before explaining the disclosed embodiments of the present invention in detail it is to be understood that the invention is not limited in its application to the details of the particular arrangements shown since the invention is capable of other embodiments . also , the terminology used herein is for the purpose of description and not of limitation . a conventional projection display system 100 includes a polarizing beam splitter ( pbs ) 110 , a reflective liquid crystal cell 120 and a light source 130 , as shown in fig1 . the reflective liquid crystal cell 120 includes a first transparent substrate 122 with a first alignment film , a second substrate 124 with a second alignment film and a liquid crystal layer 126 with a positive dielectric constant between the first substrate 122 and the second substrate 124 . the second substrate 124 includes a reflector on the inner surface , adjacent to the liquid crystal layer . the pbs 110 has a crossed polarizer and analyzer configuration , which means the polarization direction of the polarizing means is substantially perpendicular to the polarizing direction of the analyzing means . therefore , if the entrance polarization direction of the polarizing means makes an angle β with the alignment direction of the liquid crystal layer on the first substrate 122 , then the analyzing means makes β ± approximately 90 ° with the alignment direction of the liquid crystal layer on the first substrate 122 . referring back to fig1 , the unpolarized light 105 from light source 130 becomes linearly polarized light 115 after passing through the polarizing means of the pbs 110 , and impinges onto the reflective tn - lc cell 120 . when returning from the reflective tn - lc cell 120 , the reflected light 125 encounters the analyzing means of the pbs 110 . the polarization state of the reflected light 125 determines the output reflectance . in order to get a high contrast ratio , which is important for large screen projection display with high quality , such as home theater , conference projector etc , a substantially perfect dark state is preferable . to achieve a substantially perfect dark state , the incident linearly polarized light 115 should be unchanged after a round trip in the reflective tn - lc cell 120 , so that the identical reflected linearly polarized light 125 is blocked by the analyzing means of the pbs 110 , and as a result , a very good dark state is obtained . in the preferred embodiment , the linear polarized light 115 is an eigenmode of the reflective tn - lc cell in order to achieve the high contrast ratio . two different models , uniform - twist model and two - layer model , are described here before describing the eigenmodes in a reflective tn - lc cell . in a reflective tn - lc cell with positive dielectric anisotropic liquid crystals , the pretilt angle at the substrates boundary is small , approximately 1 - 5 °. the liquid crystal molecules undergo a uniform twist throughout the cell when the applied voltage is below a threshold . when the applied voltage is approximately 2 times higher than the threshold voltage , the liquid crystal molecules in the middle of the liquid crystal layer are aligned approximately parallel to the electric field . however , the boundary layers near the top and bottom substrate interfaces are hardly disturbed because of strong surface anchoring . therefore , the tn - lc cell is described by a uniform - twist model when the applied voltage is below a threshold and by a two - layer model when the applied voltage is approximately 2 times higher than the threshold voltage . in the uniform - twist model , there are two eigenmodes for the reflective tn - lc cell and both eigenmodes are linearly polarized and orthogonal to each other . the azimuthal angles of these two linear polarization states are determined by θ angle in the following equation 1 . tan ⁢ ⁢ θ = - cos ⁢ ⁢ x ± 1 - ( γ 2 ⁢ sin ⁢ ⁢ x x ) 2 ϕ ⁢ sin ⁢ ⁢ x x . ( 1 ) where , γ = 2πdδn / λ is the phase of the uniformly twisted tn - lc cell and x =√{ square root over ( φ 2 +( γ / 2 ) 2 )} is a parameter related to both twist angle and phase of twisted tn - lc cell . wherein , d is cell gap , δn is the birefringence of lc material , λ is the wavelength of incident light and φ is the twist angle . fig2 illustrates the coordinates of the system of fig1 . the entrance polarization direction 220 of the pbs 110 makes an angle β with respect to the liquid crystal alignment direction 210 on the top substrate 122 . the twist angle of the tn - lc layer 126 is φ , which is determined by the angle between the liquid crystal alignment direction 210 on the top substrate 122 and the liquid crystal alignment direction 230 on the bottom substrate 124 . the twist angle φ is defined to be positive in the counterclockwise direction based on the liquid crystal alignment direction 210 on the top substrate 122 . therefore , the left - handedness twist angle is positive and the right - handedness twist angle is negative . in a preferred embodiment of the present invention , the liquid crystal layer has a twist angle within a range of approximately approximately 40 °& lt ; φ & lt ; approximately 80 ° for a left - handed twist liquid crystal layer and approximately − 80 °& lt ; φ & lt ; approximately − 40 ° for a right - handed twist liquid crystal layer . in the two - layer model , each boundary layer can be approximately treated as a non - twisted uniaxial layer with residual phase ψ = 2πα / λ , here α is the retardation of each boundary layer . when applied voltage increases , the retardation α decreases . similarly , there exists two eigenmodes for the reflective tn - lc cell using the above mentioned two - layer model . both eigenmodes are linear polarizations and are orthogonal with each other . the azimuthal angle of the two eigenmodes is given by the θ angle in the following equation 2 . tan ⁢ ⁢ θ = - cos ⁢ ⁢ ψ ⁢ ⁢ cos ⁢ ⁢ ϕ ± cos 2 ⁢ ϕ ⁢ ⁢ cos 2 ⁢ ψ + sin 2 ⁢ ϕ sin ⁢ ⁢ ϕ ( 2 ) when the applied voltage is within an intermediate voltage range , the case is much more complicated and no approximation is made . since the reflective tn - lc cell is described by a uniform - twist model when the applied voltage is below a threshold and by a two - layer model when the applied voltage is approximately two times the threshold voltage , the azimuthal angles of the eigenmodes should be located between the obtained results of uniform - twist model and two - layer model when an intermediate voltage is applied . fig3 a and 3b illustrate the relationship between the azimuthal angles of the eigenmodes and the residual phase retardation in the case of left - handedness approximately 60 ° reflective twisted nematic tn - lc cell using both uniform - twist model and two - layer model for eigenmode 1 and eigenmode 2 , respectively . fig4 illustrates a magnified region of the graphs of fig3 a and 3b , wherein the residual phase retardation in the magnified region is between 0 - 100 nanometers . according to the graph , when the residual retardation decreases , the azimuthal angles of eigenmodes gradually reach the bisector ( φ / 2 ) of twist angle or perpendicular to the bisector ( φ / 2 ± 90 °), which is the approach used in the prior arts . the prior art placed the entrance polarization direction of pbs at the bisector or perpendicular to the bisector . however , even when the applied voltage reaches triple of threshold voltage , the residual retardation is still much larger than 0 and as a result , the azimuthal angle of the eigenmodes are not exactly parallel to the bisector or perpendicular to the bisector . for example , fig5 illustrates the residual retardation of a 60 ° tn cell with dδn = approximately 350 nm at different applied voltage . using the parameters listed in table 1 , even when the applied voltage is approximately 5 v rms , the residual retardation is approximately 50 nm . with this amount of residual retardation , the azimuthal angle of eigenmode is about 0 . 5 ° larger than the bisector , as shown in fig4 a and 4b . in projection display , it is highly desirable to decrease the driving voltage in order to minimize the fringing field effect . since the azimuthal angles of the eigenmodes deviate from the direction of bisector ( or the direction perpendicular to bisector ), the entrance polarization direction of the pbs 110 should be oriented parallel or perpendicular to the azimuthal angle of the eigenmode of the reflective tn - lc cell at the desired driving voltage . by taking the boundary residual retardation into consideration , the optimal polarization angle is determined to be approximately within a range of approximately 1 ° to approximately 3 ° higher than the bisector angle used in the prior art . for example , referring to fig5 it is seen that the residual retardation of the reflective tn - lc cell is approximately 75 nanometers when a driving voltage of approximately 3 . 5 v rms is applied . referring to fig4 a and 4b , the corresponding azimuthal angle of eigenmodes at a residual retardation of approximately 75 nanometers is approximately 1 . 50 larger than the azimuthal angle at the bisector . therefore , the optimal entrance polarizer angle β between the crossed polarizer and the reflective tn - lc cell &# 39 ; s front lc director is , β = φ / 2 + 1 . 5 ° or β =± π / 2 + φ / 2 + 1 . 5 ° to achieve an approximately perfect dark state at an intermediate driving voltage of approximately 3 . 5 v rms . if the applied voltage is further increased , the residual phase gradually decreases and the corresponding azimuthal angle of eigenmodes changes accordingly . as a result , the reflectance increases slowly when the applied voltage exceeds approximately 3 . 5 v rms . in a preferred embodiment of the present invention , the liquid crystal layer has a phase retardation within a range of approximately 0 . 4 & lt ; dδ / λ & lt ; approximately 0 . 8 . referring back to fig2 , for a left - handed tn - lc cell with twist angle φ to achieve a high contrast ratio and low operating voltage , the entrance polarization direction 220 of pbs 110 should be set at a polarizer angle β which satisfies φ / 2 & lt ; β & lt ;( φ / 2 + 15 °) or ( φ / 2 ± 90 °)& lt ; β & lt ;( φ / 2 + 15 °± 90 °). on the other hand , if the reflective tn - lc is right - handed with twist angle φ ( here φ is a negative value ), then entrance polarization direction 220 of pbs 110 is set to form a polarizer angle β which satisfies approximately ( φ / 2 − 15 °)& lt ; β & lt ; φ / 2 or approximately ( φ / 2 − 15 °± 90 °)& lt ; β & lt ;( φ / 2 ± 90 °). as previously discussed , the angles are based on the liquid crystal alignment direction 210 on the top substrate 122 , as shown in fig2 , and the counterclockwise angles are positive while clockwise angles are negative . for example , fig6 a , 6b and 6 c illustrate the electro - optical performance showing the voltage - dependent reflectance of a left - handed approximately 60 ° tn cell with dδn = 0 . 35 μm at various polarizer angles for a green light with a wavelength λ = approximately 550 nanometers . in these graphs the solid line represents the results of the prior art with the polarizer angle set at β = 30 °. assume that the pbs has a limited extinction ratio of er = 1000 : 1 , the contrast ratio ( cr ) of the final system is affected by the extinction ratio of pbs as where r is the normalized reflectance obtained in the graphs . for example , if the normalized reflectance is r = 0 . 00005 , then the system contrast ratio would be cr = 1 0 . 001 + 0 . 00005 = 952 ⁢ : ⁢ 1 . to obtain cr = approximately 950 : 1 , it is determined from the graph in fig6 c that the prior art , illustrated as the solid curve , requires a driving voltage of approximately 5 v rms . applying the method of the present invention , the boundary layers are taken into consideration to determine that the optimal polarizer angle β occurs at β = 31 . 5 ° instead of 30 ° as used in the prior art . with the polarizer angle set at approximately 31 . 5 degrees , the driving voltage required to obtain the dark state voltage decreases to approximately 3 . 5 v rms . in other words , to achieve an improved contrast ratio cr = approximately 952 : 1 , a driving voltage of approximately 3 . 5 v rms is required as compared to 5 v rms driving voltage required by the prior arts . on the other hand , if the driving voltage used by the prior art is decreased to approximately 3 . 5 v rms , then the prior art configurations produce a contrast ratio of approximately cr = 1 0 . 001 + 0 . 0012 = 455 ⁢ : ⁢ 1 . in contrast , using the present invention a much higher contrast ratio in a second example , fig7 a , 7b and 7 c are graphs the normalized reflectance with respect to the applied voltage for a left - handed approximately 57 ° tn cell with dδn = 0 . 35 μm at various polarizer angles for a green light ( λ = approximately 550 nm ). fig7 a is a graph of the overall electro - optical curve while fig7 b and 7c are graphs of the electro - optical performance at bright state and at dark state , respectively . according to the graphs , the solid line shows the results of the prior art with the polarizer angle set at β = 28 . 5 °. still assuming that the pbs has a limited extinction ratio of er = 1000 : 1 and the normalized reflectance is r = approximately 0 . 0001 , then the system contrast ratio at approximately 4 . 8 v rms is calculated to be cr = 1 0 . 001 + 0 . 0001 = 909 ⁢ : ⁢ 1 . to obtain the same contrast ratio using the present invention , β is set to and the required voltage is decreased to approximately 3 . 4 v rms . in another example , fig8 a , 8b and 8 c are graphs of the voltage - dependent reflectance of a left - handed approximately 55 ° tn cell with dδn = 0 . 35 μm at various polarizer angles for green light ( λ = approximately 550 nm ) wherein the solid line represents the results of the prior art with polarizer angle β = approximately 27 . 5 °. still assuming that the pbs has a limited extinction ratio of er = 1000 : 1 and the normalized reflectance is r = 0 . 0001 , according to the dark state graph of fig8 c , 4 . 8 v is required to obtain a contrast ratio cr = 1 0 . 001 + 0 . 0001 = 909 ⁢ : ⁢ 1 . with the configuration of the present invention , to obtain the same contrast ratio β is set to ( approximately 27 . 5 °). according to the dark state graph of fig8 c , the required dark state voltage is reduced to approximately 3 . 4 v rms for the same normalized reflectance of approximately 0 . 0001 . in another example , fig9 a , 9b and 9 c are graphs of the voltage - dependent reflectance of a left - handed approximately 50 ° tn cell with dδn = 0 . 35 μm at different polarizer angles for green light ( λ = approximately 550 nm ) wherein the solid line represents the results of the prior art with polarizer angle β = approximately 25 °. still assuming that the pbs has a limited extinction ratio of er = 1000 : 1 and the normalized reflectance is r = 0 . 0001 , according to the graphs , the prior arts require approximately 5 . 0 v rms to get a contrast ratio of using the present invention to obtain the same contrast ratio , β is set to β = 26 . 5 ° instead of approximately 25 °. referring to the dark state graph of fig9 c , required dark state voltage is reduced to approximately 3 . 4 v rms . like the previous examples , fig1 a , 10b and 10 c are graphs of the electro - optical performance showing the voltage - dependent reflectance of a left - handed approximately 45 ° tn cell with dδn = 0 . 355 μm at various polarizer angles for a green light ( λ = approximately 550 nm ) where the solid line represents the results of the prior art with polarizer angle β = approximately 22 . 5 °. still assuming that the pbs has a limited extinction ratio of er = 1000 : 1 and the normalized reflectance is r = approximately 0 . 0002 , from the dark state graph of fig1 c , an applied voltage of approximately 4 . 7 v rms is required to achieve a contrast ratio of in the prior art . using the present invention , to obtain the same contrast ratio the polarizer angle β is set to and according to the graph of fig1 c , the required dark state voltage decreases to approximately 3 . 4 v rms to achieve the same contrast ratio of 833 : 1 . additional examples are shown in fig1 a , 11b and 11 c for left - handedness 40 ° case , fig1 a - 12c for left - handedness approximately 65 ° case and fig1 a - 13c for left - handedness approximately 70 ° case . like the previous examples , the solid line in these figures represents the electro - optical performance curve according to the prior art . from the examples , it is obvious that by shifting the polarizer angle β angle away from the bisector used for the prior art , a lower applied voltage is required to obtain the same contrast ratio . alternatively , if the same driving voltage is selected , using the present invention a much higher contrast ratio is obtained . the above described examples illustrate that for a left - hand twist liquid crystal layer with twist angle φ & gt ; 0 , polarizer angle β is in the range of φ / 2 & lt ; β & lt ;( φ / 2 + 15 °) or ( φ / 2 ± 90 °)& lt ; β & lt ;( φ / 2 + 15 °± 90 °). following the approaches for the left - handed twist liquid crystal layer described above , for a right - handed twist liquid crystal layer with twist angle φ & lt ; 0 , the polarizer angle β is in the range of ( φ / 2 − 15 °)& lt ; β & lt ; φ / 2 or ( φ / 2 − 15 °± 90 °)& lt ; β & lt ;( φ / 2 ± 90 °). in summary , compared to the prior art , the present invention of reflective liquid crystal valve for projection display positions the entrance polarization direction of pbs at an angle that deviates from the bisector of the twist angle to achieve the same contrast ratio at a lower driving voltage . on the other hand , when the same low driving voltage is applied to the prior art configuration and the configuration of the present invention , the contrast ratio obtained in the configuration of the present invention is much higher than that achieved by the prior art . such a low driving voltage in the present invention eventually leads to low fringing field effect in the reflective tn - lc cell for projection display . as a result , a high image quality projection display with low driving voltage and high contrast ratio is ensured . while the invention has been described , disclosed , illustrated and shown in various terms of certain embodiments or modifications which it has presumed in practice , the scope of the invention is not intended to be , nor should it be deemed to be , limited thereby and such other modifications or embodiments as may be suggested by the teachings herein are particularly reserved especially as they fall within the breadth and scope of the claims here appended .