SU1531867A3 - Liquid crystal indicator - Google Patents

Abstract

The invention relates to devices for displaying visual information on liquid crystals, in particular in multiplexable large format indicators. The purpose of the invention is to improve the image quality by increasing the contrast and viewing angle while maintaining the degree of multiplexing. This invention relates to a liquid crystal display. The invention is based on the use of positive dielectric anisopropy in a nematic liquid crystal with chiral addition of the bistability effect. The distance between the carrier plates 1, 2 is less than 10 microns and the full twist of the liquid crystal 5 is between 180 and 360 ° C, preferably about 270 ° C. Over the entire observation surface of the indicator, statistically distributed elements 4 are provided that determine the distance between the plates. Due to these measures, the area of bistable behavior is so narrowed that the operating voltage outside this area can be controlled by the indicator by the usual multiplexing method. This achieves high contrast and increases viewing angles while maintaining the degree of multiplexing. Contrast optimization is achieved by observing a certain angle β between the direction of oscillation of the front polarizer 10 and the direction of orientation of liquid crystal molecules (projected onto the layer plane) by the orienting layer 8 applied to the electrode coating of the front plate 1 and the angle γ between the direction of oscillation of the rear polarizer 11 and the orientation direction of the liquid crystal molecules (projection onto the plane of the layer) by the second alignment layer 9. These angles lie within 20-70 ° C, preferably 35-55 ° C. At β + γ = ± 90 ° С (yellow mode) and β = 32 ° С, the maximum contrast is 22: 1, and at β + γ = 0 ° С (syn mode) and β = 38 ° С, the maximum contrast is 6, 5: 1 with control of about 100 lines in the usual multiplex way. At the same time, the on and off time at 296 K for the indicator is 0.4 s. 5 hp f-ly, 15 ill.

Description

one

(21) 3764352 / 24-25

(22) 07/10/84

(46) 12/23/89. Bul Number 47

(71) BBC AG Brown, Boveri und Co (CH)

(72) Hermann Amstu, Dieter Heimgartner, Mannolf Kaufman (CH) and Terry James Scheffer (US)

(53) 535.8 (088.8)

(56) J.of Applied Physics, 1977, V. 48, No. 4, p. 1426-1431.

J, of Applied Physics, 1982, v. 53, No. 12, p. 8599-8606.

(54) LIQUID CRYSTAL INDICATOR

(57) The invention relates to devices for displaying visual information on liquid crystals, in particular in multiplexing large format indicators. The purpose of the invention is to improve the image quality by increasing the contrast and viewing angle while maintaining the degree of multiplexing. The invention relates to

to the liquid crystal display. i The essence of the invention is based on the use of the nematic liquid kris / "{// / fу / /// // // // /////// // /////// Tuu (7 / / uh, // x f

f (/ g;

thallus with positive dielectric anisotropy with chiral addition of the bistability effect. The distance between the carrier plates 1, 2 is less than 10 microns and the full twist of the liquid crystal 5 is between 180 and 360 °, preferably about 270. Over the entire surface of the indicator's observation, statistically distributed elements 4 are provided that define the distance between the plates. Due to these measures, the area of bistable behavior is so narrowed that the operating voltage outside this area can be controlled by the usual method of multiplexing. This achieves high contrast and increases viewing angles while maintaining the degree of multiplexing. Optimization of contrast is achieved by observing a certain angle I4 between the direction of oscillation of the front polarizer 10 and the direction of orientation of the liquid crystal molecules (projected onto the plane of the layer) by the orienting layer 8 applied to the elec- tric.

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ate

with

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ABOUT)

2

eleven

12

native coating of the front plate, and the angle f between the direction of oscillations of the rear polarizer 11 and the direction of orientation of the liquid crystal molecules (projected on the plane of the layer) of the second orienting layer 9. These angles lie within 20-70, preferably 35-55 °. With / i-f | ± 90 (yellow fashion) and / i 32 is maximum

The raina contrast is 22: 1, and at / a + y - 0 ° (syn mode) and / a 38, the maximum contrast is 6.5: 1 with control of about 100 lines in the usual multiplex way. At the same time, the on and off time at 296 K for the indicator is 0.4 s. 6 3.p. F-ly, 15ip,

The invention relates to devices for displaying visual information on liquid crystals, in particular in large format multiplexed indicators.

The aim of the invention is to improve the image quality by increasing the contrast and viewing angle while maintaining the degree of multiplexing.

Figure 1 shows a liquid crystal display, a section; Fig. 2 shows the theoretical dependences of the rotation angle in the middle of the indicator cell on the operating voltage U for different angles of total twist and the angle of the director's initial installation on the surfaces of the bearing plates 28 °; Fig. 3 shows contrast curves for a reflective cell with two polarizers; 4 shows a schematic arrangement of polarizers in a liquid-crystal indicator for the first mode of operation (yellow mode), and FIG. 5 is the same for the second mode of operation (syn mode); Fig. 6 shows the contrast of the CR, depending on the position of the polarizer, measured in the device according to Fig. 4; Figure 7 is the same for the device according to Figure 5; Fig. 8 shows calculated lines of a constant contrast ratio depending on the polarizer setting and the product dp d for a device with one polarizer and another reflector; figure 9 is the same for the device according to figure 5; figure 10 is the same for the device according to figure 4; 11 and 12 show the contrast characteristics of FIG. 10 for values of 0-180 and fl 350, respectively; Figures 13-15 show the characteristics of the viewing angle in polar coordinates, the distance from the center being proportional to the angle of incidence of the light beam with the vertical axis.

Q, O 5 Q

five

by centering and sliding 90 on the periphery, for twist angles 0, equal to 180, 270 and 350 °, respectively,

The skidator contains the front carrier plate 1, the rear carrier plate 2, the gasket 3, the element 4, which determines the distance between the plates, the nematic liquid crystal 5, the electrode layers 6 and 7, the orienting layers 8 and 9, the front linear field The stripper 10, the rear linear polarizer 11, an external reflector 12. In addition, the following are indicated: - the total swirl angle of the liquid crystal inside the indicator cell; (b) the angle of inclination of the megaton optical axis (director) of the liquid crystal in the middle of the indicator cell, measured relative to the bearing plates; U is the applied operating voltage; d is the thickness of the layer crystal, p is the step size t of the liquid crystal layer, and are the angles between the direction of oscillation, respectively, of the front polarizer 10 and the rear polarizer II and the orientation direction of the alignment layer 8 and 9, respectively.

Bearing plates 1 and 2 of glass, with a gasket 3 form a cell. Gasket 3 consists of epoxy glue, which contains 4 glass fibers as spacers. Additional elements 4 are statistically distributed between the carrier plates 1 and 2 over the entire area of the indicator. The cell is filled with a nematic liquid crystal 5 with positive dielectric anisotropy, which contains a chiral additive. The inner surfaces of each carrier plate 1 and 2 have parallel strips of electrode layers 6 and 7 of, and the direction of the strips on one carrier plate I is perpendicular

5 1531867

the shipment of strips to another carrier

n m in n ta m in n x

plate 2. Thus, the indicator is constructed from matrix points. However, other forms of electrodes are possible, for example, seven-segment.

On top of the electrode layers 6 and 7, orienting layers 8 and 9 are applied over the gaps between them. On the outer surface of the front carrier plate I there is a front linear polarizer 10 glued on the film. On the outer side of the rear carrier plate 2 during transmission also the rear one is pasted Linear polarizer 11. For the reflection operation, behind this polarizer 11, a diffuse-scattering metal external reflector 12 is located (shown with the shield lines in FIG. 1). Polarizer 11 may be missing. With atoM, although the brightness increases, the contrast is reduced.

Instead of the external reflector 12, an internal reflector located between the electrode layer 7 and the alignment layer 9 can be used. With the thickness of the liquid crystal layer d, the step height p is chosen so that the ratio d / p is described by the following formula:

d / p - f / 360 it provides

(N, 4 fo state

The swirling of the liquid crystal layer is stable, does not rotate an additional 180 °, and no optical interference appears on the indicator. The magnitudes of the angles 210, 240, 270, 300, 330, and H & O therefore correspond in FIG. 2 to the d / p ratio of 0.59, O, 67,, O, 75 0.91, and 1.0. The pitch height p is hereby defined as the characteristic amount of twist, which is obtained in a non-mathematical liquid crystal by adding a chiral additive in the unperturbed state and is considered to be positive with right-hand rotation, negative when left-handed. The ratio of the thickness of the layer d to the height of the schaga p of a liquid crystal is in the range of 0.50-0.95, preferably 0.65-0.85. The pitch value p is established due to the fact that a certain weight portion of the chiral additive is mixed with the nematic liquid crystal. This part depends on the kind of liquid crystal and chiral additive and on the layer thickness d.

0

five

0

five

At least one orientation layer 8 or 9 directs neighboring molecules of a crystal with a mounting angle greater than 5 ° in the range of about 10-40, preferably 30. It should be noted that the direction of the orientation layers 8 and 9 coincides with the natural direction of rotation of the doped chiral addition of a liquid crystal 5.

The thickness of the d layer should be less than 10 µm, and the total twist in the indicator cell should be between 180 and 360 °, preferably between 240 and 300. This ensures that the indicator characteristic, i.e. the transmission curve (FIG. 3), with the applied work voltage, will be quite steep and the bistable behavior area will be so narrowed that outside the limits of this area the working voltage can be controlled by the usual multiplexing method. Within this region, the switching time is at least one hundred times longer than outside this region. The indicator characteristic is character similar to the curves in FIG. 2, except for the section with a negative steepness curve (curves III – VI), which should be replaced by a bistability region (hysteresis loop).

The product of the birefringence coefficient Dp by the thickness d of the liquid crystal should be in the region of 0.6-1.4 µm, preferably 0.8-1.2 µm.

The liquid crystal indicator in the transmission mode works as follows.

The light linearly polarized by the front linearizer 10 passes the carrier plate 1 and hits the orienting layer 8 that is oriented at an angle relative to the polarizer 10 and then to the liquid crystal 5. Due to the full twist and 0 properties of the birefringence of the liquid

Crystal 5, the initially linearly polarized light receives an elliptical polarization, and this varies depending on the applied operating voltage. The orientation direction of the orienting layer 9 and the direction of oscillations of the rear linear polarizer 11 also form a certain angle. Under the direction of orientation

0

five

0

five

five

Institute of incident light. The directions of oscillations of polarizers 10 and 11, as well as the directions of orientation of the orientation layers 8 and 9, are shown by arrows, which are in corresponding planes perpendicular to the indicated axis of the cell. This directional axis, or, corresponds to the projection of the local optical axis of the liquid crystal in the immediate vicinity of the orienting layer on the plane of the orientational layer. The direction of oscillation is the direction in which the electric field vector oscillates.

The outgoing, elliptically polarized light from the liquid crystal is in the posterior-JQ direction, the direction of incidence of the polarizer 11 is either almost fully defined by the right coordinate system is absorbed, or almost never, in which the angles of deviation from - is absorbed depending on whether the main arrow is considered to be positive if the main axis is elliptically polar, and in the opposite case - of negative light, perpendicular or perceptible. In these cases (Fig. 4, parallel to the direction of oscillation-5) for the example of the liquid molecule molecule 11. By means of an appropriate choice of indicated angles between the orientation layers 8 and 9 and the polarizers 10 and II, optical contrast is achieved. These angles in magnitude have a value of 20-70 °, preferably AO-S, and the direction of rotation can be either clockwise or counterclockwise. Moreover, the direction clockwise or counterclockwise is determined relative to the direction of incidence of the light, and the angle is determined relative to the direction oriented .30

In reflection mode, the indicator works the same as in transmission. In particular, the optimal contrast with one polarizer 10 is determined by the appropriate choice of the angle between,

the direction of oscillation of the front line is -270. The d / p ratio is 0.75. linear polarizer 10 and directions - First alignment layer 8 by fabricating the orientation of the first orientation layer 8.

crystal form a screw with a left-hand thread, which, starting from the front orientation layer 8, has a twist angle Ф equal to -270.

The directions of oscillations of polarizers 10 and 11 are deflected from the directions of polarizers shown in planes by the strokes of the directions of orientation of the orienting layers 8 and 9 by an angle of ft and 10, respectively. In the device according to FIG. 4, the angles / i and y are positive. In the device according to FIG. 5, only the angle / s is positive, but negative. The subsequent angles referred to are those taken in FIG. 4 and 5.

Consider a reflective liquid crystal indicator cell with a layer thickness of d 7.6 μm and a full spin F of a liquid crystal, fixed by tilting SiO at an angle of 5 ° to the plane of the plate, so that neighboring molecules of the liquid crystal are directed so that the installation angle between the local optical axis of the hatch crystal at the orienting layer and the projection of this optical

The indicated angles between the directions of oscillations of polarizers IO and 11 and the directions of orientation of the orienting layers 8 and 9 play a significant role in achieving the optimum contrast CR. q5 axis on the plane of the plate, i.e.

On isometric and stretched, the direction of the optionJ is

flax by tilting the SiO at an angle of 5 ° to the plane of the plate, so that neighboring molecules of the liquid crystal are directed so that the installation angle between the local optical axis of the LCD crystal near the alignment layer and the projection of this optical length-wise direction of the field (Fig.4 and 5) 10 and 11, orienting layers 8 and 9, as well as the twist of the last φ between the orientation layers of the liquid crystal 5, is shown by a chain of schematized molecules of the liquid crystal in all the square rectangular plates (n mere plate pro50

28 The direction of oscillation of the front polarizer 10 and the direction of orientation of the first orienting layer 8 form an angle of the order of the DA. The second alignment layer 9 is a rubbed polymer layer and gives the specified installation angle. However, an orientation layer of the same type as the first is also possible. Zhtsky

masonry and possible reflectors are not crystal 5 consists of a nematic cauldron). mixtures ZLI-1840 of the company Mepk Germany,

The elements of the cell are located along the 2.05 wt.% Chiral choleos additive, which is directed to the directional sterilonanoate. This zhvdky crystal

Institute of incident light. The directions of oscillations of polarizers 10 and 11, as well as the directions of orientation of the orientation layers 8 and 9, are shown by arrows, which are in corresponding planes perpendicular to the indicated axis of the cell. This directional axis or, respectively, the direction of light incidence is defined by the right coordinate system, in which the deflection angles on the hour hand are considered positive, and in the opposite case - negative. In these cases (Figures 4 and 5) for the example of a liquid molecule

Correspondingly, the direction of incidence of light is defined by the right coordinate system, in which the deflection angles along the hour hand are considered positive, and in the opposite case - negative. In these cases (Figures 4 and 5) for the example of a liquid molecule

No -270. The d / p ratio is 0.75. The first alignment layer 8 is made

crystal form a screw with a left-hand thread, which, starting from the front orientation layer 8, has a twist angle Ф equal to -270.

The directions of oscillations of polarizers 10 and 11 are deflected from the directions of polarizers shown in planes by the strokes of the directions of orientation of the orienting layers 8 and 9 by an angle of ft and 10, respectively. In the device according to FIG. 4, the angles / i and y are positive. In the device according to FIG. 5, only the angle / s is positive, but negative. The subsequent angles referred to are those taken in FIG. 4 and 5.

Consider a reflective liquid crystal indicator cell with a layer thickness of d 7.6 μm and a full spin Φ of the liquid crystal, equal to -270. The d / p ratio is 0.75. The first alignment layer 8 is made

which axis on the plane of the plate, i.e.

flax by tilting the SiO at an angle of 5 ° to the plane of the plate, so that neighboring molecules of a hard crystal are directed so that the installation angle between the local optical axis of the hard crystal near the alignment layer and the projection of this optical direction is

28 The direction of oscillation of the front polarizer 10 and the direction of orientation of the first orienting layer 8 form an angle of the order of the DA. The second alignment layer 9 is a rubbed polymer layer and gives the specified installation angle. However, an orientation layer of the same type as the first is also possible. Zhtsky

crystal 5 consists of a nematic mixture ZLI-1840 of the company Mepk Germany, with

has a positive electrical anisothypio +12.2 and a birefringence of 0.15. The temperature range is 258-363 K, the viscosity is 1.18 "10 mUs at 293 K.

Using this indicator cell, 96 lines are controlled by the usual multiplex method. Operating voltages U and Ujj, corresponding to the on and off states

must be outside the bistable region (Lig. G) and, depending on the angle Φ and the ratio d / p, have the following meanings: Φ jj cholesterylnonanoate. Double beam with 180% d / p - 0.5, and, - 1.5 V, 1.67 V; Ф 270 °, d / p

and

BkA

    ° 2 § | SL

350 °, d / p

and

Ka

- 2.06 V.

0.75,

2.10 V; F - 0.95, Ue ", - 1.71 V,

The crushing of dl of composition ZLI-1840 co is 0.15, so that the product und is 0.975. The angle ft and angle f are I-45. Figure 3 shows the contrast curves for the case when both angles are 45 and the two angles are -45 (curve A), and for the case when one angle is 45 and the other is -45 °, or vice versa (curve B). Abscissa delayed

The indicator in the open state is completely achromatic (besten), in the closed state - dark blue. If you additionally use an optical delay, for example, a quarter-wave plate between the front linear polarizer 10 and the front carrier plate I, the indicator color can be appropriately

25 applied voltage U, rto ordinate - indicator intensity in arbitrary units. In the first case (curve A), in the non-switched-on state, a light yellow indication is obtained, and in

changed The indicator is exceptionally on state - black indication. This case corresponds to the device according to Fig. 4, in which both angles (4 and 1 have the same positive or negative values. JJ (yellow mode). In the second case (curve B), we get a dark-violet indication in the non-switched state and a bright indication in the on state. This case corresponds to

but a large angle of possible observation, regardless of the direction of illumination. The switch-on and switch-off time at 296 K is 0.4 s for the id switch.

The preferred embodiment of the indicator consists of a rejection indicator cell with a carrier plate 1, 0.7 mm thick and carrier up to the device according to figure 5, in which plate 2 is 0.5 mm thick. The thickness, angles p and selected of the opposite layer d are 6.5 microns. This indicator cell provides for the front polarizer 10, the rear half of the sign (blue mode). The rate of increase is 30 mV / s. Measured contrast ratio with degree multiplexer II and external reflector 12. Both

 A and B & C and B

and iwk

-1,580 V)

1,429 times ° P ™ awn 19.9;

-}, b09 V |

“1 456) (11.8.

 IM vim then it turns out

U ratio

1.106 with a multiplex ratio of 100: I.

When using two polarizers with angles (i and y relative to the directions of orientation according to Figures 4 and 5, general conditions were found that must be fulfilled to optimize the contact

531867

. the alignment layers 8 and 9 are made by obliquely sputtering SiO at an angle of 5 ° to the plane of the plate and directing the adjacent liquid crystal molecules in such a way that the optical axis of the liquid crystal forms an angle of installation 28 to the plane of the plate. The orienting layers 8 and 9 dis. 10 are placed in such a way that the twist F is full and makes a left coil of -250. As a liquid crystal, a nematic mixture of ZLI-1840 is flooded into the cell 5 with a chiral addition of 2.56% by weight. X

cholesterylnonanoate. The birefringence dp of the composition ZLI-1840 with is 0.15, so that the product andnd is 0.975. The angle ft and angle f are -45. Figure 3 shows contrast curves for the case when both angles are 45 and the two angles are -45 (curve A), and for the case when one angle is 45 and the other is -45 °, or vice versa (curve B). Abscissa delayed

applied voltage U, rto ordinate - indicator strength in arbitrary units. In the first case (curve A), in the non-switched-on state, a light yellow indication is obtained, and in

On state - black indication. This case corresponds to the device according to Fig. 4, in which both angles (4 and 1 have the same positive or negative values (yellow mode). In the second case (curve B), a dark-violet indication is shown in the non-switched state and a bright indication is turned on condition. This case corresponds to

device. according to figure 5, in which the angles p and selected opposite

mark (blue fashion). The rate of increase is 30 mV / s. The measured contrast at a multiplex ratio of 100: 1 is the following:

55

plants CR. These conditions can be written as follows:

/ l + us ± 90 ° (figure 4), (2)

/ 5 + 7 th 0 ° (figure 5). (3)

In both cases, the range of angles is limited so that 20 70 and 20 | T1 70.

If condition (2) is fulfilled, example fb f 145, then a light yellow indication (yellow mode) is obtained (curve A, fig. 3) in the off state. If condition (3) is fulfilled, then a dark-violet indication (syn mode) is obtained (curve B, fig. 3) in the switched-off state.

The fact that conditions (2) and (3) are not sufficient for optimal contrast follows from the curves in FIGS. 6 and 7, which give the measured contrast CR depending on the angle with condition (2) or (3) for the cell with two linear polarizers in transmission mode.

In these measurements, a liquid crystal mixture of 95.6% ZLI-2392 (Merck), 2.5% 5811 (Merck), 1.9% CB 15 (BON) was used. The twist is -270, the installation angle is 24, the layer thickness is 6.3 microns, the birefringence dp is 0.15.

The results shown in Fig. 6 are valid for the yellow mode (/ + ya-a. T 90), and in Fig. 7 - for the blue mode (/ i T °. It can be seen that the angle p with the yellow mode for maximum contrast CR is about 22 : 1 is approximately 32 ° and therefore clearly differs from O. With the blue mode (Fig. 7), the maximum contrast CR is of the order of 6.5: 1, i.e. significantly lower. Here, too, pi is about 38 ° and is thus in a non-oxidized range of angles.

The values of the angle ft combined with the optimum contrast CR were confirmed by subsequent theoretical calculations, the results of which are depicted in Figures 8-10 as constant contrast lines depending on the product of the thickness of the layer d and birefringence; 3n, as well as the angle p ,.

For the calculations, the multiplexing degree is 100: 1, the layer thickness is d 6.2 µm, the refractive index for the ordinary beam is 5, the elastic constants of the liquid crystal are kj./k.

2.5; k.j / k

 eleven

1.5; the ratio of the dielectric constants (. || -): 2.5, the twist of F -270, and also its calculation of the thickness of the Layer to the size of the scale F / p is 0.75.,

In the case of a cell working on reflection with one polarizer (Fig. 8), the maximum CR contrast is of the order

five

0

five

0

five

0

five

0

five

3.6: 1 is reached only when, when, and the angle / 3 is equal to about 20 ° and / jn-d is approximately equal to 1.13 µm. Moreover, in this case, the installation angle was assumed to be 28.

In the blue mode of the indicator cell, working on reflection with two polarizers (Fig. 9), the corresponding values are obtained for d 45 ° and fln-d "0.78 µm.

In the corresponding yellow mode (Fig. 10), the values are obtained, and l p – d –A 0.84 µm. In both latter cases, the installation angle was taken 20.

The theoretically calculated optimal contrast values of 50 and 150 are much more pronounced than measured, because in the calculations. It was decided to perform the reflection work, which, due to the double use of polarizers as compared with the transmission mode, produces a contrast that is not strong.

The proposed liquid crystal indicator is harsh-plated with a high degree of multiplexing, high contrast and fast switching, the Lower Possible viewing angle and can be manufactured according to mastered production technology of twisted cells.

Claims (7)

1. A liquid crystal indicator containing two plane-parallel carrier plates, forming a cell along the perimeter with a gasket, electrode layers deposited on the inner side of each plate, orienting layers lying above them, between which there is a nematic liquid crystal with positive dielectric anisotropy and chiral additive with the axis of twist perpendicular to the surface of the plates, the local optical axis of the liquid crystal at least at one orientation layer forms an angle of the initial orientation uu more than 5 ° to the surface plasti-- us at least one front polarizer, characterized in that in order to enhance picture quality by increasing the contrast and the viewing angle while maintaining a degree of multiplexing, the thickness of the liquid crystal layer is not more than 10 μm, the twist of the liquid crystal in the cell from one alignment layer to another one module is greater than or equal to 180 and less than 360, the ratio of the layer thickness to the size of the liquid crystal step modulo more or equal to 0.50 and less than or equal to 0.95, and the direction of oscillations of the front polarizer forms an angle with the direction of orientation of the front alignment layer. 2. The indicator according to claim 1, characterized in that the product of the anisotropy of the refractive index and the thickness of the liquid crystal layer is in the range from 0.6 to 1.4 microns, preferably 0.8-1.2 microns. 3. The indicator according to claim 2, characterized in that the screw of the modulo screw is 240-300 °, preferably 270. 4. The indicator according to claim 1, characterized in that the rear lg "Guards 41G20 g five The plate has a metal diffuse reflector, and the direction of oscillation of the front polarizer forms an angle with the direction of orientation of the front alignment layer, preferably 30 °. 5. The indicator on the PP. 1-4, in which it contains an additional second rear polarizer. 6. The indicator according to claim 5, wherein the directions of oscillation of the front and rear polarizers are angles 20-70 °, preferably between 35 and 55, with corresponding orienting layers. 7. The indicator according to claim 6, characterized in that the sum of the angles formed by the direction of the oscillations of the polarizers with the corresponding alignment layers is 190 or 0, while the angles are counted clockwise. fig 2 150 / 0.5 1.0 Fig.Z / x  3 1.5 ip 2.015 i Phie. About Yu 20 SO 0 FI.5 60 70 80 90 A genus Fie.6 CR Anxd micron 0.9 30 40 50 () FIG. eight 7 yb 35 W «5 (9ff -J) Fie.9 fie.Yu Angle ao pt / sautju tpai 1.0 0.9 0.5 JI1L You go 30 4050 ba / pa, hail 1.2 Angle gI t.O 0.8 0.6 J W go 30 W 50 beta hail -te- -i, p1 II Jl 60 0ue.1lf 6 l s 5