# US 9,752,865 B1 · Height measurement using optical interference > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,752,865 B1 - Document ID: US9752865B1 - Status: Granted - Kind: B1 - Application number: 15/093,198 - Filed: 2016-04-07 - Granted: 2017-09-05 - Earliest claimed: 2016-04-07 - Assignees: International Business Machines Corporation - Applicants: International Business Machines Corporation - Inventors: Richard A. Haight; James B. Hannon; Rudolf M. Tromp - Web page: https://patentgrep.com/patent/US9752865B1 ## CPC - G01B 9/02: Interferometers - G01B 11/026: {by measuring distance between sensor and object (G01B11/0608 takes precedence)} - G01B 11/0608: {Height gauges} - G01B 11/14: for measuring distance or clearance between spaced objects or spaced apertures (G01B11/26 takes precedence; rangefinders G01C3/00) - G03F 7/70775: {Position control, e.g. interferometers or encoders for determining the stage position} - G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS - G03F: PHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR; (phototypographic composing devices B41B; photosensitive materials or processes for photographic purposes G03C; electrophotography, sensitive layers or processes therefor G03G) ## Abstract Methods and systems for measuring a distance include measuring a first interference pattern between a lens and a target surface using a light source at a first wavelength. A second interference pattern is measured between the lens and the target surface using a light source at a second wavelength, different from the first wavelength. An absolute measurement of a distance between the lens and the target surface is determined based on the first interference pattern and the second interference pattern. ## Claims ### Claim 1 A method for measuring a distance, comprising: measuring a first interference pattern between a lens and a target surface using a light source at a first wavelength; measuring a second interference pattern between the lens and the target surface using a light source at a second wavelength, different from the first wavelength; and determining an absolute measurement of a distance between the lens and the target surface using a processor based on the first interference pattern and the second interference pattern by measuring a radius of a smallest ring in the first interference pattern and a radius of a smallest ring in the second interference pattern and solving: λ 1 2 ⁢ n 0 ⁢ ( N + 1 2 - r 1 ) = λ 2 2 ⁢ n 0 ⁢ ( M + 1 2 - r 2 ) where λ1 is the first wavelength, λ2 is the second wavelength, n0 is the index of refraction of a medium between the lens and the target surface, r1 is a ratio between the radius of the smallest ring in the first interference pattern and the squared spacing between rings in the first interference pattern, r2 is a ratio between the radius of the smallest ring in the second interference pattern and the squared spacing between rings in the second interference pattern, and N and M are integers to be determined. ### Claim 2 (depends on 1) The method of claim 1, wherein the first and second wavelength are not integer multiples of one another. ### Claim 3 (depends on 1) The method of claim 1, wherein the lens is a spherical lens and the first and second interference patterns are in the form of Newton's rings. ### Claim 4 (depends on 1) The method of claim 1, further comprising positioning the lens within a maximum measurement distance from the target surface. ### Claim 5 (depends on 1) The method of claim 1, wherein the light source at the first wavelength and the light source at the second wavelength are both lasers. ### Claim 6 (depends on 1) The method of claim 1, wherein the distance is limited to be within a maximum measurement distance such that N and M are determined uniquely. ### Claim 7 (depends on 1) A non-transitory computer readable storage medium comprising a computer readable program for distance measurement, wherein the computer readable program when executed on a computer causes the computer to perform the steps of claim 1. ### Claim 8 A system for measuring a distance, comprising: a lens positioned a distance above a target surface; a camera configured to measure a first interference pattern between the lens and the target surface using a light source at a first wavelength and to measure a second interference pattern between the lens and the target surface using a light source at a second wavelength; a processor configured to determine an absolute measurement of the distance between the lens and the target surface based on the first interference pattern and the second interference pattern to measure a radius of a smallest ring in the first interference pattern and a radius of a smallest ring in the second interference pattern, and to solve: λ 1 2 ⁢ n 0 ⁢ ( N + 1 2 - r 1 ) = λ 2 2 ⁢ n 0 ⁢ ( M + 1 2 - r 2 ) where λ1 is the first wavelength, λ2 is the second wavelength, n0 is the index of refraction of a medium between the lens and the target surface, r1 is a ratio between the radius of the smallest ring in the first interference pattern and the squared spacing between rings in the first interference pattern, r2 is a ratio between the radius of the smallest ring in the second interference pattern and the squared spacing between rings in the second interference pattern, and N and M are integers to be determined. ### Claim 9 (depends on 8) The system of claim 8, wherein the first and second wavelength are not integer multiples of one another. ### Claim 10 (depends on 8) The system of claim 8, wherein the lens is a spherical lens and the first and second interference patterns are in the form of Newton's rings. ### Claim 11 (depends on 8) The system of claim 8, wherein the lens is positioned within a maximum measurement distance from the target surface. ### Claim 12 (depends on 8) The system of claim 8, wherein light source at the first wavelength and the light source at the second wavelength are both lasers. ### Claim 13 (depends on 8) The system of claim 8, wherein the distance between the lens and the target surface is limited to be within a maximum measurement distance such that N and M are determined uniquely. ### Claim 14 (depends on 8) The system of claim 8, further comprising a transmission medium between the lens and the target surface that is formed from one of air, water, and vacuum. ### Claim 15 (depends on 8) The system of claim 8, further comprising an optical system configured such that a beam of light from the first light source overlaps in space with a beam of light from the second light source and emerges from the lens at a same point as the beam of light from the second light source such that each beam of light measures a same distance between the lens and the target surface. ### Claim 16 A system for measuring a distance, comprising: a lens positioned a distance above a target surface; a camera configured to measure a first interference pattern between the lens and the target surface using a light source at a first wavelength and to measure a second interference pattern between the lens and the target surface using a light source at a second wavelength; a processor configured to determine an absolute measurement of the distance between the lens and the target surface based on the first interference pattern and the second interference pattern; and an optical system configured such that a beam of light from the first light source overlaps in space with a beam of light from the second light source and emerges from the lens at a same point as the beam of light from the second light source such that each beam of light measures a same distance between the lens and the target surface.