Patent Publication Number: US-2021191139-A1

Title: Control of Reflections of a Display Device

Description:
TECHNICAL FIELD 
     This disclosure generally relates to control of reflections of light output from a display device comprising a display panel. 
     BACKGROUND 
     In many optical arrangements, reflections from surfaces of optically transmissive material, such as bare transparent windows, are a problem, particularly when viewed at night from an illuminated interior when significant reflections occur, giving a mirror appearance. While such reflections in houses are typically avoided by shades, such an option is not available in many optical arrangements, such as vehicles where reflections of bright internal displays can cause significant distraction. 
     One method to alleviate this issue is to introduce display devices with highly directional output. Such display devices would allow viewers, for example the driver and/or passengers in the case of a vehicle, to see an image displayed on the display device, while minimizing the light directed towards surfaces of optically transmissive material. However, such display devices typically require additional components and so are relatively expensive to manufacture. 
     The present disclosure is concerned with controlling such reflections from surfaces of optically transmissive material. 
     BRIEF SUMMARY 
     According to a first aspect of the present disclosure, there is provided a method of controlling reflections of light output from a display device comprising a display panel arranged to output light that has a predetermined polarization state, the method using at least one optical retarder arranged on the output side of the display panel, the method comprising: defining a first plane of incidence in respect of a first ray of light output from the display device and a first normal to a first surface of optically transmissive material at a first point at which the first ray of light is reflected and a second plane of incidence in respect of a second ray of light output from the display device and a second normal to a second surface of optically transmissive material at a second point at which the second ray of light is reflected; and selecting the at least one optical retarder, in at least one mode of the at least one optical retarder, to cause the polarization state of the first ray of light to be linearly polarized in a direction that is in the first plane of incidence, and to cause the polarization state of the second ray of light to be linearly polarized in a direction that is in the second plane of incidence. 
     This method makes use of the reflection sensitivity of linearly polarized light resulting from Fresnel reflection at the surface. In particular, the reflectivity of a surface of optically transmissive material is lower for light that is linearly polarised in a direction in the plane of incidence (p-polarised light) than for light that is linearly polarised in a direction perpendicular to the plane of incidence (s-polarised light). The reflectivity of p-polarised light dips by a significant amount below the reflectivity of s-polarised light across most angles of incidence at the surface, reaching zero at some angles. 
     Most display panels output light that has a predetermined polarization state. For example, LCD (liquid crystal display) display devices are ubiquitous in vehicles as they deliver the high brightness levels required during daytime driving. Such LCD display devices function by modulating polarized light and provide linearly polarized output. 
     Also, this method uses the observation that a desired polarization state for a particular ray of a particular wavelength can always be transformed from any input polarization state with an arbitrary retarder whose optical axis and retardance are freely selected, and so it is possible to select optical retarders to independently control the polarisation state of two different rays of light output from a display device. This is undesirable in many optical arrangements where polarisation is used to provide a desired optical effect, but is an effect of the optical axis of the material of an optical retarder being aligned in a different direction with respect to each of the rays that is utilised to positive effect in this method. 
     Reflections of light from first and second surfaces of optically transmissive material are considered. Rays of light output from the display device and reflected from the first and second surfaces to a common viewing position are then defined. This permits definition of first and second planes of incidence in respect of the first and second rays of light and first and second normals to the first and second surfaces at first and second points at which the first and second rays of light are reflected. Thereafter, the at least one optical retarder is selected so that, in at least one mode of the at least one optical retarder, the polarization state of the first ray of light is caused to be linearly polarized in a direction that is in the first plane of incidence (i.e. p-polarised), and the polarization state of the second ray of light is also caused to be linearly polarized in a direction that is in the second plane of incidence (p-polarised). As a result, each ray of light is p-polarised with respect to reflection from its respective surface. This simultaneously minimises the amount of reflection from each surface compared to a situation in which the polarisation state is not so controlled and so some of the first and/or second rays of light may in general be, or at least include a component of, s-polarised light. 
     The selection of the at least one optical retarder may involve selection of the direction of the optical axis of the at least one optical retarder and the retardance of the at least one optical retarder to control the polarisation state of the two rays of light in the desired manner. 
     By way of example, one may consider the case of the optical arrangement being a vehicle containing an LCD display device mounted on the dashboard. The light output by the display device might advantageously be linearly polarized in a vertical direction to match the transmission of anti-glare polarized glasses when worn by a driver. In that case, the plane of incidence of a first ray of light reflected from the windshield is predominantly p-polarized with respect to the reflection geometry and so minimally reflected. This however is not the case for a second ray of light reflected from side windows, absent this method. That is, the second ray of light reflected from the side window is predominantly s-polarized and so the reflectivity is relatively high. However, with this method, the at least one optical retarder may causes the polarization state of the second ray of light to be transformed to be p-polarised, while maintain the p-polarisation of the first ray of light incident on the windshield, providing an elegant solution to the problem of reflection from the side windows. 
     According to a further aspect of the present disclosure, there is provided a display device comprising: a display panel arranged to output light that has a predetermined polarization state; and at least one optical retarder arranged on the output side of the display panel, wherein, defining a first plane of incidence in respect of a first ray of light output from the display device and a first normal to a first surface of optically transmissive material at a first point at which the first ray of light is reflected and a second plane of incidence in respect of a second ray of light output from the display device and a second normal to a second surface of optically transmissive material at a second point at which the second ray of light is reflected, the at least one optical retarder is selected, in at least one mode of the at least one optical retarder, to cause the polarization state of the first ray of light to be linearly polarized in a direction that is in the first plane of incidence, and to cause the polarization state of the second ray of light to be linearly polarized in a direction that is in the second plane of incidence. 
     Such a display device controls reflections in a similar manner to the first aspect of the present disclosure, as discussed above. 
     The display device may be incorporated in an optical arrangement that also comprises the first and second surfaces. Such an optical arrangement may be, for example, a vehicle, in which case the first and second surfaces may be surfaces of windows of the vehicle. 
     Embodiments of the present disclosure may be used in a variety of optical arrangements. The embodiments may include or work with a variety of projectors, projection systems, optical components, displays, microdisplays, computer systems, processors, self-contained projector systems, visual and/or audio-visual systems and electrical and/or optical devices. Aspects of the present disclosure may be used with practically any apparatus related to optical and electrical devices, optical systems, presentation systems or any apparatus that may contain any type of optical system. Accordingly, embodiments of the present disclosure may be employed in devices used in visual and/or optical presentations, visual peripherals and so on and in a number of computing environments. 
     Before proceeding to the disclosed embodiments in detail, it should be understood that the disclosure is not limited in its application or creation to the details of the particular arrangements shown, because the disclosure is capable of other embodiments. Moreover, aspects of the disclosure may be set forth in different combinations and arrangements to define embodiments unique in their own right. Also, the terminology used herein is for the purpose of description and not of limitation. 
     These and other advantages and features of the present disclosure will become apparent to those of ordinary skill in the art upon reading this disclosure in its entirety. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments are illustrated by way of example in the accompanying FIGURES, in which like reference numbers indicate similar parts, and in which: 
         FIG. 1 ,  FIG. 2 , and  FIG. 3  are side perspective views of alternative constructions for a transmissive display device which controls reflections within an optical arrangement; 
         FIG. 4  is a front perspective view of the optical arrangement including the display device of  FIGS. 1-3  and first and second surfaces; 
         FIG. 5  is a side view of reflections of linearly polarised light from surfaces of a sheet of optically transmissive material; 
         FIG. 6  is a graph of reflectivity of linearly polarised light from surfaces of a sheet of optically transmissive material; 
         FIG. 7  and  FIG. 8  are perspective top views of the optical arrangement of  FIG. 4  illustrating the rays in more detail; 
         FIG. 9  is a perspective view of an optical retarder showing an example of how the polarisation state of a ray of light is controlled; 
         FIG. 10  is a chart illustrating a method for selection of the optical retarders for output light having a predetermined polarization state of being linearly polarized in a direction in the first plane of incidence; 
         FIG. 11  is a chart illustrating a method for selection of the optical retarders for output light having an arbitrary predetermined polarization state; 
         FIG. 12  is a top view of an optical arrangement which is a vehicle including the display device and illustrating a reflection from a first surface which is the windscreen of the vehicle; 
         FIG. 13  is a side view of the vehicle shown in  FIG. 12  illustrating the reflection from the first surface; 
         FIG. 14  is a view of the vehicle shown in  FIG. 12  in the plane of incidence of the first ray reflected from the first surface; 
         FIG. 15  is a top view of the vehicle shown in  FIG. 12  showing the reflection from a second surface which is a side window of the vehicle; 
         FIG. 16  is a side view of the vehicle shown in  FIG. 15  illustrating the reflection from the second surface; 
         FIG. 17  is a view of the vehicle shown in  FIG. 15  in the plane of incidence of the first ray reflected from the second surface; 
         FIG. 18  is a front view of a second example of the optical stack of the display device of  FIG. 1  illustrating the polarization states of the rays of light; 
         FIG. 19  is a front view of a second example of the optical stack of the display device of  FIG. 2  illustrating the polarization states of the rays of light; 
         FIG. 20  is a side perspective view of the display panel in the display devices of  FIGS. 1-3 ; 
         FIG. 21 ,  FIG. 22 , and  FIG. 23  are side perspective views of three alternative examples of an optical retarder in the display devices of  FIGS. 1-3 ; 
         FIG. 24  is a side perspective view of the second optical retarder of  FIG. 23 ; 
         FIG. 25  is a graph illustrating the variation of luminance with polar direction for the second optical retarder of  FIG. 24  further comprising an illustrative analysing output polariser; 
         FIG. 26  is a perspective view of view angle control optical retarders that may be applied in the display panel of  FIGS. 1 ; and 
         FIG. 27  is a graph illustrating the variation of luminance with polar direction for the view angle control retarder of  FIG. 26 . 
     
    
    
     DETAILED DESCRIPTION 
     Terms related to optical retarders for the purposes of the present disclosure will now be described. 
     In a layer comprising a uniaxial birefringent material there is a direction governing the optical anisotropy whereas all directions perpendicular to it (or at a given angle to it) are optically equivalent. 
     Optical axis refers to the direction of propagation of an unpolarised light ray in the uniaxial birefringent material in which no birefringence is experienced by the ray. For light propagating in a direction orthogonal to the optical axis, the optical axis is the slow axis when linearly polarized light with an electric vector direction parallel to the optical axis travels at the slowest speed. The slow axis direction is the direction with the highest refractive index at the design wavelength. Similarly the fast axis direction is the direction with the lowest refractive index at the design wavelength. 
     For positive dielectric anisotropy uniaxial birefringent materials the slow axis direction is the extraordinary axis of the birefringent material. For negative dielectric anisotropy uniaxial birefringent materials the fast axis direction is the extraordinary axis of the birefringent material. 
     The terms half a wavelength and quarter a wavelength refer to the operation of a retarder for a design wavelength λ 0  that may typically be between 450 nm and 570 nm. In the present illustrative embodiments exemplary retardance values are provided for a wavelength of 550 nm unless otherwise specified. 
     The retarder provides a phase shift between two perpendicular polarization components of the light wave incident thereon and is characterized by the amount of relative phase, Γ, that it imparts on the two polarization components; which is related to the birefringence Δn and the thickness d of the retarder by: 
       Γ=2·πΔ n·d/λ   0    eqn. 1
 
     where Δn is defined as the difference between the extraordinary and the ordinary index of refraction, i.e. 
       Δ n=n   e   −n   o    eqn. 2
 
     Herein, a “half-wave retardance” of an optical retarder refers to the relationship between d, Δn, and λ 0  being chosen so that the phase shift between polarization components Γ is an odd multiple of π, that is π, 3π, 5π, etc. These values result in the optical retarder providing a transformation of light having a linearly polarised polarisation state into another linearly polarised polarisation state, rather than an elliptical polarisation state. To achieve this effect, then in general the relative phase shift Γ may be any odd multiple of π, although in practice it is often desirable to select the relative phase shift Γ to be π, as this reduces chromatic effects. 
     Such a half-wave retardance in general has a different value for light propagating along different rays of light which may be normal to the spatial light modulator or at an angle to the normal. Although it is common to define a retarder with respect to its retardance along the normal to the retarder, herein the methods are concerned with effects along different rays and so a half-wave retardance will be defined with respect to a given ray. 
     In the present disclosure an ‘A-plate’ refers to an optical retarder utilizing a layer of birefringent material with its optical axis parallel to the plane of the layer. The plane of the retarders refers to the slow axis of the retarders extend in a plane, that is the x-y plane. 
     A ‘positive A-plate’ refers to positively birefringent A-plates, i.e. A-plates with a positive Δn. 
     In the present disclosure a ‘C-plate’ refers to an optical retarder utilizing a layer of birefringent material with its optical axis perpendicular to the plane of the layer. A ‘positive C-plate’ refers to a positively birefringent C-plate, i.e. a C-plate with a positive An. A ‘negative C-plate’ refers to a negatively birefringent C-plate, i.e. a C-plate with a negative Δn. 
     In the present disclosure an ‘O-plate’ refers to an optical retarder utilizing a layer of birefringent material with its optical axis having a component parallel to the plane of the layer and a component perpendicular to the plane of the layer. A ‘positive O-plate’ refers to positively birefringent O-plates, i.e. O-plates with a positive Δn. 
     Achromatic retarders may be provided wherein the material of the retarder is provided with a retardance Δn·d that varies with wavelength λ as: 
       Δ n·d/λ=κ   eqn. 3
 
     where κ is substantially a constant. 
     Examples of suitable materials include modified polycarbonates from Teijin Films. Achromatic retarders may be provided in the present embodiments to advantageously minimise colour changes between polar angular viewing directions which have low luminance reduction and polar angular viewing directions which have increased luminance reductions as will be described below. 
     Various other terms used in the present disclosure related to retarders and to liquid crystals will now be described. 
     A liquid crystal cell has a retardance given by Δn·d where Δn is the birefringence of the liquid crystal material in the liquid crystal cell and d is the thickness of the liquid crystal cell, independent of the alignment of the liquid crystal material in the liquid crystal cell. 
     Homogeneous alignment refers to the alignment of liquid crystals in switchable liquid crystal displays where molecules align substantially parallel to a substrate. Homogeneous alignment is sometimes referred to as planar alignment. Homogeneous alignment may typically be provided with a small pre-tilt such as 2 degrees, so that the molecules at the surfaces of the alignment layers of the liquid crystal cell are slightly inclined as will be described below. Pretilt is arranged to minimise degeneracies in switching of cells. 
     In the present disclosure, homeotropic alignment is the state in which rod-like liquid crystalline molecules align substantially perpendicularly to the substrate. In discotic liquid crystals homeotropic alignment is defined as the state in which an axis of the column structure, which is formed by disc-like liquid crystalline molecules, aligns perpendicularly to a surface. In homeotropic alignment, pretilt is the tilt angle of the molecules that are close to the alignment layer and is typically close to 90 degrees and for example may be 88 degrees, such that there is an in-plane component that is small in magnitude relative to the component normal to the alignment layer. 
     Liquid crystal molecules with positive dielectric anisotropy are switched from a homogeneous alignment (such as an A-plate retarder orientation) to a homeotropic alignment (such as a C-plate or O-plate retarder orientation) by means of an applied electric field. 
     Liquid crystal molecules with negative dielectric anisotropy are switched from a homeotropic alignment (such as a C-plate or O-plate retarder orientation) to a homogeneous alignment (such as an A-plate retarder orientation) by means of an applied electric field. 
     Rod-like molecules have a positive birefringence so that n e &gt;n o  as described in eqn. 2. Discotic molecules have negative birefringence so that n e &lt;n o . 
     Positive retarders such as A-plates, positive O-plates and positive C-plates may typically be provided by stretched films or rod-like liquid crystal molecules. Negative retarders such as negative C-plates may be provided by stretched films or discotic-like liquid crystal molecules. 
     Parallel liquid crystal cell alignment refers to the alignment direction of homogeneous alignment layers being parallel or more typically antiparallel. In the case of pre-tilted homeotropic alignment, the alignment layers may have components that are substantially parallel or antiparallel. Hybrid aligned liquid crystal cells may have one homogeneous alignment layer and one homeotropic alignment layer. Twisted liquid crystal cells may be provided by alignment layers that do not have parallel alignment, for example oriented at 90 degrees to each other. 
     Transmissive spatial light modulators may further comprise retarders between the input display polariser and the output display polariser, for example as disclosed in U.S. Pat. No. 8,237,876, which is herein incorporated by reference in its entirety. Such retarders (not shown) are in a different place to the passive retarders of the present embodiments. Such retarders compensate for contrast degradations for off-axis viewing locations, which is a different effect to the luminance reduction for off-axis viewing positions of the present embodiments. 
     The structure and operation of various display devices will now be described. In this description, common elements have common reference numerals. It is noted that the disclosure relating to any element applies to each device in which the same or corresponding element is provided. Accordingly, for brevity such disclosure is not repeated. 
       FIGS. 1-3  are side perspective views of alternative constructions of a display device  100  which controls reflections within an optical arrangement. 
     In each of  FIGS. 1-3 , the display device  100  includes a display panel  101 . The display panel  101  includes output polariser  218  arranged on the output side of the display panel  101  so that the display panel  101  outputs light that has a predetermined polarization state of being linearly polarised. The direction of linear polarization corresponds to the electric vector transmission direction  219  of the output polariser  218 . In the case of a ray of light along the normal to the plane of the output polariser  218 , the direction of linear polarization is the same as the electric vector transmission direction  219 . In the case of a ray of light at an acute angle to the normal to the plane of the output polariser  218 , the direction of linear polarization is the projection of the electric vector transmission direction  219  onto a plane normal to the ray of light. 
     Provided that the output polariser  218  is present, the display panel  101  may be of a wide range of types, as discussed further below. 
     In each of  FIGS. 1-3 , reflections of light output from the display device  100  are controlled using at least one optical retarder arranged on the output side of the display panel  101 , as follows. 
     In the examples of  FIGS. 1 and 2 , the at least one retarder comprises a first optical retarder  801  and a second optical retarder  802 . The first optical retarder  801  comprises birefringent molecules  803 , and has an optical axis parallel to the plane of the first optical retarder  801 , so may be referred to as an A-plate. The second optical retarder  802  comprises birefringent molecules  804 , and has an optical axis at an acute angle to the plane of the second optical retarder  802  in direction o, in at least a mode of operation of the second optical retarder  802 , so may be referred to as an O-plate. 
     In general, the first optical retarder  801  and the second optical retarder  802  may be in either order with respect to the transmission of light from the display panel  101 . Thus, in the example of  FIG. 1  the first optical retarder  801  is arranged before the second optical retarder  802 , whereas in the example of  FIG. 2  the order is reversed so that the second optical retarder  802  is arranged before the first optical retarder  801 . 
     Whereas the examples of examples of  FIGS. 1 and 2  include two optical retarders, more generally any number of one or more optical retarders may be provided to provide the desired control of polarisation state of rays of light. In a simple example shown in  FIG. 3  the first optical retarder  801  is omitted so that only the second optical retarder  802  is present. In other examples (not illustrated) more than two optical retarders may be provided. 
       FIG. 4  is a front perspective view of the optical arrangement including the display device  100  of  FIGS. 1-3 , as well as a first surface  611  of optically transmissive material and a second surface  612  of optically transmissive material. 
     The display device  100  controls reflections from the first and second surfaces  611  and  612 . The optical arrangement may be any type of optical arrangement including first and second surfaces  610  and  612  from which it is desired to control reflections. In one example, the optical arrangement may be a vehicle. In the case of a vehicle, the display device  100  may be any type of display device located within the vehicle, for example being an LCD, OLED or micro-LED display device or a simple instrument display device such as provided for illuminated switches. In the case of a vehicle, the first and second surfaces  610  and  612  may be surfaces of windows of the vehicle, for example the windshield and side windows. 
     The optically transmissive material may be any optically transmissive material from which Fresnel reflection occurs, non-limitative examples including glass and plastic. 
       FIG. 5  is a side view of reflections of linearly polarised light from surfaces  601  and  602  of a sheet of optically transmissive material  610 . 
     The polarization of light relates to the time dependent direction of its oscillating electric field and can lie anywhere in the plane orthogonal to its propagation direction. If its direction remains constant while its amplitude oscillates sinusoidally it is said to have linear polarization which can be split into any two orthogonal components, each orthogonal to the propagation. For any given reflection surface there is a plane of incidence containing the surface normal vector n together with the incident ray ri and the reflected ray rr (in the plane of the drawing in  FIG. 5 ). A polarization component of the incident ray ri that is perpendicular to the plane of incidence is called the s-polarization component s and polarization component of the incident ray ri that lies in the plane of incidence is called the p-polarization component p. 
       FIG. 6  is a graph of reflectivity of linearly polarised light from surfaces of a sheet of optically transmissive material with a refractive index of 1.5. The interaction of light with the surfaces  601  and  602  of the sheet of optically transmissive material  600  is significantly differently for the s-polarization component s and the p-polarization component p, in accordance with the Fresnel equations. By way of example,  FIG. 6  shows the variation with angle of incidence θ of reflectivities Rs and Rp of a sheet of material  600  for the s-polarization component s and the p-polarization component p, respectively. As can be seen, the reflectivities Rs and Rp vary significantly, the reflectivity Rp of the p-polarization component p dipping by a significant amount below the reflectivity Rs of the s-polarization component, and reaching zero when the angle of incidence θ is at the Brewster angle θ B . 
     The reflections are controlled by selecting the first and second optical retarders  801  and  802  in the display device  100  (or in the general case the or each optical retarder), using the following method. In this example, both reflections are reduced for the same viewer. 
     Returning to the description of  FIG. 4 , firstly a viewing position  44  is defined from where a viewer  45  is intended to view the display device  100 . The viewing position  44  is a defined by a vector v relative to a predetermined point  105  on the display device  100 , typically at the centre of the display device  100 . 
     Next, there are identified first and second rays of light r 1  and r 2  output from the predetermined point  105  on the display device  100  and reflected from the first and second surfaces  610  and  612 , respectively, to the common viewing position  44 . For each of the first and second rays of light r 1  and r 2 , there is identified the first and second points  613  and  614  at which the reflections on the first and second surfaces  611  and  612  occur. The first and second rays of light r 1  and r 2  are represented by the vectors from the predetermined point  105  on the display device  100  to the first and second points  613  and  614 , respectively. The first and second normals n 1  and n 2  of the first and second surfaces  611  and  612  at the first and second points  613  and  614 , respectively, are similarly identified. 
     Next, planes of incidence in respect of the first and second rays of light r 1  and r 2  are defined. Specifically, a first plane of incidence is defined in respect of the first ray of light r 1  and the first normal n 1  and a second plane of incidence in respect of a second ray of light r 2  and the second normal n 2 . 
     For each of the first and second rays of light r 1  and r 2 , a polarisation component in a direction perpendicular to the respective plane of incidence (s-polarisation component) and a polarisation component in a direction in the respective plane of incidence (p-polarisation component) may be defined. 
     In a vector representation, given reflection of a ray of light r from point on a surface at a point with a normal n, the s-polarisation component s is perpendicular to r and ns and so given by the equation: 
     
       
         
           
             
               
                 
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                   eqn 
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                   4 
                 
               
             
           
         
       
     
     Similarly, the p-polarisation component p is perpendicular to r and s and so given by the equation: 
     
       
         
           
             
               
                 
                   p 
                   = 
                   
                     
                       r 
                       × 
                       
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                           r 
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                         r 
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                   eqn 
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     Next the first and second optical retarders  801  and  802  are selected, having regard to the predetermined polarization state of the light output from the display device  100  so that the polarization state of the first ray of light r 1  is caused to be linearly polarized in a direction that is in the first plane of incidence (i.e. p-polarised), and the polarization state of the second ray of light is to caused to be to be linearly polarized in a direction that is in the second plane of incidence (i.e. p-polarised). In the general case that the predetermined polarization states of the first and second rays of light r 1  and r 2  output from the display panel  101  are not already p-polarised, this involves the first and second optical retarders  801  and  802  transforming the polarization states of the first and second rays of light r 1  and r 2 . However, in some specific cases one of the first and second rays of light r 1  and r 2  output from the display device  100  may already be p-polarised, in which case the first and second optical retarders  801  and  802  may be selected to have no effect on that ray of light. 
     This has the effect of causing both the first and second rays of light r 1  and r 2  to be p-polarised, thereby simultaneously minimising the amount of reflection from both of the first and second surfaces  611  and  612 . 
     This is illustrated in  FIGS. 7-8  which are perspective views of an example of the optical arrangement of  FIG. 4  being a vehicle  650  in which the first surface  611  is the windshield of the vehicle  650  and the second surface  612  is a side window of the vehicle  650 .  FIG. 7  illustrates the first and second rays of light r 1  and r 2  output from the display device  100  and  FIG. 8  the p-polarization states of the first and second rays of light r 1  and r 2 . 
     Such selection of the first and second optical retarders  801  and  802  is possible because a desired polarization state for a particular ray of a particular wavelength can always be transformed from any input polarization state with an optical retarder whose optical axis and retardance are freely selected. 
     Introducing a temporal phase shift between polarization components cause their amplitudes to add at different times creating a temporally varying electric field direction thus transforming the linear state into a more general elliptical one. A retarder introduces a relative phase shift between components by selectively slowing down the polarization component aligned with its optical axis. A half-wave phase shift forces the original components to be completely out-of-phase resulting in a linear polarization state whose direction is the reflected original about the projection of the optical axis of the optical retarder. 
       FIG. 9  is a perspective view of the second optical retarder  802  showing an example of how the polarisation state of a ray of light is controlled, as follows. 
     The second optical retarder  802  has an optical axis o which lies at an acute angle α to the plane of the second optical retarder  802 . The electric vector transmission direction  219  of the output polariser  218  is shown and light output from the display device  100  along the normal n to the plane of the second optical retarder  802  is linearly polarised in a direction pi of linear polarisation that is parallel thereto. The projection of the direction of the optical axis o of the second optical retarder  802  onto the plane of the second optical retarder  802  has an azimuth angle β to the direction pi of linear polarisation. 
     A ray of light r output from the display device  100  is considered and a plane  850  normal to that ray of light r is shown. The ray of light r has an initial direction pe of linear polarisation which is the projection of the direction pi of linear polarisation onto the plane  850 . 
     The projection  852  of the birefringent molecules  804  onto the plane  850  and the projection op of the optical axis o onto the plane  850  are also both shown. The second optical retarder  802  provides a phase shift that transforms the polarisation state of the ray of light r in accordance with the projection op of the optical axis o onto the plane  850 . In this example, the second optical retarder  802  provides a half-wave retardance at a wavelength of 550 nm along the second ray of light r. In that case, the second optical retarder  802  transforms the polarisation state of the ray of light r by changing the direction of linear polarisation from the initial direction pe to a final direction po, wherein the projection op of the optical axis o onto the plane  850  bisects the initial direction pe and the final direction po. This is often referred to as a “rotation” of the direction of linear polarisation, although strictly speaking it is a transformation of the direction of linear polarisation through elliptical polarisation states. 
     Herein, all materials are assumed to have a refractive index of one for clarity of description. That is unrealistic, but the actual refractive indices may be accounted for by transforming the polarization states and ray directions at each interface, requiring extra but orthodox computation. 
     As a result, it is possible to select optical retarders to independently control the polarisation state of the first and second rays of light r 1  and r 2 . In fact, there are an infinite number of such solutions since the optical axes of any one solution can have an arbitrary component along the direction of the ray. Mathematically this falls out of the three degrees of freedom possessed by an arbitrary optical retarder to provide the required two dimensional polarization manipulation. 
     By the same argument this restricts a uniaxial optical retarder to the arbitrary manipulation of the polarization state of no more than one ray, unless the polarization transformations of one of the rays requires less restriction on the optical retarder. Such a case occurs when a linear polarization state is retained for one of the rays. Here any retarder having no component orthogonal to both ray and preserved linear polarization directions may be selected. This reduced restriction frees up two degrees of freedom for an arbitrary transformation of a second ray. Recognizing this provides a general method of providing any polarization state for any two given rays using the general approach as follows. 
     To maintain an original polarization state for certain rays while transforming others, it is possible to select an optical retarder to have an optical axis having different projected retarder orientations with respect to the initial polarization direction for the first and second rays of light r 1  and r 2 . Maintaining the polarization of the first ray of light r 1  in a given plane can be achieved by restricting the optical axis of the second optical retarder  802  to lie within that given plane. The angle of the optical axis of the second optical retarder  802  within that plane and the retardance of the second optical retarder  802  are then selected so that the projection of the optical axis onto the normal to the second ray of light r 2  provides the desired transformation of the second ray of light r 2 . This will now be described in more detail with reference to  FIGS. 10-11 . 
       FIG. 10  is a chart illustrating a method for selection of the optical retarders in the display device  100  of  FIGS. 1-2  including first and second optical retarders  801  and  802 . This method is applicable in the case that the light output from the display device  100  has a predetermined polarization state of being linearly polarized in an arbitrary direction which is not in the first plane of incidence. 
     The first ray of light r 1  output from the display device  100  has an initial polarisation state p 1   i  and the second ray of light r 2  output from the display device  100  has an initial polarisation state p 2   i.    
     In step S 1 , the first optical retarder  801  is selected to transform the direction of linear polarization of the first ray of light r 1  that is present on output from the display panel  101  (initial polarisation state p 1   i ) from into the first plane of incidence (p-polarisation state p 1 ). As discussed further below, the second optical retarder  802  does not transform the direction of linear polarization of the first ray of light r 1 , so the first optical retarder  801  has the same properties whether before the second optical retarder  802  in the example of  FIG. 1  or after the second optical retarder  802  in the example of  FIG. 2 . 
     Step S 1  is performed by selecting the optical axis of the first optical retarder  801  to have a projection onto a plane normal to the first ray of light r 1  which bisects (a) the direction of linear polarization of the first ray of light r 1  output from the display device  100  and (b) the first plane of incidence. 
     The first optical retarder  801  has an optical axis parallel to the plane of the first optical retarder  801  and for optical retarders of this type, the optical transformation may be a good approximation to isotropic with angle for many common uniaxial materials. In such cases, selection of the first optical retarder  801  may be simplified by having regard merely to the transformation of a ray normal to the plane of the first optical retarder  801 . In this case, the optical axis of the first optical retarder  801  may be selected to bisect (a) the direction of linear polarization of a normal ray of light output in a normal direction to the display device  100  and (b) the first plane of incidence. 
     Step S 1  is also performed by selecting the first optical retarder  801  to provide a half-wave retardance at a design wavelength, typically of 550 nm, along the first ray of light r 1 . As discussed above with reference to eqn. 1, the retardance may be controlled by selection of the birefringence Δn and the thickness d of the first optical retarder  801 . Where selection of the first optical retarder  801  is simplified by having regard merely to the transformation of a ray normal to the plane of the first optical retarder  801 , then the first optical retarder  801  may similarly be selected to provide a half-wave retardance at the design wavelength along the normal to the first optical retarder  801 . 
     In step S 2 , the second optical retarder  802  is selected to achieve the following effects. 
     The first effect is that the second optical retarder  802  does not transform the direction of linear polarization of the first ray of light r 1  that is incident thereon. This effect is achieved by the second optical retarder  802  being selected to have an optical axis o which lies at an acute angle α to the plane of the second optical retarder  802  and in a plane containing the first ray of light r 1  and the direction of polarization of the first ray of light r 1  that is incident on the second optical retarder  802 . As a result of the optical axis o lying in this plane, the projection of the optical axis o onto plane normal to the first ray of light r 1  is aligned with the direction of linear polarization of the first ray of light r 1 , so does not transform the polarisation state of the first ray of light r 1 . 
     However, the azimuth angle β of the optical axis o about the normal to the second optical retarder  802  depends on whether the second optical retarder  802  is before or after the first optical retarder  801 . 
     In the case of  FIG. 1  that the second optical retarder  802  is after the first optical retarder  801 , then the polarisation state of the first ray of light r 1  has been transformed into the first plane of incidence. Accordingly, in this case, the optical axis o of the second optical retarder  802  is arranged to lie in the first plane of incidence. 
     In the case of  FIG. 2  that the second optical retarder  802  is before the first optical retarder  801 , then the polarisation state of the first ray of light r 1  remains in the initial polarisation state p 1   i  of the first ray of light r 1  output from the display panel  101 . Accordingly, in this case, the optical axis o of the second optical retarder  802  is arranged to lie in a plane containing the first ray of light r 1  and the direction of polarization of the initial polarisation state p 1   i.    
     The second effect is that the second optical retarder  802  transforms the direction of linear polarization of the second ray of light r 2  that is incident thereon into a predetermined direction such that the first and second optical retarders  801  and  802  together transform the direction of linear polarization of the second ray of light r 2  into the second plane of incidence. 
     The second effect of Step S 2  is achieved by selecting the optical axis o of the second optical retarder  802  to have a projection onto a plane normal to the second ray of light r 2  which bisects (a) the direction of linear polarization of the second ray of light r 2  that is incident thereon, and (b) the predetermined direction. 
     The acute angle α between the the optical axis o of the second optical retarder  802  and the plane of the second optical retarder  802  depends on whether the second optical retarder  802  is before or after the first optical retarder  801 . 
     In the case of  FIG. 1  that the second optical retarder  802  is after the first optical retarder  801 , then the direction of linear polarization of the second ray of light r 2  has already been transformed by the first optical retarder  801  before being incident on the second optical retarder  802 , and the predetermined direction into which the direction of the linear polarisation is transformed is the final direction in the second plane of incidence. Accordingly, in this case the optical axis o of the second optical retarder  802  has a projection onto a plane normal to the second ray of light r 2  which bisects (a) the direction of linear polarization of the second ray of light r 2  after transformation by the first optical retarder  801  and (b) the second plane of incidence. 
     In the case of  FIG. 2  that the second optical retarder  802  is before the first optical retarder  801 , then the polarization state of the second ray of light r 2  remains in the initial polarisation state p 2   i  of the second ray of light r 2  output from the display panel  101  and the predetermined direction is determined taking into account the subsequent transformation of the second ray of light r 2  by the first optical retarder  801 , i.e. such that the first optical retarder  801  transforms the predetermined direction of the linear polarization of the second ray of light r 2  that is incident thereon into the second plane of incidence. Accordingly, in this case, the optical axis o of the second optical retarder  802  has a projection onto a plane normal to the second ray of light r 2  which bisects (a) the direction of linear polarization of initial polarisation state p 2   i  of the second ray of light r 2  and (b) the predetermined direction so determined. 
     Step S 2  is also performed by selecting the retardance of the second optical retarder  802  to provide a half-wave retardance at a design wavelength, typically of 550 nm, along the second ray of light r 2 . 
       FIG. 11  is a chart illustrating a method for selection of the optical retarders in the display device  100  of  FIG. 3  including only the second optical retarder  802 . This method is applicable in the case that the light output from the display device  100  has a predetermined polarization state of being linearly polarized in a direction in the first plane of incidence. In that case, the first optical retarder  801  is not needed, and the second optical retarder  802  may be selected in a similar manner to the method of  FIG. 11 . 
     Specifically, the method comprises a single step S 3  in which the second optical retarder  802  is selected to achieve the following effects. 
     The first effect is that the second optical retarder  802  does not transform the direction of linear polarization of the first ray of light r 1  that is output from the display panel  101  and incident thereon. This effect is achieved by the second optical retarder  802  being selected to have an optical axis o which lies at an acute angle α to the plane of the second optical retarder  802  and in the first plane of incidence. As a result of the optical axis o lying in the first plane of incidence, the projection of the optical axis o onto plane normal to the first ray of light r 1  is aligned with the direction of linear polarization of the first ray of light r 1 , so does not transform the initial polarisation state p 1   i  of the first ray of light r 1 . 
     The second effect is that the second optical retarder  802  transforms the direction of linear polarization of the second ray of light r 2  that is output from the display panel  101  and incident thereon into the second plane of incidence. This is achieved by selecting the optical axis o of the second optical retarder  802  to have a projection onto a plane normal to the second ray of light r 2  which bisects (a) the direction of linear polarization of the second ray of light r 2  that is output from the display panel  101 , and (b) the second plane of incidence. 
     The methods shown in  FIGS. 11-12  are examples and the first and second optical retarders  801  and  802  may be selected in other manners to provide the same effect. Moreover, the methods may be generalised to selection of the optical retarders for output light having any predetermined polarization state. 
     An example in which the optical arrangement of  FIG. 4  is a vehicle  650  is shown in greater detail in  FIGS. 12-17 . Herein, the first surface  611  is the windshield of the vehicle  650  and the second surface  612  is a side window of the vehicle  650 . The display device  100  is arranged in the dashboard  602  at a central position across the vehicle  650 . Features of the embodiments of  FIGS. 12-17  not discussed in further detail may be assumed to correspond to the features with equivalent reference numerals as discussed above, including any potential variations in the features. 
       FIGS. 12-14  illustrate the normal viewing position  44  of the viewer  45  who is the driver of the vehicle, and also a reflection from the first surface  611  (windscreen). In this example, the light output by the display panel  101  is linearly polarized in a vertical direction to match the transmission of anti-glare polarized glasses when worn by the driver  45 . The first and second optical retarders  801  and  802  are selected to transform the polarization state of the first ray of light r 1  to be in the first plane of incidence, which is close to vertical in this example. This minimizes reflections from the first surface  611  (windscreen) which would otherwise create an image  111  of the display device  100 . 
       FIGS. 15-17  illustrate a reflection from the second surface  611  (side window). In this example, as the light output by the display panel  101  is linearly polarized in a vertical direction, then in the absence of the first and second optical retarders  801  and  802  this would be close to an s-polarisation state which would provide relatively large reflectivity, thereby creating an image of the display device  100 . However, the first and second optical retarders  801  and  802  are selected to transform the polarization state of the second ray of light r 2  to be in the second plane of incidence, which is close to horizontal in this example, thereby reducing these reflections. This minimizes reflections from the second surface  612  (side window) which would otherwise create an image  812  of the display device  100 . 
     Although the display device  100  is configured to minimize reflections at a particular viewing position  44 , in fact reflections are reduced by a similar amount across a typical viewing box  46  within which eyes of different drivers are expected to be located. 
     In all the above examples, the first and second rays of light r 1  and r 2  are reflected from the first and second surfaces  611  and  612 , respectively, to a common viewing position  44 . However, the first and second optical retarders  801  and  802  could be selected to reduced reflections of first and second rays of light r 1  and r 2  are reflected from first and second surfaces  611  and  612  to different locations. That might be useful in various applications, for example to reduce reflections perceived by two viewers in different locations. In this case, the method of selecting the first and second optical retarders  801  and  812  is the same, except for the first and second planes of incidence being differently defined. 
       FIG. 18  is a front view of an example of the optical stack of the display device  100  of  FIG. 1  in which the first optical retarder  801  is arranged before the second optical retarder  802 , and illustrating the polarization states of the first and second rays of light r 1  and r 2 . In this example, the electric vector transmission direction  219  is vertical, the first plane of incidence is horizontal and the second plane of incidence is vertical. Accordingly, the first optical retarder  801  is selected to transform the direction of linear polarization of the first ray of light r 1  to be horizontal, and so also transforms the direction of linear polarization of the second ray of light r 2  to be horizontal. Therefore, the second optical retarder  802  is selected to transform the direction of linear polarization of the second ray of light r 2  from that horizontal direction to be vertical. 
       FIG. 19  is a front view of a second example of the optical stack of the display device  100  of  FIG. 2  in which the first optical retarder  801  is arranged after the second optical retarder  802 , and illustrating the polarization states of the first and second rays of light r 1  and r 2 . In this example, the electric vector transmission direction  219  is horizontal, the first plane of incidence is vertical and the second plane of incidence is horizontal. Accordingly, the first optical retarder  801  is selected to transform the direction of linear polarization of the first ray of light r 1  to be vertical and so will perform a predictable transformation of the second ray of light r 2 . Therefore, the second optical retarder  802  is selected to transform the direction of linear polarization of the second ray of light r 2  from the horizontal direction to a predetermined direction which is vertical, so that the subsequent transformation of the second ray of light r 2  by the first optical retarder  801  is from that vertical direction to horizontal direction. 
     The display device  100  may be of any type. Some non-limitative examples are as follows. The display panel  101  may be a simple instrument display panel. The display panel  101  may comprise a spatial light modulator (SLM). Such an SLM may be an emissive SLM, for example comprising light emitting diodes that may be organic (OLED) or inorganic (micro-LED) or combination of inorganic and organic. Alternatively, such an SLM may be a transmissive SLM, for example being an LCD display panel, in which case the display panel may further comprise a backlight arranged to illuminate the SLM. 
     Features of the embodiments of  FIGS. 18-19  not discussed in further detail may be assumed to correspond to the features with equivalent reference numerals as discussed above, including any potential variations in the features. 
       FIG. 20  is a side perspective view of an example of the display panel  101  in the display devices  100  of  FIGS. 1-3  that comprises a transmissive SLM  48  and a backlight  20  arranged to illuminate the SLM  48 . 
     The SLM  48  comprises comprise a liquid crystal display comprising substrates  212 ,  216 , liquid crystal layer  214  and red, green and blue pixels  220 ,  222 ,  224 . The SLM  48  further comprises an input polariser  210  arranged on the input side of the SLM  48 , as well as the output polariser  218  arranged on the output side of the SLM  48 . The input polariser  210  and the output polariser  218  are each linear polarisers. 
     The backlight  20  comprises input light sources  15 , a waveguide  1 , a rear reflector  3  and an optical stack  5  comprising diffusers, light turning films and other known optical backlight structures. Asymmetric diffusers, that may comprise asymmetric surface relief features for example, may be provided in the optical stack  5  with increased diffusion in the elevation direction in comparison to the lateral direction may be provided. Advantageously, image uniformity may be increased. 
     The first and second optical retarders  801  and  802  (or more generally all the optical retarders) may be of any type. 
     The second optical retarder  802  that has an optical axis out of the plane of the second optical retarder may have an optical axis that has a uniform direction through its thickness. Alternatively, the first optical retarder  802  may have an optical axis that is splayed through its thickness. For the sake of simplicity, the above description describes the effect of the first and second optical retarders  801  and  802  for the case that they have an optical axis that is uniform through their thickness. In the case that the optical axis is splayed through the thickness of the first and second optical retarders  801  and  802 , the optical effect is more complex in that the effect of successive layers must be considered, but this may be modelled using conventional techniques that allow the first and second optical retarders  801  and  802  to be selected to provide the effects disclosed herein. 
     The first and second optical retarders  801  and  802  may be passive retarders or may be electrically switchable between at least two modes, in any combination. In the case that either or both of the first and second optical retarders  801  and  802  is electrically switchable, then they are selected to have the effects described herein in at least one of the electrically switchable modes. This allows the display device  100  to be switchable between different states, for example between two state which each provide control of different reflections, or between a states which do and do not provide control of reflections. 
     In one example, each of the first and second optical retarders  801  and  802  are passive retarders, for example being formed of cured liquid crystal material or stretched polymer films. 
     In another example, the first optical retarder  801  is a passive retarder and the second optical retarder  802  is electrically switchable between at least two modes. 
       FIG. 21-23  side perspective views of three alternative examples of the second optical retarder  802  in the display devices  100  of  FIGS. 1-3 . In each example, the second optical retarder  802  have common elements as follows. 
     In each example, the second optical retarder  802  includes a layer  714  of liquid crystal material dispose between two substrates  712  and  716 . The substrates  712  and  716  support respective electrodes  713  and  715  arranged to provide a voltage across the layer  714  of liquid crystal material for controlling the layer  714  of liquid crystal material. A control system  350  is connected to the electrodes  713  and  715 , and is arranged to control the voltage applied thereacross. 
     The second optical retarder  802  also includes two surface alignment layers  719 A and  719 B disposed adjacent to the layer  714  of liquid crystal material and on opposite sides thereof. Each of the surface alignment layers  719 A and  719 B is arranged to provide alignment in the adjacent liquid crystal material, for example homeotropic alignment or homogenous alignment, for providing the second optical retarder  802  with appropriate properties. 
     In the example of  FIG. 21 , the second optical retarder  802  comprises no further retarder layers. 
     In the example of  FIG. 22 , the second optical retarder  802  comprises a passive retarder layer  730  having an optical axis perpendicular to the plane of the second optical retarder  802 , i.e. a C-plate. 
     In the example of  FIG. 23 , the second optical retarder  802  comprises two passive retarder layers  730 A and  730 B that have optical axes in the plane of the second optical retarder  802  and crossed with respect to each other, i.e. crossed A-plates. 
     Other passive retarder layers may similarly be included in the second optical retarder  802 . The use of such passive retarder layers allows the angular dependence of the retardance of the second optical retarder  802  to be adapted, for example to increase the range of angles over which a particular retardance is provided. 
     An illustrative embodiment of the arrangement of  FIG. 23  will now be described. 
       FIG. 24  is a side perspective view of the second optical retarder  802 , output polariser  218  and display panel  101  of  FIG. 23 . View angle compensation retarder  730  comprises passive A-plates  730 A,  730 B that comprise birefringent molecules  408 A,  408 B. The optical axes  709 A,  709 B of A-plates  730 A,  730 B are arranged at angles  710 A,  710 B of +/45 degrees to the electric vector transmission direction  219  of the polariser  218 . Active liquid crystal layer  714  comprises liquid crystal molecules  421  that may be driven to splayed state. 
       FIG. 25  is a graph illustrating the variation of luminance with polar direction for the second optical retarder  802  of  FIG. 24 . The operation of the passive retarders  730  and active retarder  714  in a driven state, output is shown with a further polarisation state analysing polariser provided to receive light from the second retarder  802 . In operation, the further polarisation state analysing polariser is not provided, and is used here for illustrative purposes only. The polarisation state analysing polariser provides illustration of output operation by converting polarisation state transformation into a measurable luminance. Thus a high luminance in  FIG. 25  illustrates a small polarisation transformation, and a low luminance illustrates a high polarisation transformation, that is a high retardance of the polariser at a given polar angle. 
     Polar locations of rays r 1  and r 2  are shown in an illustrative example for a display located in front of the driver and orthogonal first and second planes of incidence. In comparison to arrangements without passive retarders  730 , the polar area over which desirable polarisation rotation may be increased. The size of the viewing box  46  for which desirable polarisation transformation is achieved may be increased. Advantageously freedom of driver or passenger location for reduced window reflections may be increased. 
     Viewing position vector v that in this illustrative example is on-axis is also provided with no polarisation transformation. Advantageously an observer wearing polarised sunglasses may see a high contrast, bright image. 
       FIG. 26  is a perspective view of optical retarders that may be applied in the display panel  100  of  FIG. 1 . Features of the embodiment of  FIG. 26  not discussed in further detail may be assumed to correspond to the features with equivalent reference numerals as discussed above, including any potential variations in the features. 
     Display panel  101  comprises additional polariser  318  and view angle luminance control retarder  300  arranged between the additional polariser  318  and output polariser  218 . View angle luminance control retarder  300  comprises a layer  314  of liquid crystal material dispose between two substrates  312  and  316 . The substrates  312  and  316  support respective electrodes (not shown) arranged to provide a voltage across the layer  314  of liquid crystal material for controlling the layer  314  of liquid crystal material. A control system  351  is connected to the electrodes, and is arranged to control the voltage applied thereacross. 
     The view angle luminance control retarder  300  also includes two surface alignment layers (not shown) disposed adjacent to the layer  314  of liquid crystal material and on opposite sides thereof. Each of the surface alignment layers is arranged to provide alignment in the adjacent liquid crystal material, for example homeotropic alignment or homogenous alignment, for providing the view angle luminance control retarder  300  with appropriate properties. 
     The view angle luminance control retarder  300  also comprises passive retarders. In an illustrative embodiment of  FIG. 26 , the passive retarders comprise quarter waveplates  330 A,  330 B arranged on opposite sides of the liquid crystal layer  314 , and the layer  314  comprises a twisted liquid crystal material. 
       FIG. 27  is a graph illustrating the variation of luminance with polar direction for the view angle control retarder  300  of  FIG. 26 . The graph illustrates the polar variation of output luminance provided by the polarisers  218 ,  318 . This is different to the polar variation of polarisation transformation illustrated in  FIG. 25  in which for measurement purposes only an additional analysing polariser is provided. 
     In a driven state of the liquid crystal layer  314  the luminance profile is provided with a degree of rotational symmetry. Thus for the ray directions r 1  and r 2 , the luminance is reduced. Comparing with  FIG. 25 , for light ray r 1  the polarisation state is not transformed and the luminance is reduced and for light ray light ray r 2  the polarisation state is transformed and the luminance is reduced. Advantageously light ray reflections from windscreen  610  and side window  612  are reduced by means of luminance reduction, and reduction of Fresnel reflectivity. For night operation, display reflection visibility is substantially reduced. 
     Viewing position vector v is also provided with minimal luminance reduction. Advantageously a bright image may be observed. 
     Switchable directional display apparatuses for use in privacy display for example and comprising plural retarders arranged between a display polariser and an additional polariser are described in U.S. Patent Publ. No. 2019-0086706, herein incorporated by reference in its entirety. Directional display apparatuses further comprising reflective polarisers arranged between the display polariser and retarders are described in U.S. Patent Publ. No. 2019-0250458, herein incorporated by reference in its entirety. Directional display polarisers comprising passive retarders arranged between a display polariser and an additional polariser are described in U.S. Patent Publ. No. 2018-0321553, herein incorporated by reference in its entirety. 
     While various embodiments in accordance with the principles disclosed herein have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of this disclosure should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with any claims and their equivalents issuing from this disclosure. Furthermore, the above advantages and features are provided in described embodiments, but shall not limit the application of such issued claims to processes and structures accomplishing any or all of the above advantages. 
     Additionally, the section headings herein are provided for consistency with the suggestions under 37 CFR 1.77 or otherwise to provide organizational cues. These headings shall not limit or characterize the embodiment(s) set out in any claims that may issue from this disclosure. Specifically and by way of example, although the headings refer to a “Technical Field,” the claims should not be limited by the language chosen under this heading to describe the so-called field. Further, a description of a technology in the “Background” is not to be construed as an admission that certain technology is prior art to any embodiment(s) in this disclosure. Neither is the “Summary” to be considered as a characterization of the embodiment(s) set forth in issued claims. Furthermore, any reference in this disclosure to “invention” in the singular should not be used to argue that there is only a single point of novelty in this disclosure. Multiple embodiments may be set forth according to the limitations of the multiple claims issuing from this disclosure, and such claims accordingly define the embodiment(s), and their equivalents, that are protected thereby. In all instances, the scope of such claims shall be considered on their own merits in light of this disclosure, but should not be constrained by the headings set forth herein.