SUBWAVELENGTH IMAGING AND IRRADIATION WITH ENTANGLED PARTICLES

BACKGROUND OF THE INVENTION

[0001] The present invention relates to a method and an apparatus for using entangled particles. The present invention further relates to a microscope and a lithography apparatus.

[0002] In order to implement an N-fold increase in resolution in imaging and lithography, the following ingredients were conventionally needed: either (a) creation of an entangled state of the form |ψ(N)> with high photon number N, or (b) the availability of an N- particle absorbing medium able to detect N photons at a given position simultaneously, or both. As of yet, no measures were known to overcome these disadvantages. Thus, what is needed are techniques to allow for an ν-fold increase over the classical resolution limit which overcome these restrictions.

BRIEF DESCRIPTION OF THE INVENTION

[0003 ] In one embodiment of the present invention, a method is provided for using one particle out of N particles for irradiating a target. It comprises the steps of providing a radiation source with N incoherent emitters emitting a radiation, of detecting particles of said radiation by using N-I detectors located at N-I different positions, and of opening a particle barrier in dependence of an occurrence of single detections on all N-I detectors within a predetermined time range to allow a passage of said one particle to reach said target.

[0004] In another embodiment of the present invention, an apparatus for irradiating a target is provided, which comprises a radiation source with N incoherent emitters, N-I particle detectors located at N-I different positions, a discriminator adapted for identifying single particle detection events on all N- 1 detectors within a predetermined time range from

other particle detection events, and a particle barrier adapted to be opened in dependence of the discriminator.

[0005] In another embodiment of the present invention, a method for using N particles for investigating an object is provided, wherein N is greater than or equal to 2, which comprises the steps of fixing the position of the object, of detecting particles of a radiation emitted by the object by using N detectors located at N different positions, and of discriminating single particle detections detected on all N detectors within a predetermined time range from other particle detection events.

[0006] In another embodiment of the present invention, an apparatus for investigating an object is provided, which comprises a fixing unit for fixing the position of the object, N particle detectors located at N different positions for detecting particles of a radiation emitted by the object, wherein N is greater than or equal to 2, and a discriminator adapted for discriminating single particle detection events on all detectors within a predetermined time range from other particle detection events .

[0007] As was laid out, the present invention uses an entirely different scheme to achieve an optical resolution of λ/N as in the prior art. The method involves neither of the requirements of the prior art as laid out above. As with path-entangled number states, this allows for an N-fold increase in resolution compared to the first order intensity correlation function G ⁽¹⁾ (r) while keeping a contrast of 100%. As the N particles are recorded by distinct analyzers, only a single particle is registered at each detector. This means that no N-particle absorbing material is needed in this scheme, but only detectors suitable to detect one -particle events.

[0008] Further aspects, advantages and features of the present invention are apparent from the dependent claims, the description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] A full and enabling disclosure of the present invention, including the best mode thereof, to one of ordinary skill in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures wherein:

Fig. 1 : Generalised setup and coordinate system for N trapped emitters, wherein N emitters are regularly localised in an ion trap. The figure shows the case of N =

4, with a detector at position i\ at an angle Q ₁ with respect to an axis perpendicular to the row of emitters .

Fig. 2 A schematic view of an apparatus according to an embodiment of the invention. N identical two-level emitters at Ri, . . . ,R _N spontaneously emit N particles after excitation by a laser pulse. The particles are recorded in the far field by N-I detectors positioned at ri, . . . , r _N -i. The figure exemplifies the case N = 4. Three detectors are combined with one particle barrier.

Fig. 3: A schematic view of an embodiment of the invention with N=2 emitters. One detector and a target are moved circumferentially around the two emitters with angular velocities, wherein the angular velocity of the detector is m times greater than that of the target. Shown are cases for m = 2, 4, 8, and 16.

Fig. 4: Another embodiment of the invention, wherein N emitted particles are recorded by N detectors in the far field to investigate an object constituted by N emitters.

Fig. 5: A schematic view of an embodiment wherein three detectors are arranged sharing the same angle Q ₁ at different angles ψi .

Fig. 6: A schematic view of Young's double slit experiment.

DETAILED DESCRIPTION OF THE INVENTION

[0010] Reference will now be made in detail to the various embodiments of the invention, one or more examples of which are illustrated in the figures. Each example is provided by way of explanation of the invention, and is not meant as a limitation of the invention. For example, features illustrated or described as part of one embodiment can be used on or in conjunction with other embodiments to yield yet a further embodiment. It is intended that the present invention includes such modifications and variations.

[0011] In order to fully lay out the principle of the present invention, a theoretical approach to a specific example is provided in the following. The specific example includes the use of atoms as emitters and photons as radiation particles. However, it is important to note that the invention is not limited to the described system of photons and atoms. Rather, various kinds of radiation may be used, including photons, electrons, protons, neutrons, alpha particles, atoms, molecules and ions. At the same time, the emitters or scattering sites can be selected from the group consisting of atoms, ions, molecules, quantum dots, and Josephson circuits.

[0012] It is known that nonclassical correlations exist in the radiation of two atoms that are coherently driven by a continuous laser source. These include second order intensity correlations of spontaneously emitted photons, which are proportional to the conditional probability to detect a photon at r ₂ and time t + τ, given that a photon has been recorded at ri and time t. It can be shown analytically that those photons can exhibit a spatial interference pattern (in the second order correlation function) not present in a classical treatment so that bunched and antibunched light is emitted in different spatial directions, even when the atoms are initially uncorrelated. The phenomena show up even without any interatomic interaction.

[0013] The spatial interference patterns for the second order correlation function are of particular interest. One of the underlying ideas of the present invention was to find spatial interference patterns of higher order correlations in the fluorescence radiation emitted by trapped particles and to utilize them for imaging and manipulation purposes. As will be shown, this allows surpassing the resolution limits of classical optics. This is achieved by applying technical measures which are way easier to implement than methods known from the art.

[0014] Fig. 6 shows a schematic view of Young's double slit experiment. Shown are a light source 100, a collimation slit 110, a double slit 120, light beams 140, 150 as examples, and a far-field interference pattern I(r) ~ G ⁽¹⁾ (r) 130. In this experiment (or in a Mach Zehnder interferometer), the probability G^(r) to detect a photon at position r results from the interference of the two possible paths a single photon can take to reach the detector. This is expressed by the state |ψ (I)) =1/V2 (| 1 )U|0) _L +|0>U| 1> _L ) where the subscript L(U) denotes the lower (upper) arm of the interferometer. Variation of the detector position leads to a modulation of the form G^(r) = 1 + cos δ(r), where δ(r) = kd sin θ(r) is the optical phase difference of the waves emanating from the two slits and k, d and θ(r) are the wave number, slit separation and scattering angle, respectively.

[0015] Obviously, the fringe spacing of the modulation (in units of d sinθ(r)) is determined by the optical wavelength, in correspondence with the Rayleigh criterion which restricts the pattern size of the interfering beams to λ. Quantum entanglement is able to bypass the Rayleigh limit. If one considers for example the path-entangled two-photon state |ψ(2)> = 1/V2 (|2) _U |0) _L + |0) _U |2) _L ), the two-photon state |2> has twice the energy of the single photon state | 1) in a given mode. Hence, it accumulates phase two times as fast when propagating through the setup. This gives rise to a two photon absorption rate of the form G^(r, r) = 1 + cos 2δ(r) exhibiting a fringe spacing half of that of G^(r). Correspondingly, for the entangled N-photon state |ψ(N)> =1/V2 (|N) _U |0> _L + |0>u|N> _L ) the N photon absorption rate reads G ^(N) (r, . . . , r) = 1 + cos Nδ(r), displaying a fringe spacing of λ/N. This gain in resolution by a factor of N with respect to G ⁽¹⁾ (r) can be fruitfully applied for a wide range of applications, e.g., in microscopy, lithography, spectroscopy and even magnetometry.

[0016] Considered are ν identical two -level atoms excited by a single laser pulse.

After the spontaneous decay the ν resulting photons are registered by ν detectors at positions ri, . . . r _ν . In case of detection within a predetermined time interval, the Mh order correlation function can be written (up to an insignificant prefactor) as

G' ^{V )} (rj ry ) = (D ' (n ) . . . D ^' ' (r v }D{v _x ) . . £>(r ₃ )) ₍₁₎

where

[0017] Here, D is the detector operator which links the detection of a photon at i\ to the emission of a photon by one (unknown) atom of all atoms situated at R _α> α = 1, ..., N. n(iy) = Y ₁ Ir ₁ stands for the unit vector in the direction of detector i, the sum is over all atom positions R _α , k = α>o/c, with ωo the transition frequency, and σ _α ^~ = |g) _α <e| is the lowering operator of atom for the transition |e) → | g). For all atoms initially prepared in the excited state |e), one obtains from Eqs. (1) and (2):

«( \ )

^ > ^* l VS ) χ\ ~ U'ι r.v )

(3)

where

Cr _{1 1λ )} = ∑ ή _t ^, - ^{A n} . ^r .,, , ^{R ,} _

C l . ^ -= 1 " = ) ^{t l ?} ^ (4)

[0018] Equations (3) and (4) show that G ^(N) (ri, ..., r _N ) results from the interference of

N! terms, associated with all possibilities to scatter N photons from N identical atoms which are subsequently registered by N detectors. To simplify further calculations, the case of N equidistant atoms is assumed. Choosing the origin of the coordinate system in the centre of the atomic chain leads to

with u being the unit vector along the chain axis, (/the interatomic spacing andy ^' _α = -(N - l)/2, . . . , (N - l)/2 for α = 1, . . . , N (see Fig. 1). By defining

S(Ti) ~ kdn(ri ) • u ~ kd sm. θ _t

(6)

where θ; is the angle between n(r;) and the direction normal to the atomic chain (see Fig. 1), it is found

Here, j is the vector of the distances of the atoms from the origin in units of d:

and

S = (δ(rι), . . . J(r _N )) . (9)

[0019] Due to the symmetry of the configuration, the function G^ (r\, . . . , γ _N ) contains N!/2 cosine terms, each oscillating in general with a different spatial frequency. Obviously, the complexity of the expression rises rapidly with the atom number N. However, if for example the N detectors were placed in such a manner that all terms in Eq. (7) interfere to give a single cosine, one would be left with a modulation oscillating at a unique spatial frequency. The inventors have found a set of particular detector positions leading to the following general result: for arbitrary even N and choosing the detector positions such that

d(vo) = 6[V ₆ ) = ... = OU _N -! ) = — , s TT δ{r ₄ ) - δ(r _a ) - ... - (Hr _; γ _. ) - -^ ,

(10)

the Nth order correlation function G(N) as a function of detector position ri reduces to

where A _N is a constant which depends on N. For arbitrary odd N, and choosing the detector positions such that

δ(r ₂ ) = -S(T ₁ ) . δ{τ _α ) = 6(Tr ₁ ) - ... - δ(rχ ) - -T"

λ ⁷ + l

the Nth order correlation function G(N) as a function of ri reduces to

G< ^N) {π) - ,4 _λ :- [1 -f-cυsf(λ ^r + l)ό(n))].

[0020] According to Eqs. (11) and (13), for any N a correlation signal with a modulation of a single cosine is obtained , displaying the same contrast and similar fringe spacing as in the case of the maximally entangled N-photon state |ψ(N)>: for even N the fringe spacing corresponds to λ/N, for odd N it corresponds to λ/(N + 1). However, in contrast to |ψ(N)), both the necessity to generate path-entangled Fock states and the need to detect a faint multi-photon absorption signal are avoided. As in this scheme the N photons are registered by N distinct detectors, only a single photon is recorded at each detecting device.

[0021] It is emphasized that as the photons are created by spontaneous emission, the interference signal is generated by incoherent light. An achievable contrast of 100% proves the underlying quantum nature of the process, i.e., the existence of non-local correlations between the detected photons. The quantum correlations are generated by the measurement process after the detection of the first photon. In fact , just before the detection of the Nth photon, the atomic system is in an N-particle W-state with one excitation. The non-classical characteristics of this scheme are thus an example of detection induced entanglement of initially uncorrelated distant particles. To exemplify the method, the simplest situation is considered, i.e., the case of N = 2 atoms. With j=(-l/2, +1/2), it is obtained from Eq. (7):

(14)

[0022] Obviously, the modulation of the G ⁽²⁾ (ri, r ₂ )-function depends on the relative position of the two detectors (see Fig. 1): for δ(r ₂ ) = δ(ri), the second order correlation function is a constant, whereas for fixed r ₂ the two photon coincidence as a function of δ (ri) exhibits the same phase modulation and fringe spacing as G ⁽¹⁾ (r) ^m the Young's double slit experiment. The increased parameter space available for the detector positions in case of two detectors allows also to pick out the relative orientation δ(r ₂ ) = - δ(ri). In this case one gets

G ⁽²⁾ f ri - [I + cos(25(ri ))

(15)

exhibiting a phase modulation as a function of ri with half the fringe spacing of G^(r) while keeping a contrast of 100%. This corresponds to the fringe pattern achieved with the maximally entangled two-photon state |ψ(2)). The assumed condition for the direction of emission of the two photons, i.e., δ(r ₂ ) = -δ(ri), corresponds to a space-momentum correlation of the photons identical to the one present in spontaneous parametric down conversion (SPDC). This process is presently widely used for producing entangled photon pairs. Adding a beam splitter allows in addition to transform the space-momentum entangled photon pair generated by SPDC into the maximally path-entangled two-photon state |ψ(2)).

[0023] By using either correlated states, i.e., space-momentum entangled photon pairs or maximally path-entangled photon number states, sub-wavelength resolution has been obtained in several experiments, surpassing the Rayleigh limit by a factor of two, three and four. Extending these schemes to states with higher numbers of entangled photons appears however to be difficult as the use of, e.g., a X*- ^N) nonlinearity or, alternatively, N-I nonlinear X*- ²⁾ crystals in a cascaded arrangement results in very low efficiencies, dropping rapidly with increasing N. By contrast, the present scheme can be extended to N > 2 atoms straightforwardly in view of single atom trapping techniques known from the art. The complexity to produce path-entangled Fock states with high photon number N as well as the necessity of an N-photon absorbing material can thus be circumvented. Next, the third order correlation function G^(ri, r ₂ , r ₃ ) for three equidistant atoms will be examined. For arbitrary detector positions ri, r ₂ , and r ₃ it is derived from Eq. (7):

G ^{{ :} V L . I-2. r ₃ ) =— [COs(O ^' frj ) - δ( ^γ ₂ )) + cos(£(r i ) - % ₃ ) ) + i'os(dϊr ₂ ) - δ{τ ₃ )f . ₍₁₆₎

By positioning, for example, the two detectors according to Eq. (12), Eq. (16) reduces to

G ¹³ Hr ₁ ) = - ; [l + cos{4 a(r _:L ))] .

² ' (17)

[0024] Obviously, G ⁽³⁾ as a function of ri exhibits a modulation of a single cosine with a contrast of 100%, in this case with a fringe spacing of λ/4. Similarly, one finds for G^(ri) in case of the detectors placed according to Eq. (10):

G ⁽⁴⁾ (ri ) = [l + cos(4 n-(n))] . " (18)

[0025] Finally, the result will be compared with the modulation of the far field intensity G ⁽¹⁾ (ri) obtained in case of a chain of N equidistant atoms. If each atom is initially prepared in the state |φ> = 1/V2 (|g)+|e» it is derived from Eqs. (1) and (2)

λ - l

, ι I i

" ^{1 1} Vi ⁾ = - J^ ( λ - O ) C Os(O f) ^r ₁ ))

1 = 1 (19)

[0026] Equation (19) shows that (apart from an offset) G^(ri) equals the outcome of the classical grating. As is well known from this classical device, a term cos((N ^~ l) δ(ri)) indeed appears in the intensity distribution, oscillating in space with N-I times the modulation of the two slit interference pattern. However, lower spatial frequencies appear as well and contribute to G^(ri). From the point of view of microscopy , the resolution is determined by the Rayleigh limit: an object can be resolved only if at least two principal maxima of the diffraction pattern are included in the image formation (Abbe's theory of the microscope).

[0027] According to this criterion the use of G^(ri) for imaging the N atoms allows at best to resolve an interatomic spacing equal to λ. By contrast, the use of the Nth order correlation function with N detectors positioned according to Eq. (10) (or Eq. (12)) allows to resolve an atom-atom separation as small as λ/N (or λ/(N + I)) [see Eqs. (11) or (13)]. In conclusion, it was shown that N photons of wavelength λ spontaneously emitted by N atoms and coincidentally recorded by N detectors at particular positions exhibit correlations and interference properties similar to classical coherent light of wavelength λ/N. The method requires neither initially entangled states nor multi-photon absorption, only common detectors suitable for single-photon detection.

[0028] The present invention makes use of the findings described above. However, it is important to note that the invention is not limited to the described system of photons and atoms. Rather, various kinds of radiation may be used, including photons, electrons, protons, neutrons, alpha particles, atoms, molecules and ions. At the same time, the emitters or scattering sites can be selected from the group consisting of atoms, ions, molecules, quantum dots, and Josephson circuits.

[0029] Fig. 2 shows an embodiment of the invention, in which an apparatus is provided to use one particle out of N quantum entangled particles for irradiating a target. The apparatus comprises a radiation source (10) with a plurality of N incoherent emitters (20). In

this example, N is chosen to be 4. These emitters are either atoms, ions, molecules, quantum dots or Josephson circuits. They are preferably, but not necessarily arranged in a row. Typically, they are kept in the evacuated chamber (30), wherein their positions are maintained, e.g. by means of an atom or ion trap. The emitters emit radiation particles which may be chosen from the group consisting of photons, phonons, electrons, protons, neutrons, alpha particles, atoms or ions. The apparatus further comprises N-I detectors (40) to detect the emitted radiation, which are arranged in a plane with the emitters. The detectors are chosen from the various types known from the art in accordance with the type of radiation.

[0030] The detectors are connected to a discriminating device (60), which is adapted to discriminate particle detection events on all detectors within a predetermined time range. Typically, but not necessarily, the discriminating device (60) is an electronic device. Furthermore, the apparatus comprises a particle barrier (70), which is adapted to be opened in dependence of a discriminated detection on all N-I detectors. The type of the particle barrier is chosen in dependence of the type of radiation used. In the case of photons, it may for example be a LCD device. The barrier should be suitably designed to allow short opening switching times. In case of photons, these times lie in a range of nanoseconds. A target for interaction with the emitted radiation is provided so that the particle barrier is located between the radiation source and a target (90).

[0031] In an embodiment of the invention, a second radiation source (80) serves for irradiating the emitters with a radiation. Depending on the desired kind of radiation, the second source may e.g. comprise a laser, an electron source like a tube or an electron accelerator, a source of radioactive radiation of various types or a plasma device to produce ions. A part of the applied radiation interacts with the emitters and is scattered. Accordingly, these can be regarded to re-emit the radiation. The source for the applied radiation is typically, but not necessarily a laser. In an embodiment, the applied radiation is pulsed. Typically, but not necessarily, the combination of emitters and the applied radiation is suitably chosen in a way so that no more than two energetic states of the emitters are selected in the scattering process.

[0032] In an embodiment of the invention, The N-I detectors and the particle barrier are positioned in accordance with the findings described above. Hence, by arranging the setup in the manner described below, a modulation of a signal generated by the accumulation of

multiple detection events on the target takes a form of a pure sinus when at least one detector and/or the particle barrier are moved circumferentially around the target during an irradiation process.

[0033] The N-I detectors and the particle barrier are positioned about defined angular positions with respect to the radiation source. The distances of the detectors from the radiation source are substantially similar. The angular positions Q ₁ of the detectors with respect to an axis perpendicular to the row of emitters are derived from the calculations as laid out above. In particular, they are calculated from Eq. (10) in case of an even number of N and from Eq. (12) in case of an odd number of N, and by taking into account the relation of Eq. (6).

[0034] The first terms of Eq. (10) and (12) determine the angles of the first of the N-I detectors and the particle barrier (which can be regarded as a replacement of the Nth detector in the theoretical scenario above) to be of equal amount, but of opposite sign. Hence, these are positioned symmetrical about an axis perpendicular to the row of emitters by an arbitrarily chosen angle Q ₁ . Both the first detector and the target are adapted to be movable in a circumferential direction with respect to the radiation source, whereby their movement is controlled in order to maintain the previously described angular relation (see Fig. 2). The positions of the remaining N-2 detectors are also determined by Eq. (10) and (12). The results of Eq. (10) or (12) for which depend only on the number N of detectors used, are used to calculate the angles of the detectors by applying eq. (6), according to which

[0035] As d is the spacing between the emitters of the radiation source and k is the wave number of the emitted radiation, the angles Q ₁ can be derived by a simple calculation from the results of eq. (10) or (12). Q ₁ refers to the angle between the position vector of detector i and the axis perpendicular to the row of emitters (see Fig. T).

[0036] For small N, there are solutions according to which each of the N-I detectors and the particle barrier have different angular positions Q ₁ . Thus, they may be disposed in one plane, which includes the row of emitters, at different angular positions θ _l5 as is shown in the example in Fig. 2.

[0037] For any N, there are generally solutions where two or more of the detectors share the same angle S ₁ . Thus, detectors with the same angle S ₁ are disposed in a second plane perpendicular to the plane defined by the row of emitters, the first detector and the particle barrier. This further plane shares the angle S ₁ with respect to an axis perpendicular to the row of emitters. The detectors can be arranged on the further plane about arbitrary angles ψi, however taking into account the spontaneous emission pattern of the considered atomic transition. By doing so, several detectors can be deployed sharing the same S ₁ , which is exemplarily shown in Fig. 5 for three detectors.

[0038] In an embodiment of the invention, one detector and the target are moved along an angular range in opposite angular directions during an irradiation process. The size of this range depends on several individual parameters including the properties of the radiation source and the target. It has to be set up experimentally in order to achieve best results.

[0039] In a following discrimination step, particle detections detected on all N-I detectors within a predetermined time interval are discriminated from other particle detection events using a discrimination device. If an occurrence of detection events on all N-I detectors is recognized, the particle barrier is opened to allow a passage of a particle. In an embodiment, the particle barrier is only locally opened. After passing the opened barrier, the particle is used to interact with the target.

[0040] In an embodiment of the invention, particles passing the particle barrier are used for physical manipulation of a target object by means of interaction between the particle and the target object after their passage through the opened barrier. This manipulation may include lithography purposes, e.g. in the production of semiconductors. A pattern to be reproduced on a semiconductor substrate may be composed using sinusoidal modulations of different frequencies according to a Fourier decomposition of the structure of the pattern to be achieved.

[0041] Fig. 3 shows an embodiment of the invention with two scattering sites (N=2), a detector 40 and a target 90. Given Eq. (14), it can be seen that when choosing 8 ₂ = (1-m) δi, where m can take arbitrary values, the G ⁽²⁾ function takes the following form:

[0042] Given the relation δi = kd sin θ; (Eq. (6)), wherein each phase δ; is limited within the interval [ ^~ kd, +kd] as the term sin θ; runs from —1 to +1 while θi can take all values within [-π/2, +π/2], solutions exist for the interval δi = [-kd/m, +kd/m]. Within these borders, the movement of the detector and the target (respectively the particle barrier) yields an accumulated signal at the target shown in Fig. 3 for various values of m. As is shown in the figure, the angular interval of the target (determined by θi) decreases with growing m.

However, the number of modulations within the corresponding angular interval is kept constant. Thus, the optical resolution of the apparatus used for lithographic purposes increases with growing m.

[0043] Fig. 4 shows another embodiment of the invention, in which an apparatus is provided to use N quantum entangled particles for investigating an object. In this example, N is chosen to be 4. The apparatus comprises an object which acts as a radiation source (10) with a plurality of N incoherent emitters (20). These emitters are either atoms, ions, molecules, quantum dots, or Josephson circuits. They are preferably, but not necessarily arranged in a row. Typically, they are kept in the evacuated chamber, wherein their positions are maintained, e.g. by means of an atom or ion trap. The emitters emit radiation particles which may be chosen from the group consisting of photons, phonons, electrons, protons, neutrons, alpha particles, atoms, molecules or ions. The apparatus further comprises N detectors (40) located at N different positions to detect emitted radiation, which are arranged in a plane with the object comprising the emitters. The detectors are chosen from the various types known from the art in accordance with the type of radiation used. A limitation for the type of detector is that it is suitable to detect single particles of the radiation. The detectors are connected to a discriminating device (60), which is adapted to discriminate particle detection events taking place on all detectors within a predetermined time interval. Typically, but not necessarily, the discriminating device (60) is an electronic device.

[0044] In an embodiment of the invention, a second radiation source (80) serves for irradiating the emitters with a radiation. Depending on the desired type of radiation, the second source may e.g. comprise a laser, an electron source like a tube or an electron

accelerator, a source of radioactive radiation of various types or a plasma device to produce ions. A part of this radiation interacts with the emitters and is scattered. Accordingly, these are regarded as emitters re-emitting radiation. The source for the applied radiation is typically, but not necessarily a laser. In an embodiment, the applied radiation is pulsed. Typically, it is chosen in a way so that no more than two energetic states of the emitters are selected in the scattering process.

[0045] The N detectors are positioned about defined angular positions with respect to the radiation source. The distances of the detectors from the object can be chosen substantially arbitrarily, but should lie in the same order of magnitude for reasons of experimental practicability. The angular positions of the detectors with respect to an axis perpendicular to the object are derived from the calculations as laid out above. In particular, they are calculated from Eq. (10) in case of an even number of N and from Eq. (12) in case of an odd number of N, and by taking into account the relation of Eq. (6).

[0046] The first terms of Eq. (10) and (12) determine the angles of the first and second of the N detectors to be of equal amount, but of opposite sign. Hence, these are positioned symmetrical about an axis perpendicular to the row of emitters about an arbitrarily chosen angle. Both the first and second detectors are adapted to be movable in a circumferential direction with respect to the object, whereby their movement is controlled in order to maintain the previously described angular relation. The positions of the remaining N-2 detectors are also determined by Eq. (10) and (12). The results of Eq. (10) or (12) for δ(iy), which depend only on the number N of detectors used, are used to calculate the angles of the detectors by applying Eq. (6), according to which

As d is the spacing between the emitters of the object and k is the wave number of the emitted radiation, the angles Q ₁ can be derived by a simple calculation from the results of Eq. (10) or (12). &i refers to the angle between the position vector of detector i and the axis perpendicular to the row of emitters.

[0047] For small N, there are solutions according to which each of the N detectors have different angular positions Q ₁ . Thus, they may be disposed in one plane, which includes the row of emitters, at different angular positions θ _l5 as is shown in the example in Fig. 4.

[0048] For any N, there are generally solutions where two or more of the detectors share the same angle Q ₁ . Thus, detectors with the same angle Q ₁ are disposed in a second plane perpendicular to the plane defined by the row of emitters, the first detector and the particle barrier. This further plane shares the angle Q ₁ with respect to an axis perpendicular to the row of emitters. The detectors can be arranged on the further plane about arbitrary angles Cp ₁ . By doing so, several detectors can be deployed sharing the same Q ₁ , which is exemplarily shown in Fig. 5 for three detectors.

[0049] In an embodiment of the invention, the first and second detector are moved along an angular range in opposite angular directions during an irradiation process. The size of this range depends on several individual parameters including the properties of the radiation source and the object. It has to be set up experimentally in order to achieve best results.

[0050] During irradiation, particle detections detected within a predetermined time interval on all N detectors are discriminated using a discrimination device. If an occurrence of detection events on all N detectors within a specific time interval is recognized, this event is counted by a counting device.

[0051] By arranging the N detectors in the angular relation described above, a modulation of a signal generated by the accumulation of multiple N-particle detection events takes a form of a pure sinus-oscillation when the object consists of N incoherent emitters and at least one of the detectors is moved. By analyzing the modulation of the accumulated radiation, calculations can be carried out on the structure of the object, for example the interatomic spacing. Thus, the apparatus and the described method are suitable for microscopic investigations into the object constituted by the emitters.

[0052] The invention is also directed to an apparatus for carrying out the disclosed methods and including apparatus parts for performing each described method steps. These method steps may be performed by way of hardware components, a computer programmed by

appropriate software, by any combination of the two or in any other manner. Furthermore, the invention is also directed to methods by which the described apparatus operates. It includes method steps for carrying out every function of the apparatus.