Surface extraction from a three-dimensional data set

Abstract

Surface image data representing a three-dimensional surface is extracted from a three-dimensional set of data representing characteristics of a volume in space (volumetric data) that encompasses the surface of an object, so that the surface image data can be used to display the surface. The volumetric data can comprise any data set in which comparisons between data can be used to ascertain points on a surface. In one embodiment of the invention, each of the pieces of volumetric data represents the intensity of light reflected in a particular direction from a point in space on or near the surface of an object. For example, the light intensity data can represent the intensity of laser light reflected back through an optical path of a laser imaging system after the laser light has been directed toward the surface of an object such as a semiconductor wafer. The surface image data can be used to generate a three-dimensional display of the surface, or portions of the surface image data can be used to generate surface profiles or contours. Additionally, the surface image data can be used to generate a surface light intensity map.

I claim: 
     
       1. A method for constructing an image of a surface from a volumetric set of signals representing data value numbers, the volumetric set described by a Cartesian coordinate system having X, Y, and Z axes such that each number has a unique location, the volumetric set comprising at least one linear set of signals representing data value numbers arranged parallel to the Z axis, the method comprising the steps of: generating, for each linear set of signals, a first signal representing a maximum data value number and a second signal representing a location of the maximum data value number, thereby producing a set of signals representing maximum data value numbers and a set of signals representing maximum-number locations, the step of generating comprising the steps of:   comparing a third signal in the linear set to a fourth signal in the linear set to determine which of the third and fourth signals represents a greater data value number;   storing the one of said third and fourth signals representing the greater data value number as said first signal representing a maximum number for the linear set and storing the location associated with the one of said third and fourth signals representing the greater data value number as said second signal representing a maximum-number location for the linear set; and   for each signal in the linear set other than the third and fourth signals, comparing the signal to the first signal to     determine which of the signal and the first   signal represents a greater data value number; storing the one of said signal and said     first signal as the new first signal and storing   the signal representing the one of said signal   and said first signal as said second signal; and   creating the image using the set of signals representing maximum data value numbers and the set of signals representing maximum-number locations.   
     
     
       2. A method as in claim 1, wherein the image is a three-dimensional display of the surface. 
     
     
       3. A method as in claim 1, wherein each of the numbers represents the intensity of light reflected in a particular direction from a point on or near the surface. 
     
     
       4. A method as in claim 3, wherein the reflected light is sensed by a confocal laser imaging system. 
     
     
       5. A method as in claim 3, wherein the surface is the surface of a semiconductor wafer. 
     
     
       6. A method as in claim 1, further comprising, for each linear set, the step of performing a least squares curve fit to obtain a modified maximum data value number for the linear set. 
     
     
       7. A method as in claim 6, wherein each least squares curve fit to obtain a modified maximum data value number is performed using (i) the signal representing the maximum number of the linear set, (ii) a first plurality of actual or dummy numbers adjacent to the location of the signal representing the maximum number and in the linear set, and (iii) a second plurality of actual or dummy numbers adjacent to the location of the maximum data value number and in the linear set. 
     
     
       8. A method as in claim 1, further comprising the step of filtering each of the maximum data value numbers to reduce the effect of noise on the image. 
     
     
       9. A method as in claim 8, wherein the step of filtering further comprises performing a two-dimensional convolution with a 3 by 3 operator.