NBSIR 76-1129

An Improved Photographic

Edge-Artifact

William R. Smallwood

and Richard E. Swing

Institute for Basic Standards

National Bureau of Standards

Washington, D C. 20234

August 1 976

Final

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 76-1129

AN IMPROVED PHOTOGRAPHIC

EDGE-ARTIFACT

William R. Smallwood

and Richard E Swing

Institute for Basic Standards

National Bureau of Standards

Washington, D C 20234

August 1 976

Final

U S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward O. Vetter. Under Secretary

Dr. Betsy Ar&cker- Johnson, Assistant Secretary tor Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

AN IMPROVED PHOTOGRAPHIC EDGE-ARTIFACT

By

William R, Smallwood

and

Richard E. Swing

Optics and Micrometrology Section

ABSTRACT

The history of edge-objects for use in optical and photographic testing

is briefly reviewed and culminates in a short summary of the technique

developed at NBS in 1965 for producing photographic edges by x-ray

exposures on high resolution photographic plates with a tantalum strip

to generate the discontinuity. The report then covers the development

of an improved method for producing these edge-artifacts. It is shown

that with x-ray exposure, the relation of density to exposure is linear

up to densities of approximately 2.0. This linear relation is then

exploited to produce two kinds of edge-artifacts. Both artifacts contain

ten (10) values of density and three edge-discontinuities. The edges on

one artifact have the same value of contrast, with different mean densities,

while the edges on the other have different values of contrast. The use

of each type is discussed. Techniques for determining exposures, for

determining the transmi ttances of the aluminum step tablets used to

modulate x-ray exposure and for determining the linear relation between

density and exposure are presented in mathematical detail and exemplified

in subsequent illustrative experiments. Some inherent limitations of

the method are discussed. It is concluded that there is sufficient flexibility to the process and procedures to provide sharp edges, in a wide range of contrasts, on demand.

INTRODUCTION

The use of an edge-discontinuity in the determination of acutance for

photographic materials 1 and in the evaluation of optical systems through

edge-gradient analysis2 has been well-explored and documented. Implicit

in these techniques is the perfect quality of the edges used; if perfection

has not been specified or implied, their quality has always been assumed to

be significantly better than the system they are to test. Thus, a premium

has been placed on the production and calibration of near-perfect edges.

The problems associated with edges can be categorized under "usage" and

"fabrication", although they are not totally unrelated.
Fabricating a usable edge has always been difficult. Perrin describes the

difficulty in making good edges 3 and the literature is replete with references to such problems. Since the edges must be better in quality than

the systems they must test, optical imaging of an edge-discontinuity

to produce an exposure on a high resolution emulsion contains a number

of inherent limitations that preclude such a fabricating technique.

Clear and opaque edges are not useful for testing films or optical systems.

With films, if adjacency effects are present in processing, it is better

to have maximum and minimum densities on the straight-line portion of the

characteristic curve for quantitative analysis; transmittances of 1 and 0

(clear and opaque, respectively) cannot be usefully accommodated on the

majority of photographic materials since the useful dynamic range is not

large enough. In optical system testing, it is best to delimit the

input illuminance since most systems do not have a dynamic range capable

of handling that provided by a clear and opaque edge-artifact.

In use, in the determination of the acutance of photographic materials,

the edge must be held close to the photographic material so that diffraction effects are minimized. On the other hand, if excessive pressure

is used to hold the edge against the material, the material itself may be

damaged or compressed, leading to a thickness variation, sometimes a cut,

that adversely affect results. These same considerations apply to the

fabrication of an edge by photographic contact-printing.

In an optical system the edge is imaged, and it is important that the

edge-transmittance attenuate the illumination solely by absorption; i.e.,

be non-reflecting. Reflective edges tend to introduce additional nonimage forming light (usually flare or a modification of the flare already

in the system), which by virtue of its one-sidedness results in an apparent system impulse response that is asymmetric. Further, the

light introduced by the reflection, although small, limits the high-density

side of the image to values generally less than 2.0. These effects are

present even with purely absorptive materials, and the reflections exacerbate the problem.

Two Approaches to Fabrication:

. . 4 There have been various approaches to the fabrication of edges. Eyer

employed edges in contact-printing that were made by carefully folding

a piece of one-mil aluminum foil. The folded edge was then rolled under

pressure, blackened (the reference does not specify the means) and then

mounted on a glass plate. In his microdensitometer, the density of the

scanned edge dropped from "...an effectively infinite value to zero in

less than three microns." 1* The only microdensitometer parameter cited in

2
his paper is the sampling aperture, which was held constant at 1 x 300

micrometers. The instrument he reported using is generally operated with

matched numerical apertures and nearly always employs image-scanning'.

If the microdensitometer performance was at all linear, the edge was indeed

of exceptional quality.

Razor blades are a traditional tool in preliminary experiments calling

for edges, but are inadequate when useful accuracy and precision in

measurement are required. Nicks and other inhomogeneities along the

edge, its opacity and the unwanted reflections from the shiny surfaces

quickly rule out this type of artifact. In a variation of the razor blade,

use of a reflective edge was described in 1964 b

. Here, a silvered surface of glass was scored with a diamond tool and all the silver to one

side of that line subsequently scraped off. Not surprisingly, unwanted

reflections held useful instrument measurements to densities below 2.0.

When used as a master to produce photographic edges (through contactprinting on Reprolith film*) however, these reflections did not affect

exposure quality, and the resultant edges proved to be useful at higher

densities

.

These kinds of experiences, together with the preceding discussions, lead

to the specification of ideal edges for optical and photographic testing.

These edges should have the following properties:

1) A near-perfect discontinuity for the edge, blemish-free, uniform

density on either side of the edge;

2) The artifact should be free of marks, cuts, compressed or swollen

areas and, if made photographically, should be free of adjacency

effects;

3) Density should be manifested by absorption; reflective edges are

to be avoided;

4) To reduce the effects of system flare light, and to exhibit nonlinear effects (if they occur), densities should not exceed 3.0

nor be less than 0.30, approximately; transmittances of 0 and

1 are to be avoided.

^Certain commercial equipment and materials are identified in this report

primarily to specify the experimental procedure adquately. In no case

does such identification imply recommendation or endoresement by NBS,

nor does it imply that those identified are necessarily the best available for the purpose. Further, the equipment or materials may not be

identical to those products currently on the market that bear nominally

similar designations of type.

3
The Initial NBS Effort:

To realize these objectives and to provide a source for physical edge

standards in the optical and photographic community, McCamy and Berkovitz,

at the National Bureau of Standards, developed a technique for making

photographic edges of extremely high sharpness that were non-reflective

.

The work was reported at the 1965 annual conference of the SPSE 7. Briefly,

the method employed x-ray exposure of Kodak high resolution plates. The

discontinuity in exposure was obtained by inserting a 10-mil thick strip

of tantalum into the exposing radiation, in contact with the photographic

material. The edge of this strip had been optically smoothed and polished

and was clean, without nicks. Tantalum is capable of precision machining

because of its hard, compact structure, yet thin strips are not brittle.

It has a high attenuation for x-rays (particularly in the 20 to 50 kV

range) because of its relatively high atomic number. The subsequent

chemical processing of the exposed emulsion was devised to eliminate

or minimize adjacency effects. Those NBS edges have served the optical

and photographic community well, and have been available from NBS since

1965.

The Current NBS Effort:

In 1972, with the publication of papers on microdensitometer linearity 8 ’ 9 ’ 10

interest in using edges for microdensitometer performance evaluation received a new stimulus. By 1974j the supply of edges at NBS had been exhausted, and it was felt appropriate to review the entire process, so that

format changes could be considered and the tantalum strips re-worked.

By then, the original process had been modified slightly, to provide

minimum densities that were above the toe of the characterisitic curve

(by pre-fogging the material in visible light prior to x-ray exposure).

Step tablets of the same material with identical processing routinely

accompanied each edge. Thus, each edge artifact consisted of two glass

plates, 2.5 x 7.6 cm, with the one having an edge discontinuity running

the full 7.6 cm length. Edge contrasts varied from high (AD = 3.0) to low

(AD = 0.30), and were neither standardized nor reproducible.

After review, it was decided that the edges and step tablets could be

combined on the same physical standard and the two basic artifacts would

be developed and standardized:

1) ten-step tablet, incorporating three edges of different contrast;

2) ten-step tablet, incorporating three edges of identical contrast

but of different average density.

4
The first of these would be useful for normal system testing, at low,

medium or high contrast. The second would be useful for exploring the

photometric response of systems, holding the input contrast constant but

varying the mean illuminance. These artifacts are extremely useful for

evaluating microdensitometer performance. The short working distances

associated with the high numerical aperture optics commonly employed in

these instruments preclude the use of artifacts on glass plates. Thus,

it was also decided to make the artifacts available on film.

Scanning electron micrographs of the tantalum edges showed the need for

rework. After optical polishing, it was found that the edge was unsuitable and a new approach was taken. The tantalum strip was embedded in

an epoxy and given a me tal lograph ic polish; the final polishing grit

particles were nominally 0.05-/im in diameter. Scanning electron micrographs of the edge of the tantalum strip showed a definite improvement

in quality over those that were optically polished.

It was felt that a detailed investigation of the basic process was

warranted, in the expectation that a mathematical framework could be

developed for specification of exposures, contrasts and densities.

This would facilitate production of two "stock" artifacts and permit

fabrication of customer-specified edge-density differences, if demanded.

The investigation of the theoretical aspects of the process is reported

in the following section. The results of experiment are reported in

a subsequent section.

THEORY

A large amount of research has been reported on the exposure of photographic materials to x-rays. These have been so well summarized in

reference 11 that their individual citition need not be given here.

Among the many useful facts reported are the following:

1) The image with x-ray exposure is stable at room temperature

and moderate humidity; latent image-fading increases with

increased temperature and humidity.

2) There is no reciprocity law failure nor intermittency effects

with x-ray exposures.

3) Density is a linear function of exposure with x-rays, for

densities up to at least 1.0, and often as high as 2.5.

While these are all significant for the present program, the latter has

the most immediate impact. It has been found possible to extend the normal

linearity with x-ray exposures by using high resolution emulsion exposed

and processed for the toe of the normal characteristic curve. Furthermore, in contrast to what we intuitively expect from these materials

processed to low densities, the image densities are close to neutral.

5
Figure 1 contains a plot of density versus exposure for high resolution

emulsion (film and plate) exposed and processed under the conditions to

be described in the experimental section. It is clear that the lower

portions of each of the curves can be represented by an equation of the

form

D = A E + C, (1)

where D = Density;

E = Exposure;

C = Base-plus-fog density;

A = Constant: characteristic of light

intensity, film speed, chemical

processing, etc.

To modulate exposure, we can either vary the intensity of the source

or attenuate a constant illuminance by a step tablet. The latter has

a much greater range of variation and is inherently more stable. For

a given exposure time and source intensity, the density of the resultant

exposure and processing depends on the transmittance of the corresponding

portion of the tablet. With x-rays it is convenient to use a step tablet

consisting of layers of aluminum foil. Thus, for a transmittance due to

k layers of aluminum foil, the linear relation of Eq . (1) becomes

D(k) = A T(k) t + C, (2)

T(k) = transmittance for k layers of foil,

t = exposure time,

The other terms retain their previous meaning.

In the section on experiment, these constants will be determined and tne

range of validity of the equation clearly established. Until then, we

postulate the uniform applicability of Eq . (2) and next consider the

exposure of the photographic materials for edges.

Photographic Edges:

There are two basic types of edge-artifacts we consider. Both contain

three edges and ten patches of uniform density. One has edges of different

contrast (VCE) while the other has edges of constant contrast (CCE). The

uses of each have already been discussed. We will consider the techniques

6
of exposing these two artifacts, using the tantalum strip previously introduced to achieve the edge-discontinuity. We specify contrast across edges

as density difference, since this is the most useful measure, and denote

it by AD.

Variable-Contrast Edges

A tantalum strip is laid along a piece of film, approximately dividing

the width of the film in half. Over this is placed a five-step tablet

of aluminum foil layers. All three are placed in the beam of x-radiation

and exposed for a time, t]_. The exposure on that portion of the film

covered by the tantalum is zero, while that portion not covered by the

tantalum can be described by

1

E(k.) = T(k

5 ) t r (3)

where the superscript denotes the first exposure series. The exposure

history at this point is sketched in Figure 2a.

The x-radiation is now stopped, the tantalum strip is removed,

film and accompanying step tablet are exposed for a time, t 2

- second exposure adds another exposure to the format and can be

by

and the

The

described

2

E(k.) = T(k ) t 2

. (4)

The exposures of Eqs. (3) arid (4) add; the summary is sketched in Figure

2b.

The density differences AD(k) produced by these exposures and the linear

characteristic curve of Eq . (2) are given by

AD(k) = A |r(k) t

1

+ T(k) t . ? |

+ C -

|

A T (k) t £

+ c|

= A T (k) t.

(5)

This shows that the contrast of each edge

mittance of the corresponding step on the

the first exposure time.

To produce a given AD, we must have information about the sensitometry

,

since this enables us to determine T(k). In Appendix A the system

sensitometry is discussed in detail, and is based on knowledge of the

is determined by the transtablet and is proportional to

7
transmittance factors for the aluminum step table, T(k). There it is

shown that

T(k) exp + a

2

)k + a

2

k ( 6 )

where

k = number of layers of aluminum foil,

and the constants a^ and a

2 are determined by experiment and subsequent

analysis. In that same analysis, the constant A, necessary for the linear

characteristic curve, will also have been determined.

Let us specify three AD(k)'s that are to be produced on the artifact,

AD(k)^, AD(k >2 and AD(k) 3 , and order them so that AD(k)-^ is least and

AD(k )3 is the largest. From Eq . (5), with knowledge of constant A, we

can write

T( k) . t = AD( k) /A. (7)

l 1 l

It is clear that the largest value of AD(k)^/A can be attributed to the

largest AD(k)-^, since it is in the numerator. Further, since we want at

least one step on the tablet-artifact higher than any density related to

the three edges, we must choose k greater than 0; k = 1 is probably the

most effective in terms of exposure. Then if we make this choice, we

have

t L = AD(k)

3 /AT(l) . (8)

With this value of t^ established, we can now solve for T(k)^ for the

other two steps, through

T(k)t = AD( k)± /A t-L . (9)

Since the analysis that produced the value of A also produced a listing

of k versus T(k) (see, for instance, Table I), the value of k closest to

the value of T(k)^ given by Eq . (9) is taken for the given AD(k)^. Thus,

the correct values of k^ , k

2 and k

3

, as well as the first exposure time,

t^ , are determined quickly and with a reasonable accuracy. Clearly, it

is not possible to produce an edge contrast precisely through choice of

k, since T(k) is not a continuous function and only seven aluminum layers

8
are ordinarily used. However, a choice of t ^ will allow some selection

for at least one of the three edge contrasts.

An alternative method for finding the k^'s results from combining Eqs.

(5) and (6), taking natural logarithms of both sides of the equation and

solving by quadratic formula for k. The resulting relation is

int(k

±

) = a

3

/ 2 + (1/2)

^ - (4/a

2

>log

e |

(At _ ) /AD (k)

, |

where = (a^+ a^)/a^ ,

and int(k^) is interpreted as the nearest integer value

of k.

As with the first method, determination of k must start with the highest

value of the required AD(k). However, no convenient provision is made

for establishing the first exposure time, tj_, and a great deal of trialand-error is necessary before the constants are determined. The first

technique is clearly preferable, but both are acceptable.

Since the tablet-artifact will have five regions of exposure, the middle

three of which have been specified by k^, k 2 and k^, the remaining two

specifications are optional. If k^ has been chosen to be 1, the lower

value will necessarily be k = 0, since there is nothing beyond that. The

upper value can be chosen to provide densities that would be useful for

the tablet.

To keep the artifact densities on the linear portion of the densityexposure curve (and thus achieve predictable results), the upper density

limit must not be exceeded. Since the AD(k) are related to T(k) and t\,

we must determine the first-exposure time first . Then, since ^E(ki) +

2E(k-^) will be the larger exposure,

D(k)

max

= A

[

! E(k) + E(k)

]

+

max

= A T (k) (t. + t_) + C.

max 1 2

(ID

This can be solved for t so that the second exposure time is given by

(D(k)

max

- C)/A T (k) ) max

- t. ( 12 )

( 10 )

9
Then, for the variable-contrast edges, Eqs . (5), (8) and (12) determine

the parameters necessary for controlled production.

Constant-Contrast Edges

Place a five-step tablet of aluminum foil layers over a piece of film

and expose to x-rays for a time, t^. The exposure on the film can be

described by

lE(k

i

) = T(k i) t x

, (13)

where the superscript again denotes the first exposure series. The

exposure history to this point is sketched in Figure 3a.

The x-radiation is then stopped and the step tablet removed. The tantalum

strip is now laid along the film strip, approximately dividing the width

of film in half. The film and tantalum strip are then exposed to the

x-rays again, for a time, t 2- The second exposure adds another exposure

to the format and can be described by

2

E(k.) = t 2

, (14)

in those portions of the film that are not covered by the tantalum strip,

and

2 , x E(k t

) = 0,

where the film is covered. These exposures add to the first; a summary

of both is sketched in Figure 3b.

The density differences AD(k) produced by these exposures and the linear

characteristic curve of Eq . (2) are given by

AD (k) = A |t

(

k) ti + t 2 }+ C -

-Ja T(k) + C

A t

2

. (15)

This shows that the contrast of the edges is independent of the transmittances of the tablet steps, is constant, and is directly proportional

to the second exposure time.

The second exposure time is determined first , and is obtained by inverting Eq . (15). Thus

,

10
t AD(k)/A, (16)

where AD(k) is constant, and specified according to requirements. At

this point, the values of the five tablet steps can be specified. These

will depend on the density values desired for the various portions of the

edge-artifact. They will also depend on restrictions called for by the

linear characteristic curve. Since ^E(k^) + will be the larger

exposure

,

D(k) = A | T(k) t. + t 0 \ + C . max

\

y max 1 2 f ( 17 )

This can be solved for t^, so that the first exposure time is given by

< D(k)

max

- C)/A - t

2

/ T(k)

max ( 18)

Then, for the constant-contrast edges, Eqs . (15), (16) and (18) determine the parameters necessary for controlled production.

Discussion I:

In order not to interfere with the orderly development of the theory relating exposure times and step tablet layers, the discussion of several

restrictive relations was deferred. These have an important bearing on

the eventual application of the technique and require an interpretive,

discussion that would have been distracting at the time.

For both artifacts, the second calculated exposure time depends on the

previously-calculated exposure time and the maximum density of the linear

characteristic curve, as can be seen in Eqs. (12) and (18). Since the

first exposure times were determined from the specified contrast value

(or the maximum of the three required for the VCE), it is possible to

obtain negative values for the second calculated exposure times. Since

they have no physical significance, it indicates a restriction on contrast

as a function of maximum density. This can be seen from a consideration

of Eq . (12), for the VCE artifact. So that t£ not have a negative value,

it is necessary that

(D - C)/A T( 1 ) > t (19)

max 1

Since t^ was determined from Eq . (7) (using the high-contrast value,

AD(k)^), we can insert it into Eq . (19), and obtain

°< k>3 ^ “max -C- (20)

With Eq . (18) for the CCEE artifact, it can be shown that the inequality

of Eq . (20) also applies. Thus, for both artifacts, the upper limit to

contrast (in terms of AD) is given by the difference of maximum density

and base-plus-fog density.

11
• .

I

.

In like manner, there is a minimum attainable contrast for the VCE artifact

that stems from the method of determining the aluminum foil layers. The

lowest contrast value and the exposure time are used to determine the

appropriate T(k), from which the value of k is taken. This is stated

in Eq (9). Since no more than 7 layers of foil are used (see the discussion of this in Appendix A), the smallest value of T(k) will be that

equivalent to T ( 7 ) . Thus, from Eq . (9), with the appropriate subscript,

D(k) 1/A t x < T( 7 ) . (21)

When we replace the t ^ by the value determined in Eq . (8), we can see

that

AD(k)

x < AD (k)3

• H, (22)

where

H = T(7)/T(l) . (23)

Thus, the lowest contrast is limited not only by the specified high

contrast value, but also depends on the effective transmittance factors

of the aluminum foil. However, since the low contrast of the CCE

artifact is independent of the step table, no practical lower limit

to contrast exists for that artifact.

It is clear that the highest possible value of Dmax must be determined for

the material used in any application, since this clearly controls high

contrast for both artifacts and the low contrast for the VCE. Experimentally, that value should be evaluated closely to give the technique as

much contrast latitude as possible.

EXPERIMENT

To examine the limitations of the theoretical relations and to determine

practical values for ranges of densities and contrasts that can be achieved

by this technique, a limited experimental program was undertaken. The

ultimate goal of the program is the production of edge-artifacts of

prescribed properties, on film and glass plates. The experiments therefore concentrated more on the practical, engineering aspects of the problem

and less on some others (e.g., the interesting analytical relation between

the number of aluminum layers, x-ray exposure, and the corresponding

effective transmittance factors).

Photographic Materials:

Kodak High Resolution Plates in the 1 x 3-inch size have been used since

the early work and continue to provide an excellent image with x-rays.

12
i The plates are nominally ...0.060-mches thick. It was found that Kodak

Spectroscopic Safety Film, Type 649-GH in 35mm width maintained the same

image quality, although the film speed was reduced. Typical density

versus exposure curves for these two materials, under the. special

exposure conditions for these experiments, are shown in Figure 1.

Photographic Processing:

Both films and plates are processed in Kodak HRP developer (1 part HRP

diluted with 4 parts water) at 22 C, for 10 minutes. One plate or strip

is processed at a time, in a tank, with constant, but extremely active

manual agitation. Because of short-term latent image fading, processing

always takes place within five minutes of the termination of exposure.

Subsequent fixing, washing and drying are sufficiently routine to warrant

no additional comment. Densities are measured and corrected to diffuse

(visual) density through calibration tables.

X-Ray Exposure:

j The exposure device is a hybrid system consisting of an RCA Crystallof lex

II power unit (built by Siemens) coupled through a cable to a General

Electric CA-7 Collidge Tube having a copper target. The tube is mounted

approximately 115 cm* away from the photographic material and the beam expands

to approximately 25 cm in the exposure plane. Exposure is made in the most

uniform portion of that area. The unit is driven to 40 kV, at 10 mA,

j and holds constant for extended periods of time. However, it has been

found expedient to achieve long exposures (on the order of 40 minutes)

by breaking the total time into several shorter periods because of longterm power variations.

Aluminum Step Tablets:

The modulation of the x-rays to determine the density -versus exposure curve

and to provide the density steps for the edge-artifacts is accomplished by

layers of aluminum foil. The material used in this investigation is commercial ly-available extra heavy Reynolds Wrap in a 1-mil thickness. A typical

step tablet is shown in Figure 4.

Characteristic Curve for Film:

To determine the density-exposure characteristics for Kodak Spectroscopic

Film, Type 646-GH, under the standard processing conditions previously cited,

a series of exposures was made with the aid of a seven-step aluminum foil

13
tablet. These exposures were suitably replicated to assure reproducibility

and establish the necessary statistics. Since the region associated with

the unmodulated 20-minute exposure is near the end of the linear range

(and therefore most useful for producing the' higher densities), it was given

additional weighting in the analysis provided by the program described in

Appendix B. Three exposure groups were included at or near 20 minutes. The

resulting characteristic curve is shown in Figure 5. The constants of the

curve and the transmittance factors of the aluminum steps are shown in Table

I. From these values, the exposure times and step table layers necessary to

produce both types of edge-artifact on film can be determined.

Two Edge-Artifacts on Film; Typical Calculations:

1.0 and

1.5. the aid of Eq . (7), we set up the following

AD(k) i AD(k) i /A

1.5 16.1

1.0 10.7

0.5 5.3

The value of the constant, A, is given in Table I. We choose to have the

highest contrast correspond to k = 1 (for reasons to be discussed shortly),

so that is determined by

t^ = AD(k) 3 /AT( 1 ) = (16.1)/(0.68) - 24 minutes.

The value of T(l) has been taken from the listing of Table I. If we now

utilize Eq . (9) to determine the corresponding k^ for the other contrasts,

we have

T ( k

)

2 = AD(k) 2 /At 1 = ( 10 . 7 ) / ( 24) = 0.45 — > T(2),

so that k> = 2.

In a similar manner we can show that for the remaining step, T(k)^ is

approximated by T(5), and k^ thus has a value of 5.

Study of the plot in Figure 5 shows that a comfortable Dmax is 2.0. Then

the second exposure time can be calculated from Eq . (12), and for these

parameters it can be shown that

t 2 - 7 minutes.

Because we have taken the maximum density (2.0) and related it to k = 1,

the density that will correspond to an exposure for k = 0 may be off the

linear portion of the curve and thus can only be estimated. But this

14
necessary exposure will provide a density higher than the highest edgedensity, as required for instrumental calibration with eventual use. For

the first and fifth tablet steps, therefore, we choose k = 0 and k = 7,

respectively. The step tablet makeup and the exposure history for this

artifact are shown in Table II, together with the predicted densities

calculated from Eq . (2). In this instance, and for all the other calculations in this section, exposure times are rounded-off to the nearest

minute. Since these examples are intended to be illustrative, it is felt

that further precision is not warranted.

For the constant-contrast edges , we specify a contrast of 1.0. Since the

contrast is independent of the table steps, we choose to use the same set

of five transmittances used for the variable-contrast edges; i.e., k = 0,

1, 2, 5, and 7. From Eq . (16) and the value of A from Table I, we can

determine the second exposure time.

t 2 = AD(k)/A = 1/(0.09345) - 11 minutes.

From Eq . (18), the first exposure time can be calculated, and it can be

shown that for these parameters,

t^ - 15 minutes

,

where, as in the previous calculation, D max is taken to be 2.0, and the

exposure times have been rounded off to the nearest minute. The step tablet

makeup and the exposure history for this artifact are shown in Table III,

together with the predicted densities calculated from Eq . (2).

Characteristic Curve for Plates:

To determine the density-exposure characteristics of Kodak High Resolution

Plates under the processing conditions previously cited, a series of exposures

was made with the aid of a seven-step aluminum foil tablet. These exposures

were made at 2, 5, 10 and 15 minutes. The region associated with the 10-

minute unmodulated exposure was given additional weight since it is near the

end of the linear position of the curve.

The resulting characteristic curve is shown in Figure 6. The constants of

the curve and the effective transmittance factor of the aluminum steps are

shown in Table IV. From these values, the exposure times and step tablet

layers necessary to produce both types of edge-artifact on film can be

determined

.

Two Edge-Artifacts in Glass Plates:

The necessary exposure times and step table specifications for glass plates

are calculated exactly as done previously for the film except that the

characteristic curve parameters are different. Using the values of T(k)

and A for the listing in Table IV, a vari able -contrast edge-artifact is

calculated and the exposure history and step tablet makeup are shown in

Table V. Corresponding calculations for the constant-contrast artifact

are shown in Table VI.

15
Results

:

The edge-artifacts described in Tables II, III, V and VI were exposed and

processed according to the exposure times and step tablet transmittances

specified. To illustrate the process, one of each was made; measured

densities are shown in Table VII for all four artifacts, together with the

actual density differences (AD) that measure, contrast. For each artifact,

the table that described exposure and predicted density is cited in the

heading. Figure 7 contains a photograph of some of these artifacts.

Study of the actual density values (compared to those predicted) shows

that the densities are (with one exception) within the 3-sigma limits for

the materials, and the contrasts are close to specification. The one

significant discrepancy is associated with the variable-contrast edges on

glass plates. There, the actual densities are much larger than those predicted, but the predicted contrasts are amazingly close. This particular

artifact dropped out of its hanger while being processed, was manually

replaced and the processing continued to completion. It thus received

different agitation from the standard conditions (possibly a slight temperature increase). Normally, such an artifact would be discarded and

another exposed and processed properly. However, it is included here

because the densities are apparently on the correct (linear) characteristic

curve (since the contrasts were so close to the expected values). This

indicates that the linear curve probably extends to densities beyond 2.20.

Since these artifacts were intended to serve primarily as a demonstration of

the process, they were not replicated sufficiently to establish a basis for

statistical study of the process. The need for production of specific

contrasts within tight tolerances has not been established as yet, and

because of this there is simply insufficient justification to establish

process statistics at this time.

Because the techniques for obtaining sharp edges with this method had already been developed and since the purpose of this investigation was the

development of exposure techniques to produce the two specific artifacts,

no particular attention was paid to the achievement of edge-sharpness, per se . Nevertheless, in a check of the process, the variable-contrast edges

on film listed first in Table VII were scanned on the Mann-Data Microanalyzer at NBS.

The criterion used at NBS for determining the edge quality is the meansquared slope of the edge-trace, measured between two points and corrected

for density. When these points are on the upper and lower extremities of

the edge (where the value of the slope is 0.005 density units/^.m) and the

density correction is accomplished by inserting the value of AD in the

denominator, the quantity determined is equivalent to the acutance

developed by Higgins and Jones 1

. In this instance, since the edge is of

such high quality, the response of the microdensitometer is incorporated

16
in the resultant equivalent acutance value. Typically, AD's of 1.5 at

mean densities in the range of 1.2 to 1.5 produce equivalent acutance

values of approximately 50,000 (density units/jum 2

) when evaluated on the

Microanalyzer with a 2 x 100-jum sampling aperture 12

, overfilled optics,

image scanning and an efflux numerical aperture of 0.25.

The high-contrast step of the artifact tested (AD = 1.35, from Table VII)

had a measured equivalent acutance of 48,400. This is essentially at the

same level of quality as that obtained previously with the process, so that

the new exposure method(s) has apparently not caused any deterioration.

DISCUSSION

From a study of the results of Table VII, it is clear that the process is

well-characterized by the linear theory, and might be made more reproducible

if the procedures were more controlled. However, there are inherent

limitations to both the process and the analysis that need further discussion

before an assessment of possible improvement or wide-scale production is

carried out.

During the preliminary determinations that led to the linear characteristic

curve, it was found that the slope of the curve was sensitive to exposure

level; i.e., exposure of the emulsions in different parts of the beam led

to different values of slope. It was found necessary to use only one portion

of the beam for both step tablet exposure (for the curve-determination)

and for the final edge/table artifact exposures. It was presumed that this

resulted from an unevenness of illumination within the beam. As long as the

radiation level in that region remined constant, there was no variation in

system characterization. Failure to relocate the materials properly in the

exposure phase results in a change in sens i tome try

.

When the photographic process employs the linear portion of the density

versus log-exposure curve (the region of usage in nearly all applications),

the slope or "gamma" of the curve is independent of exposure. Even with

toe exposures, one can expect that for identical processing times and procedures, the slope should be exposure-independent and be only a function

of the properties of the material. However, in this case, because of

the exposing radiation and the peculiar attenuating response of the

aluminum foil layers, this relation is apparently altered and made dependent

on exposure level . Inasmuch as all the interactive factors have been

inextricably lumped together, it is difficult to explain this dependence

satisfactorily. The effect can be treated phenomenologically, and the problem obviated by fixing the position of the materials and associated

apparatus in one portion of the exposing beam.

17
The combined analytical, determination of the characteristic curve and

the effective transmittance factors of the aluminum step tablet leads

to an interesting variation in the attenuation afforded by the aluminum

foil; it is as much a property of the process as it is of the material

itself. Tables I an IV show that the T(k)'s for the high resolution

plates are higher than the corresponding T(k) for the spectroscopic

safety film for a given k (k M). This is a direct and result of lumping

together the effects of film speed, tablet attenuation and exposure and

processing of the material for the toe of the normal characteristic curve.

The variation in transmittance factors should not be construed as an

inadequacy of the model, but rather as an indication of the flexibility

of the approach and a tacit warning that the total process and procedure

must remain fixed for a given material.

The densities on the lower portion of the density versus exposure curve

(below a density of approximately 1.0) are relatively easy to control and

reproduce, while those above this value manifest a much wider variation

and are difficult to obtain in a reproducible manner. This is typified

in the plots of Figures 5 and 6. This wider variation occurs primarily

because this is the region of the particular material's response where

h igh -contras t imagery inherent in these materials is beginning to

manifest itself. The slope of the normal characteristic curve is extremely

high for these processing conditions, and with a virtually negligible toe

region, the minutest variation in processing conditions (such as temperature, agitation, solution concentration) or exposure is often reflected

in a large density variation. Thus, it is difficult to control densities

near the end of the linear density-exposure curve, and it is in these

very values that the largest deviations from the specifications of Tables

II, III, V and VI are evident in the edge-artifacts listed in Table VII.

As a result of this inherent process-limitation, the attainment of a given set of densities and contrasts in a single trial is highly unlikely.

If there is a significant restriction to the production of specific

artifacts, it lies in this problem area, and in the absence of more

stringent process-control, normal scatter among many trials must be

depended upon to meet a specified set of parameters; i.e., given enough

replications of the same exposure history and processing, one artifact

will eventually emerge that is very close to the specified characteristics.

Since the production of the artifacts for this report was primarily for

illustrative purposes, the exposure times were rounded to the nearest

minute. In actual practice, they would probably be rounded to the nearest

quarter-minute, perhaps to the nearest 2/10-minute, since there is more

control over the exposure time than over the layers of aluminum foil

(which are limited to seven, presently). Because of the necessity for

an integral number of layers of this foil, the attainment of exact

contrast for each step in the variable-contrast edge-artifact is highly

improbable. The time chosen for the first of these (the highest contrast

18
step) allows precise achievement of that contrast; the remainder depend

on how closely the available step transmi t tances approximate the required

values. Some trade-off is possible, but it will be difficult to obtain

all three contrasts exactly. On the other hand, since the contrast of

the constant-contrast artifact is determined solely by the second

exposure time, actual edge-contrast on this artifact can probably

be made artitrarily close to specifications.

CONCLUSIONS

There is presently no requirement for specific contrasts for either

artifact type. The values used in this report therefore are as representative of the process as any others, and will temporarily serve as "standard" values. Since the process is capable of producing the edgeartifacts on demand, NBS does not plan to stock large amounts of these

artifacts. The calculations for any specific requirement are trivial

(and can easily be computerized, to minimize time and cost) and the

procedures sufficiently standardized to respond rapidly to any request.

ACKNOWLEDGMENT

The authors gratefully acknowledge the help of Mr. Charles Brady of

NBS for suggesting and implementing the me tal lographic polishing of the

edge of the tantalum strip. Thanks are also due to Mr. H. Zoranski for

preparing the non-photographic figures in this report.

REFERENCES

1) G. C. Higgins and L. A. Jones, J. Soc. Mot. Piet. Telev. Engnrs.,

58, 277 (1952).

2) F. Scott, R. Scott and R. Shack, Phot. Sci. Engnr. 7, 345 (1963).

3) F. Perrin, J. Soc. Mot. Piet. Telev. Engnrs. _69, 239 (1960).

4) J. A. Eyer, J. Opt. Soc. Am. 4J3, 938 (1958).

5) R. E. Swing, Opt. Eng. 12 , 185 (1973).

6) I. Kleinsinger, A. Derr and G. Giuffre, Appl. Opt. 3, 1167 (1964).

7) C. S. McCamy and M. A. Berkovitz, Phot. Sci. Engnr. 9, 212A (1965).

8) R. E. Swing, J. Opt. Soc. Am. ^2, 199 (1972).

9) R. E. Kinzly , J. Opt. Soc. Am. 62, 386 (1972).

10) D. N. Grimes, J. Opt. Soc. Am. 61, 1263 (1971).

19
11) C. E. K. Mees and T. H. James, The Theory of the Photographic Process , 3rd ed. (Macmillan Co., New York, N. Y., 1966), Chapter 10, pp. 185-19.2.

12) R. E. Swing, "Microdensitometer Optical Performance: Scalar Theory and

Experiment," scheduled for publication in Nov/Dec 1976 issue of Optical

Engineering

.

13) C. H. Richardson, An Introduction to Statistical Analysis , (Harcourt,

Brace & Co., New York, N. Y., 1944). pp. 354-357.

20
TABLE I

Constants for use with Kodak Spectroscopic Film,

Type 649-GH, with standard processing conditions

Linear Characteristic Curve

A = 0.09345

a

1 = 0.38314

a

2 = 0.02030

C = 0.04

Effective Aluminum Step Tablet Transmittance Factors

k T(k)

0 1.00000

1 0.68172

2 0.48400

3 0.35786

4 0.27556

5 0.22098

6 0.18456

7 0.16052

21
TABLE II

Exposure History and Calculated Densities

for the Variable-Contrast Edges on Film

Step Tablet (Number of aluminum foil layers):

0 1 2 5 7

First Exposure: t^ = 24 minutes; E(k)^ = t^T(k).

24.00 16.36 11.62 5.30 3.85

0 0 0 0 0

Second Exposure: t 0 = 7 minutes; E(k)£ = t

£

T(k).

31.00 21.13 15.01 6.85 4.97

7.00 4.77 3.39 1.55 1.12

Calculated Densities (by Eq. (2) y constants from Table I):

3.0 2.01 1.44 0.68 0.50

0.69 0.49 0.36 0.18 0.14

t t

t

AD 1.52 1.08 0.50

22
TABLE III

Exposure History and Calculated Densities

for the Const ant -Contra st Edges on Film

Step Tablet (Number of aluminum foil layers):

0 1 2 5 7

First Exposure: t^ = 15 minutes; E(k)^ = t

1

T(k).

15.00 10.22 7.26 3.31 2.41

Second Exposure: t^, = 11 minutes; E^)^ = V

26.00 21.22 18.26 14.31 13.14

15.00 10.22 7.26 3.31 2.41

Calculated Densities (by Eq. (2)

,

constants from Table I):

2.5 2.02 1.75 1.38 U9

1.44 1.00 0.72 0.35 0.26

AD ——

t

1.02

t

1.02

f

1.03

23
TABLE IV

Constants f^r use with Kodak High Resolution Plates

with standard processing conditions

Linear Characteristic Curve

A = 0.19856

a

x = 0.32739

a

2 = 0.01815

C = 0.06

Effective Aluminum Step Tablet Transmittance Factors

k T(k)

0 1.00000

1 0.72080

2 0.53876

3 0.41758

4 0.33563

5 0.27973

6 0.24176

7 0.21667

24
TABLE V

Exposure History and Calculated Densities

for the Variable -Contrast Edges on Glass Plates

Step Tablet (number of aluminum foil layers):

0 1 2 5 7

First Exposure : t^ = 10 minutes; E(k )

= t^T(k).

10.00 7.21 5.39 2.80 r^ r—

1

*

CNI

0 0 0 0 0

Second Exposure : t^ = 4 minutes; E(k>

2 = t

2

T(k).

14.00 10.09 7.54 3.92 3.04

4.00 2.88 2,15 1.12 0.87

Calculated Densities (by Eq. (2), constants from Table IV):

2.6 2.06 1.56 0.84 0.66

0.85 0.63 0.49 0.28 0.23

AD —— 1.43

Tit

1.07 o.56

25
TABLE VI

Expesure History and Calculated Densities

for the Const ant -Contrast Edges on Glass Plates

Step Tablet (number of aluminum foil layers):

!

0 i 2 5 7

.

First Exposure: t. = 7 minutes; E(k) = t

1

T(k).

Second Expo

7.00 5.05 3.77 1.96 1.52

sure: t 0

= 5 minutes; E(k)

12.00 10.05 8.77 6.96 6.52

7.00 5.05 3.77 1.96 1.52

Calculated Densities (by Eq. (2), constants from Table IV):

2.5 2.06 1.80 1.44 1.35

1.45 1.06 0.81 0.45 0.36

T t T

ad ————- 1.00 0.99 0.99

26
TABLE VII

Typical Experimental Edges

Variable-Contrast, on Film (See Table II):

2.63 1.89 1.36 0.65 0.49

. ...

0.75 0.54 0.38 0.21

j 0.17

AD -

Constanta- 1.35 0.98

-Contrast, on Film (See Table III):

0.44

2.53 2.10 1.83 1.47 1.35

1.54 1.07 0.76 0.37

. 0.28

AD - 1.03 1.07 1.10

Variable-•Contrast, on Glass Plates (See Table V):

3.07 2.20 1.66 0.86 0.65

1.11 0.76 0.58 0.30 0.24

AD - 1.44 1.08 0.56

Constant-•Contrast, on Glass Plates (See Table VI):

2.60 2.06 1.88 1.52 1.44

1.65 1.11 0.85 0.44 0.34

AD - 0.95 1.03 1.08

27
OPTICAL

DENSITY

X-RAY EXPOSURE TIME (Minutes)

Figure 1: Typical density versus exposure curves for high resolution materials

exposed to x-rays. In these curves, the source intensity remained

constant while the exposure time was varied (no step tablets in use).

The curves are linear to a density value of 2.0. A; Kodak High

Resolution Plates; B: Kodak Spectroscopic Saftey Film, Type 649-GH.

28
Figure 2: Summary of exposure history for variable-contrast edges;

A; After first exposure (with tantalum strip and step tablet

in place).

B: After second exposure (step tablet in place, tantalum

strip removed).

29
IE1

Iff Ie<m + •E(k 2 ) + 1 E{k 3 ) + 1 E(k 4

)-*- 1 E(k a

)-*- — in

B

2 E(k,) 2 E( k 2 ) 2 E ( k 3 ) 2 E(k 4 ) 2 E(k 0 > Sharp

| *E(k,) ! E(k 2 )

1 E(k») •Elk.) ®E(k s >

^|edge

^ m " ii sT

"'K, . ** - v^aps sstt—

(Tantalum strip)

Figure 3s Summary of exposure history for constant-contrast edges;

A: After first exposure (step tablet alone).

B: After second exposure (step tablet removed, tantalum

strip in place).

30
Figure 4: Two exposure aids used in the production of edge-artifacts,. On the right

is the tantalum strip used to produce the sharp edge-discontinuity,, The

right edge of the strip has received a metallographic polish,, On the left

is a typical 7-step tablet of aluminum foil layers,, In use, the layers

are tightly compacted; here they have been slightly separated to exhibit

the format o Typical transmittance factors for such a tablet with x-rays

are shown in Tables I and IV„

31
OPTICAL

DENSITY

X-RAY EXPOSURE ( Intensity- minutes )

Figure 5: Linear characteristic curve for Kodak Spectroscopic Safety Film,

Type 649-GH (35 mm size), processed in HRP (ls4) at 22°C for 10 minutes with constant agitation,, The 3-sigma limits on density are shown

as dashed lines 0 The curve is linear out to at least a density value

of 2 o 0 o

32
2.5

/

/

X-RAY EXPOSURE ( Intensity - minutes

)

Figure 6: Linear characteristic curve for Kodak High Resolution Plates, processed

in HRP (Is 4) at 22°C for 10 minutes with constant agitation,, The 3-sigma

limits on density are shown as dashed lines e The curve is linear out

to at least a density value of 2„0 o

33
Figure 7: Typical edge-artifacts<> Topmost is the constant-contrast version on

films the other is the variable-contrast version on glass plate 0 The

three edges of interest on each are in the certer, flanked by larger

areas of density (one of which is ordinarily used for identifying

purposes, as illustrated) „ The sharp discontinuity runs lengthwise

and a scan of these edges (on a microdensitometer, for example) would

run across this.

34
APPENDIX A: Sensitometry with aLuminum foil step tablets

In general sens i tome try , step tablets are often used to provide a modulation of exposure for a given exposure time. In the present system,

because of the exposing radiation, layers of aluminum foil are a convenient

means for achieving the required modulation. Careful experimentation has

disclosed that the x-ray exporsure produced through these aluminum layers

is not only proportional to the total thickness (exponential absorption)

but is also a function of scattering. It has been found that the effective

transmittance of k layers of uniform foil thickness is given by the

expression

T(k) = exp + ) k + ( A— 1

)

The constant factors in this expression depend on the material (aluminum

in this instance) and the type of exposing x-radiation. Inasmuch as the

effective transmission is also related to the photographic material and

its processing to a certain extent, the constants must be determined

experimentally, for each emulsion type L

The linear relation between density and exposure for the x-radiation and

high resolution emulsion processed and exposed for utilization of the toe

region is described by

D(k) = A E(k) + C, (A- 2)

where C is the base-plus-fog density and E(k) is the exposure produced

through k thicknesses of aluminum foil. The constant, A, incorporates such

considerations as exposing intensity and film speed. In terms of tablet

transmittance and exposure time, we can write

D(k) = A T(k) t = C, (A- 3)

+This expression clearly has a limited range of applicability, inasmuch as the positive contribution in the exponential will eventually overtake the

negative, due to the k^ term, and produce transmi ttances in excess of unity.

Thus, the function has a minimum value, beyond which the physics cannot be

safely interpreted. This minimum value can be determined through the

differential calculus, and is can be shown that the maximum integer value

of k is given by

^max

- -*- nt

For the data of Tables I and IV (coincidentally), k has a maximum value

of 9. By limiting the experimental determinations of transmittance and

the eventual exposure usage of the aluminum to 7 layers (i.e., k = 7),

this inherent limit is not reached and we can retain confidence in the

efficacy of Eq . (A-l) to characterize the transmittance of the aluminum

step tablets.

h

a

2

)/(2a

2

)

(A-l)
where t is the exposure time. To determine the characteristic curve for

the material and ascertain the constants aj and a

2 necessary to describe

T(k), we make a series of exposures through an aluminum step tablet. We

then process the photographic material and measure the corresponding

densities for each tablet step. Thus, in Eq . (A-3), we know D(k), k, t and C from experiment. With these we can determine A and T(k) through

analysis, we first conbine Eqs . (A-l) and (A-3) and rearrange some of

the terms. Thus,

(D(k) - C)/t A exp -(a-^ + a2)k + ( A-4)

When we take the natural logarithm of both sides of this equation, we

obtain

log

e log (A) - (a + a )k + a k

2

, e 12 2

(A-5)

and this reduces to the relation

y = b

? k

2 + b

± k + b

Q

, (A-6)

y

= log e |(D(k) - C)/t|> ;

( A-7

)

b 0= log

e (A);

b ^ = - (ai + a

2

) 5

b 2 = a 2

•

Eq . (A-6) is a quadratic in k that can be fitted to the experimental data

by the method of least squares. This determines the fit-constants, b 0 , b]_,

and b

2

. From these values, we can obtain the constants of the characteristic curve through

A = log~ 1 (b

Q

) = exp(b Q

) ;

a

1 = — ( b + b

2

); (A-8)

3 2 = b2 •

With these parameters, it is then possible to calculate, through Eq . (A-l),

the effective transmittance of the layers of aluminum in each step. Subsequently we can convert the input values of exposure time and T(k) to

exposure and plot them (if required).

(A-2)
It is useful to have a measure of how well the function and the experimental data are related. In statistical analysis this is usually accomplished by calculating a coefficient of correlation 1 3 . This is a parameter that lies within the limits of 0 and 1, the latter denoting a perfect relationships, the former, none at all.

For any curve, the index of correlation is given by

xy 4

S

2

u

2

y y

(A-9)

whe re

xy

S

= index of correlation for two variables, x and y;

= standard error of estimate ; = standard deviation of the y-variable 8

It can be shown that the standard error of estimate is given by

( A- 1 0

)

P i N ,

where N = number of experimental points;

= sum of the squares of the y-residuals

For the curve of Eq. (A-6) , the i tk -residual is given by

2

p. = y. - b„k. - b,k. - b

l

7 i 2i li o

When the various equations are combined, using the known relations for

standard deviation, the index of correlation is given by

y, k V

1 - X>y ']p‘ (2>)

2

/n] (A-12)

(A-3)
Knowledge of Py^ will give us an indication of the verisimilitude of the , functional relation of Eq . (A-6) and a measure of the experimental measurement accuracy.

However, the correlation index applies strictly to the y-re lat ionsh i

p

defined in Eq . (A-7). This is a logarithmic quantity which is less sensitive

to variation than optical density. The index is a good measure of the

curve-fit, particularly since it gives confidence in the values of T(k)

subsequently calculated. However, it is more useful to have a measure

of the spread of density values about the linear curve after the exposures

have been calculated. The usual estimates of this spread are the 3-sigma

(standard deviation) limits: this establishes limits within which 99%

of the data lie. It can easily be determined when the input density and

calculated input exposure are listed, by applying standard statistical

procedures to the information.

The program DOODAH was written to carry out all these calculations, and

a listing, documentation and typical output are shown in Appendix B. The

characteristic curve derived from that program is plotted in Figure ( A— 1 )

.

The experimental points are shown on the plot to illustrate the high correlation index value of 0.9989 calculated for these data and curve.
OPTICAL

DENSITY

2 .0 —

X “ R A Y EXPOSURE ( Intensity -minutes)

Figure A-l: Typical sensitometric curve for high resolution material

exposed to x-rays, exposed and processed to utilize the toe

region of the normal (logarithmic) characteristic curve.

Experimental points are indicated, the 3-sigma limits on

density for this distribution are ±0,05,

(A- 5)

APPENDIX B: Computer program DOODAH

DOODAH is a program in the BASIC language that calculates the various

parameters necessary to characterize the system sens i tome try . It uses

experimental data and carries out the calculations with the aid of the

fundamental equations derived in Appendix A.

Program Synopsis:

Data is entered in lines 905 and subsequent, in groups of three: exposure

time (T), the number of aluminum foil layers in tablet step (K) and the

measured density of that corresponding step ( D 1 ) ; e.g., 20, 5, 0.44. Line

900 contains the number of groups of data and the measured base-plus-fog

density (C); e.g., 32, 0.04.

After the headings are printed and the matrices zeroed, the data is read

into the program, a listing is printed and the various matrix elements are

computed and stored (Lines 065 through 145). These elements are the

coefficients required for the least-squares curve-fit which culminates in

lines 148 and 152. Subsequently, the fit-constants are used to calculate

the parameters A, a^ and (Lines 156 through 158) that are required to

calculated the transmittance of the steps, T(k), and to convert the input

data (K,T) to exposure (lines 809 through 844).

The fit-constants (bQ , b^ and b

2

) and the constants of the characteristic

curve (A, a^ and a

2

) are then listed (Lines 175 through 190). Following

this, the coefficient of correlation is calculated and printed. At this

point the transmittance of each of the steps is calculated and printed.

The table so produced is useful for reference when determining the final

exposures for the edge-artifacts. Finally, the input values of K and T

are converted to exposure and a listing of density (Dl) versus exposure

is printed (Lines 836 through 860). This provides experimental points

that can be plotted with the fitted curve to illustrate the sensitometric

relation. The value of the 3-sigma limit is then calculated and printed.

The Listing:

The program DOODAH is listed on the following three pages. The complete

program output (derived from the data in lines 900 through 919) is then

listed and annotated. A plot of the density versus exposure data found

on the last page of this listing is the typical characteristic curve shown

in Appendix A.

0

(B-l)
I

001 * RICHARD E • SWING* 2 1 3 . 1 1 * X 2 1 59 , PROGRAMS DOODAH

002 * 003 * THIS PROGRAM IS USED TO DETERMINE EXPOSURE- DENSI T Y 004 * RELATIONS FOR THE X - RAT EXPOSURE AND PHOTOGRAPHIC PROCESS005 * ING OF NBS EDGE- TARGETS . INPUT DATA ARE ENTERED IN GROUPS

006 * OF THREES EXPOSURE TINE CD* NUMbER OF ALUMINUM LAYERS IN

007 * TABLET STEP (K> AND THE MEASURED DENSITY OF THAT STEP CD1).

008 * PROGRAM FITS DATA TO CURVE* DISPLAYS IHE CONSTANTS* CALCULA

009 * THE CORRELATION COEFFICIENT* COMPLIES AND DISPLAYS THE

010 * TRANSMI TTANCE OF THE ALUMINUM LAYERS AND CALCULATES THE

011 * EXPOSURES NECESSARY TO PLOT THE INPUI DATA. INPUT IS LlMif

012 * TO 75 TRIPLES OF DATA UNLESS ARRAYS ArE ENLARGED.

0 13 * 020 DIM A( 2* 2) * LC 2* 2) * B( 2* 0 ) * S( 2* 0)

0 22 DIM W( 7 5) * X C 75) * Y ( 7 5) * PC 7 5)

Q3QE0KJ=t*5

0 35 PRINT

0 40 NEXT J

0 42 GO SUB 7 50

0 44 MAT B = L ER

0 45 MAT A = XER

0 50 MAT S = 2EK

0 52 S = 0

0 55 G0SU8 400

o 65 READ N* C

0 70 FOR J = ! * N

0 72 READ T* K* DI

0 73 W( J) = T

0 74 XCJ) = K

0 75 YC J) = DI

0 77 D = CD! -o / r 0 78 S = S+CLOGC D) ) **2

080 AC 0* 1 ) = AC 0* 1 > + K

085 AC 1 * 2) = ACO* 1 ) 0 90 A C 0* 0 > = AC 0* 0 ) + K**2

1 00 AC 2* 2

)

= AC 0* 0 )

1 05 AC 1 * 1 ) = AC 0* 0 )

1 10 AC 1 * 0) = AC 1 * 0) + K**3

1 1 5 AC 2* 1 ) = AC 1 * 0)

1 20 AC 2 * 0 ) - AC 2* 0 ) + K** 4

1 25 BC 0 » 0 )

00 V o «» o

II L 0 G C D )

1 30 BC

1

» 0) = BC 1 * 0) K + LOGC D)

1 32 BC2.0) = BC 2* 0 ) + CK**2)*L0GC D)

1 36 PRINT* 1 38* T»K* Di

138 EMT X3» I 3*X4» I2»X2* F8 .2

1 40 NEXT J

1 45 A( 0* 2 > = N

(Continued)

(B-2)
1

48 MAT L = I tM V/ < A

)

1 52 MAT S = L + B

I b6 T1 = EXPC SC 2*0))

1 57 T2 - SC0*0)

1 58 T3 = -(S( 1*0)+SC0*0)

)

1 59 GOSUB 340

1 60 EOR J = 1*5

1 65 PRINT

1 70 NEX T J

175 PRINT ’’THE THREE E I T- C3NSTAN [ S AkE: "J

1 76 PRINT " THE CALCULATED PARAMETERS ARE:

1 78 PRINT

180 PHI NT* 182* S( 0* 0) * T

1

182 EMT X 4* "B2 = "» E8 • 5* X22# "A = "* Erf . 5

1 84 PRI MT* 186* S< 1 *0) » T2

186 EMT X 4* "B 1 = "* E8 . 5* X22* "A2 = "»E8.5

j 1 88 PRINT* 190»S<2*0)* T3

j

1 90 EMT X 4 » "BO = "* E8 • 5* X22* "A 1 = "» E8 .

5

2 80 PRINT

1 282 PRINT

300 M = S N * C S( 2* 0 ) * * 2 ) « (S( 1 * 0 ) ** 2 ) * A C 0* 0

)

3 02 M = M C SC 0* 0) + *2) *AC 2* 0) - 2* S ( 2* 0 ) * B( 0* 0 ) 304 M = M - 2* SC 1 » 0 ) * B( 1*0) - 2* S C 0 » 0 ) * BC 2* 0

)

306 M = M 2*SC2*0)*SC 1*0)*AC0» 1

)

1 3 0 7 M = M 2*SC2*0)*SC0*0)+AC0*0)

1308 M = M + 2*SC1*0)*SC0*0)*AC1,0)

310 R = SORC 1 - CM/C S- C ECO* 0)**2)/N) )

)

3 1 5 PRI NT* 320* R

320 EMT "CORRELATION CO EE E I Cl ENT IS "* E8 .

4

3 24 E OR J = 1*5

328 PRINT

3 32 NEXT J

3 35 GOTO 800

3 40 PRINT

3 42 PRINT

344 PRINT* 346*C

346 EMT "MEASURED B AS E- PL US- E 3 G IS "*E8*2

3 48 RETURN

«00 PRINT "INPUT DATA ARE: Cl = EXPOSURE TIME CMIN)>"

|401 PRINT* 402

402 EMT X 28 * " C X = NUMBER OE ALUMINUM LAYERS)

403 PRINT* 40

4

404 EMT X 28 * " C D = CORRESPOND! NG TAbLEl DENSITY)"

405 PRINT* 408

408 EMT X5* "I"*X5* "K"*X8* "D"

409 PRINT

410 RETURN

(Continued)

(B-3)
7 50

7 5?

753

7 54

7 55

7 56

7 58

8 00

805

806

8 07

8 08

8 09

8 ! 0

8 20

8 25

8 28

8 30

8 32

8 34

8 36

8 38

8 40

8 42

8 43

8 44

8 45

8 46

8 48

8 50

8 5 S 8 52

8 53

8 54

8 55

8 56

8 57

8 58

8 60

8 62

8 63

8 64

8 65

8 66

PRINT* 7 52* T1M( 1 )* II M ( 2 > * T I M ( 3 ) FMT " AL UN /X - RAT TABLE! CAL CUL A H 0NS"» X 1 6* I 3* "/ "* I 3* "/ "> I 3

PRINT " C FOR EXPOSURE OF NBS PHOIOGrApHIC EDGES)"

FOR J = 1*4

PRINT

NEXT J

RETURN

PRINT "FOR THESE CONSTANTS* THE EFFECTIVE AL UN I NUN"

PRINT "STEP- THI CKNESS TRANSMITTANCE FACIOR IS:"

PRINT

PRINT " K T(K>"

PRINT

FOR J = 0* 7

Z = EXP(-(T3+T2)*J + T2*CJ**2)>

PRINT*825* J*Z

FMT X7* I2*X 1 1 * F8 .

5

NEXT J

FOR J = 5*6

PRINT

NEXT J

GO SUB 850

FOR J = 1 * N

P(J) = W(J)*EXP(-<T3+T2)*X(J) I2*(X( J >**2>

)

PRINT*843* YC J)*P(J)

FMT X 7 * F8 ® 2 * X 7* F8 .2

NEXT J

PRINT

PRINT

GOTO 862

PRINT "THE DENSITY-EXPOSURE POINTS":

PRINT " (D = OPTICAL (DIFFUSE) DENSITY)"

PRINT "FOR THE INPUT DATA ARE: "I

PRINT " (E = EXPOSURE < I N I EN S I T Y ” M I N )

)

PRINT

PRINT

PRINT*857

FNT X 1 3* "D"* X 1 3* "E"

PRINT

RETURN

51 = 0

52 = 0

53 = 0

54 = 0

55 = 0

(Continued)

(B-4)
I 8 68 F«4K J = 1 * N

8 69 SI = si rcj)

8 70 S2 = S2 + P(J)

8 71 S3 = S3 y(j>*pcj>

8 72 S 4 = S 4 + (Y(J)**2>

8 73 S 5 = S 5 + (P<J)**2>

8 75 NEXT J

8 78 S6 = SI /N

8 79 S 7 = S2/N

8 80 S8 = SQRC(S5/N)-(S7)**2>

881 S9 = SQR< CS4/N>-( S 6 ) * * 2

)

882 R2 = ( ( S3/N ) - S 6* S 7 ) / ( S8 * S9 ) 884 R 4 = S9*SQR( 1 ~ ( R2 ) ** 2

)

886 PRINT *890* 3* R

4

8 90 EM T

" 3-SIGMA IN DENSITY IS "*h8.3

891 E3R J = 1.5

8 92 PRINT

8 93 NEXT J

8 95 Gi^T^ 999

9 00 DATA 32*0.04

9 05 DATA 20*7»0«34*20» 6*0*38*20* 5* 0 » 44* 20* 4* 0« 53* 20* 3*0* 65

907 DATA 20*2*0.8 7* 20* 1 » 1 .25* 20*0* 1.8 1 9 09 DATA 1 5* 7*0.26* 1 5* 6*0.29* 1 5* 5* 0.33* 1 5* 4* 0 • 40

9 1 1 DATA 15*3*0*51* 15*2*0*67* 15* 1*0*96* 1 5* 0* 1 * 42

9 1 3 DATA 1 5* 7*0.26* 1 5* 6*0.29* 1 5* 5*0.34* 1 5* 4* 0 . 42

9 1 5 DATA 1 5* 3* 0 . 52* 1 5* 2* 0 . 68* 15* 1*0.95* 1 5* 0* 1 . 41

9 1 7 DATA 20*7*0*32*20* 6*0.35*20*5*0*41* 20* 4* 0 . 50

9 19 DATA 20* 3* 0 . 64* 20* 2* 0 .8 6* 20* 1 * 1 .20* 20*0* 1 . 78

999 END

1

I

I

(B-5)
Typical Output Listing for DOODAH (on next three pages)

? BASIC DOODAH

K UN

ALUM/X-RAY TABLET CALCULATIONS

(FOR EXPOSURE OK NBS PHOTOGRAPHIC EDGES)

7/ IS/ 76

I NPUT DATA AKF.5

D

( T = EXPOSURE IIME ( M I N ) ) (X = NUNBEk Of ALUMINUM LATErS)

(D = COKRESPO MDING i ABLET DENSITY)

20

20

20

20

20

20

20

20

1 S

1 s

1 s

1 s

1 5

1 5

1 S

1 b

! 5

1 S

1 S

1 5

1 S

1 5

20

20

20

20

20

20

20

20

7

6

5

4

3

2

10

7

6

5

A

3

2

10

7

6

b

A

3

2

10

7

6

b

A

3

2

10

34

38

A A

• S3

• 6b

87

2b

8 1 26

29

33

. 40

- b 1

. 67

.9 6

. 42

.26

.29

.34

. 42

. b2

. 68

-9b

.41

.32

.3b

.41

. bO

. 6 4

»

8

6

.20

. 78

MEASURED BASE-PL US- FO G IS 04

(Continued) (B-6)
I

i

I

jT H E THREE F I T- CONSTANTS ARE:

B2 = .02342

B 1 = -.42271

B0 = -2.41422

I

jc ORREL ATI ON COEFFICIENT IS

THE CALCULATED PARAMETERS ARE:

A = ,08944

A 2 = .02342

A 1 = . 39929

.9989

FOR THESE CONSTANTS* THE EFFECTIVE ALUMINUM

S TEP-THICKNESS I RAN SMI TTANCE F AC TOR IS:

K T(K

)

0

12

3

4

5

6

7

1 .00000

. 67080

. 47 1 S4

. 34737

. 2 68 1 6

. 2 1 69 b

. 18392

. 1 6341

I

I

I

(Continued)

(B-7)
HE DEN SIT /-EXPOSURE POINTS (D = OPIICAL (UIHhUSE) UENSIIY)

FOR THE INPUT DATA AkEs <E = EXPOSURE < I NT ENSi T IT - M i N ) )

D E

• 34 3.27

. 38 3 . 68

. 44 4.34

* S3 b * 3 6

. 6b 6.9 b

.8 7 7 . 43

! .2b 13.42

1 .8 1 20.00

.26 2.4b

.29 2.76

• 33 3.2b

o 40 4.02

ebl b * 2 1

. 67 7.07

.9 6 10*06

! . 42 1 b.00

.26 2. 4b

.29 2.7 6

.34 3.2b

. 42 4.02

. b2 b . 2 1

. 68 7.07

.9 b 10.06

1.41 1 b.00

. 32 3.2 7 .3b 3 . 63

. 41 4.34

. bO b. 36

*64 6.9 b

.8 6 9 . 43

1 .20 13.42

1 .78 20.00

3 -SIGMA IN DENSITY IS .Ob4

999 EXIT

(B-8)
3S-H4A (REV. 7-73)

UTS. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. I'Uni.K ATION OK R K PORT NO.

NBSIR 76-1129

2. Gov’t Accession

No.

3. Recipient’s Accession No.

TITLE AND SUBTITLE

AN IMPROVED PHOTOGRAPHIC EDGE-ARTIFACT

5. Publication Date

n

6 . Performing Organization Gode

AUTHOR(S)

William R. Smallwood and Richard E. Swing

8. Performing Organ. Report No.

PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract /Grant No.

Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as No. 9

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

. SUPPLEMENTARY NOTES

. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The history of edge-objects for use in optical and photographic testing is

briefly reviewed and culminates in a short summary of the techniques developed at NBS

in 1965 for producing photographic edges by x-ray exposures of High Resolution Plates

with a tantalum strip to generate the discontinuity. The report then covers the

development of an improved method for producing these edge-artifacts. It is shown

that with x-ray exposure, the relation of density to exposure is linear up to densities

of approximately 2.0, This linear relation is then exploited to produce two kinds

of edge—artifacts . Both artifacts contain ten (10) values of density and three edgediscontinuities. The edges on one artifact have the same value of contrast, with

different mean densities, while the edges on the other have different values of

contrast. The use of each type is discussed. Techniques for determining exposures,

for determining the transmittances of the aluminum step tablets used to modulate

x-ray exposure and for determining the linear relation between density and exposure

are presented in mathematical detail and exemplified in subsequent illustrative

experiments. Some inherent limitations of the method are discussed. It is concluded

that there is sufficient flexibility to the process and procedures to provide

sharp edges, in a wide range of contrasts, on demand.

(7. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

j Densitometry; Edge objects; Microdensitometry; Photographic edges; photographic

process

8. AVAILABILITY [jC Uni imited

c For Official Distribution. Do Not Release to NTIS

I

1 Order From Sup. of Doc., U.S. Government Printing Office

Washington, D.C. 20402, SD Cat. No. Cl 3

f x! Order F rom National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

49

22. Price

$4.00

USCOMM-DC 29042-P74
.

.

*

i m