ROSÆ, Inc.
7901 52nd Ave. W.
Arvada , CO 80002
January 1, 2007
MIRIAH: An
idea whose time has come (
The Challenge.
There
is the common belief that since conventional EEE systems for imaging (SAR,
ISAR, etc.), communications, navigation, etc., can be redesigned in hundreds
(if not thousands) of different ways to accomplish the same functional purpose,
then this will also apply to MIRIAH (a new Satellite Imaging invention). But
MIRIAH is not a typical EEE system. Rather, it is a uniquely arranged set of
Interferometers - a much different technology from the conventional EEE technology
(SAR is far more sensitive to timing errors than are Interferometers).
Moreover, Interferometers have such stringent requirements for their successful
implementation, that these constraints demand great care in the choice of the
architecture. In my opinion, this demands a "marriage" of the
uniquely innovative Interferometric methods used by MIRIAH to the ROSÆ Satellite
architecture - which is also uniquely innovative. This solution, to
this
most critical
*Note: Link here to the "Mission
Requirement" - choose either the (1) short version
or the more comprehensive
(2)
long version
.
The Answer to the Challenge
Einstein
proved light has a particle nature, comprised of distinct individual points or
packets of substance possessing energy. Whereas, Huygens proved light has a
wave form nature. Yet, while these two concepts of light appear to contradict
one another, they do not according to Fourier. Fourier, a French mathematician,
related these two forms of light into a unifying concept known as the
"Fourier Pair", in which both forms exist, but are focused at two
different planes. The first of these is known as the Fourier Plane (the wave
nature plane, which has phase diversity), and the second is
known as the imaging plane (the particle nature plane, which has spatial
diversity). In nature, man has cognition in the Imaging Plane, while whales and
porpoises have cognition in the Fourier Plane (as do submarine SONAR).
Furthermore, since the electromagnetic spectrum is a continuum, which occurs at
all frequencies, then these laws of Physics are true starting at the very
lowest frequency (audio) - to Radio Frequency (RF) - to HF – to VHF – to UHF -
to microwave - to light, etc.
The
illumination coming to MIRIAH´s receiving apertures (or antennae), reflected to
them from the Field of View (FOV), and subsequently deposited on a disc(s) or
other random access high density medium, requires a plane (or area)
in order to pass energy, which this illumination contains. Yet, it is clear that
only the Fourier Plane is capable of accumulating all of the information for
every imaged object in the FOV - not the Imaging Plane. For it is only the
Fourier plane, which spreads the imagery data throughout its focused plane.
This illumination energy comes to the receiving aperture in the form of an
energy distribution, which aggregates throughout the plane during the time it
takes to "fully fill" the aperture of the recording medium. Then, in
considering these two planes, it is the Fourier Plane which has all
of the information contained in the object. This is why I prefer to call it the
Holographic Plane, rather than the Fourier Plane. Since the distribution of the
total energy in the image is present throughout a very large solid angle, then
the object (and so the FOV) must rotate and translate, in order to sample all
of the illumination energy, which each resolved object within the FOV contains
(or rotate in azimuth and elevation for complete solid angle sampling).
Clearly, this will take considerable time, which is why this is not a real aperture
(until it is later illuminated), but rather it is a 2-D matched filter
at this point in time (a kind of “delayed” synthetic aperture). Later, when
illuminated by a collimated laser, it is a real aperture, focusing a real
image (as opposed to the SAR virtual image requiring complex and
time consuming reconstruction).
However,
for maximum efficiency, the "fill time" of this Matched Filter should
be just enough to sample all of the information in the FOV onto the Holographic
Plane, coherently (i.e., phase synched). Once completely "filled", it
becomes a source, which replicates every object in the FOV (reproduced at some
later time in all of its detail, at every angle). That is, this imaging format
becomes a 2-D hologram – after the Holographic Plane is
"fully filled". And, it is efficiently "filled" (and so not
inefficiently "over filled" - thereby wasting energy), if the next
cycle of "filling" is reached just as the previous cycle completes
the "filling" process. (And besides, to provide time-sequenced
imaging, successive discs should be registered to the same phase grid).
Then
it follows that for efficiency, the satellite orbits must repeat, and they must
be symmetric, which is why we use ROSÆ in a 5:1 resonant case as our preferred
architecture and preferred orbit. And, as has been proven in other
presentations, ROSÆ is the only possible distribution of satellites, which is
symmetric, stable, orthogonal, and possesses the attributes of a
"perfect" machine. These "perfect" attributes, require the
1st and 2nd Moments of this space "machine" to be collinear, constant,
orthogonal, and balanced in all three dimensions about the
"machine's" mass center (in this case earth’s gravity center). ROSÆ
is the only such architecture possible for earth or for any other planet (since
all planets have spherically concentric gravity fields). Hence, MIRIAH – ROSÆ
has no peer concept capable of providing these three services of Imaging, Communications,
and Navigation with anywhere close to its efficiency. This efficiency improvement
is several orders of magnitude - about a billion to one (in theory) for the
case of its improvement over SAR, which is today’s most efficient microwave
imaging concept.
Some
Scientists are of the mistaken opinion that many EEE system designs can be
found to compete with MIRIAH – ROSÆ. But all of these EEE designs are
correlated and registered to the recording medium as a function of time. For
example, the range dimension requires an extremely fine determination of time
since the range gate is moving across the FOV at the speed of light, whereas,
an Interferometer is self-registering. And, an Interferometer’s grid
(interference pattern) moves across the face of the FOV at the much slower
speed of satellites. This is why, per Heizenberg´s Uncertainty Principle of
Physics, that the Interferometer has a theoretical advantage in coherence time,
resolution (both spatial and spectral), and in energy density Gain. This
advantage will be a function of the speed ratio of (1) light to (2) the speed
at which the Interferometer´s interference pattern sweeps across the FOV. In
theory, this Gain advantage is about a billion to one. For with
Interferometry, image registration is sensitive to geometry, rather than time
correlation (as needed for the image reconstruction of all of a SAR’s
EEE systems). In fact, MIRIAH's image is a real image vs.SAR’s virtual
images. Hence, SAR needs lengthy non real-time "image
reconstruction", while MIRIAH can more quickly illuminate its hologram
(coherently) and focus with conventional optics in real time.
Therefore,
MIRIAH – ROSÆ uses triads of Interferometers, which correlate and maintain
phase coherence primarily as a function of geometry rather than time.
Furthermore, MIRIAH's images are in both 2-D and 3-D. This is practical with
architectures which use Interferometers distributed in a 3-D symmetric geodesic
set of equilateral triads about the earth. This is needed to set all
phase zero lines through a satellite, to enable phase offset
"unwrapping" to the phase origin faster and more efficiently. Once
again, this defines MIRIAH – ROSÆ, since it has eight equilateral faces or
planes - the minimum number of conformal planes for data continuity throughout
each imaged surface. Plus, it has the other necessary attributes needed
(orthogonal, linear, stable, radially symmetric, focuses a large depth of field
linearly to a disc, etc.). Hence, any further exploration by Scientists to find
an alternative to MIRIAH – ROSÆ is doomed to failure.
Another
way in which government and industry microwave imaging Scientists have been
misled, is in the belief that wide bandwidth SAR will deliver more
imaging information, more efficiently, than can narrow bandwidth MIRIAH.
(For this is the case in the communications discipline – and so they reason it
should also be true in imaging). Although this assumption at first seems
reasonable, this mistake defeated the LightSAR project a few years ago. The
problem stems from the way a wide bandwidth SAR´s beam width shrinks as its
bandwidth increases. This drastically shrinks its FOV to where so many users
are left "out in the cold" (out of the supplied service area), that
the resulting extremely high unit cost creates a huge economic deficit for the
operational service. And, the signal propagation losses are so huge, its
satellites must use very low altitude orbits, which require "store and
forward" data methods, which completely cancels out the fast response time
advantage of wide bandwidth. This is so severe, that the MIRIAH imaging system throughput
time will deliver imagery much faster - even though its response time
is much slower than for a SAR.
MIRIAH generates a 2-D Matched Filter with a positive
Gain, which is impossible for an EEE system for a SAR. Likewise, it would be impossible for
an EEE system on a SAR to generate a 2nd Power – Aperture (2nd
PA) in tandem with the 1st PA. Therefore, the tremendous boost this
gives to MIRIAH´s performance (160 dB
Gain - in theory) will never be possible for a SAR. This kind of
performance is possible only for 2-D Interferometric architectures, known also
as a "sparse phased arrays", but only if the array is much
larger than the FOV. For uninterrupted coverage of the earth, this
creates the requirement for a satellite architecture, which has about two to
three times the diameter of the earth (as in ROSÆ). Such an altitude would be totally
impractical for SAR’s EEE system. In summary, no EEE system for SAR or
any other form of EE design can ever be designed to compete with MIRIAH’s
efficiency (as an architecture – which will in time have many system designs)..
All
of the above reasons are why there is no real competition for MIRIAH. Nor is
there any competition for MIRIAH – ROSÆ when it comes to global imaging,
navigation, communication services. The disparity is so great, that even the
most "hard nosed" captain of industry will be forced to switch to
this new architecture in order to survive in a competitive world marketplace.
Lest
any one still doubt this disparity in efficiency, it is on the order of a
trillion to one in favor of MIRIAH – ROSÆ (in theory). Even with the reality of
needing to use "off the shelf" components, which will degrade this
theoretical performance, we believe that the benefit/cost ratio will
remain somewhere from 10,000 to 1 - to 100,000 to 1 - in favor of MIRIAH.
This
is why we confidently "await the awakening" of the global market.
For, it is not a question of " if ", rather it is only a question of
" when ". And, given the nature of its critical mission requirement,
then the "when" has all but arrived. (If you failed to read this
Mission Requirement above, then here it is again - link here to the "Mission Requirement" -
choose either the (1) short version or the more comprehensive (2) long
version.).
William
H. Grisham ("Bill"), Inventor, President
ROSÆ,
Inc.