The CSAR (coherent synthetic aperture radar) did not use very high frequencies and short wavelengths like 3 GHz (0.1 m) or 30 GHz (0.01 m) allowing small narrow beam directional antennas.
Very low frequencies of 5 , 15 and 150 MHz and 60 , 20 and 2 m wavelength were used. These low frequencies were selected to image not only the lunar surface but also the soil below down to a maximum depth of exploration of approximately 1 km.
It was not possible to use an antenna of several wavelengths size. So I guess a "synthetic aperture" was used for beam forming using two small antennas much shorter than wavelength.
The two occurencies of the word synthetic within the Apollo Program Summary Report do not explain SAR.
But in the link found by uhoh there is the missing information about optical SAR processing:
The ERIM Precision Optical Processor Facility and the techniques used
to process the sounder data have been developed over the past two
decades for use with synthetic-aperture radar (SAR) data. These
techniques have been extensively reported in the literature [Refs.
The coherent optical processor is an analog computer which performs
linear integral trans-form operations on the data as required when
processing SAR data. The sounder, as for any other SAR, requires that
two independent operations be carried out with the data, one to
com-press the coded (or chirp) range pulses and the other to compress
the along-track synthetic aperture data records. These two independent
operations reduce to a single two-dimensional operation in the
orthogonal coordinate system of a coherent optical processor.
So the SAR processing was not done digital, it was done optical and analog using the record on film.
SOUNDER OPTICAL PROCESSOR
A simplified diagram of a typical SAR optical processor is presented
in Figure 2. The input data film is positioned in plane P 1 and
illuminated by a coherent light beam derived from a laser source. The
data film is immersed in a "liquid gate" to minimize the effects of
random film-thickness variations on the coherent light beam. The data,
recorded on film in variable density format, modulates the light-beam
intensity so that an astigmatic radar image of the lunar surface is
formed; azimuth focus occurs at some plane P A' ignoring tilted plane
effects, while range focus occurs at some plane PR. The pair of
spherical lenses (S1, s2) operates as a unity-magnification telescope
in the range dimension and transfers the range image plane to the
output plane P0. The spherical, cylindrical lens pairs (S1, c1; s2,
c2) operate as separate demagnifying telescopes in the azimuth
dimension and demagnify the azimuth focus image as well as
transferring it from P A' also, to P 0. Output film can then be used
to record the image at plane P0.
The spherical lens (S1) produces a display of the two-dimensional
Fourier transform of the input data in its rear focal plane P 1.
Various frequency-filtering functions can be carried out in this
spatial plane. Simple limiting apertures placed here act as sharp
cutoff bandpass filters. Such apertures are used to eliminate both
noise outside the data band and the conjugate data image which forms
an out-of-focus background in the image plane; the apertures are also
used to restrict the processed azimuth or Doppler bandwidth. Weighting
filters may be placed in this frequency plane to reduce the range
sidelobe levels. These filters are simple intensity modulation masks.
But how could they store an analog phase information on film? If the film resolves 100 lines per mm, a film speed of 50 m/s would be needed to store a 5 MHz signal.
But the FM modulated (by a chirp signal) radar pulses had a repetiton period of 2,520 microseconds, only about 400 pulses per second. So the minimal film speed was only 4 mm per second to store the 400 pulses as distinct lines.
The linear FM property of both the signal and the Doppler signature of
point targets may be viewed as a linearly varying diffraction grating.
The phase information for optical analog SAR processing was delivered by this diffraction grating.