An evaluation of optical aberrations in underwater hologrammetry
An iterative ray-trace procedure is developed in conjunction with semi-analytic expressions for spherical aberration, coma, and astigmatism in the reconstructed holographic images of underwater objects. An exact expression for the astigmatic difference is obtained, based on the geometry of the caustic for refraction. The geometrical characteristics of the aberrated images associated with axial and non-axial field positions are represented by ray intersection diagrams. A third order expression for the wavefront aberration introduced at a planar air/water boundary is given. The associated third order aberration coefficients are used to obtain analytic expressions for the aberrations observed in underwater hologrammetry. The results of the third order treatment are shown to give good agreement with the results obtained by geometrical ray tracing and by direct measurement on the reconstructed real image. The third order aberration coefficients are employed to estimate the limit of resolution in the presence of the aberrations associated with reconstruction in air. In concurrence with practical observations it is found that the estimated resolution is primarily limited by astigmatism. The limitations of the planar window in underwater imaging applications are outlined and various schemes are considered to effect a reduction in the extent of aberration. The analogous problems encountered in underwater photography are examined in order to establish the grounds for common solution based on a conventional optical corrector. The performance of one such system, the Ivanoff Corrector, is investigated. The spherical aberration associated with axial image formation is evaluated and the image location as a function of aperture determined from ray intersection diagrams. The equivalence of the third order wavefront aberration introduced at a planar air/water boundary to that introduced upon reconstruction by an appropriate wavelength change is shown to provide a basis for the compensation of aberrations in underwater hologrammetry. The results of experimental trials which demonstrate the correction of astigmatism and field curvature are presented. Exact expressions are obtained for the aberrations in wavelength compensated holograms and are employed to determine the conditions for optimum compensation and the degree of residual aberration. Various aspects of the principle are examined, including the effects of the reference beam geometry and factors which determine the level of correction obtained. The practical implementation of a scheme based on wavelength compensation is considered with a view to the design of an underwater holographic camera.