DE102011001106B3 - Method for distinguishing between fiber crossing and fiber bonding in fiber network, involves illuminating point of fiber network with polarized light from direction that is more than certain degree - Google Patents

Abstract

The method involves illuminating a point of the fiber network with polarized light (12) from a direction that is more than 15 degree, particularly 10 degree and not more than 5 degree from the normal line. The ellipsometric parameter of the directly reflected light (18) on the optical components (20,22) is determined. The gradient of the ellipsometric parameter is compared with a reference value. An independent claim is also included for a device for analyzing a fiber network.

Description

TECHNICAL AREA

The present invention relates to the analysis of fiber networks, such as those used in paper research. More particularly, the invention relates to an apparatus and method for discriminating fiber intersections and fiber bonds in a fiber network.

BACKGROUND OF THE INVENTION

Paper research has long been searching for a fast, non-destructive process for decoding a fiber network. Such a method should in particular make it possible to distinguish between individual fibers, background, unbound fiber crossings, also referred to as "crossing surfaces", and fiber bonds, also referred to as "bonding surfaces".

The tear strength of paper, in addition to the strength of the individual fibers, depends primarily on the ability of the fibers to form fiber bonds. The strength of the bonds depends on the size of the bonded surface and the specific binding force, for example the binding force per surface. Accordingly, the paper strength can generally be increased by increasing the flexibility of the fibers, thereby increasing the bond areas, or by increasing the bond strength by treating the fibers in a particular manner, for example by adding suitable chemicals.

To analyze a fiber network, the bonding surfaces of fiber bonds must be determined. For this purpose, a number of methods are known from the prior art. In Yang et al., Measurements of geometric parameters of fiber networks, Part 1 Bonded surfaces, aspect ratios, fiber moments of inertia, bonding state probabilities, Svensk Papperstidning 13, 426-433 (1978), the binding area was determined using images of Detects samples that have been cut with a microtome. G. Jayme and G. Hunger, Electron microscope 2- and 3-dimensional classification of fiber bonding, formation and structure of paper, Transactions of the 2nd Fundamental Research Symposium, Oxford, UK, British Paper and Board Maker's Association, Technical Section , pp. 135-170 (1961) proposed the use of an electron microscope to analyze the (previously) bonded areas of fiber bonds that were torn apart. In A Torgnysdotter, The link between the fiber contact zone and the physical properties of paper: a way to control paper properties, J. Compos. Mater. 41, 1619-1633 (2007), the contact area between fibers was examined using light microscopy and a suitable coloring.

Fluorescence resonance energy transfer was used in C.I. Thomson, Probing the nature of cellulosic fiber interfaces with fluorescence resonance energy transfer, PhD Thesis, School of Chemistry and Biochemistry, Georgia Institute of Technology, USA (2007) to analyze fiber bonds.

Already in the 1960's, Page and Tydeman (DH Page, Fiber-to-fiber bonds, Part 1. A method for their direct observation, Paper Technol. 1, 407-411 (1960) and (DH Page and PA Tydeman, Fiber-to-fiber bonds, Part 2. A preliminary study of their properties in paper sheets, Paper Technol. 1, 519-530 (1960)) introduced a method in which the bound region of a fiber bond is determined by means of polarized light microscopy was determined.

In E. Gilli et al., An optical model for polarization microscopy analysis of pulp fiber-to-fiber bonds, Composite Interfaces 16 (2009) 901-922, fiber bonds were studied using polarization microscopy and microtome sections. The experiments showed that these two known methods can lead to significantly different results. It was found that polarization microscopy can not always clearly differentiate between crossed but unbound fibers (fiber intersections) on the one hand and bonded fibers (fiber bonds) on the other hand. In this work an optical model was presented, which describes the imaging of fiber bonds in polarization microscopy, as proposed by Page and Tydeman, very reliable. On the basis of this model it was possible to explain why some fiber bonds are recognizable in polarization microscopy and others are not.

This work facilitates the correct interpretation of microscope images with polarized light, but at the same time shows the limits of this known method with regard to the distinctness of fiber bonds and fiber intersections.

SUMMARY OF THE INVENTION

There is therefore still a need for a reliable method for nondestructive decryption of a fiber network, which in particular enables a reliable differentiation of fiber intersections and fiber bonds. The object of the present invention is to specify a method suitable for this purpose and a device suitable for this purpose.

This object is achieved by a method according to claim 1 and an apparatus according to claim 16. Advantageous developments are specified in the dependent claims.

• a) Beleuchten einer Stelle des Fasernetzwerkes mit polarisiertem Licht aus einer Richtung, die maximal 15°, vorzugsweise maximal 10°, und besonders vorzugsweise maximal 5° von der Normalen abweicht,
• b) Bestimmen der Ellipsometrieparameter Ψ(Θ) und Δ(Θ) des unmittelbar reflektierten Lichtes oder von reflektiertem Licht, welches nach der Reflektion eine oder mehrere optische Komponenten durchlaufen hat, wobei in den Schritten a) und b) ein Winkel Θ zwischen einer vorbestimmten Raumrichtung des Netzwerkes und mindestens einer polarisationsempfindlichen optischen Komponente im Lichtweg des einfallenden Lichtes (12) und/oder des reflektierten Lichtes (18) eingestellt ist,
• c) Wiederholen der Schritte a) und b) für eine Mehrzahl von unterschiedlichen Winkeln Θ,
• d) Vergleichen des Verlaufs von Ψ(Θ) und/oder Δ(Θ) mit mindestens einem Referenzwert, und
• e) Entscheiden anhand des Vergleiches, ob an der betreffenden Stelle eine Faserkreuzung oder eine Faserbindung vorliegt.

The method according to the invention comprises the following steps:

• a) illuminating a position of the fiber network with polarized light from a direction which deviates from the normal by a maximum of 15 °, preferably a maximum of 10 °, and particularly preferably a maximum of 5 °,
• b) determining the ellipsometry parameters Ψ (Θ) and Δ (Θ) of the directly reflected light or reflected light which has passed through one or more optical components after reflection, wherein in steps a) and b) an angle Θ between a predetermined Spatial direction of the network and at least one polarization-sensitive optical component in the light path of the incident light ( 12 ) and / or the reflected light ( 18 ) is set,
• c) repeating steps a) and b) for a plurality of different angles Θ,
• d) comparing the course of Ψ (Θ) and / or Δ (Θ) with at least one reference value, and
• e) On the basis of the comparison, decide whether there is fiber crossing or fiber bonding at the point concerned.

In the conceptually simplest embodiment, step c) could consist in that the fiber network is rotated relative to the optical system in accordance with the angle Θ mentioned in step b). However, as will be explained in more detail below, it is also possible, and optionally, in practical terms, to prefer to leave the sample stationary and instead to rotate polarization-sensitive optical components.

According to the invention, a distinction is made between fiber intersections and fiber bonds on the basis of the course of the ellipsometry parameters Ψ (Θ) and Δ (Θ). The inventors have found that, in the case of vertical illumination, or illumination that deviates from the normal at most 15 °, preferably at most 10 ° and particularly preferably at most 5 °, fiber bonds and fiber intersections in a phase space consisting of the ellipsometry parameters Ψ and Δ and the rotation angle Θ, are separable. For this reason, it can be decided whether a fiber bond or a fiber intersection exists for a plurality of angles Θ based on the course of Ψ (Θ) and Δ (Θ).

The term "course" indicates that the ellipsometry parameters Ψ and Δ are measured for a plurality of angles Θ at the same illuminated location. The way in which this "course" is then evaluated concretely to make the decision depends on the individual case and practical considerations. For example, it would be possible to compare the "course" of Ψ (Θ) or Δ (Θ) with a reference curve. In many cases, however, this will not be necessary, but it will be sufficient to compare certain characteristic points of the course of Ψ (Θ) or Δ (Θ) with certain individual reference values in order to differentiate between fiber bonds and fiber intersections the computational effort significantly simplified. In this sense, the "comparison of the course" of Ψ (Θ) and / or Δ (Θ) is to be understood as meaning "at least one reference value". As shown below with reference to an embodiment, it may, for. B. be sufficient if a certain value of Ellipsometrieparameters from the described course is compared with a certain reference value.

wobei r_s den Reflexionskoeffizienten des s-polarisierten Lichtes (senkrecht zur Einfallsebene) und r_p den Reflexionskoeffizienten für p-polarisiertes Licht (parallel zur Einfallsebene) bezeichnet.Ellipsometry determines the change in polarization state of light when reflected on a sample. The change of polarization state can be described by the complex ratio ρ ^ of the reflection coefficients r _s and r _p :

where r _s denotes the reflection coefficient of the s-polarized light (perpendicular to the plane of incidence) and r _p the reflection coefficient for p-polarized light (parallel to the plane of incidence).

The value for ρ ^ is usually described by ellipsometry parameters Ψ and Δ, where tan (Ψ) corresponds to the magnitude of ρ ^ and Δ corresponds to the change in the phase difference between s- and p-polarized light: ρ ^ = tan (Ψ) exp [i (δ _p - δ _s )] = tan (Ψ) exp (iΔ)

Ellipsometry measurements are usually made for obliquely incident light. In the case of perpendicularly incident light, as in the preferred embodiment of the present invention, the polarization directions s and p are strictly not defined, which is why the vertical incidence ellipsometry is also referred to as "reflection anisotropy". Within the scope of the invention, the s and p directions can be determined arbitrarily. In the following embodiment, the direction of a current polarization angle Θ of linearly polarized incident light is defined without limiting the generality as the p-direction, and the s-direction is defined perpendicular thereto, ie p (Θ) = Θ and s (Θ) = Θ + 90 °.

Preferably, the ellipsometry parameters Ψ (Θ) and Δ (Θ) are measured for a sequence of rotation angles Θ covering at least an angular range of 90 ° and at which the interval between adjacent rotation angles of the sequence is at most 25 °, preferably at most 15 °. In other words, the above "history" of Ψ (Θ) and Δ (Θ) is determined for an angular range covering at least 90 ° and containing sufficiently dense data points due to the maximum distance between adjacent rotation angles of the sequence. An interval of for example 10 ° to 15 ° between adjacent rotation angles represents a good compromise between a sufficient data density for the reconstruction of the course of Ψ (Θ) and Δ (Θ) on the one hand and a moderate number of measuring points on the other.

In the preferred embodiment, the incident light is linearly polarized. However, it is also possible to perform a similar method with circularly polarized incident light. Also in this case, fiber bonds, fiber intersections and individual fibers can be separated in a phase space (Ψ, Δ, Θ). However, in this case, of course, other reference values or reference curves result in their differentiation.

In a preferred embodiment. shall be determined by comparing the course of Ψ (Θ) with a reference value as to whether there is a bond, and in the event that it is determined that there is no bond, it shall be determined by comparing Δ (Θ) with a reference value an intersection or a single fiber is present.

The comparison of the "course" of Ψ (Θ) and / or Δ (Θ) with a reference value can be, for example, that the value Ψ (Θ ₀ ) or Δ (Θ ₀ ) for a characteristic angle Θ ₀ with a associated reference value is compared. The characteristic angle Θ ₀ can be an angle for which Ψ (Θ ₀ ) or Δ (Θ ₀ ) assumes a characteristic value, in particular an extremal value.

In a preferred embodiment, Θ _{0 is} the value at which Ψ (Θ) takes a minimum, and the comparison of the course of Ψ (Θ) with the reference value is that Ψ (Θ ₀ ) is compared with a reference value Ψ _crit and it is determined that a bond exists if: Ψ (Θ ₀ ) <Ψ _crit .

With the help of the ellipsometry parameters, it is not only possible to distinguish between fiber intersections, fiber bonds and individual fibers, but at the same time the angle ξ of a single fiber can be determined from the same parameters, or in the case of a fiber bond or fiber intersection, the angle ξ of the upper one of the two fibers, respectively with respect to the predetermined spatial direction. This additional information, in addition to the distinction between single fiber, fiber crossing, and fiber binding, allows almost complete decryption of the network.

In particular, it can be determined in an advantageous development in a crossing or binding point on the basis of the angle ξ of the overhead fiber, which of the two fibers is at the top. This is additional information that can not be obtained with any conventional non-destructive method. In a preferred embodiment, the angle ξ is derived from the angle Θ ₀ , for which Ψ (Θ) assumes a minimum.

In an advantageous development, the reflected light is passed through a λ / 4 plate before the measurement of the ellipsometry parameters. The inventors have found from detailed simulations that the separability of the cases of interest in the phase space (Ψ, Δ, Θ) is particularly pronounced when such a λ / 4-plate is placed in the light path of the reflected light.

As mentioned above, the ellipsometry parameters Ψ (Θ), Δ (Θ) are determined at each point of the fiber network for a plurality of different angles of rotation Θ. For this purpose, for example, the sample can be rotated between different measurements. However, in a preferred embodiment, the different polarization angles θ are adjusted by rotating a polarizer in the light path of the incident light and, if necessary, polarization-sensitive optical components disposed in the light path of the reflected light are rotated together with said polarizer in the light path of the incident light. This embodiment has the advantage that the images produced are always congruent for different angles of rotation.

In a preferred embodiment, the ellipsometry parameters are determined using a plurality of intensity measurements at different settings of an analyzer. This measurement method of the ellipsometry parameters is also known as "Rotating Analyzer Setup" of the prior art. For example, the ellipsometry parameters Ψ and Δ can be determined from four intensity measurements at analyzer settings of 0 °, 45 °, 90 ° and 135 °. For more details, refer to Hirujuki Fujiwara (Spectroscopic Ellipsometry - Principles and Applications, John Wiley & Sons, Hoboken, NJ, USA, 2007).

In an advantageous embodiment, the reflected light is deflected by means of a partially transparent mirror in the direction of a device for measuring the Ellipsometrieparameter. In this case, the reflected light can preferably be deflected between the semitransparent mirror and the device for measuring the ellipsometry parameters with the aid of another mirror. As a result, a phase jump caused by the beam splitter is corrected, as explained in more detail below.

In an advantageous embodiment, an illumination optics is used, with which a surface area of the fiber network is illuminated, and uses imaging optics with which the light reflected at the fiber network is imaged onto an image sensor. Thus, in this embodiment, an extended area of the fiber network as a whole can be analyzed, simultaneously creating a microscope image of the fiber network, and in addition, at each point of the microscope image, determining the course of the ellipsometry parameters for a plurality of different angles of rotation. In this way, a non-destructive and real-time image of the network can be obtained as well as additional information regarding the fiber network from the ellipsometry parameters, in particular the distinction between fiber bonds, fiber intersections, single fibers and fiber angles and which of two fibers in a bond or intersection above lies.

BRIEF DESCRIPTION OF THE FIGURES

Further advantages and features of the invention will become apparent from the following description in which the invention will be described by means of embodiments with reference to the accompanying drawings. Show:

1 (a) - (c) schematic representations of the optical structure of a device for analyzing a fiber network.

2 (a) - (f) the course of the ellipsometry parameters Ψ (Θ) and Δ (Θ) as a result of a simulation of over one million fiber configurations.

3 (a) and (b) enlarged sections 2 B) ,

3 (c) and (d) enlarged sections 2 (d) ,

3 (e) and (f) enlarged excerpts 2 (f)

DESCRIPTION OF THE PREFERRED EMBODIMENT

For a better understanding of the present invention, reference will now be made to the preferred embodiments illustrated in the drawings, which are described in terms of specific terminology. It should be noted, however, that the scope of the invention should not be limited by this specific description.

1 (a) Fig. 12 schematically shows the structure of a fiber network analysis apparatus according to an embodiment of the invention. As 1 (a) can be seen, falls a ray of light 12 perpendicular to a sample 14 of the fiber network to be examined. The incident light beam 12 is tested before hitting the test 14 with a linear polarizer 16 linearly polarized.

That at the rehearsal 14 reflected light 18 is at a beam splitter 20 at least partially deflected in the horizontal direction, by a λ / 4 plate 22 and an analyzer 24 guided and attached to an image sensor (in 1 (a) not shown). The analyzer is doing this 24 together with the image sensor (not shown) represents an exemplary embodiment of the device mentioned above for measuring the ellipsometry parameters. Intensities of the reflected light are used to determine the ellipsometry parameters 18 for four different settings of the analyzer (0 °, 45 °, 90 °, 135 °) and from these intensity values the ellipsometry parameters Ψ and Θ can be calculated, as for example in the textbook Hiroyuki Fujiwara, Spectroscopic Ellipsometry - Principles and Applications, John Wiley and Sons, Hoboken, NJ, USA, 2007.

As described above, the ellipsometry parameters Ψ and Δ for a plurality of rotation angles Θ between a predetermined spatial direction of the sample 14 and polarization-sensitive optical components. In the embodiment of 1 (a) This is achieved by adding the sample 14 rotated and the optics is held. This approach is the simplest in the mathematical description below and is used as a starting point for the following calculations and simulations.

However, in practical terms, it is preferable that the sample and the image sensor (in 1 (a) not shown) and instead rotate the "polarization sensitive" optical components as shown in FIG 1 (b) and 1 (c) is displayed. The construction after 1 (b) is with that of 1 (a) identical, except that instead of a rotation of the sample by an angle Θ the polarizer 16 , the λ / 4 plate 22 and the analyzer 24 be rotated by an angle Θ.

In 1 (c) Another variant is shown in which also the sample 14 is fixed and the polarizer 16 , the λ / 4 plate 22 and the analyzer 24 be rotated by an angle Θ. Unlike the construction of 1 (b) is however in the light path of the reflected light 18 a non-polarizing mirror 26 arranged to serve a phase jump through the non-polarizing beam splitter 20 as will be apparent from the mathematical description of the optical components given below. Furthermore, in 1 (c) a light source 28 and a lighting optics 30 shown schematically, which allow a specific area of the sample 14 Further, in 1 (c) an imaging optics 32 shown schematically, with the reflection image of the sample 14 on an image sensor 34 can be displayed. Naturally, such components may also be used in the embodiments of 1 (c) and 1 (b) be provided, but there have been omitted for clarity.

The in 1 (c) Conceptually, the design shown corresponds essentially to that of a reflected-light microscope, which, however, is supplemented by a device for measuring ellipsometry parameters for different polarization angles Θ. With the device of 1 (c) can produce a conventional microscope image and simultaneously using the same optics 30 . 32 and the same image sensor 34 for each pixel the pair of ellipsometry parameters Ψ and Δ are determined.

The inventors have found that it is surprisingly possible to differentiate between individual fibers, fiber intersections and fiber bonds on the basis of the ellipsometry parameters Ψ (Θ) and Δ (Θ), which result with normal or almost vertical incidence of light and for a sequence of different polarization angles Θ. This finding is the result of simulations, which are described in more detail below.

The aim of the simulations is to make certain components of the superstructures of certain fiber models 1 (a) . 1 (b) or 1 (c) in such a way that the corresponding ellipsometry parameters Ψ (Θ) and Δ (Θ) can be calculated. For simulation, an algorithm proposed by Matthias Schubert (Polarization-dependent Optical Parameters of Arbitrarily Anisotropic Homogeneous Layered Systems, Physical Review B, 53: 4265-4274, 1996) is used. Schubert's algorithm is a general solution to a 4 × 4 transfer matrix formalism proposed by Berreman (Dwight W. Berreman, Optics in Stratified and Anisotropic Media: 4 × 4-matrix formulation.) Journal of Optical Society of America, 62 (4): 502-510, 1972).

This algorithm is able to calculate arbitrarily multi-layered anisotropic samples with any orientation of the optical axes for all angles of incidence. As a result of this algorithm, either the ellipsometry parameters can be determined directly or alternatively a Jones matrix, which reflects the optical behavior of the sample. With the help of this Jones matrix, in addition to the sample, the entire optical setup, including the polarizer, can be used 16 , Beam splitter 20 , Mirror 26 and λ / 4 plates 22 be simulated. Berreman's approach starts from a 6 × 6 matrix representation of the Maxwell equations for plane waves and describes the considered optical system as a 4 × 4 transfer matrix, which according to Schubert takes the following form:

In this case, the transfer matrix T contains all the properties of the multilayer optical system and represents an image of the incident wave in p- and s-polarization (A _p , A _s ) on the reflected wave (B _p , B _s ) and the transmitted wave (C _p , C _s ). In the above equation, the left vector thus represents the waves before the sample, the right vector the waves after the sample. Since it is assumed that there is no backward wave after the sample, the components D _p and D _s in the right wave vector are 0.

weil sich daraus unmittelbar die Ellipsometrieparameter Ψ und Δ ermitteln lassen: Ψ = arctan |ρ ^| (1.3) Δ = –arg ρ ^ = –In(Im(ρ ^)), (1.4) The transfer matrix can be constructed from individual transfer matrices for the individual layers by multipllication, the wave equation having to be solved for each layer, taking into account the boundary values. From the individual elements of the entire transfer matrix, the optical quantities of interest can now also be determined. In the present case, this is the complex reflectivity ratio

because the ellipsometry parameters Ψ and Δ can be determined directly from this: Ψ = arctan | ρ ^ | (1.3) Δ = -arg ρ ^ = -In (Im (ρ ^)), (1.4)

benötigt. Ihre Elemente ergeben sich wie folgt (s. Hiroyuki Fujiwara, Spectroscopic Ellipsometry – Principles and Applications, John Wiley & Sons, Hoboken, NJ, USA, 2007):

To embedding these results in the simulation of the optical structure is also the reflection Jones matrix of the sample

needed. Their elements are as follows (see Hiroyuki Fujiwara, Spectroscopic Ellipsometry - Principles and Applications, John Wiley & Sons, Hoboken, NJ, USA, 2007):

The optical structure according to one of the variants 1 (a) to 1 (c) contains a linear polarizer 16 , the sample 14 , a non-polarizing beam splitter 20 , optionally a non-polarizing mirror 26 , the analyzer 24 and the detector 34 , The analyzer 24 and the detector 34 however, they can be omitted in the calculation, since they only serve to measure the ellipsometry parameters in the actual experiment, but these can be determined in the simulation according to equations 1.3 and 1.4.

für den Aufbau von 1(b) (im Folgenden Aufbau „B⁰”) und J_B, für den Aufbau von 1(c) (im Folgenden Aufbau „B”) miteinander verglichen:

The following are the Jones matrices J _A for the construction of 1 (a) (hereinafter structure "A"),

for the construction of 1 (b) (in the following structure "B ⁰ ") and J _B , for the construction of 1 (c) (in the following structure "B") compared to each other:

The following applies to the Jones matrices for the optical elements:

Here it was assumed that the angle Θ corresponds to the p-polarization direction. As mentioned in the beginning, this is a pure convention question, since with a vertically incident light beam 12 the p and s polarization directions are not clearly defined. Since the simulation and the actual measurement always cover a certain range of rotation angles Θ and the course of the ellipsometry parameters Ψ and Δ is considered over this angular range, it does not matter for the result, which convention is used, as long as it is consistently used.

With this formulation, the equivalence of the configurations A, B ⁰ and B 'can be checked. The coordinate systems of the expansion B ⁰ and B 'in relation to the structure A are rotated by the angle Θ, which of course must also be taken into account. For the expansion B ⁰ results:

As can be seen from the result, the phase jump at the beam splitter, which can not be co-rotated, results in a rotation term that can not be shortened. In comparison, fit results in the construction B '

Finally, you get for the structure A

The difference between the structure B 'and A thus exists only in a twisted coordinate system and a sign difference.

Equation (1.2) thus implies equations 1.19 and 1.20 for the complex reflection ratio ρ ^

The sign difference generates, as is apparent directly from equation 1.2, a phase jump in Δ of +/- 180 °: ρ ^ _{B '} (-θ) = -ρ ^ _A (0) = ρ ^ _A (0) e ^{± iπ} = tanΨe ^{i (Δ ± π)} , Ψ _B' = Ψ _A , Δ _{B '} = Δ _A ± 180 °. (1.22)

Finally, equation 1.6 for structure A follows

Thus, the ellipsometry parameters can be determined directly from the transfer matrix elements. The underlying simulations were carried out here after construction A, since the calculation for this is the simplest and - as shown above - the results are equivalent to those from the structure B anyway. Considering the course of the ellipsometry parameters of the different simulated systems (s. 2 and 3 below), it is striking that due to the symmetry of the system, a phase jump in Δ of 180 ° corresponds to a 90 ° rotation of the fiber. For the recognition algorithm presented here, it therefore does not matter whether the structure A or B 'is used.

The simulation was based on over 3 million single-fiber, fiber-cross and fiber-bond models, simulating the fibers as a two-layer system representing the thickest layer of the fiber, the secondary wall. This wall contains over 90% of the fiber material and is the only layer with a nearly crystalline structure. Therefore, it can be assumed that it is also decisive for the optical properties. For more details, see Gilli et. al., An optical model for polarization microscopy analysis of pulp fiber-to-fiber bonds, Composite Interfaces, 16 (5): 901-922, 2009 and the disclosure WO96 / 10168 directed.

With regard to the different fiber parameters, in particular fiber wall thickness and fibril angle, literature data were used. The orientation of the sample was randomized in the simulation for each (simulated) measurement, similar to an actual fiber network, where any angle of the fibers can occur.

In the simulation, for each (simulated) measurement, the ellipsometry parameters Ψ and Δ for a plurality of polarization angles Θ were measured from a range of 0 ° to 180 °, thereby generating a profile of the ellipsometry parameters Ψ, Δ as a function of the polarization angle Θ. Since the simulation of the structure A (corresponding to 1 (a) ), different polarization angles are obtained by different rotation angles of the sample, but the same results can be achieved with the expansion B '(see FIG. 1 (c) ) receive.

In 2a to 2f The simulated results are presented for over 3 million exemplary cases, subdivided into individual fibers ( 2 (a) for Ψ and 2 B) for Δ), fiber crossings ( 2 (c) for Ψ and 2 (d) for Δ) and fiber bonds ( 2 (e) for Ψ and 2 (f) for Δ). In the simulation, a deviation φ _{a of} the angle of incidence of the incident light beam 12 considered by the normal at 0-5 °. In the diagrams, the frequency of the respective ellipsometry parameters is represented by means of contour lines.

In 3 (a) and 3 (b) are the critical areas of the diagram for decoding the fiber network 2 B) , which shows the course Δ (Θ), shown enlarged. Show in a similar way 3 (c) and (d) or 3 (e) and (f) enlarged excerpts 2 (d) respectively. 2 (f) , It can be seen from the simulation results that the different cases can be distinguished on the basis of the course of the ellipsometry parameters Ψ (Θ) and Δ (Θ). It can be seen that the course Ψ (Θ) always has a typical course with two minima, s. 2 (a) , (c) and (e). Furthermore, it can be seen that the minima are always lower in the case of a fiber bond than in the case of a fiber crossing or a single fiber. This observation can be used to differentiate between fiber bonds on the one hand and fiber intersections or single fibers on the other hand.

A possible case distinction can be made as follows: first, the angle Θ _{0 is} determined at which Ψ (Θ) assumes a minimum. At this value Θ ₀ Ψ (Θ ₀ ) is compared with a reference value Ψ _krit = 85,5 °. If Ψ (Θ ₀ ) <Ψ _crit = 85.5 °, then there is a fiber bond. The angles Θ ₀ and Ψ _crit are in 2 (a) , (c) and (e) are shown as dashed lines. To distinguish between single fiber and fiber intersection is on 3 (a) to (d), in which excerpts from the diagrams of 2 B) and 2 (d) are shown enlarged. This results in the following distinguishing criterion: If there is no fiber bonding, it is possible to distinguish between a single fiber and a fiber intersection on the basis of the ellipsometry parameter Δ. How out 2 can be seen, Ψ (Θ) has two maxima at different values Θ ₀ . Therefore, a case distinction is first made as to whether Δ (Θ ₀ )> 0 or <0.

If Δ (Θ ₀ )> 0, a single fiber is present if Δ (Θ ₀ ) <Δ _{crit +} = 106.5 °, and there is an intersection if Δ (Θ ₀ )> Δ _{crit +} = 106, 5 °.

However, if Δ (Θ ₀ ) <0, a single _{fiber is} present if Δ (Θ ₀ ) <Δ _krit- = -73.5 °. An intersection exists if Δ (Θ ₀ )> Δ _krit- . In 3 (a) bis (f) the values for Θ ₀ , Δ _{krit +} and Δ _{krit- are indicated} by dashed lines.

Note that this is only an exemplary way of distinguishing between single fibers, fiber intersections and fiber bonds based on the course of Ψ (Θ) and Δ (Θ). The general underlying insight is that the in 1 the structure of Ψ (Θ) and Δ (Θ) is characteristic for the mentioned different cases (crossing, binding, single fiber), but it is left to practical considerations, on the basis of which specific characteristics of the course ultimately the distinction is made.

The simulation has shown that according to the above criteria in more than 3 million test configurations a distinction was made in all cases between single fiber, fiber binding and fiber crossing.

The simulations also took into account that the incidence of light is not exactly normal to the sample. It could be verified that even with moderate deviations from the normal there is still a distinctness of the three mentioned cases. However, a comparison with other oblique incident light configurations, for example, at angles more than 15 ° from normal, revealed that the cases in question could be distinguished much more poorly. A structure with perpendicular or at least almost vertical incident light is therefore to be preferred.

In the simulation also a certain noise of the parameters was considered. It can be shown that for the noise band ratio ΔΔ / ΔΨ ≤ 6.75 applies. This means that a signal / noise ratio of 0.5% in the value Ψ corresponds to a signal / noise ratio in the value Δ of about 3.5%. Even for such noise, it was found that still 99% of the bindings were properly recognized as such. The susceptibility to distinction between crossbreeding and single fibers proved to be greater, at these noise levels totaled almost 15%. However, this error is relatively uncritical, since one can easily distinguish individual fibers and fiber intersections in the recorded image, the error is thus automatically corrected by the image analysis. The higher error susceptibility in the distinction between single fibers and crossing is that this decision is made on the parameter Δ, for which the noise band is wider than for Ψ. An important finding, however, is that the fundamentally more difficult distinction between fiber crossing and fiber bonding can be made with high reliability even taking noise into account.

Furthermore, it can be seen from the simulations that the angle Θ ₀ , at which Ψ becomes minimal, corresponds to a polarization which lies at an angle of 45 ° to the main fiber axis of the single fiber or of the upper one of crossed or bound fibers. Thus, from Θ ₀ , the angle ξ between the main fiber axis and the 0 ° -Polarisatorstellung be calculated. However, here again a fiber distinction with reference to Δ is necessary: ξ ≈ θ ₀ - 45 ° for Δ (θ ₀ )> 0 ξ ≈ θ ₀ - 135 ° for Δ (θ ₀ ) <0. (3.1)

In this way, at each pixel from the ellipsometry parameter at the same time the angle ξ of the fiber with respect to a predetermined direction, for example, the 0 ° position of the polarizer can be determined. In addition, in the case of a fiber bond or fiber intersection, it can be determined via the angle ξ which of the two fibers lies at the top. This requires a single fiber to be followed only up to a crossing / bond. If the angle ξ is continuous when tracing the fiber over an intersection or bond, the corresponding fiber is at the top; if it is unsteady, it is at the bottom. This is a significant new piece of information that is still not possible in investigations of fiber bonds in a light microscope, even in a polarizing microscope.

In summary, therefore, with the method of the invention it can be determined not only for each pixel whether there is a single fiber, an unbound intersection or a bond, but also the vertical position of the fiber can be determined, its major axis angle and the binding or Crossroads angle. This is, in principle, a complete set of all the information needed for a finite element based network mechanics simulation, which can then be verified from the optical measurement by means of mechanical tearing tests. No amount of known measuring technology is capable of doing something similar.

Furthermore, it is possible, subsequent to the measurement described above, to determine further ellipsometry parameters without the λ / 4 phase plate and then to estimate the parameters fiber wall thickness and fibril angle for each pixel by means of a further simulation. The additional computational effort required for this proves to be moderate. In this way, all relevant data on fiber mechanics can be determined in a single instrument and in just two measurement cycles.

It should be emphasized that the in 1 shown measuring structure is not mandatory. For example, further optical or alternative optical elements may be provided in the beam path, which will then lead to a different course of Ψ (Θ) and Δ (Θ). For each suitable structure then a correspondingly adapted simulation must be carried out, similar to the above for the construction of 1 has been described. For example, it is possible to dispense with the λ / 4 plate. Further, it is possible to use instead of the linear polarizer 16 to use a circular polarizer. The inventors' studies show that such modifications are possible, although the structure described herein is presently considered the most promising. In any case, it proves to be advantageous if the incident light is perpendicular or nearly perpendicular to the sample.

It proves to be particularly advantageous if, as in 1 (c) shown a certain area of the sample 14 with a lighting look 30 illuminated and with an imaging optics 32 on an image sensor 34 is shown. During image acquisition then different settings of the polarizer 16 made, covering a total of an angular range of at least 90 ° and in which the interval between adjacent angles of rotation is a maximum of 25 °, preferably a maximum of 15 °. For every adjustment of the polarizer 16 Then, with four different settings of the analyzer, the intensities are measured for each pixel, from which in turn the ellipsometry parameters Ψ and Δ for the respective rotation angle Θ can be determined. For example, if N different rotation angles Θ are to be measured, only 4 × N images must be taken for the entire imaged area of the fiber network. These images additionally represent an optical image of the fiber network. In this way, a microscope image of the fiber network can thus be obtained simply and in real time, and at the same time the fiber structure in terms of single fiber, fiber intersection, fiber bonding, fiber angle and vertical arrangement of crossed or bound fibers can be analyzed.

Although preferred embodiments have been shown and described in detail in the drawings and foregoing description, this should be considered as illustrative and not restrictive of the invention. It should be understood that only the preferred embodiments are illustrated and described and all changes and modifications that are presently and to the extent that they come within the scope of the appended claims should be protected.

LIST OF REFERENCE NUMBERS

10

Device for analyzing a fiber network

12

incident light beam

14

Sample of the fiber network

16

polarizer

18

reflected light beam

20

semitransparent mirror

22

λ / 4 plate

24

analyzer

26

mirror

28

light source

30

illumination optics

32

imaging optics

34

image sensor

Claims (22)

A method of distinguishing fiber intersections and fiber bonds in a fiber network, comprising the steps of: a) illuminating a location of the fiber network with polarized light ( 12 ) from a direction that deviates a maximum of 15 °, preferably a maximum of 10 °, and particularly preferably a maximum of 5 ° from the normal, b) determining the ellipsometry parameters Ψ (Θ) and Δ (Θ) of the directly reflected light ( 18 ) or of reflected light which, after reflection, has one or more optical components ( 20 . 22 . 26 ) wherein in steps a) and b) an angle Θ between a predetermined spatial direction of the network and at least one polarization-sensitive optical component in the light path of the incident light ( 12 ) and / or the reflected light ( 18 c) repeating steps a) and b) for a plurality of different angles Θ, d) comparing the course of Ψ (Θ) and / or Δ (Θ) with at least one reference value, and e) deciding on the basis of Compare whether there is fiber crossing or fiber bonding at the site in question. The method of claim 1, wherein the ellipsometry parameters Ψ (Θ) and Δ (Θ) are measured for a sequence of angles covering at least an angular range of 90 ° and wherein the interval between adjacent polarization angles of the sequence is at most 25 °, preferably at most 15 °. Method according to Claim 1 or 2, in which the incident light ( 12 ) is linearly polarized. Method according to one of the preceding claims, wherein it is determined on the basis of the comparison of the course of Ψ (Θ) with at least one reference value, whether a bond is present, and in the case that it is determined that no binding, based on the comparison of Δ (Θ) is determined with at least one reference value, whether an intersection or a single fiber is present. Method according to one of the preceding claims, wherein the comparison of the course of Ψ (Θ) and / or Δ (Θ) with at least one reference value is that the value Ψ (Θ ₀ ) or Δ (Θ ₀ ) for a characteristic Angle Θ _{0 is} compared with at least one associated reference value. Method according to Claim 5, in which Θ _{0 is} the value of the angle Θ for which Ψ (Θ) or Δ (Θ) assumes a characteristic value, in particular an extremal value. The method of claim 6, wherein Θ _{0 is} the value at which Ψ (Θ) takes a minimum, and the comparison is that Ψ (Θ ₀ ) is compared with a reference value Ψ _crit and it is determined that there is a bond if: Ψ (Θ ₀ ) <Ψ _crit . Method according to one of the preceding claims, in which the angle ξ of a single fiber or, in the case of a binding or crossing, of the overhead fiber with respect to the predetermined spatial direction of the fiber network is determined on the basis of the ellipsometry parameters. The method of claim 8, wherein it is determined in a crossing or binding point on the basis of the angle ξ of the upper fiber, which of the two fibers is above. The method of claim 9, wherein the angle ξ is derived from the angle Θ ₀ for which Ψ (Θ) assumes a minimum. Method according to one of the preceding claims, in which the reflected light ( 18 ) before the measurement of the ellipsometry parameters by a λ / 4 plate ( 22 ) to be led. Method according to one of the preceding claims, in which the different angles Θ are set by using a polarizer ( 16 ) is rotated in the light path of the incident light, and optionally in the light path of the reflected light arranged polarization-sensitive optical components ( 22 . 24 ) with said polarizer ( 16 ) are turned in the light path of the incident light. Method according to one of the following claims, wherein the ellipsometry parameters are determined by means of a plurality of intensity measurements at different settings of an analyzer ( 24 ). Method according to one of the preceding claims, in which the reflected light ( 18 ) using a semitransparent mirror ( 20 ) is deflected in the direction of a device for measuring the ellipsometry parameters, wherein the reflected light between the partially transmissive mirror ( 20 ) and the device for measuring the ellipsometry parameters, preferably with the aid of another mirror ( 26 ) is deflected. Method according to one of the preceding claims, in which an illumination optical system ( 30 ) is used, with which a surface area of the fiber network is illuminated, and in which an imaging optics ( 32 ), with which the light reflected at the fiber network ( 18 ) to an image sensor ( 34 ) is displayed. Contraption ( 10 ) for analyzing a fiber network, comprising: - a light source ( 28 ), which is suitable for illuminating a fiber network from one direction which deviates from the normal by a maximum of 15 °, preferably a maximum of 10 ° and particularly preferably a maximum of 5 °, a polarizer ( 16 ), which is suitable, the light of the light source ( 28 ) - means for setting different angles Θ between a predetermined spatial direction of the network and at least one polarization-sensitive optical component of the device ( 10 ), - a device for measuring the ellipsometry parameters Ψ (Θ) and Δ (Θ) of the directly reflected light ( 18 ) or of reflected light which, after reflection, has one or more optical components ( 20 . 22 . 26 ), and - a controller adapted to compare the course of Ψ (Θ) and / or Δ (Θ) for different angles Θ with at least one reference value and to determine, based on the comparison, whether at the relevant location there is a fiber crossing or a fiber bond. Contraption ( 10 ) according to claim 16, wherein the polarizer ( 16 ) in the light path of a falling light ( 12 ) is rotatable. Contraption ( 10 ) according to one of claims 16 or 17, in which the polarizer comprises a linear polarizer ( 16 ). Contraption ( 10 ) according to one of claims 16 to 18, in which in the beam path of the reflected light ( 18 ) a λ / 4 plate ( 22 ) is arranged. Contraption ( 10 ) according to one of claims 16 to 19, in which the device for measuring the ellipsometry parameters Ψ (Θ) and Δ (Θ) comprises an analyzer ( 24 ) and a facility ( 34 ) for measuring the intensity of the analyzer ( 24 ) passing light comprises. Contraption ( 10 ) according to one of claims 16 to 20, in which in the light path of the reflected light ( 18 ) a partially transparent mirror ( 20 ) is arranged, with which a part of the reflected light ( 18 ) is deflected in the direction of the device for measuring the ellipsometry parameters, wherein between the partially transmissive mirror ( 20 ) and the device for measuring the ellipsometry parameters, preferably another mirror ( 26 ) is arranged. Contraption ( 10 ) according to one of claims 16 to 21, with an illumination optical system ( 30 ), with which a surface area of the fiber network can be illuminated, and with an imaging optics ( 32 ), with which the light reflected at the fiber network ( 18 ) is imaged on an image sensor.

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