Measuring surface flatness using shadow moire technology and phase-stepping image processing

A method for quantifying the flatness of a surface using at least a first digitized image of a first shadow moire fringe pattern that is indicative of the flatness of the surface, a second digitized image that includes at least a second shadow moire fringe pattern that is indicative of the flatness of the surface, and a third digitized image that includes at least a third shadow moire fringe pattern that is indicative of the flatness of the surface, wherein a phase shift has been introduced between each of the first, second, and third fringe patterns, comprising:

• calculating a first two-dimensional array of phase values from at least the first, second and third digitized images;
• calculating a plurality of two-dimensional arrays of image values from the first two-dimensional array of phase values;
• applying a filter to at least one of the two-dimensional arrays of image values to create a two-dimensional array of filtered image values;
• and
• calculating a second two-dimensional array of phase values from at least the two-dimensional array of filtered image values.

A method for quantifying the flatness of a surface, comprising the steps of:

• creating a first shadow moire fringe pattern that is indicative of the flatness of the surface;
• capturing a first digitized image that includes at least the first shadow moire fringe pattern;
• creating a second shadow moire fringe pattern that is indicative of the flatness of the surface, comprising introducing a phase shift between the first and second shadow moire fringe patterns;
• capturing a second digitized image that includes at least the second shadow moire fringe pattern;
• creating a third shadow moire fringe pattern that is indicative of the flatness of the surface, comprising introducing a phase shift between the first, second, and third shadow moire fringe patterns;
• capturing a third digitized image that includes at least the third shadow moire fringe pattern;
• creating a fourth shadow moire fringe pattern that is indicative of the flatness of the surface, comprising introducing a phase shift between the first, second, third and fourth shadow moire fringe patterns;
• capturing a fourth digitized image that includes at least the fourth shadow moire fringe pattern;
• calculating a two-dimensional array of phase values from at least the first, second, third and fourth digitized images, wherein the phase values are equal to arctan((I.sub.2 -I.sub.4)/(I.sub.1 -I.sub.3)), wherein "I.sub.1 " is the light intensity of a pixel in the first shadow moire fringe pattern, "I.sub.2 " is the light intensity of the pixel in the second shadow moire fringe pattern, "I.sub.3 " is the light intensity of the pixel in the third shadow moire fringe pattern, and "I.sub.4 " is the light intensity of the pixel in the fourth shadow moire fringe pattern.

A system for quantifying the flatness of a surface, comprising means for:

• creating a first shadow moire fringe pattern that is indicative of the flatness of the surface;
• capturing a first digitized image that includes at least the first shadow moire fringe pattern;
• creating a second shadow moire fringe pattern that is indicative of the flatness of the surface, comprising introducing a phase shift between the first and second shadow moire fringe patterns;
• capturing a second digitized image that includes at least the second shadow moire fringe pattern;
• creating a third shadow moire fringe pattern that is indicative of the flatness of the surface, comprising introducing a phase shift between the first, second, and third shadow moire fringe patterns;
• capturing a third digitized image that includes at least the third shadow moire fringe pattern;
• calculating a two-dimensional array of phase values from at least the first, second and third digitized images;
• eliminating at least some of the discontinuities between adjacent phase values in the two-dimensional array, comprising:
• searching for discontinuities between adjacent phase values in a plurality of one-dimensional arrays of the two-dimensional array, wherein for each of the one-dimensional arrays the searching progresses along the length of the one-dimensional array and comprises searching for discontinuities of a predetermined value between adjacent phase values in the one-dimensional array, and
• adjusting a phase value in response to determining that a discontinuity of the predetermined value exists between the phase value and an adjacent phase value in the same one-dimensional array, wherein the plurality of one-dimensional arrays comprises a row of the two-dimensional array and a column of the two-dimensional array;
• and
• calculating displacements from at least some of the phase values.

A system for quantifying the flatness of a surface, comprising means for:

• introducing a phase shift between and digitizing at least a first shadow moire fringe pattern that is indicative of the flatness of the surface, a second digitized image that includes at least a second shadow moire fringe pattern that is indicative of the flatness of the surface, and a third digitized image that includes at least a third shadow moire fringe pattern that is indicative of the flatness of the surface;
• calculating a first two-dimensional array of phase values from at least the first, second and third digitized images;
• calculating a plurality of two-dimensional arrays of image values from the first two-dimensional array of phase values;
• applying a filter to at least one of the two-dimensional arrays of image values to create a two-dimensional array of filtered image values;
• and
• calculating a second two-dimensional array of phase values from at least the two-dimensional array of filtered image values.