WO2012056413A1

WO2012056413A1 - Device for measuring properties of a medium by scattered radiation and relative method

Info

Publication number: WO2012056413A1
Application number: PCT/IB2011/054783
Authority: WO
Inventors: Francesco Mantegazza; Doriano Costantino Brogioli; Domenico Salerno; Roberto Ziano
Original assignee: Università Degli Studi Di Milano - Bicocca
Priority date: 2010-10-27
Filing date: 2011-10-26
Publication date: 2012-05-03
Also published as: ITMI20101992A1; IT1402537B1

Abstract

The present invention relates to a method relates to a method of analysis of the structure by means of dynamic radiation scattering, the method including: irradiate a volume of a medium that contains scattering centers with an incident beam of electromagnetic radiation with short longitudinal coherence with longitudinal coherence length l_c along an incidence propagation direction, the incident beam having a coherence skewed by a skew angle ϑ with respect to the incidence propagation direction, and detect the distribution of the temporal fluctuations of the intensity of the radiation beam scattered from the irradiated volume at a detection angle a with respect to the incidence propagation direction. According to a further aspect, the present invention relates to an apparatus for the analysis of the structure of a medium containing scattering centers by means of the dynamic radiation scattering.

Description

DESCRIPTION

Title : "Device for measuring properties of a medium by scattered radiation and relative method"

^■ Among the techniques for the characterization of media that are at least partially transparent to light in a given range of wavelengths (or frequencies), the techniques based on scattering of radiation generally have the advantage of being non-invasive and they allow for online monitoring of the properties of the media.

Among the techniques that analyze the light scattered by a medium, the use of the Dynamic Light Scattering (DLS) technique makes it possible extract information on various structural features of a medium, such as the size of particles, the phenomena of aggregation of particles , the processes of nucleation and crystallization, the variations in the size distribution of microemulsions (e.g., with an application to systems for the controlled release of drugs), and phenomena- of^' condensation of DNA with high molecular weights. In DLS, the sample is illuminated by a laser beam and the resulting scattered light produced by- particles fluctuates in intensity at a speed that is dependent on the particle size. From the analysis of these temporal fluctuations in intensity (dynamics) of scattered light, which are caused by the rapid Brownian motion of the particles, it is possible to obtain the correlation function of intensity, from which the time constant of the typical thermal motion of- particles is derived, and from the latter, through the Stokes-Einstein . relation, the particle size. In the case of the measurement of the dynamic properties of the scattered radiation, the incident radiation must possess sufficient coherence, condition that is satisfied in the case of using a laser source of incident light which is generally assumed to be a source of light with both spatial and temporal coherence.

When light hits the surface of separation between two media with different refractive indexes, it is deflected changing its original trajectory due to the collision with the surface of separation. In the case of solid particles _ immersed in a liquid solution, a portion of the incident light undergoes scattering, i.e. it comes out of the solution with a direction which is different from that of incidence. In diluted media, e.g. in the case- of colloidal systems at low concentration of particles, the scattering of the incident light can be described with good approximation by using the theory of single scattering-, i.e. the light is scattered only once before being detected, without being further scattered from other scattering centers (e.g. other particles). In media with higher concentration, the contribution , originated from the phenomenon of multiple scattering becomes significant or even dominant with respect to the single scattering phenomenon, so that the dynamic properties determined on the basis of the scattered light are different from the real .properties of the particles. In general, the multiple scattering increases 'the scattering of the beam and reduces the resolution.

For this reason, .the focus has^' turned recently to DLS techniques which use an interferometer with a low coherence light source. Since it is possible to_. measure only the component of the scattered light from a defined portion of the analyzed sample equal to the longitudinal coherence length, the contribution of the multiple scattering in the detected signal decreases dramatically and media with high concentration can be measured.

The U.S. patent 6.738.144 describes an interferometric apparatus with low coherence for the determination of the size of the particles of a known concentration in a stream of a suspension of colloids or particles.- The described interferometric apparatus has a low coherence light source, a beam splitter that separates the beam into a probe beam and a reference beam which are, respectively, retroreflected from^' the sample and from a reference mirror, and then are recombihed in order to generate an interference signal. The constructive interference occurs only if the ^' difference in optical path between the two beams is less than the coherence length of the source. From the analysis of the interference signal the path length distribution of the photons is determined and . f om the latter the colloidal suspension is characterized dimensionall .

The patent -application GB 2.407.379 A discloses an apparatus for measuring dynamic light scattering by using the method of interference from phase modulation.

The development of^' coherent X-ray techniques for the examination of the dynamics and detailed structure of the matter is of considerable current interest. In .particular, the photon correlation spectroscopy with X-rays (X-ray Photo-Correlation Spectroscopy, XPCS) aims at measuring the intensity correlation function the scattered X-rays for the analysis of the temporal density fluctuations of a sample under analysis and therefore allows to study the dynamics of statistical physics of systems.- The use of this technique has been made possible mainly thanks to the development of new-generation sources of synchrotron X-ray , typically based on the use of an

K.A. Nugent, in Advances in Physics, 1460-6976, Vol 59, No 1 (2010), pages 1-99, with particular reference to pages 74-84, provides a brief overview of coherent X-ray techniques for the analysis of the dynamics of matter. . Sutton in the paper "A review of X-ray intensity fluctuation spectroscopy" , published in C.R. Physique 9 (2008), pages 76-84, is a review of the literature on XPCS technique that uses various types of scattered radiation.

The XPCS technique has been- applied in particular for the observation of order-disorder transitions in various systems,- such as crystals, colloids, liquid crystals and elastomeric polymers.

For example, Brauer S. et al. in "X-Ray Intensity Fluctuation Spectroscopy Observations of Critical Dynamics in Fe₃Al" , published in Physical Review Letters, Vol 74, No 11 (1995), pages 2010-2013, analyzes the dynamics of the critical fluctuations of a single crystal of Fe₃Al through a hard X-ray beam produced from a source with synchrotron undulator. Dierker S.B. et al. in "Photon Correlation Spectroscopy X-Ray Study of Brownian Motion of Gold Colloids in Glycerol", published in Physical Review Letters,' Vol 75, No. 3 (1995), pages 449-452, describe XPCS studies on the static structure factor and the dynamic correlation function of a gold colloid dispersed in a viscous liquid- made of glycerol.

A.C. Price - et al. in "Coherent Soft X-Ray Dynamic Light Scattering from Smectic A films", published in Physical Review Letters, Vol 82, No 4, pages 755-758, use dynamic light scattering at the Bragg peak of soft X-rays for measuring the thermal fluctuations in smectic A liquid crystals .

S.G.J. Mochrie et al. in "Dynamic of Block Copolymer Micelles Revealed by of X-Ray Intensity Fluctuations Spectroscopy" , published in Physical Review Letters, Vol 78, No 7, pages 1275-1278, reports measures of intensity f-luctuation spectroscopy of the equilibrium dynamics of fluids^' composed of polymeric micelles made of copolymer of polystyrene-polyisoprene in „a homopolymeric . matrix of polystyrene.

The Applicant has observed that . the measurement techniques that are based on the analysis of backscattered light originating from the interference signal of a probe beam and a reference beam require a measuring apparatus with a relatively complex optical scheme. Moreover, in some ranges of wavelength, the backscattered signal may be weak and do not provide measurements with sufficient ^' high ^■ sensitivity.^" The Applicant also noted that the measurement of the dynamic X-ray scattering requi es an investigation beam of radiation that is sufficiently coherent both spatially and temporally, and therefore requires intense radiation beams from which' the beam that impinges on the analyzed medium can be derived. In general, X-rays with high intensity can be obtained from synchrotron sources and free electron laser (FEL). However, these sources have the obvious disadvantage of being extremely expensive and not very easy to implement.

The Applicant understood that if a beam of radiation with low coherence is used with a coherence that is skewed with respect to the direction of propagation of the beam that hits an inhomogeneous medium, it is possible^' to suppress or at least to reduce significantly the contribution of the multiple scattering and^' at the same time get dynamic information from the analysis of the radiation scattered by the medium.

According to one aspect, the present invention, relates to a method of structural .analysis of a medium through the dynamic radiation ^' scattering, the method including: irradiate a volume of a medium that contains scattering centers with an incident beam of electromagnetic radiation with short longitudinal coherence l_c along a longitudinal direction of propagation of incidence, the incident beam having a coherence skewed at an angle of θ with respect to the propagation direction of incidence, and detect the distribution■ of the temporal fluctuations of beam intensity of scattered radiation from the irradiated^" volume at a detection angle a with respect to the direction of propagation of incidence.

A beam of radiation with short longitudinal coherence propagates having a coherence region in which ·■ the correlation function does not vanish.

The skew angle θ of the coherence of the. incident beam is defined as the angle between the unit vector of coherence defined as the unit vector perpendicular to a principal plane identified on the main section of the coherence region that penetrates, generally transversely, in the investigated volume in the medium to be analyzed, the unit vector of coherence, in the plane of propagation, being skewed by a skew angle 9· with respect to the propagation direction of incidence.

Preferably, the phase of irradiating a volume of a medium includes: generating . an emission radiation beam with short longitudinal _. coherence along a propagation direction of emission; produce a beam of incident radiation with skewed coherence having a coherence region of incidence whose section that penetrates transversally the investigated volume in the medium to be analyzed shows a second principal surface that identifies a principal plane and a unit vector of coherence perpendicular to this said principal plane, the unit vector of coherence being skewed by an angle θ with respect to the direction of -propagation of incidence, and send the beam of incident radiation through the medium. In preferred forms of embodiment, the beam of emission radiation has a coherence region of W

emission having a first principal surface parallel to the wavefronts along the propagation direction of emission. Preferably, the phase of producing a beam of incident radiation includes the introduction of a temporal delay in the emission radiation beam.

According to a further aspect, the present invention relates to an apparatus for the structural analysis of a medium containing scattering centers through the dynamic radiation scattering, in which a volume of the medium is irradiated by a beam of incident radiation, the apparatus comprising: a generation system of electromagnetic radiation able to produce a beam of incident radiation with short longitudinal coherence with longitudinal coherence length l_c along a propagation direction of incidence, the incident beam having a coherence skewed by an angle & with respect to the propagation direction of incidence, and a detection system capable of receiving^" a beam of radiation scattered by the medium to a collection aperture centered around a detection angle a with respect -to the propagation direction of- incidence, the detection, system being able to detect the distribution of temporal fluctuations of the intensity of- the radiation beam scattered by the irradiated volume.

According to certain preferred embodiments of the present invention, the method and the apparatus allow the detection of the dynamic radiation scattering by a disordered medium at ^' various angles with respect to the direction of incidence of the beam or from the direction of backscatter and in general they allow to perform the measurement of the dynamic radiation scattering at an angle of detection suitable for obtaining structural information on the medium.

Additional features and advantages of the invention result from the following detailed description made .with reference to examples of implementation of the invention given as not restricting examples and with reference to the attached figures in which:

Figure 1A illustrates from the conceptual point 'of view a region of coherence in the propagation plane for a beam of radiation with a coherent region having a principal surface extended parallel to the wavefront surfaces of the radiation beam along the propagation direction.

Figure IB illustrates from the conceptual point of view a region of coherence in a plane of propagation for a radiation beam with coherence skewed with respect to the wavefront surfaces of the radiation beam^' (i.e. coherence unit vector skewed with respect to the direction of the propagation direction) . Figure 2 is a block diagram representing an apparatus for the characterization of the properties of a medium through the analysis of the scattered radiation.

Figures 3a-3d illustrate schematically the mechanism- of radiation scattering from a medium that includes scattering centers in the case of a coherence^■ unit vector of the . incident radiation parallel to the propagation direction of the incident beam.

Figures 4a-4d illustrate schematically the mechanism radiation scattering from a medium that includes scattering centers in the case of a coherence unit vector of the radiation skewed with respect to the direction of propagation of the impinging beam. Figure 5 is a block diagram representing an apparatus for the characterization of the properties of a medium by means of - the radiation scattered from the medium itself, according to an embodiment of the present invention.

Figure 6 schematically illustrates a system for the orientation of the - coherence, according to an embodiment of the present invention.

Figure 7 illustrates schematically an apparatus - for structural analysis of a medium according to an embodiment of the present invention, in particular applicable to visible light.

Figure -8 shows the correlation function versus time (ms) calculated the from light scattered by a sample containing calibrated polystyrene nano-spheres 150 nm in diameter for different conditions of coherence and detected at a collection angle of 90°.

Figure 9 illustrates schematically an apparatus for the characterization of properties of a medium according to a further embodiment of the present invention, in particular applicable to X-rays. For longitudinal coherence, also referred to as temporal coherence in the case of waves with stationary statistical properties, we mean the coherence of ^■ the beam along a direction of propagation, or the ability of the wave field W

1 1

to cause interference with a - replica of itself to a next instant of time. A perfectly monochromatic source emits radiation with ^'complete longitudinal coherence, while the radiation emitted by a real source, not perfectly monochromatic, shows a degree of longitudinal coherence that can be represented by the longitudinal coherence length, l_c , which basically defines a length within which the beam can be considered to be coherent, i.e. the phase relations are maintained, along the propagation direction. For a point source that emits radiation at a central wavelength λ and with spectral width Δλ, the following relation holds:,

, (1)

l_c = λ²/2Δλ

The coherence transverse to the direction of propagation, for which a transverse coherence length, , is specified, is indicative of the ability of a wave field to cause interference at two different points in space along a direction parallel to the equal-phase surfaces, i.e. the wavefronts of the electromagnetic field.

The longitudinal coherence length in a beam of radiation with low coherence can be detected from a coherence region of the propagating beam. The spatial distribution of the coherence regions of a wave field depends on several factors, among them the- nature ^' of the source and the propagation distance of the latter. As an example,- the light emitted by a hot filament of a tungsten light bulb, or in general by a thermal source, at a distance relatively large, has spherical wavefronts (or equal-phase surfaces) , centered in source itself, when, it can be considered as point-like with respect ^' to the distance at which the coherence is observed. Within the coherence region, the correlation function does not vanish, or■ rather the interference/overlap is constructive. Since generally the correlation function has a maximum and then falls to lower values, the coherence region can be defined, for some purposes of this description, as a region, in space hit by the propagating beam, in which the correlation function has a value not less than a predetermined threshold value, which^' as a non-restrictive example can be equal to 1/e in the case of Gaussian beams. The geometry of the coherence region in space (or, expressed in another way, the shape of the Fourier spectrum) of the light emitted from a real source is in _ general complex. The volume of^' the coherence region, when projected onto a plane containing the propagation direction, called in the following plane of propagation, can be represented as a first approximation, ^■and for the purposes of the present- description, by a platelet with asymmetric geometric shape in the two directions perpendicular and parallel to the direction of the considered^' propagation direction. For example, an incandescent filament 2 mm in length produces locally, on the scale of millimeters, coherent regions that are expanded in the direction perpendicular with respect to the propagation direction and geometric shape of a platelet bounded by plane sections of two ellipsoidal surfaces, that will be called, only for. brevity, "coherence regions of ellipsoidal shape". This approximation of the shape of the regions of coherence can be considered to hold true in many cases of interest in optics. Figure 1A shows schematically the section of a coherence region 14 with the shape of a prolate ellipsoid in a propagation plane, which is also the symmetry plane of the ellipsoid, along a principal direction of propagation of the beam (x axis), which is assumed to be the direction of incidence along the optical path between the source and the medium to be analyzed. The minor axis 13 of the coherence region 14 is perpendicular to the propagation direction, i.e. lies along the y axis. The section of the coherence region of the portion of the propagating beam which irradiates a volume of the- medium under analysis, the incident beam, i.e. the section of the coherence^" region .falling in the investigated volume of the medium where the scattering secondary waves are generated, identifies a coherence layer with a thickness l_c along the direction of incidence and that moves in time along the same direction. In the case of coherence regions with ellipsoidal shape, the section of the coherence layer in the plane containing the main direction of propagation and the minor axis of the ellipsoid is shown in a purely conceptual way with the reference number 12 in Figure 1A.

As shown schematically in panel R of Figure 1A, the coherence layer 12 has a main surface that identifies · a first plane 19 in which the coherence layer shows longer extension and. a second plane 15 in which the coherence layer shows a shorter extension that corresponds to the longitudinal coherence length, χ . We define a coherence unit vector 16 the unit vector perpendicular to the first principal plane 19 (and in the particular illustrated case, parallel to the second principal plane). In the case of Figure 1A, the coherence unit vector 16 is parallel to the direction of incidence defined along the x axis, or, otherwise defined, the principal surface of greater extension of the coherence layer extends parallel to the wavefront surfaces of the beam that propagates along the incidence direction.

The concept of coherence layer and coherence unit vector can be applied in a more general way also in the case of coherence regions which, when projected on a propagation plane, do not show approximately a bi-dimensional platelet shape between two sections of ellipsoidal surfaces, as in the case shown in Figure 1A. Even in a more general case, it is possible to define a coherence layer, starting from a direction of propagation, as the section of the coherence volume of a portion of the incident beam, which hits in the medium under analysis, in which the coherence , layer shows a principal surface, which typically intersects transversally the medium, and a unit vector perpendicular to the principal plane of the principal surface.

In some preferred embodiments, the source is able of emitting radiation that, at a relatively long distance_, compared to the size of the source, has coherence region with a prolate ellipsoid shape with the major axis along the propagation direction. However, other embodiments may include a configuration in which the incident beam has regions of coherence with the shape of an oblate ; ellipsoid with minor axis along the propagation direction, or another form that presents an asymmetry in the two directions perpendicular and parallel to the direction of propagation.

In this description, the terms "coherent regions" or "coherent region", are used^' meaning that the radiation propagates along a direction and at different moments the coherent region will be in different positions in space.

Figure 2 is a schematic representation of an apparatus 10 for the analysis of the properties of a medium through the measurement of the light scattered by the medium. The apparatus includes a radiation source 20 capable of generating an electromagnetic radiation beam, for example a beam of light in the visible spectrum, with low coherence, more specifically with short longitudinal coherence with longitudinal ^" coherence length ]_ . The beam of ^"radiation emitted by the source has a propagation direction of incidence 21 and coherent regions with a coherence layer 18 that defines a coherence unit vector 23 parallel ^'to said propagation direction. The emitted radiation beam is optically coupled to a medium 17 to be analyzed that includes scattering centers, such as a colloidal system, for example a suspension of solid particles immersed in a solution .

The presence of a longitudinal coherence length l_c and preferably of a transverse coherence, makes sure that the secondary radiation originating in a given irradiated portion of the medium can interfere with the secondary radiation originating from a different portion of the same medium resulting in an intensity fluctuation of the scattered radiation that can be detected along a given detection direction. From the .analysis of the intensity fluctuation of the scattered radiation it is possible to derive the dimensional characterization of the medium containing a distribution of optical density changes (i.e. changes in the refractive index if the source is a light source) or more . generally, changes in electronic density comparable with the wavelength of the incident radiation.

In the^' case that the low coherence beam radiation impinge on a disordered system, namely, with a non ordered optical/electronic density distribution, which is for instance, a solid-solid or solid-liquid colloidal system, the scattered radiation is in the form of a distribution of random intensity fluctuations ("speckles") being caused by the correlation among the different scattering centers. If the spatial distribution of the disordered system varies with .time, the distribution of the "speckle" varies, according to time. Therefore, information on the dynamics of a disordered system can be derived from the analysis of the temporal correlation distribution of speckle which is represented by a temporal correlation function.

- Figures 3a-3d illustrate the mechanism of scattering by a medium that comprises a plurality of scattering centers in the case illustrated in figure 1, where the coherence unit vector is parallel to the propagation direction of the incident beam, or in other words, the coherence, layer has the greater extension main surface parallel to the wavefront surface along the said beam propagation direction. Referring to the Figure 3a, a radiation beam 30 with short longitudinal coherence with coherence length lc propagates along a direction represented in the figure from the reference axis x. The coherence layer within the radiation beam, shown in a purely conceptual way with reference number 31 has■ a greater extension main surface perpendicular to the incidence direction of the beam 30 and then a coherence unit vector 31' parallel to the incidence direction.

The incident beam 30 with coherence layer 31 penetrates into a sample under analysis, which is a cell 25 that contains a medium at least partially transparent to the incident radiation and which comprises a plurality of scattering centers. Only to simplify the description that follows, we consider that the medium includes, at . least in the volume reached by the coherence region 31, three scattering centers, for example, three particles, 24a-24c displaced, perpendicular with respect to the .direction of propagation of the incident beam. When the section of the region coherence of the incoming radiation impinges on the scattering centers, i.e. coherent layer 31 (figure 3b), each of them generates spherical secondary waves coherent with the incident wave in a coherence region of longitudinal length lc. The secondary waves propagate concentrically from each scattering center 24a, 24b and 24c with their respective coherence regions 26a, 26b and 26c in phase with each other. As a first approximation, the scattered radiation inside the volume of the medium reached by the incoming radiation is the superposition of the contributions coming from each scattering center, e.g. scattering- centers 24a-24c. In the overlapping region of coherence regions 26a-26c of the secondary waves there is interference among the scattered field from each scattering center. Because the secondary waves are generated by the various scattering centers and at the same time and propagate concentrically in phase in the respective regions of coherence, interference occurs (1) in a direction of propagation of the scatted beam which coincides with the direction of the incident beam (along the x axis) or at least in a small angular range ( i.e. less than the opening for the diffraction of the incident beam) around the incident direction, or (2) in a direction opposite to the direction of incidence, i.e.. in the direction of the back- scattering.

Figure 3c depicts a subsequent moment to the generation of. secondary waves, in which the regions of coherence 26a- 26c were propagated by defining a first overlapping or interference region 28 in the transmission direction' of_. the beam and a second overlapping region 29 in the back- scattering direction. The secondary waves propagate outside the medium 25 to form a beam of scattered radiation 27 in correspondence of the overlapping region that can be detected along the propagation propagation (fig. 3d). Conversely, in the direction orthogonal to the beam propagation direction (y axis), the coherent regions 26a- 26c coming from the different centers do not overlap, and thus will not ..contribute to the interference. More generally, in directions different from the incident radiation propagation direction and in the back-scattering, the dynamic signal is absent or -greatly reduced.

With reference 'again to figure 2 , in the case of unit vector of coherence radiation parallel to , the incidence beam ■ direction, the measurement of the dynamic light scattering is performed by a detection system 22 capable of detecting the diffuse radiation 21' by the medium 17, being the detection system positioned along the propagation direction of the incident beam.

The Applicant has observed that since the incident radiation that is not subject to the scattering by the scattering centers within the volume investigated, is transmitted through the medium and emerges from the medium along the incidence direction, the scattered radiation along the forward direction is detected together with the transmitted radiation. Since the transmitted radiation is generally the most significant component of the detected signal can be difficult to extract from the signal collected by the detection system the alone scattered component with a signal/noise ratio sufficiently high. The detected signal · along the back-scattering direction, although free from the transmitted component of the radiation, may be a weak with a signal to noise ratio that is not good for the nature of the incident radiation and / or structural characteristics of the scattering centers within the material.

The Applicant understood that if. a short coherence beam of incident radiation has^' longitudinal coherence region disposed along a direction inclined compared to the propagation direction of incidence, there is a delay between the moment in which the region of coherence impinges the^' different -scattering centers included in the volume of the investigated medium and that this delay may produce a superposition . coherent regions of secondary waves along a different direction from the axis identified by the direction of propagation. In this way, it is possible to detect the scattered radiation by the analyzed medium along different directions and therefore in conditions that may be more favorable to the analysis of the detected signal.

The mechanism of the scattering of radiation in the case of incident beam with inclined coherence regions with respect to the direction of the incident beam is shown in figures 4a-4d. A beam of incident radiation 35 impinges along a incidence direction in the x axis on the cell 25 that includes . a medium with a plurality of scattering centers 24a-24c. The incident beam has a coherence region that defines a coherence layer- 36 having a first greater extension main surface and a second minor extension main surface which length equals the width of the longitudinal coherence length lc.^' On the first main area is identified a main plan from witch the unit coherence vector 37 is defined, perpendicular to this plane, which is displaced in a direction inclined at- an angle θ respect to the incidence direction x (figure 4a) .

By convention and without any purpose of limitation, the coherence unit vector is defined in the positive half-plane towards the direction of propagation. With reference to the figure, the positive half-plane is the half-plane with positive x axis in the propagation plane (x, y) . According to^', some embodiments, the skew angle θ includes the values of angle supplementary to θ, i.e. (180^σ-θ).

In this context a reference will be done to skewed coherence beam meanings a radiation beam propagating along a direction of propagation with skewed coherence regions (i.e. not parallel) skewed by a skew angle with respect to the wavefront surfaces of the beam along the said propagation direction. ^'

The skew angle of the region of coherence of the beam is defined as the angle between the unit coherence vector defined as the unit vector perpendicular to a main plan located on the main surface of the section ,of the coherence section that transversely penetrates the region under investigation in the medium to be analyzed that, in cases of major interest, is the surface with greater extension of the volume coherence section of the portion of the incident beam in the investigated volume.

Because of the skew angle θ with respect to the direction of propagation, the scattering centers 24a-24c are not invested in the same instant from the coherence layer 36, but in a time sequence. In particular and with ^' reference to figure 4b, the first center to be invested in the region of coherence is the 24a scattering center, at a subsequent instant the 24b and at a second subsequent instant, later than the first moment, the center 24c. The radiation that impinges^' each scattering center 24a, 24b and 24c gives rise to a respective secondary spherical wave (scattered) . that spreads concentrically with the corresponding coherence regions 32a, 32b and 32c in phase ■^' with each other (figure 4c) . Because/ .that the secondary spherical wave sources (i.e. the scattering centers) originate waves at different times, at every time,, the coherence regions of secondary waves have different diameters and overlap each other at an angle a with respect to the direction of propagation of the beam (x axis) . In particular, in the situation illustrated in Figures 4a-4d, the coherence regions 32a-32c, are superimposed in the direction orthogonal towards the below to the direction of propagation of the incident beam (along the y-axis, a=90°) producing a beam of scattered radiation 34 along that direction.

The radiation beam can be detected along the y axis in the detection area\ indicated in the (x, y) with the dashed rectangle 33 in figure 4d, which represents the propagation of the coherence regions ^' of the secondary waves at a subsequent instant after that shown in Figure 4c.

With a configuration in which the beam impinges _. the medium with a coherence unit vector skewed with respect to the direction of incidence, the interference pattern produced by the envelope of secondary waves may have originated along a different direction from the axis identified by the propagation direction and along that direction it is possible to observe a dynamic signal that has a high enough intensity. If θ is the angle at which the unit vector is skewed with respect to the incident propagation beam direction, i.e., skew angle,- the interference takes place, in the plane of propagation, essentially at an angle 2θ and ^' at angles adjacent to it. Preferably, the detection angle is contained between ( 2 &-δ ) and (2θ+δ) , where δ is the diffraction angle of the medium volume hit by the incident beam. The opening diffraction angle δ is generally dependent on the incident beam diameter, in the case far field detection, i.e. at a distance significantly^■ greater than the size of the source. According to some preferred embodiments, the detection angle is approximately equal to 23.

In the three dimensional space, the overlap between the coherence regions of the scattered radiation also occurs out of the plane in which the incidence direction and ^' the .coherence unit vector lie, i.e. the plan (x, y) . Therefore, although the schematic representations of the principle of the measurement technique shown in the figures refer to a propagation plan identified by the beam propagation direction and the coherence unit vector, azimuthal angles that lie outside of this plan can be monitored. In fact, out of the considered plane, the directions of propagation of the radiation are all the directions that lie on the surface of a cone whose axis identifies the coherence unit vector and has half-open equal to 3. One of the rays of the cone corresponds to the direction of incidence propagation in the propagation plane. Preferably, the azimuthal angle of detection is greater than or equal to the opening diffraction angle of the volume invested by the incident beam and less than or equal to 23.

We note that, although to simplify the description, in Figures 3a-3d and 4a-4d is exemplified .a medium that includes scattering centers vertically displaced respect to the direction of propagation of. the incident beam, the general principle of the scattering mechanism in. function of the orientation of the coherence regions of the incident beam is also true for the more general case of a randomly distributed scattering centers inside the medium. In fact, -the coherence region impinges the scattering centers in sequence, with a time delay proportional to their position along the propagation direction, i.e. x axis. In this way, the delay produces a superposition of the coherence regions in directions different from the propagation direction and, in the case illustrated in figures 4a-4d, in the direction orthogonal to that of the incident beam.

According to certain preferred embodiments, the beam of incident radiation is a. radiation beam in a spectrum of the visible or near infrared and preferably the angle Θ between the coherence unit vector and incidence direction lies between 5° and 85°, still more preferably between 20° and 70°. In a particularly preferred embodiment the skew angle θ is about 45°.

In some preferred embodiments, the beam of incident radiation is a beam of radiation in the spectral wavelength range from about 1 to 30 nm and preferably the skew angle between about 0.01 rad (^¾ 0.57° ■) and 10°. At these skew angles the detection of the signal scattered from the medium occurs at low angle, preferably at a detection angle equal to or less than 10° and greater than or equal to. the aperture diffraction angle of the radiation scattered by the medium. In other embodiments, the skew angle ranges from about 10° to 90° .

More generally, the minimum- skew angle depends on the relation between the average size of distribution centers in the medium and the wavelength of the incident .radiation and is preferably selected to be greater than the aperture diffraction angle of the incident beam.

Figure 5 is a schematic representation of an apparatus for the properties characterization medium through the analysis of the scattered radiation, according to an embodiment of the present invention. The radiation beam with coherence region that defines a coherence layer 18 with longitudinal coherence length l_c and coherence unit vector 23 parallel to the propagation direction 21 - is emitted from the source 20 and enters a system for skewing the coherence 45 act to skew of an angle & of the coherence unit vector of the incident beam on the system, hereafter called system for skewing the coherence. The radiation beam 41 leaves the system 45 with coherence layer 48 having a first greater extension main surface and a second surface having a smaller extension with width equal to lc, in which the first- main surface of greater extension identifies . a unit coherence vector 49 inclined at an angle 9 different from zero with- respect to the direction of incidence. The radiation beam with a_. skewed coherence unit vector impinges on the medium 17 under investigation reaching a volume into the medium which thickness^' is of the order of magnitude of l_c and impinging on the scattering centers within the volume. In general, the investigated volume includes a plurality of scattering centers. If the region of coherence of the beam emitted from the source 20 in a propagation plane is in the form of volumetric platelet whose minor axis is perpendicularly oriented respect to the direction of^' propagation (as shown in . figure 1A) , at the device output 45 the coherence region has the minor axis oriented at an angle different from 90° respect to the considered direction of propagation. More generally, the section of the main surface of the coherence region of the beam portion which impinges the medium to be analyzed is not more parallel extended, to the wavefront surfaces. With reference to figure IB, which shows a projection of the coherence region, approximate by- a volumetric platelet in the propagation plane (x, y) where the beam propagation direction x and the minor axis 46 of the plane of symmetry of the ellipsoids lie. The coherence unit vector 49 in skewed by an angle 3 and then, the minor axis 46 of the ellipsoid is inclined by a complementary angle to 3, (90°- 3), respect to the direction of incidence x. This type of skewed coherence with coherence regions inclined respect to wavefront surfaces^' of the beam that propagates (or, as- defined above, with coherence unit vector not parallel to the considered direction of propagation) , is described, as well as through a transverse coherence length and a longitudinal coherence length, by the angle of skewness 3. In figure IB is shown the coherence layer 48 of the incident beam 48 which irradiates, the investigated volume.

Preferably, the beam of radiation that impinges on the medium has transverse coherence^■ with transverse coherence length, It, which corresponds to the transverse beam dimension or at least with transverse coherence length not less than the transverse dimension of the volume of the medium investigated by the beam .If the source is not suitable to emit a beam with transverse coherence sufficient for the purposes of the measurement technique, the apparatus may . include a spatial filter as a transmission mask with an aperture (pinhole) of the same order of magnitude of the desired transverse coherence length.

For example, in the case of a spatial filter which includes a circular opening that transmits the beam

(pinhole), Dl _r where is the diameter of the aperture. With reference again to figure 5, the beam of scattered radiation 42 from the medium 17 is collected at an angle a with respect to the direction of propagation of the Incident beam by a detection system 43 which includes a detector^' (not shown) . In the example in figure 5, the skew angle 3· of the coherence unit vector 49 of the beam that impinges the medium is about 45° and the angle of detection a is 20, that is about 90°.

In some preferred embodiments, the collector opening of the revelation system around the detection angle a is contained within a cone centered at the angle a and of half-open equal to the opening diffraction angle δ of the volume of medium invested by the incidence radiation beam. In some embodiments, angles outside the cone can reduce the amplitude of the signal. The _.intensity of the scattered radiation collected by the detector is processed electronically in order to determine the time correlation function of the intensity fluctuations by solving the scattering direction of the radiation through one of. the known methods that include homodyne and heterodyne techniques. From the time correlation function is possible to obtain information about the dishomogeneity of the medium, i.e. change in the optical density, such as the size of the particles that constitute the scattering centers. Preferably, and particularly in case of the detection system set that includes^' a single channel detector, such as a photodiode, and the medium under analysis is disordered, the system is 'equipped with an optical device capable of selecting a single speckle. In a different embodiment, the detection system - includes a multiple channel detector, such as a CCD (Charge Coupled Device) , the analysis of the correlation function is preceded from the elaboration of the detected signal in order to extract from it a single speckle, i.e., in order to proceed with the analysis the fluctuation of a single coherence region.

The device 45 of coherence orientation of a longitudinal short coherence beam includes at least one element of spectral dispersion, i.e. an element that spatially deflect different wavelengths inside the beam impinging on it. The skew angle is caused by spectral dispersion introduced by the dispersive device. More generally, the element of spectral dispersion^■ introduces a time delay among the spectral components of the beam. An example of a set up act to skew the coherence is shown in figure 6. The system 45 includes as a dispersive element a reflecting diffraction grating 50 on which impinges a radiation beam 21 having a coherence region with a coherence layer 18 that identifies a coherence unit vector (not shown in the figure) parallel to the direction of propagation of the beam itself (θ=0) . A reflecting diffraction grating can be used for light radiation with visible wavelengths and in the near infrared wavelengths (e.g. 380 to 1400 nm) . The diffraction grating introduces an angular dispersion .in the incident beam 21 that generates diffracted beams of spectral order m (m = 0,1/2 ,...) which emerge from same incidence side of the grating. The incidence and diffracted beams follow the known relationships of diffraction:

Sin Ψ-sin γ = τ .λ/ά

Where and Ψ (not shown in the figure) are the angles between the -normal to the plane of the grating (i.e. the diffraction plane) and, respectively, the incident and the diffracted beams, d is the grating pitch and _m is the spectral diffraction order.

For m.=0r a reflection grating acts as a mirror producing a reflected beam 57 having a coherence layer 58 with coherence unit vector still parallel _. to its direction of propagation. For the diffraction order greater than zero , m = 1, 2,..., following known relationships in the field of diffraction of radiation, the^■ angular dispersion, which is a function of the diffraction angle, in turn dependent on the incident wavelength, introduces a delay in the diffracted beam. The delay introduced by the angular dispersion gives rise to a skew angle θ of the coherence unit vector. Therefore, the diffracted beam 51 with order m^ 0 , which propagates along a propagation direction has coherence layer.54 whose coherence unit vector is skewed by an angle with respect to that direction -of propagation.

The angle θ between the coherence unit vector and direction of propagation of the diffracted beam depends on several factors such as the grating pitch, the ^' beam incidence angle γ and ^■ the deflection angle ψ of the diffracted beam and can be selected by acting on one or more of these parameters. For example, the skew angle can be varied by varying the angle of incidence of the beam on the- grating. From purely geometrical considerations, the angle can be calculated using the equation: tan θ = tan -siny/cos¹!'.

The orientation ^' system of the coherence 45 of the radiation is preferably configured to extract the first order diffracted beam. Preferably, the system 45 is equipped with a first converging lens 52 and a second converging lens convergent 53, being the diffraction grating placed in the front focus (focal length/) of the first converging lens and the second converging lens being positioned at a ^'distance 2/ from the first lens to form the image of the diffraction grating 50 in a given image plane

59 and to select the first order diffracted beam ^' ( ^m= 1 ) . The first order diffracted beam 56 of ^■ radiation with coherence layers 55 skewed with respect to its direction of propagation (upside of 90° from ^'passing through the pair of glasses) leaves the system 45 to be directed to the medium to be analyzed. The optical system formed by , two lens creates an image of the field near the grating equal in intensity and phase in the medium investigated. Preferably, the medium is positioned at a distance approximately equal to the focal length f of the second converging lens, so that the components of the scattered radiation beam at the different wavelengths overlap. Within the investigated volume, secondary radiation beams have coherence regions with longitudinal coherence length which grows with distance from the overlapping area among the scattered beams .

Other embodiments of the- coherence orientation system 45 of figure 6 may include various devices for- the selection of ^' the order of diffraction of the diffracted radiation. For example, the system 45 can include a converging lens, in which the grating is positioned in the front focus of the lens that converges the first order diffracted beam in a given ex-ternal plane to the system 45, being the medium under analysis, positioned so that this plane conjugate to the grating goes through it. It 'is understood that the system can be configured to generate beams with of an order grater that the first.

In another embodiment, the system includes a diffraction grating consistent orientation operating in transmission that can be used in case of incident radiation in ^' the visible spectral region (380-760 nm) or soft X-ray (e.g., 1-20 nm) .

In a further embodiment the system includes, a prism of dispersion that introduces a progressively increases time delay across the incident beam and then a skew of the coherence regions. Without wishing to be bound by any particular theory, relations that govern the time delay in a laser pulse of ps are described for example in the "Group velocity dispersion in the PRISMS and Its application to pulse compression and traveling-wave excitation" of Zs. Bor and B. Racz,^' published in Optics Communications (1985), vol. 54, No. 3, page 165. A system comprising a dispersive prism can be used in devices that analyze mediums by means of incident radiation in the spectral region of the visible or X-rays, either hard than soft. In a different embodiment, the orientation coherence system includes a diffractive device with a multilayer structure that acts as a Bragg reflection device, such as a multilayer structure of Si/Mo typically ^■ used for diffraction in the spectral region which ranges from the soft X-ray to extreme ultraviolet radiation field, e.g. 1 - 30 nm. The multilayer structure can be configured so that the reflection occurs - in a symmetrical, or in a nonsymmetrical manner , i.e. can be configured with its outer surface, respectively, parallel or not parallel to the planes that generate the Bragg reflection.

A still further embodiment is directed to a system capable of tilting the regions of coherence that includes a diffractive element which includes a crystal grating of bi- or tri-dimensional , such as a photonic crystal. For example, a single silicon crystal can be used in an apparatus that analyze a medium by a radiation in the spectral region which includes the hard X-ray int the range of wavelengths ranging from 0.1 to 1 nm approximately. The crystal grating can be configured such that the reflection occurs in a symmetrical or non-symmetrical^' manner, i.e. the grid can be configured with its outer surface, respectively, parallel or not parallel to the planes that generate the Bragg diffraction. In some embodiments, the tilt mechanism of the coherence regions of the radiation in a range of wavelengths from 0.1 nm^' to 1400 nm includes at least one spectral dispersion element constituted by a diffractive and / or refractive element . Although the preferred embodiments are directed to a method and an apparatus in which the the beam of investigation is selected in a range of wavelengths suitable for the characterization of disordered systems and / or dynamic information on the order-disorder transitions or changes of symmetry, the present invention does not exclude that the radiation impinging the medium. to analyze is a beam of electrons, for example, with wavelengths of the order of 0.1 nm. In this case, a possible application is the characterization of the crystallographic classes through the analysis of the scattered radiation from^' an ordered medium which a solid crystalline structure.

Figure 7 illustrates schematically an apparatus for characterizing properties of a sample through an embodiment of the present invention. The apparatus of the embodiment of figure 7 is particularly suitable for the characterization of a colloidal system such as a colloidal suspension in a liquid medium through the dynamic light scattering. The analysis apparatus 60 includes a source 61 that includes a laser diode 62, electrically connected to a power supply 63 which provides a current with intensity that is less than the' threshold value for the laser effect (i.e. below threshold power) . referably, in the_ case of visible Tight, the laser diode is a semiconductor laser, in which the front face is treated with an anti-reflection coating. For example^", the diode laser is a commercial laser SAL-660-25 produced by Sacher Lasertechnik typically^' used for external cavity with a central wavelength of the emission band of 660 nm, full width half maximum bandwidth (FWHM) of 8 nm, when maintained below threshold, and output power of the order of 0.2 m . The beam exits the laser diode is collimated by a collimating optical element, e.g. an aspheric lens 64, in order to obtain a collimated beam 67 of a diameter of about 1 mm. When operated ^' below threshold, the laser described in the example produces a beam with coherence regions with, two-dimension elliptical ring^' shaped of longitudinal coherence length, l_c, of about 20 μπι and transverse coherence length, It, downstream of the collimator device, approximately equal to the diameter of the beam (i.e.., single, transverse mode). The beam emitted by the source of the above example, when collimated by ^{' '}the optical collimator element, can maintain the coherence properties up to a few meters away from the optical collimation element.^' The coherence unit vector of the beam emitted from the source is parallel to the direction of propagation.

In a different embodiment, the source 61 may include a super-luminescent LED diode, such as a commercial super- luminescent diode module produca-d by Diodes Ltd Superlum. and which operates in the visible spectrum.

If the source is not likely to generate a beam of coherent radiation in the transversal direction, the- incident radiation can be made coherent by means of a spatial filtering, for example by forcing the beam emitted from the source to pass through an aperture ("pinhole", not shown) of dimensions ^'of the same order as the desired transverse coherence length.

The light beam 67 is impinges on a system of coherence orientation 65 for low coherence radiation. The system 65 is for example ' of the type described with reference to figure 6 and includes a' diffraction grating 66 operating in reflection, such as a reflective layer with a pitch of 600 lines per millimeter angled (blazed) of 17.5°. The position of the grating is adjusted so that the angle of deviation between the beam 67 which impinges on the grating and the resulting beam diffracted by the grating, γ + ψ in equations (2) and (3), is about 115°. The diffracted beam has . coherence regions with the longitudinal coherence length equal to the coherence length of the beam emitted from the source but with coherence unit vector skewed. with respect to the direction of propagation, of about 45 °. The first-order diffracted light beam 70 is collected by a pair of converging lenses 68 and 69, each having focal length f = 15 cm, and pointed the beam 71 towards the sample under analysis. The medium (not shown in the figure), such as a colloidal suspension in water, is contained in a cell 72 of square section, for example of square section with parallel flat sides, transparent glass with 1 cm optical path. The direction of incidence of the radiation beam is perpendicular to the incidence face 25 of the cell 72. The incident beam 71 strikes a volume in the medium having a thickness of the same order of magnitude of the longitudinal coherence length of the beam (i.e. about 20 u- m) . The scattered light from the scattering centers (i.e. particles) in^' the investigated volume is collected at an angle . with respect to the incidence direction. In the apparatus of figure 7, a detection system 80 is positioned so that the detector is capable of collecting the scattered light at an angle a of about 90°. Preferably, the detector angular aperture has smaller than the opening diffraction angle of the scattering center in the volume reached by ^■ the beam.

The detection system consists of a converging lens 73, for example, with a- focal length of 2 cm, which sends the collected light in an optical fiber 78, which input terminal side is optically coupled to a lens with a graded refractive .index (GRIN lens ) 74 of 2.5 mm in length and wheelbase of 0.25 to match the numerical aperture of the light collected by the lens with the numerical, aperture of the optical fiber and select a single speckle in the speckle pattern of scattered light from the colloidal system. The output light from the optical fiber is sent to a detector 77 which includes an avalanche photodiode, which returns an output electrical signal. In another embodiment, the detection system comprises a photomultiplier tube.

The dynamic portion of the electrical output signal from the detector contains the information on the temporal intensity fluctuations of light scattered by the medium (i.e. dynamic signal). The electrical output signal from the detector is sent to a correlator device 76, such as an electron correlation, which analyze the dynamic portion of the signal and it calculates the . time-correlation function of the intensity of scattered light, by well known methods. For example, the output signal from the optical fiber is sent to an avalanche photodiode included in a commercial- tool for the analysis of the dynamic light scattering, Brookhaven ZetaPlus of Brookhaven Instruments, which includes a digital electronic correlator that can compute time correlation functions that ranges from the order of microseconds to the second.

Finally, the device can be interfaced to co-processing unit (e.g. the Central Processing Unit, CPU),, such as a PC 75, which captures the _. temporal correlation function from the correlator device and analyzed it. For example, the analysis includes the interpolation (fitting) of the correlation function with a mathematical function that is the sum of a plurality of decreasing exponential and having the amplitude and the decay time as interpolation parameters for each exponential. The amplitude and the exponential decay time of each exponential allow to find out the diameter and density of the colloids in suspension and in general of the scattering centers in the medium.

In the analysis apparatus 60. of this embodiment, a homodyne detection scheme is used, i.e. the scattered light beam directly hits the detector. However, this embodiment may comprise a system with a heterodyne detection scheme, in which a part of the beam incident on the medium to be analyzed is superposed to the scattered beam.

In some embodiments, the' detection system may include a multiple channel detector such as a CCD sensor.

Figure 8 shows the time correlation function, C(x), of the light scattered by a sample containing calibrated polystyrene nano-spheres of 150 nm in diameter as a function of time τ (ms) for various coherence conditions. The scattered light is detected at a detection angle of approximately 90°. The solid line curve- is the correlation function derived from the light scattered from the sample irradiated by coherent laser light (i.e., with longitudinal coherence length of several mm) at 660 nm and follows the typical law of exponential decay, characteristic of the Brownian motion of colloids. The contrast is close to 30%. The other two curves represent the correlation function calculated from light scattered by the sample irradiated by short longitudinal coherence, with a central wavelength of 660 nm and the longitudinal coherence length of about 17 microns. In dashed line curve, the incident light has a coherence- unit vector parallel to the incidence direction on the sample, while the dotted line curve the incident light has coherence^■ region with coherence unit vector skewed by an angle of 45°. In the case of the coherence unit vector not inclined with respect to . the beam propagation direction, the curve is essentially flat, due to the fact that the longitudinal coherence length is shorter than the differences in optical path length between the beams scattered by different regions of the sample. By skewing the coherence, the correlation function is clearly visible, with a contrast of about 13%, and enables to evaluate . the time and / or decay amplitudes from the exponential decay of the curve and then to derive structural information of the medium, such as the diameter of the colloids contained in the colloidal suspension. The^■ measurement of the dynamic light scattering in the visible spectrum according to the present invention can be used, for example, for the measurement of the diameters of colloids in colloidal systems. Colloids of larger diameters, e.g. from 800 nm to about 1 urn, can be studied with the incident light in the near infrared spectrum, if the liquid medium of the colloidal suspension is not opaque to infrared rays. As an example, the colloidal systems that can be analyzed include colloids compo-sed of polymers, solids or liquids, glues and paints in particular; micelles and liposomes composed of lipids, of interest for the production of drugs or para-pharmacy products, micrometer- sized or nanometer-sized powders, of interest both as products (cements, cosmetics) and for environmental monitoring of pollutant elements^"' (toxic nanoparticles , P 10 asbestos dust). In general, the technique enables the monitoring of production processes, in which it is needed to check step by step the size distribution of particles, both in the disintegration phase (e.g., grinding) and growing phase (e.g., growth of particles with a controlled diameter) . Preferably, the light source for the investigation of the medium is capable of emitting radiation with longitudinal coherence length of less than 1 mm, more preferably less than 100 microns. We note, however, that the selection of the radiation with a short with a suitable longitudinal coherence length depends on the average size of the scattering centers to be investigated. It is noted that the use of a radiation beam with skewed coherence enables the measurement of dynamic scattering also _. with radiation having longitudinal coherence length less than the optical path difference of the radiation scattered by various parts of- the . investigated volume of the medium, in the detection ■ direction.

The use of short-longitudinal-coherence incident light removes or reduces drastically the contribution of the multiple scattering in the detected signal. This fact is particularly advantageous in the case of the analysis of turbid samples or samples with high particle concentration, in which the multiple scattering prevents a correct evaluation■ of the diameters or of the concentration of the particles.

The Applicant understood that the measurement technique according to the general principles .of present invention can be used to measure structural features of size of the order of about 1-30 nm, or, less than one nm, in media with variation of electron density, by analyzing the scattering of the X radiation, in general including in the spectrum the wavelengths typically referred to . as extreme ultraviolet ^' (UV) , e.g. 20-30 nm. Structural characterizations by means of X-rays generally require that the investigation beam possesses a suitable longitudinal coherence, i.e. that it impinges on the medium with almost monochromatic radiation. Typically, in order to achieve a suitable longitudinal coherence length ^J in the X-ray radiation emitted by a source, it is necessary to use a monochromator but it reduces drastically, even by three orders of magnitude, the power of the radiation used for the investigation and thus the sensitivity of the measures that use the scattered radiation. With the availability of sources of synchrotron radiation, characterized by a high intensity, it was possible to use the X-ray radiation with a sufficient degree of coherence in order to perform dynamic scattering measurements. However, the synchrotron sources have the obvious drawback of being extremely expensive ^' and not easily implementable .

Figure 9 illustrates schematically an embodiment of the present invention. The apparatus of the embodiment of Figure 9 is particularly suited for the characterization of the structure of a medium through the scattering of soft X- rays, within the wavelength range form about 1 nm to 20 nm. The apparatus 90 includes a source 91 of electromagnetic X- ray radiation. For example, the source includes a microfocus X-ray tube 92, with emission area with a diameter of 10 micrometers, which emits "bremsstrahlung" radiation, with a maximum emission power at a wavelength of 1 nm and bandwidth of the order of 50% of the peak wavelength. This source can then represent, for the purposes of some embodiments of the present invention, a source of both longitudinally and transversally incoherent radiation .

The radiation emitted by the source 91 passes through a system for the orientation of the coherence 93 that includes an spectral dispersion element. The spectral dispersion element is a diffractive which includes a first mask 97, placed for example at a distance L of about 10 cm from the X-ray tube, which includes a metal sheet 96 opaque to X-rays (e.g. made of platinum), on which a region transparent to X-rays transmission has been created. For example, the transparent region includes a passing-through hole or aperture 95 (pin-hole) , for example, a 12 μπι diameter hole■ made in the metal, and a grating 98 of parallel strips made of a radiation-opaque material, such grating being superimposed to the hole. The grating 98, for example with a pitch of 100 nm and a- coverage ratio of 50%, coupled with the region transparent to the transmission of X rays acts as a diffraction grating operating in transmission and which introduces, an angular dispersion in the beam passing through it giving rise to diffracted beams of radiation of spectral order m (m = 0.1, .. ) that emerge from the side opposite to that of incidence ■ on the grating. For m>0, the angular dispersion skews the coherence regions by a skew angle θ of the diffracted transmitted beams. The first mask 97, and in particular the diffractive element constituted by the grating 98 placed next to the^{^} aperture of the first mask, has therefore two main functions: it increases the transversal coherence length and skews the coherence regions of the radiation. Preferably, the first mask is capable of making a spatial filtering in order to obtain the transversal spatial coherence. It is noted that a pin-hole, such as the hole 95 which is included in the first mask, acts as a spatial filter by introducing a transversal coherence length corresponding to the size of its aperture.

The non-zero-order beam diffracted by the device 93 has coherent regions with coherence layer skewed at an angle θ with respect to the propagation direction shown in figure by the arrow 111 and passes through a second mask 101 placed at a distance of about 2 mm from the first mask 97. The second mask 101 is capable, of selecting the first diffraction order ( rn=± l ) _ancj includes a metal sheet 103 opaque to the radiation which includes a pinhole 102. For a pinhole with diameter of about 10 μπι the first diffraction order of the radiation is transmitted with a skew angle of θ of about 0.01 radians, equal to the^' diffraction angle of the grating, with respect to the beam 112 transmitted by the mask { m= 0 ) .

Moving away from the first mask the^■ diffracted beams become progressively separated and hence the longitudinal coherence length grows. With reference to the above- mentioned example, at the output of the second mask 101, a beam with spectral width., Δλ , of about 10% with respect to the peak wavelength is selected, which-^' corresponds to a longitudinal coherence with coherence length about 10 times the central wavelength of the radiation emitted by the source, e.g. 10 nm for emission wavelength of 1 nm and Δλ = 0.1 nm. The radiation beam output from the second mask

101, which has a longitudinal coherence with length^ and a transversal coherence of about 12 μπι irradiates a medium to be analyzed 100 which includes a plurality of scattering centers. For example, the medium is composed of a composite with a thickness about 10 um along the incidence direction formed by an elastomer loaded with palladium colloids of 5 nm in diameter. The scattering centers generate a beam of scattered radiation which emerges from the medium in theory at any direction in the space (depending in practice on the configuration and on the structure of the medium) . In the case of colloids of the order of few nm in diameter, such as the above-mentioned palladium colloids, thus with a size that is significantly greater than the incident wavelength (1 nm) , the scattering takes place predominantly in the forward direction. It may therefore be beneficial to configure the measuring apparatus so that it collects the radiation scattered at low angle, for example at about a= 0.02 rad (α= 29·) , in order to detect a signal with relatively high intensity. A detection of radiation scattered from a medium at small angles is generally named Small-Angle X-ray scattering (SAXS) . In ^' a "preferred embodiment, the angle of detection of the scattered radiation is between 0.01 rad (-0.57°) and 10°.

In the case of analysis of a medium that includes a disordered system, the ^' radiation scattered from the medium preferably passes through a third mask 107, placed downstream to the medium to be analyzed, . which includes a sheet 104 made of a material which is opaque to the radiation with a pinhole 105, for example an aperture 10- microns wide. The third mask is capable of selecting a single speckle produced by the radiation scattered by the medium at a certain angle, -for example, about 0.01 radians, with respect to the transmitted beam. The scattered radiation that passes through the third mask 107 is detected by a detector -device 110 that includes a photomultiplier tube sensitive to soft X-ray 106. The dynamic portion of the electrical signal output from photomultiplier contains the information on the temporal intensity fluctuations of the light scattered by the medium (i.e. the dynamic signal) . The electrical signal output from the photomultiplier is sent to a correlator device 108, for example an electronic digital correlator that analyzes the dynamic portion of the signal and, from it, calculates the time-correlation function of the intensity of scattered light, by already known methods. Finally, the correlator device can be interfaced to a CPU, for example a PC 109, which acquires the temporal correlation' function calculated by the correlator devices ^• and analyzes it.

It can be noted that when in disordered systems the differences in optical path in the waves diffracted by the different colloids are of the order of 100. nm, . so much greater than the coherence length of about 10 nm, in the absence of a skew of the coherence region, the dynamic signal would be absent. If the medium is a medium with an ordered structure, such as a single crystal, a single coherence region, i.e. a speckle, coincides with the distribution of diffraction of the- diffracted beam at a given order. In this case, the apparatus of Figure 9 may not include the third mask 107, resulting in an increased of the power of the beam which impinges on the medium.

In some forms of preferred embodiment, the apparatus of Figure 9, or at least the portion of the apparatus from the source to the detector, is kept in vacuum, preferably at a pressure less than lxlCT³ atm, more preferably lxlO^"4 atm, or low-pressure atmosphere of helium.

According to certain preferred embodiments in which the incident radiation is an X-ray beam, the longitudinal coherence length, taken in the incidence plane of the medium to be analyzed, is equal to or greater than 5 times the central wavelength of the incident beam. In practice, in some cases of interest, in which a commercial source is used, such as an X-ray tube, an beam impinging on the medium is obtained with adequate power in order to allow the analysis of the radiation scattered by disordered media for longitudinal coherence lengths equal or less than 10 times the central wavelength of the incident beam. However this value should not be taken as limiting value.

According to a preferred aspect, the present invention- makes it possible to use an investigation beam in the X-ray emission spectrum of relatively high power,, without losses due to the monochromator . In the case of sources that are both longitudinally and transversely incoherent, it is preferable to filter the beam emitted by the source through at least one coherence filter capable of selecting one transverse mode of the beam and of producing a. short longitudinal beam coherence.

According to some embodiments, the apparatus includes a first and a second coherence filter, each including respectively a 'first and second pinhole arranged in sequence along the direction of propagation of the beam. According to some .embodiments, and assuming pinholes with circular aperture, the diameters Dl and D2 _Q the first and second pinhole of the coherence filter are selected according to the following already known relationship:

Lc= [Dl / (D2-D1) ] .λ (4)^"

According to some embodiments, the transverse coherence length is selected by setting the value of Dl _t i._e. ^~ Dl . According to an already known relationship Dl j__s selected to be equal to Ι.λ/s, where L is the distance, along the direction of propagation, between the source and the first pinhole and ^s is the diameter of the source.

In the apparatus of Figure 9,- the first coherence filter includes the mask 97 and the second filter includes the mask 101. In the embodiment of Figure 9, the system for the orientation of the coherence is placed next to the first coherence filter because the pinhole of the first filter is acting both as a spatial and temporal filter for the radiation passing through it and as transparent region which together with the grid 98 forms the transmission diffraction grating. However, it is to be understood that other embodiments may include a system of coherence orientation next to . the second coherence filter or downstream of the first or second coherence filter.

It's worth noting that although the transmission through a pinhole typically used for the transverse and longitudinal mode selection causes a significant loss of intensity of the emitted radiation, this loss is less than the loss, obtained if an additional wavelength filtering or ■ a more selective filtering is needed, in order to obtain a "complete" longitudinal coherence.

The measurement technique of the present invention ^' allows to make measurements of dynamic scattering with devices that use experimental parts with relatively low cost. It is however not excluded the application of the measurement technique according to the present invention for investigation beams produced by a synchrotron, for example in the cases in which a significantly increase the beam power is desired. The X-ray dynamic scattering measurement according to the general principles¹ of the present invention allows to analyze important properties of the media in various fields of industrial interest.

A possible application is in the field of crystallography, in which the analysis technique described above allows to study the dynamics of phase transitions, both solid-liquid and solid-solid, and^' in particular the symmetry changes or order-disorder transitions. In particular, in the field of metallurgy the static diffractometers are often traditionally used for the determination of the characteristics of metal alloys in ^'preparation, such as their composition or structural changes caused by heat treatments (such as hardening, annealing)^'. The present invention allows to obtain, dynamic information on the production of metals or metal alloys by using a measurement technique which is compatible for both costs for space with the industrial production of metals. For example the measurement technique allows to analyze the metal compositions near the critical points, and then to obtain information on the time needed for the processes or on the expected life of an obtained product.

The study of the transitions in crystals of industrial interest, such as piezoelectric crystals or ferroelectric ^' perovskites , of the static or dynamic disorder in macromolecular crystals, such as protein crystals, are other possible fields of application of this invention with X-ray investigation radiation. Intermediate sizes between the colloids and individual molecules can be analyzed with ultraviolet rays, in the. case of materials that are at least partially transparent to them. Moreover, . the applications of X-ray dynamic scattering include the analysis of the -composition and formulation of liquid crystals and the. study of very turbid colloidal systems, in which the multiple scattering phenomenon takes place even with visible light beams with low coherence or colloidal systems that are too absorbent to visible light.

Claims

1. A method of structural analysis of a medium by means of the dynamic radiation scattering, the method comprising:

• Irradiating -a volume of the medium which includes scattering centers with an incident beam of electromagnetic radiation with short longitudinal coherence with coherence length ]_ along a longitudinal direction of propagation of incidence, the incident beam having a coherence skewed by a skew angle of θ with respect to the propagation direction of incidence, and

• detect the distribution of temporal fluctuations of the intensity of the beam of radiation scattered from the irradiated volume at an angle a with respect to the propagation direction of incidence.

2. The method according to claim 1, in which the angle of detection is in the range between (2θ-δ) and (2θ+δ), where δ is the angle of the opening for diffraction, of the volume irradiated by the beam of incident radiation. 3. The method according to claim 1, in which the angle of detection is 20.

4. The method according to claim 1, in which the detection step includes receiving the beam of radiation scattered by the medium at a detection angle greater than or equal to the opening angle of diffraction of the volume of the medium hit by the incident beam and encompassed within a collection cone with half-aperture equal to the skew angle θ.

^'5. The method according to any of the preceding claims, in which' the phase of irradiating a volume of the medium includes :

• generating a beam of emission radiation with short longitudinal coherence along an emission propagation direction;

• producing a beam of incident radiation with skewed coherence having an incidence coherence region whose section which penetrates transversally the investigated volume in the medium to be analyzed has a main surface identifying a main plane and a coherence unit vector perpendicular to said principal plane, the coherence unit vector being skewed by an angle θ with respect to the incidence propagation direction, and sending the incident radiation beam onto the medium.

6. The method according to claim 5, in which the phase of producing an incident radiatidn beam with skewed coherence region includes introducing a delay in the emission radiation beam.

7. The method according to claim 6, in which the introduction of a time delay in the emission radiation beam includes sending the emission radiation beam onto at least one spectrally, dispersing element and spread angularly the emission radiation beam into the different spectral components by means of the spectrally dispersing element.

8. The method according to claim 5, in which the phase of producing a beam of incident radiation with skewed coherence region includes :

• diffracting the emission radiation beam separating angularly the emission radiation beam into distinct diffracted beams, each having a diffraction order and

• selecting a diffracted beam · with non-zero diffraction order, and the stage of sending the incident radiation beam onto the medium includes sending the selected diffracted beam onto the medium.

9. The method according to any of the preceding claims, in which the phase of detecting includes generating a signal representative of the distribution of the temporal fluctuations of the detected intensity.

10. The method according to claim 9, which also includes:

• processing the signal representative of ^■ the distribution of temporal fluctuations of the detected intensity by correlating the intensity measured as a function of time in order to produce a time correlation function of the intensity detected at the detection angle a, and

• determining at least one parameter indicative of the structure of the medium from the analysis of the time correlation function.

11. The method according to any of the preceding claims, in which the radiation beam, is a radiation beam centered at a wavelength between 1 nm and- 30 nm, preferably between 1 nm and 20 nm.

12. The method according to claim 11, where the skew angle θ is equal to or greater than 0.01 rad and^' equal to or less than 90°, and preferably between 0.01 rad and 10°.

13. The method according to . any one - of claims from 1 to 10, in which the radiation beam is a beam of light centered at a wavelength in the range from 380 nm to 1400 nm, preferably in the range from 380 nm to 760 nm.

14. The method according to claim 13, where the skew angle ^Dis between 5° and 85°, preferably between 20° and 70° .

15. A structural analysis apparatus of a medium comprising scattering centers by means of dynamic radiation scattering, in which a volume of the medium is irradiated by an incident radiation beam, the apparatus comprising:

• a system of generation of electromagnetic radiation able to produce an incident radiation beam with short longitudinal coherence with longitudinal coherence length l_c along an incidence propagation direction, the incident beam having a skew angle θ with respect to .the propagation direction of incidence, and

• a detection system capable of receiving a beam of radiation scattered from the medium to an collection- aperture centered around a detection angle '- with respect to the incidence propagation direction, the detection system being capable of detecting the distribution of temporal fluctuations of the intensity of the radiation beam scattered from the irradiated volume.

16. The apparatus according to claim 15, in which the collection aperture is centered at a detection angle a about equal to 2θ, preferably the opening angle for diffraction from the volume irradiated by the incident radiation beam has an aperture equal to 2δ, where δ is the opening angle for diffraction of the volume irradiated by the beam of incident radiation.

17. The apparatus of claim 15 or 16, where the system generating the radiation of the incident beam includes:

• a source capable of emitting an emission radiation beam with short longitudinal coherence along a propagation emission direction, the emission beam having a coherence region that has a first principal surface parallel to the wavefront surfaces along along the emission propagation direction, and

• a system for the orientation of the coherence optically coupled to the source, the system being capable of orienting the coherence region in order to produce an incident beam with a skewed coherent region with a skew angle θ with respect to the incidence propagation direction.

18. The apparatus of claim 17, in which the system for the orientation of the coherence includes a spectrally dispersing element configured in order to introduce a temporal delay in the emission radiation beam. 19. The apparatus of any one of claims from 15 to 18, in which the detection system includes at least one detector capable of detecting the distribution of temporal fluctuations of the intensity of the radiation beam scattered from the irradiated volume and of generating a signal representative of the distribution of the detected intensity temporal fluctuations.

20. The apparatus of claim 19 that also includes an analysis system able to receive and process the signal representative of the distribution of the detected intensity temporal fluctuations by correlating the intensity detected as a function of time to produce a temporal correlation function of the intensity detected at least at an angle within the collection aperture.

21. The apparatus of claim 20, in which the analysis system includes an electronic correlator capable of correlating the intensity detected as a function of time to produce a temporal correlation function of the intensity detected at least at an angle- within the collection aperture, the correlator being connected to a processing unit capable of analyzing the temporal correlation function and of determining at least one parameter indicative of the structure of the medium.

22. The apparatus of any one of the claims from 15 to 21, in which the incident radiation beam has a transverse coherence length l_t equal at least to the transversal size of the incident radiation beam.

23. The apparatus according to any one of claims 17-18 and from 19 to 22, where dependent on claim 17, in which the source is able to generate a beam of light centered at a wavelength in the range from 380 nm to 1400 nm, preferably in the range from 380 nm to 760 nm.

24. The apparatus of claim 23, in which the orientation of the system for the orientation of the coherence comprises:

• a diffraction grating optically coupled to the source and configured to separate the light beam emitted from the source into separated diffracted

. beams and

• an optical device capable' of selecting a diffracted beam of non-zero diffraction order that constitutes the incidence radiation beam.

25. The apparatus of claim 24, in which the diffraction grating is placed^' in a diffraction plane and is capable of receiving the emission radiation beam emitted by the source at an incidence angle with -respect to the normal to said diffraction plane and of producing a spectral component with non-zero diffraction order at a diffraction angle with respect to the normal to said diffraction plane, the skew angle of the coherence being determined on the basis of the incidence and diffraction angles of the diffraction grating.

26. The apparatus according to claim 15, in which the radiation generation system of the incident radiation beam includes:

• a source (91) capable of generating a beam of radiation;

• a first coherence filter (97) optically coupled to the source and capable of producing a first beam of radiation with short longitudinal coherence and coherence region that has a first main surface .parallel to the wavefront. surfaces along the emission propagation direction, and

• a system for coherence orientation (93) placed downstream of the first coherence filter and optically coupled to it, the system being capable of ^' skewing the coherence region of the emitted radiation beam with respect to the propagation direction in order to produce as output a radiation r beam with coherence skewed by an angle ^D with respect to the incidence propagation direction. 27. The apparatus according to claim 26 which also includes a second coherence filter (101) optically coupled to the first filter of coherence (97) and placed downstream of it ,^' the^■ second spatial filter being capable of producing a second radiation beam with short longitudinal coherence with a longitudinal coherence lengthK , the second radiation beam forming the incident radiation beam on the medium.

28. The apparatus according to claims from 26 or 27, in which the coherence orientation system (93) includes a spectral dispersion element (^'98) configured to introduce a time delay in the beam impinging on said spectral dispersion element, the spectral dispersion element including a diffraction grating (95, 98) operating in transmission and configured to separate the radiation beam emitted by the source into distinct diffracted beams and to transmit at least one of the distinct diffracted beams with non-zero diffraction order.

29. The apparatus according to claim 28, where^' dependent on claim 27, in which the diffraction grating comprises a pinhole (95) and a grating (98) comprising a plurality of regions opaque to radiation, said grating being placed next to the pinhole so that the pinhole of the first diffraction grating acts as a first coherence filter (97) .

30. The apparatus according to any one of claims from 26 to 29, in which the source is capable of emitting an emission beam of X-ray centered at a wavelength in the range from 1 nm to 20 nm.