US4848907A
Expired / Lapsed
US
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Method of and apparatus for analyzing interference fringes
Assignee: Topcon Corp
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Filing: 1987-08-31
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Granted: 1989-07-18
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Expires: 2007-08-31
Abstract
Abstract A method of analyzing interference fringes for use in a holographic interferometry process for measuring, by using a computer generated hologram, the shape of an object to be examined. The method comprises: a first step of obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes; a second step of obtaining a coefficient A k relative to the wave surface (xl, yl, zl) of the surface, from a coefficient a ij of a series of the object wave which has been obtained based on the hypothesized coordinates on a computer hologram at the time when the computer generated hologram is made, and from a coefficient b ij of a series of the object based on the hypothesized coordinates on the object, the coefficient A k minimizing the square sum or the maximum value of a function of Xl, Yl, Zl, and a third step of obtaining a shape error from the ideal shape of the object by calculating the function on the basis of the A k .
Inventors
- 👤 Takashi Yokokura
- 👤 Takashi Gemma
- 👤 Satoh Takuji
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-27 06:10
CPC Classifications
G; G01; G01B; G01B9/00; G01B9/02; G01B9/021; G01B11/00; G01B11/24; G03; G03H; G03H1/00; G03H1/04; G03H1/08
Claims Analysis
Total Claims: 8
Claim 1
Independent Claim
210 words
A method of analyzing interference fringes for use in a holographic interferometry process for measuring, by using a computer generated hologram, the shape of an object to be examined, said method comprising: a first step of obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; a second step of obtaining a coefficient A k relative to said wave surface (xl, yl, zl) of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU24## which has been obtained based on the hypothesized coordinates on a computer generated hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU25## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU26## a third step of obtaining a shape error from the ideal shape of said object by calculating said Formula ○3 on the basis of said A k determined in said second step.
Claim 2
Independent Claim
210 words
A method of analyzing interference fringes for use in a holographic interferometry process for measuring, by using a computer generated hologram, the shape of an object to be examined, said method comprising: a first step of obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; a second step of obtaining a coefficient A k relative to said wave surface (xl, yl, zl) of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU24## which has been obtained based on the hypothesized coordinates on a computer generated hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU25## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU26## a third step of obtaining a shape error from the ideal shape of said object by calculating said Formula ○3 on the basis of said A k determined in said second step.
Claim 3
Independent Claim
215 words
A method of analyzing interference fringes for use in a holographic interferometry process for measuring, by using a computer generated hologram, the shape of an object to be examined, said method comprising: a first step of obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; a second step of obtaining a coefficient A k relative to said wave surface (xl, yl, zl) of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU27## which has been obtained based on the hypothesized coordinates on a computer generated hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU28## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU29## a third step of calculating, on the basis of said A k determined in said second, a deviation from said computer generated hologram or from the position in which said object to be examined is normally disposed.
Claim 4
Independent Claim
215 words
A method of analyzing interference fringes for use in a holographic interferometry process for measuring, by using a computer generated hologram, the shape of an object to be examined, said method comprising: a first step of obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; a second step of obtaining a coefficient A k relative to said wave surface (xl, yl, zl) of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU27## which has been obtained based on the hypothesized coordinates on a computer generated hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU28## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU29## a third step of calculating, on the basis of said A k determined in said second, a deviation from said computer generated hologram or from the position in which said object to be examined is normally disposed.
Claim 5
Independent Claim
211 words
An apparatus for analyzing interference fringes for use in a holographic interferometer for measuring, by using a computer generated hologram, the shape of an object to be examined, said apparatus comprising: wave surface calculating means for obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; coefficient calculating means for obtaining a coefficient A k relative to said wave surface (xl, yl, zl) of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU30## which has been obtained based on the hypothesized coordinates on a computer hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU31## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU32## shape error calculating means for obtaining a shape error from the ideal shape of said object by calculating said Formula ○3 on the basis of said A k obtained by said coefficient calculating means.
Claim 6
Independent Claim
211 words
An apparatus for analyzing interference fringes for use in a holographic interferometer for measuring, by using a computer generated hologram, the shape of an object to be examined, said apparatus comprising: wave surface calculating means for obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; coefficient calculating means for obtaining a coefficient A k relative to said wave surface (xl, yl, zl) of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU30## which has been obtained based on the hypothesized coordinates on a computer hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU31## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU32## shape error calculating means for obtaining a shape error from the ideal shape of said object by calculating said Formula ○3 on the basis of said A k obtained by said coefficient calculating means.
Claim 7
Independent Claim
218 words
An apparatus for analyzing interference fringes for use in a holographic interferometer for measuring, by using a computer generated hologram, the shape of an object to be examined, said apparatus comprising: wave surface calculating means for obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; coefficient calculating means for obtaining a coefficient A k relative to said wave surface of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU33## which has been obtained based on the hypothesized coordinates on a computer hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU34## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU35## deviation calculating means for obtaining a deviation from said computer generated hologram or from the position in which said object to be examined is normally disposed, by calculating said Formula ○3 on the basis of said A k obtained by said coefficient calculating means.
Claim 8
Independent Claim
218 words
An apparatus for analyzing interference fringes for use in a holographic interferometer for measuring, by using a computer generated hologram, the shape of an object to be examined, said apparatus comprising: wave surface calculating means for obtaining a wave surface (xl, yl, zl) of a surface to be measured from measurement interference fringes, on the basis of an interference fringe analyzing method or phase scanning method; coefficient calculating means for obtaining a coefficient A k relative to said wave surface of said surface to be measured, on the basis of the method of least squares or Min-Max method, from a coefficient a ij of a series of the object wave ##EQU33## which has been obtained based on the hypothesized coordinates on a computer hologram at the time when said computer generated hologram is made, and from a coefficient b ij of a series of the object wave ##EQU34## based on the hypothesized coordinates on said object to be examined, said a coefficient A k minimizing the square sum or the maximum value of ##EQU35## deviation calculating means for obtaining a deviation from said computer generated hologram or from the position in which said object to be examined is normally disposed, by calculating said Formula ○3 on the basis of said A k obtained by said coefficient calculating means.
References Cited (Backward Citations)
US3642374A
Cited
US4396289A
Cited
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| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
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| 3.5 Years (Year 4) | 1992-07-17 | 1993-01-16 | 1993-07-18 | $2000.00 | Window Closed / Lapsed |
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