A computer program to determine photographic emulsion calibration curves

Spectrochimica Acta,Vol. 24B,pp.313to 323. Pergamon Press1969. Printedin Northern Ireland

A computer program to determine photographic emulsion calibration curves A. CARNEVALE and A. J. LINCOLN Instrumental Analysis Laboratory, Engelhard Industries Division Engelhard Minerals and Chemicals Corporation, Newark, New Jersey 07114 (Received

13 June 1968;

revised 29 January 1909)

AbstractThe two-line method of emulsion oalibration is used to produce a set of related transmittance readings for a pair of homologous iron lines bearing a 6xed ratio of intensity to each other. These data are converted to Seidel densities and fitted to a linear regression equation. This preliminary curve equation is utilized to select a set of transmittances to be correlated with a series of relative intensities which are an exponential funotion of the line pair intensity ratio. This data output, which is the final H & D curve, is then fitted to two curvilinear regression equations which are required to intersect at 50.0 o/otransmittance. The equations are normalized

to produce relative intensities from 100.0 to about 1.0 for transmittances from 1.0 to 99.9%. The coefficients are then employed to generate tables whioh indicate a relative intensity for all transmittances from 1.0 to 99.9 y0in increments of 0.1% transmittance. The program is suitable for any emulsion calibration using Seidel density in conjunction with linear preliminary curves and where the intensity function is derived from a geometric or exponential series. INTRODUCTION CHURCHILL [l] describes a number of methods involving the calibration of the emulsion response in terms of relative intensities. The two-line [ 1, 2, 41 method avoids most of the disadvantages of other methods while retaining many of their advantages The line pair used in the calibration should be homologous, should not differ by more than 100 A in wavelength-the less the better, and should be centrally located, if possible, in the wave-length region of interest. This report is based on data obtained from a number of homologous Dieke iron lines in the 3100 A region for SA-1 film generally used in optical emission spectrochemical analysis. The spectic approach to emulsion calibration described is applicable to other wavelength regions in the same film, and in a more general sense, to other types of film or applications. EXPERIMENTAL

Early in 1965 we undertook an extensive survey of the parameters involved in the photographic emulsion calibration used in spectrographic analyses. This exp&ment included two spectrographs, two developing machines, five microphotometers, and a number of film readers. Eleven Dieke homologous iron lines were evaluated in a series of eight spectrograms taken under various exposure conditions with a d.c. arc. The information was doubled by passing the radiation through a split field filter with a nominal 2: 1 ratio. All data were converted to Seidel (Baker-Sampson) [l] [Z] [3] [4]

J. R. J. J.

R. CHUFXHILL,Ind. Eng. Chem. Anal. Ed. 16,653 (1944). SCHMIDT,Rec. Trav. Chim. 07, 737 (1948). NOAR, Photo. J. 91B, 64, 99 (1951). W. ANDERSONand A. J. LINCOLN,ApI. Spectry 22, 753 (1968). 313

314

A. CARNEVALEand A. J. LINCOLN

densities and plotted in a linear coordinate system as a function of the titer factor, and secondly, as in the two-line method. These data have been summarized by ANDERSON and LINCOLN [4] who conclude that the two-line method provides linear Seidel preliminary curves for 1.5 I %T 4 97 % ( % t ransmittance), as long as certain other factors are held within specified limits. As a result of the above experiment we abandoned the filter factor method of emulsion calibration and instituted the two-line method as routine procedure in our laboratory. Table 1. Preliminary curves Standard deviation

Intensity* ratio

Intsrcept

Slope

0.240 0.353 0.620 0.679 1.472 1.923 2.830 4.167

1.158 0.866 0.547 0.371 -0.404 -0.624 -1.064 -1.543

0.748 0.812 0.877 0.915 1.090 1.141 1.230 1.333

%T 0.41 0.86 0.44 1.29 1.16 0.56 1.24 1.52 4 x = 0.93 4 a, = 0.43 4 V, =46%

hide1 saturation 4.595

4.591 4.438 4.377 4.478 4.454 4.635 4.640 4.526 0.101 2.2 %

Correlation coefficient 0.9993 0.9988 0.9999 0.9989 0.9994 0.9999 0.9993 0.9989 0.9993

0.0004 0.04 %

* Dieke line pair.

The two-line method as performed in our laboratory adheres to the requirements described in the introduction. Four Dieke homologous iron lines with listed or empirically determined relative intensities were selected in the 3100 A region for our study [4]. A number of combinations of the selected lines were used to obtain preliminary curves for the ratios 1.472, 1.923, 2.830 and 4.167. These data were also calculated in reverse to provide reciprocal preliminary curves with the intensity ratios of 0.679, 0.520, 0.353 and 0.240 respectively. The intensity ratio for a line pair is given by: IR = Relative intensity (strong line) Relative intensity (weak line) The %T (% transmittance) of the selected lines was read in each spectrum, converted to Seidel densities, and plotted in a linear coordinate system with the strong line as abscissa and the weak line as ordinate. The data included all readings as they were obtained on the microphotometers with %T as low as 1.2 and as high as 93. These plots were useful in the early stages of the experiment to make some initial estimates on the characteristics of the system. Each curve was checked with least squares equations through the 6th degree. No significantly better definition of the curves was obtained using 2nd degree or higher equations. The linear preliminary curve data as obtained on the computer has been summarized in Table 1 and plotted in Fig. 1. In Fig. 1, the dashed line is postulated for a line pair with an intensity ratio of

A computer program t,o determinephoto~ap~e emulsion calibration curves

316

5.0

4.0 ~

-4.oL

70 1 1.0

I

(

1.0

I

2.0

I

I

3.0

4.0

I

!5.0

Fig. 1. “Least squaxes” preliminary curves for a number of Dieke line pairs with intensity ratios ranging between 0.24 and 4.17.

one. All curves above the dashed line are for line pairs whose ratio is less than one; correspondingly, all curves below the dashed line are for intensity ratios greater than one. Each curve has been linearly extended to intersect the dashed line which has a slope of unity and passes through the origin. INT~R~~CTIOXPOINT NOAR [3] defines this intersection as “the maximum developable blackening” and uses the intersection and related preliminary curve data to derive an equation relating pho~graphic blackening and exposure. A~RE~o~ and LINCOLNf4J refer to the intersection as the “saturation point” and use the intersection as a reference point or bench mark to obtain the emulsion calibration curve directly from the preliminary curve. These definitions of the intersection are compatible with their subsequent calculations and respective derivations, and each demonstra~s a useable working equation. It is our current feeling that the “limit” concept [3,4] does not adequately describe the intersection point. The intersection may be more aptly described as “that point at which there is no detectable difference in the %T of the two lines being compared”; i.e. lack of contrast

316

A.

t%RNEVALE

and A. J.

LINCOLN

and the apparent intensity ratio of the line pair is unity. It is obvious that this limit can be applied regardless of whether the lines are read at the extreme dark or light end of the scale. At the dark end of the scale, the intersection will occur in the first quadrant, whereas at the light end of the scale the intersection will occur in the third quadrant. A search of the literature has not disclosed any other suitable explanation for two intersection points for preliminary curves, whether they are linear or nonlinear. It should be noted that the non-proportional development of the two lines actually begins at some distance ( x5”) from the calculated limit (light or dark). This observation indicates that extremes of light and dark should not be used in calibrations or in quantitative work, as has been general knowledge in the field. In this respect the true “limit of development or saturation point” is almost impossible to determine and is of no real use in most applications in any case. As defined by NOAR [3] and further developed by ANDERSON and LINCOLN [4], the intersection is simply another point on the linear preliminary curve which can be easily determined since the intensity ratio of the lines is no unity. Each of these reporters uses the defined point as a reference to determine the intensity ratio for any other pair of lines. The authors concur with NOAR, ANDERSON and LINCOLN in their findings but developed the computer program to closely simulate the more conventional approach to emulsion calibration. PRELIMINARY CURVES In general, the preliminary curve is used to smooth the experimental data and to provide a number of paired readings from the smoothed data which now represents the final H & D curve. Transforms of the Seidel (BAKER-SAMPSON) type were claimed to provide linear preliminary curves. It was only after careful equipment checks and limiting of other parameters that we were successful in obtaining such linearity. The results of our experiment showed close agreement with the findings of the previous investigations [2-41. The computer program requires as input, the identification of the data set, the intensity ratio of the line pair used in the calibration, the number of points in the data set, and the %T of the dark and light step for each datum point. The computer converts data to a linear regression equation to determine the coefficients A and B of the equation:

U=A+BV where

Pa)

27 = Seidel density of weaker line

V = Seidel density of stronger line and Seidel density = log [(lo0 - T)/T]. The computer will list the identification of the data set ; the coefficients A and B of the fitted curve; the empirical transmittances for each datum point and the respective Seidel density ; the individual error in transmittance for the weaker line from the curve, and the sum of the errors of the complete data set. In addition, there will also be listed the mean value of the weaker line, the standard deviation, and the coefficient of correlation for the data set. This computer sequence will be repeated for as many emulsion calibration data sets as has been previously specified to the computer in the data card entry.

A computer program to determine photographic

317

emulsion calibration curves

Table 1 is a consolidation of the computer determined statistics for the line pair(s) used in the experiment. The first column lists the intensity ratio of the line pair(s) used in each case. These ratios are listed in the same order as the curves are drawn in Fig. 1, from top to bottom. Successive columns indicate the calculated values of the intercept and slope for each curve, the standard deviation ( XT) of the data about the curve, the Seidel value of the “saturation point”, and the coefficient of correlation for each line pair(s). The mean value, standard deviation, and correlation coefficient for the last three columns are shown in an individual table at the Table 2. Seidel “saturation

0.353* 0.520* 0.679* 1.000* 1.472* 1.923* 2.830* 4.167*

point”,

all possible PC combinations

0.240*

0.353*

0.520*

o.f379*

1.000*

1.472*

1.923*

2.830*

4.605 4.744 4.705 4.595 4.563 4.544 4.613 4.620

4.879 4.766 4.591 4.554 4.532 4.615 4.622

4.575 4.439 4.454 4.446 4.566 4.585

4.377 4.428 4.424 4.565 4.586

4.476 4.453 4.634 4.639

4.412 4.737 4.700

4.917 4.774

4.650

* Dieke line pair intensity ratio.

Mean = 4.594.

u = 0.128.

V = 2.8%.

bottom of the respective column. For lack of a better term, the authors continue to use the “saturation point” terminology to name their definition of the intersection. The “saturation point” was tested for all the line pairs used in the experiment, the premise being that the limit is the same, regardless of which pair of linear preliminary curves is used to determine its value. These data, in the form of Seidel densities, are tabulated in Table 2 which lists this value for all lines used in the experiment, taking each by each. The mean value, the standard deviation, and the coefficient of variation, are listed elsewhere in the table. The H & D curve is developed by the computer from the preliminary curve in the conventional manner, as follows :

U,=A+BV

(lb)

U, = A + BU, U, = A + BU, and ;

U, = A + BU,,_,

The number of points to be determined by this process depends upon the intensity ratio of the line pair used in the calibration. The program will automatically select the required number of data points to be derived from equation (1) and will determine that value of V to be introduced such that the mid-point in the U, series is exactly 0.0; i.e., the Seidel density for 50.O%T. In general, these data are insufficient to precisely define the final H & D curve, and some form of interpolation is used to produce additional data for plotting, etc. The program will insert a number of interpolations within the U, series to develop a new U, series which is fixed at the

A. CARNEVALEand A. J.

318

LINCOLN

same points as the original series in 17,. The number (.M) of the interpolations inserted also depends upon the intensity ratio of the line pair used in the calibration and conforms to the equation: m Z 2”-’ n. = 1, 2, 3, . . . etc,

m=l,3,7

,...

etc.

This original intensity ratio of the line pair is then reduced geometrically to G where ; log a = 112” log I The data to produce the final H & D curve is obtained by the computer from: u, = &a+“)

(2)

where k = I, 2, 3, . . . n. Table 3. H & D curves from four Dieke line pairs t

1.472; 4

t

1.923s h

t

2.831* -w

c4.1678

K

%T

R.I.

%T

R.I.

%T

R.I.

%Z’

1 9 17 25 33 41 49 67 86 73 81 89 97 106 113 121 129

16.3 19.1 22.4 26.9 29.9 34.6 39.6 44.7 60.0 65.8 61.4 66.8 71.7 76.6 80.8 84.4 87.6

4.70 4.26 3.87 3.61 3.19 2.90 2.63 2.39 2.17 1.97 1.79 1.62 1.47 1.34 1.21 1.10 1.00

8.6 11.0 14.0 17.7 22.1 28.0 34.8 42.2 60.0 68.9 67.2 74.6 80.8 86.4 90.6 93.6 96.6

13.67 11.61 9.86 8.37 7.11 6.04 6.13 4.36 3.70 3.14 2.67 2.26 1.92 1.63 1.39 1.18 1.00

2.6 3.9 6.7 8.3 12.0 18.3 27.0 37.8 60.0 64.8 77.3 86.3 92.1 96.1 98.1 99.1 99.6

64.14 49.45 38.13 29.40 22.67 17.47 13.47 10.39 8.01 6.17 4.76 3.67 2.83 2.18 1.68 1.30 1.00

0.9 1.6 2.6 4.0 6.6 11.9 20.9 33.9 60.0 70.8 86.6 93.6 97.2 99.1 99.7 99.9 100.0

--, R.I. 301.5 211.0 147.7 103.4 72.4 60.6 36.46 24.81 17.36 12.16 8.61 6.95 4.17 2.92 2.04 1.43 1.00

* Dieke line pair intensity ratio.

The compu~r will hat the XT, the relative intensity, K, and 100 - XT. This last value is sometimes useful when plotting the H & D curve on calculator boards often seen in spectrographic laboratories. Some examples of the computer output for his part of the program are given in Table 3. In Table 3 each double column is headed by the intensity ratio of the line pair used in the calibration. For the specific K listed in ordered sequence in the leftmost Column U, and G%” have been converted to percent trana~ttan~e and relative intensity for each intensity ratio line pair. In the program, values of relative intensity and percent transmittance are printed for all values of K where K = 1,2,3 . . . n. These functions which represent the llnal H & D curve in each case have been plotted in Figs. 2 and 3. In Fig. 2 the statistical “ogive ” type distribution can be recognized while Fig. 3 presents the same data in the more familiar “normal curve” format. Although the listing of transiting vs. relative intensity is comprehensive and can be used for plotting purposes on calculator boards, it is unsuitable for table presentation. Because we did not have random access to a computer, we took the computer program one step further in processing the emulsion data.

A computer program to determine photographic emulsion calibration curves 100

319

c

so-

80-

‘OP 5

60- p 8

sYMBoL-lNT RAT. x1.472 . -1923 O-2831 A 4.167

40

30

K4 -

I

60

80

I

IO0

120

Fig. 2. Emulsion calibrationcurves obtained from the preliminarycurves, plotted on “ogive” type presentation.

The correlated %T vs. I data points equations in the form:

are fitted to two curvilinear

log T = A + B log I + C (log l)a, log T = A + B.I + C12,

%T I 50.0 %T > 50.0

regression

(3) (4)

The coefficients of the above equation are used to normalize the H & D curve to give a relative intensity of 100.0 for 1 .O%T and to obtain intersection of the two curves at 50.0 XT. The equations are then used to generate tables which list a relative intensity for 1.0 I %T I 99.9, in increments of 0.1 XT. It is left to the individual to select the range of transmittance he or she considers desirable or usable. A portion of one such table is shown in Table 4. The coefficients A, B and C from equation (3) are listed at the top of the table. The body of the table indicates the relative intensity for the transmittance listed in the leftmost column. Incremental changes in transmittance are provided for at the top of each column. The computer method for the emulsion calibration, as it has been described, has been in continuous use for the last few years. It has proven to be more reliable and precise than manual methods and can be applied to any method which uses a Seidel preliminary curve and which develops a geometric intensity series. The ouput of

320

A. CARNEVALEand A. J. LENCOLX 5C

-

SYMBOL X . -

40

-

INTRAT. I.472 1.923 2.831 4.167

ui?6!i

30

T=lOO-T

2c

IC

Fig. 3. Emulsion calibration curves plotted in the familar “normal distribution” format.

our program was tested for the same input data using an equation proposed by AXDERSON and LINCOLN[4]. The equation as proposed by ANDERSONand LXNCOLN is presented in the form: log (~~~~~)= 76log tts - ~~~~(~- &)I

(5)

where: Is = A/(1 - B) A =

Intercept of preliminary curve

B = Slope of preliminary curve R = log (IR*)/log

B

S, = Seidel reference transmission S, = Seidel of any other tra~s~ssio~

JR* = Line pair intensity ratio This equation is attractive in that it can produce a tabulated output of transmittance vs. relative intensity directly from the Seidel pre~rni~~ curve, e~nat~g equations (2-4) from the program. The computer program was revised from the end of the regression analysis of the preliminary curve to utilize equation (5). A complete table of transmittance vs. relative intensity was printed by the computer as before.

A computer program to determine photographic emulsion oalibration curves Table 4. Computer tabulation,

SA-I emulsion response curve

A* = 6.188'7 B* = 0.7923 C*= Y 1

2 3 4 6 6 7 8 9 10 11 12 13 14 lb 18 17 18 19 20 21 22 23 24 26 26 27 28 29 30 31 32 33 34 36

YP= 0.0 100.00 71.13 67.79 49.66 44.04 39.86 36.67 33.92 31.71 29.84 28.22 26.81 25.67 24.46 23.46 22.66 21.73 20.98 20.29 19.66 19.06 18.60 17.99 17.60 17.06 16.63 16.22 16.84 16.48 16.14 14.82 14.61 14.22 13.93 13.67

Y=

0.1

96.62 69.40 66.81 49.01 43.66 39.48 36.28 33.68 31.61 29.66 28.07 26.68 26.46 24.36 23.36 22.47 21.66 20.91 20.22 19.69 19.00 18.46 17.94 17.46 17.01 16.68 16.18 15.81 16.46 16.11 14.79 14.48 14.19 13.91 13.64

Y=

0.2

91.68 67.78 66.87 48.38 43.11 39.13 36.00 33.44 31.31 29.49 27.92 26.66 26.33 24.26 23.27 22.38 21.68 20.84 20.16 19.62 18.94 18.40 17.89 17.41 16.96 16.64 16.16 16.77 16.41 16.08 14.76 14.46 14.16 13.88 13.61

Y = 0.3 88.08

66.26 64.98 47.77 42.66 38.78 36.72 33.21 31.12 29.33 27.78 26.42 26.22 24.16 23.18 22.30 21.60 20.77 20.09 19.46 18.88 18.34 17.84 17.37 16.92 16.60 16.11 16.73 16.38 16.04 14.72 14.42 14.13 13.86 13.69

321

0.1604

Y = 0.4

Y = 0.6

Y = 0.6

84.94 64.84 64.12 47.19 42.23 38.46 36.44 32.99 30.92 29.16 27.64 26.30 26.11 24.04 23.09 22.22 21.42 20.70 20.02 19.40 18.83 18.29 17.79 17.32 16.88 16.46 16.07 16.70 16.36 16.01 14.69 14.39 14.10 13.83 13.66

82.10 63.60 63.30 46.62 41.80 38.12 36.18 32.76 30.74 29.00 27.49 26.17 26.00 23.94 22.99 22.13 21.36 20.63 19.96 19.36 18.77 18.24 17.74 17.27 16.84 16.42 16.03 16.66 16.31 14.98 14.66 14.36 14.07 13.80 13.64

79.62 8 62.23 62.62 46.07 41.39 37.79 34.92 32.66 30.66 28.84 27.36 26.06 24.89 23.84 22.91 22.06 21.27 20.66 19.90 19.29 18.72 18.19 17.69 17.23 16.79 16.38 16.99 16.63 16.28 14.96 14.63 14.33 14.06 13.77 13.61

Y = 0.7 Y = 0.8 Y = 0.9 77.16 61.03 61.76 46.64 40.99 37.48 34.66 32.33 30.37 28.68 27.22 26.92 24.78 23.76 22.82 21.97 21.20 20.49 19.83 19.23 18.66 18.14 17.66 17.18 16.76 16.34 16.96 16.69 16.24 14.91 14.60 14.30 14.02 13.76 13.49

74.99 69.89 61.03 46.02 40.60 37.17 34.41 32.12 30.19 28.63 27.08 25.80 24.67 23.66 22.73 21.89 21.12 20.42 19.77 19.17 18.61 18.09 17.60 17.14 16.71 16.30 16.92 16.66 16.21 14.88 14.67 14.27 13.99 13.72 13.46

72.99 68.81 60.33 44.62 40.22 36.87 34.16 31.91 30.01 28.37 26.94 26.68 24.66 23.66 22.64 21.81 21.06 20.36 19.71 19.11 18.66 18.04 17.66 17.10 16.67 16.26 16.88 16.62 16.18 14.86 14.64 14.24 13.96 13.69 13.43

* Coeffioients, equation (8).

A total of 72 paired transmittances which covered the full range of the table were used to calculate 72 intensity ratios. The same data were tested in the curve fitting method and the results compared. The coefficient of variation between the two methods was 2.6 ‘A and was not considered signifkant. In addition to the advantages of a faster and shorter program, equation (5) can also be used with a simple modifmation to determine the intensity ratio of any impurity line by: log (IX)

= K log [(S -

S,)/(S

-

S,)]

where : i3, = Seidel density of impurity line S, = Seidel density of internal standard A = Intercept

of preliminary

B = Slope of preliminary S = A/(1 = Intensity

IR = Intensity 3

curve

B)

K = log (IR*)/log IR*

line

curve

B

ratio used in calibration ratio of impurity

line.

of the emulsion

(6)

A. CARNEVALE and A. J.

322

LINCOLN

Equations (5) and (6) (ANDERSON and LINCOLN) were used to verify the authors’ technique and results, but have not been adopted to replace those of the authors’ more conventional approach to emulsion calibration. DISCUSSION The computer has been programmed to fit a linear regression equation to the Seidel function preliminary curve data. Introduction of the Seidel function, many years ago, was helpful in producing a longer range of linearity. The transition of the calibration to the two-line method was even more successful in the extension of the linear range. Optical alignment of the spectrographs, primary slit settings, light and dark films, scattered light in the microphotometers, operator influence, and other tests were made and any malfunctions corrected or limiting parameters defined, prior to the accumulation of both the authors and ANDERSON and LINCOLN [4] experimental data. The results on the experimental data indicated linearity even though we included all readings in the calculations from about 1.5 to 93 %T. The correlation coefficients listed in Table 1 reflect the linearity of the preliminary curve in the experimental results. This relationship has been maintained in all calibrations for the last 3i years. The premise that the slope of the preliminary curve should be unity does not hold in the two-line method of calibration. Except by accident (poor data) the slope will be something other than unity in the two-line method. The empirical relationship of intensity ratio and the slope of the preliminary curve (PC) was found to conform to: log (IR)

= A + Be

where 19= tan-l (slope of PC) For the data listed in Table 1, the indicated slopes are for 36.8” < t9 < 53.1’. These data are shown plotted in Fig. 4. The correlation coefficient for these data was determined to be 0.996. The preliminary curve, as stated previously, is used to derive the final H & D curve from the relationship: U,, = A i- BU,_, Repeated

substitutions

in this equation for decreasing

V = -A[1

U, reveals that :

+ (B + B2 + B3 + . . . B”-l)]/B”

(7)

v = u,

where

The expression in parentheses is the sum of a geometric series whose ratio is B and whose sum 8 is given by: S = B(B”-1 - l)/(B - 1) Substitution

of this sum in (7) results in:

V = A(1 -

l/Bn)/(l -

B)

If B > 1 and N is sufficiently large, l/B” --t 0

and

V = A/(1 - B)

A computer program to determine photo~aphic emulsion calibration curves IO.

,

SL

i

’

e

_

7

_

6

_

5

_

4

_

3

_

I

,

.,

ds

A

z

-m _

.’ -

I

n

2 .o -

1

Q

z -2 1

I

323

0

ifi

2

A

.s _ _ .(I A _

4

5 4

J

_

4 .1

t .I

I

3s

THETA (PEGREES) 40

*4

41)

32

I

,

56

60

Fig. 4. The logarithm of the intensity ratio of the Dieke line pair used in the calibration as a function of 8, where 13is the angle whose tangent is the slope of the preliminary curve.

It is of considerable interest to note that the value of l’ which is indicated by: V = A/(1 -

B)

is the Seidel value of the infraction of any Seidel function linear pre~mina~ curve and a Seidel curve with a slope of unity which passes through the origin, i.e., “the limit of development” concept of NOAR, “the saturation point” of ANDERSON and LINCOLN,or the “constant limit” of the authors. The family of curves described in Table 1 indicate the above limit is certainly a valid limit. Table 2 shows that this contrast limit, in the first quadrant in Fig. 1, is on the order of about O.O03%T. The limit value in the third quadrant is of no consequence and was not experimentally or empirically determined. CONCLUSION The conclusions of the authors are in agreement with those of NOAR,SCHMIDT, ANDERSONand LINCOLN. The program will duplicate the conventional manual technique for producing the final H $ D curve provided the user commits himself to linear p~l~ary curves in the usable range of % transmittance. The two-line method of emulsion calibration has advantages over other methods of emulsion calibration and is to be preferred whenever possible.