EP2089758A1

EP2089758A1 - Method of determining the pretilt angle in a liquid-crystal cell

Info

Publication number: EP2089758A1
Application number: EP07822738A
Authority: EP
Inventors: Umberto Rossini
Original assignee: Thales SA
Current assignee: THOMSON LICENSING
Priority date: 2006-11-28
Filing date: 2007-11-20
Publication date: 2009-08-19
Also published as: WO2008065025A1; FR2909193A1; FR2909193B1; US7855787B2; US20100045992A1

Abstract

To determine the tilt angle ?tilt in a twisted nematic liquid-crystal cell, the transmission of the cell is calculated as a function of the angle of incidence a of a light ray of given wavelength l using the apparent values of the thickness d of the cell cavity, the extraordinary index ne and the twist angle ?twist. To obtain a plurality of simulation curves Sim1, Sim2, one per given pretilt angle ?tilt, the transmission curve M(C) as a function of the angle of incidence of the cell along the YY' axis, passing through the high T and low B positions of the cell, is measured for the light ray of wavelength l, using a contrast measurement device, and the coincidence of this measurement curve with one among the plurality of simulation curves gives the pretilt angle of this cell.

Description

METHOD FOR EVALUATING THE PRE-TILT ANGLE IN A LIQUID CRYSTAL CELL

The present invention relates to a method for measuring the inclination or pre-tilt angle of liquid crystal molecules of liquid crystal cells of the helical nematic type, or TN for Twisted Nematic ,.

A liquid crystal cell TN is usually formed of two transparent substrates assembled to form between them a cavity in which the liquid crystal molecules are injected. A liquid crystal molecule has an elongate shape along a longitudinal axis, such as a stick. The pre-tilt angle can then be defined as follows: consider a normal position of such a molecule, flat against the surface plane of a substrate. One end of the molecule is anchored on this plane and the other end is forced into a position such that the longitudinal axis of the molecule forms an angle with the surface plane of the substrate: this is the pre-tilt angle .

This angle makes it possible in particular to impose on the liquid crystal molecules of the cell the direction of unwinding in a helix in the thickness of the cavity. It has a direct impact on the performance of a liquid crystal display. It is obtained in a well-known manner by depositing on each of the faces of the substrates internal to the cavity, a transparent alignment layer, typically polyimide, which is rubbed for example by means of a fabric roll along an axis of orientation. determined, so as to create anchoring lines on the surface in this axis, and which is subjected to various cleaning and thermal annealing. The friction operations performed on the two substrates and their assembly are such that there is a torsion angle called a twist angle between the friction axes of the two alignment layers. For example, this twist angle or twist is 90 ° or π / 2 rad. It may be lower, for example 80 ° or greater, for example 280 °, typically for the so-called supernatant liquid crystal STN helix. In the following, the term TN liquid crystal means for any torsion or twist angle. The liquid crystal molecules all have at rest the determined inclination, called the pre-tilt angle, with respect to the plane of the substrate. When an electric field is applied, a helical unwinding direction of the liquid crystal molecules is required in the thickness of the cavity. The directions of the axes of friction of the two alignment layers in the assembled cell define the top position or Top and Bottom or Bottom of the cell in a display, which are concepts associated with the contrasts according to the angle of view.

The effective pre-tilt angle obtained at the output of manufacture depends on various factors, among which mention may be made of the conditions of friction of the alignment layers, the cleaning steps, the topography of each of the substrates, the material or materials. (Polyimides) used to make the alignment layers, the properties of the liquid crystals injected ... In particular, the topographies of the two substrates are different.

Typically, if one takes the example of a liquid crystal display comprising an active matrix type cell and colored filters, a first substrate corresponds to the active matrix, which notably comprises the TFT transistors, the selection lines, the lines of data and the first pixel electrodes of the image points of the screen, and a second substrate corresponds to the counter-electrode forming the other common pixel electrode at all image points, and also includes the red green-blue color filters. The filter network on the substrate 2 and the TFT array with the pixel electrodes on the substrate 1 give very different topographies of the substrates. Because of these different topographies of the two substrates, the value of the pre-tilt angle of the cell depends on the point of the surface where it is observed. In practice, the pre-tilt angle of a cell is a mean value. Indeed the value of this angle can be different on one and the other substrate; it can vary according to the three dimensions, that is to say if one considers a molecule, the value of the angle can vary according to the position of this molecule in the plane of the substrates and in the thickness of the cavity. Yes any one or more steps of the manufacturing process are defective, it is understood that this can have a direct impact on the value of the pre-tilt angle of the cell, and consequently on the qualities of the display.

In the invention, in the case where display defects are noted at the end of manufacture during the testing phase and measurements on the cell, for example if we observe the lagging, leakage of lights, contrast defects in angle, one wants to be able to check the average value of the pre-tilt angle of the cell, to ascend quickly if necessary to one or more phases of the manufacturing process responsible for the flaw or defects found: pollution, obsolescence or defects of the polyimide , error in the operation of friction.

Usually the measurement of the pre-tilt angle is used in the process of developing new manufacturing processes or processes using a new material. In this development context, the measurement is carried out by means of a well-known method called rotating crystal and described by Messieurs TJ. Scheffer and J. Nehring. In this method, specially manufactured cells are used. These cells can be immersed in a liquid of suitable index in order to suppress so-called Fresnel reflections, which makes it possible to improve the accuracy of the measurement.

This method of measurement is well adapted for cells specially designed for it, and which are simplistic sets adapted to the parameter that one wants to characterize. But it can not be used to test defective LCD displays at the end of production. It is not suitable for measuring a pre-tilt angle in a cell that is a real product completed in all its complexity, leaving the production lines.

In the invention, a solution to this technical problem is proposed with a method which does not require the production of special cells, and which can be easily used directly on the production lines of the liquid crystal cells. In a method according to the invention, an average value of the pre-tilt angle of a liquid crystal cell is evaluated, in particular by a comparison of an angle transmission measurement in a plane defined by the cell tested, with a calculated theoretical value. More specifically, to evaluate the value of the tilt angle in a twisted nematic liquid crystal cell, the transmission of the cell is calculated as a function of the angle of incidence α of wavelength light radiation. given λ using apparent values of the thickness d of the cavity of the cell, the extraordinary index ne and the torsion angle θ _tW i _st , to obtain a plurality of simulation curves, one per value d pre-tilt angle given; the transmission curve is measured as a function of the angle of incidence of the cell along the axis YY 'passing through the high positions T and low B of the cell, for the light radiation of wavelength λ, using a contrast measuring device. The coincidence of this measurement curve with one of the plurality of simulation curves gives the value of the pre-tilt angle of this cell.

As claimed, the invention thus relates to a method of evaluating a pre-tilt angle in a liquid crystal cell, said cell comprising a cavity between two substrates containing liquid crystal molecules, each side of the substrates being interior of the cavity comprising an alignment layer such that the liquid crystal molecules are each inclined relative to the plane of the substrates of said pre-tilt angle, said liquid crystal being of nematic helical type with a determined torsion angle, and said cell having high and low positions defining a median vertical axis in front view, characterized in that it comprises using a contrast measuring apparatus to establish a measurement curve along said vertical axis of the cell for transmitting a light radiation at a determined wavelength of said cell as a function of an angle of incidence of a light radiation on said cell, and a comparison of said measurement curve with a plurality of simulation curves of the transmission of said cell as a function of the angle of incidence of the light beam along said vertical axis of the cell, each of said plurality of simulation curves being calculated for a predetermined pre-tilt value and said plurality of curves being calculated taking values apparent of the thickness d of the liquid crystal cavity between the two substrates, the extraordinary index of the liquid crystals and the torsion angle of the cell determined by the following formulas:

^d a _PP => ^θ ,,, s, ~ a = where γ is the angle of transmission of the light ray in the liquid crystal, a function of the value of the angle of incidence, and no the ordinary index of the liquid crystals, d and not being the thickness of the cavity and the extraordinary index in normal incidence.

The evaluation of the pre-tilt angle of said cell is given by the selection of a simulation curve among said plurality of curves which substantially coincides with said measurement curve.

Other advantages and features of the invention are detailed in the following description with reference to the illustrated drawings of one embodiment of the invention, given by way of non-limiting example. In these drawings:

FIGS. 1a and 1b illustrate, in front view and in transverse view, a liquid crystal cell display of the active matrix type with colored filters; FIGS. 2a to 2d illustrate the contrast measurement mounts used in the invention for measuring the transmission response of a cell; FIG. 3 gives an example of the optical images showing the response in white and in black of a cell obtained with a measurement assembly of the contrast function of the angle of incidence;

FIG. 4 illustrates the angles of incidence and refraction in the cell of a light beam; FIG. 5 illustrates the path of the refractive angle γ of the light beam in the liquid crystal cavity, as a function of the angle α of incidence of the beam on the cell;

FIG. 6 is a diagram illustrating the variation of the so-called twist angle with the angle of incidence α, with respect to a normal incidence with respect to the surface plane of the cell;

FIGS. 7 and 8 illustrate a comparison method between the measurement of the transmission from the contrast measurements and the approximate theoretical curves of this response, allowing an evaluation of the average value of the pre-tilt angle of a cell.

Note that in the following description the different elements are each designated by the same reference in all figures.

The invention generally applies to liquid crystal cells of the TN-helical nematic type: with a passive or active matrix, with or without colored filters. The invention is more particularly described for a twist angle of 90 ° (π / 2 rad), but it applies generally whatever the value of the twist angle.

For purposes of illustration only, FIGS. 1a and 1b illustrate a liquid crystal cell, of the active matrix and color filter type, to which the invention can be applied.

Figure 1a is a front view, and Figure 1b a cross sectional view. They illustrate a conventional structure of a cell C: two transparent substrates 1 and 2 assembled to one another so as to form a cavity 3 in which the liquid crystals X1 are injected. The substrate 1 is the one that comprises the pixel electrodes and associated switching devices for addressing, typically TFTs in the case of an active matrix. The substrate 2 is the one that has the counter-electrode common to all image points of the cell. Note that in the case of a passive matrix type cell, there would not be a common counter electrode but a pixel electrode array, and associated switching devices. The substrate 2 also comprises a network of filters colored, which is symbolically illustrated on the figure by a black and white checkerboard. Each substrate is covered on the cavity side with an alignment layer, typically a polyimide, which is rubbed: this is the layer 1.1, respectively 2.1 of the substrate 1, respectively 2. The direction of friction on each layer 1.1, 2.1 is indicated on the figures by a corresponding arrow, F1 and F2 respectively. In practice, the substrate 1 receives the incident radiation L to be transmitted by the cell.

In known manner, the directions with respect to each other of the friction axes F1 and F2 in the assembled cell determine the high T and low B positions, called Top and Bottom, of the cell, as it will have to be. positioned in a display in front view. These positions T and B are indicated in these figures and the following figures. In practice, on a display, these positions define a vertical axis YY 'median of the cell in front view, typically on the surface plane of the substrate 2 (Figures 1a and 1b).

FIGS. 2a to 2d and 3 illustrate steps of a first phase of a method for evaluating the tilt angle of a liquid crystal cell C of any type, and for example of an active matrix cell and color filters as described above in connection with Figures 1a and 1b. In this phase, the transmission of the cell is measured by means of a commercial contrast measuring device 4, which provides luminance measurements collected at each point, simultaneously for different incidences α of the light beam arriving on the surface plane. of the substrate 1. The optical figures provided by the device show corresponding contrast maps or isocontrast diagrams. For example, an ELDIM-EZContrast device marketed by ELDIM SA may be used.

Two series of two measurements are made, by means of a display device in four configurations A1 to A4 illustrated in Figures 2a to 2d. The first two configurations A1 and A2 are respectively the contrast measurements of the cell when the display device aims to block the light (A1 configuration) or let all the light (A2 configuration). More precisely in the configuration A1, the display device comprises the LED light box, an input polarizer Pin, the cell C, an output polarizer Pout. The cell is illuminated by the rear face of the substrate 1. The polarizers Pin and Pout are parallel polarized and the cell is used without applied voltage: Under these conditions, if we take the example of a cell C liquid crystal TN, the polarization of the light undergoes a rotation of π / 2 through the liquid crystal cavity: as the output polarizer is identical to the input polarizer, the light polarized along a different axis does not pass the output polarizer. In this configuration A1, a transmission measurement is carried out for the "black" state. To carry out the transmission measurement of the "white" state (all the polarized light passes), it suffices to remove the output polarizer Pout from the previous configuration A1: this is the configuration A2 illustrated in FIG. 2b.

Figure 3 shows an example of the optical images obtained for the black state (Mb) and for the white state (Mw). The total transmission T of the cell is obtained by making the ratio of the two, for all the points situated on the vertical section Y and Y ", ie between the top T and the bottom B of the cell. from 0 in the center to 60 on the outer circle gives the value of the angle of incidence (or observation) α.The angle of orientation φ varying from 0 ° to 360 ° in the directions of the d a watch shows the luminosity variations observed, with particular attention to the variations observed on the vertical axis YY '(90 ° -270 °) corresponding to the high T and low B positions of the screen: the map contrast shows the variation observed on this axis by varying the angle of observation from -60 ° (for φ = 270 °) to + 60 ° (for φ = 90 °). the contrast observed at normal incidence N on the surface of the substrate 1 (FIG. 1a), ie with an angle of incidence α = 0 ° relative to normal N.

In the example, a black concentration is observed for the black state following a butterfly zone offset from the central point. For the black state, there is a lower brightness for the highest incidence angles.

The transmission of the cell as a function of the angle of incidence is obtained by making the ratio at each point of the luminosities obtained between the "black" state and the "white" state, for incident radiation at a length of given wave. However, this transmission of the own contribution of the output polarizer Pout must be corrected. Indeed, the transmission in the polarizer varies in practice with the angle of incidence. The transmission of the polarizer is measured according to the same principle as before, ie with and without the output polarizer Pout, but without the cell, and at the same wavelength: these are the configurations A3 and A4 illustrated on FIG. Figures 2c and 2d.

Thus, in this phase of the method of the invention, after reading the brightness maps relating to the configurations A1 to A4, the brightness values are recorded at each of the points of the right-hand portion [T; B] as a function of the angle of incidence relative to normal. For each of the points, we make the report (black state / white state) obtained for the cell at this point, which is divided by the ratio (black state / white state) obtained at this point for the output polarizer Pout . A transmission curve M (C) is obtained as a function of the angle of incidence α as illustrated in FIGS. 7 and 8, with α varying from -60 ° to + 60 °.

It should be noted that the measurement of the transmission for the polarizer is done once for a particular, determined output polarizer. We only need to do this again if we have to change the output polarizer. Figures 4 to 8 illustrate another phase of the process that can be performed in parallel, before or after the measurement phase of the transmission of the C cell as a function of the incidence anal. This other phase is a phase essentially of theoretical calculation of the transmission T as a function of the angle of incidence, on the vertical axis between the high position T and the low position B on the cell. In this phase, we start from the general theoretical formula of MHL Ong giving the transmission of the cell for a normal incidence, that is to say for α = 0 °. This formula, well known to those skilled in the art, is as follows:

r)) ² cos (2 # _{Am /} ) Eq. 1

In this formula, λ represents the wavelength of the incident radiation, θ _tw i _st the twist angle, d the thickness of the liquid crystal cavity between the two substrates 1 and 2 and no and are the ordinary indices. and extraordinary characteristics of the liquid crystals used.

The formula given by Eq 1 is however not valid for any non-normal incidence. In the case of a non-normal incidence, there is, as illustrated in FIG. 4, a refraction in the various mediums traversed, as a function of the differences in indices between the mediums, which modifies the apparent value of certain characteristics, and consequently the transmission. In Figure 4 there is shown a liquid crystal molecule xl.

It has a known elongated shape, and the longitudinal axis of this molecule forms with the surface plane a pre-tilt angle θ _t i _tt -

An incident light ray Fj _nc arrives on the rear face of the substrate 1 with an angle of incidence α ≠ 0 ° relative to the normal N to this face. It passes through the substrate 1 forming an angle β with the normal. In the liquid crystal cavity 3, the F _ms beam obtained forms an angle γ with the normal. It passes through the substrate 2 forming an angle β 'with the normal, and _out (F _out ) at an angle α' with the normal. A helical nematic liquid crystal is considered such that the direction of rotation of the helix is to the right.

As illustrated in FIG. 5, by varying the angle of incidence α of the light beam F _ιnc , there is a variation of the angle γ of the beam F _ns in the cavity. This variation has an influence on the extraordinary indices ne, the angle of twist as well as the thickness of the cell.

The idea of the invention is to approximate the apparent value of these parameters, by equations function of the angle of incidence α, to obtain an approximate value of the transmission as a function of the angle of incidence α to from the formula Eq 1 recalled above.

In the invention there is provided the following approximations: For the extraordinary index, we show that the apparent value _app that index based on the value of the angle of incidence can be written only n ^e app = ^"

+ (- _τ - \) sm (γ-tilt) nυ ^~ which brings an apparent value Δn _app of the difference between the extraordinary and ordinary indices which is written: Δn _app = ne _app -no.

It is shown that the apparent value of the twist angle is also modified, which is illustrated in FIG. 5 for an expected twist angle of π / 2 under normal incidence. The refraction axis R _{N is considered} in a TN-type liquid crystal corresponding to the normal incidence. In this case the twist angle θtwist is π / 2. If we switch this axis by an angle γ, backward in the example, the apparent twist angle is different, in the example it is greater. It is shown that this apparent value θ _tW ιst-a of the twist angle can be written as a function of the refraction angle γ in the liquid crystal:

0 _Λm , _ ,, = 2.Arctg (- ± -). cos (γ) The _app of apparent value of the thickness of the cavity can be written to - _iL_

""'cos (/) ^' We show that the relation between the angles α and γ can be approximated by considering that the refractive index for the liquid crystal in the vertical section (according to YY ') can be approximated by the apparent value of the extraordinary index, which gives:

γ≈ arcsin (sin (βr)). n ^E "PP

We deduce a formula of approximation of the transmission as a function of the angle of incidence, by using these apparent values T (α), by replacing in the formula Eq 1, ne, θ _tW ιst, and d by their values. apparent, that is:

T (a) = {cos ² θ _twnt _ _a) + ± - sm (2v.θ _tmt _ _a) sm (2θ _m ,, _ _a) - ^ sm (v.θ _tmt _ _a)) cos ² (20 _{/ im} , _{_fl} )

2v v

with v = Vl + M and w - no For a given cell, we know d, ne and no, which are manufacturing parameters.

In practice, d is measured using a conventional device with a rotating polarizer, d can be adjusted to perfect the coincidence between the theoretical and measurement simulated curves: the value d is changed in normal incidence of the thickness of the the cavity, and the value for which the best coincidence is obtained between the simulation curve calculated with this value and the measurement curve, gives the value of the thickness of the cell. The method according to the invention thus advantageously makes it possible to determine both the pre-tilt angle and the thickness of the tested cell. We take λ equal to the value used for the measurement of the response of the cell in the previous phase, with a device for measuring contrast. Then for a value of the given pre-tilt angle θm _t , we can simulate a corresponding curve T (α), for example for α varying -60 ° to + 60 °. In practice, and because the angle β is close to the angle γ, it is advantageous to make the approximation: γ≈β in the formula giving the apparent value of the extraordinary index, namely: ne

This approximation makes it possible to reduce the number of iterations to calculate T for each value of α.

Figures 7 and 8 illustrate the curves measured for radiation at λ = 550 nm, and the simulated curves calculated for this same wavelength, for different pre-tilt values for different cells. In each case, the pre-tilt value of the cell C is deduced by the coincidence between the measured curve and a determined simulated curve.

More specifically, FIG. 7 relates to a cell defined in particular by a reference liquid crystal 6694-015, and polyimide alignment layers P1 of reference NISSAN7492, by which a small pre-tilt angle is obtained, typically between 3 ° and 4 °. The typical values of d, ne, no and dn = nθ-ne for this cell are shown in the figure. In this example, four simulation curves Sim1 to Sim4 have been calculated for four different pretilt angle values. The coincidence is achieved between the measured curve M (C) and the simulated curve Sim2 calculated for an angle of pre-tilt θ _tι i _t = 3.4 °, which gives the evaluation of this angle for the cell in question.

FIG. 8 relates to a cell defined in particular by a reference liquid crystal 6694-070, and polyimide alignment layers P1 of the reference NISSAN7792, by which a pre-tilt angle greater than in the preceding case is obtained, typically between 6 ° and 8 °. The typical values of dn, d, ne, and no for this cell are shown in the figure.

In this second example, three simulation curves Sim4 to Sim6 have been calculated for three different pretilt angle values. The coincidence is achieved between the measured curve M (C) and Sim5 simulated curve calculated for a pre-tilt angle θ _tι i _t = 7.5 °, which gives the evaluation of this angle for the cell considered.

In practice, if the measured curve M (C) does not correspond quite well with a simulated curve, it suffices to slightly vary the value of d. Indeed, this value has a great influence on the transmission, and the typical value given for the manufacturing process of the cell concerned is given with a tolerance interval.

For example, for the example of FIG. 5, the measurement of the thickness d of the cavity was obtained, which gave 4.35 μm, whereas the typical value d given for the process and used for the calculation of simulated curves Sim1 to Sim4 was d = 4.33μm as shown in the figure.

In practice, by varying the value of d, the simulated curve is translated along the vertical axis. By varying the pre-tilt angle, and as can be seen in Figures 7 and 8, the simulated curves change from a symmetrical shape at 0 relative to the vertical axis, to non-symmetrical shapes.

The evaluation method which has just been described is simple to implement and has shown in practice good repeatability and sufficient accuracy, better than 0.5 °, which is sufficient to detect a significant problem in the manufacturing process or in the polyimide materials used. It is used whenever a display fault is found on a liquid crystal cell is found at the output of manufacture.

Claims

1. A method for evaluating a pre-tilt angle θ _t fi _t in a liquid crystal cell, said cell (C) comprising a cavity (3) between two substrates (1, 2) containing molecules (Xl) of liquid crystal, each side of the substrates (1, 2) inside the cavity comprising an alignment layer (1.1, 2.2) such that the liquid crystal molecules are each inclined relative to the plane of the substrates of said angle of pre-tilt, said liquid crystal being of nematic helical type with a determined torsion angle (θ _tW i _st ), and said cell having high (T) and low (B) positions defining a median vertical axis (YY ') in front view, characterized in that it comprises the use of a contrast measuring apparatus (4) for establishing a measurement curve (M (C)) along said vertical axis (YY ') of the cell transmitting a light radiation at a determined wavelength (λ) of said cell according to an angle e incidence (α) of light radiation on said cell, and a comparison of said measurement curve (M (C)) to a plurality of simulation curves (Sim1, Sim2, Sim3) of the transmission of said cell at the same wavelength (λ) as a function of the angle of incidence of the light beam along said vertical axis (YY ') of the cell, each of said plurality of simulation curves (Sim1) being calculated for a predetermined pre-tilt value and said plurality of simulation curves being calculated by taking apparent values of the thickness d of the liquid crystal cavity (3) between the two substrates, the extraordinary index does not include liquid crystals and the torsion angle (θ _tw i _st ) of the cell determined by the following formulas:

^d to _PP =) where γ is the angle of transmission of the light ray in the liquid crystal, a function of the value of the angle of incidence (α), no the ordinary index of the liquid crystals, d and not being the thickness of the cavity and the extraordinary index in normal incidence.

2. Method according to claim 1, characterized in that the evaluation of the pre-tilt angle of said cell is given by the selection of a simulation curve among said plurality of curves which coincides substantially with said measurement curve. .

3. Method according to claim 2, characterized in that the coincidence is obtained by varying the value of the thickness (d) of the cavity at normal incidence in the calculation of said plurality of simulation curves, to obtain a value d the thickness of the cavity for which the best coincidence is obtained.

4. Method according to one of claims 1 to 3, characterized in that obtaining the measurement curve of the transmission as a function of the angle of incidence comprises a first measurement and a second contrast measurement on the said cell respectively in the white state and in the black state, and the ratio between the two measurements along the vertical axis (YY '), said first measurement being obtained by placing said cell in a display device comprising a light box (LED) emitting radiation in said determined wavelength, said cell (C) being placed for the first measurement between an input polarizer (Pin) and an output polarizer (Pout) with parallel polarizations, the second measurement being performed by removing said output polarizer from the display device.

5. Method according to claim 4, characterized in that obtaining said measurement curve further comprises a correction of said ratio by the transmission of said output polarizer, obtained by performing a first measurement and a second contrast measurement on said polarizer in the white and in the black state respectively, and the ratio between the two measurements along the vertical axis (YY '), said first measurement being obtained with a display device comprising a light box (LED) emitting radiation in said determined wavelength, said polarizer input signal (Pin) and said output polarizer (Pout), the second measurement being performed by removing said output polarizer from the display device.

6. Method according to any one of the preceding claims, characterized in that the said simulation curves are obtained by the following equation of the transmission for a light ray of incidence α normal to the plane of the cell, a function of the pre-tilt angle θ _t ii _t :

T = cos ² (θ _mnl ) + ^ -sin (2v.0 _ftm ,) sin (20 _{/ ιm} ,) - (-sin (v. ^ _I4 ,)) ² cos (20, _ιm ,)

2v v with v =

λ being the wavelength of the incident radiation, θ _tWιst being the twist angle, v = 2πλ, d being the thickness of the liquid crystal cavity between said first and second substrates, replacing in this formula the apparent values the thickness (d), the extraordinary index (n _e ), the torsion angle (θtwi _st ) functions of said angle of incidence (α).

7. Evaluation method according to any one of claims 2 to 5, characterized in that the value obtained from the extaraordinary index is the value obtained by the following formula:

HC does not _app = where β is the angle of transmission of the radius of incidence α in the substrate (1) receiving the incident radiation to be transmitted.

The method of any of the preceding claims applied to detect a pre-tilt angle defect in a liquid crystal cell.

The method of any of the preceding claims applied to measure a cavity thickness in a liquid crystal cell.