Holographic Images - Part 2
Resolution, diffusion and the encoding of signals
Initially,
Dennis Gabor was not trying to invent a holographic process. He was trying to enhance the
resolution of the pictures taken through electron microscopes.
Resolution
concerns the problem of separating or sorting out the details, one from the other, in an
image of some object, irrespective of whether the image is in the form of a photograph or
a reflection. Although there are a variety of factors affecting the degree of
resolution obtainable in a given instance, one of the more essential shaping factors is
the wavelength of the form of radiation being used to 'illuminate' the details of the
object one is trying to resolve. In general, the shorter the wavelength of the
illuminating radiation, the better will be the resolution of the object being illumined
and the better will be the resolving power of one's means of illumination.
Gabor
believed that if one could get an electron picture containing all the
available information in relation to a given object, and, then, if one corrected this
picture through optical means, one might obtain a far greater degree of resolution than
one could get otherwise. However, everything depended on being able to preserve the phase
information which is often lost.
An essential
tenet in Gabor's ideas concerning the enhancing of resolution through optical means was
his belief that one tended to lose phase information because one had nothing with which to
compare such information. He believed he had a way to preserve the phase information that
was usually lost.
Gabor
proposed to split the waves of a light source. One of the split beams would make contact
with a target object. The other beam did not interact with the target object but would be
permitted to recombine with the 'target-object wave' later on.
Gabor
believed that if one split the light in the foregoing manner, the subsequent,
'post-object-engagement' interference pattern of the two beams of light would allow phase
information to be preserved. In other words, the interference pattern would
provide a means of keeping track of the differences in amplitude and phase between the
object wave and the reference wave from the time that the two were split from the initial
light beam, until they came together again in the form of an interference pattern.
The
information concerning amplitude and phase differences was to be stored on a photographic
plate. Gabor believed that if one reconstructed the wave-front of the interference pattern
stored on the photographic plate, one should be able to give enhanced resolution to the
object's image because the hologram would have preserved all of the relative phase
variations as well as a record of the changes in amplitude.
Gabor's
technique is referred to as the 'in-line' method due to the way the
object to be photographed is placed in a direct line between the light source and the
photographic plate. As originally developed by Gabor, the in-line method was limited to
objects which were transparent. It could not handle non-transparent or dense objects.
The
diffuse-illumination hologram was developed by Juris Upatnieks and Emmett Leith in the
1960s. Unlike Gabor's 'in-line' method, the diffuse-light hologram used
reflected light rather than direct light and, consequently, was referred to as an 'off-axis'
hologram.
In the
Upatniek-Leith method, the initial light beam was passed through a partially coated mirror
which split the light beam. The split beams of light were then, transmitted along their
respective paths by a series of mirrors.
One series
of mirrors conveyed one of the light beams to an object and, then,, onto a juncture where
it would meet up with the reference beam. The reference beam had been transmitted by
another series of mirrors through an alternate route which by-passed the object being
photographed. When reunited, the beams created an interference pattern that preserved
variations in phase and differences of amplitude.
Leith and
Upatnieks used laser light (lasers were invented in 1960) as their coherent
light source. Laser light consists of twin emissions of light which are perfectly
identical both with respect to phase as well as amplitude.
In addition,
Leith and Upatnieks put a diffuser on the light source of the laser. This had the effect
of scattering the light somewhat.
However, the
light was scattered in in a way that did not affect or alter the coherency of phase
relationships of the twin emissions. The addition of the diffuser had the remarkable
effect of permitting each and every point of an illuminated object to act as a light
source.
Furthermore,
each and every point of the photographic plate was able to store a complete record of the
information received from the multiple light source of the object being illuminated by the
diffuse but coherent laser light. In short, each point of the photographic
plate preserved all amplitude changes and phase variations which resulted from the
interference pattern created by the interaction of the object beam and the reference beam.
While the
stored message is believed to be whole and complete at every point of a hologram,
nonetheless, resolution of the message is lost as the size of the fragment of the hologram
becomes smaller and smaller. The reason for the lost of resolution is due to the
increasing weakness of the signal with decreasing size of the signal carrier.
As the
signal grows weaker, it becomes more susceptible to the effects of noise or competing
signals. This results in an eroding of the image being transmitted by the signal. How
badly the image is eroded will depend on the ratio of noise to signal.
Theorists,
however, consider the eroding of the image to be a problem of the signal carrier rather
than the actual message itself. Therefore, they believe that although
resolution is lost as the size of the hologram fragment decreases, the message always
remains intact.
As indicated
above, theorists believe there is no lower limit on the size of the point of the
photographic plate that can retain all the amplitude changes and phase variations. The
absence of a lower size limit is because of the supposedly 'sizeless' nature of relative
phase. However, there are certain questions which might be raised about this contention.
To be sure,
relative phase is a relational rather than a purely quantitative relationship. Yet, in the
case of holograms, the relationship still involves physical entities in the form of energy
interference patterns. Consequently, one may not be able to escape entirely from the realm
of the material or physical and, therefore, quantitative and 'sized'. At some point on the
far side of the Planck length, one might suppose the physical disappears and with it the
'things' which are being related through relative phase.
In any
event, intuitively, one might presume that the smallest possible means of storing, as well
as transmitting, an optical hologram is the photon which is the carrier of the
electromagnetic force. This raises some interesting questions about how a single photon
could transmit and store the entire interference code of a hologram.
For example,
how does the structural character of a single photon (which is, supposedly, like a
sizeless, geometric point-particle) allow the photon to preserve the amplitude changes and
phase variations which occur when the photon engages some, given target object? If one
supposes that the field generated by a photon, or that accompanies a photon, is where a
signal is 'inscribed', the fact is, something has to keep the structural character of the
encoded field intact. Something has to permit the phase relationships to be preserved so
that the message does not dissipate prior to being recorded on the plate at the point of
interference.
Presumably,
this 'something' is the dialectic of forces and/or dimensions which establishes the set of
constraints and degrees of freedom that are described in the field equations governing a
given phenomenon. In this case, the phenomenon consists of coherent optical processes that
are: (a) separated into reference beam and object beam, (b) sent along different paths
(one of which encounters an object) and, then, (c) rejoined in the form of an interference
pattern.
A field
cannot account for the existence of the forces generating and shaping it. The field is
merely the phenomenal expression of the dialectic of such forces. Consequently, the
capacity of photons or the photon field to encode or store messages seems to depend on an
underlying substratum of ordered or ordering activity. This ordering activity permits
encoded signals to be preserved by organizing the way photons, photon-photon interactions,
or photon fields manifest themselves.
Neural activity: a generator of holograms?
Holograms
need not be restricted to instances using light as the only means of creating the
reference waves and object waves which subsequently interfere with one another. Any kind
of wave phenomenon could be used, including: electrons, X-rays, microwaves, and so on.
In fact,
since wave motion is equivalent to any kind of periodic or harmonic motion, theoretically,
one should be able to generate a hologram using any sort of periodic motion as long as one
can find a means of preserving the changes of amplitude and the phase variations involved
in such motions. In other words, what is important is the set of relationships that
capture the character of amplitude and phase, together with any transitions occurring with
respect to amplitude and phase.
Frequency
modulation of radio waves utilizes the phenomenon of phase modulation. In FM
radio waves, the amplitude is kept constant while the frequency of the wave is modulated.
The modulation of the wave's frequency which is conveying the signal is what constitutes
the message being transmitted. Since phase is the primary index of the location of
amplitude, and since the location of the crest and trough of amplitude shifts as the
frequency of the wave is altered, frequency modulation is actually a matter of phase
modulation, and phase modulation is central to the holographic process.
For quite
some time, neurophysiologists knew that neural signals utilize principles of frequency
modulation. Consequently, these signals revolve around phase variation.
The neural
impulse is represented on an oscilloscope as a moving wavefront. This wavefront
constitutes the fluctuation in voltage along the exterior of the neuron's cell membrane
subsequent to the ebb and flow of ions brought on by, first, the collapse, and, then, the
restoration of, the resting membrane potential. The moving wavefront on the
oscilloscope is usually referred to as a spike.
The neural
impulse is governed by the all-or-none law of transmission.
Essentially, this law stipulates that: (a) unless the critical value of a neuron's
threshold is reached, the cell will not generate an impulse wave; (b) once the threshold
value has been achieved, the subsequent impulse will travel down the axon in a wave of
uniform amplitude and constant velocity; and (c) neither the amplitude's uniformity nor
constancy of transmission velocity will be affected by increasing the intensity of the
signal triggering the neural impulse.
People such
as Karl Pribram believe sensory receptors produce signals which trigger
different sets of on/off or excitation/inhibition combinations of neurons. These different
sets collectively form interference patterns. Where there are interference patterns,
there, too, are phase modulations.
The
magnitude of frequencies and energies required to generate holograms in the laboratory are
not to be found in the nervous system. Consequently, one cannot draw direct comparisons
between holographic theory and what goes on in the nervous system. However, the means by
which events are encoded and stored in the nervous system may be an analog for the
holographic process (or vice versa).
An analog
is a structure or latticework or pattern capable of preserving a certain kind of logic,
principle, relationship or set of relationships that is found in some other structure,
latticework or pattern. Furthermore, the character of the two structures, latticeworks or
patterns that are analogs of one another involve different mediums.
Oscillations,
periodicies, vibrations, cycles, undulations, and so on which occur in a variety of
different mediums are all analogs of wave phenomena. In each case, the logic, principles
and relationships of amplitude and phase are preserved despite differences in the
character of the medium in which, and through which, these phenomena occur or take place.
Therefore, if a given medium has a means of preserving phase relationships, it has the
potential for being an analog for a hologram.
Consequently,
the brain or the mind, in some analog fashion, may be able to preserve data on amplitude
and phase relations, as well as provide a means of reconstructing this data, without
requiring the high energies necessary to produce the intensities associated with coherent
light. In fact, what may be most important, if there were an analog process for the
holograph in the mind or nervous system, is not even amplitude.
In the mind,
neither amplitude nor energy, per se, may be as important as being able to have a means of
recording gradations in the intensity of intentional orientation or focus. This aspect of
the intensity of focal orientation (together with the feature of phase relationships which
locates or orients that focal intensity within an aspect of the phenomenology of the
experiential field) may be the means by which the latticework of an event's structural
character is encoded to form a memory.
Alexander
Metherell believes the heart of the hologram is actually phase. In fact, he
was able to produce the phase-only hologram by keeping amplitude constant at one
level and just focusing on the variations of phase. Metherell's discovery
suggests that one may, yet, be able to show that memory is rooted in the idea of a
hologram - but a phase-only hologram.
Similarly,
one might want to treat the vectoral interaction of ideas and concepts as interference
patterns of a special sort. For example, instead of conceiving of the interference of
ideas as a simple function of amplitude, frequency and phase spectrum, or instead of
conceiving of such interference as merely giving rise to some simple daughter wave as a
function of whether the interference is constructive (i.e., additive) or destructive
(i.e., subtractive), the interference of ideas may best be construed in terms of being
dialectic, multi-dimensional and non-linear in character. In short, the ideational or
conceptual waveform may be a complex latticework which behaves differently than normal
waves usually do - yet, still retains some qualitative properties of wave phenomena in an
analogical form.
Normal waves
give expression to the principle of superposition ing in which they 'flow' through one
another without their structures being affected when they come out the other side of the
interaction. During the course of interference, naturally, the 'daughter' wave resulting
from the constructive/destructive interference of the parent waves will give expression to
an altered structural character. However, once the interaction is over, the parent waves
revert to their original character.
In the case
of hermeneutical interference, the interaction may be less like a standard case of
interference and more like a holographic context. In the latter case, the light wave is
distorted or warped or altered by the structural character of the object with which it
comes into contact. Furthermore, the light wave remains in a distorted or warped condition
even after the wave departs from the scene of object-engagement.
In other
words, as ideas move through one another, a dynamic, dialectical vectoral field is
generated which is capable of altering the structural character of one or more of the
ideas involved in the interaction. Which, if any, ideas will be altered, or to what extent
and in what way, will really depend on the character of the ideas involved. Moreover, the
character of the alteration will depend on how the individual brings the ideas together in
a given context and how susceptible each of the ideas is to certain kinds of motivational,
emotional, physical and spiritual forces that may be impinging on the interaction.
Inferential/mapping
functions may play an especially prominent role in this vectoral, dialectical process of
ideational interference. In this sense, the field generated by the interaction of the
ideas is, or can be, greater than the sum of the parts since the phase relationships given
expression through the inferential mapping functions have a tendency to generate further
phase relationships and inferential mapping functions - somewhat as an electromagnetic
field continues to propagate itself at right angles to the direction of primary
propagation. As a result, the initial ideas involved in dialectical engagement begin to be
altered by the very properties of the hermeneutical field which such ideas have helped to
establish.
In the
context of hermeneutical interference patterns, notions of phase, relative phase and phase
difference are likely going to be a be more structurally complicated, subtle, dynamic and
dialectical than is the case for ordinary waves of even an irregular and compound nature.
Under such circumstances, phase may have a lot to do with the hermeneutical orientation of
an individual at a given time as different ideas, concepts, values and so on are brought
into juxtaposition with one another and begin to interfere with one another.
Moreover, in
the case of hermeneutical interference processes, relative phase and phase difference may
involve inferential/mapping relationships that become manifest, or are generated, during
the period of ideational interference. Such inferential/mapping relationships may not
establish what the ultimate truth is, but the phase differences of such relationships
allow one to orient oneself with respect to the ideational interference at hand and to
grasp the structural character of the 'daughter' latticework resulting from such
interference. This provides one with a point of engagement through which to attempt to try
to work out the character of the interaction between certain aspects of ontology and
phenomenology which makes possible experiences of an observed structural character.
The
relationship between focus and horizon often constitutes a relative phase difference and
not necessarily an absolute one. An 'absolute' phase difference would be indicated if the
relationship between focus and horizon was congruent with, or reflective of, some aspect
of reality.
Even in the
case of congruency, however, there would be a certain relativity of phase difference
inherent in the situation since the truth being expressed or reflected would not
necessarily constitute the deepest, most essential penetration of the truth concerning a
given aspect of the structural character of reality. Nevertheless, a phase difference
latticework having some degree of congruency with the structural character of the scene
being reflected is certainly more objectively accurate than a phase difference latticework
which has little or no congruency with the structural character of the scene to which
identifying reference is being made.
In any
event, when an 'object' is encountered in the phenomenology of the experiential field
(irrespective of whether that object is a sensory experience, a concept, a dream, an
emotion or some other kind of experiential latticework), the beam of consciousness is
split, with horizon and focus traversing different paths until they reunite to create the
dialectic of interference in which focus and horizon play off against one another to
generate an n-dimensional hermeneutical holograph of the scene to which identifying
reference is being made.
The term
"n-dimensional hermeneutical process" has been used above in order to draw
attention to the way, in the phenomenological context, one gets a multi-faceted point of
view with the hermeneutical holograph, just as one does with a normal holograph. However,
in the phenomenological case, one is not restricted to merely the exterior surface and
contours of what is being holographed. One also has access to the qualitative,
non-physical 'surfaces' and 'contours' of the structural character of the n-dimensional
dialectical product of a hermeneutical holographic process.
In other
words, the penetrating power and capacity for resolution of understanding goes far beyond
the limits of purely physical/material process. Indeed, in a sense, one could say that the
penetrating and resolving power of even material/physical techniques is a function of the
underlying hermeneutical latticeworks in which such techniques are rooted and which shape
and direct and orient the latter processes.
|
