WO2000036462A1 - Achromatic compound retarder - Google Patents

Abstract

This invention provides achromatic compound retarders, achromatic polarization switches, and achromatic shutters using the liquid crystal compound retarders. It further provides achromatic variable retardance smectic and nematic liquid crystal retarders. The achromatic compound retarders according to the invention are used to create achromatic inverters for display applications. The display comprises one or more retarders (320a-320n) having in-plane retardance and in-plane orientation, at least one of the retarders being an actively controlled liquid crystal retarder, and a ferroelectric liquid crystal display (370), wherein the one or more retarders work in combination with the ferroelectric liquid crystal display (370) to provide four states of brightness.

Description

ACHROMATIC COMPOUND RETARDER

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. Patent Application No.

09/215,208, filed December 18, 1998, which is a continuation-in-part of U.S. Patent

Application No. 08/901,837, filed July 28, 1997, which is a continuation of U.S.

Patent Application Serial No. 08/419,593, filed April 7, 1995 (Patent No.

5,658,490), both of which are herein incorporated by reference in their entirety.

This application also claims priority from U.S Provisional Applications Nos.

60/113,005, filed December 18, 1998, and 60/121,494, filed February 24, 1999.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to compound retarders. More

specifically, the present invention is directed to the use in display devices of achromatic

compound retarders that exhibit an achromatic composite optic axis orientation

and/or an achromatic composite compound retardance at each of at least two

composite retarder orientation states. Further, the present invention is directed to the

use of such achromatic compound retarders to create achromatic inverters for display

applications. 2. Background of the Related Art

Liquid crystal retarders are increasingly utilized within optical devices such as

tunable filters, amplitude modulators and light shutters. Planar aligned smectic liquid

crystal devices function as rotative waveplates wherein application of an electric field

rotates the orientation of the optic axis but does not vary the birefringence. In

contrast, homeotropically aligned smectic liquid crystals, homogeneous aligned

nematic devices, and nematic pi-cells function as variable retarders, wherein application

of an electric field varies the birefringence. Chromaticity is a property of birefringent

elements, both passive and active liquid crystals. There are two main components to

chromaticity: (1) dispersion, which is the change in the birefringence (Δn) with

wavelength λ; and (2) the explicit dependence of retardance on 1/λ due to the

wavelength dependent optical pathlength. Both components contribute to increased

birefringence with decreased wavelength. A birefringent material having a particular

retardance at a design wavelength has higher retardance at shorter wavelengths and

lower retardance at longer wavelengths. Chromaticity places limitations on the

spectral operating range of birefringent optical devices.

Chromaticity compensation for passive retarders was addressed by S.

Pancharatnam, Proc. Indian Acad. Sci. A41, 137 [1955], and by A.M. Title, Appl. Opt.

14, 229 [1975], both of which are herein incorporated by reference in their entirety.

The wavelength dependence of passive birefringent materials can be reduced by

replacing single retarders with compound retarders. The principle behind an

achromatic compound retarder is that a stack of waveplates with proper retardance and relative orientation can be selected to produce a structure which behaves as a pure

retarder with wavelength insensitive retardance. Pancharatnam showed, using the

Poincare sphere and spherical trigonometry, that such a device can be implemented

using a minimum of three films of identical retarder material. A Jones calculus

analysis by Title (supra) verified the conditions imposed on the structure in order to

achieve this result: (1) the requirement that the composite structure behave as a pure

retarder (no rotation) forces the input and output retarders to be oriented parallel and

to have equal retardance; and (2) first-order stability of the compound retarder optic

axis and retardance with respect to wavelength requires that the central retarder be a

half-wave plate. These conditions yield design equations that determine the retardance

of the external elements and their orientation relative to the central retarder for a

particular achromatic retardance. Because these design equations specify a unique

orientation of the central retarder and a unique retardance for the external retarders,

they have never been applied to active liquid crystal devices and the problem of active

retarder chromaticity remains.

For the specific example of an achromatic half-wave retarder, the design

equations dictate that the external retarders are also half-wave plates and that the

orientation of the external retarders relative to the central retarder is π/3. By

mechanically rotating the entire structure, wavelength insensitive polarization

modulation is feasible. Furthermore, Title showed that the compound half-wave

retarder can be halved, and one section mechanically rotated with respect to the other

half to achieve achromatic variable retardance. Electromechanical rotation of such compound half-wave retarders has been used extensively to tune polarization

interference filters for astronomical imaging spectrometers.

The primary application of ferroelectric liquid crystals (FLCs) has been shutters

and arrays of shutters. In the current art, on- and off-states of an FLC shutter (Fig. 1)

are generated by reorienting the optic axis of FLC retarder 10 between π/4 and 0 with

respect to bounding crossed or parallel polarizers 20 and 22. In the off-state, x-

polarized light is not rotated by the liquid crystal cell and is blocked by the exit

polarizer. In the on-state, the polarization is rotated 90° and is therefore transmitted

by the exit polarizer.

For maximum intensity modulation, the cell gap is selected to yield a half-wave

retardance at the appropriate design wavelength. The on-state transmission of x-

polarized light is theoretically unity at the design wavelength, neglecting absorption,

reflection and scattering losses. At other wavelengths the transmission decreases. The

ideal transmission function for an FLC shutter as in Fig. 1 is given by

l -sin²δ/2 ON (α=π/4 )

(1)

T =

OFF (α - o :

where δ is the deviation from half-wave retardance with wavelength. This expression

indicates a second-order dependence of transmission loss on δ. The off-state

transmission is in principle zero, but in practice it is typically limited to less than 1000:1 due to depolarization by defects, the existence of multiple domains having

different alignments, and fluctuations in the tilt-angle with temperature.

High transmission through FLC shutters over broad wavelength bands is

feasible for devices of zero-order retardance, but it is ultimately limited by the inverse-

wavelength dependence of retardation and the rather large birefringence dispersion of

liquid crystal materials. For instance, a visible FLC shutter device that equalizes on-

state loss at 400 nm and 700 nm requires a half-wave retarder centered at 480 nm. A

zero-order FLC device with this retardance, using typical FLC birefringence data, has

a thickness of roughly 1.3 microns. The transmission loss at the extreme wavelengths,

due to the departure from half-wave retardance, is approximately 40%. This

significantly limits the brightness of FLC displays and the operating band of FLC

shutters and light modulators. In systems incorporating multiple FLC devices, such

as tunable optical filters or field-sequential display color shutters, this source of light

loss can have a devastating impact on overall throughput and spectral purity.

The above references are incorporated by reference herein where appropriate

for appropriate teachings of additional or alternative details, features and/or technical

background.

SUMMARY OF THE INVENTION

This invention provides achromatic compound retarders, achromatic

polarization switches, and achromatic shutters using the achromatic compound

retarders. It further provides achromatic variable retarders utilizing smectic liquid crystals. An achromatic shutter according to this invention is demonstrated which

provides excellent on-state transmission over the entire visible, >94% from 400 nm to

700 nm after normalization for polarizer loss, and high contrast, 1000:1 from 450 nm

to 650 nm.

One embodiment of the achromatic compound retarder of this invention

comprises a central rotatable smectic liquid crystal half-wave retarder and two external

passive retarders positioned in series with and on either side of the liquid crystal

retarder. The external retarders are equal in retardance and oriented parallel to each

other. Design equations determine the retardance of the external elements and their

orientation relative to the central retarder to obtain a particular retardance for the

compound structure. A reflective version of the achromatic compound retarder

described above is constructed with a smectic liquid crystal quarter-wave retarder

positioned between a single passive retarder and a reflector.

In the achromatic compound retarders of this invention there is, in general, an

orientation of the central retarder for which the structure has maximum achromaticity

in both orientation and retardance. Important aspects of this invention are the

discoveries that (1) the composite retardance at the design wavelength does not change

when the optic axis orientation of the central retarder is changed and (2) there are

optic axis orientations of the central retarder for which the optic axis orientation of

the compound retarder is stable (achromatic) even though the composite retardance

is not achromatic. The central retarder may comprise a liquid crystal retarder, as described above.

In the case of a smectic liquid crystal cell, application of an electric field rotates the

optic axis between two or more orientations. One of the orientations provides

maximum achromaticity of the compound retardance. As discussed above, there is

also at least one other optic axis orientation for which the optic axis of the compound

retarder is achromatic, even though the composite retardance is not. Furthermore, the

composite retardance at the design wavelength does not change when the optic axis

orientation of the smectic liquid crystal cell is changed.

The central retarder may also comprise a spatially switched planar-aligned

passive retarder, in which the orientation of the optic axis varies as a function of

position on the spatially switched passive retarder. The spatially switched passive

retarder has at least two optic axis orientations states, with one of the orientations

causing the retardance of the compound retarder to be substantially achromatic, and

the second orientation causing the optic axis orientation of the compound retarder to

be substantially achromatic, even though the composite retardance may not be.

The achromatic properties discussed above are utilized in the achromatic

polarization switch of this invention, comprising a linear polarizer and the compound

achromatic retarder, and in the achromatic shutter of this invention, comprising the

compound achromatic retarder positioned between a pair of polarizers. In one optic

axis orientation state of the central retarder (the "ON-state") the compound retarder

is achromatic and in a second optic axis orientation state of the central retarder (the

"OFF-state") the compound retarder is oriented parallel to one polarizer and the light therefore does not "see" the compound retarder. In the off-state, fixed retardance with

wavelength is therefore not necessary. Providing achromatic orientation of the

compound retarder in the off-state yields high contrast shutters. Reflection-mode

shutters are further provided in this invention.

In alternative liquid crystal compound retarder embodiments, the rotatable

smectic liquid crystal half-wave retarder is replaced by first and second liquid crystal

variable birefringence retarders. The first and second variable birefringence retarders

have first and second fixed optic axis orientations, respectively, and retardances which

can be switched between zero and half-wave. In operation, when one retarder is

switched to zero retardance, the other is switched to half-wave, and vice-versa, so that

the composite retardance of the pair is a half-wave retardance with orientation

switchable between the first and second optic axis orientations.

The achromatic variable retardance smectic liquid crystal compound retarder

of this invention comprises an active section rotatable with respect to a passive section.

The active section comprises two liquid crystal retarders: a half-wave plate and a

quarter- ave plate oriented at angles ₂ and oc₂ + π/3, respectively, where the angle ₂

is electronically switchable. The passive section comprises two retarders: a quarter-

wave plate and a half-wave plate oriented at angles _x and cCj-f- π/3, respectively, where

the angle a₁ is fixed. The quarter-wave plates are positioned between the half-wave

plates. The composite retardance of the compound structure is 2(π/2-<^χ ₂+ α₁). To vary

the retardance, the liquid crystal retarders in the active section are both rotated. The planar-aligned smectic liquid crystal cells of this invention have

continuously or discretely electronically rotatable optic axes. The smectic liquid

crystal cells can utilize SmC^* and SmA^* liquid crystals, as well as distorted helix

ferroelectric (DHF), antiferroelectric, and achiral ferroelectric liquid crystals. The

variable birefringence liquid crystal cells of this invention can include homogeneously

aligned nematic liquid crystals, pi-cells, and homeotropically aligned smectic liquid

crystal cells.

The present invention may be achieved in whole or in part by an achromatic

compound retarder that exhibits a compound retardance and a compound optic axis,

comprising: (1) a first passive retarder unit having a predetermined retardance at a

design wavelength, and having a predetermined optic axis orientation; (2) a second

passive retarder unit having the same retardance as the first passive retarder unit at the

design wavelength, and having substantially the same optic axis orientation as the first

passive retarder unit; and (3) a central retarder unit positioned between the first and

second retarder units, the central retarder unit having a retardance π at the design

wavelength, and having an optic axis orientation that varies as a function of position

on the central retarder unit, wherein the optic axis orientation varies between at least

a first orientation state, in which the compound retardance is substantially achromatic,

and a second orientation state.

The present invention may also be achieved in whole or in part by a reflection

mode achromatic compound retarder, comprising: (1) a first passive retarder unit

having a predetermined retardance at a design wavelength, and having a predetermined optic axis orientation; (2) a reflector; and (3) a spatially switched retarder unit

positioned between the first retarder unit and the reflector, the spatially switched

retarder unit having a retardance π/2 at the design wavelength, and having an optic

axis orientation that varies as a function of position on the central retarder unit,

wherein the optic axis orientation varies between at least a first orientation state, in

which the compound retardance is substantially achromatic, and a second orientation

state.

The present invention may also be achieved in whole or in part by an

achromatic compound retarder that exhibits a composite optic axis orientation and a

composite retardance, comprising: (1) a first passive retarder unit having a

predetermined retardance at a design wavelength, and having a predetermined optic

axis orientation; (2) a second passive retarder unit having the same retardance as the

first passive retarder unit at the design wavelength, and having substantially the same

optic axis orientation as the first passive retarder unit; and (3) a central retarder unit

positioned between the first and second retarder units, the central retarder unit having

a retardance π at the design wavelength, and having an optic axis orientation that

switches between at least two orientation states as a function of position on the central

retarder unit, wherein the composite optic axis orientation and/or the composite

retardance is substantially achromatic at two orientation states of the central retarder

unit.

The compound retarder according to the invention can also be employed to

provide a novel achromatic inverter in a reflective or transmissive type display. The achromatic inverter works in combination with a liquid crystal display panel to

provide four states of intensity or brightness, two high and two low, so that the

reflective or transmissive display is capable of displaying an inverse image frame.

In particular, in accordance with one embodiment of the invention, a reflective

display comprises one or more retarders having in-plane retardance and in-plane

orientation, at least one of the retarders being an active retarder, and a ferroelectric

liquid crystal display. The one or more retarders work in combination with the

ferroelectric liquid crystal display to provide four states of brightness.

In accordance with another embodiment of the invention, a reflective display

comprises a linear polarizer, an actively controlled liquid crystal retarder and a

ferroelectric liquid crystal display. In accordance with a further embodiment, a

reflective display comprises a polarizing beam splitter, an actively controlled liquid

crystal retarder and a ferroelectric liquid crystal display. In both embodiments, the

actively controlled liquid crystal retarder and the ferroelectric liquid crystal display are

both switchable between at least two orientations to provide four states of brightness.

In accordance with still another embodiment, a transmissive display comprises a first

linear polarizer, a first actively controlled liquid crystal retarder and a ferroelectric

liquid crystal display, a second actively controlled liquid crystal retarded and a second

linear polarizer.

The active retarder can be either a smectic or a nematic liquid crystal retarder.

In the accordance with another embodiment of the invention, a reflective display

comprises a linear polarizer, an actively controlled nematic liquid crystal retarder and a ferroelectric liquid crystal display. In accordance with a further embodiment, a

reflective display comprises a polarizing beam splitter, an actively controlled nematic

liquid crystal retarder and a ferroelectric liquid crystal display. In both embodiments,

the actively controlled nematic liquid crystal retarder and the ferroelectric liquid

crystal display are both switchable between at least two orientations to provide in

combination four states of brightness. Additionally, a passive retarder can be provided

between the actively controlled nematic liquid crystal retarder and a ferroelectric

liquid crystal display. Further, the actively controlled nematic liquid crystal retarder

can comprise one or more pi-cells. Where one or more pi-cells are employed as the

actively controlled nematic liquid crystal retarder, a passive retarder can be located

between the one or more pi-cells and the ferroelectric liquid crystal display or between

adjacent pi-cells. Further, in addition to the one or more pi-cells, the display may

include additional actively controlled liquid crystal retarders, arranged adjacent to the

one or more pi-cells or in between the one or more pi-cells.

Additional advantages, objects, and features of the invention will be set forth

in part in the description which follows and in part will become apparent to those

having ordinary skill in the art upon examination of the following or may be learned

from practice of the invention. The objects and advantages of the invention may be

realized and attained as particularly pointed out in the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in detail with reference to the following

drawings in which like reference numerals refer to like elements wherein:

Figure 1 is a light shutter comprising a ferroelectric liquid crystal between

crossed polarizers;

Figure 2(a) illustrates a first embodiment of an achromatic compound retarder,

in accordance with the present invention;

Figure 2(b) illustrates a second embodiment of an achromatic compound

retarder, in accordance with the present invention;

Figure 2(c) illustrates a third embodiment of an achromatic compound retarder,

in accordance with the present invention;

Figure 3 (a) is a reflective achromatic compound retarder, in accordance with the

present invention;

Figure 3(b) illustrates a second embodiment of a reflective achromatic

compound retarder, in accordance with the present invention;

Figure 4 illustrates an achromatic shutter utilizing the achromatic compound

retarder of the present invention;

Figures 5(a) and 5(b) are plots showing the calculated on- and off-state

transmission spectra of crossed polarizer shutters having (a) the achromatic compound

retarder of the present invention, and (b) a single retarder; Figure 5(c) and 5(d) are plots showing the calculated on- and off-state

transmission spectra of parallel polarizer shutters having (c) the achromatic compound

retarder of the present invention, and (d) a single retarder;

Figure 6 is a plot showing measured on-state transmission spectra of (a) a

compound-retarder achromatic shutter, in accordance with the present invention, and

(b) a single-retarder shutter;

Figure 7 is the measured off-state transmission spectrum of a compound-retarder

achromatic shutter, in accordance with the present invention;

Figure 8 is a plot showing the calculated on-state transmission, as a function of

the deviation from half-wave retardance δ, of (a) a compound-retarder achromatic

shutter, in accordance with the present invention, and (b) a single-retarder shutter;

Figure 9 is a plot showing the calculated off-state transmission, as function of

δ, of a compound-retarder achromatic shutter, in accordance with the present

invention;

Figure 10 is a plot showing the calculated contrast ratio, of a function of δ, of

a compound-retarder achromatic shutter, in accordance with the present invention;

Figure 11(a) is a plot showing the calculated on-state transmission spectra of an

achromatic shutter utilizing a compound quarter-wave retarder, in accordance with the

present invention;.

Figure 11 (b) is a plot showing the calculated off-state transmission spectra of an

achromatic shutter utilizing a compound quarter- wave retarder, in accordance with the

present invention; Figure 12(a) shows a multiple-pixel reflection-mode achromatic shutter having

parallel polarizers, in accordance with the present invention;

Figure 12(b) shows a multiple-pixel reflection-mode achromatic shutter having

crossed polarizers, in accordance with the present invention;

Figure 13 is multiple-pixel transmission-mode achromatic shutter, in accordance

with the present invention;

Figure 14 is a compound achromatic variable retarder comprising a pair of

liquid crystal retarders and a pair of passive retarders, in accordance with the present

invention;

Figure 15(a) shows an arrangement of a general reflective display according to

the invention;

Figure 15(b) shows an unfolded revision of the reflective display of Figure 15(a);

Figure 16 is a table that illustrates that the optimal modulation of a

conventional LCD panel is between an OFF-state orientation of 0 (π/2) and an ON-

state orientations of ± π/4;

Figure 17 is a table illustrating that when a passive retarder is oriented at 7.5°,

the LCD panel rotates between 60° (ON), and 105° (OFF) ;

Figure 18 is a table illustrating the performance for half-wave retarders centered

at 500 nm, where the dispersion of polycarbonate is used for all elements;

Figure 19(a) illustrates a first embodiment of a reflection-mode achromatic FLC

display that includes an achromatic inverter, in accordance with the present invention; Figure 19(b) illustrates a second embodiment of a reflection-mode achromatic

FLC display that includes an achromatic inverter, in accordance with the present

invention;

Figure 20 is a table that shows the output of one pixel of the FLC display of Fig.

19(b) for different orientations of the LC retarder and the FLC retarder;

Figure 21 is a plot of the optical transmission of the FLC display of Fig. 19(b)

in the on-state as a function of wavelength for different tilt angle combinations;

Figure 22 illustrates a transmission-mode achromatic FLC display that includes

an achromatic inverter, in accordance with the present invention;

Figures 23(a) and 23(b) show optical inverters according to the invention

implemented with a nematic liquid crystal variable retarder;

Figure 23(c) shows an optical inverter implemented with a pair of nematic

liquid crystal variable retarders with improved field of view (FOV) according to the

invention;

Figure 24 shows an optical inverter according to the invention implemented

with a nematic liquid crystal variable retarder and a passive retarder;

Figure 25 illustrates preferred orientations of the passive retarder of the

embodiment of Figure 24;

Figure 26 illustrates a preferred difference in angle between the optic axes of the

NLC and passive retarder of Figure 24;

Figure 27(a)-27(d) illustrate in diagrammatic form a preferred polarization

manipulation of all four states of brightness in the embodiment of Figure 24; Figure 28-30 are plots of transmission versus wavelength for preferred

configurations according to the invention;

Figure 31 shows another embodiment of a FLC display device with improved

FOV according to the invention;

Figure 32 illustrates how off axis rays "see" a twisted liquid crystal director

profile;

Figure 33 shows another embodiment of a FLC display device according to the

invention;

Figure 33(a) illustrates preferred orientations of the various wave plates in the

embodiment of Figure 33;

Figure 34 shows another embodiment of a FLC display device according to the

invention;

Figure 34(a) illustrates preferred orientations of the various wave plates in the

embodiment of Figure 34;

Figure 35 shows another embodiment of a FLC display device according to the

invention;

Figure 35(a) illustrates preferred orientations of the various wave plates in the

embodiment of Figure 35;

Figure 36 shows the basic structure of another reflective display according to

the invention;

Figures 37(a) - 37(b) show head-on spectra of four states of the embodiment of

Figure 36; Figures 38(a) - 38(b) illustrate a total of four states of intensity of the

embodiment of Figure 36;

Figure 39 shows the basic structure of another reflective display according to

the invention;

Figures 40(a) - 40(b) illustrate a total of four states of intensity of the

embodiment of Figure 39;

Figure 41 shows the basic structure of another reflective display according to

the invention;

Figure 42(a) - 42(b) illustrate a total of four states of intensity of the

embodiment of Figure 41;

Figure 43 shows the basic structure of another reflective display according to

the invention; and

Figures 44-47 show various display devices incorporating an achromatic inverter

according to the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The elements in the devices of this invention are optically coupled in series.

The orientation of a polarizer refers to the orientation of the transmitting axis, and the

orientation of a birefringent element refers to the orientation of the principal optic

axis of that element. Orientations are herein defined with respect to an arbitrary axis

in a plane perpendicular to the light propagation axis z. This arbitrary axis is labeled

the "x" axis in the figures. In the illustrations of birefringent elements, the orientation is shown by arrow-headed lines and the retardance is labeled on the side of the

element. When the retardance is switchable between two values, the values are both

labeled on the side and are separated by a comma. The retardance refers to the

retardance at a design wavelength. Note that a π retardance is equal to a half-wave

(λ/2) retardance.

The term fixed retarder refers to a birefringent element wherein the orientation

and retardance can not be electronically modulated. The term active retarder refers

to a birefringent element wherein the orientation and/or the retardance can be

electronically modulated. Rotatable liquid crystal retarders of this invention have

electronically rotatable orientation and fixed retardance at the design wavelength.

Liquid crystal variable retarders or, equivalently, liquid crystal variable birefringence

retarders have electronically variable retardance (birefringence) and fixed orientation.

The term compound retarder is used for a group of two or more retarders which

function as a single retarder. The composite retardance of a compound retarder is

characterized by an orientation and a retardance.

A spatially switched retarder refers to an active or passive retarder in which the

orientation and/or the retardance varies as a function of position on the retarder.

The terms design wavelength and design frequency (υ₀) refer to the wavelength

and frequency at which the individual retarders within the compound retarder provide

the specified retardance. The term achromatic retarder refers to a retarder with

minimal first-order dependence of both the retardance and the orientation on the

deviation of the incident light from the design frequency (Δυ/υ₀). The term achromatic orientation refers to an orientation of the optic axis with minimal first-

order dependence on the deviation of the incident light from the design frequency.

A first embodiment of the achromatic compound retarder of this invention

(Fig. 2a) comprises planar-aligned smectic liquid crystal retarder 30 having an

orientation which is electronically rotatable between angles α₂ and α₂'. These

orientations are herein termed the on-state and the off-state, respectively. Retarder 30

provides a half-wave retardance (T₂°= π) at the design wavelength. Outer retarders 40

and 42, with orientation a₁ and retardance r ° at the design wavelength, are positioned

on either side of central retarder 30. In an alternative embodiment, the outer retarders

40 and 42 are crossed instead of parallel. In this application the design equations are

derived for the case of parallel retarders. Analogous equations can be derived for

crossed retarders.

In this embodiment, the central retarder is an FLC, but it can be any material

with an electronically rotatable optic axis, including planar aligned SmC^* and SmA

liquid crystals, as well as distorted helix ferroelectric (DHF), antiferroelectric, and

achiral ferroelectric liquid crystals. The retarder switches between at least two

orientations, α₂ and α₂'. It can, depending on the liquid crystal employed and the

electric field applied, rotate continuously between a range of orientations including α₂

and o-₂', switch between bistable states α₂ and α₂', or be switched between two or more

discreet but not necessarily stable orientations.

In a second embodiment of the achromatic compound retarder (Figure 2(b)),

rotatable retarder 30 is replaced by a spatially switched retarder 100. The spatially switched retarder 100 is prefereably a planar-aligned passive retarder with an optic axis

orientation that varies as a function of position on the spatially switched retarder 100.

In the embodiment shown in Figure 2(b), the spatially switched retarder 100 has a

fixed optic axis orientation α₂ in one portion 100a of the retarder 100, and an optic axis

orientation a₂' in a second portion 100b of the spatially switched retarder 100. The

retardance of the spatially switched retarder 100 at the design wavelength is preferably

fixed and the same in both the first and second retarder portions 100a and 100b.

Similar to the embodiment shown in Figure 2(a), the orientations α₂ and α₂' are

termed the on-state and the off-state, respectively. The spatially switched retarder 100

preferably provides a half-wave retardance (T₂°= π) at the design wavelength in both

the first portion 100a and the second portion 100b. The spatially switched retarder

100 is divided into at least two portions 100a and 100b, with respective optic axis

orientations

α₂ and ₂'. However, the spatially switched retarder 100 can be divided into additional

portions that exhibit other optic axis orientations.

The spatially switched retarder 100 can be any birefringent material. Suitable

materials include crystalline materials, such as mica or quartz, stretched polymeric

films, such as mylar or polycarbonates, and polymer liquid crystal films.

In a third embodiment of the achromatic compound retarder (Figure 2(c)),

rotatable retarder 30 is replaced by variable retarders 31 and 33 having fixed

orientations of α₂ and α₂', respectively. The retardance of 31 and 33 can be switched

between zero and half-wave. The retardances are synchronously switched which, as used herein, means that when one has zero retardance the other has half-wave

retardance and vice-versa. Thus the composite retardance of 31 and 33 is always a half-

wave and the composite orientation is switchable between α₂ and ₂ .

Liquid crystal variable retarders 31 and 33 can include, but are not limited to,

homogeneously aligned nematic cells, nematic π- cells, and homeotropically aligned

smectic liquid crystal retarders. As is known in the art, homogeneously aligned

nematic cells and nematic π-cells are sometimes incapable of being electrically driven

to zero retardance. In this case, the liquid crystal cell can be combined ("shimmed")

with a passive retarder to compensate for the residual retardance. The passive retarder

is oriented orthogonal to the liquid crystal retarder if the birefringence has the same

sign and parallel if the birefringence has opposite sign. In the present invention,

variable retarders 31 and 33 optionally include passive retarders to compensate for non¬

zero residual retardance.

This invention is described herein with the rotatable liquid crystal retarder (Fig.

2(a)) as the representative species of Figs. 2(a)-2(c). It is to be understood that in all

embodiments of the present invention that utilize a tunable retarder, a liquid crystal

rotatable retarder can, in the manner of Fig. 2(c), be replaced by a pair of liquid crystal

variable retarders. The species of Fig. 2(a) is preferred over the species of Fig. 2(c) for

several reasons. The construction is simpler because it uses a single liquid crystal cell

instead of two active cells. In addition, the switching speed of smectic liquid crystals

is orders of magnitude faster than nematics. Finally, the field of view is greater. The passive outer retarders can be any birefringent material. As discussed

above, in connection with the spatially switched retarder, suitable materials include

crystalline materials, such as mica or quartz, stretched polymeric films, such as mylar

or polycarbonates, and polymer liquid crystal films. In a preferred embodiment, the

dispersion of the passive outer retarders is approximately matched to the dispersion

of the central retarder. Mylar, for example, has a similar dispersion to some FLCs.

The achromatic compound retarder of this invention is designed to be

achromatic in the on-state when the central retarder is oriented at ₂. For

achromaticity of the orientation and retardance, one solution for the relative

orientations of the retarders is:

cos2Δ = -π (²)

2r°

where Δ = ₂-(x.₁. In addition there are isolated orientations for specific design

frequencies that also yield achromatic orientation and retardance. The retardance, V,

of the compound retarder is obtained from

sinr. cos (r/2 ) π (3) The orientation, Ω + o-_j, of the compound retarder is obtained from

(4)

where Ω is the orientation of the compound retarder with respect to the orientation

of the outside passive retarders.

Based on the above design equations, the retardance of the outer retarders and

the relative orientations of the retarders can be chosen to provide the desired

retardance of the compound retarder and to ensure achromaticity. For example, for

an achromatic compound half-wave retarder (T = π), Eq. 3 provides the solution T °

= π, and Eq. 2 provides the relative orientation of the retarders as Δ = 60°. Eq. 4

gives the relative orientation of the compound retarder as Ω = 30°. Therefore, to

obtain an orientation of Ω + c = 45° for the compound half-wave retarder, the outer

retarders are oriented at = 15°. Since Δ = 60°, the orientation of the central

retarder must then be α₂ = 75°. Similarly, for an achromatic compound quarter-wave

retarder (T = π/2), the equations yield V = 115°, Δ = 71°, and Ω = 31°. Thus, for

an orientation of Ω + _x = 45°, the outer retarders are oriented at a = 14° and the

central retarder is at α₂ = 85°.

In the achromatic compound retarder of Fig. 2(a), the liquid crystal central

retarder has an optic axis rotatable between ₂ and ₂'. When the liquid crystal

retarder is at α₂', the orientation relative to the outer passive retarders is Δ' = o^'-c-_! and the orientation of the compound retarder relative to the outer retarders is Ω'. Since

Eq. 2 gives a unique solution for the absolute value of Δ, at which the compound

retarder is achromatic, it teaches against changing the orientation of the central

retarder with respect to the outer retarders. An aspect of the present invention is the

discovery that (1) at orientations ₂ of the central retarder which do not satisfy Eq.

2, the composite retardance -T is nevertheless unchanged at the design wavelength and

(2) there are orientations ₂ of the central retarder for which, even though the

composite retarder is not achromatic, the optic axis orientation is stable with respect

to wavelength.

A further aspect of this invention is the realization that in many devices the

composite retardance does not affect device output in certain switching states and,

therefore, it need not be achromatic in those states. In particular, when the compound

retarder is oriented parallel to a polarizer, the polarized light is not modulated by the

retarder and hence any chromaticity of the retardance is unimportant. Only stability

of the orientation of the optic axis is required so that the orientation remains parallel

to the polarizer throughout the operating wavelength range. These properties lead to

numerous useful devices utilizing the compound retarder with a rotatable or spatially

switched central retarder.

In a preferred embodiment of the achromatic compound retarder, the optic axis

orientation of the compound retarder is achromatic when the central retarder is

oriented at ₂ . The first order term of the frequency dependence of the orientation

of the retardation axis is dΩ , -i2r? tan2Δcos²2Ωsin r? _{0 Π} δi ¹ "^e ^ΪZ ⁽ r₁ccs2^{Λ .} -_J ⁾

(5) e=0

where e is the relative frequency difference Δv/v₀. Note that in the on-state, wherein

Eq. 2 is satisfied, Eq. 5 gives dΩ/de = 0. This confirms that the on-state orientation is

achromatic. For off-state orientations, ₂ , Eq. 5 can be used to determine the

magnitude of dΩ'/de. For the special case of an achromatic half-wave retarder, T ° =

π, and sin T ° = 0, so dΩ/de = 0 for all values of ₂ , i.e., the optic axis orientation is

achromatic at all orientations.

Because of the symmetry of the achromatic retarder, it can be implemented in

reflection-mode, as illustrated in Figs. 3(a) and 3(b). Fig. 3(a) is the reflection-mode

embodiment of the retarder of Fig. 2(a), and utilizes a single passive retarder 40, with

retardance T ° and orientation α_l5 liquid crystal quarter-wave retarder 32, with

orientation switchable between ₂ and ₂ , and reflector 50. Because the reflector 50

creates a second pass through the liquid crystal quarter-wave retarder 32, the net

retardance of the liquid crystal quarter-wave retarder 32 is a half wave. A forward and

return pass through the reflection-mode device is equivalent to a single pass through

the compound retarder of Fig. 2a. The reflection-mode embodiment of the retarder

of Fig. 2(c) (not shown) uses a pair of variable retarders switchable between zero and

quarter-wave retardance in lieu of rotatable quarter-wave retarder 32 in Fig. 3(a).

Figure 3(b) illustrates a reflection mode embodiment of the retarder of Figure 2(b), and utilizes a spatially switched quarter-wave retarder 110, with retarder portions 110a and

110b, in lieu of the liquid crystal quarter-wave retarder 32 of Fig. 3(a).

The reflector in the embodiments shown in Figs. 3(a) and 3(b) has R = 1 but it

can also have R< 1. The reflector can transmit an optical signal for addressing the

liquid crystal retarder of Fig. 3(a).

This invention further includes devices employing the achromatic compound

retarders described above. The polarization switch of this invention comprises a linear

polarizer in combination with the achromatic compound retarder. The polarizer can

be neutral with wavelength or can be a pleochroic polarizer. Light is linearly

polarized by the polarizer and the polarization is modulated by the achromatic

compound retarder. For the case of a half-wave achromatic compound retarder, the

polarization remains linear and the orientation is rotated. Other achromatic

compound retarder embodiments produce elliptically polarized light. The

polarization switch functions as a polarization receiver when light is incident directly

on the achromatic compound retarder rather than on the polarizer.

In a preferred embodiment, the achromatic compound retarder is achromatic

in the on-state ( ₂) and is oriented parallel to the polarizer in the off-state (cc₂'). With

this preferred off-state orientation, achromaticity of the composite retardance is not

needed because, with the orientation of the achromatic compound retarder parallel to

the polarizer, the polarized light does not " see " the achromatic compound retarder and

is not modulated by it. In a more preferred embodiment, the orientation of the

achromatic compound retarder is stable in the off-state, i.e., dΩ'/de is small. In the most preferred embodiment, the orientation of the achromatic compound retarder is

achromatic, i.e., dΩ'/de is zero.

A particularly useful embodiment of the polarization switch of the present

invention is illustrated in Fig. 4. The polarization switch 110 comprises polarizer 20,

outer retarders 40 and 42, and liquid crystal retarder 30. Outer retarders 40 and 42 are

half-wave retarders (T^ = π) oriented at ₁ = π/12. The liquid crystal retarder 30 is a

half-wave retarder, and is switchable between on- and off-state orientations of α₂ =

5π/12 and ₂ = 8π/12, respectively. This gives a compound retardance T = λ/2 and

orientations Ω + a = π/4 and Ω' + cCj = 0. In the off-state, light remains polarized

along the x-axis and in the on-state, light is oriented parallel to the y-axis. Because the

achromatic compound half-wave retarder has an achromatic orientation for all values

of ₂ , it can be used to achromatically rotate the polarization between the input

polarization state and any other linear polarization state.

The polarization switch 110 can be used in combination with any polarization

sensitive element. In combination with an exit polarizer 22 it forms an achromatic

shutter, as shown in Fig. 4. In the embodiment of Fig. 4, the polarizers 20 and 22 are

crossed, but they can alternatively be parallel. The shutter shown in Fig. 4 is

analogous to the shutter shown Fig. 1 in that the achromatic compound retarder has

a half-wave retardance, and on- and off-state composite retarder orientations of π/4

and 0, respectively. Like the shutter of Fig. 1, the shutter of Fig. 4 requires only one

active retarder. One advantage is that the shutter of the present invention is

achromatic. A mathematical analysis of the achromatic compound half-wave retarder and

the achromatic shutter demonstrates the wavelength stability of the devices of this

invention. The Jones matrix for the compound half-wave retarder is the product of

the matrices representing the three linear retarders. The Jones matrix that propagates

the complex cartesian field amplitude is given by chain multiplying the matrices

representing the individual linear retarders. For the on- and off-states these are given,

respectively, by the equations

W_β(π/4) = W(π + δ,π/12)W(π + δ,5π/12)W(π + δ,π/12) (6)

and

W_c(0) = W{τι + δ,π/12)W(π + δ,2π/3) (π + δ,π/12) (7)

where the general matrix for a linear retarder with retardation T and orientation α is

given by

_.„,,_, . , cosr/2-icos2c.sinr/2 -i-3in2c.sinr/2

-isin2cts±nT/2 cosT/2 + icos2otsinT/2

(8)

and the absolute phase of each retarder is omitted. For the present analysis, each

retarder is assumed identical in material and retardance, with half-wave retardation at

a specific design wavelength. This wavelength is preferably selected to provide optimum peak transmission and contrast over the desired operating wavelength band.

The retardance is represented here by the equation -T = (π + δ), where δ is the

wavelength dependent departure from the half-wave retardance. For the present work,

the dispersion is modeled using a simple equation for birefringence dispersion that is

suitable for both FLC and the polymer retarders used (Wu, S.T., Phys. Rev. (1986)

A33:1270). Using a fit to experimental FLC and polymer spectrometer data, a

resonance wavelength was selected that suitably models the dispersion of each material.

Substituting the three matrices into Eqs. 6 and 7 produces on- and off-state

matrices that can be written in the general form

t _l \ e -i t w 12 I c =

-i t iθ

12 t l e

(9)

where | t_;j | denotes the magnitude and θ the phase of the complex t^ matrix

components of the compound structure. The specific elements for the (achromatic)

on-state are given by:

'12

θ = tan .-^'l¹r[> ^:3¹,cotδ/2] (12)

The components for the off-state are given by:

'11

'12 = (1 -^)sin²δ/2cosδ/2, (14)

θ = tan- (15)

In the achromatic shutter device, the achromatic compound retarder is placed

between crossed polarizers. The Jones vector for the transmitted field amplitude is

given by the matrix equation

-E(λ) = P W_cP E_o (X) . (16)

The polarizers are taken to be ideal

1 0

P = 0 0 (17)

^{P" = l} 0 1 ) ' (18)

and the input field spectral density, E₀(λ), is taken to be x polarized, with unity

amplitude. Under these conditions, the Jones vector for the transmitted field is the

off-diagonal component of W_c. The y component of the output Jones vector

gives the field transmittance of the structure.

Since the components of W_c are given above in terms of their magnitudes, the

intensity transmission of the on- and off-states of the achromatic compound retarder

are given by simply squaring the off-diagonal terms of Eqs. 11 and 14, or T = | t \ ².

This gives the two intensity transmission functions of the shutter — sin , 4⁴>δ/ /2 ( ηl + - s .iJ -n,2²δ, ,/2 ) ON ( *2, = 5π/12 )

T = (19)

^■ 1 - J^ ) sin⁴δ/2cos²δ/2 OFF (α, = 2π/3 )

The above outputs illustrate the desirable result that the second -order

dependence

of transmitted intensity on δ vanishes. The loss in transmission in the on-state and the

leakage in the off-state have at most a fourth-order dependence on δ.

Like a simple FLC shutter, the mechanism for modulating polarization with the

smectic liquid crystal compound retarder is by rotating the orientation of the

compound retarder rather than by varying the birefringence. This can clearly be seen

by considering wavelength bands sufficiently narrow that the second (and higher)

order terms of the Jones matrices in δ can be neglected. In this instance the matrices

representing on- and off-states reduce respectively to

w. - j ° ^~i I , (20)

and

The on-state matrix reduces, to this degree of approximation, to an ideal

achromatic half-wave retarder oriented at π/4, while the off-state matrix reduces to an

ideal linear retarder oriented at 0, with retardation 2θ. Since only an off-diagonal

component is utilized in a shutter implementation, the output is ideal to this degree

of approximation.

The elimination of the second-order term is achieved using a 3-element structure

that achieves ideal half-wave retardation at two wavelengths, rather than a single

wavelength for the simple FLC shutter. This behavior can be seen by slightly varying

the relative orientation of the central and outer retarders in the on-state. The two ideal

transmission states, as well as the two null states, can be further separated in this way,

increasing the operating band but producing a more pronounced dip (leakage) between

maxima (nulls).

Based on the above equations, comparisons can be drawn between the

achromatic compound retarder shutter and the conventional FLC shutter. A 10% loss

in transmission for a conventional shutter occurs for a retardation deviation of δ =

37°, while the same loss for the achromatic shutter occurs for δ = 72°. This is very

nearly a factor of two increase in δ. Fig. 5(a) shows a transmisstion spectrum, created

using a computer model for the structures, for an achromatic shutter optimized for

visible operation (400-700 nm). The shutter has a 90% transmission bandwidth of 335

nm (409-744 nm). Fig. 5(b) shows the transmission spectrum for a conventional

shutter with a design wavelength of 480 nm. The conventional shutter has a 90%

bandwidth of 122 nm (433-555nm). The use of an achromatic compound retarder in the shutter results in a factor of 3.75 increase in bandwidth. Calculated spectra for

parallel polarizer shutters with a compound retarder, shown in Fig. 5(c), and a single

retarder, shown in Fig. 5(d), show the tremendous improvement in the off-state

provided by the achromatic compound retarder of this invention.

The increase in operating bandwidth is accompanied by a theoretical loss in

contrast ratio. The first-order orientation stability requirement of the optic axis allows

off-state leakage due to the presence of higher order terms. In practice, little if any

actual sacrifice is observed when incorporating the achromatic compound retarder.

An FLC optimized for visible operation (half-wave retardance at 480 nm) gives a

maximum departure in retardance of δ = 75°. Using this value, and assuming that the

outer retarders have dispersion identical to the FLC, a worst-case contrast ratio of

667: 1 is found for operation in the 400-700 nm band. For most of this band, theory

predicts contrast far in excess of 1000:1.

The conventional and the achromatic shutters were experimentally

demonstrated to verify the performance predicted by computer modeling. The FLC

device was fabricated using ZLI-3654 material from E-Merck. The ITO coated

substrates were spin coated with nylon 6/6 and were rubbed unidirectionally after

annealing. Spacers with a diameter of 1.5 microns were dispersed uniformly over the

surface of one substrate and UV cure adhesive was deposited on the inner surface of

the other substrate. The substrates were gapped by applying a uniform pressure with

a vacuum bag and subsequently UV cured. The FLC material was filled under

capillary action in the isotropic phase and slowly cooled into the C^* phase. After cooling, the leads were attached to the ITO and the device was edge-sealed. The FLC

cell had a half-wave retardance at 520 nm.

A conventional shutter, such as the one shown in Fig. 1, was formed by placing

the FLC cell with the optic axis oriented at 45° between parallel polarizers. Polaroid

HN22 polarizers were used due to their high contrast throughout the visible

wavelength range. The structure was probed by illuminating it with a 400 W Xenon

arc lamp, and the transmitted light was analyzed using a SPEX 0.5 m grating

spectrometer system. The on-state transmission of the conventional shutter is shown

in plot (b) of Fig. 6.

The achromatic shutter was assembled using the same FLC device positioned

between two Nitto NRF polycarbonate retarders having half-wave retardance at 520

nm. Since the FLC device is not dispersion matched to the polymer film, a loss in

contrast ratio is anticipated for the achromatic compound retarder due to increased off-

state leakage. The polycarbonate films were oriented at 15° with respect to the input

polarizer, which was crossed with the exit polarizer. The FLC was switched between

orientations of 5π/12 and 8π/12. The on-state spectra shown in plot (b) of Fig. 6, and

the off-state spectra, shown in Fig. 7, were measured. Both of these spectra were

appropriately normalized to remove leakage due to non-ideal polarizers, depolarization

by the retarders, and the polarization dependence of the lamp spectrum.

The measured transmission spectra indicate excellent agreement with the model

results. Figure 6 is striking evidence of the increased transmission over the visible

spectrum provided by the achromatic shutter of this invention. The model was further used to calculate the on-state transmission of a

compound-retarder achromatic shutter (Eq. 19) and a single retarder shutter (Eq. 1) as

a function of the deviation from half-wave retardance δ. The calculated transmission

spectra are shown in Fig. 8. Figure 9 is the calculated off-state transmission of a

compound-retarder shutter as a function of δ, and Fig. 10 is the calculated contrast

ratio.

Using the achromatic shutter at slightly longer center wavelengths, where FLC

dispersion is greatly reduced, enormous operating bands are feasible. For instance, the

calculated 95% transmission bandwidth of a shutter centered at 600 nm is

approximately 400 nm (480 nm-880 nm), while that of a simple FLC shutter is only

150 nm (540 nm - 690 nm).

The achromatic polarization switches and shutters of this invention can also

utilize compound retarders with composite retardances other than half-wave. For

example, a polarization switch can be fabricated using a linear polarizer and an

achromatic compound quarter-wave retarder. In one embodiment, the orientation

of the achromatic compound retarder switches between π/4 and 0 with respect to the

input polarizer, i.e. Ω + α_x = 45° and Ω' + ₁ = 0°. To achieve this, Eqs. 2-4 give T °

= 115°, Δ = 71°, CL^ = 14° and α₂ = 85° in the on-state, and in the off-state Δ' = 96°,

and α₂' = 111°. In the on-state, the compound quarter-wave retarder switches the

linear light to circularly polarized light, and in the off-state the linear polarization is

preserved. Addition of a second polarizer oriented perpendicular to the first polarizer

results in a shutter which switches between 50% transmission in the on-state and zero transmission in the off -state. The on- state transmission spectrum, shown in Fig. 11(a),

and the off-state transmission spectrum, shown in Fig. 11(b), were calculated assuming

no dispersion. Note that the off-state transmission spectrum is shown on a logarithmic

scale in Fig. 11(b).

The achromatic compound retarder, polarization switch and shutter of this

invention have been illustrated with FLCs having two optic axis orientations. They

can alternatively utilize more than two optic axis orientations and can have a

continuously tunable optic axis.

The achromatic shutter of this invention can be utilized in applications such as

CCD cameras, eye protection systems, glasses in virtual reality systems, three-color

shutters in field-sequential displays, beamsteerers, diffractive optics and for increasing

the brightness of LC flat-panel displays.

For many display applications the achromatic shutter can be used in a multiple-

pixel array, as shown in Figs. 12 and 13. In these figures, optical elements are shown

in cross section and are represented by rectangular boxes. The retardance of

birefringent elements is listed at the top of the respective box, and the orientation is

listed at the bottom. When elements can rotate between two or more orientations,

both orientations are listed in the box and are separated by a comma.

Reflection-mode embodiments are shown in Figs. 12(a) and 12(b). FLC retarder

32 has a quarter-wave retardance at the design wavelength and the optic axis is

rotatable between 5π/12 and 8π/12. The FLC cell is formed with substrates 90 and

92. Voltages are applied to the FLC using transparent electrode 95 and pixellated mirror electrodes 52. Each pixel can be separately addressed to provide the desired

display pattern. The compound retarder is formed by the FLC in combination with

passive half-wave retarder 40, oriented at π/12.

In Fig. 12(a) the shutter array uses linear polarizer 20 oriented at 0°. Since, in

reflection-mode, polarizer 20 is both the input and output polarizer, this is a parallel

polarizer embodiment. The array is illuminated by ambient light 100 and the viewer

is represented by an eye. In Fig. 12(b), the array uses polarizing beam splitter 25 to

create a crossed polarizer embodiment. White light 101 illuminates the array and

modulated gray light is output to the viewer.

A transmission-mode array is illustrated in Fig. 13. In this embodiment, the

FLC has a half-wave retardance. Voltages are applied using transparent electrode 95

and pixellated transparent electrode 96. The compound retarder is formed by the FLC

retarder in combination with outer retarders 40 and 42. The shutter is formed by

polarizers 20 and 22 which, in this embodiment, are crossed. The array is illuminated

by backlight assembly 103, which can be collimated by lens 104. The display is viewed

in transmission mode.

The achromatic compound retarder of this invention has been demonstrated

within an achromatic shutter. In addition, it can be used in many other optical devices

known in the art. In particular, it is suited to devices in which the retarder needs to

be achromatic in only one orientation and in which slight achromaticity in other

retarder orientations can be tolerated. Specific examples include polarization

interference filters and dye-type color polarizing filters. Numerous previous devices by the inventors can be improved by using the

achromatic compound retarder of this invention. In the polarization interference

filters of U.S. Patent Nos. 5,132,826, 5,243,455 and 5,231,521, all of which are herein

incorporated by reference in their entirety, a smectic liquid crystal rotatable retarder

and a passive birefringent element are positioned between a pair of polarizers. In a

preferred embodiment, the birefringent element is oriented at π/4 with respect to a

polarizer.

In the split-element polarization interference filters of U.S. Patent No.

5,528,393, which is herein incorporated by reference in its entirety, a center retarder

unit and a pair of split-element retarder units are positioned between a pair of

polarizers. The retarder units can include a rotatable liquid crystal retarder. The

individual liquid crystal rotatable retarders of the above-mentioned polarization

interference filters can be replaced with the achromatic compound retarders of the

present invention.

The liquid crystal handedness switch and color filters described in U.S. Patent

No. 5,619,355, which is herein incorporated by reference in its entirety, can also be

improved by using the achromatic compound retarders of the present invention. The

circular polarization handedness switch and the linear polarization switch comprise

a linear polarizer and a rotatable liquid crystal retarder. The color filters use the

polarization switch in combination with a color polarizer, such as a cholesteric circular

polarizer or a pleochroic linear polarizer. The simple liquid crystal rotatable retarders described in the handedness switch patent can be replaced with the achromatic

compound retarders of the present invention.

The achromatic compound retarder can also be used to improve other color

filters known in the art, for example as described in Handschy et al., U.S. Patent

5,347,378, which is herein incorporated by reference in its entirety. These color filters

comprise a linear polarizer and a rotatable liquid crystal retarder. In some

embodiments, they further comprise pleochroic polarizers, and in other embodiments

they further comprise a second linear polarizer and a passive birefringent element.

The simple liquid crystal rotatable retarder of the Handschy et al. invention can be

replaced with the achromatic compound retarders of the present invention.

The color filters of this invention can be temporally multiplexed, wherein the

output color is switched on a timescale which is rapid compared to a slow response

time detector, such as the human eye. The achromatic compound retarder of Fig. 2a,

employing a smectic liquid crystal cell, is particularly suited to this application.

The criterion for replacing a single retarder with the achromatic compound

retarder of this invention is that the single retarder must be rotatable between two or

more orientations of the optic axis. The achromatic compound retarder is especially

suited for use in devices wherein it is positioned adjacent to a linear polarizer and

wherein the orientation of the retarder is, in one of its switching states, parallel to the

linear polarizer. The achromaticity of the compound retarder is particularly

advantageous in color filtering devices because it can increase the throughput across

the entire visible spectrum. The achromatic compound retarder of this invention can also be used in optical

devices to replace a pair of variable retarders in which the first and second variable

retarders have first and second fixed orientations, and have retardances switchable

between first and second valves, and wherein the retardances are synchronously

switched between opposite valves. In addition, since the achromatic half-wave retarder

can be used to rotate the orientation of linearly polarized light, it can replace twisted

nematic cells in optical devices.

In addition to the achromatic compound retarder, this invention provides an

achromatic variable retarder, illustrated in Fig. 14. An active section comprises

smectic liquid crystal half-wave retarder 60, oriented at α₂, and smectic liquid crystal

quarter-wave retarder 65, oriented at α₂+π/3. Angle α₂ of retarders 60 and 65 is

electronically tuned, preferably synchronously. A passive section comprises passive

quarter-wave retarder 75, oriented at o + π/3, and passive half-wave retarder 70,

oriented at _v Angle o-j is fixed. The angle ₂ of the liquid crystal retarder orientation

can be rotated discreetly or continuously to at least one other angle ₂ . The

retardance of the compound structure is 2(π/2-α₂ + α₁).

The achromatic compound retarders of the present invention can be used to

provide an achromatic inverter for an FLC display. FLCs are generally binary electro-

optic devices that are operated in a one-bit mode, where (relative to the input

polarizer) a 0° orientation results in an off state (a black state) and a 45° orientation

results in an on state (a white state). Due to the ionic impurities in liquid crystal materials, LCDs are operated with

zero net DC voltage drive schemes. This is particularly important when making active

matrix displays using chiral smectic liquid crystals, such as FLC on silicon, as they are

generally two orders of magnitude less pure than their active matrix compatible

nematic counterparts. This means that if a positive voltage is applied to the LC, then

a voltage of equal and opposite polarity must be applied, preferably immediately

following, and generally for the same amount of time. This is called "DC balancing"

the waveforms across the LC.

The problem with DC balancing an active matrix FLC display is that, unlike

a nematic LC, FLCs respond to the polarity of applied voltage. That is, the optic axis

rotates in-plane by twice the molecular tilt angle, when the sign of an electric field

applied normally is reversed. When illuminated with polarized light, the two optical

frames will appear contrast reversed. What is white becomes black and vice versa. In

order to visually observe the displayed data effectively, the inverse frame must be

blanked (lamp turned off, or modulated with a shutter to emit no light) resulting in

loss of light through the optical system. For some applications, such as head mounted

displays, losses in brightness are more tolerable than, for example, front data

projection or rear projection systems for computer monitors and televison systems,

where brightness is important.

Prior art inverters for FLC displays are single pixel FLC devices that can be

crossed with respect to the FLC display panel. This method allows the display to

recover light from the inverse frame because inverting the voltages on both the FLC display panel and the FLC inverter cell yields the same image. Prior art inverter/FLC

display panel combinations are limited by the fact that both the FLC display panel

and inverter are chromatic devices.

Figure 15(a) shows an arrangement of a general reflective display according to

the invention. In particular, the reflective display of Figure 15(a) comprises a stack of

single-pixel retarder devices 320a-n with in-plane retardances T_N and in-line

orientations α,-α_N, at least one of which may be active, sandwiched between a

polarizing beam splitter (PBS) 310 and a FLC display panel (LCD panel) 370

comprising a FLC retarder 360 with mirror 380. The LCD panel 370 may comprise,

for example, an FLC retarder 360 sandwiched between a transparent electrode (not

shown) and pixellated mirror electrodes (not shown) for applying voltages across the

FLC retarder 360, similar to the arrangement shown in Figure 19(a). The display is

illuminated by white light 101 and the viewer is represented by an eye 300.

To more clearly illustrate the path light takes through the display of Figure

15(a) an "unfolded" version of the display is shown in Figure 15(b). The arrows a and

b show the direction of polarization of the input and output light, respectively.

The following is a hierarchy of structures that fall within the general case shown

in Figures 15(a) and 15(b):

(1) N=0: A standard FLC panel with no inverter, previously discussed in

this application. (2) N= l: A standard FLC display panel with the addition of a passive

retarder, as previously discussed in this application. This type of structure still has two

logic states but a compound retarder is used to achromatize the on-state.

(3) N= l: A standard FLC display panel with the addition of an active

retarder. This is the simplest structure that can implement an inverter according to

the invention. There are solutions using either a nematic or a smectic single pixel

device, as will be discussed below.

(4) N≥2: A standard FLC display panel with one active and one or more

passive retarders. This structure improves the overall performance of the display

device relative to the structure of case (3). This structure can have improved contrast

ratio, reduce flicker, or both.

A few assumptions are made about the various systems. First, the display of

Figure 15(a) is a reflective (two pass) device. The in-plane orientation of the molecular

director of the FLC retarder 360 rotates when the polarity of applied voltage is

switched. The in-plane retardance is identical in both states and the FLC retarder 360

has linear eigenstates (no twist). From this, we conclude that optimum performance

is achieved when the LC retarder 360 has a quarter-wave retardation in a single pass

(half-wave in a round trip), and the in-plane switching angle is π/4. Designs are

generated assuming this preferred arrangement, though it is understood that a suitable

adjustment in design can be made for non-ideal FLC behavior.

The LCD panel 370 is preferably a chiral smectic liquid crystal (CSLC) spatial

light modulator or display. For example, classes of CSLCs that can be used include SMA*, SMC'¹' including ferroelectric displays currently being commercialized by

Displaytech, Inc. in their Light Lasers series of products and their alliance with

Hewlett Packard, and distorted helix ferroelectric displays.

In order to implement the inverter, two on-states and two OFF-states are

required (four logic states) given by an auxiliary single-pixel switch. The single-pixel

switch can either be a nematic liquid crystal (NLC) or smectic (FLC) device.

For example, the single-pixel switch can be an electronically controlled

birefringence (ECB) cell, a pi-cell, a hybrid aligned nematic cell, a vertically aligned

nematic cell or another LC device that allows switching between a non-zero retardance

and zero retardance. A NLC behaves as a zero-twist retarder in the low-voltage state,

and becomes isotropic (vanishes) in the driven state. The term "vanishes", as used

herein, refers to a retarder state in which the polarization of input light is not affected.

Thus, the retarder is effectively not seen by the input light (i.e., vanishes). Note that

a double nematic (crossed cell) solution is identical in design to a single nematic

solution. The second cell improves switching speed, but the combination can be

considered a single zero-twist retarder in any voltage state. Because a nematic cell

vanishes in the driven state, the scheme in general modulates between structures with

N values that differ by unity.

The single-pixel FLC device switch is also taken to behave as an in-plane switch,

as described above. The tilt angle and retardance can in principle be selected to

accommodate the design. Unlike nematic solutions, FLC solutions modulate between

structures with a fixed N value, because the in-plane retardance is fixed. The only exceptions are designs in which the FLC is made to mimic the behavior of a nematic.

That is, the FLC device switch is directly adjacent to the polarizer oriented along an

eigenstate in one voltage state. Therefore, FLC solutions can either have a fixed N

value, or modulate between solutions that differ by unity.

As discussed above, structures with NLC switches modulate between structures

that differ in N value by unity. Let M (2N+ 1) represent the total number of retarders

required in the unfolded structure. First, consider the requirements placed on the

structure with the lower N value (NLC driven to high state). When no passive

retarders are used, the design reduces to the N=0 case. The LCD panel optimally

modulates between an OFF-state orientation of 0 (π/2) and on-state orientations of

±π/4, as shown in Figure 16. The OFF-state has unlimited contrast ratio in theory,

while the on-state is given by a zero-order half-wave plate.

Given this configuration, the insertion of the nematic waveplate (by driving the

NLC to the low state) produces the additional states. The NLC orientation is

preferably selected to maximize the contrast ratio of the OFF-state. The angle

between the NLC retarder and the FLC retarder (in the LCD panel) in this state is

Δ' = 67.5°, per the M= 1 requirements, which limits the wavelength stability of the

optic axis. The chrominance of the on-state is fixed by the OFF-state requirements.

For this case, the on state is less chromatic than an LCD panel alone. The M=3

structure is a compound retarder with compound optic axis switchable by the NLC

only. This design methodology can be extended to include modulation between

higher order structures. When a NLC is used in combination with a passive half-wave retarder (N = 2) it is possible to modulate between M= 3 and M = 5 structures. The

passive retarder can be placed either between the PBS and the NLC, or between the

NLC and the LCD panel.

First, consider the M = 3 structure (NLC driven high). The symmetric structure

forms a compound retarder, with compound retardation determined by the

retardation of the passive retarder. Regardless of the passive retardation selected,

orientations can be selected for an OFF-state corresponding to an eigenstate of the

structure. Given this flexibility, one preferred on-state has maximum transmission

throughout the visible spectrum, as previously described in this application This

requires that the compound retarder is an achromatic half-wave plate, which requires

that the passive retarder is also a half-wave plate. The OFF-state is obtained as an

eigenstate of the compound retarder, which is produced by reorienting the optic axis

of the NLC only.

Using this M=3 optimization, the passive retarder is oriented at 15° and the

NLC rotates between orientations of 75° and 120°. What remains is to select the

NLC retardance and orientation.

The higher order structure can also be considered a half-wave compound

retarder, as required to optimize on-state transmission. This forces the NLC to

provide a half-wave of retardation. The NLC must be used to determine the

orientation of the M = 5 compound retarder optic axis. With the LCD panel oriented

at 75°, the NLC must generate an OFF-state, which is done by orienting an

eigenpolarization of the compound retarder along the polarization of the input light. With the NLC placed between the PBS and the passive retarder, the highest

density OFF-state occurs with the NLC optic axis oriented at -67.5%. This M = 5

OFF-state has significantly better wavelength stability than the previous M = 3 OFF-

state. Furthermore, the M= 3 OFF-state of the present design is also significantly more

wavelength stable than the previous M= 3 example.

With the NLC placed between the passive retarder and the LCD panel, the

process can be repeated. The highest density OFF-state is obtained with the NLC

optic axis oriented at -83°. It should be noted that the wavelength stability of the

OFF-state is better for the previous M=3 example.

The NLC switch design approach, according to the invention, for modulating

between M = 3 and M = 5 is discussed below. Again, the performance of the M = 3

structure is considered first for the case where the NLC switch is modeled as an in-

plane switch with a 45° rotation angle. We are free to select Δ, the angle between the

passive retarder and the optic axis of the FLC in the LCD panel that generates the

OFF-state. The optimum optic axis stability occurs when Δ = 90°, where the structure

degenerates to a single zero-order half-wave plate. This forces the outside retarder(s)

to be oriented along the input polarization, the on-state being generated by the FLC

retarder in the LCD panel alone. This is not the most achromatic structure for

retardance, which occurs for Δ = 60°. However, the optic axis stability, and therefore

the contrast ratio, degrades for any Δ either greater or less than 90°. Therefore, one

must balance the contrast ratio against the on-state chrominance. For the inverter where we modulate between M = 3 and M = 5 on-states, we also balance on-state spectra

for the purpose of minimizing luminance modulation between true and inverse frames.

For aparticular passive half-wave orientation, there is an FLC orientation of the

FLC retarder in the LCD panel that produces an OFF-state (an eignepolarization of

the M = 3 structure) . When the FLC retarder in the LCD panel is switched by 45 ° , the

on-state is generated. This on-state is somewhat less chromatic than a zero-order half-

wave, but greater weight is assigned to maximizing contrast and balancing transmission

with the M = 5 on-state. Figure 17 shows that when the passive retarder is oriented at

7.5°, the FLC switch rotates between 60° (ON), and 105° (OFF). When the NLC

switch is inserted between the PBS and the passive retarder at -67.5°, the output is

effectively inverted. Note that this angle is consistently used, regardless of the details

of the M = 3 design (it was also used in the design that modulated between M= 1 and

M = 3 structures). This angle is used because the M=3 structure is in general a

compound retarder with an optic axis either along the input polarization, or at 45° to

the input polarization. As such, the requirement for inverting the output is that the

outside retarder apply an additional 45° change in orientation. In addition, the specific

angle is selected such that the chrominance of the NLC compensates for the

chrominance of the compound retarder. This is particularly important for achieving

stability of the optic axis in the M = 5 OFF-state.

The performance is given in Figure 18 for half-wave retarders centered at 500

nm, where the dispersion of polycarbonate is used for all elements. The effects of

dispersion, as well as non-ideal tilt angles, require small adjustments to the angles. However, the design methodology still applies. Figure 18 shows that the M= 5

structure produces an OFF-state transmission of < -27db, while the M= 3 OFF-state

has < -46 db transmission (theoretical). In another optimization, these OFF-state

leakages could be balanced. This particular example has the desirable characteristic

that on-state and OFF-state transmission spectra are nearly identical. The adjustment

of the M = 3 structure sacrifices some of the potential achromatic behavior in order to

improve the M = 5 spectrum.

Mathematically, the methodology can be summarized as follows:

1) α₂: Select to control chrominance (typically 5°-15°)

2) α' =90° +2α₂

3) α = α'-45° (or twice the tilt angle of the FLC retarder in the LCD panel if less than

45°)

4) α_! = 67.5° (or the tilt angle of the FLC retarder -90° if less than 22.5°)

If the tilt angle of the FLC retarder in the LCD panel is less than 22.5°, for

instance 18.6°, we have α = α'-37.2°. Forthis example, if we choose α₂ = 6.5°to balance

the ON-state spectra, the resulting design is:

α₂: 6.5°

α': 103°

α: 65.8°

Figures 19(a) and 19(b) show specific configurations, of a reflective achromatic

display that utilizes an achromatic inverter implemented with a compound retarder switch according to the invention. The reflective display 500 of Fig. 19(a) comprises

a linear polarizer 510; an actively controlled liquid crystal (FLC) retarder 520 (switch),

preferably a half-wave plate; transparent substrates containing electrodes 530 and 540

for applying a voltage across the FLC retarder 520; an FLC retarder 560, preferably a

quarter-wave plate; and a transparent substrate containing electrode 570 and a

transparent substrate containing pixellated mirror electrodes 580 for applying voltages

across the FLC retarder 560 in accordance with image data. The transparent substrate

containing electrode 570, the transparent substrate containing pixellated mirror

electrodes 580 and FLC retarder 560 collectively make up an LCD panel 600.

In the embodiment of Fig. 19(a), the linear polarizer 510 is oriented at 0°.

Since, in reflection-mode, polarizer 510 is both the input and output polarizer, this

embodiment is a parallel polarizer embodiment. The display 500 is illuminated by

ambient light 100 and the viewer is represented by an eye 300. The LCD panel 600

modulates the input light 100 in accordance with image data.

In the reflective display 505 of Fig. 19(b), the linear polarizer 510 is replaced

with a polarizing beamsplitter 511, which is used as both an input polarizer and an

output polarizer for the display 505. The polarizing beamsplitter 511 is illuminated

by white light 101, reflects light having a first polarization and transmits light having

a second polarization that is orthogonal to the first polarization. Thus, the

embodiment of Fig. 19(b) is a crossed polarizer embodiment. In the embodiments of

Figs. 19(a) and 19(b), the achromatic display is formed by the LCD panel 600 in combination with the actively controlled FLC retarder 520 (switch), which functions

as an achromatic inverter.

The FLC retarder 520 has an orientation that is electronically switchable

between at least two orientations, + a_x and -α_1} by applying a voltage across the FLC

retarder 520 with electrodes 530 and 540. The FLC retarder 560 has an orientation

that is electronically switchable between at least two orientations + ₂ and - ₂. The

orientation of sections or "pixels" of the FLC retarder 560 can be independently

switched by applying voltages to a corresponding pixel in the pixellated mirror

electrode 580. Thus, the LCD display 600 polarization modulates the input light 100

and 101 in accordance with image data that drives the electrodes 570 and 580.

Because the embodiments of Figs. 19(a) and 19(b) are reflective, the light 100 and

101 makes two passes through the FLC retarder 520 and the FLC retarder 560. The

retardances provided by the FLC retarder 520 and the FLC retarder 560 at the design

wavelength are preferably chosen so that the retardance provided by the FLC retarder

560 after two passes is approximately half the retardance provided by the FLC retarder

520 after two passes. In the embodiments of Figs. 19(a) and 19(b), the FLC retarder

520 preferably provides a half-wave retardance at the design wavelength for a single

pass (full-wave for two passes), and the FLC retarder 560 preferably provides a quarter-

wave retardance at the design wavelength for a single pass (half-wave for two passes).

In smectic liquid crystals, the angle between the liquid crystal layer normal and

the molecular director is generally referred to as the tilt angle θ of the liquid crystal.

FLCs, which are a class of smectic liquid crystals, are typically bistable in that the molecular director (the liquid crystal orientation) can be switched between + θ and -θ

either side of the brushing direction.

In the embodiment of Fig. 19(b), the FLC retarder 520 and the FLC retarder

560 are preferably positioned so that the rubbing direction of the liquid crystals that

make up the FLC retarder 520 is orthogonal to the rubbing direction of the liquid

crystals that make up the FLC retarder 560. Further, the FLC retarder 520 is

preferably positioned so that its rubbing direction is parallel or perpendicular to the

polarization direction of the input light 101, which is the x-axis direction in the

embodiment of Fig. 19(b).

In order to optimize the contrast ratio of the display, the tilt angle of the FLC

retarder 560 (θ^ is preferably approximately twice the tilt angle of the FLC retarder

520 (θ_t) in the embodiment if Fig. 19(b). In addition, the achromaticity of the FLC

display is preferably optimized, while maintaining a symmetric switching

arrangement. In view of these preferences, the FLC retarder 560 tilt angle (θ₂) is

preferably chosen to be approximately 22.5°, and the FLC retarder 520 tilt angle (Θ

is preferably chosen to be approximately 11.25° in the embodiment of Figure 19(b).

The operation of the achromatic inverter (the FLC retarder 520) in conjunction

with the FLC retarder 560 will now be explained in connection with the embodiment

of Fig. 19(b). As explained above, orientation angles are given with respect to an

arbitrary "x" axis. Because the rubbing direction of the FLC retarder 520 is parallel

to the x-axis in the embodiment of Fig. 19(b), + _l is equal to +0_! (approximately

11.25°) and -c-_j is equal to -θ₁ (approximately- 11.25°). However, because the rubbing direction of the FLC retarder 560 is perpendicular to the x-axis, + α₂ is equal to

approximately 90°- θ₂ (approximately 67.5°) and - ₂ is equal to 90° + θ₂

(approximately 112.5°, which is equivalent to -67.5°).

Fig. 20 is a table that shows the output of one pixel of the display 505 of Fig.

19(b) for different orientations of the FLC retarder 520 and the FLC retarder 560. As

shown in Fig. 20, when the sign of the orientation angle of the FLC retarder 560 is

changed in order to drive the FLC retarder 560 with the inverse frame, the output of

the display can remain the same by simultaneously changing the sign of the orientation

angle of the FLC retarder 520.

In the embodiment of FIG. 19(b), the orientations of the FLC retarder 520 and

the FLC retarder 560 are set to approximately + 11.25° and approximately +67.5°,

respectively, to obtain an achromatic white state. The pixel of the FLC retarder 560

is driven with the inverse image frame by adjusting the pixel driving voltage. This

reverses the polarity of the orientation angle of the FLC retarder 560 (e.g., switches the

orientation to approximately -67.5°). When the pixel of the FLC retarder 560 is

driven with the inverse frame, the voltage driving the FLC retarder 520 is adjusted to

switch the orientation of the FLC retarder 520 to approximately -11.25°, so that the

output of the LC display 505 remains an achromatic white state. This allows the

inverse frame to be viewed.

Similarly, the orientations of the FLC retarder 520 and the FLC retarder 560

are set to approximately + 11.25° and approximately -67.5°, respectively, to obtain a

high contrast black state. When the polarity of a pixel drving the FLC retarder 560 is reversed (by setting the orientation to approximately +67.5°) to drive that portion

of the FLC retarder 560 with the inverse frame, the orientation of the FLC retarder

520 is switched to approximately -11.25° so that the output of the display 505 remains

a high contrast black state.

As discussed above, the tilt angles of the FLC retarder 520 and the FLC retarder

560 are preferably chosen to optimize the achromaticity of the display 505, while

maintaining a symmetric switching arrangement. Fig.21, which is a plot of the optical

transmission of the display 505 of Fig. 19(b) in the ON-state as a function of

wavelength for different tilt angle combinations, illustrates why a tilt angle of

approximately 22.5° is preferred for the FLC retarder 560 and a tilt angle of

approximately 11.25° is preferred for the FLC retarder 520. As is shown, the best

achromaticity is obtained when θ_j = 22.5° and θ₂ = 11.25°.

A transmission-mode achromatic display 507 is shown in Fig. 22. The

transmissive display 507 is similar to the reflective displays, except that an FLC

retarder 620, that preferably provides a half-wave of retardance at the design

wavelength, is used because the input light only undergoes a single pass through the

FLC retarder 620. In addition, a transparent substrate containing a transmissive

pixellated electrode 630 is used with the FLC retarder 620, instead of a reflective

electrode. The transparent substrate containing electrode 570, transparent substrate

containing transmissive pixellated electrode 630, and FLC retarder 620 collectively

make up a transmissive LCD panel 602. Because the input light passes through the FLC retarder 620, a second FLC

retarder 640 that preferably provides a half-wave of retardance at the design

wavelength is positioned after the FLC retarder 620. The transparent substrates

containing electrodes 650 and 660 are used to apply a voltage across the second FLC

retarder 640. An output polarizer 670 is positioned to analyze the output light. In the

embodiment of Fig. 22, the input and output polarizers 510 and 670 are crossed. The

display 507 is illuminated by a light source 103, which can be collimated by lens 104.

Alternative materials such as diffusers or light control films can also be inserted

between the light source 103 and the display 507. The display 507 is viewed in

transmission mode.

In the transmissive display 507 of Fig.22, the first and second FLC retarders 520

and 640 operate together as the achromatic inverter for the display 507. Thus, the

orientations of FLC retarders 520 and 640 are simultaneously switched to allow

viewing of the inverse frame.

In the embodiments of Figs. 19(a), 19(b) and 22, the FLC retarder and the FLC

retarder are implemented with FLCs. However, they can also be implemented with

any other material that has an electronically rotatable optic axis, including planar-

aligned SmC* or SmA* liquid crystals, as well as distorted helix ferroelectric (DHF),

antiferroelectric, and achiral ferroelectric liquid crystals. In addition, the FLC retarder

can also be implemented with two retarders that have fixed orientations and

retardances that are electronically switchable between 0 and half-wave. The achromatic inverter of the present invention can also be implemented with

a nematic liquid crystal variable retarder, such as an electrically controlled

birefringence (ECB) cell, pi-cell, hybrid aligned nematic cell, vertically aligned nematic

cell, or any other liquid crystal device that allows switching between a non-zero

retardance, and zero retardance. Such a device is low in cost and easily

manufacturable. Examples of such devices are shown in Figures 23(a)-(b).

The reflective display 712 of Figures 23(a) comprises a linear polarizer 710; an

in-line compensator, or shim 716; a switchable nematic liquid crystal (NLC) device 720

(single pixel device); transparent substrates containing electrodes 730, 740; a FLC

retarder 760, preferably a quarter-wave plate; and a transparent substrate containing

electrode 770 and a transparent substrate containing pixellated mirror electrodes 780

for applying voltages across the FLC retarder 760 in accordance with image data. The

transparent substrate containing electrode 770, the transparent substrate containing

pixellated mirror electrode 780 and the FLC retarder 760 collectively make up a

reflective LCD panel 795. The compensator 716, the NLC 720 and the transparent

substrates containing electrodes 730 and 740 collectively make up a NLC switch 785.

The display is illuminated by ambient light 100 and the viewer is represented

by an eye 300. In the embodiment of Figure 23(b), the linear polarizer 710 is replaced

with a polarizing beamsplitter 711, which is used both as an input polarizer and an

output polarizer for the display 713. The polarizing beamsplitter 711 is illuminated

by white light 101, reflects light having a first polarization and transmits light having a second polarization that is orthogonal to the first polarization. Thus, the

embodiment of Figure 23(b) is a crossed polarizer embodiment.

The NLC 720 is preferably a half-wave plate in the visible part of the spectrum,

and is preferably oriented at approximately -67.5° to the incident polarized light. The

optical axis of the FLC retarder 760 is preferably switched between two states, one that

is parallel to the incident polarization, and one that is approximately +45° to the

incident polarized light (or twice the tilt angle when the tilt angle is approximately

22.5 degrees, as is common for SmC* ferroelectric materials).

The structure operates as follows. During the normal view frame, the NLC

device 785 is "energized" (maximum voltage is applied to the NLC 720 resulting in

zero or near zero retardance, and it is, ideally, as if the retarder has vanished).

Incident polarized light sees one of two states at the FLC retarder 760, optic axis

oriented parallel or at approximately 45° to the direction of incident polarization. The

parallel orientation results in no net rotation of polarization. When viewed in a

crossed polarization configuration (such as through beamsplitter 711 in the

embodiment of Figure 23(b)) pixels in this state appear black. Pixels with optic axis

oriented at approximately 45° to the incident polarization undergo approximately 90°

rotation of polarized light, which is transmitted by the crossed polarizer (beamsplitter

711) and these pixels appear white. As discussed below, a single passive retarder film

can be placed between the NLC device and the LCD panel 795 to make the LCD panel

795 appear like a half-wave plate in reflection for all wavelengths in the visible

spectrum (i.e. an achromatic compound retarder). Now, when opposite voltages are applied to the LCD panel 795 during the

inverse frame (for DC balancing the LCD panel 795), the NLC device 785 is not

energized such that it provides a half-wave of retardance (ideally achromatic but in

practice this is difficult to do, so preferably half-wave at approximately 500 nm).

Incident polarized light sees the half-wave NLC 720, and its polarization is rotated by

approximately a net 135° or +45°. This new polarization state sees the inverted ON

pixel optic axes in the LCD panel 795 oriented at approximately 0° to the original

polarization direction, and hence is rotated by approximately a net 90° to +45°. The

reflected polarized light now makes a net angle of approximately 67.5° with the NLC

720, and rotates by approximately twice 67.5° or to -90° with respect to the original

polarization state of the incident light, and is transmitted by the crossed polarizer

(beamsplitter 711) and again appears as an ON pixel with the correct optical polarity.

Inverted OFF pixels have optic axis orientations during the DC balanced frame

at approximately +45° relative to the original state of polarization of the incident

light. The NLC 720 is oriented at approximately -67.5° to the OFF pixel optical axis

orientation in the LCD panel 795. After traversing the NLC, the polarization at the

design wavelength is then oriented at approximately 45° parallel to the optic axis of

the FLC in this inverted OFF-state. The polarization is therefore left unaltered to be

rotated back to approximately 0° by the NLC on its return path. Thus, the pixel

appears dark. The specific orientation of the NLC/FLC retarders ensures a good

achromatic (i.e., black) OFF-states as it forms a compound retarder as per the basic

invention. In order to achieve a good OFF state in the DC balanced frame, the NLC 720

must have approximately the same retardance as the FLC retarder 760, such that there

is a good dispersion match between the LC mixtures. This means that either the NLC

720 must also be an achromatic retarder in the ON-state, or one may not want to

make the FLC retarder 760 achromatic in order to achieve a high contrast ratio and

a bright display using this optical inverter method.

One drawback of using a nematic retarder instead of a FLC retarder for the

switch is that the NLC retarder 720 has an asymmetrical response time to applied

voltage. Switching to the energized state is fast, but relaxing back to the non-energized

state is slow (approximately less than one millisecond). However, if the LCD panel

795 is loaded with the view frames (for an 8 bit display, this mean loading eight

frames), and then loaded with the inverse frames, then speed is not a problem because

a dual ECB or pi-cell configuration can be used, as discussed below.

The reflective display 714 of Figures 23(c) comprises a polarizing beamsplitter

711; a first switchable nematic liquid crystal (NLC) device 720 (single pixel device),

preferably a half-wave plate; transparent substrates containing electrodes 730, 740; a

second switchable nematic liquid crystal (NLC) device 721 (single pixel device),

preferably a half-wave plate; transparent substrates containing electrodes 721a, 721b;

a FLC retarder 760, preferably a quarter-wave plate; and a transparent substrate

containing electrode 770 and a transparent substrate containing pixellated mirror

electrodes 780 for applying voltages across the FLC retarder 760 in accordance with

image data. The transparent substrate containing electrode 770, the transparent substrate containing pixellated mirror electrode 780 and the FLC retarder 760

collectively make up a reflective LCD panel 795. The NLC 720, the transparent

substrates containing electrodes 730 and 740; the NLC 721; and the transparent

substrates containing electrodes 721a and 721b collectively make up aNLC switch 785.

The NLC 721 is aligned and switched as for the previous NLC embodiments

and is situated preferably nearest the FLC panel. The NLC 720 is aligned at

approximately 90° to the NLC 721 and acts as a dynamic compensator. During the

view frame, both nematic cells are energized, and effectively vanish. At an appropriate

time during the loading and displaying of the view frames (i.e., during the approx. 1

millisecond from finishing loading the frames to displaying the frames), the energizing

voltages are removed from the two nematic cells, and they relax back to the non-

energized state together. As they relax back to the non-energized state together, their

optic axes remain crossed such that they still together exhibit a net zero retardance

(i.e., they are invisible to the normally incident light). When the inverse frames are

viewed, only the NLC 721 is energized, such that the incident polarization sees only

one half-wave plate, instead of two, and the structure operates in the same manner as

described above.

Figure 24 shows another display embodiment employing an inverter, according

to the invention. The reflective display 815 of Figure 24 comprises a linear polarizer

810; an in-line compensator 816; a switchable nematic liquid crystal (NLC) device 818,

preferably a half-wave plate; a passive retarder 821, preferably a half-wave plate; and

an LCD panel 825. The LCD panel 825 comprises a FLC retarder 860, and a transparent substrate containing electrode 870 and a transparent substrate containing

pixellated electrodes 880 for applying voltages across the FLC retarder 860 in

accordance with image data. The NLC switch 818 comprises a nematic liquid crystal

retarder (NLC) 820 and transparent substrates containing electrodes 830 and 840 for

applying a voltage across the NLC 820 along with the in-line compensator 816 and

passive retarder 821. The display 815 is illuminated by ambient light 100 and the

viewer is represented by an eye 300. The display 815 exhibits good contrast, better

achromatic performance and twice throughput than the bare LCD panel 825 and has

the advantage of having near optically equivalent high reflectivity states, thus avoiding

flicker.

The NLC 820 is, for example, an out of plane untwisted nematic liquid crystal,

such as, for example, a pi-cell or ECB. However, other configurations may also be

used. In one switched state, the NLC 820 is relaxed such that light propagating

through the NLC 820 experiences a retardance, and in another switched state the LC

molecules in the NLC 820 are essentially normal to the light propagation direction and

impart little or no retardance to the polarization of the light.

The approach is to have two high, and two low reflectivity states corresponding

to the four possible states of the combined compound retarder. For accurate optical

inversion, the two high reflectivity states associated with the two electrically inverted

FLC retarder 860 states are preferably nearly optically equivalent and as achromatic

as possible, and the two low reflectivity states preferably exhibit as low a reflectivity as possible over the entire visible spectrum to give good contrast. The design of a

practical inversion scheme preferably ensure both these properties.

The following methodology, used to design a compound retarder inversion

scheme, according to the invention, preferably results in two good low reflectivity

states; chooses the two optic axes of the two FLC retarder 860 states to allow the most

achromatic high reflectivity performance; and alters the passive retarder 821 alignment

to equate (as best as possible) the spectra of the two high reflectivity states. The

following mathematical approach is consistent with the previously discussed M = 3 and

M = 5 analysis. With respect to the achromatic inverters according to the invention,

it is desirable to trade off achromatic ON-states with good OFF-states. Mapping

polarization onto the central retarder gives good OFF-states, which is mathematically

equivalent to orienting the compound optic axis along the input polarization direction.

As previously discussed, low reflectivity with a compound retarder can be

obtained between crossed polarizers. This is achieved when the polarization at the

design wavelength (at which all retarders of the compound retarder are substantially

half-wave) is mapped onto, or at approximately 90° to, the optic axis of the central

retarder in the display 815, the central retarder corresponds to the FLC retarder 860.

Assuming in one of its states the FLC retarder 860 has an orientation Θ_A to the input

polarization direction, and we wish to have a low reflectivity state with the NLC 820

driven high (i.e. effectively vanishing), then the passive retarder 821 must be oriented

at either

θ_P = θ_A/2±90 (22) or

*,- = θ_A/2 + 45 (23)

or

θ_p = θ_A/2 (24)

degrees from the direction of input polarization, as shown in Figure 25.

These expressions can be understood from the fact that the passive retarder 821

reflects the orientation of the input polarization about its optic axis (at the design

wavelength).

The second low reflectivity state is when the FLC retarder 860 is oriented in its

other orientation Θ_B, where:

and θ_s is the switching angle of the FLC retarder 860. In this state, the NLC 820 is in

its relaxed, non-driven mode and acts like a retarder. In the same way as above, the

orientation Θ_N of the NLC 820 is chosen such that the input polarization is mapped

on the new orientation of the FLC retarder 860. In general, the effect of having two

retarders in sequence is to rotate the design wavelength by the difference in angle

between the optic axes of the two elements, as shown in Figure 26.

Therefore, by simple geometry θ_p-θ_N= θ_B/2 or θ_B/2 + 90. Rearranging this

expression and substituting for Θ_B, we get either:

Θ_B - θ_{A +} θ_s θ — ^p

N ± ^ ± 90 (25) or

or

Substituting (22)-(24) into (25)-(27) yields the following options for the NLC 820

orientation angle:

(θ λ

Θ_N = ± 90 (28) 2 ⁾

or

Θ θ N ± 45 (29)

or

θ _ θ s

N (30)

The two high reflectivity states are the remaining two options for the FLC

retarder 860 and NLC 820 states, namely i) when the FLC retarder 860 is at Θ_A and the NLC 820 is oriented at Θ_N, and ii) when the FLC retarder 860 is at Θ_B and the NLC

820 is driven high and effectively vanishes. Computer modeling indicates that the

most achromatic high (and low) reflectivities in the case of a switchable compound

retarder are obtained when successive retarders are oriented with angles as close to 90°

as possible from each other, and when the polarization impinging on the FLC retarder

860 in the low reflectivity configurations is at 90 ° to its optic axis. In the case of small

Θ_P < 10°, this yields the following expressions for the most achromatic compound

retarder inverter system:

0, = y - 45 (31)

Θ_B = Θ_A - θ_s (32)

0 N_, = -*- ± 90 (33)

2

For any given FLC retarder, θ_s is fixed which implies Θ_N is also fixed. This

means there is only one degree of freedom in the above set of defining equations that

can be altered to equate the high reflectivity spectra. Fortuitously, by altering the by

small angles (3-7°) from the direction of the input polarization the spectra can indeed

be made near equivalent. This is a key feature of this embodiment. The polarization

manipulation of all four states can be shown in diagrammatic form as shown in Figures

27(a)-(d). The design procedure above has been carried out for two specific cases here.

For θ_s = 38 ° the following solution is close to optimum assuming typical LC dispersion

and a design wavelength of 550nm.

Θ_P=4°

Θ_A=98°

Θ_B=60°

Θ_N= 109°

The four output states yield the spectra shown in Figure 28, assuming typical

dispersion and a design wavelength of 540mn.

For θ_s=45° switching

θ_P- 5°

Θ_A= 100°

Θ_B= 55°

0^= 112.5°

The four outputs yield the spectra shown in Figure 29, assuming typical LC dispersion

and a design wavelength of 550 nm. Comparing these outputs with the inverter

solution, using no passive retarders, as follows:

θ_s=45°

Θ_A=0°

0^= 112.5° clearly shows the improvement in the matching of high reflectivity states. The four

outputs yield the spectra shown in Figure 30.

As discussed above, one example suggested for the NLC 820 is the pi-cell.

While pi-cells (i.e. bent mode) have poor field of view (FOV) characteristics due to the

large amount of retardance that is present in the device, it is nevertheless attractive due

to its fast switching speed and its use of a thicker (> 4μm), lower cost cell. Proposed

here is a method that can be used to increase the FOV of the pi-cell when used in a

reflective type device, for example, in an inverter.

Figure 31 shows another example of a display device 915 according to the

invention. The display device 915 comprises a polarizing beamsplitter 911; an in-line

compensator 916; a first passive retarder 920, preferably a quarter-wave plate; a first

pi-cell retarder 921, preferably a half-wave plate; transparent substrates containing

electrodes 921a, 921b for applying voltages across the first pi-cell retarder 921; a second

passive retarder 922, preferably a quarter-wave plate; and LCD panel 925. LCD panel

995 comprises a FLC retarder 960, preferably a quarter-wave plate; and transparent

substrates containing electrodes 970, 980 for applying voltages across the FLC retarder

960 in accordance with image data.

The orientations of the quarter-wave FLC retarders 920, 960 are parallel and

perpendicular to the pi-cells 921, 922, respectively. That is, the quarter-wave retarder

nearest between the LCD panel 995 and the pi-cell has its optic axis at approximately

90° to the optic axis of the pi-cell, and the other quarter-wave being approximately 90°

to this or parallel to the pi-cell optic axis. This approach, according to the invention, employs the fact that rays that are

off axis see a twisted liquid crystal director profile. The effect of this twist is shown

in Figure 32. As can be seen in this specific case of a half-wave pi-cell the effect of

going off-axis is to produce a polarization that is elliptical and is oriented at an angle

relative to the optic axis of the pi-cell. By placing a quarter-wave retarder (half-wave

in reflective type devices) between the pi-cell and the LCD panel, this polarization

major axis is reflected about the optic axis of the quarter- wave retarder and the

ellipicity is reversed (i.e. left hand rotation to right hand or visa versa). The effect then

of passing through the pi-cell for the second time is to undo this effect and the

resultant polarization becomes linear. The additional quarter-wave layer is added to

the other side of the pi-cell to negate the additional in-plane retardance from the other

half-wave layer.

This compensation scheme works particularly well for the inverter device

according to the invention, and is compatible with the inverter in which an extra

retardation film is added between the active inverter cell and the FLC retarder.

Figure 33 shows a display embodiment comprising a polarizer 1010; a in-line

compensator 1016, preferably having an in-line compensation _T of approximately 30

nm; a first pi-cell retarder 1020, preferably a quarter-wave plate; transparent substrates

containing electrodes 1020a, 1020b for applying voltages across the first pi-cell retarder

1020; substrate 1050a; a second pi-cell retarder 1021, preferably a quarter-wave plate;

and transparent substrates containing electrodes 1021a, 1021b for applying voltages

across the second pi-cell retarder 1021. The LCD panel 1095 comprises a FLC retarder 1060, and transparent substrates containing electrodes 1070, 1080 for applying voltages

across the FLC retarder 1060 in accordance with image data. The orientations of the

various plates are shown schematically in Figure 33 a. The orientation of the integrated

display device is along the rubbing direction of the two parallel half-wave pi-cells.

Figure 34 shows another display embodiment comprising a polarizing

beamsplitter 1111; a in-line compensator 1116, preferably having an in-line

compensation T of approximately 30 nm; a first pi-cell retarder 1120, preferably a

quarter-wave plate; transparent substrate containing electrodes 1120a, 1120b for

applying voltages across the first pi-cell retarder 1120; a first passive retarder 1121,

preferably a half -wave plate; a second pi-cell retarder 1122, preferably a quarter-wave

plate; transparent substrate containing electrodes 1122a, 1122b for applying voltages

across the second pi-cell retarder 1122; a second passive retarder 1123, preferably a half-

wave plate; and LCD panel 1195. The LCD panel 1195 comprises a FLC retarder

1160, and a transparent substrate containing electrode 1170 and a transparent substrate

containing pixilated mirror electrode 1180 for applying voltages across the FLC

retarder 1160 in accordance with image data.

The orientations of the various plates are shown schematically in Figure 34a.

The orientation of the integrated display device is parallel to the orientation of the

central achromatic half -wave plate. The two pi-cell retarders 1120, 1122 are then

oriented at approximately +45° and -45° to this direction, respectively. Since the

integrated display device acts as a net half-wave plate with a defined optic axis, it can

also be used with further passive half-wave retarders to equalize ON/STATES. It is, however, considered fast enough not to use the dynamic relaxation compensation of

the two pi-cell embodiment previously discussed.

The display embodiments shown in Figures 35 and 35a overcome the effect on

contrast due to unwanted reflection in the display device. Figure 35 shows an example

of a display device comprising a polarizer 1210; a first pi-cell retarder 1220, preferably

a quarter-wave plate; transparent substrate containing electrodes 1220a, 1220b for

applying voltages across the first pi-cell retarder 1220; a passive retarder 1221,

preferably a half-wave plate having an in-line compensation T of approximately 50 nm;

a second pi-cell retarder 1222, preferably a quarter-wave plate; transparent substrates

containing electrodes 1222a, 1222b for applying voltages across the second pi-cell

retarder 1222; and LCD panel 1295. The LCD panel 1295 comprises a FLC retarder

1260, preferably a quarter-wave plate; and a transparent substrate containing electrode

1270 and a transparent substrate containing pixilated mirror electrodes 1280 for

applying voltages across the FLC retarder 1260 in accordance with image data. The

orientations of the various plates are shown schematically in Figure 35a.

Real devices have interfaces between layers that cause unwanted reflection that

compromises contrast. In particular, the field of view compensation schemes so far

discussed have significant reflection deriving primarily from current methods of LC

cell fabrication. To overcome this problem and ensure adequate FOV, there are

approaches that utilize the fact that thinner cells have inherently better FOV. So in

using cells that are to thin to switch a full half-wave at the design wavelength, a push-

pull dual cell embodiment can be used which has similar dynamic compensation to the of the two pi-cell embodiment previously discussed, but requires an additional small

(preferably approximately 50nm) retarder aligned with the switching retarder. In its

relaxed state, the approximately 50 nm retardance adds to the switching element's

retardance and, in its driven state, the dynamic compensator cell is not driven quite so

high to negate the approximately 50 nm retardance plus any residual retardance from

the switching element. That is, the cell furthest from the LCD panel is driven high

(e.g., > 24V) for one state of the inverter and not so high (e.g., ~ 12V) in the other.

These correspond to the high and low driven states of the switching cell, respectively.

Since the dynamic compensator cell is effectively driven with high voltage throughout,

masking of the relaxation, and hence effective high switching speed, can still be

achieved.

Figures 36-43 show configurations for the various reflective display

embodiments shown in Figures 33-35(a). The basic structure of the display is

illustrated in Figure 36. The FLC retarder has two states, depending on the polarity

of applied voltage. The NLC switch has two states depending on high and low voltage

applied. Therefore, there are a total of four states, two of high brightness and two of

low brightness, as shown in Figures 38(a)-38(d). Figures 37(a)-37(b) show the head-on

spectra of four states.

Additional reflective display embodiments are illustrated in Figures 39 and 41,

with the respective combined four states illustrated in Figures 40(a)-40(d) and Figures

42(a)-42(d), respectively. An additional display or embodiment is illustrated in Figure

43. The configurations of Figures 39, 41 and 43 provide decent field of view for an f/2.5 application. The response time can also be below 100 μs at 50°C, since

birefringence of LC cell is about 550 nm (green cell).

Figures 44-47 show various display devices incorporated an inverter according

to the invention. In particular, Figure 44 shows a full color sequential display

implemented with a transmissive liquid crystal display, and utilizing an achromatic

inverter according to the invention. The sequential display comprises a light source

2500, a two-polarizer digital color sequencer 2455, a first inverter 2555, a transmissive

pixelized liquid crystal display 2560, a second inverter 2565, a polarizer 2570, a

projection lens 2580 and a display screen 2590.

The light source 2500 is suitably a metal halide lamp and preferably emits

optical power in all three primary color bands. Alternatively, the light source 2500

can be implemented with an active lamp system or with a lamp/color wheel

combination.

In operation, the light source 2500 and the sequencer 2455 sequentially

illuminates the liquid crystal display 2560 with red, green and blue light. The liquid

crystal display 2560 is sequentially driven with red, green and blue image information

in synchronism with the red, green and blue illumination from the light source 2500

and the color sequencer 2455. The liquid display 2560, in combination with the

polarizer 2570, modulates the intensity of the light that is sent to the screen 2590, in

accordance with image information. The inverters 2555, 2565 in combination with the

liquid crystal display 2560 provide four states of brightness, two high and two low. The inverters 2555, 2565 effectively double the brightness of the display, by allowing

the negative image frame to be viewed, as previously discussed.

The full color sequential display of Figure 44 can be implemented as a front

projection display in which the screen 2590 is viewed from the same side as the

projection optics, or as a rear projection display, in which the screen 2590 is viewed

from the side opposite the projection optics.

Figure 45 shows a full color sequential display using a reflective liquid crystal

display, and utilizing an achromatic inverter according to the invention. The display

of Figure 45 is similar to the display shown in Figure 44, except that a reflective liquid

display 3600 is used instead of a transmissive liquid crystal display. In this

configuration, a polarizing beamsplitter 3610 is used as both the output polarizer for

the digital color sequencer 2455 and as the input/output polarizer for the reflective

liquid crystal display 2600. Thus, the polarizing beamsplitter 3610 reflects light whose

polarization is crossed with respect to the polarization axis of the input polarizer 2450.

In operation, light that passes through the color sequencer 2455 is reflected by the

polarizing beamsplitter 2610 to the reflective liquid crystal display 3600. The reflective

liquid crystal display 3600 polarization modulates the light in accordance with the

image information and reflects the polarization modulated light back towards the

polarizing beamsplitter 3610. The polarizing beamsplitter 3610 passes components of

the light reflected from the liquid crystal display 3600 that are orthogonally polarized

with respect to the light that was reflected from the polarizing beamsplitter 3610

towards the liquid display 3600. Accordingly, image information is displayed on the screen 2590. The inverter 3565 in combination with the display 3600 provide four

states of brightness, two high and two low. The inverter 3565 effectively doubles the

brightness of the display 3600 by allowing the negative image frame to be viewed, as

previously discussed.

Figure 46 shows another display using a reflective liquid display and utilizing

an achromatic inverter according to the invention. Figure 46 is similar to the display

shown in Figure 45 except the three reflective liquid displays 3601, 3602,3603 are

utilized. Beamsplitter 3610 divides white light into the primary colors, red, green and

blue, which are displayed at displays 3601, 3602, 3603. The inverter 3566 working in

combination with the displays 3601, 3602, 3603 provide four states of brightness, two

high and two low. The inverter 3566 effectively doubles the brightness of the displays

3601, 3602, 3603 by allowing the negative image frame to be viewed, as previously

discussed.

Figure 47 shows still another display using a reflective liquid display and

utilizing achromatic inverter according to the invention. Figure 47 is similar to the

display shown in Figure 45, with the exception that achromatic inverters 3567, 3568,

3569 is provided for each of the three liquid crystal displays 3601, 3602, 3603. The

beamsplitter 3610 divides white light into the primary colors, red, green and blue,

which are displayed at displays 3601, 3602, 3603. The inverters 3567, 3568, 3569 work

in combination with the respective displays 3601, 3602, 3603 to provide four states of

brightness, two high and two low. The inverters 3567, 3568, 3569 effectively double the brightness of their corresponding displays 3601, 3602, 3603 by allowing the

negative image frame to be viewed, as previously discussed.

In the displays shown in Figure 44 and 45, the digital color sequencer 2455 is

position between the light source 2500 and the liquid crystal display (2560 in Figure

44 and 3600 in Figure 45). However, the digital color sequencer 2455 can be positioned

at other locations in the display system, provided that it effectively controls the

illuminating color at the output, i.e., the screen 2590.

By placing the digital color sequencer 2455 between the light source 2500 and

the liquid crystal display 2560 or 3600, the image at the screen 2590 is not sensitive to

any wave-front distortion caused by the digital color sequencer 2505.

The foregoing embodiments are merely exemplary and are not to be construed

as limiting the present invention. The present teaching can be readily applied to other

types of apparatuses. The description of the present invention is intended to be

illustrative, and not to limit the scope of the claims. Many alternatives, modifications,

and variations will be apparent to those skilled in the art. In the claims, means-plus-

function clauses are intended to cover the structures described herein as performing

the recited function and not only structural equivalents but also equivalent structures.

For example, although quartz and mylar may not be structural equivalents in that

quartz is a crystalline material, whereas mylar is a polymeric material, in the area of

birefringent materials, quartz and mylar may be equivalent structures.

Claims

WHAT IS CLAIMED IS:

1. A display, comprising:

one or more retarders having in-plane retardance and in-plane

orientation, at least one of the retarders being an actively controlled liquid crystal

retarder; and

a ferroelectric liquid crystal display, wherein the one or more retarders

work in combination with the ferroelectric liquid crystal display to provide four states

of brightness.

2. The display according to claim 1, wherein the display is a reflective

display and the one or more retarders are disposed on a light input side of the

ferroelectric liquid crystal display.

3. The display according to claim 1, wherein the display is a transmissive

display and the one or more retarders are disposed on a light input side of the

ferroelectric liquid crystal display.

4. The display according to claim 3, further comprising one or more

retarders having in-plane retardance and in-plane orientation disposed on a light output

side of the ferroelectric liquid crystal display , at least one of the retarders being an

active retarder.

5. The display according to claim 2, further comprising a linear polarizer

disposed on a light input side of the one or more retarders.

6. The display according to claim 2, further comprising a beamsplitter

disposed on a light input side of the one or more retarders.

7. The display according to claim 3, further comprising a linear polarizer

disposed on a light input side of the one or more retarders.

8. The display according to claim 4, further comprising a linear polarizer

disposed on a light output side of the one or more retarders disposed on a light output

side of the ferroelectric liquid crystal display.

9. The display according to claim 1, wherein the at least one actively

controlled liquid crystal retarder comprises at least one smectic liquid crystal retarder.

10. The display according to claim 1, wherein the at least one actively

controlled liquid crystal retarder comprises at least one nematic liquid crystal retarder.

11 The display according to claim 10, wherein the at least one nematic liquid

crystal retarder comprises at least one pi-cell.

12. The display according to claim 10, wherein the at least one nematic liquid

crystal retarder comprises two pi-celsl, the two pi-cells having parallel orientations.

13. The display according to claim 1, wherein the one or more retarders

further comprises a passive retarder.

14. The display according to claim 2, wherein the one or more retarders

further comprises a passive retarder.

15. The display according to claim 3, wherein the one or more retarders

further comprises a passive retarder.

16. The display according to claim 4, wherein one or more retarders disposed

on a light output side of the ferroelectric liquid crystal display further comprises a

passive retarder.

17. The display according to claim 2, wherein the actively controlled liquid

crystal retarder is a half-wave retarder and the ferroelectric liquid crystal display

comprises a quarter-wave retarders.

18. The display according to claim 4, wherein each of the actively controlled

liquid crystal retarders is a half -wave retarder and the ferroelectric liquid crystal display

comprises a half-wave retarder.

19. The display according to claim 10, wherein the at least one nematic liquid

crystal retarder is a half-wave retarder and the ferroelectric liquid crystal display

comprises a quarter-wave retarder.

20. The display according to claim 10, wherein a passive retarder is disposed

between the at least one nematic liquid crystal retarder the ferroelectric liquid crystal

display.