Improvement of the performance of thetwisted-nematic liquid-crystal display

as a phase modulator

Baiheng Ma,1,2 Baoli Yao,1,* Ze Li,1,2 and Tong Ye1

1State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences, Xi’an 710119, China

2Graduate School of the Chinese Academy of Sciences, Beijing 100039, China

*Corresponding author: yaobl@opt.ac.cn

Received 4 January 2011; revised 11 April 2011; accepted 11 April 2011;posted 14 April 2011 (Doc. ID 140395); published 3 June 2011

A twisted-nematic liquid-crystal display (TN-LCD) placed between two linear polarizers (P) generallyproduces coupled intensity and phase modulations. For the purpose of phase-only modulation, quar-ter-wave plates (QWPs) are often used in front of or behind the LCD. In this paper, we demonstratetheoretically and experimentally the QWPs’ effect on the modulation properties of the TN-LCD basedon the general Jones matrix descriptions for all the devices, which circumvents the inconvenience of thetraditional method on the basis of the TN-LCD’s internal parameters. We prove that the phase modula-tion depth of the TN-LCD can be further increased in the configuration of P1-QWP1-LCD-QWP2-P2 witheach component properly oriented, provided that the mean intensity transmission is decreased to a lowerlevel. By observing the diffracted patterns of the Ronchi phase grating or blazed grating addressed ontothe TN-LCD, we verify the validity of the proposed method. Improved reconstructed image quality fromthe kinoform loaded on the TN-LCD is obtained in this configuration. This approach is valuable when theTN-LCD is employed as a phase modulator, especially for the modern, thinner TN-LCD. © 2011 OpticalSociety of AmericaOCIS codes: 060.5060, 230.6120, 230.3720.

1. Introduction

Recently, phase-only modulation by the liquid-crystal (LC) spatial light modulator has increasingpotential use in many fields, e.g., in holographic op-tical tweezers [1], beam shaping [2], and the opticalcorrelator [3]. Among all kinds of LC devices, thetwisted-nematic liquid-crystal display (TN-LCD) isextensively studied and utilized due to its availabil-ity and relatively lower price resulting from its wideapplication in panel display and projection systems.Unfortunately, coupled intensity and phase modula-tions arise because of the LCD’s inherent twist mo-lecular align structures, evoking many approaches

proposed to optimization of the phase modulationresponse of TN-LCD.

For the early TN-LCD with a thick LC layer, it ispossible to get good phase-only modulation by simplyplacing the LCD between two linear polarizers prop-erly oriented and keeping the applied voltage belowthe optical threshold [4,5]. However, the LC layer be-comes thinner and thinner to pursue a higher framerate and resolution, and consequently the simpleconfiguration mentioned above cannot offer suffi-cient phase modulation depth (PMD) in such a smallsignal range. To avoid this drawback, special polar-ization states, e.g., eigenpolarization states [6] andequiazimuth polarization [7], are employed to getbetter phase-only modulation by these thin devices.These special polarization states are demonstratedto be elliptical polarization, and consequently

0003-6935/11/172588-06$15.00/0© 2011 Optical Society of America

2588 APPLIED OPTICS / Vol. 50, No. 17 / 10 June 2011

quarter-wave plates (QWPs) are often used in frontof or behind the LCD to generate and detect thesepolarization states besides two linear polarizers. TheJones or Mueller description [8] is necessary for thedetermination of each device’s orientation. The tradi-tional Jones models [9–13] for TN-LCD is based onthe internal parameters of the LC layer, e.g., theorientations of LC molecules at each surface andthe birefringence of the material, which may lead toinconvenience in practice use because these param-eters are usually not available for the commercialproducts and are difficult to determine precisely.An ingenious approach proposed byMoreno et al. [14]is to determine the general Jones matrix for theTN-LCD by a series of intensity and phase measure-ments, and we [15] improved this method by makingit much simpler and more accurate.

In our previous paper [16], we theoretically calcu-lated the modulation properties of the TN-LCD inthree configurations, of which null, one, and twoQWPs are used, respectively, besides two polarizers.In this paper, we present some experimental resultsto confirm the validity of our numerical methods anddemonstrate how the QWPs influence the modula-tion properties of the TN-LCD for phase-only modu-lation purposes. Finally, we prove that the PMD ofthe TN-LCD can be further extended by reducingthe mean intensity transmission (IT), which is veryuseful when the TN-LCD is used as a phase modu-lator and the ratio between the intensities of the de-sired diffracted order relative to the other diffractedorders is required to be higher. Our results arequalitatively the same as Martínez et al.’s work [17],in which they used the traditional Jones descriptionsfor TN-LCD and the method of eigenpolarizationstates.

2. Theoretical Modeling

Figure 1 is a schematic of a TN-LCD placed betweena polarization state generator (PSG) and a polariza-tion detector (PSD), and both the PSG and PSD arecomposed of a linear polarizer and a QWP. The de-tailed theoretical description has been presented inour previous works [15,16], and here we just reviewit briefly. The Jones descriptions for TN-LCD, PSG,and PSD are

M ¼ c expð−jβÞ�

X − jY Z − jW−Z − jW X þ jY

�; ð1:1Þ

jJ1i ¼ jχ1;ϕ1i ¼�

cosðχ1Þsinðχ1Þ expðjϕ1Þ

�; ð1:2Þ

hJ2j ¼ hχ2;ϕ2j ¼ ðcosðχ2Þ sinðχ2Þ expðjϕ2ÞÞ; ð1:3Þrespectively, and the meanings of all the parametersare illustrated in [15]. The coefficients X, Y , Z, W,and β are exclusive for a specific TN-LCD, and theyhave been calibrated by a series of intensity mea-surement and interferometric methods in [15]. Thesecoefficients are of no direct relationship with theLC layer’s internal parameters, and what we consid-er is just their variations with the addressed graylevel (GL).

The Jones vector of the transmitted light can besimply described as

jJi ¼ jχ2; 0ihJ2jMjJ1i ¼ jχ2; 0ihχ2;ϕ2jMjχ1;ϕ1i¼ Fðχ1;ϕ1; χ2;ϕ2Þ: ð2Þ

It is obvious that the phase shift and intensity of thetransmitted light are only related to the four para-meters χ1, ϕ1, χ2, and ϕ2 determined by the PSGand PSD except for M. As a result, the task to getthe desired modulation response is simplified to finda proper parameter combination (χ1;ϕ1; χ2;ϕ2) by thenumerical method, and the detailed analytic expres-sion is presented in [16], in which we calculated outsome potential results for phase-only modulation foreach configuration. Nowwe will present some experi-ment results to verify the validity of our method.

3. Experimental Results and Discussion

The transmission-type 1:3 in: TN-LCD we used is aproduct of Sony Corporation, which has 1024 × 768pixels with 25:8 μm× 25:8 μm pixel size. The phaseshift induced by the TN-LCD is measured by aMach–Zehnder interferometer [14]. A linearly polar-ized He–Ne laser (λ ¼ 632:8nm) is employed toilluminate the TN-LCD placed in one path of theinterferometer. Two parts of equally divided TN-LCD are addressed with different GL signals, ofwhich one is the reference (GL ¼ 0), and the otheris the GL to be measured. The resulting phase shiftbetween the two GL signals then can be obtained bycalculating the fringe displacement on the interfer-ence plane.

It should be noted that the vector jϕ1; χ1i does re-present a polarization state generated by the PSG,but jϕ1; χ1i does not indicate the practical orienta-tions of the linear polarizer P1 and the QWP1directly, and the same issue exists for the PSD.For specific polarization states jϕ1; χ1i and hϕ2; χ2j,the orientations of the linear polarizers and QWPsare discussed in detail in [18]. We employ θ1, θ2,

Fig. 1. (Color online) Schematic of the setup to obtain phase-onlymodulation by TN-LCD.

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θQWP1, and θQWP2, respectively, to indicate the orien-tations of the linear polarizers’ transmission axis andthe QWPs’ slow axis with respect to the laboratoryreference frame.

The curves of the phase shifts and normalized in-tensities for the four optimized configurations aremeasured, and the corresponding results are shownin Figs. 2(a)–2(d), respectively, which coincide wellwith the theoretical prediction. Generally, phase-only modulation means a large PMD and a flatand high IT throughout the GL range, which is thecriterion to judge the performance of the TN-LCD forphase-only modulation. In the absence of the QWPsshown in Fig. 2(a), the PMD is only about 0:7π, andthe IT is of great fluctuation. This indicates that thissimple configuration of P1-LCD-P2 fails to offer goodphase-only modulation. While in Fig. 2(b) and 2(c),when a QWP is placed in front of or behind theLCD, the PMD is nearly doubled and the IT is muchflatter, but unfortunately, the mean IT is reduced tobe about 50%, which means great energy loss in prac-tice use. Finally, when two QWPs are placed in frontof and behind the LCD, a high and flat IT curve isobtained with a PMD of 1:3π. Apparently, the config-uration P1-QWP1-LCD-QWP2-P2 with each compo-nent properly oriented is capable of offering thebest phase-only modulation.

Traditionally, the eigenpolarization state of theTN-LCD is employed to obtain phase-only modula-tion [6,17,19,20]. The eigenpolarization state forthe TN-LCD is an elliptical polarization. The ellipti-city of the transmitted eigenvector undergoes nochanges during the LC layer and only the major andthe minor axes are rotated with the twist angle, andconsequently by properly arranging the PSD, we canget good phase-only modulation response. The deter-mination of the eigenpolarization state is based onthe Jones description of the TN-LCD, for which theinternal parameters of the TN-LCD is needed. Thisis a heavy workload, and it may be an inconveniencefor commercial products. For instance, it is compli-cated to obtain the birefringence of the LC layersbecause it is related to the orientations of the LCmolecules changing with the GL signals addressedto the TN-LCD, which is difficult to describe precisely[12]. As a result, an average eigenvector is defined asan approximation in practical use, which is a fataldefect leading to the difference between the real mod-ulation properties and the ideal eigenpolarizationstate’s response. In contrast, our method is mucheasier in practical use, because it simplifies the com-plicated procedure mentioned above, and the deter-mination of each component’s orientation is carriedout by simple numerical simulations.

However, it can be found that even in the lastconfiguration [Fig. 2(d)], the PMD of the TN-LCDis much less than the ideal value 2π for TN-LCDto work as an ideal phase modulator. Recently,Martínez et al. [17] proposed a compromised methodto increase the PMD by reducing the average ITvalue, in which they employed a proper polarization

state composed of the two traditional eigenpolariza-tion states of the TN-LCD for this purpose. Here wedemonstrate this by a much simpler approach.Generally, a lower IT leads to the loss in light energy,

Fig. 2. (Color online) Comparison of light modulation propertiesof TN-LCD in four optimized configurations for phase-only modu-lation. (a) χ1 ¼ −23°, χ2 ¼ 12°, ϕ1 ¼ ϕ2 ¼ 0, correspondingly, θ1 ¼−23°, θ2 ¼ 12°, and no QWP is used. (b) χ1 ¼ 36°, χ2 ¼ 23°, ϕ1 ¼90°, ϕ2 ¼ 0, correspondingly, θ1 ¼ 36°, θ2 ¼ 23°, θQWP1 ¼ 0° andonly QWP1 is used. (c) χ1 ¼ −18°, χ2 ¼ 49°, ϕ1 ¼ 0, ϕ2 ¼ 55°, corre-spondingly, θ1 ¼ −18°, θ2 ¼ 49°, θQWP2 ¼ 22° and only QWP2 isused. (d) χ1 ¼ 38°, χ2 ¼ −35°, ϕ1 ¼ 90°, ϕ2 ¼ 48°, correspondingly,θ1 ¼ 38°, θ2 ¼ −35°, θQWP1 ¼ 0°, θQWP2 ¼ −13° and both QWP1 andQWP2 are used.

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and consequently we usually restrict the IT to behigher than a certain value in simulation for search-ing the proper orientation for each component. In or-der to get a larger PMD, we can simply adjust thecriterion in the procedure of optimization to reducethe weight of the average IT, and different optimizedresults can be obtained. Figure 3 shows our opti-mized results. The phase modulation is enlarged tobe about 1:8π, and the average IT is reduced to be15% in the configuration of P1-QWP1-LCD-QWP2-P2 with different orientations from Fig. 2(d). Thisresult is qualitatively the same as Martínez’s works;however, we simplify the complicated theory analysisand it becomes much easier.

In addition, we will show how the TN-LCD withlarger PMD and reduced IT can increase the relativediffraction efficiency and improve the performance ofthe TN-LCD when it is used as a phase modulator.First, we address the TN-LCD to form a 0-π Ronchiphase grating shown in Fig. 4(a). Theoretically, boththe þ1st and −1st diffracted order pattern of thisphase grating should have about 40.5% of the totalenergy, respectively, and the intensity of the zero-order pattern should be zero. However, as shownin Fig. 4(b), the zero-order pattern is even strongerthan the �1st order because of the diffraction ofthe periodic structure formed by the TN-LCD’s inher-ent pixels, which is undesirable in practice. Then weaddress the TN-LCD to form a blazed grating.Figure 5(a) is a schematic of the blazed gratingand the corresponding GL signal addressing to theTN-LCD. It is well known that the blazed gratingis capable of transferring all the emerging energyonto the þ1st diffraction order if the induced phaseshift linearly changes from 0 to 2π in a period. Inother words, if the TN-LCD can provide a flat ITversus GL signal, the deeper PMD the TN-LCD canoffer, the stronger the þ1st diffraction order will be.The diffracted patterns of two configurations withdifferent PMD are shown in Figs. 5(b) and 5(c), re-spectively, which correspond to the configurationsshown in Figs. 2(d) and 3, respectively. It can be seenthat the þ1st diffraction order pattern in Fig. 5(c) ishigher in intensity than that in Fig. 5(b) because ofthe deeper PMD, although the average IT is much

lower in the configuration of Fig. 5(c). In Fig. 5(b),the zero-order pattern is still strong due to the lim-ited PMD. These facts prove that when the TN-LCDis used as a diffractive device, the ratio between theintensity at the desired diffraction order relative tothe rest of undesirable orders will be greatly in-creased by enlarging the PMD of the TN-LCD. Thiscompromised approach is of more importance for themodern, thinner TN-LCD having a reduced PMD.

Finally, we present another example to show thevirtue of this technique by hologram reconstruction.Figure 6 schematically shows the experimentalsetup. A linearly polarized He–Ne laser beam, con-verted to circular polarization by the QWP being

Fig. 3. (Color online) Configuration of P1-QWP1-LCD-QWP2-A2

with extended PMD and reduced mean IT. χ1 ¼ −24°, χ2 ¼ −83°,ϕ1 ¼ 19°, ϕ2 ¼ −8°, correspondingly, θ1 ¼ −24°, θ2 ¼ −83°, θQWP1 ¼−17°, θQWP2 ¼ 8°.

Fig. 4. Schematic of (a) Ronchi phase grating and (b) diffractionpatterns when addressing it to the TN-LCD. The phase step φ hereis set to be π.

Fig. 5. Schematic of (a) blazed grating and (b) diffraction patternswhen addressing it to the TN-LCD. (b) δdepth ¼ 1:3π. (c) δdepth ¼1:8π.

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properly oriented, is expanded and collimated to illu-minate the TN-LCD placed between the PSG andPSD. The TN-LCD is addressed by the optimizedkinoform generated by the Gerchberg–Saxton algo-rithm [21], and then a Fourier-transform lens LF isfollowed to reconstruct the hologram. A small hole isplaced in the back focal plane of the LF to block otherdiffracted orders except for the zero order, and thenlens LP projects the reconstructed image onto theCCD target. Figures 7(a1), 7(b1) are the two origi-nals, and 7(a2), 7(b2) are the two optimized kino-forms, correspondingly. When the LCD is workingin the configuration of Fig. 2(d), the reconstructionresults are shown in Figs. 7(a3), 7(b3), respectively,and Figs. 7(a4), 7(b4) show the reconstruction resultswhen the LCD is working in the configuration ofFig. 3. In the process of optimizing the kinoform,the phase modulation range of the diffractive opticalelement is assumed to be 2π, but the maximum PMDoffered by our TN-LCD is less than 2π, which meansthat the reconstruction quality will be lower than thetheoretical prediction. However, comparing Figs. 7(a3), 7(b3), it is obvious that the reconstruction re-sults of Figs. 7(a4), 7(b4) are of a higher quality,and the intensities of the zero order spots are muchweaker. These results demonstrate that the con-figuration shown in Fig. 3 is better for phase-onlymodulation purposes, especially when the absolute

intensity of the diffraction pattern is not inten-sively desired.

4. Conclusions

Instead of the traditional complicated eigenpolari-zation state analysis on the basis of the TN-LCD’smicrocosmic parameters, this paper experimentallyverified that the modulation properties of the TN-LCD for phase-only modulation can be greatly im-proved by adding QWPs in front of or behind theLCD based on the general Jones description of TN-LCD. The experimental results coincide well withour predictions, and the best result is obtained in theconfiguration of P1-QWP1-LCD-QWP2-P2 with eachcomponent properly oriented. In addition, we demon-strate that the PMD can be further extended by re-ducing the IT, which is valuable for the modern thinTN-LCD when it is designed as a phase modulator.This paper only offers a method to improve the per-formance of TN-LCD as a phase modulator with lessregard to the absolute IT. To obtain perfect purephase modulation with high IT, it may be necessaryto resort to the improvement of the fabrication of theLCD, e.g., more sophisticated hardware and new LCmaterials with a higher birefringence index.

This research is supported by the NaturalScience Foundation of China (NSFC) (10874240and 61077005).

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