Project Cyclops, A Design... - Department of Earth and Planetary ...

arriveon thehorizontalaxisa little fartherfromthe
central spothanthe original spots A 1 and A2.
As a single sinusoid is swept upward in frequency a
succession of pairs of diffraction spots traces out a series
of almost vertical lines to form two rasters, one to the
left and one to the right of the central spot. Thus,
frequency is mapped into two rasters in the transform
plane. Each line of each raster maps a frequency interval
of fs Hz where fs is the scanning frequency used in the
recording process.
Time-Bandwidth
Product
The resolution of the spots along the raster lines of
the power spectrum is determined by the height of the
gate, which in turn is proportional to the time duration
of the recorded signal contained in the gate. The spot
intensity versus distance along the raster lines is the
square of the transform of the gate transmission versus
height. Expressing the distance along the raster line in
terms of frequency f and the gate height in terms of
duration T of the signal sample contained in the gate, we
find (see Appendix O) for a rectangular gate
I {sinTt(f-fo)TI2
7o= l
where I is the intensity at a point on the raster line
corresponding to frequency f, and Io is the intensity at
the center of the spot, corresponding to the frequency
of the sinusoid, f0. We shall take the resolving power to
be the frequency interval, Af, from the center of the
spot to the first null. Thus, from equation (7):
(7)
1
Af =-- (8)
T
The gate transmission versus height can be tapered to
produce other kinds of selective filters, such as gaussian,
or ideal bandpass. The latter (and any filter having an
oscillatory impulse response) would require half wave
plates to produce phase reversals with height in the gate.
We have not studied the merits, if any, of different
equivalent filter shapes.
If B is the highest recorded frequency, then with a
rectangular gate, there will be a maximum of N = BT
cycles in the gate. We shall call N the time-bandwidth
product. From equation (8) we see that the total
number of resolved frequency intervals is
B
= BT
zxf
--- N (9)
'At present, time-bandwidth products of 106 have been
achieved and 107 is believed to be possiblefl
A single spectrum analyzer having N = 107 could
resolve a 100 MHz band into 107 channels each 10 Hz
wide (provided the recording process could handle a 100
MHz band). Since we will probably want higher resolution
than 10 Hz we will need several analyzers for each
IF signal. Using bandpass filters and mixers we can
divide each 100 MHz IF band into m basebands each
lO0[m MHz wide. Thus, if we wish 1 Hz channels we
choose m = 10 and use 10 analyzers each fed with a 10
MHz signal. For 0.I Hz channels we choose m = 100 and
use 100 analyzers.
Recording
Materials
Any material whose optical transmission over its
surface can be varied in magnitude or phase could, in
principle, be used. However, just as phase or frequency
modulation of a carrier produces higher order sidebands,
so a sinusoidal phase grating diffracts light into several
orders. If more than one frequency is present, intermodulation
products are also generated. (These can be
avoided by keeping the modulation index small, but this
sacrifices dynamic range.) Since both phenomena represent
spurious spectral responses, phase materials appear
undesirable for Cyclops.
Several new recording media such as magneto-optic
films, ceramics, and photochromics are being developed.
So far as could be determined, all of these materials have
serious shortcomings such as poor resolution, low
diffraction efficiency, and low sensitivity. The major
advantages to be gained from these materials are
reusability and the elimination of chemical processing.
At present, ordinary silver halide photographic film
seems to be best suited to our purposes. However, high
resolution diazo films deserve further consideration.
They are grainless, optically smooth, require only
ammonia vapor processing, and are very inexpensive.
Since they are ultraviolet sensitive no dark room handling
is required, but a powerful UV laser is needed in
the recorder.
Film Usage
The rate of film consumption is determined by the
total bandwidth B to be analyzed and by the resolving
2Private communication from Robert V. Markevitch of the
Ampex Corporation
128