### Abstract:

Acoustic scanned holography is a method of lensless photography
which uses sound waves to construct the hologram and light waves to
reconstruct the image. The receiving transducer scans a plane area
containing the sound field generated or scattered from the objects. In
simultaneous source receiver scanning, both the source and receiver are
scanned together. A cathode ray tube is used to construct the hologram
and the receiver's position and velocity components are simulated
electronically to control the beam position. The simulated position
and velocity signals contain errors that adversely affect the quality
of the images. This thesis presents an analysis of scanning errors in
holography when both the receiver and source are scanned. These errors
affect the hologram resolution, magnification and image position. The
analysis assumes the simulated velocity and position errors are random
and normally distributed. The hologram resolution, magnification and
image position are derived and the functions linearized to obtain the
approximate variances and expected values. The law of propagation
of errors is assumed valid in the analysis. Its proof is based on the assumption that the errors are small with respect to the measured
values of the variables. The maximum deviation from the expected value
is assumed never to exceed 10%.
The approximate variance, standard deviation and expected value
are derived for the hologram resolution using both stationary and
moving source illumination. The most exciting results were obtained
by simultaneously scanning the source and receiver. The expected
value of the hologram resolution is increased by a factor of two
compared with the stationary source value. The variance is decreased
by a factor of four with respect to the variance of the stationary
source resolution. Thus, in addition to the increase in resolution
there is a decrease in the standard deviation in the hologram
resolution as a result of simultaneously scanning the source and
receiver.
The expected value of the simultaneous source receiver scanned
radial magnification was decreased by a factor of two compared with
the stationary source value and the expected value of the lateral
magnification remained the same. These results were unique in that
scanning both the source and receiver together makes the object appear
closer to the hologram plane. In other words, using the identical
stationary source reconstruction geometry the image appears magnified
in the lateral direction.
The expected value of the image position in the reconstruction for
simultaneous source receiver scanning is equal to approximately one-half
the stationary source value. If a plane wave reconstruction source is used, the expected value of the simultaneous source receiver
scanned image position is exactly half the stationary source value.
The variance of the image position is less in the simultaneous source
receiver scanned hologram than in the stationary source case.
A number of experiments were successfully performed to verify the
theory. The experimental results of the expected values of hologram
resolution, magnification and image position agreed with our
predictions.