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5-1-1981 The alH ftone effect in color photographic enlargements Rick Crowsey
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Recommended Citation Crowsey, Rick, "The alH ftone effect in color photographic enlargements" (1981). Thesis. Rochester Institute of Technology. Accessed from
This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. THE HALFTONE EFFECT IN COLOR PHOTOGRAPHIC ENLARGEMENTS
by
Rick Crowsey
A thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in the School of Photographic Arts and Sciences in the College of Graphic Arts and Photography of the Rochester Institute of Technology
Hay, 1981
Rick Crowsey Signature of the Author . Photo~iiphic Science and Irtstrumentation
C. N. Nelson Certified by -.····.········.······ . Thesis Adviser
Accepted by . Supervisor, Undergraduate Research THE HALFTONE EFFECT IN
COLOR PHOTOGRAPHIC ENLARGEMENTS
by
Rick Crowsey
Submitted to the Photographic Science and Instrumentation Division in partial fulfillment of the requirements for the Bachelor of Science degree at the Rochester Institute of Technology
ABSTRACT
Effect" In continuous-tone photography, a 'Halftone
sometimes occurs that alters the tone reproduction in a distinctive way. Highlight contrast is decreased and middletone densities are lowered. Published data show that
this effect occurs in black-and-white photography when the grain pattern of the negative is reproduced very sharply in the print . High-magnification enlargements are especially
susceptible. Does a corresponding effect occur in color photography? A search of the literature reveals no answer.
The research here described is to determine, by direct measurements of densities in sharp and blurred enlargements, the magnitude of the halftone effect in particular color enlargements from color negatives. The validity of the procedure and the adequacy for the enlarger was tested by using black-and-white enlargements that demonstrate the halftone effect. The magnitude of the halftone effect was measured for color prints produced at a magnification of
25X. Grainless prints for comparison were obtained by rotating the print material during the exposure. The experimental results showed that the expected changes in density and contrast do not occur in the color materials
studied . ACKNOWLEDGMENTS
My thanks to all those who without their help this research would not have been possible, especially to C. N. Nelson, my
adviser always a gentleman and an encouraging scientist; to
Pat and Ray at Color Methods, who graciously allowed me to have free run of their company and smilingly endured; and to
the CIA for their financial support.
11 TABLE OF CONTENTS
List of Tables iv
List of Figures v
Introduction 1
Theory of the Halftone Effect 3
Experiments 13
Results and Conclusion 17
Notes 19
Bibliography 22
Appendices 24
m LIST OF TABLES
Table 1. Densities of the Wedge in a KODAK Process Control Sensitometer, Model 101 27
Table 2 . Camera Exposure Information 29
IV LIST OF FIGURES
FIGURE 1 The Density Difference in Black-and-White 4 Enlargements Due to the Halftone Effect
FIGURE 2 A tone reproduction diagram showing the 7 large difference in curve shape and density which exists, theoretically, between two prints from the same negative, one print having the grain pattern of the negative sharply reproduced in the print as a two- tone image of black-and-white spots and the other print having the grain pattern sufficiently blurred so that a continuous- tone image is obtained.
FIGURE 3 An idealized example of the halftone effect. 10
FIGURE 4 The mean reflectance, Rm, of the resolved 12 pattern is usually greater than the reflec tance, Ru, which results from the mean exposure, Eu, of the unresolved pattern.
FIGURE 5 A photograph of the target used in the 26
experimentation .
FIGURE 6 Sensitometer illumination measurement and 28
setup .
FIGURE 7 Top view of portrait setup. 31
FIGURE 8 Density - Log H showing halftone effect in 35 black-and-white, the change in contrast is 21 percent and the density drop is significant.
FIGURE 9 Density - Log H showing lack of halftone 36 effect in color materials used. Red, green, blue, and neutral density plots did not show a halftone effect. The change in contrast and middletone density was statistically
ins ignificant .
v INTRODUCTION
For most photographic prints, the principles governing
continuous-tone printing apply- The print densities can be
predicted by means of tone reproduction analysis based on
normal sensitometric procedures. When the grain pattern
of the negative is produced sharply onto the paper, it will
begin to behave like a halftone-dot pattern. This is known
as the halftone effect. The halftone effect can be briefly
defined as follows: !'For a given printing exposure, the
average density produced in a continuous-tone print is
usually lower when the granular structure of the negative material is reproduced sharply in the print image than it is when the granular structur-e is not resolved or when it does 2 exist." not The present study was made to determine the magnitude of the halftone effect in color photographic
enlargements .
The halftone effect has been previously investigated in 3 black-and-white materials by Altman and Peden, and Clark 4 and Nelson. Clark and Nelson found that the halftone effect lowered the highlight contrast of grainy enlargements by 25 percent at a print density of 0.20. A change in middletone density because of the halftone effect was found to be significant, but the magnitude of this drop was
small. An extensive search of the literature reveals no estimate of the halftone effect with regard to color photographic enlargements.
This study entails research geared to determine the magnitude of the halftone effect in color photographic
enlargements . The same procedures used for color materials are also used for black-and-white photographic
enlargements . The purpose of the work in black-and-white is to achieve and insure an experimental line of action able to detect any halftone effect that may occur in color
photographic enlargements .
In black-and-white printing, a loss of contrast is sometimes attributed to stray light when large (10X or more) prints are made. Stray light may be the culprit occasion ally; but if the enlargement is such that the grain is imaged sharply in the print, the halftone effect can be the cause for the apparent degradation. This study was initiated to determine if this same problem is encountered in color photographic enlargements. THEORY OF THE HALFTONE EFFECT
The halftone effect has been defined earlier. This
effect is most often encountered in enlarging because of the
increased size of the grain images, and its effect on the
tone reproduction of black-and-white enlargements has been
described by Clark and Nelson . When the grain pattern of
the negative is reproduced with unusual clarity in the print, as would be the case in some enlargements, the pattern will behave like a halftone-dot pattern to a degree which is dependent on the sharpness of the grain image produced on the print. Figure 1 shows the experimental halftone effect using black-and-white photographic
enlargements .
Tone reproduction curves may be used in continuous-tone systems to accurately predict the resulting density or tone reproduction in a finished print. A tone reproduction curve is a description of the macroreproduction characteristics of the photograph. The required densities are usually measured on the photograph with instrument apertures having diameters greater than 0.5 mm and the luminances are measured on corresponding large areas in the scene. The tone repro duction curve is an important factor in the analysis of fine Rotated
Fig. 1. The density difference in black and white enlargements due to
the halftone effect. detail reproduction also. For example, if the gradient of a
certain portion of the curve is nearly zero, the fine detail
reproduced at densities lying on that portion of the curve
is likely to be invisible or of poor quality. Increasing or
decreasing the overall gradient of the tone-reproduction
curve normally produced a corresponding increase or decrease
in small area density differences in the fine detail of the 7 8 photograph. The halftone theory described by Ives is
based on the rule that the reflectance R of the print is
related to the transmittance T of the negative consistent
with the following formula:
R = 1 - Tn
where Tn - percent area occupied by the dots.
Therefore, if 40 percent of an area of a negative is clear,
then 60 percent of the corresponding area of the print will be black. The above formula fails to take into account that
"black" the dots of the halftone print do not have zero 9 reflectance. It has been suggested that this formula be
corrected. The corrected formula, presented in log form, is
shown below:
Dp = L0G| 1-Tn (1-r)
Where Dp is the reflection density of the print and r is the
"black" reflectance of the dots of the print. The print densities predicted by the halftone theory are
independent of changes in the gradient characteristics of
"black" the photographic paper if the densities to which the
"white" dots and the areas are printed remain constant. For
continuous-tone printing, the densities of the print are dependent on the gradient characteristics of the print material . The only way to achieve results that are
equal, in a comparison of continuous and halftone systems,
is to use print systems for which the reflectance vs exposure function is linear. Actual photographic papers are, however, extremely nonlinear. Figure 2 is a tone- reproduction diagram showing the large theoretical difference in curve shape and density between two prints made from the same negative. One print has the grain pattern of the negative sharply reproduced in the print as a two-tone image of black-and-white spots. The other print has the grain pattern sufficiently blurred so that a continuous-tone image is obtained. The tone-reproduction
12 curves in Figure 2 were derived from the negative density vs log exposure curve in the lower right quadrant and the two transfer functions shown in the lower left quadrant. The transfer function for the continuous-tone
exposure curve for printing is the density vs log the photographic paper that was used to make the print. The transfer function of the sharp-grain print was calculated by Oneg
0.5 1.0 Oprint
Fig. 2. A tone-reproduction diagram showing the large difference in curve shape and density which exists, theoritically, between two prints from the same negative, one print having the grain pattern of the
negative sharply reproduced in the print as a two-tone image of black
and white spots and the other print having the grain pattern sufficiently blurred so that a continuous-tone image is obtained. assuming the use of the same negative material and applying
the theory of halftone printing described by Ives, 14 15 n f> Murray, Yule, and Clapper and Yule. The
halftone effect occurs as a result of the different ways in
which the density is distributed in a halftone negative and
a continuous-tone negative. Suppose that two negatives are
available, each with a minimum density of zero and a maximum
of 2.0. of One the negatives is completely uniform, the
other has fine structure such that at any point it either
transmits 100 percent or 1 percent of the light incident on
it. Suppose also that a suitable broad area on each
negative transmits 50 percent of the light incident on it.
These two areas would be identical visually and each would
give a density reading of 0.30 on a standard densitometer.
In the continuous-tone negative the absorption would take
place equally throughout the region. The fine structure
negative would pass about 50 percent of the light in a large
area.
Suppose now that a positive print is made from each of
these negatives onto a material with an idealized straight-
line characteristic curve which yields a density equal to the log exposure. If the exposure is so adjusted that the maximum density of 2.0 in the negative gives a density which is just perceptible in the positive, then the print from the density region of 0.30 in the continuous-tone negative would have a density of 1.70. For the negative with the fine
structure, half of the area on the positive would yield a
density of zero, and the remainder a density of 2.00. These
would combine to give a total transmittance of about 50
or percent, a density of 0.3 . This example is shown
graphically in Figure 3.
In figure 4 a different way of considering the halftone
effect is shown. Consider again the case of a grainy pattern
which is opaque over 50 percent of its area. This corres
ponds to a negative whose density above base is 0.30. If
this pattern is sharply imaged onto a photographic paper,
the characteristic curve of the paper would idealy be that
of the straight line in Figure 4. When the print is made,
the exposure E-. received by an element of area of the
positive stock under a grain is fairly low. Likewise, the
exposure E2 received under a clear area is high. On
processing, these areas produce the reflectance R-, and
R9 respectively, according to the characteristic curve.
The measured reflectance of a finite area of the sample will
be the average Rm of R, and R^ .
If, on the other hand, the same exposure is given under
conditons such that the granular structure is not resolved,
the curved line in figure 4 best repesents the
characteristic curve of the paper. Now instead of producing
Rm from the average exposure, the result will be Ru. As we 10
HALFTONE CONTINUOUS TONE
D = 2.0 NEGATIVES T=0.01
V
Logh a, ^a. .30
IDEALIZED PAPER D-LOG H
1.0
Dpos
2.0
D= 2.0 POSITIVES
-D = 0
D = 0.30
Fig. 3. An idealized example of the halftone effect. 11
can see, the difference in curve shape between the sharp and unsharp case in figure 4 has the most dramatic effect in the middle portion of the curve, and very little effect at the high and low ends. In terms of density, the density in the nongranular case will be higher than it is when the granular pattern is resolved. It is apparent from Figure 4 that the difference between Rm and Ru depends on the difference
1 ft between the two levels of exposure E-, and E2 In other words, the greater the difference between the minimum and maximum exposures in the grainy image, the lower will be the overall level of density of the developed print. This means that improving the imagery of the individual grains contributes to the halftone effect as well as to the improved transfer of information from the negative. 12
R1
\ \ POSITIVE PAPER CHARACTERISTIC
REFLECTANCE(%)
V-ajJ ^k \ V R vs E for the Blurred Case
= Rmean (R1 + R2)/2 a- _4r
X RvsE for the Sharp Case
Ru
R2 ^^"**>*,.^^
El Eu = (E1 + E2V2
Fig. 4. The mean reflectance, Rm, of the resolved pattern
is usually greater than the reflectance, Ru, which results from the mean exposure, Eu, of the unresolved pattern. 13
EXPERIMENTS
The hypothesis that was tested is, "Does the halftone
effect occur in color enlargements as in black-and-white
enlargements?" . The progress of the experimental work can
be partitioned into four, somewhat consecutive, tasks:
(1) obtain suitable black-and-white and color negatives,
"blurring" (2) construction of a easel, (3) producing
suitable black-and-white and color prints from the negatives
and, (4) analysis. The method that was adopted to determine
the magnitude of the halftone effect on print density in projection printing was to make two enlargements from the
same negative, one with the grain pattern of the negative
sharply focused and one with the grain pattern blurred by a rotating easel at the paper plane of the projection printer.
The densities of the two prints were then measured with a reflection densitometer which read an area large enough to include many grains. Using these densities to construct tone reproduction curves for each print, the halftone effect would then become immediately obvious by comparing the two tone reproduction curves.
KODhAK TRI-X Pan Film and KODACOLOR 400 Film were chosen to be used because of the grain structure in each. It was 14
hoped that by working with films that had a coarse grain
the structure, halftone effect would be easier to see if it
is present.
The target chosen was a combination of gray and color
scales and a suitable model. Since, in black-and-white, the
halftone effect is most apparent in enlargements, simulaton
of actual use of film would reveal information pertinent to
consumers of the film as well as being scientifically perti
nent. The target consisted of the following items: (1) grey
card, (2) grey scales and, (3) color patches. A fourth year-
professional photography student at Rochester Institute of
Technology was hired to photograph a model and the target as
a portrait. The films were kept at 30F except for warm-
up and exposure until 24 hours before processing. The
appendix contains detailed information on sensitometric
exposures, processing, the target, and the recording of the
scene .
Initially a vibration sander, masonite, and hardware were obtained in the hopes of constructing an easel which would blur any one point on the easel into a circle of about
1-3 mm in diameter. This device was discarded as a blurring easel when, upon activation, it persisted in vibrating across the workbench toward the floor. A phonographic turntable
was then obtained and proved to be delightful to work with and capable of blurring the grainular pattern of the negative suitably- 15
A Chromega D Dichroic II enlarger with a 25 mm f/1.9
Kodak Ektar II lens was used to produce the black-and-white
and color prints at a magnification of 25X. This is
"normal" approximately three times the magnification used in
printing, and will display the halftone effect if any is
present. Enough of the two papers, Kodak Polycontrast rapid
II RC type F paper, and Kodak Ektacolor 74 RC paper, type F,
was obtained to complete the project using the same
emulsion, so that no variability would be introduced via
different paper emulsions. The black-and-white prints were
processed with a Kodak Ektamatic processor using Kodak
Ektamatic A10 activator and Kodak Ektamatic S30 stabilizer
chemistry. The color prints were processed using a Colenta
processor and Kodak Ektamatic II chemistry. Control strips
were run before and after processing to insure that the
processed prints were in control. Data was collected from
the processed prints using a MacBeth TR-524 densitometer.
All the prints were replicated six times. Six runs of
"good" each print required the production of 128 prints. To have replicated more than six times would have meant that I would still be in the dark making prints, and to have done fewer than six would have yielded a poor estimate of v
and a . The sample standard deviation, sample mean, and 95 percent conficence limits around the mean were calculated and plotted in the form of a tone reproduction curve. The formula used and sample calculation can be found 16 in the appendix. A significant middletone density
(middletone density range is D = 0.40 to D = 1.5) difference was indicated by at least three of the four density levels in the middletone density range being statistically different (i.e., the confidence limits on the sharp and unsharp prints could not overlap) . The merit function for a
"contrast" difference in between the sharp and unsharp images was chosen as follows: If the contrast between the sharp and unsharp tone reproduction curves differed by more than 20 percent, they were considered statistically
"contrast" different. A 20 percent difference in was the minimum experimental difference which was statistically significant. The contrast was calculated as the slope of the straight line between the valves corresponding to relative log exposure equal to 0.70 and 1.60. 17
RESULTS AND CONCLUSIONS
Using the materials and experimental methods outlined,
it was determined that the halftone effect is not noticeably
present in color photographic enlargements. Appendix C
shows the results, in summary, in the form of comparison
tone reproduction curves. The black-and-white setup dis
played the halftone effect, confirmed the integrity of the
experimental setup, and agreed well with previous work. The
color photographic enlargements failed to manifest a
signficant difference in contrast or middletone density- A
slight drop of the curve for the sharp color images in the
middletone density was noticed, but by the criteria chosen,
difference" a verdict of "no was handed down.
Two possible reasons can be given for the failure of
the halftone effect to appear in color photographic
enlargements. First, in the color negative film, the
"image" is composed of three layers of dye clouds rather
than silver grains. The black-and-white negative is
"clear" composed of discrete silver grains suspended in a
gelatin. The discrete nature of the black-and-white
emulsion lends itself readily to becoming a psuedo-halftone dot pattern upon sufficient magnification, producing 18
"black" "white" discrete grains in a surround. The color
emulsion, on the other hand, appears as a conglomeration of
three color dye clouds somewhat overlapping. Even under
high "discrete" "clear" magnifications, no grains in a
surround are apparent. For the halftone effect to occur,
"dots" "clear" there must be discrete in a surround.
Second, the greater the difference between the minimum and
maximum exposures in the grainy image, the lower will be the 21 overall level of density of the developed print. With
the color emulsion, the differences between the minimum and
maximum exposures in the grainy image are smaller than the
differences when using the black-and-white emulsion.
The halftone effect in color photographic enlargements
is small enough to be neglected and is statistically not
significant. The halftone effect was demonstrated using black-and-white photographic enlargements to insure the validity of the experimental setup, and the results obtained 22 agreed well with previous work. The major causes for the nonappearance of the halftone effect are thought to be the nondiscrete nature of the color emulsion and the smaller
clouds" differences in exposure between the "dye and the
"clear" surround. 19
NOTES 20
NOTES
1. L. D. Clark and C. N. Nelson, Photographic Science and Engineering, Volume 6, Number 2, p. 84, 1962.
2. J. H. Altman and R. M. Peden, Photographic Science and Engineering", Volume 6, Number 3, p. 130, 1962.
3. Ibid.
4. Clark.
5. Clark.
6. Clark.
7. The Theory of the Photographic Process, Fourth Edition, ed. T. H. James, p. 536-561, 197 7 .
8. H. E. Ives, Journal of the Optical Society of America, 13:537 (1926)
9. Clark.
10. Ives.
11. Clark.
12. L. A. Jones, The Photographic Journal, 89B:126 (1949)
13 . Ives .
14. A. Journal of the Franklin Institute, Murray,(19363- 221:721
15. J. A. C. Yule, Journal of the Franklin Institute, 236:473 (1943).
16. E. R. Clapper and J.A.C. Yule, Journal of the Optical Society of America, 43:600 (1953).
17. Principles of Color Photography, R. M. Evans, W. T. Hanson, Jr., and W. Lyle Brewer, Wiley St Sons, 1953, p. 224-225. 21
18. Altman.
19. Clark.
20- An "Statistics, Introduction", A. D. Rickmers and H. A. Todd, McGraw-Hill, NY, p. 96-98, (1967).
21. Altman
22 . Altman. BIBLIOGRAPHY 23
BIBLIOGRAPHY
J. H. Altman, and Peden, R. M. Photographic Science and Vo 6 May- Engineering , lume , Number 37 June 1962, p. 130-134?
Clapper, F. R. and Yule, J. A. C., Journal of the Optical Society of America, Volume 43, p. 600 (1933)
L. D. and C. N. Clark, Nelson, , Photographic Science and Volume Number 2 Engineering, 6, , March-April 1962, p. 84-91.
R. M. W. T. and Evans, , Hanson, , Jr., Brewes, L. W., Principals of Color Photography, John Wiley and Sons, New York, 1953,
H. R. Journal of the Optical of Ives, , Society America Volume 13, p. 537, 1926.
James, T. H. (ed.),The Theory of the Photographic Process,
Fourth Macmillian Co. Inc . New Edition, Publishing , , York, 1977, p. 536-562, Chapter 17 "Tone and Color Reproduction" I. Tone Reproduction - C. N. Nelson
Jones L. A., The Photographic Journal, Section B, Volume 89B, 1949, p. 126.
Murray, A., Journal of the Franklin Institute, Volume 221 p. 721 (1936).
D. and H. W. An Rickmars, A. Todd, , Statistics, Introduction, McGraw-Hill Book Company, New York, 1967 p. 96-98.
Yule, J. A. L., Journal of the Franklin Institute, Volume 236, p. 473 (1943). 24
APPENDICES 25
APPENDIX A 26
APPENDIX A
+ 3
I
in the Fig. 5. A photograph of the target used
experimentation.
with a model for the The above is the target used upper right quadrent is an 18 photographic print. The lower half is a large gray scale, percent gray card. The the left quadrant is a small and the uppermost half of top a of the left quadrant is scale. The lower half top gray qualitative color scale. 27
TABLE 1
Densities of the Wedge in the KODAK Process Control Sensitometer, Model 101
Step Density
1 3.13 2 2.98 3 2.83 4 2.64 5 2.54 6 2.40 7 2.26 8 2.11 9 1.95 10 1.80 11 1.66 12 1.52 13 1.37 14 1.21 15 - 1.05 16 0.91 17 0.76 18 0.61 19 0.44 20 0.29 21 0.12
Black-and-white and color films and papers were
"customer" processed at color methods as normal film. Kodak control strips were run with all processing. The lab has a good history of quality control. All processes which were
control" used had been "in for 30 business days prior to my use and for at least 10 days after my use.
The equipment used was as follows: Kreonite color processor, Kodak Ektamatic processor, and the Colenta tube processor. All processors were being run by manufacturers suggested procedures. 28
Sensitometric exposures were recorded on each of the films using a KODAK Process Control Sensitometer, Model 101, Serial No. 101-881, RIT No. 58732, lamphouse setting -.5, lamp Serial No. 207, calibration current 0.780 A. Below is: (1) A diagram of the setup used to determine the flux incident at the film plane, (2) a list of the filters used, (3) and a table of the densities of the sensitometer step wedge, KODAK Serial No. 101-882, RIT No. 58732.
DETECTOR z 101 SENSITOMETER ?
FILTER HOLDER
*. n 2 5116 Inches
Fig. 6. Sensitometer illumentation measurement setup.
Configuration Flux
103 No filter 1.70 x lux 80B + 80D 341.00 lux 80B + 80D + 1.50ND 14.12 lux 7.53 lux 2 . 40ND 29
TABLE 2
Camera Exposure Informat ion
Stops from B&W Shutter Color Shutter "Normal" f/Stop Speed (seconds) Speed (seconds)
11-16 +5.0 1.00 2 .00
11 +4.5 .50 1 .00
11-16 +4.0 .50 1 .00
11 +3.5 .25 .50
11-16 +3.0 .25 .50
11 +2.5 .125 .25
11-16 +2.0 .125 .25
11 +1.5 .067 .125
11-16 +1.0 .067 .125
11 +0.5 .033 .067 "normal" 11-16 .033 .067
11 -0.5 .0167 .033
11-16 -1.0 .0167 .033
11 -1.5 .008 .0167
11-16 -2.0 .008 .0167
11 -2.5 .004 .008
11-16 -3.0 .004 .008
11 -3.5 .002 .004
11-16 -4.0 .002 .004
11 -4.5 .001 .002
11-16 -5.0 .001 .002
"Normal" exposure was determined by the photographer as
- he would in any portrait job. f/11 f/ll-16 gave enough depth of field so that all the scene would be in focus.
Only the shutter (focal plane) speed was changed to change exposure so that no variability would be introduced because
of different aperture sizes. 30
APPENDIX B 31
APPENDIX B
The following items can be found in Appendix B:
(1) camera/scene exposure information and, (2) statistics used in analysis.
Camera equipment used to photograph scene:
Nikon FE 135 mm Nikon f/2.8 background 2 scoop lights 1 plat light 1 light with an umbrella 1 hairlight
BACKGROUND
HAIRLITE
PERSON
TARGET
PLAT
LIGHT WITH UMBRELLA SCOOPS
? CAMERA
Fig. 7. Top view of the portrait setup. 32
The sample mean (x) and the sample standard deviation
"canned" (s) were calculated using programs available to
TI-58/59 owners . The formula used for each program is as
follows :
Sample Mean _ x = E x.
N
Sample Standard Deviation
I x - 0 s = N
N - 1
Where N is the number of samples taken and x . is the
data point.
The confidence limits around the mean point, plotted in
the comparison tone-reproduction curves, were calculated with the following formula:
x " < V < x + V 2 J* V f (/)
v A-2 of Where t , was found in Table , Critical Values
Students Distribution, in Statistics, An Introduction by
Rickmers and Todd. v is (N-l) and a was chosen as 0.05 to allow 95 percent confidence in our limits. 33
Sample Calculation
Sample Density
1 1.56 2 1.54 3 1.52 4 1.53 5 1.56 6 1.54
T. x,
1 - x = N = 6 N
1.54
2 -i 1/2 E x (2 = X..) S = 0.16 N
N
t5, 0.025 = 3.1634
x - t5, 0.025 < y < x + t5, 0.025 V1 V1
1.52 < y < 1.56 34
APPENDIX C 35
1.9 BLACK AND WHITE
1.6
DENSITY vs LOG H
1.3 m
)
1.0
0.70
SHARP
0.40
0.10 .^^.^AfftAiaflBaji^G^^^Qr
1 t
0.10 1.6
Relative Log H
I I 1 1 I I I 95 percent confidence lines data points
Fig. 8. Density-Log H showing the halftone effect in black and white, the change in contrast is 21 percent and the density drop is significant. 36
COLOR
2.2
DENSITY vs LOG H
1.0
0.40
0.10 Il. 0.40 0.70 1.0 1.3 Relative Log H
data points 1 1 1 1 1 1 1 1 95 percent confidence lines
Fig. 9. Density-Log H showing the lack of the halftone effect in the color material used. Red, green, blue and neutral density plots did not show a halftone effect. The change in contrast and middletone density was statistically insignificant.