The possibility of imaging the sea surface in three dimensions by means of microwave holography from a low-flying aircraft is considered. Data cover a brief feasibility study and a review of some computer experiments in which it was demonstrated that it is possible to compute three-dimensional images of objects from raw holographic data recorded on magnetic tape. These experiments used synthetic data

Wells, W.

English

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FEASIBILITY OF MICROWAVE HOLOGRAPHY FOR IMAGING THE
SEA SURFACE
Willard Wells
Tetra Tech, Incorporated
Pasadena, California 91107
22
N73-15391
This paper considers the possibility of imaging the sea surface in three
dimensions by means of microwave holography from a low-flying aircraft.
This is a solution looking for a problem; perhaps it is applicable to
oceanography or to the calibration of satellite-borne instruments. Others
have attempted another means of imaging in three dimensions, namely
stereo photography, but with only limited success. This paper is in two
parts, the first of which is a brief feasibility study. The second part
briefly reviews some computer experiments (published elsewhere) in
which we have demonstrated the feasibility of computing three-dimensional
images of objects from raw holographic data that have been recorded on
magnetic tape. These experiments used synthetic data.
Let us begin by reviewing a well known two-dimensional imaging technique
as a useful basis of comparison, namely side-looking radar. As shown
in Figure 1, the resolution in the range direction to the side of the aircraft
is achieved by range gate in the ordinary radar fashion, in the angular
direction the resolution is achieved by using a long antenna aperture in the
fore-and-aft direction. The scheme is necessarily side-looking because
the range and angular resolution contours will fail to intersect at app-
ropriate angles for a resolution grid in any other direction.
For high resolution the aperture length must be a great many times longer
than the wavelength of the radar. The length may be either the physical
length of a very long antenna, or the length may be snythesized by the
forward movement of the aircraft. The latter requires that the phase of
the return signal be recorded so that a data reduction procedure can add
the signals in the same phase relationship as a long physical antenna. _In
22-I
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Fig. 1. S i de-Look i ng Radar
22-2
the synthetic case, the radar beam illuminates a much wider area than
the angular resolution to be achieved after data reduction. The number
of resolution cells within the beam width, lZ in Figure 1, is equal to
the number of signals added during aperture synthesis.
To the side-looking radar system compare the down-looking holographic
ii system shown in Figure Z. A real lateral receiver aperture is formed
by an array of simple receiving antemlas beneath the aircraft. Almost
certainly they would all fit in one row beneath either the fuselage or a
:_ wing, but the figure shows them staggered and situated on both the wing
and fuselage to emphasize that computer data processing can introduce
corrections that permit such arrangements when desired. The forward
' movement of the aircraft synthesizes the aperture in the fore-and-aft
direction. This dimension may be only half as long as the lateral real
_ aperture owing to the translation of the transmitter as well as the receiver•
The signal from each element Of the receiving array is stored on a separate
track of a multi-track tape recorder. The number of elements in array
determines the number of resolution ceils across the swath in the final
image.
u_
Figure 3 shows typical major lobes in the antenna patterns of the receiving
array, the 7 thin antenna lobes, and a single wide lobe of the transmitter
illuminating the swath. If the receiving antennas were dense, e.g. dipoles
spaced a half wavelength apart, ,or paraboloidal reflectors that are almost
touching, then the receiving pattern would have only a single major lobe
instead of 7 as shown. A sparce array would give the multiple grating
lobes as indicated in the figure, but these lead to no spurious signals
g that the transmitting antenna pattern is narrow enough to
lluminate only one of these as shown in the figure. This provision trans-
lates into a physical requirement that the transmitting aperture be at
least as large as the spacing of the receiving elements.
i
22-3
I• : "i¸ : " :
Transmitter
_ ] Synthetic J
]Aperture
I__L
Fig. 2. Down-Looking Holographic Radar
22-4
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For the ocean application let us compare the systems just described on
the basis of the amount of aperture that may be synthesized for high
resolution. An expression derived below is valid for any synthetic
aperture in either side-or down-looking systems. The linear resolutions
on the waterts surface is given by
r
¢ = ), r / (ZLs), (1)
where ), is the radar wavelengthl r is range to the target (which might be
called altitude h in the down-looking case), and L is the length of the
s
synthetic aperture. Note that X/L is ordinary angular resolution of an
aperture, the factor of 1/Z applies to synthetic aperture since the transmitter
as well as the receiver is in motion and phase shifts are thereby doubled,
and r is the lever arm that gives linear resolution. The maximum length
that may be synthesized is
L = Vt
s
where V is the velocity of the aircraft and t is the time during which the
target holds still to sufficient accuracy. This time is
t = kl(4_)lu,
where u is the random component of the movement of the sea surface
projected along the line-of-sight. (A steady movement of a frozen sea
surface is indistinguishable from a correction to the aircraft velocity.
Such correction must be found by trial and error anyhow.) The above
equations combine to give
¢ = Z_r (u/V) (2)
22-6
!,
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which curiously is independent of the microwave frequency. For high
resolution (small e ) both r and u should be small,as they are in the down-
looking case, r because the vertical distance represents minimum range,
and u because the minimum projection of the random movements of the
sea is along a vertical line-of-sight.
Both r and u are difficult to estimate well. Consider first a down-looking
system. The range r depends on how low the pilot is willing to fly, which
in turn depends on weather and the pilot's daring. Let us say r ranges
from 50 to 200 feet. The surface velocity component u does not fall
readily out of the theoretical models for sea states, but a value near
0.5 knots seems reasonable in moderate seas. As an example let us
assume
r = 100 ft =h
u = 0.5 knots
V = 200 knots, and find
e = 19 inches.
Recall that this is horizontal resolution; vertical resolution will be that
of the radar range gate. Thus sea states 1 and 2 will not be resolved,
but a down-looking synthetic system will give an image of the larger
structure in moderate to high seas, providing the radar is the nano-
second type that generates sufficiently short pulses.
Clearly the resolution on the order of 20" is needed, so synthetic aperture
side-looking radar is not applicable to the problem of imaging the sea. A
side-looking system witha real aperture L is not unreasonable however.
r
To estimate its size, let us assume some values compatible with the
previous estimates, namely
22-7
r =
C =
L =
r
1 inch
ZOO feet (slant height when h=100 feet)
20 inches, and find
10 feet.
These and some other comparisons between the two systems are shown
in the table on the following page. In this table note the rather self-
. explanatory items that are not discussed here in the text, such as optical
storage of bulk data, shadowing, etc.
:!
To complete the brief feasibility study of microwave holography, let us
estimate the data bandwidth that results from the previous assumptions.
The bandwidth will depend on the fidelity demanded of the recording, the
coding of the signals, and other electronic factors, but for a rough estimate
let us allow 10 cycles for each information bit in the hologram, or 20 cycles
for each resolution cell, since the information capacity of the image is less
than or about equal to the information capacity of the hologram. Thus the
bandwidth is determined by the speed of the aircraft and the size of the
linear resolution cell. Let N stand for the number of vertical resolution
v
cells or range increments. If N = 5 we find:
v
B _ 20 N V/¢per channel
V
20 kHz per channel,
where the previous assumptions were used again. This modest bandwidth
applies to each recording channel, and the number of channels equals the
number of resolution cells across the width of a swath. (Of course, if
desired, channels could be multiplexed in some fashion and the results
recorded with megahertz bandwidths. )
22-8
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1 This concludes the discussion of feasibility. The proof that pulse holographicimages may be computed with reasonable speed is published elsewhere
[W. Wells, Acoustical Holography, Vol. Z, p. 87, ed. Metherell & Larmore,
Plenum Press, N.Y., 1970; D. M. Milder and W. Wells, IBM 5. Res. &
Dev.__._.z,Vol. 14, p. 49Z (Sept. 70)]. A sizable frame, say 50 x 50 maybe
computed in less than a minute on a moderate speed computer.
i
Several of the published images are reproduced here for convenience.
In two dimensions the images of very small triangles were computed.
Figures 4, 5, and 6 show a specular triangle; Figure 7 a diffuse one.
These figures are analogous to a microscope view that shows the fine
detail caused by edge diffraction. The contours connect points of equal
image intensity. The theoretical resolution is indicated on the figures.
The blooming effect at the right angle in Figure 4 is an anomoly which
occurs when both legs of the triangles are parallel to the edges of the
aperture and the receiver is in the direct glare of the specular reflection.
The effect goes away when the triangle is rotated about the line of sight.
Figure 5, or tilted very slightly, Figure 6. Figure 7 shows a diffusely
reflecting triangle; often the fine structure of ocean waves will make
them diffuse reflectors. The blotches of high and low intensity in this
image are completely analogous to those seen when laser light illuminates
a diffuse reflector. They are characteristic of coherent illumination.
Finally Figure 8 shows range slices through a three-dimensional radar
image. At R=16.5 a plane greek letter II comes into focus; its true
shape is indicated by straight lines, the image by the contours. Similarly
at R=17.5 a 0 comes into focus.
22-10
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::1 ...........
: :_ :::::.::: :::: : :::t .-7 ...........
:::::::_:: _ ::::::::::::::::::::::::
Figure 4
Specular Glare, Sides Parallel
to Aperture Sides
Figure 5
Specular Glare, Rotated
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22-11
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Figure 6
Tilted Off Specular-
Figure 7
Diffus e Refle cto r
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= > 36.8% of F_k intcli<,ily (_
22-12
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Fig. 8. Greek Letters I_ ande Come into Focus at Ranges 16.5 and 17.5
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22-13


Feasibility of microwave holography for imaging the sea surface

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