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ABSTRACT

A HOLOGRAPHIC SOLUTION
TO THE PROBLEM OF
THREE-DIMENSIONAL DISPLAY
IN THEMATIC CARTOGRAPHY
By
Robert H. McKay

Thematic cartographers, over the last fifty years.
have attempted to incorporate the use of the third di-
mension in the product output of their field. Early
attempts were inadequate by today's standards. owing to
perceptual and portrayed dimensional inconsistancies.
Subsequent development frequently failed to account for
the needed realism expressed in terms of angular per-
spective. The culminating factor attributed to the
failure in attaining the goal of three-dimensional rep-
resentation was the inability of the existant two-
dimensional media to portray a true three-dimensional
message.

The development of holography has changed all of
that. This technique offers the capability of present-
ing a three-dimensional image on an essentially two-

dimensional medium of expression. a piece of film or

Robert H. McKay
glass. Additional attractions. such as the ease of mea-
surement and chronologically oriented multiplexing. can
also be presented as definite advantages over conventional
thematic cartographic techniques. The use of holography
is the next step in the evolution of the cartographic
field. The characteristics of holography demonstrated in
this thesis prove that it is indeed a viable method for
recording three-dimensional cartographic output on rela-

tively conventional photographic film.

A HOLOGRAPHIC SOLUTION
TO THE PROBLEM OF
THREE-DIMENSIONAL DISPLAY
IN THEMATIC CARTOGRAPHY

BY

Robert N. McKay

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF ARTS

Department of Geography
1975

ACKNOHLEDGMEMTS

I should like to thank those that assisted in the

development of this thesis:

Dr.
Dr.
Dr.
Dr.
Dr.
Dr.

Mr.

Gary Higgs, Committee Chairman

Gary Cloud, MSU Dept. of MMM

Dieter Brunnschweiler. Committee Member
Robert Nittick, Committee Member

Jack Hilliams. Committee Member

Michael Chubb. MSU Dept. of Geography

Lawrence H099. MSU Dept. of Geography

ii

TABLE OF CONTENTS

Chapter I - The Problem
Introduction
Statement of Problem
Objectives
Hypotheses
Definitions
Data Sources
Hypotheses Testing
Graphic Representations

Chapter II - The Historical Basis of Dimensional
Perception and Display

Early Man
The Renaissance
Early Cartographers
Chapter III - Three-Dimensional Composition
Axes
Perspective
Parallel Perspective

Angular Perspective

iii

10
10
ll
13
16
16
20
22

24

Chapter IV - “Three-Dimensional" Thematic Cartography
Derivation from Topographic Mapping
Dimensional Inconsistency

Symbolism
Perspective View

Neglect in Landform Mapping

Neglect in Thematic Computer Cartography

Possibilities with Computer Mapping
Induced Parallax

Stereoscopic Models

Inadequacies of Stereoscopic Drawings

Basic Limitations of Standard
Two-Dimensional Media

Three-Dimensional Ends Using
Three-Dimensional Means

Three-Dimensional Perception
.1 Problems with Models
Chapter V - Holography

Background

Composition
Elements
Recording
Reconstruction

Production of Holograms

Model

iv

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29
29
36
41
43
48
50
51
54

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56
58
59
59
60
60
62
64
66
66

Instrumentation
Operating Parameters
Exposure Time
Film Plate Processing
Reconstruction of Holographic Image
Procedure
Photographic Limitations
A Second Holographic "Set-Up“
Elements
Photography

Chapter VI - Findings of Qualitative Analysis of
Holographically Reconstructed Images

"Proof“ of Three-Dimensionality
Advantages in Image Lacking Physical Existence
Mensuration in All Three Dimensions
Additional Advantages
Nonexistent Limitations of Physical Presence
Multiplexing of Scenes
Chapter VII - Conclusion
Continued Research Possibilities
References Cited
Appendix

Bibliography

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Figure
Figure
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Figure

Figure

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LIST OF FIGURES

Analysis Process
Two-Dimensional Axes

More Common x-v-z Relationship
Alternate X-V-Z Relationship
Projections

Perspective Views

Raisz's Block-Pile

Projection Planes Used by Raisz
Zelinsky's Isometric Cube
Projection Planes Used by Zelinsky
Consistent Projection Planes
Superimposed Projection Planes
Total Isometric Perspective
Parallel Perspective

Isometric Perspective
Two-Point Angular Perspective
Stereogram: Corner View
Stereogram: End View

Coherent Light

vii

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Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure
Figure

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Al

Resultant Interference Pattern
Holographic Recording
Holographic Reconstruction

Air Cushioned Holographic
Hork Platform

Holographic Recording Equipment

Photographed Holographically
Reconstructed Image

Secondary Holographic
Recording “Set-Up“

Photographic Evidence of Depth in a
Holographically Reconstructed Image

Photographically Multiplexed
Holographically Reconstructed
Image and a Steel Measuring Tape
Photographically Multiplexed
Holographically Reconstructed
Image and an Engineer's Scale
Midwestern U.S. Population in 1910
Midwestern U.S. Population in 1970

An Excerpt from Smith's 1920
Population Map of Ohio

viii

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Appendix

CHAPTER I

The Problem

Introduction

Off-axis holography is a technical process that can
realize its result in a three-dimensional visual output of
a three-dimensional diffuse object or scene. This process
achieves this end by recording the interference pattern.
resulting from the interaction of two coherent light wave-
fronts (emitted from a laser light source), on a photographic
plate. One of these wavefronts is a complex wavefront pro-
duced by the reflectance of laser light off the physical
components of a given diffuse object or scene. The other
wavefront involved in this process is a plane wavefront that
issues forth directly from the same light source. Hhile
off-axis holography was originally applied to two-dimensional
Graphic information, subsequent development of the technique
has established the unique capability of three-dimensional
display as its single greatest attribute.

As do holographers. so too, thematic cartographers seek

the graphical display of information. Since the 1920's

2

considerable attention has been paid to the portrayal of the
third dimension by those of this field. Unfortunately, the
three-dimensional limitations of the various media employed
by thematic cartographers have negated any final realiza-
tion of the three-dimensional objective.

It would seem, then, that the ability of holographic
means to display the third dimension could be augmented by
the desires of thematic cartographers so anxious to achieve
those same ends. The result of this union could be the

birth of a true three-dimensional thematic cartography.

Statement of Problem

The problem to be investigated might initially be
stated as, “Is this union possible?“ That is more of a
technical question than the greater philosophical query of,
“Should this union be made possible?“ Both eventually must
be answered; with the former, perhaps, most legitimately
being based only upon affirmation of the latter.

To achieve this determination, the heritage of “three-
dimensional“ thematic cartography must be examined. False
assumptions, inconsistencies, and shortcomings of various
methods used in contemporary “three-dimensional“ thematic
cartography first must firmly be delineated. Hhile the
suggested creation may rightfully be true three-dimensional

thematic cartography, it must still prove itself viable in

3
a field that has been dominated since its genesis by two-
dimensional graphics that utilized visual cues to gain the
title (but not the body) of “three-dimensionality“.

In this light, the importance of this thesis might be
in terms of its search for truthfulness. The adoption of
this technique could dispel the need for presenting illu-
sions of three-dimensionality. If realism in any way sub-
tends the “cartographic conscience“ then that alone should

serve as raison d'etre for this conception.

Objectives

It is probably apparent that certain objectives of
this thesis are couched within the previously broached
questions. However, perhaps the ultimate goal of this work
is to prove that three-dimensional thematic cartographic
results can be achieved through the use of the essentially

two-dimensional film plate used in the holographic process.

flypgtheses

I would first hypothesize that over the last fifty
years thematic cartographers have been attempting to intro-
duce and develop a concern for the portrayal of the third
dimension. Secondly, these attempts. while coming closer
t0 that goal with the passage of time, have not actually

been able to portray the third dimension via two-dimensional

4

media. In conclusion, it is hypothesized that the use of

the holographic process allows for the production of a

three-dimensional thematic cartographic output on an

essentially two-dimensional medium of expression.

Definitions

X-Axis

Y-Axis

Z-Axis

Two-Dimensional

“Three-Dimensional"

Three-Dimensional

Physical Model

Holography

Object Beam

Reference Beam

the first rectangular
coordinate

the second rectangular
coordinate

the third rectangular
coordinate

defined by x and y axes

defined by x and y axes.
but giving an illusion
of the z-axis

defined by the x, y, and
z axes

a three-dimensional structure,

cartographic in nature, that is
composed of statistical planes

on the z-axis

a recording and viewing process
that allows reconstruction of
three-dimensional images of
diffuse objects or scenes

a complex wavefront resulting
from reflectance of a plane
wavefront off a diffuse object
or scene

a plane wavefront emitted from
the same source as the object
beam

5

Hologram - the photographic record of the
interference pattern resulting
from object beam and reference
beam interaction

Off-Axis Holography - producing holograms by separate
object beam and reference beam,
offset at an angle to one another

Data Sources

The nature of this thesis does not call for the col-
lection of quantitative data, so prevalent in contemporary
geographic research. Rather, the comparative and contras-
tive format of the investigation requires the use of quali-
tative data. The products of differing variable viewing
angle techniques will be examined in regard to their res-
pective abilities to meet the objective of achieving “three-
dimensional” (and ggtggl’three-dimensional) portrayal of
thematic information.

Owing to the static viewing angle of ninety degrees.
“three-dimensional“ hill shading techniques. such as Tanaka's
inclined contour method, Brassel's oblique hill shading
method, and other variations on the same theme will not be
analyzed in the context of this thesis.

Several modes of representation will be applied to a
common subject, total State populations of the midwestern

United States. The techniques to be investigated are as

follow:

l)
2)

3)

6
two-dimensional base maps with volumetric symbols
block diagrams

physical models

In addition to these methods of representation, a new

technique will be applied to the thematic mapping problem.

This technique is that of:

4)

off-axis holography

Data gathering will be accomplished by assembling and

illustrating graphical products generated by the author.

This output will consist of:

I)
2)
3)
4)
5)

6)

7)

3)

manually constructed drawings

SYMVU computer plot outputs

manually constructed physical model
off-axis transmittance holograms of model

multiplexed off-axis transmittance holograms
of the model

photographs of holographically reconstructed
image of model

photographs of multiplexed holographically
reconstructed images of model in time sequence

photographs of holographically reconstructed
images of model photographically multiplexed
with a physical mensuration device in
reconstructed image plane

IQKthheses Testing

The testing of the hypotheses will consist of apply-

i"£l the data to the qualitative analysis format illustrated

7

in Figure 1. The questions asked in the analysis are re-
flective of greater awareness toward three-dimensionality

as one progresses further through the process. Thus. the
first hypothesis will be tested by noting at what point the
various cartographic techniques respectively leave the
questioning process. If the techniques are input according
to the chronology of their development, and each successive
input leaves the mainstream of the analysis at a greater
level of penetration, the first hypothesis will be accepted.

If all techniques. except the newly proposed method
which utilizes off-axis holography, reach, "Conclusion:

The product is not the optimal method for portraying three-
dimensionality on a two-dimensional medium“, the second
hypothesis will be accepted.

If the newly proposed method that employs the off-axis
holographic technique, reaches, "Conclusion: The product
{1; the optimal method for portraying three-dimensionality
on a two-dimensional medium“, the third hypothesis will be

accepted.

Graphic Presentations

Presentation of "three-dimensional" graphics will be
accomplished by standard two-dimensional cartographic tech-
niques utilizing pen and ink. Computer generated graphics

will be used to display the output from the SYMVU computer

 

 

 

 

FIGURE l - ANALYSIS PROCESS

N0

 

NO

 

YES

YES

 

 

 

 

 

 

 

 

Conclusion: The product
is not the optimal method
for portraying three-
dimensionality on a two-
dimension medium.

 

 

 

 

 

Conclusion: The product
.13 the optimal method for
portraying three-
dimensionality on a two-
dimensional medium.

Input representation by various
cartographic techniques.

Is the product dimensionally
consistent?

Does the product exhibit
parallel perspective?

The product exhibits angular
perspective.

Does the product exhibit actual
three-dimensionality?

Does the product physically
exist in three dimensions?

Can mensuration be accomplished
in all three dimensions?

Do any additional disadvantages
of the product void its use?

Do additional advantages exist
with the method or product?

List those advantages.

 

 

 

 

 

mappit
Men:
photo:

image:

recon
image:
entia'
will \

natur-

9
mapping program. Photographs will be taken of all three-
dimensional material relevant to the thesis. This includes
photos of the model and the holographically reconstructed
images.

Since photography is a two-dimensional form of visual
recording, the three-dimensionality of three-dimensional
images will be compromised somewhat, by necessity. Differ-
ential focusing, dependent upon photographic depth of field,
will be submitted as “proof“ for the three-dimensional

nature of the holographically reconstructed images.

CHAPTER II
The Historical Basis of

Dimensional Perception and Display

Early Man

The first physical observance of depth undoubtedly
occurred in the early pre-history of mankind. It was not
a conscious observation, but a natural one. It was natural
in the same terms as the perception of heat or pain. It
was simply a small part of the "total man“.

Man utilized his natural attention to depth in his
daily regimen. It was this attribute of depth perception
that allowed him to survive. His success at obtaining food
depended directly upon the keen edge of distance judgment.
So, too, did the success of avoiding physical harm from
beast or other men depend upon this perception.

As life continued, man found the desire to record his
achievements. Recording took the form of graphical output
upon cave walls. The meaningful highlights were rendered
to future generations through pictorial accounts. These
graphics attempted to portray life through the eyes of the

beholder.
lO

ll

Commitment to realism had a place in these illustra-
tions, too. It may have been a chance occurrence that first
prompted early man to apply color to these figures. but it
was certainly not mere happenstance that promoted the con-
sistent application of brown to the figures of creatures
that were, in reality, brown in color.

An additional aspect that relates to realism is that
of the distance-size relationship. The cave dwellers might
have first recognized this when noticing the apparent size
of a creature from a distance. The closer the creature
ventured, the greater its apparent size became. This real-
ization, too, was incorporated in their drawings. In il-
lustrating an assemblage of beasts. those that were a
greater distance from the imaginary point of observation

were drawn as smaller beasts.

The Renaissance

The Renaissance ushered forth an increased awareness of
realism. Throughout the art-work of this time. fine atten-
tion was paid to distance-size and angular relationships.
Man was trying to illustrate via the essentially two-
dimensional medium of brush and canvas the actual perceptions
he obtained from his three-dimensional optical abilities.
However, no amount of toil and tribulation could actually

achieve these ends. The fact remained that at that time

12
there existed no method for utilizing two-dimensional means
to achieve three-dimensional results. The use of distance-
size and angular relationships worked toward giving all the
visual cues that were associated with depth. but in no way
could the elusive quality of realism be delivered.

The Renaissance not only emphasized the importance of
realism, but provided the technique and media necessary for
the portrayal of depth. This was achieved by the many
artists who made use of sculpting techniques. Frequently,
these men were the same that used brush and canvas. It is
rather difficult to determine which area of their talents
most influenced the other, but one might theorize that the
acute perception of depth so necessary for sculpting dra-
matically influenced the perceptions rendered to canvas.

In the case of sculpting, these people were presented with
a medium that was entirely suitable for the presentation of
three-dimensionality.

The actual material used for the portrayal of sculpting
is of little concern in the context of three-dimensionality.
Hhether the finished product was stone or bronze, it was
three-dimensional just the same. The unfortunate aspect of
this artistic form was that the achievement of the three-
dimensional quality had to be paid for by the price of

existence in physical space.- As opposed to a painting of

13
the Last Supper. a sculpture would have achieved depth at
the cost of obfiscating the usefulness of that portion of

the room in which the sculpture was situated.

Early Cartographers

There is no doubt that the actual origins of carto-
graphy go back to the first person who traced his path,
the location of animals, or the course of a river in the
sand with a stick. However, cartographers of the western
world generally seem to trace the pragmatic foundation of
their discipline to the fifteenth century. It was during
this period that man sought the need to record his location
relative to the larger geographical area of his concern.

By the Age of Discovery, this area of concern had ex-
tended to well beyond the horizon. It was no longer
feasible to portray all essential information to an assoc-
iate by means of a few crude line-drawings in the sand.
Furthermore, there arose the need to take this information
away from the point of original composition to other
locals.

The realm of the world was expanding rapidly. The
services of cartographers were employed to meet this chal-
lenge, primarily through the production of portolani and
other forms of nautical charts. The world trade routes

were developing upon the oceans. The guidance of vessels

14
over these unknown surfaces to their ports-of—call became
a paramount concern to many. including the cartographers.

It is significant to note that the fundamental under-
pinnings of this field had not changed one iota from the
time when cave dwellers drew lines in the sand. The in-
tegral importance of man, land, and water had been carried-
on throughout the evolution of mankind. However, so too,
another fundamental aspect did carry through from time
immemorial . . . . the recording of the man-land-water
significance upon a two-dimensional medium.

It is easy to see why nautical charts developed to
indicate only the x and y axes. Since the water bodies
travelled were perceived as planar surfaces, there was no
need to portray a z-axis. All necessary information could
be shown to relate only to that plane. Even the three-
dimensional qualities of shoals and reefs had little im-
portance to the seafarers other than the fact of their
location upon that two-dimensional perceptual plane.

The point being made is that the eventual development
of the two-dimensional Cartesian Coordinate System in the
seventeenth century by DesCartes was a very systematic and
predictive occurrence. Given the fact that the direction of
travel and relative location were viewed in planar terms,

it is quite logical to assume that any representation of

15
the same would be viewed in similar terms. The importance
of the Cartesian Coordinate System is most pointed in its
direct and meaningful applicability to the representation
of the situation from which it had been derived.

Eventually, this planar view of the earth changed.
Perhaps it was due to exploration inland from the seacoasts.
In any case, as man traversed the land surface, cartographers
were required to include new types of information to the
products of their trade. If mountains were found at a cer-
tain location, it became the responsibility of the carto-
graphers to portray this aspect. A form of crude symbol-
ization was first adopted to achieve this representation,
but in no way did it even come close to anything that could
be deemed realistic.

Inappropriately, instead of developing a method from
the newly existent situation. cartographers manipulated the
situation to fit their existing method. Nautical charts
assumed a constant plane and the subsequent necessity of
portraying only the x and y axes upon that plane. The addi-
tion of landforms or other three-dimensional items, while
obligating consideration. did not receive consideration for
the portrayal of that heretofore unrecorded dimension, the

z-axis.

CHAPTER III

Three-Dimensional Composition

Ages

The Cartesian Coordinate System was originally deve10p-
ed from the mathematical modeling of Rene DesCartes in the
seventeenth century. While some contemporary cartographers
might scoff at the need for definition of this system, it is
necessary in the context of this thesis.

”Cartesian Coordinate System -- l) A two-dimensional
coordinate system in which the coordinates of a point are
its distances from two intersecting, often perpendicular
straight lines, the distance from each being measured along
a straight line parallel to the other. 2) A three-
dimensional coordinate system in which the coordinates of
a point are its distances from each of three intersecting.
often mutually perpendicular, planes along lines parallel
to the intersection of the other two."'

It is clear that both denotative meanings are derived
from a common philosophical vantage. However, in practice,

the connotative meanings accepted by many cartographers are

16

17
derived from the realm of their experiences. This is to
say that those cartographers whose experience has been pre-
dominantly confined to two-dimensional work will find it
difficult to think in terms of a three-dimensional context.
For that reason. these relationships will be examined.

Owing to the first definition, two axes must be de-
fined. Those are the abcissa and the ordinate. The abcissa
is the x-axis, the first rectangular coordinate”; that mea-
sured on the horizontal axis. The ordinate is the y-axis.
the second rectangular coordinate'; that measured on the
vertical axis. The relationship of these axes is shown
graphically in Figure 2. The representation is functionally
planar and therefore ideally suited for the two-dimensional
character of a pen and ink drawing.

The three-dimensional definition introduces a third
coordinate. This is the zenith -- the z-axis. the third
rectangular coordinate'. The standard graphic mathematical
portrayal of the x, y. and z axes' interrelationship is
shown in Figure 3A. The '0' indicates the origin in this
right-handed coordinate system. The dashed line indicates
that the axis is extending out of the page toward the
viewer.

This imaginary three-dimensional figure could be “laid

on its back“ without destroying the relationship of the

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axial planes. If this were done, the illustrated version
would appear as in Figure 3B. The z-axis should be imagin-
ed extending back through the page. Applying this relation-
ship to a cubical structure would result in the portrayal
shown in Figure 3C. Broken lines are utilized on the far
side of the cube in an attempt to minimize the possibility
of optical illusion.

Hhile Figure 3 illustrates the more common x-y-z re-
lationship, another visual portrayal is also acceptable.5
This is shown in Figure 4A. Figures 48 and 4C have re-
ceived the same relative adjustments in their visual rep-
resentations as did Figures 38 and 3C. The purpose of
pointing out these differing modes of x-y-z relationship
is not to confuse the reader. It is merely to set the
stage for continued discussion. He will find that thematic
cartographers have utilized both of these representations
in their art. Consequently, a working base of common

understanding must be established at this time.

Perspective

Simply stated, perspective is the way in which we see
an object dependent upon the viewing point. the elevation
of that point above the horizon, and the azimuth on the
horizon.‘ Perspective is utilized significantly for carto-

graphic purposes in the attempt to provide a mapping

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22

technique that is responsive to the three-dimensional
nature of spatial data. This attempt is commonly re-
ferred to as “three-dimensional“ mapping.7

The medium of “paper and ink" can never actually
achieve true three-dimensional results. This is due to
the inherent lack of the third dimension in which to work.
Therefore, this “three-dimensional" mapping attempts to
provide certain visual cues to the reader that will create
the illusion of depth.“ The most singularly convincing
item that can be attributed to the success of this illusion
is that of perspective.

Perspective is a very general term. In "three-
dimensional“ mapping. differing types of perspective may
be employed. He shall examine these types and various
sub-types in terms of their construction methods and re-

sulting products.

Parallel Perspective

Parallel perspective utilized parallel projectors
extending from a planimetric map.’ See Figure 5A. This
map is assumed to be lying thirty degrees off the hori-
zontal plane. The parallel projectors extend to the plane
of perspective view, which is normal to the angle of view.
The image appearing on the plane of perspective view is

referred to as a parallel perspective transformation, such

 

 

 

 

FIGURE 5 - PROJECTIONS

PARALLEL ANGULAR

 

   

GEOMETRY OF PROJECTIONS

 

 

 

 

 

 

 

 

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MAP TRANSFORMATIONS

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24
as that shown in Figure SB. The surface is then elevated
along the vertical axis in a manner described by Stacey to
provide a parallel perspective “three-dimensional” map as

shown in Figure 5C."

Angular Perspective

Angular perspective differs in theory from parallel
perspective in that the projectors converge, rather than
extend in a parallel manner, at the plane of perspective
view. A cross-sectional illustration is shown in Figure SD.
The transformation at the plane of perspective results in
the transformation appearing as in Figure 5E. An angular
perspective ”three-dimensional“ map constructed from this
transformation would appear as in Figure SE.

A significant difference exists between the graphics
that result from angular perspective and those that owe
their form to parallel perspective. In the transformations
of parallel perspective, the x and y axes are perpendicular
to one another. This is not the case with that trans-
formation resulting from angular perspective. The “sides“
of the transformation are sloping inward. If these ”sides"
were extended, they would eventually intersect. Conse-
quently, it may be noticed in Figure 5E that the horizontal
line above “b“ is longer than the horizontal line located

under “a”. Visual contrast and comparison can be

25
facilitated by examining the transformations and the “three-
dimensional” maps, resulting from the parallel and angular
perspectives, side by side in Figures 5C and 5E.

Furthermore, while it may be difficult to perceive,
convergence takes place on the vertical plane as well as on
the horizontal plane when angular perspective is used.'1
Since this fact is not accounted for in parallel perspective,
that type of perspective can only result in a vertical ex-
aggeration being expressed in the cartographic results. In
viewing Figures 5C and SF again. it can be seen that the
”three-dimensional" map resulting from parallel perspective
extends further along the vertical axis than does the pro-
duct generated by the employment of angular perspective.

A sub-type determination can additionally be made in
the case of angular perspective. This generally applies
to the azimuth on the horizon above which the viewing point
is located. These sub-type classifications are referred to
as one-point and two-point perspective.

One-point perspective assumes the leading edge of the
block base to be parallel with the horizon. As one pro-
gresses vertically. it will be noticed that the "sides" of
the block will slope in a manner to intersect at a single
point upon the horizon. A drawing is shown in Figure 6A

to illustrate an example of one-point perspective.

26

 

 

FIGURE 6 - PERSPECTIVE VIEWS

 

A. / X
L 1

ONE- POINT PERSPECTIVE

3.

TWO -POINT PERSPECTIVE

 

 

27

Two-point perspective is assumed when a model is pre-
sented with a corner toward the viewer. The “sides“ on
the x-axis and those on the y-axis each focus, respectively,
upon separate points located on the horizon. An example of
a block viewed in two-point perspective is seen in Figure 68.

Through the preceeding discussion, a theme has been
developing. The basis of this theme is that types of per-
spective have differing degrees of "legitimacy". This is
to say that in relation to the manner in which we would per-
ceive an actual physical model with our eyes, angular per-
spective is the most successful method of alluding to that
perception in contemporary "three-dimensional" cartography.

However, perspective, as we have seen illustrated thus
far, has not always been used by those aspiring to intro-
duce the third dimension into cartographic output. An evo-
lution took place that must be understood to evaluate the
state of the art today. H0pefully, we can subject examples
from this evolution to a form of qualitative analysis that
will allow us to perceive the limiting characteristics of
these differing methods utilized in the portrayal of "three-

dimensionality”.

CHAPTER IV

“Three-Dimensional“ Thematic Cartography

Derivation from Tppographic Mappipg

”Since the eighteenth century the map has been used as
a tool to show the spatial distribution of physical, social,
and economic phenomena. Such maps, which present a partic-
ular theme. are often distinguished from the topographic
map by the term thematic maps."" Some might say that
thematic cartography begins where topographic cartography
“leaves off'. This is to say that thematic mapping generally
takes place on a topographic base map. From the preceeding
statement of Hodgkiss', it is apparent that the reliance of
thematic cartography upon topographic cartography is
chronological as well as physical.

Likewise. ”three-dimensional“ cartography owes its
genesis to topographical mapping, as this sort of mapping
was first fostered in the United States by the U.S. Geo-
logical Survey.

Early in the twentieth century. the two aspects of
three-dimensionality and thematic cartography were merged.
The results combined a thematic attitude with a ”three-

28

29

dimensional“ mode of portrayal. Many of the early attempts
in this field set firm precedents upon which subsequent
development arose. An examination of this development will
strive to show us the “three-dimensional” thematic carto-

graphy of today by understanding the work of yesterday.

Dimensional Inconsistency

Sten De Geer published an article in 1922 entitled
“A Map of the Distribution of Population in Sweden: Method
of Preparation and General Results'." This method was
developed in a response to the need for displaying quanti-
tative data. De Geer felt that the "averaging" effect of
the choropleth technique was detrimental to the develop-
ment of a genetic-quantitative geography."

As a solution to the prevailing inadequacies of the
contemporary methodology, De Geer proposed the use of
“three-dimensional“ representation based upon the existing
theory of the dot method. It was his belief that the
graphical representation of spheres could be drawn in a
manner coexistent with dots. The fundamental dichotomy of
two-dimensional representation versing that of three dimen-

sions had just found the basis of its origin.

Symbolism
It is strange, though. that this was not noticed by

the cartographic community. Instead, in 1928 Guy-Harold

30

Smith published ”A Population Map of Ohio for 1920" uti-
1izing the same basic technique." The only distinction
between the two methods was Smith's alteration of the sym-
metrical arrangement of dots utilized by De Geer to an
asymmetrical arrangement of dots.

In that well-known product of Smith's (excerpt shown
in Appendix A), we notice that the "spheres" are actually
circles. Appropriate shading is rendered in an attempt to
create the illusion of spherical structure, but apparently
Smith conceptually viewed these figures as circles. This
argument can be supported by noting the locations of these
symbols. If these figures actually were perceived by Smith
as spheres, their relative locations would be positioned
by consideration of the point of spherical tangency on each
sphere-plane interface. Thus, the “resting point" of each
sphere would be commencerate with the planar location of
the respective cities of which the spheres represent the
population. Instead, it can be noticed that if the
"spheres” are perceived as circles, the respective centers
are accurately positioned over the appropriate city loca-
tions.

Dimensional inconsistency is a problem of this method.
Hhile this topic will be discussed subsequently in ref-

erence to symbology in total versing the base map, it is

31
apparent that in this case dimensional consistency has not
been considered even in the portrayal of all symbology.
“Three-dimensional“ figures have been interspersed with two-
dimensional dots. The result is one of dimensional con-
fusion on the part of the reader, derived from dimensional
inconsistency of symbology presented by Smith.

As was mentioned earlier, dimensional consistency can
also be viewed in terms of two map components. The first
is the physical base on which the quantitative data rests,
and the second is the symbology itself. Hhile Smith failed
on the latter count, Erwin Raisz overcame this problem
through the use of cube-like symbols referred to as “block
piles“, only to fail on the larger scale of consideration
that places these two elements in concert.“

Raisz presented an article entitled ”Block-Pile
System of Statistical Maps“ in l939." It was his desire
to provide a technique that could overcome the lack of
commensurability and the subdivision difficulty inherent
with the use of ”spheres“. A publication entitled “Geo-
graphical Distribution of the Mineral Industry of the
United States“ appeared two years later.H An example of
that technique is shown in Figure 7.

Throughout Raisz's work we find that the States were

drawn in respect only to two dimensions, while the "block-

32

 

 

FIGURE 7 - RAISZ'S BLOCK-FILE

 

 

 

 

 

 

 

 

 

 

33
piles“ were constructed to portray the illusion of three-
dimensionality.

Referring to Figure 8, we can see that a cross-
sectional view shows tha planes to which the base map and
the "block-piles“ are oriented, respectively. The ”block-
piles" have been constructed in such a manner that the
imaginary base upon which they rest is forty-five degrees
off the plane on which the base map has been constructed.
This disparagement, while perhaps not immediately notice-
able to all map readers, should be recognized as dimensional
inconsistency to anyone at all familiar with the observance
of depth in the real world.

Hilbur Zelinsky utilized isometric symbology in an
article entitled “An Approach to the Religious Geography of
the United States: Patterns of Church Membership in 1952"."
The use of these particular volumetric symbols did offer the
possibility of overcoming the weakness presented in the
works of Raisz. Unfortunately, Zelinsky was apparently
unaware of this and thusly proceeded to induce the same
problem in his cartographic output.

Figure 9 shows several midwestern States with an iso-
metric cube constructed and displayed in the same manner
as those used by Zelinsky. Again, we see by cross-

sectional illustration in Figure 10 that inconsistency

34

 

 

 

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exists. However, consistency could have been realized by
Zelinsky had he adjusted either the projection plane of the
base map or the projection plane of the imaginary base upon
which the isometric cubes rest. By adjusting the former to
fit the latter, the product as shown in Figure 11 can be
derived.

The cross-sectional diagram of this derivation, Figure
12, illustrates that the two planes in question are super-
imposed on one another. Furthermore, dimensional consistency
can be achieved by utilizing the isometric symbolism com-
bined with an isometric projection of the base map. Hhile
Figure 11 is consistent in terms of the projection planes,
true dimensional consistency can be gained by incorporating
a form of total isometric perspective that would view the

scene from the southeast and appear as in Figure 13.

Perspective View

While the cartographic examples, both reproduced and
newly generated, have shown an increase toward a greater
appearance of “three-dimensionality”, it may be noticed that
they are all deficient in terms of angular perspective.
This is not too difficult to believe when we realize that
angular perspective has been essentially disregarded by
thematic cartographers throughout the field, from past to

present. This point is substantiated by the conspicuous

 

 

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41
absence of documentation concerning either theoretical or
methodological considerations of angular perspective in
“three-dimensional“ thematic cartography. Furthermore,
actual cartographic products of a thematic nature employing
the use of angular perspective are yet to-be found in the

literature.

Neglect in Landform Mapping

Occasionally, reference to angular perspective in the
broader classification of cartography pgg_§g can be found.
However, these references are usually concerning topographic
cartography. Axel Schou applied this consideration to land-
forms in 1941.’° Additionally, commentary on one-point and
two-point perspective in the graphical rendering of land-
forms is highly stressed by Lobeck." Generally, though,
its use even in block-diagrams (of landforms) or perspective
maps of the terrain is discouraged. Jenks and Brown des-
cribe the use of angular-perspective maps as not being
economically feasible,” while Monkhouse and HilkinSon say,
"block-diagrams (of landforms) can be constructed in either
one-point or two-point perspective, with considerably more
labour."” It is significant, then, that the application
of angular perspective has yet to be introduced to “three-

dimensional" thematic cartography.

42

It is quite understandable that the use of angular
perspective has not yet penetrated the entire field of
"three-dimensional'I thematic cartography. The basis of
"three-dimensional" cartography, in general, has been
topographic, not thematic. In light of this, the physio-
graphic method attributed to those such as Lobeck and
Raisz’“ was fundamentally concerned with the correct plani-
metry of maps.”

Thematic cartographers have traditionally been follow-
ers of methods used for topographic mapping. Quite fre-
quently, thematic and topographic cartographers have been
one in the same. Owing to this, those in the field of
thematic cartography have not been original, but instead
have applied methods developed for the portrayal of topo-
graphy to the problems of portraying thematic information.
Methodology applied to topographic mapping was never ser-
iously challenged as to its thematic suitability. One such
method is the physiographic method. Another is the terrain
diagram proposed by Dufour." The result has been the
adoption of methods for portraying planimetrically correct
three-dimensional topographic information to the thematic
arena in which three-dimensionality might be of importance,

but in which planimetry is of lesser consequence.

43

Neglect in Thematic Computer Mapping

The upsurging utilization of computer plotting capa-
bilities in recent years has furthered the disregard for
angular perspective. Numerous programs have been developed
to portray statistical data in ”three-dimensional" form.
Some of these programs have been adopted by thematic carto-
graphers. One such example is the SYMVU program that was
developed at the Harvard Laboratory for Computer Graphics
and Spatial Analysis as it operates on Michigan State Univ-
ersity's CDC 6500 computer.27

The SYMVU program allows for the construction of a
“three-dimensional“ drawing. It may be applied in a manner
to graphically portray a statistical surface defined by
points or one composed of conformant areas. He shall be
concerned with its relevance in the latter case. Hhen this
program is applied to a subject such as population in the
States of the Union, the States are drawn to appear as geo-
metric solids. The height, or z-axis, is scaled so as to
be proportioned to the predetermined variable. This figure
is constructed upon a “block” to further enhance the three-
dimensional effect.

Computer graphics of this nature are appreciated by
many people for a variety of reasons. Consistent line work

is one. Far more important, though, is the capability of

44

this program to portray the data easily from differing
points of view. The altitude, or viewing angle, can be
adjusted from zero to 359 degrees. Scaling and shading
patterns are variable within limitations, as well. Most
significant, however, is that all of these alterations can
be performed merely by changing a few numbers on two control
cards. -

Incidentally, while the SYMVU program does retain the
capability to produce output in two-point angular perspec-
tive, this option requires deliberate action on the part of
the user. Assuming that most people using a “canned“ pro-
gram will take advantage of as many default options as
possible, the isometric projection would be unconsciously
selected most of the time. This owes to the fact that the
isometric projection is the default option for projection
type in the SYMVU program.

Figure 14 shows the SYMVU program as applied to pop-
ulation of the midwestern United States in 1970. Mensur-
ation of the population is accomplished by either visual
comparison or by physical means utilizing the scale con-
structed on the apparent z-axis. It might be worthy to
mote that determination of population cannot be made
directly from the “three-dimensional“ representation,
itself. Hithout the scale appearing in concert, the map

is quantitatively meaningless.

FIGURE I4 - PARALLEL PERSPECTIVE

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45

 

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Figure 14 presents an additional problem, as well. In
it the significance of angular perspective has been ignored,
totally. In this case the angular perspective would be one-
point perspective. The sides of the “blodk” (y-axis) should
appear to be sloping inward to a focal point on the horizon.
Hhile the exact slope could be determined from knowing the
base dimensions, viewing angle, and distance of viewing, it
is still valid to state that line AB should be shorter than
line CD.

Figure 15 views the isometrically projected “three-
dimensional“ structure from a corner. In this case the
lack of two-point perspective is much less noticeable than
was the lack of one-point perspective in the preceeding
figure. However, the violation of angular perspective has
occurred none the less. If this drawing was in two-point
perspective, we would find that lines AB and AC were shorter
than lines CD and CB, respectively. Unfortunately, this is
not the case, and the drawing is concluded as not being in
two-point angular perspective.

Again, we have found another example of contemporary
cartographic acceptibility that fails to distinguish itself
in terms of realism. This aspect's importance has been
stated by Jenks and Crawford along with those of clarity

and aesthetic qualities." However, without any consid-

47

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eration for realism as expressed through angular perspec-
tive, output based upon the faulty assumptions of the past
has gained acceptance and legitimacy in the ”three-

dimensional“ thematic cartography of today.

Possibilities with Computer Mapping

SYMVU, unlike some ”three-dimensional“ mapping pro-
grams, does have the capability of viewing a particular
data set in two-point angular perspective. Unfortunately,
however, since the importance of portraying three-
dimensionality in a consistant and realistic manner has not
been stressed by thematic cartographers, the significance
of this capability of SYMVU is yet to be discovered by many.
The reason for lack of popularity may be conscious rather
than subconscious.

Previous reference to two-point perspective stated,
in effect, that convergence of straight lines (a function
of angular perspective) is applicable to the z-axis in
addition to those labelled x and y. In Figure 16 extension
lines have been added to the basic two-point perspective
drawing to illustrate this point. Line segment 0-0' is
noticeably greater than line segment E-E' situated on the
extension lines. While making the drawing more represen-
tative of the way in which we would actually perceive a

physical three-dimensional object, the use of two-point

49

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perspective has fostered the development of an additional
problem . . . . mensuration.

It may be noticed in Figure 20 that a scale has been
computed and displayed. However, we must realize that the
scale portrayed in this sense is virtually meaningless.
Since we have empirically determined that the apparent
z-axis scale is variable in relation to changes in the x
and y axes, any scale used to measure this z-axis must be
variable in that respect, as well.

Needless to say, that is an awkward problem for a
situation such as that presented. If the “three-
dimensional“ map was truly three-dimensional in a physical
sense, we could achieve these measurement objectives.
Unforutnately, since the presentation is limited to two
dimensions, we have no way to thrust any type of device
“back“ into the portray 1. Hithout a variable two-
dimensional mensuration device, we cannot actually deter-
mine the quantitative difference between portion of the

map such as Michigan and Illinois.

Induced Parallax

Through the use of parallax, it might be assumed that
the two-dimensional limitations of pen and ink might be
overcome. Several systems could be applied to the situa-

tion as possible solutions. These include the familiar

51
blue and red lensed glasses, the horizontally and verti-
cally oriented Poloroid lensed glasses, or the stereoscOpe.
All work on the same fundamental principle of each eye
viewing the same scene from a slightly different angle.
Hence, by constructing a drawing that makes use of in-
ducing parallax and placing it next to the original symbol,
a stereopair has been formulated. Quite importantly, the
viewing point displacement must be determined to be on the

linear axis of the viewer's eyes.

Stereoscopic Models

Figure 17, when viewed with a pocket stereoscope, can
be used to demonstrate induced parallax in two stereomodels
featuring corner views. Figure 17A is an isometric cube,
while Figure 178 is a cube in two-point perspective. The
inpropriety of the isometric cube as a three-dimensional
symbol becomes readily apparent when parallax is induced
and a stereoscope is used for viewing. Thus, the importance
of two-point perspective in a corner view is extremely sig-
nificant if the goal of a realistic portrayal is to be
attained.

Figure 18 provides a similar stereomodeled contrast
between the ”block-pile“ utilized by Raisz (Figure 18A)
and a similar structure modified in a manner to account

for one-point perspective (Figure 188). Again, that

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54
stereomodel incorporating angular perspective is far

superior in projecting that more realistic appearance.

Inadequacies of Stereoscopic Drawings

While it does, at first glance, appear that this
method offers a possible solution to our previously
identified cartographic problem, the use of artificial
stereoviewing is not really an adequate approach. The
first problem with its use is that artificial stereo-
models provide for parallax along the x-axis, only. This
is quite reasonable, given the relative location of eyes
upon human beings. However, this limitation very severely
restricts the viewing orientation of the reader in a manner
quite unlike the natural stereoviewing observed in the
real three-dimensional world. Additionally, a thorough
mathematical understanding and explanation of the third
dimension in this artificial system is yet to be developed.
LaPrade pointed out, ”More than twelve equations involving
different combinations of at least ten variables have been
proposed.“” The conclusion derived from this issue is
that accurate three-dimensional reconstruction by this

method is preseltly an impossibility.

Basic Limitations of Standard Two—Dimensional Media

The entire situation can be rendered to certain rel-

55

atively basic elements. Those elements are as follow:

1) There has not yet been devised a map that exhibits all
the characteristics of three dimensions, on a two-
dimensional medium. 2) Therefore, so-called three-
dimensional maps are actually two-dimensional maps.

3) Some of the so-called three-dimensional maps give better
visual cues toward the illusion of three-dimensionality
than do others, and 4) since these maps are actually two-
dimensional, any measurement taking place upon these maps
must be limited, therefore, to the horizontal and vertical
axes of the two-dimensional medium upon which these maps

appear.

Three-Dimensional Ends Using Three-Dimensional Means

The facts and conclusions stated do not mean that the
realization of three-dimensional goals cannot be achieved.
To date, it simply means that those goals cannot be achiev-
ed through conventional two-dimensional media. Instead,
just as did the artists of the Renaissance, cartographers
of today can find it possible to achieve three-dimensional
ends by utilizing three-dimensional means. These means
consist of constructing physical models. Interestingly
enough, this suggestion is nothing new to cartographers.
John Evelyn recalled an account of a terrain model of the

Isle of Antibe being produced in the year 1665, according

to Spooner.’°

56
Three-Dimensional Perception

Three-dimensional models have been used for a variety
of reasons over the years, however under cartographic con-
siderations this use has been limited primarily to the
portrayal of topography. This is probably a result of
mankind's inherent awareness of the z-axis when thinking
of topography. Who in our society can find himself un-
aware of the fact that he is walking up or down a ten
degree slope when doing so?“ Hho does not notice hills and
valleys when peering from a significant vantage?

The answers are obvious. These exhibitions of aware-
ness are fundamental perceptions to which man can relate.
Hhile it may be a little difficult for most men to per-
ceive the spatial dimensions (x, y, and z) of a high pres-
sure center, it is quite realistic to assume that it can
actually exist in those three dimensions, none the less.
Therefore, the development of models for the portrayal of
an item of easy three-dimensional conceptualization is
probably of greater legitimacy than is the rendering of a
situation, perceived three-dimensionally, onto a two-
dimensional medium.

Mama and Misulia point out the importance of relief
to man. The military uses include: strategic or tactical

planning, training, engineering design studies, intelligence,

57
amphibious operations, and interrogation of prisoners of
war." The overriding element pervading all these examples
is the three-dimensional basis of the man-land relation-
ship. It is easier for man to perceive topography on a
model than it is for him to perceive same on a two-
dimensional topographic map.

The lack of perceptual identity is, then, probably the
reason three-dimensional models have not been used to any
degree of significance in thematic cartography. While many
geographic variables are actually three-dimensional in
nature, it is interesting that few are ever conceptualized,
let alone mapped, by three-dimensional means. If a var-
iable of a thematic sort is not perceived or identified as
three-dimensional, it will not be portrayed in a three-
dimensional manner.

Is this lack of perception in three dimensions an
adequate reason for not striving toward three-dimensional
goals in output? If perception is a function of our ex-
periences, so too, are our experiences a function of our
perceptions. Thusly, three-dimensional perception can only
be gained through actual three-dimensional experience. In
the case of geographers, this means that to understand a
variable as truly spatial (all three dimensions), one must

educate himself so-as-to perceive variables in three-

CHAPTER V

Holography

Background

Holography is basically "a recording and viewing pro-
cess which allows reconstruction of three-dimensional
images of diffuse objects.“” It differs from photography
on several counts, but most significantly on its capability
to record the third dimension. Photographic methods employ
the recording of light intensities in a focused image. The
resulting image is two-dimensional. The production of a
hologram is quite different.

Nhile the incubus of holography goes back to Gabor in
1943, the real development began in the early l960's."
It was at this time that a suitable light source, the laser
(Light Amplification by the Stimulated Emission of Rad-
iation), became available. With this coherent light source,
it became possible to record a photographic image of a com-
plex wavefront reflecting off an object and interfering with
a coherent reference beam." This procedure was made known

by Leith and Upatnieks in 1964 and subsequently was termed

59

60
"off-axis holography"." Eventually, the distinguishing
aspect of “off-axis” was dropped, as the form of holo-
graphy known as ”on-axis“ has all but disappeared from
practice. This has occurred primarily for practical
reasons, as well as for those of safety in respect to the

dangerous effects of laser light upon the human eye.
Composition

Elements

The nature of coherent laser light is shown in Figure
19. It is essentially light of constant wavelength (Figure
19A). Coherence is obtained by the additive effects of
amplitude (Figure 198) and phase (Figure 19C). The re-
sulting light is an intense beam of emission in terms of
the preceeding factors. The beam is split by means of a
partial mirror known as a beam splitter. One sub-beam is
then used to illuminate the object to be holographed and
is consequently referred to as the object beam. The other
sub-beam is caused to impinge upon the light reflected from
the object toward the film plate. This impinging sub-beam
is referred to as the reference beam. The interaction of
the object beam and the reference beam results in an inter-
ference pattern being produced. When this occurs, certain

minute portions of the film plate will receive no light

 

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62
(destructive interference), while other minute portions
will receive illumination (constructive interference). A
simplistic drawing of coherent light interfering upon im-

pingement at a film plate is shown in Figure 20.

Recording

In reality, the light reflected from the object does
not come to the film plate as a planar wave. The light
that originally illuminated the object is cast out in many
directions through reflection off the object. "Every
point in the surrounding space receives light simultaneously
from every illuminated point on the surface of the object.""
The resulting wavefront that reaches the film plate from
the object becomes a complex wavefront. The interference
pattern produced by the interaction of the complex and the
plane (reference beam) wavefronts will vary throughout
space. A recording of any cross-section of this pattern
can then be obtained by introducing a film plate at any
location in the interference zone. (See Figure 20.)

The interference fringes are generally in the neigh-
borhood of 2000 per millimeter when utilizing a helium-
neon laser with an output wavelength of approximately
6328 A. Consequently, it is important to realize the ele-
ments that are essential to this high degree of resolution.

The first requirement is that of photographic material

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64
capable of this fine resolution. The second is a mechan-
ical stability of all aspects of the optical system in
which movement may not exceed one eigth the wavelength of
the light source.”

Hith the preceeding aspects clearly in mind, it is
possible to portray a hypothetical holographic ”set-up” in
the schematic diagram of Figure 21. In this diagram we
see some of the laser light illuminating the object. The
remainder passes through the beam splitter. The result-
ing interference pattern is subsequently recorded at the
film plate. This film plate is then processed and the
resultant pattern on that plate is not a picture of the
scene or object that was holographed, but a recording of
the interference pattern generated by the interaction of

the reflected object beam and the reference beam.

Reconstruction

Reconstruction of a virtual image can be obtained at
any time in the future. The only requirement is that a
laser beam must be oriented to strike the film plate at
the same degree of incidence as did the original reference
beam. This beam is referred to as the reconstruction beam.

The film plate then acts as a transmittance filter.
Since its processing, that plate has retained dark spots

where destructive interference took place, and remains

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clear where constructive interference occurred. These
light and dark spots (a fraction the wavelength of the
light source) then serve as a transmittance filter to the
reconstruction beam. The "flow" of light travelling in the
reconstruction beam is therefore attenuated at the film
plate. The result of this action is the construction of a
virtual image of the original object or scene. Figure 22
illustrates this aforementioned reconstruction arrangement.
The most amazing point about this reconstructed image
is the fact that it is virtually indistinguishable from the
original scene or object. It appears to be the same dis-
tance from the film plate as was the original and has the
same reflected light intensities as did the original.
Furthermore, it has all the same apparent dimensions as
did the original, the inclusion of the x, y, and z axes

notwithstanding.
Production of Holpgrams

Model

Owing to the fact that a three-dimensional scene of a
cartographic nature was necessary for the production of
subsequent holograms, one was built specifically for this
purpose. The subject and areal scope of the model was

population figures for the respective midwestern United

States.

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These data for both the years of 1910 and 1970 were
taken from the 1960 and 1970 Census of Population, Number
of Inhabitants,pUnited States Summary, respectively. The
base map to which these statistics were applied was de-
rived from a polyconic projection of the United States of
America, published in the Hammond Comparative World Atlas.

The population figures for the States of Ohio, Indiana,
Illinois, Michigan, Wisconsin, Minnesota, and Iowa were
then "rounded off" to the nearest one-half million persons
for the years of 1910 and 1970. These figures appear in
Table I. The block-pile nature of the model prescribed the
use of one cardboard layer equalling a certain amount of
population. This was set at each layer equalling one-half
million people. Table II illustrates the number of card-
board layers necessary to achieve the derived populations
of each State in both the years of 1910 and 1970.

Each cardboard layer was approximately one-sixteenth
of an inch in thickness. Consequently, the most populous
State, Illinois, was determined to rise no more than one
and three-eighths of an inch off the model surface. This
surface consisted of one-eighth inch drawing board (card-
board) that held equal x and y dimensions of fifteen inches.
The surface of this board was air-brushed with a mottled

composition of purple, brown, red, and green inks in a

69

Table I

Midwestern United States' Population to the Nearest
One-Half Million Persons: 1910 and 1970.

(times one million)

1910 1970
Ohio 4.5 10.5
Indiana 2.5 5.0
Illinois 5.5 11.0
Michigan 3.0 9.0
Wisconsin 2.5 4.5
Minnesota 2.0 4.0

Iowa 2.0 3.0

70

Table II

Necessary Number of Cardboard Layers to Represent
Midwestern United States' Population in the Years
1910 and 1970 on the Model.

1910 1970
Ohio 9 21
Indiana 5 10
Illinois 11 22
Michigan 6 18
Hisconsin 5 9
Minnesota 4 8

Iowa 4 6

7l
manner that produced an overall gray tone which provided
contrast with the cut-out layers of the States. These cut-
out layers all had a white surface, while edges on the
z-axis were alternately shaded black and white.

Three-dimensional alphabetic characters were used for
appropriate wording on the structure. This consisted of the
title, “Midwestern U.S. Population“, the appropriate year of
representation, and a legend, “Each Layer Equals 1/2 Million
People”. These characters were three-quarters of an inch
on the y-axis, one-eighth of an inch on the z-axis, and
variable from three-thirtysecondthsto oneahalf~of an inch
on the x-axis.

A wooden carriage was designed and constructed to sus-
pend the model's z-plane at thirty degrees off the horizon.
This would, in effect, result in any photography or holo-
graphy conducted along a plane parallel to the horizon
being elevated thirty degrees off the horizon. This part-
icular observation altitude was chosen to provide the max-
imum amount of interpretation along the z-axis, while still
allowing adequate cartographic assessment along the x-axis

and, particularly, the y-axis.

Instrumentation
The holographic recording instrumentation was mounted

on a cast iron milling bench. This bench was supported by

72
a wooden framework that “floated" upon air bags to reduce
any possible detrimental vibrational effects in the super-
structure of the building. These items are shown in Figure
23.

All instrumentation was placed upon the top of the
milling bench. This instrumentaion consisted of one Jodon
HN-ZO laser (helium-neon), one shutter and cable release
mechanism, one variable beam splitter, five mirrors, two
spatial filters, one film plate holder, and a necessary
number of black screens to minimize stray light in the
system. The arrangement of these items with the model in

place is shown in Figure 24.

Operating Parameters
Several operating parameters were observed during the
actual holographic recording sessions. Generally speaking,
they were as follow:
1) All recording was conducted at night when
building vibration and other possible dis-

turbances could be minimized

2) Object and Reference beam pathlengths were
equalized

3) One and one-half hour warm-up periods were
allowed for laser mode stabalization

4) Variable beam splitter was adjusted to pro-
duce a reference beam to object beam intensity
ratio.of two or three to one

Figure 23 - Air Cushioned Holographic Hork Platform

3
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Figure 24 - Holographic Recording Equipment

74
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75
Exposure Time
Exposure time was calculated from the object beam and
reference beam intensities. These intensities were sub-
mitted to the following formula:

.02

(I + 1'} 10‘5

In this formula, “Io" signifies object beam intensity,
"Ir" refers to the reference beam intensity, and “5" stands
for the scale setting of the photometer. This formula was
only used as a very “rough“ guide provided by the manufac-

turer of the photometer.

Film Plate Processing

Agfa-Gevaert, Scientia, 10E75, two by three inch photo
plates were used for recording purposes. These were pro-
cessed with Kodak materials. That processing consisted of
the following procedure:

1) Develop in Kodak HPR Developer for seventy
seconds

2) Fix in Kodak Rapid Fixer, Solution A, for
three minutes

3) Hash in distilled water for one minute

4) Hash with Mallinckrudt Methyl Alcohol,
. Anhydrous (CH3OH), for one minute

5) Allow to air dry for one or two minutes

76

Reconstruction of Holographic Image

Procedure

Reconstruction took place by reinserting the pro-
cessed plate into the plate holder and adjusting the beam
Splitter to conduct all light through the reference beam
(which is then considered the reconstruction beam) path-
way. The model was either summarily removed from position
or a black screen placed between it and the film plate.
The resulting view through the holographic plate was
identical to the original diffusely illuminated object
from which the hologram had been produced. The preceeding
description applies to work conducted in Room 254,

Engineering Building, Michigan State University.

Photographic Limitations

Figure 25 is a photograph of the holographically re-
constructed image derived through the previously mentioned
process. The reconstructed image was photographed with
Poloroid Type 57 film using a bellow camera equipped with
a 135 millimeter lens. This photographic record of a
holographically recorded image is somewhat misleading,
though, since the photographic process is limited to two-
dimensional results. Consequently, the three-dimensional

quality of the work is lost. This photograph can do no

Figure 25 - Photographed Holographically
Reconstructed Image

77

Figure 25

 

78
more justice to the three-dimensionality of the recon-
structed image than could a photo of the original model.
He are "bound“ in the nature of our display dimensionality
by the most limiting characteristics of the standard photo-
graphic process.

The polygonal "spots" in the photo are also attribut-
able to the photographic procedure. In this case, a cer-
tain amount of collimated light was reflected off certain
lens fittings of the camera. 8y reflection, this light

then entered the lens to produce the noticeable “noise".
A Second Holographic “Set-Up"

Elements

Owing to mechanical failure at the East Lansing lab-
oratory, additional holographic work was, of necessity,
conducted at Jodon Engineering of Ann Arbor, Michigan.
The holographic “set-up" was essentially the same and is
pictured in Figure 26. Again, an HN-ZO Jodon laser was
utilized with appropriate spatial filters and mirrors.
However, the film plates used in Ann Arbor were a high
speed experimental type being developed by Kodak. These

plates were of a four by five inch format.

Photography

Subsequent photography of the holographically recon-

Figure 26 - Secondary Holographic Recording "Set-Up"

79

Figure 26

 

80
structed images derived from the Ann Arbor holographic
recording session took place at the Michigan State Univer-
sity facility. Consequently, a certain degree of distor-
tion will be noticed in the subsequent photographs of the
holographically reconstructed images. The distortion is
due to the disparity between the optical systems used in
the recording and reconstruction sessions.

A Canon FT-QL camera fitted with a 50 millimeter lens
was used for the additional photos. The film type was
Kodak Tri-X Pan. As a result of using a 35 millimeter
ASA 400 film, the enlargements contained herein will be
subject to a great deal of graininess. The enlarging
process will also amplify the effects of "laser speckle“.
However, it must be kept in mind while viewing this sub-
sequent photography th't "laser speckle" is not neces-
sarily a disturbing characteristic of actual reconstructed
images. As can be noted from Figure 25, "laser speckle" is
negligible when more appropriate photographic recording
processes are applied to recording the holographically re-

constructed images.

CHAPTER VI
Findings of Qualitative Analysis of

Holographically Reconstructed Images

"Proof" of Three-Dimensionality

The holographically reconstructed images are three-
dimensional by definition of the process. However, to
illustrate this point, Figure 27A_and 8 show that the
three-dimensionality can be sensed by the camera in an
indirect manner. The photographic depth of field was
limited purposely to sense this aspect. Figure 27A finds
the “close” portion of the photo in focus. The "far"
portion of the photo is blurred and out of focus. By
refocusing the camera upon the "far" part of the holo-
graphically reconstructed image, the "close" portion is
then caused to be out of focus, as shown in Figure 278.
The resulting inference from this episode is that by uti-
lizing the focusing properties of conventional optics, we
can additionally verify the three-dimensional nature of
holographically reconstructed images of a holographed three-
dimensional model. Drawing upon the actual three-

81

Figure 27 - Photographic Evidence of Depth in a
Holographically Reconstructed Image

82

Figure 27

 

83

dimensional character of the imagery, we can also say that
the product will exhibit angular perspective and be dimen-

sionally consistent, as well.

Advantages in Impge LackingpPhysical Existence

Hhile the holographically reconstructed image appears
to be three-dimensional, it is not a physical object. Thus,
it does not exist in physical space. By not existing in
physical space, the problems associated with a model exis-
tent in physical space are nullified. Height, storage, and
physical degradation due to the effects of time are all

nonexistent with the holographically reconstructed image.

Mensuration in All Three Dimensions

Mensuration in a hologram is easily accomplished with
portable measuring rules. Figure 28 is a photographic
multiplex of the holographically reconstructed image and a
steel measuring tape. The tape measure can be placed in
any of the x, y, or 2 planes of the image. Hhen it is
separately illuminated, the resultant photograph will be
a multiplex of the tape and the holographically recon-
structed image.

Unlike the two-point perspective computer map's
scaling device, this measure (or scale) will adhere to the

distance-size relationship inherent with linear placement

Figure 28 - Photographically Multiplexed
Holographically Reconstructed Image
and a Steel Measuring Tape

84

Figure 28

 

85
on any given plane in the image. As the apparent size of
Michigan's northern peninsula would, for example, appear
“smaller" by being in the background, so to, would the
increments upon an imposed measuring device such as that

used in Figure 28.
Additional Advantages

Nonexistent Limitations of Physical Presence

Given the fact that the image does not exist in space,
this also introduces another pertinent point. The ruling
device is not restricted by the physical existence of the
image, as would be the case with a physical model. Instead,
it may be adjusted so-as-to appear to transcend the bound-
aries of the apparent physical elements composing the
cartographic scene. Differential lighting can be adminis-
tered to the scaling device to either increase or decrease
its apparent presence in the image plane in much the same
manner as does the Bausch and Lomb Zoom Transfer Scope
accomplish a similar feat. Figure 29 illustrates this
effect with the use of an engineer's scale. Note how the
scale and the State of Illinois are actually locationally
infringent upon one another. Of course, this attribute of
the holographic display system could also be applied to

measurement on the x and y axes as well.

Figure 29 - Photographically Multiplexed
Holographically Reconstructed Image
and an Engineer's Scale

86

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87
.Multiplexing of Scenes

An additional advantage provided by holography is the
mutually exclusive multiplexing of images.H This, in
effect, means that two, three, or greater numbers of scenes
can be holographed on the same film plate. Hhen recon-
struction occurs, these images remain independent of each
other and do not appear as the familiar multiple exposure
of conventional photography. Each scene's image is sep-
arate, clear, and distinct from one another.

This multiplexing process merely requires differential
orientation of the film plate to the reference and object
beams for each separate scene. The ultimate number of
sequential multiplexed scenes is determined by the emulsion
thickness on the photographic plate. This attribute of
multiplexing scenes then ushers forth the possible con-
sideration of sequential chronological scenes of a carto-
graphic nature being presented on the same medium of dis-
play. The scene "time shift" would then be totally con-
trolled by the map reader merely by altering the holo-
graphic plate by a few degrees of axial rotation.

The accomplishment of this multiplexing process is
shown in Figures 30 and 31, in which the population of
several midwestern States in the years of 1910 and 1970

are represented, respectively. Of these figures, photo A

Figure 30 - Midwestern U.S. Population in 1910

88

Figure 30

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89

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90
in each case is of the original model. Photos 8 are of
holographically reconstructed multiplexed images, both of
which were recorded on the same photographic plate. Perhaps
needless to say, the usefulness of multiplexing could be
viewed as being of economic importance a well as account-
ing for a possible decreased need for physical storage

space of either models or maps.

CHAPTER VII

Conclusion

Thematic cartographers, over the last fifty years,
have attempted to incorporate the use of the third dimen-
sion in the product output of their field. Early attempts
were inadequate by today's standards owing to perceptual
and portrayed dimensional inconsistancy. Subsequent dev-
elopment frequently failed to account for the needed real-
ism expressed in terms of angular perspective. The cul-
minating factor attributed to the failure in attaining
the goal of three-dimensional representation was the in-
ability of the existing two-dimensional media to portray
a true three-dimensional message.

The development of holography has changed all that.
This technique offers the capability of presenting a three-
dimensional image on an essentially two-dimensional medium
of expression, a piece of film or glass. Additional ad-
vantages such as the ease of measurement and chronologically
oriented multiplexing can also be presented as definite

91

92
advantages over conventional thematic cartographic tech-
niques. Holography is the next step in the evolution of
the cartographic field. Its characteristics demonstrated
in this thesis prove that it is, indeed, a viable method
for recording three-dimensional cartographic output on

relatively conventional photographic film.

Continued Research Possibilitieg

Owing to the far-reaching implications of possible
holographic applications, it is an understatement to say
that additional investigation must be conducted in this
area. Holography is presently being applied to problems
in many disciplines. However, of most immediate concern
to geographers is its application to mapping.

Computer constructed holograms are in the embryonic
stages of development. From there, it is only one step
to computer constructed holographic mapping capabilities.
Involved study has already taken place in applying holo-
graphic techniques to topographic mapping.H

The applicability of this three-dimensional record-
ing and display system, just to one aspect such as climatic
data alone, offers wide latitude to anyone wishing to begin
investigation in that area. The development of three-
dimensional “isosurfaces” and related aspects of true

three-dimensional cartography could provide for almost

93
unlimited academic exploration. Indeed, holographic tech-
niques applied to the field of cartography afford a true

research frontier.

REFERENCES CITED

1. The American Heritage Dictionary of the Engligh
Language, (1973), s.v. ”Cartesian Coordinate System.”

2. Robert C. Heast, ed., C.R.C. Standard Mathematical
Tables, 13th ed. (Cleveland, Ohio: The Chemical Rubber Co.,
1964), p. 543.

3. Ibid.
4. Ibid.
5. Ibid.

6. George F. Jenks and Paul'Crawford;¥ijeWinngoints
for Three-Dimensional Maps, (Lawrence, Kansas: The Univer-
sity of Kansas, 1967), p. l.

7. George F. Jenks and Dwight A. Brown, ”Three-
Dimensional Map Construction,“ Science 154 (November 1966),
p. 857.

8. Ibid.

9. Ibid., p. 859.

10. John R. Stacey, “Terrain Diagrams in Isometric
Projection - Simplified,” Annals of the Association of
American Gepgraphers 48 (September 1958), pp. 232-236.

11. Jenks and Brown, "Three-Dimensional Map Con-
struction,” p. 858.

12. A. G. Hodgkiss, Maps for Books and Theses,
New York, New York: PICA Press, 1970), p. 13.

94

95

13. Sten De Geer, "A Map of the Distribution of
Population in Sweden: Method of Preparation and General
Results," Gepgraphical Review 12 (January 1922), pp.
72-83.

14. Ibid., p. 72.

15. Guy-Harold Smith, "A Population Map of Ohio
for 1920," Geographical Review 18, (July 1928), pp.
422-427.

16. Arthur H. Robinson and Randall 0. Sale,
Elements of Cartography, 3d ed., (New York, New York:
John Wiley and Sons, 1969), p. 130.

17. Erwin Raisz, "Block-Pile System of Statistical
Maps,‘I Economic Geggraphy 15, (April 1939), pp. 185-188.

18. Erwin Raisz, "Geographical Distribution of the
Mineral Industry of the United States," Mining apg
Metallurgy 22, (March 1941), pp. 158-166.

19. Hilbur Zelinsky, "An Approach to the Religious
Geography of the United States: Patterns of Church
Membership in 1952,“ Annals of the Association of
American Geographers 51, (June 1961), pp. 139-193.

20. Axel Schou, Atlas of Denmark, Vol. II,
(Copenhagen, Denmark: H. Hagerup, 1949), pp. 1-32.

21. Armin Kohl Lobeck, Block Diagrams and Other
Graphic Methods Used in Geology and Geography, (Amherst,
Massachusetts: Emerson-Trussell Book Company, 1958),
pp. 1-212.

22. Jenks and Brown, "Three-Dimensional Map
Construction,“ p. 858.

23. F. J. Monkhouse and H. R. Hilkinson, Maps and
Diagrams, 2d ed., (London, United Kingdom: Methuen and
Co. Ltd., 1963), p. 136. .

24. Tau Rho Alpha and Robert E. Hinter, "Quantitative
Physiographic Method for Landform Portrayal," The
Canadian Cartpgrapher 8, (December 1971), p. 126.

96

25. Arthur H. Robinson and Norman J. H. Thrower,
“A New Method of Terrain Representation,“ Geographical
Review 47, (October 1957), p. 509.

26. Erwin Raisz, General Cartography, (New York,
New York: McGraw-Hill Book Company, Inc., 1938), p. 298.

27. Robert Hittick, SYMVU: Perspective Views
DepictingpArea Outlines, Technical Report 73-2, (East
Lansing, Michigan: Michigan State University Computer
Institute for Social Science Research, 1973), pp. 1-7.

28. Jenks and Crawford, Viewing Points for Three-
Dimensional Maps, p. 2.

29. George L. LaPrade, ”Stereoscopy - A More General
Theory,“ hotogrammetric Engineerigg 38, (December 1972),
p. 1177.

30. C. S. Spooner, Jr., “Modernization of Terrain
Model Production,“ Geographical Review 43, (January 1953),
p. 60.

31. Arthur A. Noma and Michael G. Misulia,
“Programming Topographic Maps for Automatic Terrain Model
Construction,“ Surveyipg and Mapping 19, (September 1959),
p. 355.

32. A. E. Goodson, "Telescopic Model Making,"
Cartographic Journal 4, (December 1967), p. 105.

33. David D. Dudley, Hologpaphy - A Survgy, (Falls
Church, Virginia: Computer Sciences Corporation, 1973),
p. 120. '

34. Dennis Gabor, "Holography, 1948 - 1971,"
Science 177, (28 July 1972), pp. 299-300.

35. Dennis Gabor et al., “Holography,” Science 173,
(2 July 1971), pp. ll-12.

36. Emmett N. Leith and Juris Upatnieks,
“Havefront Reconstruction Hith Diffused Illumination and
Three-Dimensional Objects,“ Journal of the Optical Society
of America 54, (November 1964), pp. 1295-1301.

97
37. Gabor, ”Holography," p. 11.

38. Gary Cloud, "MMM 806," (East Lansing, Michigan:
Michigan State University, 1974), (Mimeographed class notes),
p. 12 14.

39. Joseph T. Carcel et al., “Simplification of
Holographic Procedures," _pp1ied Optics 5, (July 1966),
p. 1199.

40. J. D. Trollinger et al., "Multiple Exposure
Holography of Time Varying Three-Dimensional Fields,”
Applied Optics 7, (August 1968), p. 1640.

41. Maurice K. Kurtz, Jr. et al., Study of Potential
Application of Holographic Techniques to Mapping,
(Lafayette, Indiana: Purdue Research Foundation, 1971),
pp. 1-250.

APPENDIX

Figure Al - An Excerpt from Smith's 1920 Population
Map of Ohio

Figure Al

 

 

 

 

 

 

 

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BIBLIOGRAPHY

BIBLIOGRAPHY

List of References

Periodicals

Alpha, Tau Rho and Winter, Robert E. ”Quantitative
Physiographic Method of Landform Portrayal." ng_
Canadian Cartogpapher 8 (December 1971): 126-136.

Carcel, Joseph T.; Rodemann, Alfred H.; Florman, Edward;
and Domeshek, S. “Simplification of Holographic
Procedures.“ Applied Optics 5 (July 1966): 1199-1201.

Gabor, Dennis: Kock, Hinston E.; and Stroke, George H.
"Holography." Science 173 (2 July 1971): 11-23.

Gabor, Dennis "Holography, 1948 - 1971." Science 177
(28 July 1972): 299-313.

De Geer, Sten “A Map of the Distribution of the Population
In Sweden: Method of Preparation and General Results.”
Geographical Review 12 (January 1922): 72-83.

Goodson, A.E. "Telescopic Model Making.” Cartographtg
Journal 4 (December 1967); 104-107.

Jenks, George F. and Brown, Dwight A. "Three-
Dimensional Map Construction." Science 154 (18 November
1966): 857-864.

LaPrade, George L. "Stereoscopy - A More General Theory.”
Photogrammetric Engineering 38 (December 1972): 1177-1187.

Leith, Emmett N. and Upatnieks, Juris "Havefront
Reconstruction Hith Diffused Illumination and Three-
Dimensional Objects." Journal of the Optical Society
of America 54 (November 1964): 1295-1301.

 

Noma, Arthur A. and Misulia, Michael G. “Programming
Topographic Maps for Automatic Terrain Model Construction."
Surveying and Mapping 19 (September 1959): 355-366.

Raisz, Erwin "Block-Pile System of Statistical Maps."
Economic Geography 15 (April 1939): 185-189.

Raisz, Erwin "Geographical Distribution of the Mineral
Industry of the United States." Mining and Metallurgy 22
(March 1941): 158-166.

Robinson, Arthur H. and Thrower, Norman J.H. "A New
Method of Terrain Representation." Geographical Review 47
(October 1957): 507-520.

Smith, Guy-Harold "A Population Map of Ohio for 1920.“
Gepgraphical Review 18 (July 1928): 422-427.

Spooner, C.S. Jr. "Modernization of Terrain Model Pro-
duction." Geographical Review 43 (January 1953): 60-68.

Stacy, John R. ”Terrain Diagrams in Isometric Projection -
Simplified.“ Annals of the Association of American
Geographers 48 (September 1958): 232-236.

Trolinger, J.D.: Farmer, H.M.; and 8e12, R.A. “Multiple
Exposure Holography of Time Varying Three-Dimensional
Fields." Applied Optics 7 (August 1968): 1640-1641.

Zelinsky, Hilbur "An Approach to the Religious Geography
of the United States: Patterns of Church Membership in
1952.” Annals of the Association of American Gepgraphers

Books

Davies, Peter: ed. The American Heritage Dictionary of
the English Language. New York, New York: Dell Publishing
Co., (1973).

Hodgkiss, A.G. Maps for Books and Theses. New York, New
York: PICA Press, (1970).

Lobeck, Armin Kohl Block Diagrams and Other Graphic
Methods Used in Geologyyand Geography 2d Edition.
Amherst, Massachusetts: Emerson-Trussell Book Co., (1958).

Monkhouse, F.J. and Hilkinson, H.R. Maps and Diagrams
2d Edition. London, United Kingdom: Methuen & Co., (1963).

Raisz, Erwin General Cartography. New York, New York:
McGraw-Hill Book Co., (1938).

Robinson, Arthur H. and Sale, Randall 0. Elements of
Cartography 3d Edition. New York, New York: John Wiley
& Sons, (1969).

Heast, Robert C.: ed. C.R.C. Standard Mathematical Tables
13th Edition. Cleveland, Ohio: The Chemical Rubber Co.,
(1964).

Published Reports

Dudley, David D. Holography - A Survey. Falls Church,
Virginia: Computer Sciences Corporation, (1973).

Jenks, George F. and Crawford, Paul V. Viewing Points for
Three-Dimensional Maps. Lawrence, Kansas: The University
of Kansas, (1967).

Kurtz, Maurice K., Jr.; Mikhail, Edward M,; and Stevenson,
Harren H. Stugy of Potential Application of Holographic
Techniques to Mapping. Lafayette, Indiana: Purdue Research
Foundation, (197T)[—T

Hittick, Robert SYMVU: Perspective Views Depictipg Area
Outlines, Technical Report 73-2. East Lansing, Michigan:
Michigan State University Computer Institute for Social
Science Research, (1973).

Atlases

Hammond Horld Atlas and Gazetteer. Maplewood, New Jersey:
Hammond Incorporated, (1967).

Schou, Axel Atlas of Denmark Vol. II. Copenhagen, Denmark:
H. Hagerup, (1949).

Additional Materials

Cloud, Gary MMM 806, (mimeographed class notes). East
Lansing, Michigan: Michigan State University, (1974).

General References

Periodicals

Agnard, J.P. "Tolerances in Holography." Photogrammetric
Engineering 38 (January 1972): 51-53.

Baetsle, P.L. "Conformal Transformations in Three
Dimensions." Photogralmetric Engineering 32 (September
1966): 816-824.

Baldock, E.D. "Production of Terrain Models." Canadian
Cartographer 4 (December 1967): 128-135.

Bonfiglioli, Luisa "Stereoscopic Model for Four Dimensions."
Photogrammetric Engineering_32 (May 1966): 495-499.

Brassel, Kurt; Little, James; and Peucker, Thomas K.
PAutomated Relief Representation." Annals of the Associatiop
of American Geographers 64 (December 1974): 610-611.

Carmichael, L.D. "A Technique for the Preparation of Block
Diagrams." Cartographic Journal 4 (June 1957): 50-52.

Caulfield, H.J. "Multiplexing Double Exposure Holographic
Interferograms.“ Applied Optics 11 (November 1972):
2711-2712.

Collier, Robert J. "Holography and Intergral Photography."
Physics Today 21 (July 1968): 54-63.

Gerritsen, H.J.: Hannan, H.J.; Ramberg, E.G. "Elimination
of Speckle Noise in Holograms Hith Redundancy." Applied
Optics 7 (November 1968): 2301-2311.

Hopkins, John "Computer Generated Stereograms.“
Photogrammetric Engineering 32 (November 1966): 1011:1014,

Jenks, George and Coulson, R.C. "Class Intervals for
Statistical Maps." International Yearbook of Cartography 3
(1963): 119-134.

Jenks, George F. and Caspall, Fred C. "Error On Choropleth
Maps: Definition, Measurement, Reduction." Annals of the
Association of American Geographers 61 (June 1971):
217-2440

Jenks, George F. "Generalization in Statistical Mapping."
Annals of the Association of American Geographers 53
(March 1963): 15-26.

Jenks, George F.; Steinke, Theodore: Buchert, Beverly;
Armstrong, Lewis "Illustrating the Concepts of the Contour
Symbol, Interval and Spacing Via 3-D Maps.” The Journal
of Geography 70 (May 1971): 280-288.

Kitiro, Tanaka "The Orthographical Relief Method of
Representing Hill Features on a Topographical Map."
The Geographical Journal 79 (March 1932): 213-219.

Leith, Emmett N.; Brumm, Douglas 8.; and Hsiao, Stephen S.H.
"Holographic Cinematography." Applied Optics 11
(September 1972): 2016-2023.

Leith, E.N.: Kozma, A.; Upatnieks, J.: Marks, J.; and
Massey, M. “Holographic Data Storage in Three-Dimensional
Media." Applied Optics 5 (August 1966): 1303-1311.

Leith, Emmett N. and Upatnieks, Juris “Progress in
Holography.“ Physics Today 25 (March 1972): 28-34.

Leith, Emmett N. and Upatnieks, Juris "Havefront
Reconstruction Hith Continuous-Tone Objects." Journal
of the Optical Society of America 53 (December 1963):
1377-1381.

MacKay, J. Ross "A New Projection for Cubic Symbols on
Economic Maps.” Economic Geographer 29 (January 1953):
60-62.

McDonnell, Michael M. “Speckle in Holograms.“
Photogrammetric Engineering 37 (June 1971): 587-589.

Meier, Reinhard H. "Magnification and Third-Order
Aberrations in Holography.“ Journal of the Opticgl
Society of America 55 (August 1965): 987-992.

Meierding, Thomas C. "Stereoscopic Images From lsoline
Maps." The Journal of Geography 70 (April 1970): 214-218.

Mikhail, Edward H. "Hologrammetry: Concepts and
Applications.‘I Photogrammetric Engineering_40
(December 1974): 1407-1422.

Mikhail, Edward M. “Mensuration Aspects of Holograms."
Photogrammetric Engineering 37 (March 1971): 267-276.

Mikhail, Edward M. ”Hologrammetric Mensuration and
Mapping System.“ Photogrammetric Engineering 37
(May 1971): 447.

Miller, O.M. "Thematic-Map Generalization." Tho
Geographical Review 54 (January 1964): 13-19.

Oberlander, Theodore M. "A Critical Appraisal of the
Inclined Contour Technique of Surface Representation."
Annals of the Association of American Geogpaphers 58
(December 1968): 802-813.

Real, R.R. ”Concept of 3-D Map Display Hith Stereo-
Orthophoto.“ Applied Optics 11 (June 1972): 1427-1429.

Saunders, Bernard G. "Stereoscopic Drawing by Computer -
Is It Orthoscopic?“ Applied Optics 7 (August 1968):
1499-1503.

Hinter, Heinrich "The Origin of the Sea Chart." Imago
Mundi 13 (1956): 39-52.

Yacoumelos, Nick G. ”The Geometry of the Stereomodel."
Photogrammetric Ehgineering 38 (August 1972): 791-798.
Books

DeVelis, John 8. and Reynolds, George 0. Theory ano
Applications of Holography. Reading, Massachusetts:
Addison-Hesley Publishing Co., (1967).

Greenhood, David Mapping. Chicago, Illinois: The
University of Chicago Press, (1964).

Keates, J.S. Cartographic Design and Production.
New York, New York: Halsted Press Division of John
Wiley 8 Sons, (1973).

Klein, H. Arthur Holography. Philadelphia, Pennsylvania:
J.8. Lippincott Company, (1970).

Lawrence, G.R.P. Cartographic Methods. London, United
Kingdom: Methuen & Co. Ltd., (1971).

Smith, Howard M. Principles of Holography. New York,
New York: Interscience Division of John Wiley 8 Sons,
(1969).

Published Reports

Brunsman, Howard 6., Division Chief, 1960 Census of
Population, Number of Inhabitants, United States Simmaay.
Washington, D.C.: U.S. Department of Commerce, Bureau
of the Census, (1960).

Miller, Herman P., Division Chief, 1970 Census of
Population, Number of Inhabitants, United States Summary.
Washington, D.C.: U.S. Department of Commerce, Bureau
of the Census, (1970).

Muehrcke, Phillip Thematic Cartography (Resource Paper
No. 19). Washington D.C.: Association of American
Geographers Commission on College Geography, (1972).

Peucker, Thomas K. Computer Cartography (Resource Paper
No. 17). Washington, D.C.: Association of American
Geographers Commission on College Geography, (1972).

Young, C.; Dugger, Donald 0.: and Wittick, Robert I.
SYMAP (Technical Report No. 100). East Lansing, Michigan:
Michigan State University Computer Institute for Social
Science Research, (1969).

Published Proceedings

Balasubramanian, N. and Leighty, Robert 0., eds.,
Coherent Optics in Mapping (Proceedings of the Society of
Photo-Optical Instrumentation Engineers). Rochester, New
York: American Society of Photogrammetry and The Society
of Photo-Optical Instrumentation Engineers, (1974).

MICHIGAN STATE UNIV. LIBRARIES

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