A System to Digitize Bathythermograph Aperture Cards

Abstract

This paper describes a system which allows the automatic transformation of bathythermograph (BT) data to their digital equivalent. The BT data now stored on aperture cards, a technique described by Sauer (J. Fish. Res. Bd. Canada, 21(3), 1964), form the input to digitization equipment especially modified for this application. A description of the system and required equipment is followed by the mathematical approach employed in the Cartesian to BT grid coordinate transformation. It comprises a type of double inverse interpolation in the coordinates of the major grid intersections. Firstly, a point P on the BT trace is localized in or near a group of four "cells" in the grid. Secondly, the grid data belonging to this four-cell block are used in an iterative process based on two separate Lagrangian interpolations. The latter, both 3-point formulae, appear more than adequate in coping with BT grid distortions. This, in turn, leads to a two-dimensional fit up to fourth order terms. Any subsequent needs for translation, rotation, and linear amplification or reduction of the BT trace relative to its grid may be dealt with by means of a linear transformation.