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WO1998036237A1 - Procede pour determiner une grandeur optique, mecanique, electrique ou autre - Google Patents

Procede pour determiner une grandeur optique, mecanique, electrique ou autre Download PDF

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Publication number
WO1998036237A1
WO1998036237A1 PCT/DE1998/000375 DE9800375W WO9836237A1 WO 1998036237 A1 WO1998036237 A1 WO 1998036237A1 DE 9800375 W DE9800375 W DE 9800375W WO 9836237 A1 WO9836237 A1 WO 9836237A1
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WIPO (PCT)
Prior art keywords
measured variable
shear
window
measured
difference
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Ceased
Application number
PCT/DE1998/000375
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German (de)
English (en)
Inventor
Ingolf WEINGÄRTNER
Stefan Loheide
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Bundesrepublik Deutschland Vertreten Durch Den Bundesminister fur Wirtschaft Dieser Vertreten Durch Den Prasidenten Der Physikalisch-Technischen Bundesanstalt Braunschweig und Berlin
Federal Government of Germany
Original Assignee
Bundesrepublik Deutschland Vertreten Durch Den Bundesminister fur Wirtschaft Dieser Vertreten Durch Den Prasidenten Der Physikalisch-Technischen Bundesanstalt Braunschweig und Berlin
Federal Government of Germany
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from DE19720122A external-priority patent/DE19720122C2/de
Application filed by Bundesrepublik Deutschland Vertreten Durch Den Bundesminister fur Wirtschaft Dieser Vertreten Durch Den Prasidenten Der Physikalisch-Technischen Bundesanstalt Braunschweig und Berlin, Federal Government of Germany filed Critical Bundesrepublik Deutschland Vertreten Durch Den Bundesminister fur Wirtschaft Dieser Vertreten Durch Den Prasidenten Der Physikalisch-Technischen Bundesanstalt Braunschweig und Berlin
Priority to AU64945/98A priority Critical patent/AU6494598A/en
Publication of WO1998036237A1 publication Critical patent/WO1998036237A1/fr
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
    • G01J9/0215—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods by shearing interferometric methods

Definitions

  • a measurand should be defined along its finite extent. Examples are spatially, temporally or otherwise extended but limited signals: the properties of a length division and the phase distribution of the topography of a wavefront as spatially extended signals
  • the difference between the measured variables generated by a measurement is referred to below as the measured variable difference.
  • This measured variable difference is determined from the measured variable at two points along the finite extent of the measured variable with a constant distance from one another.
  • the spatial, temporal or other displacement of the measured variables relative to one another is also referred to below as shear or shear.
  • the measurement interval is the expansion of the measured variable difference.
  • Fourier filtering is a successive implementation of Fourier transformation or harmonic analysis, multiplication of the Fourier transform with a so-called transfer function and Fourier inverse transformation or. called harmonic analysis.
  • the frequency is the reciprocal of the period length of a temporally periodic signal (time frequency, frequency) and in the case of spatially extended signals the reciprocal of the period length of a spatially extended signal (spatial frequency).
  • the difference between the wave fronts (ie their phases or topographies) generated by a shear ing interferometer is referred to below as the wavefront difference.
  • a subsystem is also referred to as an interferometer, which does not yet have to include the recording of the intensity (of the interferogram).
  • the image field is the extent, measured in an angular unit or a unit length, of the image of an object originating from an imaging system.
  • the pupil of an imaging system is the area (plane) of the system in which the beam-limiting diaphragm (aperture diaphragm) is located, or an image thereof.
  • An electronic detector is referred to as a CCD camera, which consists of an array of radiation-sensitive detector elements (pixels).
  • the invention relates to a method for determining a measured variable along a finite extent from at least one measured variable difference, provided that these measured variable differences are determined at two sampling points, each of which has the same distance from one another in pairs.
  • Applications are conceivable in various areas of mechanics, optics, electronics or general tasks. Examples are Expressions listed for measuring the errors of length divisions, the flatness of flat plates with. Scanning methods, the characteristics of electronic components, the topography of wave fronts with interferometric methods and the propagation of electromagnetic waves in the atmosphere.
  • Difference methods are often used to implement reference-free measurements (examples of this are length divisions and shearing interferometry) and / or to separate device errors from measured variables (examples of this are flatness and straightness).
  • Interferometry has been established as a measuring method for examining the topography of high-quality surfaces and for characterizing aberrations (wave aberrations) in lenses and lenses.
  • a wave influenced by the device under test is coherently superimposed on a reference wave. From the resulting interference pattern, the wave aberration or the topography of a surface can then be determined taking into account the experimental parameters [1].
  • the generation of a reference wave is complex because the optical components required for this introduce additional aberrations [2].
  • shear interferometry [1] [3] offers the option of doing without a reference wave.
  • image errors wave aberrations
  • the adjustment of shear interferometers is much easier compared to that of other interferometers such as Twyman-Green interferometers.
  • the plane wave disturbed by the wave aberration to be determined is rather coherently overlaid with a laterally shifted copy.
  • Shear interferometry is therefore also referred to as a self-referencing measurement method. There are various methods for the implementation. On the one hand, the wave to be examined is reflected on the front and on the back of a plane-parallel plate, the surface quality of which is very well known [4].
  • Another possibility is to use two identical gratings, whereby the plus first and the minus first order, by diffraction at the first grating, provide the copies that are combined again laterally displaced by the second grating [5]. After splitting, there are two waves with the same wave aberration that are laterally shifted from each other. The wave aberration can be calculated from the interference pattern created by superimposition.
  • a fundamental disadvantage of shear interferometry is that periodic parts whose periodicity corresponds to the shear cannot be reconstructed. This is a fundamental difficulty in shear interferometry, but it does not exist in the method according to the invention. This difficulty is not mentioned again in the further course of the description of the method according to the invention as one of its basic requirements.
  • the interference pattern does not contain the information about the wave aberration, but only about the difference between the wave fronts that are laterally displaced. Problems also arise due to the limitation of the wavefront to be examined through the pupil. An interference pattern that contains information about the wavefront difference only arises where the two waves overlap. Outside this overlap area, especially where only one of the waves exists, the information about the wavefront difference is lost.
  • Various methods have been proposed to obtain complete information about the wavefront using shear interferometry [6] [7] [8].
  • the evaluation takes place in two steps.
  • the wavefront difference is determined from the intensity pattern. It should be taken into account that the cosine function is not monotonic and therefore the inverse function is not unique. Solutions to this fundamental problem of interferometry are discussed in the literature and referred to as "phase unwrapping" [15] [16] [17]. This problem will not be discussed in the following seeks and also in the method according to the invention it is assumed that the wavefront difference is present and from this the wavefront must be reconstructed.
  • the shear must be equal to the distance between the considered points of the interference pattern [22]. This means either a low lateral resolution or a very small shear and thus a very small measurement signal (deflection of the interference fringes or modulation of the interference pattern).
  • the wavefront difference is analyzed harmoniously by Fourier transformation and before the back transformation with the transfer function
  • At least one measured variable difference is determined from two measured variables each at two sampling points, which have a constant distance from each other in pairs, b) that the measured variable has a finite extent and does not have to be periodically recurring in type, c) that the function resulting from the harmonic analysis of the at least one measured variable difference with the transfer function
  • the measured variable differences are subjected to Fourier filtering for the purpose of determining the measured variable with the aid of the transfer function specifically intended for this purpose, provided that the discontinuities in the transfer function are not matched by a frequency of the harmonic elementary functions in the harmonic analysis of the measurement by suitable selection of the shear - size differences coincide.
  • the transfer function is
  • the periodic disturbance of the measured variable for the inner, undisturbed area of the measuring interval can be calculated. Then, moreover, by expanding the periodic
  • the periodic disturbance can be calculated over the entire extent of the measurement interval. Finally, by subtracting the malfunctioning measured variable determined with the steep window and the periodic disturbance, the measured variable can be clearly reconstructed.
  • a measurement can be carried out in such a way that two scanning heads are arranged with a finite distance (shear, shear) and that measurements along the length division are carried out with both scanning heads, the distance between the two scanning heads remaining constant.
  • the two scanning heads supply the position on the length division as a measurement signal, from which the difference in the measured values results as the difference between the two measurements.
  • the measured variable in this case the error in the length division, scanned by the scanning heads, can be determined by the evaluation method according to the invention.
  • Several scanning heads and several combinations of measured values can also be used to obtain several measured variable differences.
  • an angle scan is carried out with the aid of autocollimation telescopes or other methods in such a way that two scanning systems are guided over the flat plate, which measure the angles of the surface at two locations, each with a constant distance.
  • the measured variable difference is then the difference between the two individually measured angles.
  • the measured variable can be used to determine the measured variable from the difference in the measured variables, and the topography of the plane surface can be determined from this using known standard methods. Several combinations of measured values can also be used to obtain several measured variable differences.
  • characteristic curves of electronic components can be determined by temporal difference measurements and application of the method according to the invention.
  • the method according to the invention is applicable to general, temporal or spatial measurements, such as measurements through the turbulent atmosphere.
  • shearing interferometry there is a wavefront difference in the form of two-dimensional information over the entire area of the shearing interferogram.
  • the method according to the invention is applied to one-dimensional cuts across the surface of the two-dimensional interferogram in order to reconstruct the wavefront one-dimensionally along each cut.
  • Two evaluations are expediently carried out with shears orthogonal to one another, the information of which can be combined to form complete two-dimensional information about the wavefront, which is then present in the entire pupil of the system.
  • the evaluation method according to the invention allows the use of large shear forces.
  • General procedures for the evaluation of differential measurements with large measurement signals are otherwise not known.
  • the differential method allows the effects of device errors to be eliminated by separating the device errors and the measured variables.
  • optics there are particular advantages when used for photo lenses, aerial photo lenses, collimators, microscope lenses and photolithography lenses.
  • an angle scan is carried out with the help of autocollisions telescopes or other methods in such a way that two scanning systems are guided over the plane plate, which measure the angles of the surface at two points, each with a constant distance.
  • the measured variable difference is then the difference between the two individually measured angles.
  • the measured variable can be used to determine the measured variable from the difference in the measured variables, and the topography of the plane surface can be determined from this using known standard methods.
  • Several combinations of measured values can also be used can be used to obtain several measured variable differences. This enables a reference-free, highly precise measurement of the flatness of flat surfaces.
  • the characteristics of electronic components can be measured by measuring the difference in time and using the. inventive method can be determined. Furthermore, the method according to the invention is applicable to general temporal or spatial measurements, such as measurements by the turbulent atmosphere. Here, too, reference-free, highly precise measurements of the corresponding measured variables are possible.
  • shear interferometry offers the essential advantage of being able to do without a reference wave.
  • image errors wave aberrations
  • the adjustment of shear interferometers is much easier compared to the adjustment of other interferometers such as Twyman-Green interferometers.
  • the plane wave disturbed by the wave aberration to be determined is rather coherently overlaid with a laterally shifted copy. Therefore, shear interferometry is an absolute, self-referencing measurement method.
  • shear interferometers are made up of far fewer optical components than other interferometers, so they have fewer potential equipment errors that must be avoided.
  • advantages of shear interferometry can only be exploited if there are quantitative, reliable and sufficiently precise evaluation methods that were not previously available. This essential previous lack of shear interferometry is remedied with the method according to the invention.
  • the wave to be examined is reflected on the front and on the back of a plane-parallel plate, the surface condition of which is very well known.
  • Another possibility is to use two identical gratings, the plus first and the minus first order by diffraction at the first grating providing the copies which are laterally combined again by the second grating.
  • After splitting there are two waves with the same wave aberration that are laterally displaced from each other.
  • the wave aberration can be calculated from the interference pattern created by superimposition.
  • the lateral resolution of the method according to the invention does not have all the disadvantages of the polynomial method because its resolution is only determined by the detector with which the interferogram and thus the wavefront difference is detected, because no prerequisite for the Form of the wavefronts to be determined must be made and because the computation is only very small.
  • N x N support points are taken into account in the description of the wavefront, the matrix to be inverted has at least the size N 2 x N2. Furthermore, the shear must be equal to the distance between the reference points of the interference pattern that are taken into account. That means either a slight lateral
  • the wavefront difference is analyzed harmoniously by Fourier transformation and before the back transformation with the transfer function
  • Unit and s is the shear.
  • the shear is restricted to the distance between the considered support points of the interference pattern in the same way as with the matrix method.
  • the method according to the invention does not have all the disadvantages of the conventional Fourier transformation method because it can work with shears that are up to a third of the pupil and not like the conventional Fourier transformation method with shears which are generally only about a hundredth to two thousandths of the pupil.
  • the complete measured variable can be determined over the entire extent of the measured variable from the measured variable differences, b) a high degree of accuracy is achieved, c) relatively large shears of up to one third of the Expansion of the measurand are permitted, d) whereby no restrictions with regard to the shape of the measured variable have to be assumed e) and a high resolution with regard to the variation of the measured variable is achieved.
  • the shear is preferably chosen to be approximately one tenth of the extent of the measured variable.
  • b is the width of the inner undisturbed area, here chosen as two times the shear s
  • p is the extent of the measured variable
  • nd represents the frequency in the harmonic analysis.

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  • Physics & Mathematics (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • General Physics & Mathematics (AREA)
  • Instruments For Measurement Of Length By Optical Means (AREA)

Abstract

Un filtrage de Fourier des différences de grandeurs à mesurer, obtenues par des mesures de différences desdites grandeurs, est réalisé pour déterminer la grandeur à mesurer au moyen de la fonction de transfert spécialement prévue à cet effet, à condition que les points de discontinuité de la fonction de transfert ne coïncident pas, par le choix approprié du cisaillement, avec une fréquence des fonctions élémentaires harmoniques lors de l'analyse harmonique des différences des grandeurs à mesurer et à condition qu'au moins deux cycles d'évaluation soient réalisés avec différentes fonctions fenêtre pour déterminer la grandeur à mesurer, afin de permettre l'utilisation de cisaillements représentant jusqu'à un tiers de l'extension de la grandeur à mesurer, qui entraîneraient normalement des erreurs lors de la détermination de la grandeur à mesurer par filtrage de Fourier des différences de grandeurs à mesurer avec des cisaillements représentant jusqu'à un tiers de l'extension de la grandeur à mesurer.
PCT/DE1998/000375 1997-02-12 1998-02-11 Procede pour determiner une grandeur optique, mecanique, electrique ou autre Ceased WO1998036237A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU64945/98A AU6494598A (en) 1997-02-12 1998-02-11 Method for determining an optical, mechanical, electric or other measurement variable

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
DE19705609 1997-02-12
DE19705609.1 1997-02-14
DE19720122A DE19720122C2 (de) 1997-02-12 1997-05-14 Verfahren zur Ermittlung einer optischen, mechanischen, elektrischen oder anderen Meßgröße
DE19720122.9 1997-05-14

Publications (1)

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WO1998036237A1 true WO1998036237A1 (fr) 1998-08-20

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4265534A (en) * 1977-12-23 1981-05-05 Remijan Paul W Optical apparatus and method for producing the same
US5004345A (en) * 1988-12-05 1991-04-02 Hung Yau Y Dual-lens shearing interferometer

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4265534A (en) * 1977-12-23 1981-05-05 Remijan Paul W Optical apparatus and method for producing the same
US5004345A (en) * 1988-12-05 1991-04-02 Hung Yau Y Dual-lens shearing interferometer

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
I.WEINGÄRTNER ET AL: "A simple shear-tilt interferometer for the measurement of wavefront aberrations", OPTIK, vol. 70, no. 3, 1985, STUTTGART,DE, pages 124 - 126, XP002066653 *

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