Method and apparatus for measuring surface roughness

Claim 1

A method of measuring surface roughness comprising the steps of: (a) spacing a plurality of sensors along said surface at predetermined distances apart from one another, each of said sensors generating sensor-surface distance data, said spacing sleected such that the response characteristic of said plurality of sensors is non-zero for all wavelengths of surface roughness in excess of a predetermined folding wavelength, (b) relatively moving said sensors and said surface, (c) while relatively moving said sensors, sampling data from sensors at fixed sample distance intervals L, (d) storing data from said sensors measured over a region of said surface, (e) converting said data into second finite difference data over said region, (f) converting said second finite difference data into data representative of a space curve of said surface, and (g) displaying said space curve representative data to provide an indication of surface roughness.

Claim 2

A method of measuring surface roughness comprising the steps of: (a) spacing a plurality of sensors along said surface at predetermined distances apart from one another, each of said sensors generating sensor-surface distance data, said spacing sleected such that the response characteristic of said plurality of sensors is non-zero for all wavelengths of surface roughness in excess of a predetermined folding wavelength, (b) relatively moving said sensors and said surface, (c) while relatively moving said sensors, sampling data from sensors at fixed sample distance intervals L, (d) storing data from said sensors measured over a region of said surface, (e) converting said data into second finite difference data over said region, (f) converting said second finite difference data into data representative of a space curve of said surface, and (g) displaying said space curve representative data to provide an indication of surface roughness.

Claim 3

A method of measuring surface roughness comprising the steps of: (a) securing first, second, third and fourth sensors to a rigid support, (b) relatively moving said rigid support with said secured sensors and said surface, (c) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (d) said securing step including positioning said first and second sensors apart by a distance mL, said second and third sensors by a distance nL, and said third and fourth sensors by a distance mL, where m and n are integers having no common factors, said sensors thereby positioned to form a first asymmetric cord configuration, comprising sensors one, two and three, and a second asymmetric cord configuration comprising sensors two, three and four, said first and second asymmetric cord configurations being mirror images of one another about a plane midway between sensors two and three, (e) processing said sampled data outputs in a data processing device, said processing step including (i) weighing the data outputs from said first, second and third sensors in accordance with their relative displacements as defined by the integers m, n, to form a first asymmetric cord offset (ACO) measurement, (ii) weighing the data outputs from said second, third and fourth sensors in accordance with their relative displacements as defined by the integers m, n, to form a second ACO measurement, said first and second ACO measurements insensitive to rigid body motion, (iii) combining said first and second ACO measurements to form at least one midcord offset (MCO) measurement corresponding to weighted data from first, second and third hypothetical sensors positioned one sample distance interval apart, (iv) converting said MCO measurement into second finite difference data, and (v) converting said second finite difference data into data representative of a space curve of said surface, and (f) displaying said space curve representative data for providing a measurement of surface roughness.

Claim 4

A method of measuring surface roughness comprising the steps of: (a) securing first, second, third and fourth sensors to a rigid support, (b) relatively moving said rigid support with said secured sensors and said surface, (c) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (d) said securing step including positioning said first and second sensors apart by a distance mL, said second and third sensors by a distance nL, and said third and fourth sensors by a distance mL, where m and n are integers having no common factors, said sensors thereby positioned to form a first asymmetric cord configuration, comprising sensors one, two and three, and a second asymmetric cord configuration comprising sensors two, three and four, said first and second asymmetric cord configurations being mirror images of one another about a plane midway between sensors two and three, (e) processing said sampled data outputs in a data processing device, said processing step including (i) weighing the data outputs from said first, second and third sensors in accordance with their relative displacements as defined by the integers m, n, to form a first asymmetric cord offset (ACO) measurement, (ii) weighing the data outputs from said second, third and fourth sensors in accordance with their relative displacements as defined by the integers m, n, to form a second ACO measurement, said first and second ACO measurements insensitive to rigid body motion, (iii) combining said first and second ACO measurements to form at least one midcord offset (MCO) measurement corresponding to weighted data from first, second and third hypothetical sensors positioned one sample distance interval apart, (iv) converting said MCO measurement into second finite difference data, and (v) converting said second finite difference data into data representative of a space curve of said surface, and (f) displaying said space curve representative data for providing a measurement of surface roughness.

Claim 20

A method of measuring surface roughness comprising the steps of: (a) securing at least first and second sensors to a rigid support, said sensors being of the contact-type and having at least an operative portion thereof connected for measuring the relative displacement between said support and surface at first and second sensor contact points, respectively, (b) contacting said support and said surface at first and second support contact points distinct from said sensor contact points, (c) relatively moving said support and surface thereby moving said sensors and support contact points along said surface, (d) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (e) said securing step including positioning said first sensor contact point and said first support contact point a distance mL apart, m being an integer, said second sensor contact point and said second support contact point a distance mL apart, and one of: (1) said first and second sensor contact points a distance nL apart, n being an integer and m, n selected to have no common factors, thereby forming a first asymmetric cord offset (ACO) configuration defined by said first support contact point, said first sensor contact point and said second sensor contact point; and a second ACO configuration defined by said first sensor contact point, said second sensor contact point and said second support contact point, said first and second ACO configurations being mirror images of one another about a plane midway between said first and second sensor contact points, and (2) said first and second support contact points a distance mL apart thereby forming one ACO configuration defined by said first sensor contact point, said second support contact point and said third support contact point; and another ACO configuration defined by said first support contact point, said second support contact point and said second sensor contact point, said one and another ACO configuration being mirror images of one another about a plane midway between said first and second support contact points, (f) processing said sampled data outputs in a data processing device, said processing step including: (i) weighing the data outputs from said sensors in one of: (1) said first and second ACO configurations in accordance with the relative contact point displacements defined by m, n to form a first and second ACO measurement, said ACO measurements being insensitive to rigid body motion of said support, and (2) said one and another ACO configurations in accordance with the relative contact point displacements defined by m, n to form one and another ACO measurement, said one and another ACO measurements being insensitive to rigid body motion of said support, (ii) combining one of: (1) said first and second ACO measurements to form at least a first mid-cord offset (MCO) measurement corresponding to hypothetical contact points having relative displacements defined by m=n=1 and (2) said one and another ACO measurements to form at least one MCO measurement corresponding to hypothetical contact points having relative displacements defined by m=n=1, (iii) converting one of: (1) said first MCO measurement into data representative of a space curve of said surface and (2) said one MCO measurement into data representative of a space curve of said surface, and (g) displaying said space curve representative data for providing a measure of surface roughness.

Claim 21

A method of measuring surface roughness comprising the steps of: (a) securing at least first and second sensors to a rigid support, said sensors being of the contact-type and having at least an operative portion thereof connected for measuring the relative displacement between said support and surface at first and second sensor contact points, respectively, (b) contacting said support and said surface at first and second support contact points distinct from said sensor contact points, (c) relatively moving said support and surface thereby moving said sensors and support contact points along said surface, (d) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (e) said securing step including positioning said first sensor contact point and said first support contact point a distance mL apart, m being an integer, said second sensor contact point and said second support contact point a distance mL apart, and one of: (1) said first and second sensor contact points a distance nL apart, n being an integer and m, n selected to have no common factors, thereby forming a first asymmetric cord offset (ACO) configuration defined by said first support contact point, said first sensor contact point and said second sensor contact point; and a second ACO configuration defined by said first sensor contact point, said second sensor contact point and said second support contact point, said first and second ACO configurations being mirror images of one another about a plane midway between said first and second sensor contact points, and (2) said first and second support contact points a distance mL apart thereby forming one ACO configuration defined by said first sensor contact point, said second support contact point and said third support contact point; and another ACO configuration defined by said first support contact point, said second support contact point and said second sensor contact point, said one and another ACO configuration being mirror images of one another about a plane midway between said first and second support contact points, (f) processing said sampled data outputs in a data processing device, said processing step including: (i) weighing the data outputs from said sensors in one of: (1) said first and second ACO configurations in accordance with the relative contact point displacements defined by m, n to form a first and second ACO measurement, said ACO measurements being insensitive to rigid body motion of said support, and (2) said one and another ACO configurations in accordance with the relative contact point displacements defined by m, n to form one and another ACO measurement, said one and another ACO measurements being insensitive to rigid body motion of said support, (ii) combining one of: (1) said first and second ACO measurements to form at least a first mid-cord offset (MCO) measurement corresponding to hypothetical contact points having relative displacements defined by m=n=1 and (2) said one and another ACO measurements to form at least one MCO measurement corresponding to hypothetical contact points having relative displacements defined by m=n=1, (iii) converting one of: (1) said first MCO measurement into data representative of a space curve of said surface and (2) said one MCO measurement into data representative of a space curve of said surface, and (g) displaying said space curve representative data for providing a measure of surface roughness.

Claim 25

A method of measuring surface roughness comprising the steps of: (a) securing at least first, second and third sensors to a rigid support, said sensors being of the contact-type and having at least an operative portion thereof connected for measuring the relative displacement between said support and surface at first, second and third sensor contact points, respectively, (b) contacting said support and said surface at a first support contact point distinct from said sensor contact points, (c) relatively moving said support and surface thereby moving said sensor and support contact points along said surface, (d) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (e) said securing step including positioning said first and second sensor contact points a distance mL apart, m being an integer, said third sensor contact point and said first support contact point a distance mL apart, and said second and third sensor contact points a distance nL apart, where n is an integer and m, n are selected to have no common factors, thereby forming a first asymmetric cord offset (ACO) configuration defined by said first sensor contact point, said second sensor contact point and said third sensor contact point and a second ACO configuration defined by said second sensor contact point, said third sensor contact point and said first support contact point, said first and second ACO configurations being mirror images of one another about a plane midway between said second and third contact points, (f) processing said sampled data outputs in a data processing device, said processing step including: (i) weighing the data outputs from each sensor in said first and second ACO configurations in accordance with the relative contact point displacements defined by integers m, n to form first and second ACO measurements, (ii) combining said first and second ACO measurements to form first mid-cord offset (MCO) measurements corresponding to hypothetical contact points defined by m=n=1 and (iii) converting said first MCO measurements into data representative of a space curve of said surface, and (g) displaying said space curve representative data for providing a measure of surface roughness.

Claim 26

A method of measuring surface roughness comprising the steps of: (a) securing at least first, second and third sensors to a rigid support, said sensors being of the contact-type and having at least an operative portion thereof connected for measuring the relative displacement between said support and surface at first, second and third sensor contact points, respectively, (b) contacting said support and said surface at a first support contact point distinct from said sensor contact points, (c) relatively moving said support and surface thereby moving said sensor and support contact points along said surface, (d) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (e) said securing step including positioning said first and second sensor contact points a distance mL apart, m being an integer, said third sensor contact point and said first support contact point a distance mL apart, and said second and third sensor contact points a distance nL apart, where n is an integer and m, n are selected to have no common factors, thereby forming a first asymmetric cord offset (ACO) configuration defined by said first sensor contact point, said second sensor contact point and said third sensor contact point and a second ACO configuration defined by said second sensor contact point, said third sensor contact point and said first support contact point, said first and second ACO configurations being mirror images of one another about a plane midway between said second and third contact points, (f) processing said sampled data outputs in a data processing device, said processing step including: (i) weighing the data outputs from each sensor in said first and second ACO configurations in accordance with the relative contact point displacements defined by integers m, n to form first and second ACO measurements, (ii) combining said first and second ACO measurements to form first mid-cord offset (MCO) measurements corresponding to hypothetical contact points defined by m=n=1 and (iii) converting said first MCO measurements into data representative of a space curve of said surface, and (g) displaying said space curve representative data for providing a measure of surface roughness.

Claim 29

A method of measuring surface roughness comprising the steps of: (a) securing first, second, third and fourth sensors to a rigid support, (b) relatively moving said rigid support with said secured sensors and said surface, (c) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (d) said securing step including positioning said first and second sensors apart by a distance nL, said first and third sensors apart by a distance mL and said third and fourth sensors apart by a distance nL, m, n being integers having no common factors, said first and second sensors being the mirror image of said third and fourth sensors with respect to a plane midway between said second and third sensors, (e) processing said sampled data outputs in a data processing device, said processing steps including: (i) weighing the data outputs from all of said sensors to form a first measurement which is insensitive to rigid body motion, (ii) weighing the data outputs from all of said sensors to form a second measurement which is insensitive to rigid body motion, (iii) combining said first and second measurements to form a mid-cord offset (MCO) measurement corresponding to weighted data from first, second and third hypothetical sensors positioned one sample distance interval apart, (iv) converting said MCO measurement into data representative of a space curve of said surface, and (f) outputting said space curve representative data for displaying a measurement of surface roughness.

Claim 30

A method of measuring surface roughness comprising the steps of: (a) securing first, second, third and fourth sensors to a rigid support, (b) relatively moving said rigid support with said secured sensors and said surface, (c) while relatively moving said support and surface, sampling data outputs of all of said sensors at fixed sample distance intervals L, (d) said securing step including positioning said first and second sensors apart by a distance nL, said first and third sensors apart by a distance mL and said third and fourth sensors apart by a distance nL, m, n being integers having no common factors, said first and second sensors being the mirror image of said third and fourth sensors with respect to a plane midway between said second and third sensors, (e) processing said sampled data outputs in a data processing device, said processing steps including: (i) weighing the data outputs from all of said sensors to form a first measurement which is insensitive to rigid body motion, (ii) weighing the data outputs from all of said sensors to form a second measurement which is insensitive to rigid body motion, (iii) combining said first and second measurements to form a mid-cord offset (MCO) measurement corresponding to weighted data from first, second and third hypothetical sensors positioned one sample distance interval apart, (iv) converting said MCO measurement into data representative of a space curve of said surface, and (f) outputting said space curve representative data for displaying a measurement of surface roughness.

Claim 33

A method of measuring surface roughness comprising the steps of: (a) securing a first and second sensor to a rigid support, said sensors being of the non-contact type, (b) contacting said support in said surface at first and second contact points, said contact points being removed from said position of said sensors, (c) relatively moving said support and surface thereby moving said support contact points along said surface, (d) said securing step including positioning said first contact point and said first sensor apart by a distance mL, said second contact point and said second sensor apart by a distance mL and one of (1) said first and second sensors spaced apart by a distance nL, where m, n are integers having no common factors and said distances are measured along the direction of relative motion of said surface and support, thereby forming a first asymmetric cord offset (ACO) configuration defined by said first contact point, said first sensor and said second sensor, and a second ACO configuration defined by said first sensor, said second sensor and said second contact point, said first and second ACO configurations being mirror images of one another about a plane midway between said first and second sensors, and (2) said first and second contact points spaced apart by a distance nL thereby forming one ACO configuration defined by said first sensor, said first contact point and said second contact point, and another ACO configuration defined by said first contact point, said second contact point and said second sensor, said one and another ACO configurations being mirror images of one another about a plane midway between said first and second contact points, (e) processing said sampled data outputs in a data processing device, said processing steps including: (i) weighing the data outputs from said sensors in one of (1) said first and second ACO configurations in accordance with the relative displacements of said sensors and contact points defined by m, n, to form a first and second ACO measurement, said first and second ACO measurements insensitive to rigid body motion of said support, and (2) said one and another ACO configurations in accordance with the relative displacements of said sensors and contact points defined by m, n to form one and another ACO measurement, said one and another ACO measurements insensitive to rigid body motion of said support, (ii) combining one of (1) said first and second ACO measurements to form at least a first mid-cord offset (MCO) measurement corresponding to hypothetical contact points and sensors having relative displacements defined by m=n=1 and (2) said one and another ACO measurements to form at least one MCO measurement corresponding to hypothetical contact points and sensors having relative displacements defined by m=n=1, and (iii) converting one of (1) said first MCO measurement into data representative of a space curve of said surface and (2) said at least one MCO measurement into data representative of a space curve of said surface, and (f) outputting said space curve representative data for displaying a measurement of surface roughness.

Claim 34

A method of measuring surface roughness comprising the steps of: (a) securing a first and second sensor to a rigid support, said sensors being of the non-contact type, (b) contacting said support in said surface at first and second contact points, said contact points being removed from said position of said sensors, (c) relatively moving said support and surface thereby moving said support contact points along said surface, (d) said securing step including positioning said first contact point and said first sensor apart by a distance mL, said second contact point and said second sensor apart by a distance mL and one of (1) said first and second sensors spaced apart by a distance nL, where m, n are integers having no common factors and said distances are measured along the direction of relative motion of said surface and support, thereby forming a first asymmetric cord offset (ACO) configuration defined by said first contact point, said first sensor and said second sensor, and a second ACO configuration defined by said first sensor, said second sensor and said second contact point, said first and second ACO configurations being mirror images of one another about a plane midway between said first and second sensors, and (2) said first and second contact points spaced apart by a distance nL thereby forming one ACO configuration defined by said first sensor, said first contact point and said second contact point, and another ACO configuration defined by said first contact point, said second contact point and said second sensor, said one and another ACO configurations being mirror images of one another about a plane midway between said first and second contact points, (e) processing said sampled data outputs in a data processing device, said processing steps including: (i) weighing the data outputs from said sensors in one of (1) said first and second ACO configurations in accordance with the relative displacements of said sensors and contact points defined by m, n, to form a first and second ACO measurement, said first and second ACO measurements insensitive to rigid body motion of said support, and (2) said one and another ACO configurations in accordance with the relative displacements of said sensors and contact points defined by m, n to form one and another ACO measurement, said one and another ACO measurements insensitive to rigid body motion of said support, (ii) combining one of (1) said first and second ACO measurements to form at least a first mid-cord offset (MCO) measurement corresponding to hypothetical contact points and sensors having relative displacements defined by m=n=1 and (2) said one and another ACO measurements to form at least one MCO measurement corresponding to hypothetical contact points and sensors having relative displacements defined by m=n=1, and (iii) converting one of (1) said first MCO measurement into data representative of a space curve of said surface and (2) said at least one MCO measurement into data representative of a space curve of said surface, and (f) outputting said space curve representative data for displaying a measurement of surface roughness.