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

power of the film and associated optical system. If the
overall resolving power is k line pairs per centimeter,
then the rate of film usage is
B
R = .--77 cm2/sec
k"
(10)
which is simply the film area per second needed to
record B Hz and is independent of the frequency
resolution desired. If we use m analyzers to increase the
frequency resolution by a factor m the film runs l/m
times as fast through each analyzer.
Taking B = 200 MHz (to account for both polarizations)
and k = 3000/cm (which seems to be possible
with modern lenses and slow film), we find R_22
cm2/sec. The usable width of 35-mm film is about
24-mm so the consumption rate would be about 9
cm/sec. At 4.5 cents/ft this amounts to 1.3 cents/sec or
$47/hr.
While this is not at all an unreasonable cost, the
economics of reusing the film stock should be investigated.
In any event the silver should be totally
reclaimed to conserve our resources of this truly
precious
metal.
Doppler Rate Compensation
The minimum channel width that can be used in the
analyzer is fixed by the frequency drift rate v of the
received signal and is given by Afmin _ X/_. If the local
oscillators used to beat the IF signals down to the
baseband signals for the spectrum analyzers have a drift
rate that matches that of the received signal, the
difference frequency will be drift free. Since we do not
know the Doppler drift rate, we must anticipate a range
of drift rates by providing banks of oscillators having
drift rates separated by 2Af over the interval 2kma x.
Each bank of mixers would feed a corresponding bank
of spectrum analyzers. In this way the Doppler rate
could be reduced (in one of the banks) by the ratio
r2 = _max/A,f. This reduces the channel width by r, and
requires r times as many analyzers per bank. Since there
are r2 banks a grand total of r 3 times as many analyzers
is needed. Thus, the equipment cost mounts at a staggering
rate.
The film usage per bank is unchanged but with r2
banks the total usage increases by this factor. To try to
reduce the channel to one tenth its initial value by this
method would require 1000 times as many analyzers
(20,000 in all) and would require a film usage of
$4700/hour.
Because of the complexity and cost of achieving a
significant bandwidth reduction through Doppler rate
compensation, this approach is not recommended for
Cyclops.
System
Cost
Assuming no Doppler rate compensation, the number
N a, of optical recorder-spectrum analyzer combinations
required to handle two IF signals each B Hertz wide is
Na
2B
-
NAf
01)
where N is the time-bandwidth product of each recorder
analyzer and Af is the channel width, or frequency
resolution. Taking B = 100 MHz, we obtain the cost data
given in Table 11-1
Ai
TABLE 1I-1
N = 10 6 N = 107
Na $ Million Na $ Million
10 Hz 20 2 2 0.24
1 Hz 200 20 20 2.4
O. 1 Hz 2000 200 200 24
The above cost figures are based on an estimated unit
cost of $200 K for an N = l0 6 system and $240,000 for
an N = ! 07 system.
Although the equipment cost is appreciable it is only
1/250 to 1/2000 as much as would be needed to do the
job with hard-wired Cooley-Tukey transformers. Although
the equipment cost of $200 million for 2000
processors having an N = 10 6 is still small compared with
the antenna cost, as a practical matter the care and
feeding of this many machines would require a large
crew and represent a substantial operating cost. The
analysis of 100 MHz bands into 0.1 Hz channels using
N = 107 analyzers appears reasonable.
The cost of a film processor capable of processing six
films in parallel with a time delay of 5 min dry-to-dry is
about $18,000 or $3000 per spectrum analyzer. Since
this cost is less than the uncertainty in the other figures,
it has been ignored.
POWER SPECTRUM
PROCESSING
The optical spectrum analyzer described in the last
section provides a power density spectrum of the entire
received signal on a (delayed) real-time basis. We now
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