Methods for enhancing performance and data acquired from three-dimensional image systems

A computer-readable storage medium whereon is located a computer program that causes a computer sub-system having at least a processor unit to improve actual (x,y,z) measurements by correcting elliptical error in a system that uses energy transmitted from an emitter at a first location on a plane, said energy reflecting at least in part from a target object and being detected by independent sensors defining a sensor array on said plane but spaced-apart from said first location, the computer program upon execution carrying out the following steps:

• (a) defining a spherical coordinate for said sensors in said sensor array, and constructing a look-up table containing spherical coordinates for each of said sensors, where a spherical coordinate for sensor Pij is given by (pij,−aij,−bij);
• (b) defining a spatial coordinate of said emitter from a spherical coordinate system defined in step (a) such that said spatial coordinate of said emitter has a same origin as said spherical coordinate system, where said spatial coordinate of said emitter is (Cx, Cy, Cz) and defining a constant k as square of distance between said emitter and said origin of said spherical coordinate system;
• (c) For each sensor Pij, constructing a look-up table of a constant hij where hij is calculated as follows:
• hij=2(pij+Cx cos(aij)sin(bij)+Cy sin(aij)sin(bij)+Cz cos(bij))
• where (pij, −aij, −bij) is the spherical coordinate of said sensor Pij defined at step (a), and where (Cx, Cy, Cz) is the spatial Cartesian coordinate of said emitter defined at step (b);
• (d) identifying sensors {circumflex over (P)}ij that actually detect energy reflected from said target object;
• (e) using measured rountrip distance dij from said emitter to sensors {circumflex over (P)}ij identified at step (d) to calculate distance rij from an imaging portion of said target object and said sensor {circumflex over (P)}ij according to rij=((dij−pij)2−k)/(2dij−h ij), using values of k determined at step (b), values of hij determined in step (c), and {circumflex over (p)}ij determined in step (a);
• and
• (f) calculating actual Cartesian coordinate (Ax,Ay,Az) of imaging portion of said target objection according to Ax=rij cos(âij)sin({circumflex over (b)}ij), Ax=rij sin(âij)sin({circumflex over (b)}ij), and Ax=rij cos({circumflex over (b)}ij), where rij is obtained in step (e) and âij, {circumflex over (b)}ij of sensor {circumflex over (P)}ij are obtained in step (a).