1. An apparatus for estimating the thickness of a substrate, said apparatus comprising: a chuck assembly holding the substrate; a probe assembly mounted relative to the chuck assembly, said probe assembly measuring the thickness of a region of the substrate that is aligned with the probe assembly; a motorized assembly moving either the substrate relative to the probe assembly or the probe assembly relative to the substrate and thereby enabling the probe assembly to examine a two-dimensional area of the substrate; measurement circuitry generating an image of the two-dimensional area of the substrate that is examined by the probe assembly, said image comprising a two-dimensional array of measurements, each measurement of said two-dimensional array of measurements representing a substrate thickness measurement by said probe assembly of a different region of said two-dimensional area, said two-dimensional array of measurements being represented by a measured column tensor; a memory for storing the measured column tensor; and a computer programmed to left multiply the measured column tensor stored in said memory by a reconstruction tensor T to obtain an estimate of a desired measurement column tensor, where said reconstruction tensor T is equal to R.sub.dm R.sub.mm.sup.-1, R.sub.dm being a cross-covariance tensor computed for d, a desired measurement column tensor, and m, the measured column tensor, and being an auto-covariance tensor computed for m, the measured column tensor, and wherein the estimate of a desired measurement column tensor represents an estimate of substrate thickness measurements that would be obtained from a hypothetical probe assembly having a different resolution from said first mentioned probe assembly.