Method and apparatus for carrying out a time-resolved inter- ferometric measurement

Background of the invention

The invention inter alia relates to a method for carrying out a time-resolved interferometric measurement comprising the steps of generating at least two coherent waves, overlapping said at least two coherent waves and producing an interfer ^¬ ence pattern, measuring the interference pattern for a given exposure time, thereby forming measured interference values, and analyzing the measured interference values and extracting amplitude and/or phase information from the measured inter ^¬ ference values.

It is known in the art that a method as described above may be used in transmission electron microscopy systems, for in ^¬ stance. Transmission electron microscopy is a key method for the understanding of materials on the nanoscale, as it grants access to structural or atomic causes of macroscopic observa ^¬ tions. Electron holography (EH) even deepens this microscopic insight, as it directly measures the associated electric and magnetic fields with the same spatial resolution. So far, EH is limited to static specimen. The extension to dynamic proc ^¬ esses is challenging, as the time-resolution of EH is limited by relatively long exposure times (typically in the seconds range), which are needed to obtain data well above noise.

Objective of the present invention

An objective of the present invention is to provide a method and apparatus for carrying out a time-resolved interferomet- ric measurement with increased time-resolution despite con ^¬ straints imposed by relatively long exposure times.

Brief summary of the invention

An embodiment of the invention relates to a method for carry ^¬ ing out a time-resolved interferometric measurement compris ^¬ ing the steps of

- generating at least two coherent waves,

- overlapping said at least two coherent waves and producing an interference pattern,

- measuring the interference pattern for a given exposure time, thereby forming measured interference values, and

- analyzing the measured interference values and extracting amplitude and/or phase information from the measured in- terference values,

wherein

- in at least one time segment, hereinafter referred to as disturbed time segment, of the exposure time, the inter ^¬ ference pattern is intentionally disturbed or destroyed such that the corresponding measured interference values describe a disturbed or destroyed interference pattern,

- in at least one other time segment, hereinafter referred to as undisturbed time segment, of the exposure time, the interference pattern is undisturbed or at least less dis- turbed compared to the disturbed time segment such that the corresponding measured interference values describe an undisturbed or less disturbed interference pattern,

- the measured interference values that were measured during the entire given exposure time, are filtered, wherein those interference values that were measured during the at least one disturbed time segment, are reduced, suppressed or discarded, and - the filtered interference values are analyzed and the am ^¬ plitude and/or phase information is extracted from the filtered interference values. According to this embodiment, the exposure time is divided into a at least one disturbed time segment and at least one undisturbed disturbed time segment. By filtering the informa ^¬ tion that is related to the at least one undisturbed dis ^¬ turbed time segment, the sought-after amplitude and/or phase information solely relates to the at least one undisturbed disturbed time segment which is smaller than the entire given exposure time. Therefore the resulting time-resolution is smaller than the exposure time. In the at least one disturbed time segment, the interference pattern may be disturbed or destroyed by shifting the wave fronts of the coherent waves relative to each other. Alterna ^¬ tively or additionally, the interference pattern may be dis ^¬ turbed or destroyed by tilting the coherent waves relative to each other. The shifting and/or tilting may be carried out in a continuous fashion.

Said step of filtering the measured interference values is preferably carried out in the Fourier space and comprises: - subjecting the sequence of interference values that were measured during the entire given exposure time, to a Fou ^¬ rier analysis and calculating transformed values in the Fourier space,

- selecting one side band of the transformed values in the Fourier space, and

- subjecting the transformed values of the selected side

band to an inverse Fourier analysis and thereby forming the filtered interference values. The coherent waves are preferably overlapped by an overlap device. The overlap device may be a biprism. During the at least one disturbed time segment, a noise sig ^¬ nal is preferably applied to the overlap device. The noise signal may be a white noise signal.

The biprism preferably comprises a filament that is on a first electrostatic potential and bracketed by two counter electrodes. The two counter electrodes are preferably on electrostatic potentials that are different from the first electrostatic potential. The noise signal is preferably ap ^¬ plied to the filament.

The method described above can be used in electron holography systems where the required exposure times are quite long (typically in the range of a few seconds) in order to in ^¬ crease the time-resolution. The time-resolution will be de- termined by the duration of the undisturbed time segments, only .

Alternatively, other types of coherent waves such as, for in ^¬ stance, coherent electromagnetic waves, coherent pressure waves (e.g. coherent acoustic or water waves) or other types of coherent particle waves may be used to generate the inter ^¬ ference pattern.

A further embodiment of the present invention relates to an apparatus for carrying out a time-resolved interferometric measurement comprising

- a source for generating at least two coherent waves, - an overlap device for overlapping said at least two coher ^¬ ent waves and for producing an interference pattern,

- a measurement device for measuring the interference pat ^¬ tern for a given exposure time, thereby forming measured interference values, and

- an analyzer for analyzing the measured interference values and extracting amplitude and/or phase information from the measured interference values,

- wherein the apparatus comprises a temporal interference switch or gate which is configured

- to disturb or destroy the interference pattern in at

least one time segment, hereinafter referred to as dis ^¬ turbed time segment, of the given exposure time such that the corresponding measured interference values de- scribe a disturbed or destroyed interference pattern, and

- to disturb the interference pattern less or leave it un ^¬ disturbed in at least one other time segment, hereinaf ^¬ ter referred to as undisturbed time segment, such that the corresponding measured interference values describe an undisturbed or less disturbed interference pattern, and

- wherein the analyzer is configured to filter the measured interference values that were measured during the entire given exposure time, wherein those interference values that were measured during the at least one disturbed time segment, are reduced, suppressed or discarded, and to ana ^¬ lyze the filtered interference values in order to extract the amplitude and/or phase information from the filtered interference values. By dividing the exposure time into at least one disturbed time segment and at least one undisturbed disturbed time seg ^¬ ment and by filtering the information that is related to the at least one undisturbed disturbed time segment, the sought- after amplitude and/or phase information may be restricted to the at least one undisturbed time segment which is smaller than the entire exposure time. As such, the time-resolution is disentangled from the exposure time. The apparatus may be an electron holography system.

The temporal interference switch or gate preferably comprises a noise generator which is connected with the overlap device and configured to apply a noise signal to the overlap device during the at least one disturbed time segment.

The analyzer preferably comprises

- a Fourier unit configured to subject the sequence of in ^¬ terference values that were measured during the entire given exposure time, to a Fourier analysis and to calcu ^¬ late transformed values in the Fourier space,

- a Fourier space filter unit configured to select one side band of the transformed values in the Fourier space, and

- an inverse Fourier unit configured to subject the trans- formed values of the selected side band to an inverse Fou ^¬ rier analysis and thereby form the filtered interference values .

Brief description of the drawings

In order that the manner, in which the above-recited and other advantages of the invention are obtained, will be read ^¬ ily understood, a more particular description of the inven ^¬ tion briefly described above will be rendered by reference to a specific embodiment thereof, which is illustrated in the appended figures. Understanding that these figures depict only a typical embodiment of the invention and is therefore not to be considered to be limiting of its scope, the inven ^¬ tion will be described and explained with additional speci ^¬ ficity and detail by the use of the accompanying drawings in which

Figure 1 shows an exemplary embodiment of an electron

holography system.

Figure 2 shows an exemplary control signal that may be

used to control an overlap device of the electron holography system of Figure 1.

Figure 3 shows an exemplary distribution of transformed measured interference values in the Fourier space .

Figure 4 shows the transformed interference values of Fig ^¬ ure 3 after selecting a single sideband in the Fourier space.

Detailed description of a preferred embodiment

A preferred embodiment of the present invention will be best understood by reference to the drawings, wherein identical or comparable parts are designated by the same reference signs throughout .

The following more detailed description of the exemplary em ^¬ bodiment is not intended to limit the scope of the invention, but is merely representative of a presently preferred embodi ^¬ ment of the invention. For instance, the present invention is not limited to electron holography systems as described here ^¬ inafter in further detail. The present invention may also be used in systems which are based on or use other types of co ^¬ herent waves such as, for instance, coherent electromagnetic waves, coherent pressure waves (e.g. coherent acoustic or wa ^¬ ter waves) or other types of coherent particle waves.

Figure 1 shows an exemplary embodiment of an apparatus 10 for time-resolved interferometric measurements. The apparatus 10 may form or be comprised by an electron holography system.

The apparatus 10 comprises a source 20 for generating two co ^¬ herent electron waves, which are hereinafter referred to as reference wave RW and object wave OW. The source 20 comprises an electron emitter 21 which emits a first partial electron wave Wl and a second partial electron wave W2. The first par ^¬ tial electron wave Wl is transmitted through vacuum and forms the reference wave RW. The second partial electron wave W2, which is coherent with the first partial electron wave Wl, passes an object 22 and forms the object wave OW.

The reference wave RW and the object wave OW passes an objec ^¬ tive 30 and an overlap device 40. The overlap device 40 over ^¬ laps the reference wave RW and the object wave OW and pro- duces an interference pattern IP that is measured by a meas ^¬ urement device 50. Each measurement cycle lasts a given expo ^¬ sure time T and generates measured interference values I(x,y) in case of a two-dimensional interference pattern. In the exemplary embodiment of Figure 1, the overlap device

40 is a biprism comprising a filament 41 that is bracketed by two counter electrodes 42 and 43. The filament 41 is on a first electrostatic potential. The two counter electrodes 42 and 43 are on electrostatic potentials that are different from the first electrostatic potential. For instance, the two counter electrodes 42 and 43 can be on ground potential, whereas the first electrostatic potential may be positive po- tential relative to ground potential.

The apparatus 10 further comprises a temporal interference switch or gate 60. The temporal interference switch or gate 60 disturbs or destroys the interference pattern IP in at least one time segment, hereinafter referred to as disturbed time segment [0, tl] (see Figure 2), of the given exposure time T such that the corresponding measured interference val ^¬ ues I(x,y) describe a disturbed or destroyed interference pattern IP .

In at least one other time segment, hereinafter referred to as undisturbed time segment [tl, t2] (see Figure 2), the tem ^¬ poral interference switch or gate 60 disturbs the interfer ^¬ ence pattern IP less or leaves it undisturbed.

For instance, the temporal interference switch or gate 60 may be a mechanical device which mechanically moves the apparatus or parts thereof and thereby influences the interference pat ^¬ tern IP mechanically. In the embodiment of Figure 1, the tem- poral interference switch or gate 60 is formed by the overlap device 40 and a noise generator 61 which controls the overlap device 40 via a control signal S. The control signal S may be a voltage signal that modulates the electric potential of the filament 41. The control signal S is depicted in Figure 2 versus time in an exemplary fashion.

During the disturbed time segments [0, tl] (see Figure 2) of the given exposure time T, the noise generator 61 applies an electric noise signal to the filament 41 such that the elec ^¬ trostatic potential of the filament is unstable and the over ^¬ lap functionality of the biprism is jeopardized. During the undisturbed time segments [tl, t2] (see Figure 2) of the given exposure time T, the noise generator does not apply noise to the filament 41 and the biprism can overlap the waves RW and OW and generate the interference pattern IP in the usual way.

Furthermore, the apparatus 10 comprises an analyzer 70 for analyzing the measured interference values I(x,y) and ex ^¬ tracting amplitude and/or phase information from the measured interference values I(x,y) . To this end, the analyzer accord- ing to the exemplary embodiment of Figure 1 comprises a Fou ^¬ rier unit 71, a Fourier space filter unit 72, an inverse Fou ^¬ rier unit 73 and an extraction unit 74.

The Fourier unit 71 subjects the sequence of interference values I(x,y) that were measured during the entire given ex ^¬ posure time T, to a Fourier analysis and calculates trans ^¬ formed values F(I(x,y)) in the Fourier space.

Figure 3 shows an exemplary distribution of the transformed values F(I(x,y)) in the Fourier space. The transformed values F(I(x,y)) form two side bands SB1 and SB2 in the Fourier space. The two side bands SB1 and SB2 are arranged symmetri ^¬ cally with respect to a central band ZB. The two side bands SB1 and SB2 correspond to the undisturbed time segment [tl, t2] (see Figure 2), in which the temporal interference switch or gate 60 does not destroy the interference pattern IP. In contrast, the other areas outside the sidebands SB1 and SB2 are influenced by the noise which is applied to the filament 61 during the disturbed time segment [0, tl] .

The Fourier space filter unit 72 selects one of the side bands SB1 or SB2 of the transformed values in the Fourier space. The selection may be based on image recognition meth ^¬ ods or neural networks known in the art .

Figure 4 shows the selected side band SB1 in the Fourier space after the selection process. In Figure 1 and 4, the transformed values of the selected side band SB1 are desig ^¬ nated by reference numeral F' (I(x,y)). The selection of the side band SB1 corresponds to filtering the measured interfer ^¬ ence values that were measured during the entire given expo- sure time T, wherein those interference values that were measured during the disturbed time segment [0, tl] are re ^¬ duced, suppressed or discarded.

The inverse Fourier unit 73 subjects the transformed values F' (I(x,y)) of the selected side band SB1 to an inverse Fou ^¬ rier analysis and thereby forms filtered interference values I' (x,y) ) .

The extraction unit 74 extracts amplitude and/or phase infor- mation A, φ from the filtered interference values I' (x,y) . The extracted values A and φ may be calculated as follows:

A = I I' (x,y) I

φ = arg (I ' (x, y) )

As already emphasized above in the introductory part, the present invention is not limited to electron holography sys ^¬ tems. The present invention may also be used in systems which