Claims
- 1. A device for measuring a characteristic of an optical element, said device comprising:
- means for forming an interference fringe pattern using a reference light beam reflected from a reference surface and a test light beam that is guided from said optical element by a light refracting element;
- means for detecting said interference fringe pattern, said detecting means outputting data corresponding to said interference fringe pattern;
- means for processing said output data, said processing means outputting information of wave front aberration representative of said interference fringe pattern as a predetermined form of a polynomial expression, wherein said polynomial expression includes mathematical terms representative of position errors of said optical element and mathematical terms representative of said characteristic of said optical elements;
- means for calculating said mathematical terms;
- means for correcting at least one of said mathematical terms representative of said characteristic of said optical element based on a predetermined calculation utilizing a value of at least one of said mathematical terms representative of said position errors; and
- means for displaying said corrected mathematical terms representative of said characteristic of said optical element.
- 2. The measuring device of claim 1, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting means corrects at least one of said mathematical terms, representative of a symmetrical condition of said surface of said optical element, based on at least one of said mathematical terms, representative of said position errors, representing a defocus of said surface.
- 3. The measuring device of claim 2, wherein said correcting means corrects said mathematical terms representative of said characteristic of said optical element by substituting said at least one of said mathematical terms representative of said position errors into a predetermined equation.
- 4. The measuring device of claim 3, wherein said light refracting element satisfies the sine condition.
- 5. The measuring device of claim 2, wherein said correcting means corrects said mathematical terms representative of said characteristic of said optical element by substituting said mathematical terms representative of said position errors into an equation that is experimentally determined during a calibration stage.
- 6. The measuring device of claim 1, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting means corrects at least one of said mathematical terms, representative of an asymmetrical condition of said surface of said optical element, based on at least one of said mathematical terms, representative of said position errors, representing a tilt of said surface.
- 7. The measuring device of claim 6, wherein said correcting means corrects said mathematical terms representative of said characteristic by substituting said mathematical terms representative of said position errors into an equation that is experimentally determined during a calibration stage.
- 8. The device for measuring a characteristic of an optical element according to claim 1, each said mathematical term representative of said position error comprising a coefficient, said correcting means yielding corrected coefficients.
- 9. A method for measuring a characteristic of an optical element, said method comprising:
- forming an interference fringe pattern using a reference light beam reflected from a reference surface and a test light beam that is guided from said optical element by a light refracting element;
- detecting said interference fringe pattern;
- outputting data corresponding to said detected interference fringe pattern;
- calculating information of wave front aberrations, corresponding to said output data, representative of said interference fringe pattern as a predetermined form of a polynomial expression, wherein said polynomial expression includes mathematical terms representative of position errors of said optical element and mathematical terms representative of said characteristic of said optical element;
- calculating said mathematical terms;
- correcting at least one of said mathematical terms representative of said characteristic of said optical element based on a predetermined calculation utilizing a value of at least one of said mathematical terms representative of said position errors; and
- displaying said corrected mathematical terms representative of said characteristic of said optical element.
- 10. The method of measuring a characteristic of an optical element according to claim 9, each mathematical term representative of said position error comprising a coefficient, the correcting step yielding corrected coefficients.
- 11. The measuring method of claim 9,
- wherein in said step of calculating said information, said wave front aberrations are given by an equation as follows: ##EQU14## where, .rho.=h/h.sub.max
- h:incident height,
- h.sub.max :maximum incident height,
- .phi.:polar coordinate angle,
- k,l,n:non-negative integers(0,1,2, . . . ), W.sub.11, W.sub.12, W.sub.20, W.sub.22, W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60 :coefficients of each aberration.
- 12. The measuring method of claim 11, wherein said correcting step corrects said fourth order coefficient W.sub.40 by substituting said coefficients of said defocus term W.sub.20 into an equation, given as: ##EQU15## where NA.sub.0 is a numerical aperture of a light converging element, and A.sub.4 is a correction coefficient of said coefficient W.sub.40.
- 13. The measuring method of claim 11, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting step corrects fourth and higher even order coefficients W.sub.40, W.sub.60 . . . which represent symmetrical aberrations of said surface based on a second order coefficient W.sub.20 which represents a defocus term.
- 14. The measuring method of claim 11, wherein said correcting step corrects a sixth order coefficient W.sub.60 by substituting said coefficient W.sub.20 into an equation, given as; ##EQU16## where NA.sub.0 is numerical aperture of a light converging element, and A.sub.6 is a correction coefficient of said sixth order coefficient W.sub.60.
- 15. A device for measuring a characteristic of an optical element, said device comprising:
- means for forming an interference fringe pattern using a reference light beam reflected from a reference surface and a test light beam that is guided from said optical element by a light refracting element;
- means for detecting said interference fringe pattern, said detecting means outputting data corresponding to said interference fringe pattern;
- means for processing information representative of said interference fringe pattern, said information defining wave front aberrations W(.rho.,.phi.) as: ##EQU17## where, .rho.=h/h.sub.max
- h:incident height,
- h.sub.max :maximum incident height,
- .phi.:polar coordinate angle,
- k,l,n:non-negative integers (0,1,2, . . .),
- W.sub.11,W.sub.12,W.sub.20,W.sub.22,W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60 : coefficients of each aberration;
- a means for calculating said coefficients W.sub.11,W.sub.12,W.sub.20, W.sub.22,W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60. . . ;
- means for correcting at least one of said coefficients W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60 . . . which are representative of said characteristic of said optical element, based on values of at least one of said coefficients W.sub.11, W.sub.12 , W.sub.20 which are representative of a position error of said optical element; and
- means for displaying said corrected coefficients corresponding to said coefficients W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60 . . . .
- 16. The measuring device of claim 15, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting means corrects one of fourth and higher order even coefficients W.sub.40, W.sub.60 . . . which represent symmetrical aberrations of said surface of said optical element based on a second order coefficient W.sub.20 which represents a defocus of said surface.
- 17. The interference fringe pattern measuring apparatus of claim 16, wherein said correcting means corrects fourth and higher order even coefficients W.sub.40, W.sub.60 . . . during a measurement stage by substituting said coefficient W.sub.20 into an equation that is determined during a calibration stage, given as:
- W.sub.n0 "=W.sub.n0'-( a.sub.n s.sup.n-2 W.sub.20 '+b.sub.n s.sup.n)
- Where,
- W.sub.n0 ":corrected cofficients of n-th order term;
- W.sub.n0 ", W.sub.20 ':coefficients in said measurement stage;
- a.sub.n,b.sub.n :coefficients of correction experientially determined by said calibration stage;
- n:even number equal to and more than 4; ##EQU18## h.sub.1 :an incident height of a light beam on said light converging element in said measurement stage;
- r.sub.1 :a radius of an interference fringe pattern measured in said measurement stage;
- h.sub.0 :an incident height of said light beam on said light converging element in said calibration stage;
- r.sub.0 :a radius of said interference fringe pattern image in said calibration stage.
- 18. The measuring device of claim 16, wherein said correcting means corrects said fourth order coefficient W.sub.40 by substituting said coefficient W.sub.20 into an equation: ##EQU19## where NA.sub.0 is a numerical aperture of said light converging element, and
- A.sub.4 is a corrected value of said coefficient W.sub.40.
- 19. The measuring device of claim 16, wherein said correcting means corrects said sixth order coefficient W.sub.60 by substituting said coefficient W.sub.20 into an equation; ##EQU20## where NA.sub.0 is numerical aperture of said light converging element, and A.sub.6 is a corrected coefficient of sixth order coefficient W.sub.60.
- 20. The measuring device of claim 15, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting means corrects third and higher order odd coefficients W.sub.31, W.sub.51 . . . and/or W.sub.32, W.sub.52 . . . , which represent asymmetrical aberrations of said surface based on said first order coefficients W.sub.11, and/or W,.sub.12 which represent a tilt of said surface.
- 21. The measuring device of claim 20, wherein said correcting means corrects said third and higher order odd coefficients W.sub.31, W.sub.51 . . . and/or W.sub.32, W.sub.52 . . . during a measurement stage by substituting said coefficients W.sub.11 and/or W.sub.12 into an equation that is determined during a calibration stage, given as:
- W.sub.nm "=W.sub.nm '-(a.sub.nm s.sup.n-1 W.sub.lm '+b.sub.nm s.sup.n)
- Where,
- W.sub.nm ":corrected coefficients of n-th order terms;
- W.sub.nm ', W.sub.lm ':coefficients in said measurement stage;
- a.sub.nm, b.sub.nm :coefficients of correction experientially determined by said calibration stage;
- .sup.n :odd number greater than or equal to 3; ##EQU21## h.sub.1 :a height of a light beam incident on a light converging element in said measurement stage;
- r.sub.1 :a radius of an interference fringe pattern in said measurement stage;
- h.sub.0 :a height to said light beam incident on said light converging element in said calibration stage;
- r.sub.0 :a radius of said interference fringe pattern image in said calibration stage.
- 22. A method of measuring a characteristic of an optical element, said method comprising:
- forming a reference interference fringe pattern using a reference light beam reflected from a reference surface and a test light beam that is guided from a reference optical element by a light refracting element;
- detecting said reference interference fringe pattern;
- determining effects of at least one of defocus and tilt of said reference optical element on said detected interference fringe pattern by a predetermined calculation;
- storing said determined effects in a memory;
- forming an interference fringe pattern using said reference light beam reflected from said reference surface and another test light beam that is guided from said optical element by said light refracting element;
- detecting said interference fringe pattern;
- outputting data corresponding to said detected interference fringe pattern;
- calculating information, corresponding to said output data, representative of said interference fringe pattern as a predetermined form of a polynomial expression; and
- correcting said polynomial expression using said determined effects stored in memory as correcting data.
- 23. The method of measuring a characteristic of an optical element according to claim 22, each mathematical term representative of said position error comprising a coefficient, the correcting step yielding corrected coefficients.
- 24. A device for measuring a characteristic of an optical element, said device comprising:
- a system that forms an interference fringe pattern using a reference light beam that is reflected from a reference surface and a test light beam that is guided from said optical element by a light reflecting element;
- a system that detects said interference fringe pattern, said detecting system outputting data corresponding to said interference fringe pattern;
- a system that processes said data, said processing system outputting information of wave front aberration representative of said interference fringe pattern, as a predetermined form of a polynomial expression wherein said polynomial expression includes mathematical terms representative of position errors of said optical element and mathematical terms representative of said characteristic of said optical element;
- a system that calculates said mathematical terms;
- a system that corrects at least one of said mathematical terms representative of said characteristic of said optical element based on a predetermined calculation utilizing a value of at least one of said mathematical terms representative of said position error; and
- a system that displays said corrected mathematical terms representative of said characteristic of said optical element.
- 25. The measuring device of claim 24, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting system corrects at least one of said mathematical terms, representative of a symmetrical condition of said surface of said optical element, based on at least one of said mathematical terms, representative of said position errors, representing a defocus of said surface.
- 26. The measuring device of claim 25, wherein said correcting system corrects said mathematical terms representative of said characteristic of said optical element by substituting said mathematical terms representative of said position errors into an equation that is experimentally determined during a calibration stage.
- 27. The measuring device of claim 25, wherein said correcting system corrects said mathematical terms representative of said characteristic of said optical element by substituting said at least one of said mathematical terms representative of said position errors into a predetermined equation.
- 28. The measuring device of claim 27, wherein said light refracting element satisfies the sine condition.
- 29. The measuring device of claim 24, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting system corrects at least one of said mathematical terms, representative of an asymmetrical condition of said surface of said optical element, based on at least one of said mathematical terms, representative of said position errors, representing a tilt of said surface.
- 30. The measuring device of claim 29, wherein said correcting system corrects said mathematical terms representative of said characteristic of said optical element by substituting said mathematical terms representative of said position errors into an equation that is experimentally determined during a calibration stage.
- 31. A device for measuring a characteristic of an optical element, said device comprising:
- a system that forms an interference fringe pattern using a reference light beam reflected from a reference surface and a test light beam that is guided from said optical element by a light refracting element;
- a system that detects said interference fringe pattern, said detecting means outputting data corresponding to said interference fringe pattern;
- a system that processes information representative of said interference fringe pattern, said information defining wave front aberrations W(.rho., .phi.) as: ##EQU22## where, .rho.=h/h.sub.max
- h:incident height,
- h.sub.max :maximum incident height,
- .phi.:polar coordinate angle,
- k,l,n:non-negative integers (0,1,2, . . . ),
- W.sub.11, W.sub.12, W.sub.20, W.sub.22, W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52,W.sub.60,:coefficients of each aberration;
- a calculating system that calculates said coefficients W.sub.11, W.sub.12, W.sub.20, W.sub.22, W.sub.31, W.sub.32 , W.sub.40, W.sub.51, W.sub.52, W.sub.60. . . ;
- a system that corrects at least one of said coefficients W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60 which are representative of said characteristic of said optical element, based on values of at least one of said coefficients W.sub.11, W.sub.12, W.sub.20 which are representative of a position error of said optical element; and
- a system that displays said corrected coefficients corresponding to said coefficients W.sub.31, W.sub.32, W.sub.40, W.sub.51, W.sub.52, W.sub.60 . . . .
- 32. The measuring device of claim 31, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting system corrects one of fourth and higher order even coefficients W.sub.40, W.sub.60, . . . which represent symmetrical aberrations of said surface of said optical element based on a second order coefficient W.sub.20 which represents a defocus of said surface.
- 33. The measuring device of claim 32, wherein said correcting system corrects said fourth order coefficient W.sub.40 by substituting said coefficient W.sub.20 into an equation:
- A.sub.4 =W.sub.40 -1/4.multidot.NA.sub.0.sup.2.multidot. W.sub.20
- where NA.sub.0, is a numerical aperture of a light converging element, and
- A.sub.4 is a corrected value of said coefficient W.sub.40.
- 34. The measuring device of claim 32, wherein said correcting system corrects said sixth order coefficient W.sub.60 by substituting said coefficient W.sub.20 into an equation;
- A.sub.6 =W.sub.60 1/8.multidot.NA.sub.0.sup.4.multidot. W.sub.20
- where NA.sub.0 is a numerical aperture of a light converging element, and
- A.sub.6 is a corrected coefficient of said sixth order coefficient W.sub.60.
- 35. The measuring device of claim 32, wherein said correcting system corrects a fourth and higher order even coefficients W.sub.40, W.sub.60 . . . during a measurement stage by substituting a coefficient W.sub.20 into a calibration stage determined equation:
- W.sub.n0 "=W.sub.n0 '-(a.sub.n s.sup.n-2 W.sub.20 '+b.sub.n s.sup.n)
- where,
- W.sub.n0 ":corrected coefficients of n-th order term;
- W.sub.n0 ', W.sub.20 ':coefficients in said measurement stage;
- a.sub.n,b.sub.n :coefficients of correction experimentally determined by said calibration stage;
- n:Even number greater than or equal to 4;
- s=r.sub.1 /r.sub.0 -h.sub.1 /h .sub.0
- h.sub.1 :an incident height of a light beam on said light converging element in said measurement stage;
- r.sub.1 :a radius of an interference fringe pattern measured in said measurement stage;
- h.sub.0 :an incident height of said light beam on said light converging element in said calibration stage;
- r.sub.0 :a radius of said interference fringe pattern image in said calibration stage.
- 36. The measuring device of claim 31, wherein said characteristic of said optical element is related to a shape of a surface of said optical element,
- wherein said correcting system corrects third and higher order odd coefficients W.sub.31, W.sub.51 . . . and/or W.sub.32, W.sub.52 . . . , which represent asymmetrical aberrations of said surface based on first order coefficients W.sub.11 and/or W.sub.12 which represent a tilt of said surface.
- 37. The measuring device of claim 36, wherein said correcting system corrects said third and higher order odd coefficients W.sub.31, W.sub.51 . . . and/or W.sub.32, W.sub.52 . . . during a measurement stage by substituting said coefficients W.sub.11, and/or W.sub.12 into a calibration stage determined equation:
- W.sub.nm "=W.sub.nm '-(a.sub.nm s.sup.n-1 W.sub.lm '+b.sub.nm s .sup.n)
- where,
- W.sub.nm ":corrected coefficients of n-th order terms;
- W.sub.nm ', W.sub.lm 40 :coefficients in said measurement stage;
- a.sub.nm, b.sub.nm :coefficients of correction experimentally determined by said calibration stage;
- n:Odd number greater than or equal to 3;
- s=r.sub.1 /r.sub.0 '=h.sub.1 /h.sub.0
- h.sub.1 :a height of a light beam incident on a light converging element in said measurement stage;
- r.sub.1 :a radius of an interference fringe pattern in said measurement stage;
- h.sub.0 :a height to said light beam incident on said light converging element in said calibration stage;
- r.sub.0 :a radius of said interference fringe pattern image in said calibration stage.
Priority Claims (2)
Number |
Date |
Country |
Kind |
5-281963 |
Oct 1993 |
JPX |
|
5-353505 |
Dec 1993 |
JPX |
|
Parent Case Info
This application is a continuation of application Ser. No. 08/321,853, filed Oct. 14, 1994, now abandoned.
US Referenced Citations (10)
Foreign Referenced Citations (1)
Number |
Date |
Country |
62-129707 |
Jun 1987 |
JPX |
Continuations (1)
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Number |
Date |
Country |
Parent |
321853 |
Oct 1994 |
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