US4633171A
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Window function for an aperture window
Assignee: Siemens AG
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Filing: 1985-02-08
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Granted: 1986-12-30
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Expires: 2005-02-08
Abstract
Abstract A window function optimum for apodization of diffraction at an aperture of a Bragg Cell spectral analyzer. A window function is derived which is simpler to realize and which comes very close to an optimum window function.
Inventors
- 👤 Eckhard Storck
- 👤 Ulrich Wolff
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-02 06:48
CPC Classifications
G; G02; G02F; G02F1/00; G02F1/01; G02F1/11; G02B; G02B27/00; G02B27/58
Claims Analysis
Total Claims: 12
Claim 1
Independent Claim
113 words
A Bragg cell spectral analyzer aperture window, comprising: aperture window means for apodization of diffraction, thereat and comprising a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU12## Where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 2
Dependent Claim
113 words
A Bragg cell spectral analyzer aperture window, comprising: aperture window means for apodization of diffraction, thereat and comprising a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU12## Where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 3
Dependent Claim
113 words
A Bragg cell spectral analyzer aperture window, comprising: aperture window means for apodization of diffraction, thereat and comprising a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU13## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 4
Dependent Claim
113 words
A Bragg cell spectral analyzer aperture window, comprising: aperture window means for apodization of diffraction, thereat and comprising a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU13## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 5
Dependent Claim
123 words
In a Bragg cell spectral analyzer wherein a window function is provided for apodization of diffraction at an aperture thereof wherein the improvement comprises: said aperture having for said apodization a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on raditaion passing through said aperture except for a prescribable standardization factor, the window function A(x) being defined by ##EQU14## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 6
Dependent Claim
123 words
In a Bragg cell spectral analyzer wherein a window function is provided for apodization of diffraction at an aperture thereof wherein the improvement comprises: said aperture having for said apodization a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on raditaion passing through said aperture except for a prescribable standardization factor, the window function A(x) being defined by ##EQU14## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 7
Dependent Claim
123 words
In a Bragg cell spectral analyzer wherein a window function is provided for apodization of diffraction at an aperture thereof wherein the improvement comprises: said aperture having for said apodization a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on radiation passing through said aperture except for a prescribable standardization factor, the window function A(x) being defined by ##EQU15## wherein X 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 8
Dependent Claim
123 words
In a Bragg cell spectral analyzer wherein a window function is provided for apodization of diffraction at an aperture thereof wherein the improvement comprises: said aperture having for said apodization a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinate (x) to be impressed on radiation passing through said aperture except for a prescribable standardization factor, the window function A(x) being defined by ##EQU15## wherein X 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 9
Dependent Claim
109 words
An aperture window comprising aperture window means for apodization of diffraction thereat and comprisng a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinates (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU16## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 10
Dependent Claim
109 words
An aperture window comprising aperture window means for apodization of diffraction thereat and comprisng a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinates (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU16## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 11
Dependent Claim
109 words
An aperture window comprising aperture window means for apodization of diffraction thereat and, comprising a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinates (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU17## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
Claim 12
Dependent Claim
109 words
An aperture window comprising aperture window means for apodization of diffraction thereat and, comprising a window function (A(x)) defining a spatial intensity distribution over a specific spatial coordinates (x) to be impressed on radiation passing through the aperture window means except for a prescribable standardization factor, the window function A(x) being defined by ##EQU17## where I 1 ( . . . ) denotes the modified Bessel function of the first kind and first order, k is a prescribable number which defines a target level of apodization, D denotes an aperture width of the aperture along the spatial coordinate (x), and δ( . . . ) denotes Dirac's delta function.
References Cited (Backward Citations)
US4262996A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1989-12-29 | 1990-06-30 | 1990-12-30 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1993-12-29 | 1994-06-30 | 1994-12-30 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1997-12-29 | 1998-06-30 | 1998-12-30 | $7700.00 | Window Closed / Lapsed |