WO2021151792A1 - Procédé et dispositif de caractérisation d'un champ lumineux cohérent en amplitude et en phase - Google Patents

Procédé et dispositif de caractérisation d'un champ lumineux cohérent en amplitude et en phase Download PDF

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Publication number
WO2021151792A1
WO2021151792A1 PCT/EP2021/051457 EP2021051457W WO2021151792A1 WO 2021151792 A1 WO2021151792 A1 WO 2021151792A1 EP 2021051457 W EP2021051457 W EP 2021051457W WO 2021151792 A1 WO2021151792 A1 WO 2021151792A1
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WIPO (PCT)
Prior art keywords
light field
area
light
detector
transmission
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PCT/EP2021/051457
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German (de)
English (en)
Inventor
Jens Limpert
Jan ROTHHARDT
Getnet Kassa Tadesse
Wilhelm Eschen
Original Assignee
Gsi Helmholtzzentrum Für Schwerionenforschung Gmbh
Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V.
Friedrich-Schiller-Universität Jena
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Publication of WO2021151792A1 publication Critical patent/WO2021151792A1/fr

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Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/46—Systems using spatial filters
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4205—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive optical element [DOE] contributing to image formation, e.g. whereby modulation transfer function MTF or optical aberrations are relevant
    • 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
    • G01J2009/002—Wavefront phase distribution

Definitions

  • the invention relates to the characterization of light fields, in particular of focused light fields in the range of 10 12 Hz (THz - Terra Hertz) to 10 19 Hz (10 Exahertz - X-ray radiation), in particular a characterization of the Light field of a light source (especially before passing through an object).
  • a characterization of the Light field of a light source especially before passing through an object.
  • emitted radiation must be determined directly in terms of amplitude and phase.
  • the radiation to be examined can be terahertz radiation, visible light, XUV radiation (extreme ultraviolet radiation XUV in the order of 10 15 Hz (PHz - Petahertz)) or X-rays, as long as the radiation is coherent.
  • XUV radiation extreme ultraviolet radiation XUV in the order of 10 15 Hz (PHz - Petahertz)
  • X-rays as long as the radiation is coherent.
  • focused radiation is often used, the amplitude and phase of which must be precisely known in the focus spot (ie in a small area in which it strikes the object).
  • a light wave (light field) (emitted by a light source) is characterized by measuring the intensity distribution lo (x, y) in a two-dimensional plane (x, y), mostly transverse to the direction of propagation and its phase phio (x, y).
  • the phase phi indicates in which section within a period the wave is at a reference time and place. The phase phi therefore describes the course of the intensity distribution when the wave propagates in space and time.
  • a method of coherent diffracting imaging for characterizing light radiation, which reconstructs a light wave after it has passed through an object by measuring a diffraction image, i.e. the intensity of the light wave in a plane after the object has passed through , reconstructed.
  • a complex object with many structural details is used for this, for which a complex transmission function in amplitude and phase must be determined, which describes the behavior of the light wave when passing through the object at each point (x, y). With this information it is then possible to determine the properties of the light wave before the passage of the object in the object plane.
  • a reconstruction algorithm is used to reconstruct the light wave, as can be seen, for example, from the review article J. R. Fientrup, "Phase retrieval based on wave-front relay and modulation", Appl. Opt., Vol. 21, No. 15, pages 2758-2769, 1982 results.
  • DE 102007009661 A1 describes a method for spatially resolved determination of the phase in the image of an object, in which the phase and / or the amplitude of the light is modified by spatial frequency filtering in a pupil plane between the object and the image plane, i.e. after the passage of the Light field through an object. Between the object and the image or detector plane. For this purpose, a spatial frequency filter is introduced into the light beam between the object and the detector, and the phase and / or amplitude of the light is modified in a predetermined manner. At least two images with different modifications are generated. The phase in the image of the object in the image plane is determined in a spatially resolved manner from the images generated.
  • lo (x, y) describe the intensity distribution of the light wave
  • phio (x, y) describe the phase of the light wave in a plane perpendicular to the direction of propagation 100 of the light wave.
  • the light wave now has the properties uo (x, y).
  • the complex function u ′ (x, y) contains the spatial intensity distribution l ′ (x, y), which is measured by the detector 120.
  • the phase phi '(x, y) is unknown and cannot be measured.
  • the light wave can be reconstructed.
  • the light propagation of the light field 101 in front of the object uo (x, y) can be described mathematically in two steps.
  • the light propagation between the object plane 111 and the detector plane 121 which takes place in the free space, can always be described in the forward direction by a suitable propagator.
  • the propagator can be described mathematically by a Fourier transformation F (as an example for propagators).
  • F a Fourier transformation
  • a far field is used when the distance between the detector 120 and the object 110 is greater than 2 D 2 / lambda, where D is the largest dimension of the diffracting object 110 and lambda is the wavelength of the diffracted radiation.
  • the aim is now to determine the light field 101 in the object plane 111, i.e. the complex function uo (x, y), with knowledge of the experimental setup and the transmission function T (x, y) from the measured intensity distribution l '(x, y).
  • this is possible, please include by mathematical inversion (backward calculation) of the light propagation of the light field 101 from the object plane 111 to the detector plane 121.
  • the fictitious plane 125 is an imaginary plane which - lies directly behind the object in the direction of propagation 100 - and which writes the plane after the light wave 101 has passed through the object 110.
  • phase reconstruction algorithm with which u (x, y) can be determined in the result.
  • Random phase distribution also includes the case that an initial phase can be and is estimated from certain information (if available). Random phase means that the phase phi ‘(x, y) is not exactly known, and a phase phi‘ (x, y) is assumed to be an arbitrarily selectable starting value for the reconstruction of the light wave.
  • the light field 101 i.e. the complex light wave function u (x, y)
  • the light field 101 i.e. in the plane 125 behind the object 110 and thus also behind the object plane 111. Because the light field 101 is described there by the light wave function u (x, y), the light wave function u (x, y) is also referred to as the light field in this text for short.
  • the iterative phase reconstruction algorithm comprises several steps which are run through repeatedly.
  • the light propagation from the detector plane 121 to the plane 125 is calculated.
  • a support condition P Su support constraint
  • the support condition being e.g. on the shape and size of the object 110 in the object plane 111 results.
  • the Fourier transformation F is used to transform the complex light field u (x, y) q back into the detector plane 121, ie into the light field u '(x, y) q .
  • u '(x, y) q F (u (x, y) q ).
  • a modulus condition Pmo d (modulus cons traint) is then applied in the detector plane 121, in which the magnitude of the complex field u '(x, y) q is determined by the measured intensity distribution l' (x, y) (amplitude) while maintaining the be calculated phases is replaced, i.e.
  • SQRT (l '(x, y)).
  • the algorithm can determine the correct phase phi '(x, y,) finai in the detector plane with the aid of the boundary conditions used, ie the modulus condition (modulus contract Pmod) and the support condition (support constraint P S up) .
  • the light wave in front of the object uo (x, y) can also be finally calculated at all points of the object with sufficient transparency from the determined complex light wave u (x, y) finai.
  • This is the goal of beam characterization. In principle, only the recording of a single diffraction image is necessary for this (single-shot beam characterization).
  • This method which has been described by way of example with reference to FIG. 2 and can be applied accordingly by the person skilled in the art, is also used in the characterization of the coherent light field according to the invention in terms of amplitude and phase.
  • the object of the invention is therefore to propose a method and a device for characterizing a coherent light field in amplitude and phase, which is easy to use and also allows beam characterization of focused light fields in the range from about 10 12 to about 10 19 Hz.
  • the transmission mask can be implemented by an absorber layer, for example an absorbing metal film, as a strongly absorbing area (T «0) with openings in the metal film as non-absorbing areas (T « 1).
  • Such transmission masks can be produced with very high precision, so that correspondingly small structures in the sub-wave range (for example in the nanometer range) can be produced.
  • the openings in the absorber layer, for example a metal film can be produced, for example, with a focused ion beam.
  • the object can have a transmission mask which is highly absorbent (optically impermeable to the light wave) outside a defined structure area, ie has a transmission of T «o.
  • the structure area of the object is surrounded by a diaphragm area which only provides strongly absorbing areas with a transmission T «o.
  • the delimitation between the aperture area and the structure area of the object can be done, for example, by an (imaginary) line-like and closed contour curve, which envelops the non-absorbing areas in the outer area of the structure area (hereinafter also referred to as openings), for example by the contour curve connects external openings in such a way that all openings of the structural area lie within the closed contour curve.
  • the closed contour curve can be made as small as possible, for example by making the length of the (imaginary) contour curve line as short as possible.
  • the structural area can be formed, for example, by a metal or any other absorber layer that is impermeable to the light wave and, for example, in the form of a matrix having arranged openings.
  • a linear curve can be selected as the contour curve, which connects the openings of the first and the last row and column with one another and completely includes all openings.
  • the strongly absorbing area outside the closed contour curve surrounding the matrix arrangement of the openings forms the diaphragm area.
  • the object simultaneously takes on the function of an entrance aperture that is frequently used in the prior art.
  • the inventive reduction in the number of optical elements used when applying the proposed method leads to a higher stability of both the apparatus (in the mechanical sense) and the characterization of the light field obtained by the method (in the sense of a solution for iteratively carried out Reconstruction of the light wave function).
  • boundary conditions also make it possible to reduce the requirements for the signal-to-noise ratio. This leads to shorter measuring times. It is particularly advantageous to determine the entire structure of the object (ie its structural area) and to apply this boundary condition.
  • the object can be examined or recorded, for example, by an electron microscope and the holes or the areas of the metal film or more generally the strongly absorbing areas (for example in the sense of material Areas) of the structure of the object are measured.
  • another material that is optically non-transparent for the light field can also be selected by the person skilled in the art, that is to say any absorber material suitable for the light wave for forming an absorber layer.
  • Another aspect of the invention provides that an object with an asymmetrically designed structure, ie an asymmetrically designed structure area, is used.
  • Simple periodic or symmetrical test objects cannot be used because the reconstruction of the light wave due to the so-called "twin-image" problem is not unambiguous: Without additional knowledge of an asymmetry of the object, the result gives an image behind the test object as well as a twin image that has been rotated 180 degrees an unambiguous assignment of the coordinates in the object plane is not possible, and the light wave function u (x, y) cannot be unambiguously reconstructed.
  • FIG. 2 This is illustrated in FIG. 2 by two reconstructed images 140 of the object 101, which are currently mirror images of one another.
  • a known asymmetry of the object results in a further boundary condition for the reconstruction (support condition or support constraint Psup), which allows an unambiguous reconstruction.
  • additional statements about the coherence of the radiation can be obtained from the contrast of the diffraction image.
  • the invention relates to a device for characterizing a coherent light field in amplitude and phase with the following elements:
  • Computing device which is connected to the area detector and is designed to carry out the previously described method for reconstructing the light wave function u (x, y) or parts thereof.
  • the object has a structure area which is defined by a transmission mask which provides only strongly absorbing areas with a transmission T «o and non-absorbing areas with a transmission of T « 1. This makes it easy to describe the transmission function T (x, y) of the object.
  • the structural area of the object is designed asymmetrically in order to avoid the "twin-image" problem already described.
  • the object can preferably have a strongly absorbing diaphragm area which only provides strongly absorbing areas with a transmission T «o and which surrounds the structural area.
  • the object itself thus forms a screen for the light field, so that parts of the light field that illuminate around the structure area of the object are absorbed and this prevents these parts of the light field from being detected by the area detector.
  • the device can have the object and the area detector as the only optical elements (ie elements that interact with the light field).
  • This described device (structure) has a further important advantage that it has only two static optical elements (ie that cannot be changed during the measurement), namely the object as a sample in the beam and the area detector behind the sample.
  • the area detector can have a pixelated sensor, ie a sensor consisting of a large number of individual pixel elements with which a spatial distribution of the intensity distribution of the diffraction image of the light field in the detector plane can be detected.
  • the resolution of the spatial distribution is given by the pixel structure (spatial arrangement of the pixels on the detector surface or sensor surface) and the pixel size (surface size of a pixel).
  • the area size can be in the range // m 2 (square micrometers), for long-wave light (eg IR and THz) also in the range mm 2 (square millimeters).
  • the area detector can be designed to detect the light of the light wave in a wavelength-selective manner, in particular in order to minimize incidence of light not generated by the light wave.
  • the term "light” in the context of this text is not restricted to visible light, but rather includes the wavelength or frequency range specified at the beginning.
  • the method described above and the structure described above are so precise that a characterization of the light field can be carried out with the acquisition of only one diffraction image, i.e. single shot measurements are possible. This enables short measurement and evaluation times for the characterization of the light field, so that de facto real-time measurements are possible by using the method according to the invention.
  • the rapid convergence of the inversion algorithm also contributes to this.
  • the reconstruction can also be accelerated by parallelization and methods of artificial intelligence. Corresponding methods from the prior art are known. Because the method also enables very small objects to be used due to the simple optical structure of the object used, very large wavefront curvatures can also be measured, for example with measuring angles of up to +/- 90 ° to the optical axis. The invention is therefore also particularly suitable for characterizing small focus spots of light waves.
  • the invention also makes it possible to achieve spatial resolution down to the sub-wavelength range (for example with a numerical aperture of NA> 0.5). This covers practically all applications (even with small focus spots of the light wave).
  • the invention described can preferably be used to adjust objects in optical structures and / or to adjust light sources in optical structures.
  • Fig. 1 schematically shows the passage of a light field through an object and the detection of the resulting diffraction image in the detector plane in a structure that can also be used for the device according to the invention and the implementation of the method for characterizing a coherent light field in amplitude and phase; ts
  • FIG. 3 schematically shows the implementation of the method proposed according to the invention in a device according to the invention according to a preferred embodiment.
  • FIG. 3 also shows schematically an object 10 or its structure area 12 used in the device and the method.
  • the structure area 12 is defined by a transmission mask, the strongly absorbing areas 13 (shown in light color in FIG. 3) and non-absorbing areas surface 14 (shown in dark in FIG. 3), for example in the form of an absorption layer such as a metal foil or some other material that absorbs the wavelength (s) of the light field.
  • the known structure of the object 10 makes it possible to identify all locations with the intensity of zero.
  • the known information about the object is used as a boundary condition P S up (support constraint) in the iterative algorithm. According to the invention, this improves the convergence of the algorithm enormously and accelerates the finding of a solution during the iteration.
  • the non-absorbent areas 14 are openings in the absorption layer, and a transmission of T «1 applies there. Also the phase of the object is not influenced by the non-absorbing area of the object.
  • the structure area 12 of the object 10 is constructed asymmetrically. This is a further boundary condition that enables the image points to be clearly assigned to the object, so that the “twin-image” problem, as described in connection with FIG. 2, can be avoided.
  • the object 10 is highly absorbent, that is to say that a transmission T «o can be assumed.
  • the structural area 12 of the object 10, which causes the detected diffraction image 22, is thus de facto an isolated object, the size (maximum extent) of which is known. This defines the maximum size of the measuring field, which defines the minimum number of pixels required for the detector can.
  • the distance of the detector 20 from the object 10 or the object plane 11 from the detector plane 21 can then be selected so that the detector 20 can scan the diffraction image 22 with sufficient precision.
  • the transmission mask only has an amplitude modulation of the light wave or the light field 1 because the openings (non-absorbing regions 14) have a transmission of T «1. This does not modulate the phase of the light wave. This, too, represents a boundary condition that leads to faster convergence of the iterative algorithm.
  • a light wave function u (x, y) is reconstructed which reconstructs the image 40 of the object 10 well from the diffraction image 22 recorded in the detector 20.
  • the light wave 1 in the object plane 111 can then pass through using the known transmission function of the object T (x, y) the object uo (x, y) can be determined.
  • the amplitude and phase of the light wave 1 are thus characterized.
  • the known structure can be used to accelerate the convergence of the reconstruction algorithm and / or to reduce the requirements for the signal-to-noise ratio (to allow shorter measurement times).
  • the object 10 has a known transmission characteristic T (x, y) with areas of a transmission of T «1 which do not influence the phase of the light wave, and with areas of a transmission of T « o which completely absorb the light wave striking the object 10 .
  • This simple geometric structure of the object 10 can be determined before the method is carried out, for example by recording with an electron microspot or another suitable determination method. All areas with a transmission of T «o can be used as boundary conditions in which the light wave function u (x, y) in the object plane 11 is equal to zero. This accelerates the convergence of the reconstruction algorithm.
  • F 1 described as an inverse Fourier transformation propagator for the light wave between detector and object

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Investigating Or Analysing Materials By Optical Means (AREA)

Abstract

L'invention concerne un procédé et un dispositif de caractérisation d'un champ lumineux cohérent (1) en amplitude et en phase, le procédé comprenant les étapes suivantes : • fournir un objet (10) avec une fonction de transmission connue T(x,y) pour le champ lumineux (1) en amplitude et en phase ; • irradier l'objet (10) avec le champ lumineux cohérent (1) à caractériser dans un plan objet (11) dans lequel l'objet (10) est agencé ; • détecter une distribution d'intensité l'(x,y) de l'image de diffraction (22) du champ lumineux (1) spatialement derrière l'objet irradié (10) dans un plan de détection (21) au moyen d'un détecteur plat (20) ; • reconstruire la fonction d'onde lumineuse u(x,y) après le passage de celle-ci à travers l'objet (10) par détermination itérative de la phase et de l'amplitude de l'onde lumineuse à partir de la distribution d'intensité l'(x,y) détectée ; • calculer l'onde lumineuse (1) avant le passage à travers l'objet par application de la fonction de transmission connue T(x,y) à la fonction d'onde lumineuse reconstruite u(x,y). Selon l'invention, un objet présentant une zone de structure (12) est utilisé en tant qu'objet (10), la région de structure (12) de l'objet (10) étant définie par un masque de transmission qui fournit uniquement des régions d'absorption fortes (13) avec une transmission T ≈ 0 et des régions non absorbantes (14) avec une transmission de T ≈ 1.
PCT/EP2021/051457 2020-01-28 2021-01-22 Procédé et dispositif de caractérisation d'un champ lumineux cohérent en amplitude et en phase WO2021151792A1 (fr)

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DE102020101989.0 2020-01-28
DE102020101989.0A DE102020101989A1 (de) 2020-01-28 2020-01-28 Verfahren und Vorrichtung zur Charakterisierung eines kohärenten Lichtfelds in Amplitude und Phase

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CN115984120B (zh) * 2022-10-30 2024-02-02 华南农业大学 叠层成像中物体片层透射函数的恢复方法、装置和存储介质

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DE102007009661A1 (de) 2006-08-31 2008-03-13 Carl Zeiss Sms Gmbh Verfahren und Vorrichtung zur ortsaufgelösten Bestimmung der Phase und Amplitude des elektromagnetischen Feldes in der Bildebene einer Abbildung eines Objektes

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