FINAL REPORT ADVANCED COLOR IMAGE ASSESSMENT CONCEPTS

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B04747A001100020006-2
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 165
• Document Creation Date: December 28, 2016
• Document Release Date: December 2, 2004
• Sequence Number: 6
• Publication Date: July 1, 1968
• Content Type: REPORT

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FINAL REPORT
ADVANCED
COLOR IMAGE ASSESSMENT
CONCEPTS
STATINTL
Declass Review by NGA/DOD
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ADVANCED COLOR IMAGE ASSESSMENT CONCEPTS
July 1968
by
STATINTL
STATINTL
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STATINTL
The programming capabilities of
cannot go unacknowledged. Their efforts have made the theoretical proce-
dures described within this report operational facts.
The optical evaluation of the performance of achromat objectives in a color Micro-
Analyzer system was performed by
standing of the advantages and disadvantages of the current
Analyzer system has been very valuable.
STATINTL
His contribution to the under- STATINTL
Trichromatic Micro- STATINTL
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Image assessment procedures currently exist for black-and-white materials only.
Color image assessment and densitometry are defined only on the macroscale at pre-
sent. It is the objective of this report to combine these two fields to generate a color
image assessment technique based on those current image assessment measures that
can be applied to color tripack materials. The vector and matrix properties of color
materials are defined and applied to noise assessment, ensemble averaging, and modu-
lation transfer function. The shortcomings of the effective exposure technique are dis-
cussed, and a method is described for generating valid effective exposure tables for
color materials. It is possible that similar methods may be used in the generation of
target spectral signatures from color imagery. Quality control methods applicable
for color trichromatic and black-and-white microdensitometers are reviewed. Infor-
mation concerning the integral to analytical density conversion for three-color material
is presented, and all auxiliary experimental work in support of this program is reported.
Of particular interest is the investigation of the problems associated with the use of
achromat objectives in trichromatic microdensitometers.
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Section Title Page
I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1
II SPECTRAL PROPERTIES OF COLOR AND COLOR MATERIALS . 3
A. Properties of Groups . . . . . . . . . . . . . . . . . 3
1. Closure . . . . . . . . . . . . . . . . . . . . . 3
2. Associativity . . . . . . . . . . . . . . . . . . . 3
3. Id entity Element . . . . . . . . . . . . . . . . . 3
4. Inverse . . . . . . . . . . . . . . . . . . . . . 4
5. Commutativity . . . . . . . . . . . . . . . . . . 4
B. Integral and Analytical Densities . . . . . . . . . . . . 4
C. Vector Properties . . . . . . . . . . . . . . . . . . . 9
III AVERAGING OF MICRODENSITOMETER RECORDS . . . . . . 19
A. Necessity of Gaussian Assumptions . . . . . . . . . . . 19
B. Calculating the Gaussian Mean and Standard Deviation . . 19
IV NOISE MEASUREMENT . . . . . . . . . . . . . . . . . . . 27
A. Classical Methods . . . . . . . . . . . . . . . . . . 27
B. Correlation Method . . . . . . . . . . . . . . . . . 32
1. Autocorrelation . . . . . . . . . . . . . . . . . 35
2. Cross Correlation . . . . . . . . . . . . . . . . . 37
3. Matrix Formulation . . . . . . . . . . . . . . . . 38
C. Binomial Methods . . . . . . . . . . . . . . . . . . . 40
V EFFECTIVE EXPOSURE CONCEPTS FOR COLOR MATERIALS . 45
A. Basis for Effective Exposure Concept . . . . . . . . . . 45
B. Effective Exposure Concept and Color Materials . . . . . 49
C. Exposure Table Generation for Color Materials . . . . . 55
D. Summary . . . . . . . . . . . . . . . . . . . . . . 61
VI MODULATION TRANSFER FUNCTIONS FOR COLOR MATERIALS 65
A. Introduction . . . . . . . . . . . . . . . . . . . . . 65
B. Modulation Transfer Function Generation . . . . . . . . 65
C. Color Materials . . . . . . . . . . . . . . . . . . . 67
VII QUALITY CONTROL OF THE MICRODENSITOMETER . . . . . 69
A. Introduction . . . . . . . . . . . . . . . . . . . . . 69
B. Ideal Development of Quality Control System . . . . . . . 69
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CONTENTS (cont'd.)
Section
Title
Page
C. General Program Objectives . . . . . . . . . . . . . .
. 70
D. Drift Analysis . . . . . . . . . . . . . . . . . . . .
. 71
E. Frequency Response Stability . . . . . . . . . . . . .
. 75
F. Noise Injection Analysis . . . . . . . . . . . . . . . .
. 81
G. Summary of the Quality Control Procedures . . . . . . .
. 83
H. The Quality Control Target . . . . . . . . . . . . . .
. 85
VIII
LITERATURE REFERENCES . . . . . . . . . . . . . . . .
. 91
Ap
pendix
A
IN
TH
TEGRAL TO ANALYTICAL DENSITY CALIBRATION OF
REE-COLOR TRANSPARENCY MATERIALS . . . . . . . .
. A-1
B
CO
DIS
MPUTATION OF ALPHA RISKS FOR VARIOUS
TRIBUTIONS . . . . . . . . . . . . . . . . . . . . . .
. B-1
C
NO
MA
ISE MEASUREMENT STUDIES PERFORMED ON COLOR
TERIALS . . . . . . . . . . . . . . . . . . . . . . . .
. C-1
D
RE
AN
LATION BETWEEN ANALYTICAL AND INTEGRAL AUTO
D CROSS CORRELATIONS . . . . . . . . . . . . . . . .
. D-1
E
PR
SO
ODUCTION OF STEP WEDGES FROM NON-NEUTRAL
URCES . . . . . . . . . . . . . . . . . . . . . . . .
. E-1
F
SA
MPLE PROBLEM IN MULTIVARIATE COMPONENT ANALYSIS
F-1
G
OP
TICAL EVALUATION AND RECOMMENDATIONS FOR THE
STATINTL
I
PRECISION TRICHROMATIC MICRODENSI -
TO
METER 1032T . . . . . . . . . . . . . . . . . . . . .
. G-1
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Fig. No. Title
Page
1 Dye Spectral Density Curves of l1SO-151 Transparency STATINTL
Material . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Minor Density as a Function of Major Density: Emulsion 155-16-32 8
3 Idealized Block Dye System . . . . . . . . . . . . . . . . . . 11
4a Two Block Dye System that Obeys Beer's Law . . . . . . . . . 13
4b Two Block Dye System that Does Not Obey Beer's Law . . . . . 14
5 Angular Relationship of Dye Vectors . . . . . . . . . . . . . . 15
6 Spectral Density Curves . . . . . . . . . . . . . . . . . . . 16
7 Example of Density Frequency Histogram . . . . . . . . . . . 21
8 Selwyn's Relation for Two Black-and-White Materials . . . . . . 28
9 RMS Granularity vs Scanning Spot Diameter for Two Color
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 30
10 Differences Between Integral and Analytical Noise Records . . . . 31
11 Typical Autocorrelation Function for Black-and-White Material
at a Given Density Level . . . . . . . . . . . . . . . . . . . 34
12 Power Spectral Density Functions for Black-and-White Materials . 34
13 Experimental Data and Model Bernoulli Curve (Not Normalized) 41
14 Callier's Q as a Function of Diffuse Density and Gamma for a
Given Material . . . . . . . . . . . . . . . . . . . . . . . . 47
15 Characteristic Curve of Cyan Dye Layer of SO-151 Emulsion
Exposed to a Neutral and Resulting Exposure Table . . . . . . . 50
16 Characteristic Curves as a Function of Object Color . . . . . . . 52
17 Color Samples and Spectral Reflectance Curves . . . . . . . . . 53
18 Wavelength Dependence of Yellow Dye Layer of 8442 STATINTL
Emulsion . . . . . . . . . . . . . . . . . . . . . . . . 54
19 Exposure Table Generation System . . . . . . . . . . . . . . . 62
20 Quality Control Computation Flowchart . . . . . . . . . . . . . 84
21 Fourier Transform of Comb Target . . . . . . . . . . . . . . 86
22 Fourier Transform Envelope Function . . . . . . . . . . . . . 88
23 Microdensitometer Quality Control Target . . . . . . . . . . . 89
v11
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ILLUSTRATIONS (cont'd. )
Fig. No.
E2
E3
E4
E5
E6
E7
E8
E9
E10
Ell
E12
E13
E14
E15
Title Page
Spectral Sensitivity of SO-151 Emulsion . . . . . . . . . . . . A-2
Spectral Sensitivity of SO-155 Emulsion . . . . . . . . . . . . A-3
Spectral Sensitivity of 8442 Emulsion . . . . . . . . . . . . . A-4
Minor vs Major Density and Characteristic Curves . . . . . . . A-7
Minor vs Major Density and Characteristic Curves . . . . . . . A-8
Minor vs Major Density and Characteristic Curves . . . . . . . A-9
Minor vs Major Density and Characteristic Curves . . . . . . . A-10
Minor vs Major Density and Characteristic Curves . . . . . . . A-11
Minor vs Major Density and Characteristic Curves . . . . . . . A-12
Minor vs Major Density and Characteristic Curves . . . . . . . A-13
Minor vs Major Density and Characteristic Curves . . . . . . . A-14
Minor vs Major Density and Characteristic Curves . . . . . . . A-15
Optical Arrangement Used to Generate Non-Neutral Microstep
Wedges . . . . . . . . . . . . . . . . . . . . . . . . . . . E-2
Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-5
Spectral Reflectance Curve . . . . . . . . . . . . . . . . .
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
Spectral Reflectance Curve
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E-5
E-5
E-6
E-6
E-6
E-7
E-7
E-7
E-8
E-8
E-8
E-9
E-9
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ILLUSTRATIONS (cont'd.)
Fig. No.
Title Page
STATINTL
E16 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-9
E17 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-10
E18 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-10
E19 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-10
E20 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E- 11
E21 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-11
E22 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-11
E23 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-12
E24 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-12
E25 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-12
E26 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . . E-13
E27 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-13
E28 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-13
E29 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-14
E30 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-14
E31 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-14
E32 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . . E-15
E33 Spectral Reflectance Curve . . . . . . . . . . . . . . . . . . E-15
GI Schematic ofE~richromatic Microdensitometer 1032T . . . . G-2
G2 Schematic Representation of Wavelength Dependence of Epiplan 8
Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . G-4
Epiplan 8/0.2 . . . . . . . . . . . . . . . . . . . G-6
Ultrafluar 10/0.2 . . . . . . . . . . . . . . . . . G-7
Epiplan 16/0.35 . . . . . . . . . . . . . . . . . G-8
Defocusing Effect . . . . . . . . . . . . . . . . . . . . . . G-9
Schematic Representation of a Multilayer Color Film . . . . . . G-9
Three-Bar Target Focused with 546 Millimicron Filter and Traced
with 546 Millimicron Filter . . . . . . . . . . . . . . . . . . G-11
G9 Three-Bar Target Focused with 436 Millimicron Filter and Traced
with 546 Millimicron Filter . . . . . . . . . . . . . . . . . . G-13
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Because of increasing utilization, the area of color reconnaissance has come under
scrutiny in terms of its operational effectiveness and actual usefulness as a detection
tool. Color reconnaissance methods have been pressed into use without detailed evi-
dence of actual enhancement of the photo interpretation results. Because of the sub-
jective factors inherent in photo interpretation tasks, it is questionable if this detailed
evidence can be derived. Nevertheless, color imagery is being used, and for this
reason it is desirable to assess the quality of this imagery in manners similar to those
to which the reconnaissance community is already accustomed in the assessment of
black-and-white materials.
Research into color image assessment, with thoughts of retaining the basic methods
used in black-and-white image assessment (along with all its problems plus a few more),
may not represent the peak of scientific advancement. The basic question, however, is
purely pragmatic: "Can we, with suitable modification, develop a color image assess-
ment technique for transparency materials using the accustomed microdensitometric
techniques?" The objective of this program is to answer this question and to place
constraints, where necessary, upon the answer.
A search of the literature to determine what previous work has been done with this
problem has been futile for the most part. The results of this search are cited as refer-
ences on the following pages. Some work of Russian researchers is applicable. 1, w ? ,7
In the literature, color density has been studied primarily from the macroscale view-
point. Whenever color microdensitometry results have been reported, the microden-
sitometric methods are not given. Thus, the assumption must be made that a standard
black-and-white instrument was used to trace color materials. This is commonly
accomplished by placing the red, green, or blue filter at the light source or over the
photomultiplier (PMT) housing. If red, green, and blue records are desired from
* For convenience, all references are listed in Section VIII rather than when they
occur in the text.
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the same sample, then three scans must be performed. Since it cannot be assumed
that the sampled points correspond spatially on the three separate records, the use
of such techniques as crosscorrelation for granularity analysis is eliminated. The
record alignment required in order that analytical filter densities (AFD) may be
obtained from integral filter densities (IFD) is also difficult to accomplish. The
importance of working with analytical densities is discussed in the following section.
It must be assumed that the red, green, and blue records can be aligned and that
AFD's can be used in image assessment; this dictates the use of a trichromatic micro-
STATINTL densitometer.
metry in general:
present a necessary philosophy to color densito-
"Mere possession of a good color densitometer is not sufficient. Even the
best color densitometer will not be fully effective unless it is used with a
complete understanding of its limitations and the care that is necessary to
realize its full capabilities. "
This report represents a summary of the theoretical routes that may be taken in
developing a color image assessment capability similar to presently existing black-
and-white capabilities. Many procedures used in black-and-white image assessment
have been retained, others changed or broadened, and some new concepts added.
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SPECTRAL PROPERTIES OF COLOR AND COLOR MATERIALS
A. PROPERTIES OF GROUPS
Color photography has its basis in the laws of colorimetry. If it can be shown
that a set of colors, under the operation of addition or mixing, forms a group, then
certain mathematical procedures applicable to groups may be performed6 . The basic
group requirements that must be met are: (1) closure, (2) associativity, (3) an identity
element, (4) an inverse. If a fifth condition of commutativity is maintained, the set of
colors will form anAbelian group under the operation of addition.
1. Closure
C1iC2,,C3,...Ci,...
be a field of colors.
The rules of closure state that: in a given field, there is an element that exists
that is the result of an operation of one element on another, i. e. ,
C1 + C2 = C3
The experiments of Maxwell confirm that: given any two colors, there is a third
color that is the sum of the pair.
2. Associativity
The results of the operation must be identical, independent of the manner of
grouping:
(Cl + C2) + C3 = C1 + (C2 + C3)
Whether we add the first two of three colors together, then add the third; or add
the first to the sum of the last two, the result is the same.
3. Identity Element
The existence of an identity element means that the operation of this element upon
any other element in the field results in no change in the element operated upon:
Ci + I = Ci
In colorimetry, the identity element I is termed a neutral.
3
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4. Inverse
If the inverse of an element operates upon that element, the result is the identity
ci + Ci-' = I
In colorimetry, the inverse is termed the complementary color.
Hence, colors form a group under the operation of addition.
5. Commutativity
The order of operation of one element upon another must not affect the result:
Ci + C; = C1 + Ci
The order of addition is of no importance for nonfluorescent colors. Therefore,
nonfluorescent colors meet the requirements of anAbelian group for addition or mixing.
B. INTEGRAL AND ANALYTICAL DENSITIES
These findings are of significance for they allow the defining of spectrophotometric
properties of dyes in terms of an N -dimensional space and, thereby, allow the genera-
tion of critical tests that color materials must meet if image assessment techniques
are to be applied.
Figure 1 is a plot of the spectral density curves of the cyan, magenta, and yellow
dyes of a typical color material. By adding the densities of these dyes (at 10 milli-
micron intervals) the upper integral density curve may be generated. If a densitometer
were used to read the red, green, and blue densities of this integral tripack, it would
be determining not only the major density contribution of the dye having maximum
absorption in the waveband being measured, but also the minor contribution to the
total density of the other two dyes. Obviously, the total blue density, Db , is a sum
of the densities of primarily the yellow dye, as well as the magenta and cyan dyes to
a lesser extent. Thus:
Db = all Y + alb M + a13 C
(1)
The individual terms of the equation can be written explicitly because of Beer's
law, which states that the narrow-band, or spectral, density of a dye is directly pro-
4
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Figure 1. Dye Spectral Density Curves of
Transparency Material
500 540 580
Wavelength, A mp
STATINTL
protional to the concentration of the dye, i. e. ,
spectral density of cyan dye = aA Y
where Y is the dye concentration and aA is termed the spectral absorption coefficient
at wavelength k. .
For spectral or narrow-band densitometry, Beer's law holds; and Equation (1)
may be written as the sum of the absorption coefficients ai3 of the particular dye.
In this case the subscript i denotes the color being measured; j denotes the dye with
which the absorption coefficient is associated.
Similar equations may be written for the green DD and red Dr densities:
a.-1 Y + a22 M + ae3 . C
a31 Y + a33 M + a33 C
By arranging these three equations into a matrix, one finds that Dr , Dg , and
Db may be expressed as a multiplication of a column vector of C , M, and Y concen-
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tration elements by a 3 x 3 order matrix of absorption coefficients:
Dh
all are a13
Y
(4)
DD
=
a 21 a 22 a 23
M
Dr
a31 a32 a33
Ci
By writing the absorption coefficient matrix as A, the equation becomes
Db
r
Dg
A
Y
M
(5)
L
Dr
C
If the elements of the density matrix Dr , D, , Db
are measured with narrow-
band filters, they are termed integral filter densities (IFD) ; if measured on a spectral
densitometer or converted from spectrophotometric measurements to density, they
are termed integral spectral densities (ISD). The elements of the YMC dye matrix
are concentrations or densities of individual dyes; hence they are termed analytical
densities. The terminology becomes analytical filter densities (AFD) or analytical
spectral densities (ASD), with filter and spectral having the same meaning as before.
Integral filter densities are the most common measurements and are easily obtained.
Analytical densities are impossible to measure directly on imagery without physical
destruction of the image. However, analytical densities may be calculated from inte-
gral densities if the inverse of the absorption coefficient matrix is computed:
Y Db
M = A-1 ? D9
C Dr
(6)
Before the description of methods for obtaining the absorption coefficient matrix
is undertaken, the necessity of working with analytical densities will be explained.
Let us assume that a trichromatic scan of an edge is performed, and the red record
is taken through an appropriate dynamic transfer curve to yield effective exposure values.
If the modulation transfer function (MTF) is computed for this red record, it essen-
tially has no meaning,since it is the MTF of the cyan dye layer operated upon in some
manner by the MTF of the magenta and yellow layers because of the dye absorption
bands in the red of these latter two dyes. The manner in which dye cross absorptions,
such as these, affect the MTF is not known. Therefore, at the present time the trans-
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form of a red microdensity record has no meaning since no knowledge is gained con-
cerning the emulsion by computing such a transform. If the densities of the red records
are mapped using Equation (6) to obtain cyan, magenta, and yellow dye concentration
or densities, then the resulting MTF will describe the spatial frequency response of the
red-sensitive, cyan dye forming layer only. In this case, something is now known con-
cerning a specific layer in the emulsion. If, at a later time, one learns how one layer
of a subtractive color system operates upon another layer in terms of spatial frequency
response through the complex arrangement of sensitivity crossover and dye crossover,
then perhaps meaningful information may be obtained by transforming integral density
records. However, in the initial stages the image assessment work will be accomplished
by using analytical densities.
Three methods may be utilized in obtaining the absorption coefficients; all three
represent various methods of gaining access to one dye layer of the emulsion. (1) The
dye layers may be consecutively removed by gelatin-eating bacteria; (2) the emulsion
may be separately coated; or (3) the emulsion layers may be isolated by exposure.
Each method presents its inherent difficulty. In the operational case the most feasible
method involves exposing two layers of the reversal emulsion, leaving only the one
layer of interest unexposed. Obviously, if a wedge is then exposed in the remaining
layer using white light, a step wedge modulation of the dye formed in that layer will
be obtained. This has been accomplished for three films: SO-151, 8442, and SO-155.
The results are listed in Appendix A.
Each of the single dye layers is read on the densitometer or microdensitiometer
for which the matrix A is to provide IFD-to-AFD mapping. It is read for each of the
color filters that is to be used in reading or scanning the imagery. This yields three
sensitiometric curves for each dye layer: one set of major density values is generated
when the dye layer is read with the filter that is its complement; the other two sets of
densities are generated when the layer is read with the two remaining filters. A plot
of the minor densities, determined with the latter two filters, as a function of major
density is generated for each of the dye layers. The absorption coefficients of the major
densities fall on the main diagonal of the absorption matrix and are all unity (a? - a-2 - a33 =1.00).
The secondary absorption coefficients are determined from the slope of the line formed
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when a minor density is plotted as a function of the major density. The linearity of
this plot confirms the validity of Beer's law. If a straight line is not obtained when
minor densities are plotted as a function of major densities, it is an indication that
Beer's law is not valid. The reasons for Beer's law failure may be several; for example,
the density contribution may not have been reduced to zero through preexposure, or
densitometer problems may be the cause. However, when a straight line is obtained,
the slope of this line is the corresponding cross absorption coefficient.
Figure 2 is a specific example for the yellow dye layer of SO-155. The cross
absorption of the yellow dye to red and green light has been plotted as a function of the
blue light density. The absorption coefficient all = 1.00 . From the graph, the slope
of the straight line for green density as the dependent variable is a21 = 0.12 and for
red plotted as a minor density the absorption coefficient is a ,1 = 0.02 . These relation-
ships, and therefore the absorption coefficients, are valid only on the densitometer and
filters, used to determine the IFD's (in this case a
filters). In this case the complete absorption coefficient matrix for SO-155 is
I 1.00 0.21 0.11
0.12 1.00 0.15
0.04 0.17 1.00
0.8
U,
0 0.4
0
DD = 0.43
N DD = 0.12
Dr = 0.30
--- 4 Db = 1.00 .
Major Density, Db
Dr = 0.34
Figure 2. Minor Density as a Function of Major Density; Emulsion 155-16-32
STATINTL
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1.0276 -0.2017 -0.0827
A` -0.1202 1.049 8 -0.1442
-0.0206 -0.1704 1.0279
Let us assume the blue, green, and red densities for SO-155 in a particular instance
are 0. 24, 0. 56, and 0, 39 respectively. Solving for the yellow, magenta, and cyan dye
concentrations becomes a matrix multiplication problem:
Y 1.0276 -0.2017 -0.0827 ] . [ 0.24
L M = -0.1202 1.0498 -0.1442 0.56
C -0.0206 -0.1704 1.0279 0.39
Y = 1.0276 ( 0.24) - 0.2017 ( 0.56) - 0.0827 ( 0.39) = 0.10
M = -0.1202 (0.24) + 1.0498 (0.56) - 0.1442 ( 0.39) = 0.50
C = -0.0206 ( 0.24) - 0.1704 (0.56) + 1.0279 ( 0.39) = 0.30
The same principle is used to calibrate a trichromatic color microdensitometer.
A microstep wedge is produced separately in each of the single dye layers. These
microstep wedges are scanned and the red, green, and blue microdensities of each
step are averaged. The minor densities for each dye layer are plotted as a function
of the major densities. The slopes of the resulting straight lines (if Beer's law holds)
are the elements of the absorption matrix. The inverse of the matrix is taken, thus
yielding the mapping matrix of integral filter microdensities (IFMD) to analytical
filter microdensities (AFMD).
Emphasis is placed on the validity of Beer's law because of the necessity of using
mathematical models in building an image assessment procedure. If Beer's law is not
valid, then models based on the linear additive properties of dye layers are not valid.
Image assessment of color materials includes colorimetric assessment of the dye-
forming system. It has been shown that colorimetric procedures for nonfluorescent
color meet group requirements. This fact may now be utilized in testing the interrela-
tionships between the dyes.
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A spectrophotometric curve for a given dye is generated by reading the transmission
of the dye as a function of wavelength, generally in 10 m? intervals. It is assumed that
the measurement intervals are independent and are, therefore, orthogonal. If this
assumption is validated by the bandwidth of the measuring equipment, then a unit vector
xi may be defined at each measurement interval (i. e. , every 10m? over some wave-
length closed domain, say 380 < A
1
6
.
c 1.6
0
1.2
0
1.2
U
0
8
.
as 0.8
CL
N
a
h
0.0 h-- ----
L-- ---
"-g 1\3 "2
Wove length Wavelength
Figure 4b. Two Block Dye System That Does Not Obey Beer's Law
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Figure 5. Angular Relationship of Dye Vectors
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2.0
a
U 0.8
0
a
0.4
I-T
Wavelength, A m?
Yellow Dye Layer
151-23-32
Magenta Dye Layer
151-23-32
460 540 620 700
Wavelength, A m?
Cyan Dye Layer
151-23-32
Wavelength, A m?
Figure 6. Spectral Density Curves
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n {{
Fb = !hz
(16)
where f are the wavelength-dependent logarithmic output values for a nonspectral
absorbing sample in the scanning plane of the microdensitometer. Thus, for a micro-
densitometer to be used for color image assessment, the following condition must be
met in terms of direction cosines:
Fr ? Fg - F, - Fb F, . Fb
~Frl IFj IFr1 IFbI JFJ jFbI
= 0 (17)
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AVERAGING OF MICRODENSITOMETER RECORDS
A. NECESSITY OF GAUSSIAN ASSUMPTIONS
The scanning of color film samples with a small diameter spot, or a slit of small
width, generates a trichromatic record of densities with a significant noise variance.
Conversion of the IFD record to an AFD record retains the noise variance but modifies
its characteristics as described in the following section. To determine the density
level of each layer being scanned, the obvious method is to utilize a simple averaging
scheme based on a Gaussian process. In working with black-and-white material, evi-
dence has been presented that the distribution of noise in both density and transmittance
is not Gaussian. However, the distributions are not greatly skewed about the mean;
hence, a Gaussian assumption may be a good approximation. 7 There is an obvious
difference between mean density and mean transmittance of the sample since
~ logo (1/) (18)
For a microdensitometer operating in a digital mode, the average density corre-
sponds to the left side of Equation (18) and is obtained by computation of the mean of
the record. Generally, the photometric large area densitometer determines a spatial
transmittance average corresponding to the right side of Equation (18), which is then
displayed as density.'
The significance of this inequality for color material and the microdensity distri-
bution characteristics have not been reported. Until such information becomes avail-
able, it will be necessary to compute the average density of a sample using Gaussian
assumptions. It is desirable that the average density of an analytical trichromatic
record be determined in an automatic and non-arbitrary manner.
B. CALCULATING THE GAUSSIAN MEAN AND STANDARD DEVIATION
Let the open domain of analytical filter microdensities (AFMD) be expressed as
0 :< Di _< 4.00, (i = 1, 2, 3, ..., r) the density space being expressible by all densities in the
domain that can be grouped in cell interval of width A . In practice, the recording
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precision is two decimal digits; thus, the cell interval is A = 0. 01 and r = 400, yielding
an upper density limit of 4. 00.
If an analytical microdensity record of N densities is computed for one dye layer
from the IFMD for the tripack, there are two ways the Gaussian mean and standard
deviation may be calculated. The most direct method is by averaging the sample and
computing the standard deviation by the usual sum of squares technique. The second
method retains the actual distribution characteristics of the record by formation of a
frequency histogram. The abscissa of the histogram is the previously defined density
space arranged from 0 to 4. 00 in cell intervals of A = 0. 01. The ordinate of the histo-
gram is the frequency fi with which a specific density level Di is found within the
record.
After formation of the histogram, the least and greatest cell values for which there
are entries are determined, and the median cell between these two extremes is com-
puted as DM .
The cell values of the histogram are next renumbered with integers, li , taking
the median entry D. as the origin; the renumeration goes positive with increasing
density and negative for densities less than the median (Figure 7).
Di = DM li = 0
Di < DM l i < 0
Di>DM l;>0
The mean and standard deviation may now be computed from the histogram by the
following two equations, respectively:
= DM + (A/N) E fi li
A {i1N f~:li2
i = 0
fi li )2J /[N(N-1)] '1
i = o
(19)
(20)
The histogram retains the distribution properties of the sample and allows rejec-
tion of all anomalous samples that fail to satisfy a criterion such as:
I id
then fi = 0 (21)
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D1
.01
D5
.05
.10 .12 1.35
-8 -6
D140
1.40 D 1
-4 -2 0
D 150 D,?90
1.50 3.90
Figure 7. Example of Density Frequency Histogram
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D395
3.95
rTy
D400 ni
4.00 Density
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This eliminates all large density fluctuations that may be due to dirt particles, emul-
sion scratches, and other defects.
The alpha risk taken in performing this rejection, at 3. 5 times the standard devia-
tion from the mean, is small, as are the consequences of the risk. The mean and stan-
dard deviation, as expressed by Equations (19) and (20), are recomputed on the modified
frequency histogram.
In this case the modified sample size N'is used, where:
fz - E;
i = m2
M 1 (DM - 3.5 s) 100
nn2 _ (P, + 3.5s ) 100
(22)
Use of the histogram method also allows computation of the mean transmittance of
the standard deviation of the transmittance by the following relations:
_ (1/N') f~ exp (-2.30 D,,) (23)
n
2
N' f, exp (-4.60 Di)- fi exp (-2.30 ) 1z)
= a z= o
/ [N'(N- 1) 1' (24)
The density corresponding to the mean transmittance may be then computed as
D = logro (1/) (25)
Microdensitometry does not concern itself with constant density records but rather
with imagery, step wedge, and, in general, records in which different density levels
exist. The ensemble averaging concept must be applied so that changes in density levels
may be detected.
Since the density sample rate and the approximate dimension of the smallest object
to be detected are known variables, this allows the selection of a subsample of densities
ni from the total record N . The histogram technique is used for the determination
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of the AFMD subsample mean Dj and standard deviation s j (or variance sj ). To
detect changes in density level or in standard deviation, it is necessary to define an
ensemble average and variance 91.i and sej as running values determined by pooling
past subsample values that are of the same population.
Initially, a subsample mean and variance are computed for the first subsample
(j = 1). The next mean and variance are computed for the record sample (j = 2) and
compared to the initial values, which are taken to be the ensemble parameters. If the
just-computed values are the same as the ensemble values, then standard pooling tech-
niques are used. The new ensemble average becomes
Dej+I = (nej De. + nj + I Di + I )/(nej + nj + I )
where the new ensemble sample size is
nej + 1 nej + nj + I
s7 + 1 = [(nej - 1) s~ + (nj + I - 1) S + 1~ / (nej + nj + 1 - 2 )
(26)
(27)
(28)
The pooling procedures are identical in transmittance values. The criterion for deter-
mining if the subsample average differs from the ensemble average, or if the subsample
variance differs from the variance of the ensemble, is based on normal statistical test
procedures for a Gaussian-distributed population.
The test procedure requires that an F-test be performed on the variance of the sub-
sample, as compared to the ensemble variance. The null hypothesis in this case is
that the ensemble and subsample variances are equal:
2
H
2
p : Qe
j =
The alternative is that an inequality exists:
Qj + 1
(29)
Hr : ae2
j ~
2
of +
(30)
The F-ratio formed is subject to the following constraints:
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paal - Sej /S+ 1
Sjf + 1 /SFe a l = e j
The critical F-value may be selected from tabulated values' and is based on the
degrees of freedom of each variance and the alpha risk desired. Alternatively, the
alpha risk incurred with the rejection of the null hypothesis, for any computed F-value,
may be computed from the equations given in Appendix B. This procedure is more
amenable to computer operation.
If the variances can be taken to be equal, then they are pooled by using Equation
(28), provided the mean density level has not shifted.
A shift in density level is detectable using a calculated T-distribution value:
Tcal = (Dej - D j + 1 ) { ~ne, - 1 / ) ? s + (nj+ 1 - 1) 8i2+ 1 1 / (n,,; + nj +1 - 2) iz
X [ (1/n,, ) + (+ 11 + l ) ]-`z
(31)
with v := n,, + n,+ 1 - 2 degrees of freedom. The best procedure in running this test
is to compute the alpha risk associated with T,.,LI and v (Appendix B) and compare the
computed risk value with the acceptable risk. The null hypothesis in this case is that
the two means are the same:
110 : 11ej = ?j + i
The alternative is that the mean density level has shifted:
HI : Fte, ~ ?j + i
(33)
If both the mean and variance tests indicate no change between the ensemble and
the subsample, then the pooling of both the variance and mean density is allowable
24
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to form a revised estimate of the ensemble average.
If either the variance or mean density of a subsample is significantly different
from the ensemble values, then the ensemble values are set aside (stored, printed out,
etc.) and the new ensemble average is taken as the subsample parameters just com-
puted, i. e. ,
or Pei ~ 11j + I
Del+1 Di +I
2
Se7 +1 _ S7 +1
and the subsample averaging and variance computation and comparisons are carried
out using the next subsample j + 2. This procedure essentially "walks through" the
entire record and detects all shifts in mean and variance and sets aside the ensemble
average and variance for any stationary ensemble. Obviously, if there is a monotonic
trend in density level or variance throughout the record, then each subsample will differ
from the previous one, and no ensemble value with a large degree of freedom will be found.
This procedure may be used in the determination of RMS granularity, as will be
explained in the next section.
Since trichromatic records are involved here, this procedure must be accomplished
for each of the dye layers. A detection of density or variance shift in any one or two
dye layers, or differential shifts between dye layers, indicates that a change in hue has
been encountered. To detect hue shifts requires that all three dye layers be entered
into separate histograms on an individual spatial trichromatic sample basis (the tri-
chromatic values must first be converted from IFMD to AFMD).
If one or two layers shift in density, then a hue shift has occurred. If shifts occur
in all three layers, a hue shift or a neutral density shift may have occurred. If no shift
occurs in any of the three layers, then no hue shift has occurred.
The necessity and explicit method of detecting hue shifts within a density record
will be explained in Section V.
25
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26
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Processing a negative or positive black-and-white material produces particles of
essentially opaque silver. The growth of these silver particles and their form, spatial
constraints, and filamentary construction are determined by the gelatin environment and
the conditions and type of development. Since (1) the grains are individually opaque,
(2) the grains are small with respect to the diameter of the scanning aperture, and (3)
the grains are randomly distributed, then Selwyn's law is obeyed. This law states that
for a given material at a given density the product of the standard deviation of the density
(D) and the scanning aperture diameter d,L is a constant, i. e. ,
a(D) ? dp = G (34) .
where G = Selwyn's granularity constant. (A plot of this relation for two typical black-
and-white materials appears in Figure 8.) This permits computation of the RMS gran-
ularity of a material for any given scanning aperture once G is obtained. To realize
the full usefulness of this relation, granularity - a purely objective, numerical measure
of noise - must be related to the subjective measure of noise: graininess. Stulty and
Zweig10 stated this relationship by defining the viewing magnification, V., under which
the material was to be viewed and the effective point spread function of the eye. The
result is the simple computation of the aperture with which the material must be scanned
in order to obtain a measure of granularity that best corresponds to graininess. This
relationship
dli 513
Vm
(35)
is valid whether or not Selwyn's law holds. (In Equation (35) du is the required scan-
ning aperture in microns. )
Positive or negative dye-forming systems, based on a silver halide as the photore-
ceptor, form a dye image around the silver developed in the color developer stage.
Since the dye formation is a coupling reaction with the oxidized developing agent,
27
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3 4 5 10 20 30 40 50
Scanning Spot Diameter, dt, (microns)
Figure 8. Selwyn's Relation for Two Black-and-White Materials
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4 1 1 1 1 1 1
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the dye is formed in the vicinity of the grain being developed although obviously it can-
not be formed in the exact location. This fact, plus diffusion of the oxidized develop-
ing agent away from the reaction site, means that the image-forming unit in modern
color materials is a cloud of dye formed around the image silver. Of course, the
bleaching of silver leaves only the dye. Because of the diffusion condition, the assump-
tion of randomness of the image-forming units cannot be made. Because of the failure
of its basic assumption, Selwyn's law does not hold in the case of dye image-forming
systems" . The relation between a (D) and d? takes the form shown in Figure 9.
Since this means that the granularity of color materials cannot be computed, it there-
fore must be measured by using the aperture that will best simulate the effective aper-
ture properties of the system in which the material will be used (for human interpre-
tation see Equation (35)). There is some question concerning the validity of Equation
(35) in color materials since the fundamental unit visualized as grain is not a funda-
mental granular unit but may be an agglomeration of dye clouds 12 . Because of the
transparency of the dyes, the agglomeration is not necessarily confined to dyes in one
layer of the emulsion but may be dye clouds in other layers (Figure 10).
Because of the possible spatial superposition of dye units in different layers of the
film and because of the dye cross absorption, it is actually misleading to express gran-
ularity in terms of red, green, and blue densities.
The ensemble averaging methods, explained in the last section, will actually yield
the RMS granularity, a (D), as output. It is the simple standard density deviation of
a constant density sample of sample size Ne 5000. In other words, to adequately
estimate the RMS granularity of a material the sample size must be at least 5000. If
each density sample is taken through the mapping function A-1 (see Equation 6) to
obtain analytical filter microdensities (AFMD), then three analytical RMS granularity
values - namely a (C) , a (M) , and a (Y) - are determined in place of the integral
RMS granularity values a (Dr) , a (D9) , and a (Db) . The latter values contain errors
due to cross absorption of underlying dye clouds, as just explained. Using AFMD conver-
sion of each density sample, before computation of the RMS granularity, allows the noise
to be attributed to the proper layer of the emulsion. To recognize the significance of this,
the use of autocorrelation and cross correlation functions in noise measurement must be
discussed.
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0.05 1
0.04
Note : Both materials developed to same neutral density and
traced with a black-and-white microdensitometer.
Scanning Spot Diameter, du (microns)
Figure 9. RMS Granularity vs Scanning Spot Diameter for Two Color Materials
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Blue -
Sensitive Layer
Green -
Sensitive Layer
Red -
Sensitive Layer
Ii
Dye Cloud
Yellow Dye
Magenta Dye
Cyan Dye
O C~
A
Ll1
nn A P
f A - R-.. A
n n
Figure 10. Differences Between Integral and Analytical Noise Records
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Consider two continuous density records as a function of distance, namely f, (x)
and f2 (x) . The autocorrelation function of either of these records is defined as
Prr (r) = T lira
fe (x) /I (x+ r)dx (36)
The cross correlation of these two records, i. e. , the correlation of the first with the
second,is
(x)f
(x+ r dx
f f
37
,
2
(
)
P21
(r) = Jim_
T T.
1
2T f r
(x) f, (x+r)dx
(38)
P 12
(-r) = P21
(r)
(39)
Equivalent information results from use of auto and cross correlation functions
as from a determination of the RMS granularity as a function of aperture diameter '?'
However, the correlation method allows easier visualization of the influence of the
individual components of the photographic system on granularity. Explaining the inter-
pretation of correlation functions requires the definition of the power spectral density
of the noise, i. e. , the Fourier transform of the autocorrelation function:
0o T
Pit (.) = lim f 1
f fr (x) fr (x
T , - __ 27 T
f Prr (r) exp (-j a) r) dr
+ r) exp (-ja) r) dx dr
(40)
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P11 (r) = 1 J Prr (a) )exp(jc) r)da) (41)
2rr -o
giving the transform pair
P.rr (r r)P1j GO (42)
The same definition exists for the cross power density spectrum:
P12 ((D )
lim ~~
T-?? -. 2T T
J.
(43)
Pty (r) = 1
f P12(o)exp(jc)7)d6i (44)
2rr --
yielding the transform pair
P12 (r)-P12 (co) (45)
No great physical significance can be associated with the autocorrelation formula other
than it indicates the likelihood of correlation between the function at fi (x) with a value
of the function fi (x + 7)at the location x + r . Of course, when r = 0 , the correlation
should be perfect since
P11 (0) = lim
T --
x) 12 (x + r) exp (-ja) r) dx d7-
( r) exp ( -jw r) dr
1 r /__\r I_ \, lim 1 .0, ,.
f
which is a maximum. Of course, correlation should be expected throughout the interval
r < d
in other words, when the lag variable r is less than the aperture diameter. The
reason for this is that the aperture is of finite width, and several points on the emul-
sion may appear in the aperture at one time's . These effects can be seen in the corre-
lation function for a typical black-and-white emulsion in Figure 11. It has beeP2( 1V's
Review by
T
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Spot Diameter
Scanning Spot Size =: 2.0 microns
Correlation Distance or Lag, r (microns )
Figure 11. Typical Autocorrelation Function for Black-and-White
Material at a Given Density Level
observation" that the autocorrelation function of a print equals the autocorrelation of
the positive stock plus the autocorrelation of the negative stock, as modified by the
modulation transfer characteristics of the printer. The transfer of granular noise in
black-and-white materials can best be visualized by use of the power spectral density
function (Wiener spectrum). A hypothetical example of this function for a coarse- and
fine-grain emulsion, and a print of the former on the latter, is shown in Figure 12.
Material A
Print of A on B
2 3 4 5 10 20 30 40 50 100
Spatial Frequency, w (cycles/mm)
Figure 12. Power Spectral Density Functions for Black-and-White Materials
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The falloff of the function at the higher frequencies is due to the filtering effect of the
aperture. Doerner16 derived the relation for the determination of the Wiener spectrum
for a print P (wj D) , as a function of the gamma y to which the positive material is
developed, the Wiener spectrum of the positive material PP ((Oj D) and original negative
material PN (wj D) and the combined modulation transfer function of the negative material
and the printer I M (") ) I :
P r (w ; D ) = P N (w ; D ) [y I M (w )I ]2 + PP (w ; D) (47)
Obviously density, D , must be introduced as a parameter since the Wiener spectra
of the materials and the print are dependent upon the density level.
This type of granularity transfer analysis is important from the standpoint of the
determination of noise propagation characteristics through printing or reproduction
systems.
1. Autocorrelation
Published research' , 18, 19, 20 does not deal directly with the noise pro-
pagation of color reproduction systems. It does not even deal satisfactorily with the
color noise analysis of camera original materials. It is, therefore, necessary to initi-
ate color image noise assessment techniques for camera original and reproduction
materials. The first step is the examination of autocorrelation techniques for individual
dye layers of the color emulsion. In terms of analytical filter microdensity records,
the autocorrelation function may be written for each of the three dye layers:
yellow
(r) lim
Py~ _
T-4 ~
1
2T
fT
Y(x) Y(x+r)dx (48)
magenta
(r) lim
Pmm = T
T
1
f M(x)M(x+r)dx
2T T
(49)
(r) lim
Pow = T
~m
T
1 fC(x)C(x+1)dx (50)
2T fT
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In addition, six cross correlation functions may be written. First the cross corre-
lation of the noise record of the yellow layer with that of the magenta layer:
T
Pym. (r) = lim Y (x) M (x + r) dx (5t)
2T T
and similarly the yellow layer cross correlated with the cyan layer: Py? (7) (the cyan
record contains the lag variable); and the magenta layer cross correlated with the cyan
layer: Prc (r) . The three remaining cross correlation functions are the same as the
above three except that the other AFMD record contains the lag variable, i. e. ,
r
Pay = 7f M(x)Y(x+r) da
2T T
From Equation (39) it follows that
It will be standard procedure in this report to express the correlation function such that
the lower of the two dye layers contains the lag variable. When this cannot be accom-
plished, the notation of Equation (53) will be utilized. Then the remaining two correla-
tion functions are
f', ,r (r) = Py oo (v,axx(i)/x(i) x(1))~a X(i) = Ar B(') = V(')
(97)
(98)
This means that the sum of the squares of the elements of V (J) equals A, since
B(l)'B(l) = 1 (99)
Using Simond's notation, the modified covariance matrix S2 for the computation of the
second characteristic vector is
S2 = S - V(l) V(l),
(100)
The finite number of characteristic vectors (each a 400 x 1 array) extracted from S
may be arrayed to form a character matrix V . An example of this procedure is given
in Appendix F.
The physical significance associated with the characteristic matrix is that each
400 x 1 characteristic vector comprising the matrix describes a "principal source"
of variance of a sample exposure table from the neutral exposure table. Any exposure
table in the group of sample exposure tables may be regenerated by adding together
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certain multiples of the characteristic vectors. This is equivalent to stating that a
particular scalar multiple y, , 1 = 1, 2, 3, ... , p (where p is the number of charac-
teristic vectors) of the characteristic vector V(1) plus the amount yet + r) of vector
V 0 + 1) will, when added to the neutral exposure table, generate a perturbed sample
exposure table. Thus, the set E, may be regenerated by the simple matrix equation
E,. = V, Y, + E,~ (101)
where Y is the p x 1 array of scalar multiples. (Note: Subscript c denotes the equa-
tion representing the exposure table regeneration for the cyan dye. )
Equation (101) is the key to the exposure table regeneration routine. If the array
of scalars Y can be determined as a function of dominant wavelength and purity of the
image then the correct exposure table can be generated and the effective exposure
concept retained in color microdensitometry. Obviously the scalar multiples must
be determined as a function of the analytical densities Y , M , and C . This may
be accomplished by regression techniques, which implies that a sample of scalar
multiples must be generated. This,in turn, may be readily accomplished by defining
the weighting values W from the characteristic matrix. As stated by Simonds
W V B (a) /Air
From (101), then,
W, (E, - E~, )
(102)
(103)
Through regression analysis, the scalar multiples Vi, 1 = 1, 3, ... , p may be related
to the Y , M , and C analytical dye densities by determination of the coefficients
2j ,, j = 0, 1, 2, ... , 9 of the following equation:
2 pZ + 21 Z Y + 221 M + 231 C + 2k 1 M/Y + 25, Y/C
(104)
1 261 C/M + 271 Y2/MC + 28, M2/YC + 291 C2/YM
Once V, , Vm, , V? , and the set of coefficients for determining scalar multiples
(namely 2;:, 2;1,n, 2;1v , l = 1, 2, 3, ... , p , where p = the number of charac-
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teristic vectors in each V) have been established, the calibration procedure is
completed.
The operational system for the generation of the correct set of effective exposure
tables is presented in the flowchart in Figure 19.
Knowledge of the emulsion type and processing conditions allows the selection
of the appropriate data base from which the system works. This data base consists of,
first, the characteristic matrices for each of the analytical dye layers: V, for the cyan
or red sensitive layer, V,n and V,, for the magenta and yellow layers, respectively.
Each of the matrices is composed of p characteristic vectors, each characteristic
vector being a 400 x 1 array of values. Thus, each characteristic matrix is of dimen-
sion 400 x p . Secondly, the coefficients for scalar multiple computation (Equation
(104)) are required. There are nine coefficients for each equation and p equations for
each characteristic matrix.
The system neutral wedge analytical microdensities, representing the sensito-
metric characteristics of the particular emulsion batch in use, are used to compute
the set of neutral exposure tables Eon
Ern , Ez,,n by the standard curve fit and
inversion procedure. Once this information is known, the system is ready to operate
with image microdensity records.
Incoming integral microdensities (IFMD) are converted to analytical microdensities
(AFMD) through Equation (6). The resulting Y , M , C densities are used to deter-
mine the scalar multiples from the set of equations represented by (104), using the
coefficients as described above. This computation results in three matrices of scalar
multiples: Y0 , Y?L , and Y? , each of dimension p x 1 . Each exposure table is
then regenerated, the cyan exposure table by (101) and the magenta and yellow tables,
respectively, by
E, = Vm Y?, + Enzn, (105)
k = V~, Y, + E,.,n, (106)
61
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 DETERMINE COLOR
EMULSION TYPE
AND PROCESSING
CONDITIONS
EXPOSE & PROCESS
NEUTRAL WEDGE
ON EMULSION
BATCH USED A
PROCESS WITH
IMAGERY
SCAN NEUTRAL
WEDGE, ALONG
WITH IMAGERY,
WITH MICRO-D
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UBROUTINE
0 oSEMBLE AVG.
STEP AVERAGE
DENSITIES OUTPUT
GENERATE
NEUTRAL EXP.
TABLES FROM CRY
STEP WEDGES BY
CURVE FIT AND
INVERSION
COLOR
EXPOSURE
TABLE
GENERA-
N
O
CHARACTERISTIC
VECTORS FOR
GIVEN EMULSION d
SPECIFIC PROCESS
COEFFICIENTS FOR
DETERMINATION OF
SCALAR MULTIPLES
FROM CMY
DENSITIES
NEUTRAL
EXPOSURE
TABLES
VI/
~Vm
\yl
`zYP
MP
K- I
-- Et
"Emn
E(,n
LOAD EXPOSURE
TABLE GENERATOR
INTO COMPUTER
LOAD
CHARACTERISTIC
VECTOR DATA
BASE
LOAD COEF-
FICIENTS FOR
SCALAR MULTIPLE
DETERMINATION
FROM CMY
DENSITIES
LOAD NEUTRAL
EXPOSURE TABLES
FOR EMULSION
BATCH TO BE
USED
INITIALIZE FIRST
SET OF EXPOSURE
TABLES ON
ARBITRARY BASIS
SUBROUTINE:
CONVERSION OF
RCB INTEGRAL TO
CMY ANALYTICAL
DENSITIES
/15UTPUT'-,
FFEC TIVE
EXP. VALUES
FOR EACH
DYE
A PER
Figure 19. Exposure Table Generation System
SOLVE MATRIX EOS.
FOR NEW TABLES
Em= VmYm+ Emn
Ey=VyYy+Eyn
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The regeneration of the exposure tables is thus based solely on the incoming image
densities. Should the "color" of the image being processed change (a color change
being any change except the effective addition of neutral density), then the correct set
of exposure tables are generated. The procedure described allows generation of these
tables in 1/1000 the time required to generate the exposure tables from a set of char-
acteristic curves.
One problem remains unsolved at this time: what is the criterion to be used to
detect specifically when a new set of exposure tables should be generated? This cri-
terion is very situation dependent insofar as its method of solution depends on the
errors and risks that are allowable and the use to which the effective exposures will
be placed. Visual measures based on the CIE MacAdam system and MacAdam units
may be desirable, or a non-visual statistical detection method may be employed.
The procedure of exposure table generation may possibly be applied to the genera-
tion of the spectral signature of targets; however, no work has been performed along
this line within this program.
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1 1"
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SECTION VI
MODULATION TRANSFER FUNCTIONS FOR COLOR MATERIALS
A. INTRODUCTION
Articles and information dealing with the theory and uses of modulation transfer
functions abound in the literature and will not be discussed in detail within this report.
The program, which has just been completed, devoted little time to the investiga-
tion of color modulation transfer functions on an empirical basis. A few theoretical
concepts were generated that are of importance when considering the modulation trans-
fer function of color tripacks. These are described below.
As already mentioned in Section V, the photographic system may be considered
to be a linear process (point or line spread function) combined with a nonlinear process
(dynamic transfer function). The modulation transfer function (MTF) allows descrip-
tion of the linear process in terms of spatial frequency. It has also been mentioned
that there is evidence that nonlinearities do exist in the amount of 3-8% distortion when
the first three harmonics are considered. The cause of this apparent nonlinearity
in black-and-white materials has not been investigated. It may result from inadequacies
in the effective exposure concept, use of incorrect effective exposure tables, nonlin-
earities inherent in the emulsion proper, or the microdensitometer.
B. MODULATION TRANSFER FUNCTION GENERATION
There are basically three methods by which the MTF of an emulsion may be
evaluated. The first, and simplest in terms of computation, is to image sine waves
directly on the emulsion", 38 . Since the exposure is known, the input modulation for
a given frequency is computed as
Min = (Emax - Emin)/(Emax + Emir )
(107)
The modulation transfer factor is defined as the ratio of output modulation to input
modulation and is a function of spatial frequency, co :
Modulation transfer factor = Mout (w) / Min (w )
(108)
..r
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This function, when normalized to unity at w = 0 , is termed the MTF.
A second method of MTF generation is the utilization of an edge or step function
exposed on the photographic material. Assume that a perfect edge can be exposed on
the film, then the Fourier transform of the output edge derivative yields the impulse
response function of the material. Of course, the output edge function H (x) is ex-
pressed in terms of effective exposure.
Normalization at W = 0 then yields the MTF:
(109)
MTF = G ((,,)/G (0) (110)
Other methods involve the use of special functions which are imaged on the photo-
graphic material. These functions are divided into two groups: continuous and dis-
continuous. A sinc function is a prime example of the former, and the various bar
targets are examples of the latter.
Sinc functions 39 sine (x) = (sin x )lx have been acclaimed as an optimum target
for the evaluation of the spatial frequency response of the photographic material.
Problems exist, however, in the generation of this function as a continuous tone image;
therefore, widespread use of this function has not occurred.
Two types of bar targets are currently under investigation, the comb40? 41and
the binary comb" . These targets are easily produced on photographic materials.
However, to determine the MTF of the system the target transform must be removed
from the Fourier transform of the photographic output. If HT (x) is the target function
and Hr (x) is the resulting image function expressed in terms of effective exposure,
then the Fourier transforms are simply
GT (c~) HT (x) exp x)dx
GI (w) = f Hr (x) exp (-jcox) dx
(112)
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for the target and image functions, respectively. The normalized MTF of the photo-
graphic material is
MTF = G, (w)/GT (co) G (0) (113)
The computation of the MTF is performed using effective exposures derived from
the microdensity records. This, of course, assumes that the proper inverse dynamic
transfer function or exposure table was used in converting from analytical microdensi-
ties to exposure values.
The application of modulation transfer functions to color tripacks introduces a
significant complexity into their interpretation. Examples exist in which color MTF
curves have been reported. Verbrugghe' has reported red, green, and blue integral
modulation transfer functions for color materials. However, to go from integral MTF
to analytical modulation transfer functions, at the present time, is not as easy as it is
to obtain analytical Wiener noise spectra from integral data. This is because the sensi-
tivity crossovers for the three layers are operating in the exposure-optical diffusion
process and because the MTF curves are computed from effective exposure values
rather than density values.
It is suggested that in future programs the relation between integral and analytical
modulation transfer functions be investigated from both an empirical and analytical
standpoint. This research becomes essential once color photographic materials are
used in the estimation of spectral signatures.
Up to this time, a search of the literature reveals that consideration has only been
given to the neutral modulation of color materials. However, from an operational
standpoint this is almost a trivial case. There are several parameters that must be
more fully understood than at present. Not only does the output modulation vary as a
function of the input modulation, but the dominant wavelength and purity (or hue and
chroma) of the input modulation must also be considered. For example, in an opera-
tional situation the critical situation may be the detection of an edge generated by a
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green object on a greenish-brown background. Neutral modulation transfer functions
convey, at present, no information concerning the detectability of this situation with
a given material under given exposure conditions. The added dimension of the "color"
of the target then becomes a nontrivial operational parameter which is extremely signi-
ficant in the proper assessment of color imagery.
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 STATINTL
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QUALITY CONTROL OF THE MICRODENSITOMETER
STATINTL
STATINTL
0
Techniques for the quality control of microdensitometers were developed at
This study 4.4 resulted in
a procedure requiring the existence of a computer facility and the development of a
quality control target. It is a description of this program that is presented in this
section. The fact that the procedure was developed for black-and-white microdensi-
tometers is of no significance,as it may be adapted directly for trichromatic use. A
neutral target must still be used because the high resolution quality control target
can be produced to sufficient quality and stability only on black-and-white glass plates
at the present time. This target would be traced, however, in a trichromatic mode
and the trichromatic data analyzed to obtain quality control on each channel of the
microdensitometer.
B. IDEAL DEVELOPMENT OF QUALITY CONTROL SYSTEM
In an ideal situation (one that conforms to theory), a quality control system would
be established in accordance with the following sequence45.
Establishment of Policy. A decision to establish a quality control system represents
the initial desire for knowledge concerning the past, probable present, and probable
future status of a process or instrument.
Establishment of Objectives. In the second phaseythe goals of the quality control sys-
tem are dictated. If possible, the level of performance that the completed control
system is to achieve should be stated.
Adoption of a Plan. The next logical step is to formulate and adopt a plan whereby
the established objectives can be attained. (The establishment of a plan to meet the
quality control objectives is the goal of this section. )
Organization. Organization to carry out the plan is accomplished in basically two
phases: research and implementation. Research concerning the nature of the vari-
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ables of microdensitometry and how these variables are reflected in a quality control
measure is necessary prior to finalization and implementation of a quality control plan.
Personnel Selection and Training. The selection and training of people to operate the
system are, indeed, important phases in making a quality control system design an
operational entity meeting the initial objectives. The operators must be sufficiently
informed to maintain the quality control system, and they must be unbiased to the point
that they will not force out-of-control conditions to in-control situations by arbitrarily
resetting the limits.
Motivation. Stimulating people to meet the planned objectives may become a large
problem, especially if many people utilize an instrument which is monitored on a quality
control basis. Rather than allow the quality control procedure to be handled by many
or by whomever is utilizing the machine at the time, it is desirable to assign this task
either to a single individual or to a department handling all such tasks.
Reevaluation. Once established, the quality control system should not be abandoned,
unless the system does not meet the planned objectives or unless the basic quality
policy changes. Continued updating of expectations and control limits must be part
of the system procedure. Reviewing the system against its objectives and attempting
to correct its deficiencies are time consuming steps whose accomplishment may re-
quire considerable control system background history. Nevertheless, the reevaluation
of the system is necessary, not only to approach the final objectives of the program but
also to streamline the system to an efficient procedure.
C. GENERAL PROGRAM OBJECTIVES
The establishment of a quality control system for a microdensitometer must be
based on a meaningful measure of system performance, such that the information
gained from the control system will be useful in the diagnosis of machine failures.
This system must be designed to allow cross comparison of quality control informa-
tion between machines, thus allowing relative calibration on this basis. The procedure
for obtaining the basic (raw) control data must involve as little setup time and run time
as possible. Likewise, mathematical computations or manipulations must be computer
programmable for short throughput times. The output from the program must be
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readily interpretable in terms of the status of the system as well as the diagnosis of
machine failure. In other words, the quality control system for the microdensitometer
must operate with the utmost efficiency in order to generate a maximum of useful infor-
mation with the minimum possible expenditure of energy in man-hours (training and
running), microdensitometer time, computer time, etc.
The following results are anticipated from the implementation of the proposed
quality control system.
1. It will increase reliance on the data taken from a microdensitometer to which
the control system has been rigorously applied,since the probable operational status
of the instrument will be known at a time not remote from the time of measurement.
2. It will give assurance that data taken from any single microdensitometer may
be mapped to correlate with data taken from the same input to a second microdensi-
tometer, providing that the quality control system has been applied to both instruments
and that both are in control. (This concept arises from a hypothesis that microdensi-
tometers are not easily calibrated on an absolute density basis and that an ensemble
average taken from a finite record is not directly relatable to the diffuse density value
determined from a standard large area or macrodensitometer, except perhaps on an
effective exposure basis. )
3. It will establish routines for the diagnosis of causes of machine failures in
situations considered out of control.
In the evaluation of standard diffuse macrodensitometers, quality control efforts
are generally concerned with maintaining the dc response of the instrument. In the
general case, control information is gathered in three portions of the dynamic range
of the instrument, i. e. , high, medium and low densities. Drifting of the instrument
response can be detected by zeroing and recalibrating (rereading a "calibrated" step
wedge or a series of selected points from a step wedge) periodically. The length of
this calibration period is determined by the risk the operator wishes to take in the
detection of short-term drift errors.
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Similar dc problems disturb the world of microdensitometry, but in this case
there is also a lateral, longitudinal, or rotational translation of the image during the
measurement period. This gives rise to concern for the spatial frequency response
characteristics of the microdensitometer. However, it is reasonable to assume that
shifts in the spatial frequency response characteristics of the microdensitometer will
be of a long term nature and will be caused either by improper operation of the instru-
ment or by operational failure of the instrument.
Shifts and changes in the spatial frequency response of the system may be detected,
providing that any dc drifting is first detected and removed from the data. Given a
specific image to be scanned, the drift of the instrument during the scanning period may
be reasonably estimated by observing the initial dc calibration or setup points and then
recalibrating at the end of the image scan. Observing the differences between the ini-
tial and final calibration points yields an indication of the drift of the instrument over
the measurement period.
From these observations, a basic procedure may be evolved for collecting quality
control information from a microdensitometer. The basic procedure encompasses an
initial setup or scanning of a step wedge, so that the zero point and dynamic range of
the instrument may be established. This may then be followed by the scanning of a
target suitable for the measurement of the spatial frequency response characteristics
of the instrument. Following this, a rescan of the step wedge or of a selected number
of setup calibration points may be accomplished, thus providing a determination of the
amount of dc drift in the instrument during the intervening time. (Short term instabil-
ities would not be detected by this method but would be reflected in the spatial fre-
quency response variations of the instrument.) If the drift interval is constant (i. e. ,
if the measurement interval At is constant), then a determination of the difference
between the first and second dc calibrations will measure the average drift rate. This
involves an assumption of a drift function that is linear with time. Estimation of the
drift rate may be a trivial point, as any detectable dc shift during the measurement
period is undesirable. In testing for the presence of dc drift, it is necessary to real-
ize that such shifts may be detectable only on a statistical basis.
The dc calibration of a microdensitometer is performed on an effective exposure
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basis. This means that the establishment of the calibration curve for the microdensi-
tometer is performed from a constant input, just prior to the scanning of the test target.
Generally, this input consists of a step wedge of i = 1, 2, 3, ..., n discrete levels,
such that the input function range is compatible with the dynamic range of the micro-
densitometer. After the scanning of the "unknown" sample, the step wedge is again
scanned. The data so determined are taken through the initial calibration curve, so
that drift errors appear as effective exposure errors.
Let represent the initial calibration value for the i th step. This is an
ensemble average effective exposure taken over the i th step of finite width. After
the scanning of the unknown sample, the step wedge is again scanned, and the effective
input value for the ith step is again determined as .
A correlated pair analysis" (paired observation analysis) may be performed upon
the differences A = - . This type of analysis will permit the detection
and estimation of the probable magnitude of any drift occurring during the measurement
interval At . To perform this analysis, two parameters are computed: one is the
average difference, d , across the n steps of the calibration wedge,
n
d A
(114)
The second parameter is the standard deviation of the differences across the cali-
bration wedge
En (A - a)E
i=i n-
(115)
The main assumption in this case is that the values obtained for the average deviation
estimates d are distributed normally about the true mean difference 8 . This being
the case, from the above values a test statistic may be calculated which follows a
student's T -distribution function with n - 1 degrees of freedom:
TCAL =
d (116)
Sd
In all cases, the null hypothesis Ho is that no drift 5 occurred during the interval At:
Ho : 8 = 5o = 0
(117)
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The alternate hypothesis that must be accepted, if the null hypothesis is rejected, is
that drifting of the instrument occurred over the interval in which the ac response char-
acteristics of the microdensitometer were evaluated, i. e. , during the interval At
II : 3 / 8r, (118)
Rejection of H0 then indicates acceptance of the occurrence of a significant amount of
drift during the estimation of the ac response characteristics of the instrument and
brings into play the alpha risk taken when the null hypothesis is rejected. In this case,
a rejection, or alpha error, occurs when a set of ac response data is rejected as con-
taining microdensitometer drift when, in truth, no drifting occurred. In stating the
rejection error or the specific alpha probability that would be acceptable, two factors
come into play: the first of these concerns the alpha risk directly, and the second
takes into account the allowable beta or acceptance risk. The two factors, considered
together, determine the magnitude of the drift error that can be detected.
The consequence of rejecting a set of data as containing microdensitometer drift,
when actually it does not (alpha risk), requires the rescanning of the quality control
target and a loss of man-hours, microdensitometer time, and a small amount of com-
puter time. On the other hand, acceptance of a set of data containing drift (beta risk)
could (1) indicate an out-of-control situation in the analysis of the ac response of the
system, thus bringing into play the diagnostic program with the consequences of clos-
ing down the system until the problem is diagnosed (the only actual machine error,
in this case, being do drift); or (2) the drift problem could remain undetected, thus
influencing production data; or (3) the machine could stabilize, and the drift problem
could disappear in future time. The only data influenced in this case would be the ac
quality control data. (As can be seen, the time of day when quality control data are
gathered from the machine may influence the result obtained. )
In terms of consequences, the risk involved in accepting the existence of dc drift,
when in truth there is none, is less than the risk involved in accepting data as being
drift-free when, in truth, it is not. Thus, the acceptable alpha and beta risk proba-
bilities may be set on a relative basis as a >_ a .
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E. FREQUENCY RESPONSE STABILITY
The mention of quality control monitoring of the ac response characteristics of the
microdensitometer system involves many implications and problems. The first of
these is that it is, at best, an exceedingly difficult problem to assess the absolute fre-
quency response of a microdensitometer in terms of spatial frequencies. However,
by placing quality control restrictions upon the utilization of frequency response data,
the problem becomes of lesser magnitude in that the stability of the response can be
monitored without regard to the absolute frequency transfer function of the apparatus.
The observation that spatial frequencies, when scanned, are mapped into temporal
frequencies brings into consideration the flutter and wow idiosyncracies of the drive
mechanism. Drive instabilities may be diagnosed through proper inspection of the
quality control data.
A possible error source exists in the ability of the operator to focus the instrument;
if the focus is far from optimum, attentuation of the higher spatial frequencies results.
This leads to questions concerning what optics and what slit dimensions or spot diameter
should be utilized in the quality evaluation procedure. Since there are many possible
combinations of slit size, spot size, scan speed, digital conversion rate, and chart
velocity, quality control information obviously cannot be generated for all possible
permutations. The alternative is a practical choice of one or a few conditions based
on some criteria such as a median condition, a most often utilized situation, or an
extreme condition that is likely to illustrate system problems with a high sensitivity.
The method of approach to developing the basic diagnostic and quality control
procedure is threefold. First, we must develop a method of relating, numerically,
the information gained through frequency plane analysis of a specific target to the
operational status of the microdensitometer. Ideally, this basic quality control mea-
sure would be a single number reflecting the effects of all the critical parameters of
the microdensitometer. Once a mathematical method of dealing with spatial frequency
data, on a quality control basis, has been established, the second step then consists of
applying this knowledge to the design of a specific quality control target configuration
that will satisfy the demands of the mathematics of the quality control procedure. The
Approved For Release 2005/02/10 : Cl RDP78B04747A001100020006-2
 Approved For Release 2005/02/10 : CIA-RDP78BO4747AO01100020006-2
third step is the simulation of machine failures on a mathematical basis, resulting in
the establishment of the diagnostic procedure to be utilized when the general quality
control measure indicates an out-of-control situation.
The basic quality control target will be a configuration that varies as some function
of distance in the xy plane. It is desirable that the y domain of the target be so defined
that to the microdensitometer it would appear that the configuration is constant in the
y direction, that is, F (y) = constant for -- _ l ndc%)
r
21, - it
L n even)
77
1. Abramowitz, M., Stegun, I. A. Handbook of Mathematical Functions AMS55. Washing-
ton, D. C. : Government Printing Office;(June, 1964). p. 948.
A (Ti )= f TT (vIx)dx
where T (vi x) = Student's distribution function
v = degrees of freedom
ITI = closed domain end point over which
area is computed. This T-value is
computed by the statistical T-test.
a = the risk taken in rejecting the null
hypothesis Ho .
A (Tip) = the area under Student's T-distribution,
bounded by -T _< x