WO2021151792A1

WO2021151792A1 - Method and device for characterising a coherent light field in amplitude and phase

Info

Publication number: WO2021151792A1
Application number: PCT/EP2021/051457
Authority: WO
Inventors: 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
Priority date: 2020-01-28
Filing date: 2021-01-22
Publication date: 2021-08-05
Also published as: DE102020101989A1

Abstract

The invention relates to a method and a device for characterising a coherent light field (1) in amplitude and phase, the method having the following steps: • providing an object (10) with known transmission function T(x,y) for the light field (1) in amplitude and phase; • irradiating the object (10) with the coherent light field (1) to be characterised in an object plane (11) in which the object (10) is arranged; • detecting an intensity distribution l'(x,y) of the diffraction image (22) of the light field (1) spatially behind the irradiated object (10) in a detector plane (21) by means of a flat detector (20); • reconstructing the light wave function u(x,y) after passage of same through the object (10) by iterative determination of phase and amplitude of the light wave from the intensity distribution l'(x,y) detected; • calculating the light wave (1) before passage through the object by applying the known transmission function T(x,y) to the reconstructed light wave function u(x,y). According to the invention, an object with a structure region (12) is used as the object (10), the structure region (12) of the object (10) being defined by a transmission mask which provides for only strong absorbing regions (13) with a transmission T ≈ 0 and non-absorbing regions (14) with a transmission of T ≈ 1.

Description

Method and device for characterization of a coherent light field in amplitude and phase 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). Knowing the exact intensity distribution (proportional to the square of the amplitude) and the wavefront (phase) of light fields is of enormous importance for many applications that use light as a (examination) tool or as an information carrier. In these applications, light fields (light radiation) are often focused and directed at objects to be examined (samples) or optics whose properties are to be determined or which are to be adjusted. For other applications, e.g. for scientific experiments, 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. When examining objects, 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 is known 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. In the publication F. Zhang, J. M. Rodenburg, "Phase retrieval based on wave-front relay and modulation", Phys. Rev. B 82, 1-4 (2010), for example, describes such a method in which an entrance aperture and, in addition, a modulator with a complex transmission function are used as the object. This method can be used for coherent light fields, i.e. light waves of the light field with the same frequency and phase.

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.

Nakajima, N., "Experimental verification of coherent diffractive imaging by a direct phase retrieval method with an aperture-array filter", OPTICS LEITERS, 36, 2011, 12, 2284-2286, describes a method for reconstructing an object by means of a coherent scatter pattern , in which a single diffraction image is evaluated in a non-iterative process. A plate with aperture arrangements is placed in the beam path between the object and the detector. The object is then reconstructed from the diffraction image measured in the detector using the known transmission function of the plate with diaphragm arrangements. To do this, the light field of the light source must be known in order to reconstruct the object. The present invention, on the other hand, relates to the case in which the amplitude and phase of the light field of the light source before it hits an object is not known.

The functional principle of the known coherent imaging is explained in a generally understandable manner with reference to FIGS. 1 and 2 (see end of the document): FIG. 1 shows a light field 101 which is mathematically described by the complex function uo (x, y) as a light wave uo (x, y) = SQRT (lo (x, y)) ^* exp (i ^* phi ₀ (x, y)) Here lo (x, y) describe the intensity distribution of the light wave and phio (x, y) describe the phase of the light wave in a plane perpendicular to the direction of propagation 100 of the light wave.

At the location where the light field 101 hits the object 110 (also referred to as a sample) (ie in the object plane 111), the light wave now has the properties uo (x, y). The diffraction image 122, which is recorded by a detector 120 (area detector) after the light field 101 has passed through the object 110 in the detector plane 121, is described by the complex function u '(x, y): u' (x, y) = SQRT (l '(x, y)) ^* exp (i ^* phi' (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.

However, with knowledge of the experimental setup and the transmission function of the object 110, 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. First, after passing through the object, the light field u (x, y) can be at any point (x _n, y _m ) by multiplying uo (xn, y _m ) with the complex transmission function of the object T (x _n, y _m ) become true: u (x _n , y) = T (x _n, y) u ₀ (x _n , ym).

Thereafter, 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. If the detector plane 121 is in the far field to the object plane 111, the propagator can be described mathematically by a Fourier transformation F (as an example for propagators). For the sake of simplicity, this far-field case is described below, which results in u '(x, y) = F (u (x, y)). 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). In principle, 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 reverse light propagation from the detector plane 121 to a (fictitious) plane 125 behind the object 110 can be described by an inverse Fourier transformation: u (x, y) = F ¹ (u '(x, y)). 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.

For this purpose, however, in addition to the detected intensity distribution l '(x, y), the unknown phase phi' (x, y) must be determined. This is implemented by a so-called phase reconstruction algorithm, with which u (x, y) can be determined in the result.

In addition, knowledge of the transmission function T (x, y) of the object 110 is necessary in order to detect the light field 101 in the object plane 111 before it passes through the object according to uo (xn, ym) = u (x _n , ym) / T ( x _n, y _m ) from u (x, y). This then characterizes the light wave 101 uo (x, y) before the interaction of the light field 101 with the object 110.

The determination of the unknown phase phi ‘(x, y) by a phase reconstruction algorithm is illustrated in FIG.

For this purpose, the measured intensity distribution l '(x, y) is initially used with a random (arbitrarily selected) phase distribution phi' (x, y) i _nitiai to form an initial assumption 130 for the complex light wave function u '(x, y) i _nitiai = SQRT (l '(x, y)) ^* exp (i ^* phi' (x, y) initiai) added, which describes the light field in the detector plane 121. This is illustrated in the first line of FIG.

The term "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.

Then the light field 101 (i.e. the complex light wave function u (x, y)) behind the object 110, i.e. in the plane 125 behind the object 110 and thus also behind the object plane 111, is determined iteratively. 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.

In a first step, the light propagation from the detector plane 121 to the plane 125 is calculated. The complex light field u (x, y) after passing through the object 110 (ie in the plane 125) is then calculated using the inverse Fourier Transformation F ^_1 from the diffraction image 122, ie the light field u '(x, y) in the detector plane 121 with the measured intensity distribution l' (x, y) to u (x, y) = P ¹ (u '(x, y )).

This then becomes the starting point for the first or each further iteration and can accordingly be referred to as an iteration support point or as u (x, y,) _q , where q is the index of the iteration, ie runs from q = 1 to N for N iterations .

As long as the iteration is carried out (ie the running index q <N), a support condition P _Su (support constraint) is applied to the complex light field u (x, y) _q in level 125, the support condition being e.g. on the shape and size of the object 110 in the object plane 111 results. Then 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. | u '(x, y) | = SQRT (l '(x, y)).

The loop shown in FIG. 2 in the middle of the lower line is iteratively run through several times (for a total of N iterations). An iteration loop q consists in the application of the steps described mathematically below: u (x, y) q = F ¹ (u '(x, y) q) and u' (x, y) _q = F (u (x, y) _q ), whereby the supporting condition P _SUp and the modulus condition Pmo _{d are} applied accordingly. By running through this loop multiple times, 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)} .

In Figure 2 it is provided that the iteration loop is exited if, when applying the modulus condition P _{mod, it is} established that the reconstruction of an amplitude u '(x, y) _final with the measured amplitude sqrt (l' (x, y)) agrees with sufficient (desired) accuracy. After leaving the iteration loop, the light wave function u (x, y) _{finai is} transformed back into the object plane 111 with the inverse Fourier transformation F ¹ from the detector plane 121 and an image 140 of the object 110 (u (x, y)) is _final ) thus reconstructed.

Then, after passing through the object, 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.

In the prior art, this method of single-shot beam characterization was demonstrated only with complex objects whose amplitude and phase transmission function was precisely known. In particular, the transmission must be known for each wavelength at which measurements are to be made. Especially with exotic wavelengths, for example in the XUV or X-ray range, the Production of such objects and the characterization of their transmission function are very complex and difficult. Since the beam characterization should often take place with strongly focused beams (light fields), it must be done on very small spatial scales. The size of the objects ultimately limits the spatial resolution of the beam characterization method. The more complex the object, the more difficult it is to scale the object to small sizes and to characterize it precisely.

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.

This object is achieved by a method for characterizing a coherent light field in amplitude and phase with the following method steps:

• Providing an object with known transmission function T (x, y) for the light field in amplitude and phase

• Irradiating the object with the coherent light field to be characterized in an object plane in which the object is arranged

• Detection of an intensity distribution l '(x, y) of the diffraction image of the light field spatially behind or after the irradiated object in a detector plane by means of an area detector

• Reconstructing the light wave function u (x, y) (as a mathematically complex function, ie as a function in complex space) after it has passed through the object by iteratively determining the phase phi (x, y) and amplitude l (x, y) of the light wave from the detected intensity distribution by repeatedly calculating the propagation of the light wave between the detector plane and the object plane (after the light wave has passed through the object, the above for clarification also as a plane io behind the object) by applying propagators and in verse propagators and applying boundary conditions for the diffraction image in the detector plane and in the object plane (after the light wave has passed through the object)

• Calculate the light wave before it passes through the object (i.e. the light wave function uo (x, y)) by applying the known transmission function T (x, y) to the reconstructed light wave function u (x, y).

When using this method, which is already known in principle, it is proposed to use an object whose structural area is or is defined by a transmission mask that only has strong absorbing areas (in the sense of being at least almost completely opaque to the light wave) with a transmission T (x, y) «0 and non-absorbing areas (in the sense of optically at least almost completely transparent areas for the light wave, for example openings) with a transmission of T (x, y)« 1. Such a structure of the object only effects an amplitude modulation through the diffraction of the light wave on the object. A change in the phase of the light wave at the object does not occur. This facilitates the numerical calculation of the propagation of the light wave between the object plane and the detector plane, because the transmission function can be described simply (digitally with the values 0 and 1).

In addition, according to a preferred embodiment of the proposed method, all impermeable areas with T = 0 can be used as support constraint P _SUp in the phase reconstruction, which makes the convergence of the algorithm faster and more reliable. This enables faster and more accurate measurements. Such transmission masks are also easy to manufacture. Thus, 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.

According to a further aspect, 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. In other words, 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. In other words, there is no non-absorbing area (opening) outside the contour curve. This area lying outside the closed contour curve is correspondingly the diaphragm area, which completely absorbs the parts of the light wave hitting the diaphragm area in the sense that these parts of the light wave are not detected in the area detector. According to one embodiment, 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. As an illustrative example, without this being intended to restrict the type and nature of a structural area and the aperture area in any way, 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. In this case, 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. Thus, it is precisely the matrix arrangement of the openings with the highly absorbent areas between the openings that forms the structural area. The strongly absorbing area outside the closed contour curve surrounding the matrix arrangement of the openings forms the diaphragm area.

In this way, 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).

This can also be realized by an object in the form of a metal film which has no openings outside the structural area. This results in a maximum size of the measurement field in the object plane that produces the diffraction image. This ensures a convergence of the iterative determination of the phase of the light field in the sense described above.

Furthermore, an intensity of u (x, y) = 0 of the light field function can be assigned to the light field function as a boundary condition (all or a selection of the) strongly absorbing areas of the object (in particular the structural area of the object) with T «o. This accelerates the convergence of the iterative reconstruction algorithm (inversion algorithm). These 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.

In practice, this can be done in such a way that the light wave function u (x, y) in the object plane is set to the value u (x, y) = 0 at all locations (x, y) of the structural area with a transmission of T «o . Since all other locations in the structure area have the value T «1, this represents a determination of the entire structure of the object.

In order to identify the areas with T «o in the object, 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.

Instead of a metal film, 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.

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.

In addition, additional statements about the coherence of the radiation can be obtained from the contrast of the diffraction image. The spatial and temporal coherence of the radiation can be determined by analyzing the interference contrast in the diffraction image, especially since the selected transmission structure generates diffraction images with sharp maxima and minima with fully coherent illumination (contrast = max-min / max + min = 1). While the spatial coherence reduces the contrast in the entire diffraction image (contrast <1), a limited temporal coherence causes a reduction in the contrast for increasing diffraction angles. This happens as soon as the transit time differences between partial waves, which come from both outer ends of the sample (object), come to the order of magnitude of the temporal coherence length. This transit time difference is calculated as ds = sin (theta) * a, where theta is the diffraction angle and a is the size of the sample.

Furthermore, the invention relates to a device for characterizing a coherent light field in amplitude and phase with the following elements:

• Object with known transmission function for the light field in amplitude and phase in an object plane in the beam path of the light field;

• Area detector behind the object in the beam path of the light field diffracted on the object in a detector plane, the area detector for Detecting an intensity distribution of the diffraction image of the light field is formed;

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.

According to the invention, 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. In a preferred embodiment, 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.

According to a particularly preferred embodiment of the device according to the invention, it can have the object and the area detector as the only optical elements (ie elements that interact with the light field). This makes the device very easy to adjust. 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. According to a preferred embodiment, 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). In possible designs of the area detector, 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).

By means of suitable filters, 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).

Thus, the invention described can preferably be used to adjust objects in optical structures and / or to adjust light sources in optical structures.

Further advantages, features and possible applications of the invention also emerge from the following description of exemplary embodiments and the drawing. All of the features described and / or shown in the figures belong together or in any technically meaningful combination to the subject matter of the invention, regardless of how they are summarized in the described or illustrated exemplary embodiments or in the claims.

Show it:

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

2 schematically shows the method steps for reconstructing the light wave function u (x, y) of the light field with the basically known method of coherent imaging; and

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.

Figure 1 and Figure 2 have already been described in detail to explain the background of the invention. These steps are also part of the method according to the invention and are no longer described in detail at this point.

The method proposed according to the invention is described in a preferred embodiment with reference to FIG. 3, the features already described with reference to FIGS. 1 and 2 no longer being explained in detail. The person skilled in the art understands that he can also use these basically known method steps in the method according to the invention in a device as is shown schematically in FIG. The basic process sequence is similar, and the same reference numerals, subtracted by 100, are used to designate comparable features, which are also entered in FIG.

_{As in FIG. 2, an initial light wave function u '(x, y) i nitiai is} determined from the intensity distribution l' (x, y) detected in the detector 20 and any phase phi '(x, y). 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.

For the strongly absorbing areas 13 there is no transmission of the light wave 1, or the transmission is so low that a transmission T «o. 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.

As indicated by a shift in the arrangement of the openings in part of the object 10 (in the illustration in the upper right quadrant of the matrix arrangement of the openings) compared to the arrangement of the other openings, 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.

Outside of the structural region 12 of the object 10 shown in FIG. 3, 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.

Due to the described structure of the structural region 12 of the object 10, 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.

The iteration is carried out as already described with reference to FIG. As a result, 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. From the determined light wave function u (x, y) behind the object 10 (ie in the plane 25 according to FIG. 1), 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.

According to the invention, 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.

List of reference symbols:

I light field

10 object

I I object level

12 Structure area

13 highly absorbent area

14 non-absorbent area

20 area detector

21 detector level

22 diffraction pattern

40 image of the object

100 Direction of propagation of the light field or the light wave

101 light field

110 object

I I I object level

120 area detector

121 detector level

122 diffraction pattern

125 plane behind the object 140 image of the object u (x, y) light wave or light wave function of the light field uo (x, y) light wave in the object plane u '(x, y) light wave in the detector plane

F as a Fourier transformation described propagator for the light wave between the object and detector

F ^{1 described} as an inverse Fourier transformation propagator for the light wave between detector and object

N number of iterations of the reconstruction algorithm

Claims

Expectations:

1. Process for characterizing a coherent light field (1) in amplitude and phase with the following process steps:

• Providing an object (10) with known transmission function T (x, y) for the light field (1) in amplitude and phase;

• irradiating the object (10) with the coherent light field (1) to be characterized in an object plane (11) in which the object (10) is arranged;

• Detection of an intensity distribution l '(x, y) of the diffraction image (22) of the light field (1) spatially behind the irradiated object (10) in a detector level (21) by means of an area detector (20);

• Reconstruction of the light wave function u (x, y) after it has passed through the object (10) by iteratively determining the phase and amplitude of the light wave from the recorded intensity distribution l '(x, y) by repeatedly calculating the propagation of the light wave (1) between the detector plane (21) and the object plane (11) by applying propagators (F) and inverse propagators (F ^_1 ) and applying boundary conditions for the diffraction image in the detector plane (21) and in the object plane (11) );

• Calculating the light wave (1) before it passes through the object by applying the known transmission function T (x, y) to the reconstructed light wave function u (x, y); characterized in that an object with a structure area (12) is used as the object (10), the structure area (12) of the object (10) being defined by a transmission mask which only contains strongly absorbing areas (13) with a transmission T. «O and non-absorbing areas (14) with a transmission of T« l provides.

2. The method according to claim 1, characterized in that an object is used as the object (10), the structure area (12) of which is surrounded by a strongly absorbing aperture area which only provides strongly absorbing areas with a transmission T «o.

3. The method according to claim 1 or 2, characterized in that strongly absorbing areas (13) of the object (10) with T «o an intent of u (x, y) = 0 is assigned to the light field function as a boundary condition.

4. The method according to claim 3, characterized in that strongly absorbing areas (13) of the object (10) are determined by examining and measuring the object (10).

5. The method according to claim 4, characterized in that all strongly absorbing areas (13) of the object (10) are detected in the structure area (12) and are assigned the boundary condition of an intensity of u (x, y) = 0 of the light field function.

6. The method according to any one of the preceding claims, characterized in that an object (10) with an asymmetrically shaped structure area (12) is used.

7. The method according to any one of the preceding claims, characterized in that the characterization of the light field (1) is carried out with the acquisition of only one diffraction image (22).

8. Device for characterizing a coherent light field (1) in amplitude and phase with the following elements: • Object (10) with known transmission function T for the light field (1) in amplitude and phase in an object plane (11) in the beam path of the light field (1);

• Area detector (20) behind the object (10) in the beam path of the object (10) diffracted light field (1) in a detector plane (21), the area detector (20) for detecting an intensity distribution l '(x, y) des Diffraction image (22) of the light field (1) is formed;

• Computing device which is connected to the area detector (20) and is set up to carry out the method described in claims 1 to 7 for reconstructing the light wave function u (x, y); characterized in that the object (10) has a structure area (12), the structure area (12) of the object (10) being defined by a transmission mask which only contains strongly absorbing areas (13) with a transmission T «o and provides non-absorbent areas (14) with a transmission of T «1.

9. The device according to claim 8, characterized in that the object (10) has a strongly absorbing aperture area which only provides strongly absorbing areas with a transmission T «o and which surrounds the structural area (12).

10. The device according to claim 8 or 9, characterized in that the object (10) has an asymmetrically designed structural area (12).

11. Device according to one of claims 8 to 10, characterized in that the device has the object (10) and the area detector (20) as the only optical elements.

12. Device according to one of claims 8 to 11, characterized in that the area detector (20) has a pixelated sensor.

13. Device according to one of claims 8 to 11, characterized in that the area detector (20) is designed by means of a filter for this purpose

Detect light of the light field (1) wavelength-selective.

14. Use of the method according to one of claims 1 to 7 and / or a device according to one of claims 8 to 13 for adjusting objects (10) in optical structures and / or for adjusting light sources in optical structures.