the cell 1 shown in fig1 comprises two glass walls , 2 , 3 , spaced about 1 - 6 μm apart by a spacer ring 4 and / or distributed spacers . electrode structures 5 , 6 of transparent indium tin oxide are formed on the inner face of both walls . these electrodes may be of conventional line ( x ) and column ( y ) shape , seven segment , or an r - θ display . a layer 7 of liquid crystal material is contained between the walls 2 , 3 and spacer ring 4 . polarisers 8 , 9 are arranged in front of and behind the cell 1 . the alignment of the optical axis of the polarisers 8 , 9 are arranged to maximise contrast of the display ; ie approximately crossed polarisers with one optical axis along one switched molecular direction . a d . c . voltage source 10 supplies power through control logic 11 to driver circuits 12 , 13 connected to the electrode structures 5 , 6 , by wire leads 14 , 15 . the device may operate in a transmissive or reflective mode , in the former light passing through the device e . g . from a tungsten bulb 16 is selectively transmitted or blocked to form the desired display . in the reflective mode a mirror 17 is placed behind the second polariser 9 to reflect ambient light back through the cell 1 and two polarisers . by making the mirror 17 partly reflecting the device may be operated both in a transmissive and reflective mode with one or two polarisers . prior to assembly the walls 2 , 3 are surface treated eg by spinning on a thin layer of a polymer such as a polyamide or polyimide , drying and where appropriate curing ; then buffing with a soft cloth ( e . g . rayon ) in a single direction r1 , r2 . this known treatment provides a surface alignment for liquid crystal molecules . the molecules ( as measured in the nematic phase ) align themselves along the rubbing direction r1 , r2 , and at an angle of about 0 ° to 15 ° to the surface depending upon the polymer used and its subsequent treatment ; see article by s . kuniyasu et al , japanese j of applied physics vol 27 , no 5 , may 1988 , pp827 - 829 . alternatively surface alignment may be provided by the known process of obliquely evaporating eg . silicon monoxide onto the cell walls . the surface alignment treatment provides an anchoring force to adjacent liquid crystal materials molecules . between the cell walls the molecules are constrained by elastic forces characteristic of the material used . the material forms itself into molecular layers 20 each parallel to one another as shown in fig3 which is a specific example of many possible structures . the sc is a tilted phase in which the director lies at an angle to the layer normal , hence each molecular director 21 can be envisaged as tending to lie along the surface of a cone , with the position on the cone varying across the layer thickness , and each macro layer 20 often having a chevron appearance . considering the material adjacent the layer centre , the molecular director 21 lies approximately in the plane of the layer . application of a dc voltage pulse of appropriate sign will move the director along the cone surface to the opposite side of the cone . the two positions d1 , d2 on this cone surface represent two stable states of the liquid crystal director , ie the material will stay in either of these positions d1 , d2 on removal of applied electric voltage . in practical displays the director may move from these idealised positions . it is common practice to apply an ac bias to the material at all times when information is to be displayed . this ac bias has the effect of moving the director and can improve display appearance . the effect of ac bias is described for example in proc 4th idrc 1984 pp 217 - 220 . display addressing scheme using ac bias are described eg in gb patent application number 90 . 17316 . 2 . pct / gb 91 / 01263 , j . r . hughes and e . p . raynes . the ac bias may be data waveforms applied to the column electrodes 15 . fig4 shows the switching characteristics for the material sce8 . the curves mark the boundary between switching and nonswitching : switching will occur for a pulse voltage time product above the line . as shown the curve is obtained for an applied ac bias of 7 . 5 volts , measured at a frequency of 50 hz . suitable materials include catalogue references sce8 . zli - 5014 - 000 . available from merck ltd . those listed in pct / gb88 / 01004 , wo 89 / 05025 , and : ## str1 ## another mixture is lpm 68 = h1 ( 49 . 5 %), as 100 ( 49 . 5 %), igs 97 ( 1 %) h1 = mb 8 . 5f + mb 80 . 5f + mb 70 . 7f ( 1 : 1 : 1 ) as100 = pyr 7 . 09 + pyr 9 . 09 ( 1 : 2 ) ## str2 ## in one conventional display a (-) blanking pulse is applied to each line in turn ; this causes all pixels in that line to switch to or remain black . sometime later a strobe waveform is applied to each line in turn until all line are addressed . as each line receives a strobe , appropriate data - on or data - off waveforms are applied to each column simultaneously . this means that each pixel in a line receives a resultant of strobe plus data - on or strobe plus data - off . one of these resultants is arranged to switch a pixel to white , the other resultant leaves the pixel in the black state . thus selected pixels in a line are turned from black to white , whilst other pixels remain black . the time taken to blank all lines then address all lines is a frame time . the blanking and strobing are repeatedly applied in sequence . to maintain net zero dc balance , the blanking pulses are dc balanced with the strobe pulses . alternatively , all waveforms are regularly inverted in polarity . this conventional type of display can only show two levels of greyscale , ie black and white . although a given pixel can only adopt two switched states , namely a dark ( eg black ) and a light ( eg white ) appearance , four levels of greyscale can be provided by addressing each line twice per frame . to obtain the appearance of a contrast level between black and white ( eg a grey ), the pixel is repeatedly switched black for a time period t1 and switched white for a time period t2 . providing such a switching is above a flicker frequency of about 35 hz , an operator will observe a contrast level or greyscale between black and white , eg grey . the darkness of the grey will depend upon the ratio of t1 : t2 . providing t1 does not equal t2 , then four different levels of intensity can be observed , ie four levels of greyscale . when the pixel is black for t1 and t2 the pixel is black ; when the pixel is white for t1 and t2 the pixel is white . when t1 & gt ; t2 then dark grey is obtained when the pixel is black for t1 and white for t2 , and the pixel is light grey when the pixel is white for t1 and black for t2 . in practice it is difficult to provide the desired ratio between the different levels of greyscale . odd values of temporal ratios ( t2 : t4 ) are quite easy to produce , even values are required but are difficult to obtain . the principle of a uniform greyscale temporal addressing system is shown with reference to fig5 which shows diagrammatically a resultant waveform at one pixel in a line being addressed . as shown in fig5 a pixel is switched to black by a blanking pulse vb1 . a time t1 later the pixel is addressed by a strobe pulse va1 . after a further period of t2 a blanking pulse vb2 again switches the pixel to black . after a time of t3 a second strobe pulse va2 addresses the pixel . after further time t4 the blanking pulse vb1 is applied and the process repeated . the time between applications of the blanking pulse vb1 . ie t1 + t2 + t3 + t4 . is the frame time of a display . both strobe pulses va1 and va2 are capable of switching a pixel to white or leaving it black . this means that the pixel is always black for t1 and t3 . the pixel can be either black or white for period t2 , and either black or white for period t4 . by varying the period t2 and t4 , the pixel can have the appearance of any two greyscale levels between black and white as well as black and white . varying t1 and t3 varies the overall display brightness . the following table 1 shows different greyscales for addressing where t2 & gt ; t4 . table 1______________________________________period t1 t2 t3 t4 greyscale______________________________________state black white black white ( almost ) whitestate black white black black light greystate black black black white dark greystate black black black black black______________________________________ fig6 shows a display having four lines ; the number of columns is immaterial . the number of line address time periods is eight . the letter a is used to show addressing of a pixel in a given line ; this is diagrammatic only and presumes blanking and immediate strobing in one time slot . l1 is addressed in periods 1 and 3 ; l2 in periods 2 and 4 ; l3 in periods 5 and 7 ; l4 in periods 6 and 8 . thus a pixel can be say black for 2 time periods and white for 6 periods , ie a greyscale temporal weighting of 1 : 3 . the greyscales are 0 / 8 ; 2 / 8 ; 6 / 8 ; 8 / 8 , ie intervals of 1 : 3 , and 3 : 4 . this can be extended to much larger displays by addressing the lines in groups , and dividing the time periods into sub periods , for example in fig7 the lines are grouped as lines 1 + 4q , lines 2 + 4q , lines 3 + 4q , lines 4 + 4q where q is an integer , eg 1 to 60 giving a total of 240 lines . each period is then divided into 60 subperiods . line 1 is addressed in subperiod 1 of period 1 : line 5 ( 1 + 4q q = 1 ) is addressed in subperiod 2 of period 1 ; line 9 ( 1 + 4q , q = 2 ) is addressed in subperiod 3 of period 1 , etc until line 237 is addressed in subperiod 60 of period 1 . then line 2 is addressed in subperiod 1 of period 2 , lines 6 . . . 238 , lines 3 , . . . 239 , lines 4 . . . 240 etc . however , the greyscale temporal ratio is still 1 : 3 which does not give a linear spacing of the greyscale levels . fig8 shows the addressing of a six line display in a total of twelve time periods . line l1 is addressed in periods 1 and 6 , other lines are addressed as indicated . the position of the addressing pulse appears to move around in a non ordered manner . the reason for this is the double requirement of addressing each line twice in each frame time , and not being able to address two different lines at the same time . the illustrated 12 periods is only a snap - shot in time : the 12 periods repeat whilst the display is in operation . each pixel can be in say a black state for 5 time periods and a white state for 7 time periods . the greyscale weighting is 5 : 7 which is still not a linear spacing of greyscale levels . fig9 shows the addressing of 16 lines over 32 periods , the figure shows a snapshot over 32 periods . this would normally give a temporal weighting of 1 : 3 with both blanking pulses preceding the strobing pulse by the same minimum interval . blanking pulses are arranged so that the temporal weighting is 1 : 2 . as shown the strobing pulses are in the time ratio 8 : 24 . ie 1 : 3 . taking the times indicated in fig5 . then fig9 gives t1 = 10 ; t2 = 7 ; t3 = 1 ; t4 = 14 . this gives the following greyscales : table 2______________________________________ level of white______________________________________bbbb - black for all 32 periods 0bwbb - black for 25 and white for 7 periods 7bbbw - black for 18 and white for 14 periods 14bwbw - black for 11 and white for 21 periods 21______________________________________ clearly this can be extended for a 256 line display by arranging the 16 lines in groups of 16 and dividing each period up into 16 subperiods as explained earlier . fig1 shows the addressing of 16 lines in 32 time periods with strobing pulse s immediately preceded by blanking pulse b . the two periods where the display can be white are 20 time periods , and 10 time periods . the temporal weighting is thus 10 : 20 ie 1 : 2 which is an even weighting . the maximum brightness is 30 / 32 . however , the effect of blanking just before strobing is to slow down switching of the liquid crystal material . it is common to blank a few lines ahead of strobing ; typically blanking is 4 to 7 lines ahead of strobing and reduces switching times . taking the arrangement of fig 10 and making the blanking occur 4 lines ahead of strobing results in a temporal weighting of 7 : 17 which is not an even weighting . the maximum brightness is 24 / 32 . fig1 shows the addressing of 16 lines in 32 time periods . in every line one blanking pulse is 4 lines ahead of strobing , and the other blanking pulse is ahead of strobing by 7 lines . the display can be white for both 14 and 7 time periods , ie a temporal weighting of 7 : 14 . which is an even weighting . maximum brightness is 21 / 32 . waveforms for addressing a 16 line 4 columns matrix with four levels of greyscale are shown in fig1 . shown are 4 of the 16 lines and columns marked 1 , 2 , 3 , 4 , with each line and column intersection left unshaded , lightly shaded , darkly shaded , or completely black , to respectively indicate white , light grey , dark grey , and black . line 3 is marked to show white , light grey , dark grey , and black in columns 1 , 2 , 3 , 4 respectively . waveforms applied to the lines ( rows ) are shown ; they comprise blanking pulses - vb , and strobe pulses + vs , applied twice per frame time . column waveforms are ± vd pulses each pulse lasting one time slot ( ts ). the illustrated pattern of column waveforms provide the greyscale pattern of display shown . the resultant waveforms at pixels a , b , c , d , in line 3 are shown . under each resultant is a graph showing light transmission through the associated pixel ; pixel a shows the most time with a high transmission and is therefore the lightest , ie white , pixel . in contrast pixel d has zero transmission and is therefore black . the addressing of a 16 line matrix can be expanded to 256 lines or more as described above by addressing lines : 1 , 17 , 33 , 49 - 241 ; 7 , 23 , 39 , 55 - 246 ; 2 , 18 , 34 , 50 - 242 . increasing the number of columns does not affect the complexity . one circuit for addressing a 16 or more line display is shown in fig1 ; it modifies the line driver circuits of fig1 ; no change is needed for the column driver . as shown in fig1 four line drivers are used 20 , 21 , 22 . 23 . line driver 20 has its successive outputs connected to lines 1 , 5 , 9 , 13 etc ; line driver 21 has its successive outputs connected to lines 2 , 6 , 10 , 14 ; line driver 22 has its successive outputs connected to lines 3 , 7 , 11 , 15 , and line driver 23 has its successive outputs connected to lines 4 , 8 , 12 , 16 . this arrangement can be cascaded to use all driver outputs , eg the addressing of 256 lines by using 64 driver outputs . in a modification , blanking pulses are replaced by strobes . this requires four subframes of addressing in order to obtain four different periods of switched states . a pixel can be divided up into a number of areas of equal or different sizes . the apparent darkness of a pixel is related to the area of black compared to the area of white . for example fig1 shows a pixel divided into 2 areas in the ratio of 1 : 2 which could be arranged to be consecutive lines of a display . this allows 4 greyscale levels , ie both areas black , both areas white , the large area black with the other white , and the large area white and the other black . fig1 shows a pixel subdivided into 4 areas in the ratio 1 : 2 : 2 : 4 which allows a total of 10 levels . this requires two adjacent lines and columns per pixel . in high resolution displays the overall size of a pixel can be quite small eg 25 × 25 μm , subdividing the pixel can cause difficulties in manufacturing the smallest subpixel . this problem may be overcome by varying the apparent size of a subpixel . the apparent size of one subpixel relative to an adjacent subpixel is related both to the area of the subpixels , and to their relative brightness . thus by making the smallest subpixel darker than its neighbour , then the smallest subpixel appears to be even smaller than its physical size would indicate . this allows the subpixel to made slightly larger in area than expected for a given greyscale level . the greyscale level ( and hence relative darkness ) of one subpixel relative to another may be altered by varying the time between blanking and addressing pulses shown in fig5 ie varying t1 + t3 in adjacent lines . this varies the length of time spent in a black state in the different greyscale levels . as described above , uniform greyscale levels in a display may be achieved by temporal weighting alone , or in combination with spatial weighting . furthermore the spatial weighting may be modified to varying the apparent size of adjacent subpixels . for example 256 greyscales may be provided by the following combinations : table 3______________________________________ temporal ratio spatial ratio______________________________________ 1 : 2 1 : 4 : 16 : 64 1 : 4 1 : 2 : 16 : 32 1 : 16 1 : 2 : 4 : 8______________________________________ it may not be desirable to produce linearly spaced grey levels . the eye does not respond linearly to uniform increments of brightness , the apparent difference in lightness between adjacent levels being much less at the light end of the scale than at the dark end ( r w g hunt , measuring colour , second edition , published by ellis horwood ltd . 1991 ). a feature of the present invention , is that any desired weighting may be obtained by addressing the lines in the required ( non - sequential ) sequence and making correction to any small errors in the weighting by use of the variable blanking to strobe separation . the required addressing sequence , for a required temporal ratio of r 1 : r 2 : r 3 : . . . : r x ( x is number of bits of greyscale ). may be arrived at from the following algorithm which will be correct as m ( the number of lines ) approaches infinity ; ______________________________________ ( 1 ; r . sub . 2 + r . sub . 3 + . . . + 3 . sub . x + 1 ; r . sub . 3 + . . . + r . sub . x + 1 ; . . . ; r . sub . x + 1 ) first bracket ( 2 ; r . sub . 2 + r . sub . 3 + . . . + 3 . sub . x + 2 ; r . sub . 3 + . . . + r . sub . x + 2 ; . . . ; r . sub . x + 2 ) second bracket ( 3 ; r . sub . 2 + r . sub . 3 + . . . + 3 . sub . x + 3 ; r . sub . 3 + . . . + r . sub . x + 3 ; . . . ; r . sub . x + 3 ) third bracket ..( r ; r . sub . 2 + r . sub . 3 + . . . + 3 . sub . x + r ; r . sub . 3 + . . . + r . sub . x + r ; . . . ; r . sub . x + r ) rth bracket______________________________________ where r equal the summation of r i ( for i = 1 to x ) and where the addressing sequence follows the first bracket for the first r lines , then that sequence is repeated on the next r lines until all ( m / r ) groups of lines have been addressed , then the addressing sequence follows the second bracket for all ( m / r ) groups of lines , and so on until the sequence has followed the r th bracket to all ( m / r ) groups of line ; modulo r arithmetic is used to keep the numerical expression within the relevant group of r lines . for example consider a desired temporal ratio of 1 : 2 : 4 and a total of 14 lines . then r 1 = 1 , r 2 = 2 , and r 3 = 4 , ( r x = r 3 = 4 ), x = 3 the number of temporal bits , r = 1 + 2 + 4 = 7 , and m = 14 . ______________________________________first group of r lines second group of r lines______________________________________first bracket 1 , r . sub . 2 + r . sub . 3 + 1 , r . sub . 3 + 1 7 + 1 , 7 + r . sub . 2 + r . sub . 3 + 1 , 7 + r . sub . 3 + ______________________________________ 1 ______________________________________first bracket 1 . 2 + 4 + 1 , 4 + 1 7 + 1 , 7 + 2 + 4 + 1 , 7 + 4 + 1second bracket 2 . 2 + 4 + 2 , 4 + 2 7 + 2 , 7 + 2 + 4 + 2 , 7 + 4 + 2third bracket 3 . 2 + 4 + 3 , 4 + 3 7 + 3 , 7 + 2 + 4 + 3 , 7 + 4 + 3fourth bracket 4 . 2 + 4 + 4 , 4 + 4 7 + 4 , 7 + 2 + 4 + 4 , 7 + 4 + 4fifth bracket 5 . 2 + 4 + 5 , 4 + 5 7 + 5 , 7 + 2 + 4 + 5 , 7 + 4 + 5sixth bracket 6 . 2 + 4 + 6 . 4 + 6 7 + 6 , 7 + 2 + 4 + 6 , 7 + 4 + 6seventh bracket 7 . 2 + 4 + 7 . 4 + 7 7 + 7 , 7 + 2 + 4 + 7 , 7 + 4 + 7______________________________________ this gives the following sequence of addressing , showing the modulo conversion thus ( x & gt ;) x - 7 : ______________________________________ first group of r lines second group of r lines______________________________________first bracket 1 . 7 , 5 , 8 . 14 , 12second bracket 2 . ( 8 & gt ;) 1 , 6 9 . ( 15 & gt ;) 8 , 13third bracket 3 . ( 9 & gt ;) 2 , 7 10 . ( 16 & gt ;) 9 , 14fourth bracket 4 . ( 10 & gt ;) 3 , ( 8 & gt ;) 1 11 . ( 17 & gt ;) 10 , ( 15 & gt ;) 8fifth bracket 5 . ( 11 & gt ;) 4 , ( 9 & gt ;) 2 12 . ( 18 & gt ;) 11 , ( 16 & gt ;) 9sixth bracket 6 . ( 12 & gt ;) 5 , ( 10 & gt ;) 3 13 . ( 19 & gt ;) 12 , ( 17 & gt ;) 10seventh bracket 7 . ( 13 & gt ;) 6 , ( 11 & gt ;) 4 14 . ( 20 & gt ;) 13 , ( 18 & gt ;) 11______________________________________ the temporal ratio is 7 : 13 : 22 which is 1 : 1 . 86 : 3 . 14 . this addressing sequence is illustrated in fig1 , where the solid squares represent addressing , ie blanking followed by strobe .