1 . 42 1 . 43 1 . 44 1 . 45 1 . 46 1 . 47 1 . 48 1 . 49 1 . 50

INSTKUM

KEADI.NIG 1 .50

1.51 1 . 52 1 . 53 1 . 54 1 . 55 I . 56 I . 57 I . 58 1 . 59 1 . 60 1 . 61 1 . 62 1 . 63 1 • 64 1 . 65 I • 66 1 . 67 I . 68 I . 69 1 . 70

1.71 1 . 72 1 .73 1 .74 1 .75

1.76 1 .77 1 . 78 1 . 79 I .80 1 .81 1 .82 I .83 1 .84

1.85 1 .86 1 .87 1 .88 1 .89 1 .90

1.91 1 .92 1 .93 1 .94 1 .95 1 .96 1 .97 1 .98 1 .99

2.00

DI FfUSE

DENSITY 1 . 50 1 . 51 1 . 52 1 . 53 1 . 54 1 . 55 I . 56 1 . 57 1 . 58 1 . 59 1 . 60 1 . 61 1 • 62 1 . 63 1 . 64 1 . 65 1 . 66 1 . 67 1 . 68 1 . 69 1 .70

1.71 1 . 72 1 .73 1 .74

1.75 1 .76 1 . 77 1 . 78 1 . 79 1 .80 1 .8 1 1 .82 1 .83 1 .84 1 .85 1 .86 1 .87 1 .88 1 .89 1 .90 1 .91 1 .92 1 .93 1 .94 1 .95 1 .96 1 .97 I .98

2.00

2.01
INSTRUM DIFFUSE INSTKUM DIFFUSE

READING DENSITY READING DENSITY

2.00 2.0! 2. 50 2. 53

2.01 2. 02 2« 51 2. 54

2.02 '.f^' f 2.03 2. 52 2. 55

2.03 ' 2.04 2. 53 2. 56

2.04 2.0 5 2. 54 2. 57

2.05 2.06 2. 55 2. 58

2.06 2.07 2.56 2 . 59

2.07 2.08 2. 57 2. 60 2 e 08 2.09 2. 58 2. 61 2 » 09 - 2.11 2. 59 2* 62 2 o 1 0 2.12 2« 60 2. 63

2.11 ' 2.13 .)• 2.61 2* 64 2 0 1 2 2.14 2 . 62 2* 65

2.13 2.15 ' 2. 63 2. 66

2.14 2. 64 2. 67

2.15 2.17 2.65 2* 68

2.16 2. 18 2.66 2* 69

2.17 2.20 1 2*67 2. 70

2.18 2.21 2 . 68 2.71

2. 19 2. 22 V:.' -:l i 2 • 69 2. 72 2 . 20 2. 23 .^^ -^ 2. 70 2. 73

2.21 2.24 2.71 2. 74 2 . 22 2.2 5 2.72 2.75

2.23 2.26

V " 2.73 2.76

2.24 2.27 ^ ; 2.74 2.77

2.25 2. 28 2.75 2. 78

2.26 2 . 29 2.7 6 2. 79 2 « 27 2. 30 2.77 2.80

2.28 2.31 f 2 . 78 2.8 1 2.29 2. 32 . 2.79 2.82

2.30 2.33 : 

2*80 2.83

2.31 2. 34 2« 8 1 2*84

2.32 2.36 2»82 2.85

2.33 2.37 ; 2*83 2 • 8 S

2.34 ' : 2 . 38 s 2*86

2.35 2. 39 2.85

2.36 2 . 40 'V f;:.-

C P • R8

2.37

w ? • R 7 P • R9

2.38 2 . 42 s P • 90 2 • 39 ; 2.43 P • R9 P • 90

2.40 2.44 P • 90 P . 9 1 2.41 2.45 P . 9 1 P . 9 P 2 . 42 2.46 P • 9 P P . 9 T

2. 44 ts 2.47 2.94 2.94

2.45 2 . 48 2.95 2.95

2.4 6 2. 49 2.96 2.96

2.47 2.50 2.97 2.97

2.48 2.51 2.98 2.98

2. 49 2. 52 2.99 2.99

2. 50 2. 53 3.00 2.99
I.MSTKUM

READING

3i00

3.01

3.02

3.03

3.04

3.05

3.06

3.07

3.08

3.09

3.10

3.11

3.12

3.13

3.14

3. 1 5

3.16

3.17

3. 18

3. 19

3. 20

3.21

3.22

3.23

3.24

3.2b

3.26

3.27

3.28

3.29

3. 30

3.31

3. 32

3.33

3. 34

3.35

3.36

3.37

3. 38

3. 39

3. 40

3.41

3. 42

3. 43

3. 44

3. 45

3. 46

3. 47

3. 48

3. 49

3. 50

DIF"hUSE

DENSITY

2.99

3.00

3.01

3.02

3.03

3.04

3.06

3.07

3.08

3.09

3. 10

3. 12

3. 13

3. 1 4

3. 1 6

3. 1 7

3. 18

3. 19

3.20

3.21

3.23

3.24

3.24

3.25

3.26

3.27

3.28

3. 28

3.29

3. 30

3. 30

3.31

3.31

3. 32

3. 32

3. 33

3. 33

3. 34

3.34

3.35

3. 35

3.36

3.36

3.3 7 3. 38

3. 39

3. 39

3. 40

3.41

3. 42

3. 43

INSTKUM

HEADING

3. 50

3.51

3. 52

3. 53

3. 54

3. 55

3. 56

3. 57

3. 58

3. 59

3. 60

3.61

3. 62

3. 63

3. 64

DI FFUSE

DENSITY

3. 43

3. 44

3. 45

3. 47

3. 48

3.49

3.51

3. 53

3.55

3.56

3. 58

3. 61

3. 63

3. 65

3. 68
NBS.114A <REv. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. mm K A 1 ION OK Ki;i^ORT NO.

NBSIR 75-682

2. Cjov 't Aci t ssion No.

3. Rc T ipit-nl 's Aci cs.sion No.

4. TITl.H AND .SIlHl lTl.i;

BASIC CONSIDERATIONS OF DENSITOMETER ADJUSTMENT AND

CALIBRATION

5. Publication Date February 1975

6. Performing Organization ( ode

7. AU rilOR(S)

Richard E« Swing

8. Performing Organ. Report No.

9. pi:ki ()rmin(, ok(,ani/.ation nami- and addri;ss

national bureau of standards

department of commerce

washington, d.c. 20234

10. Proiect/Ta.sk/Work Unit No. 2320187

11. f ontract/Grant No.

12. Sponsoring Org.in i/.at ion Name aiul ( ompltte Address (Street, City, Stale, ZIP)

Same as No. 9

13. Type of Report & Period

(-overed

Intermim Report

14. Sponsoring Agency Code

15. suppi.i-:mkntarv no i t s

, This is a revised version of NBS Report 10 970

issued December 1972,

16. ABSTRAC 1 (A 200-word or less factual summary of most sif^ificant information. If document includes a significant

bibliography or I iterature survey, mention it here.)

The adjustment and calibration of a denaitometer are considered. This

is accomplished through the use of physical measurement standards with a procedure appropriate for the instrument, and brings the instrument response

' in line with measurements traceable to NBS. The difference between primary

and secondary physical measurement standards for diffuse (visual) density is

discussed. A calibration table is suggested for best use of the instrument

and a computer program (BASIC language) is provided that will calculate and

print a table relating instr\iment reading to diffuse (visual) density.

17. KF.Y WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Calibration; Calibration table; densitometer; Densitometry;

Optical density; Optical density standard

18. AVAILABILITY I 'nl nil n eti

I

' For Official Distribution. Do Not Release to N I IS

I

^ Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C:n

Order f rom National Technical Information Service (N IIS) Springfield, Virginia 221'il

19. SFCIJRITY CLASS

(THIS REPORT)

UN( 1. ASSIITFD

20. SL( URN Y CLASS

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UNf LASSIFIFD

21. NO. OF PAGES

18

22. Price

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