Error analysis in scanned holography

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.