A simple and efficient compensation method for the full correction of both the anisotropic and isotropic nonuniformity of the light phase retardance in a liquid crystal (LC) layer is presented. This is achieved by accurate measurement of the spatial variation of the LC layer’s thickness with the help of a calibrated liquid crystal wedge, rather than solely relying on the light intensity profile recorded using two crossed polarizers. Local phase retardance as a function of the applied voltage is calculated with its LC thickness and a set of reference data measured from the intensity of the reflected light using two crossed polarizers. Compensation of the corresponding phase nonuniformity is realized by applying adjusted local voltage signals for different grey levels. To demonstrate its effectiveness, the proposed method is applied to improve the performance of a phase-only liquid crystal on silicon (LCOS) spatial light modulator (SLM). The power of the first diffraction order measured with the binary phase gratings compensated by this method is compared with that compensated by the conventional crossed-polarizer method. The results show that the phase compensation method proposed here can increase the dynamic range of the first order diffraction power significantly from 15~21 dB to over 38 dB, while the crossed-polarizer method can only increase it to 23 dB.
© 2014 Optical Society of America
Light modulating capability of liquid crystals (LCs) has been known since the early twentieth century. By constructing a suitable spatial phase modulation profile, light can be steered to go to a desired direction or to form an arbitrary replay field. Liquid crystal on silicon (LCOS) technology has been an active research area since the early 1980’s. This is because the combination of the highly functional complementary metal oxide semiconductor (CMOS) integrated circuits and non-linear optical modulation of liquid crystals provides an unique opportunity in realizing powerful spatial phase modulators (SLMs) with high performance driving circuitry, high pixel fill factor, and scalability of feature sizes [1–3]. Such advantages have led to a wide range of applications, e.g. head mounted displays , optical tweezers , holographic projection  and wavelength selective switches [7–9].
The main reason for the variation of phase retardance from the ideal situation in an LCOS SLM is the thickness variation in its liquid crystal layer. It is usually caused by the curvature difference between the silicon backplane and the glass cover plane and the presence of dust particles with a greatest size larger than the space size (which can modify the local thickness of both the LC layer and alignment layers). Other factors such as the thickness variation of all other isotropic materials including the cover glass can also affect the phase retardance. For the applications with incoherent lights, like liquid crystal displays, the phase nonuniformity is generally less important because the LCOS SLMs there are used to modulate the amplitude of the incident light only. However, when the LCOS SLMs are used with coherent lights for phase modulations, the phase nonuniformity can severely affect their performance and an appropriate compensation procedure is necessary for achieving good results.
To calibrate and compensate the phase retardance nonuniformity of a phase-only LCOS device, different methods have been developed during the last few decades. The crossed-polarizer (C-P) method has been conventionally used to calibrate the phase retardance due to the anisotropic effect in the LC layer . It measures and compensates the local phase retardance difference between the polarization components along the ordinary and extraordinary directions of the LC molecules in their initial aligned state. However, this method cannot correct the part of phase variation due to the isotropic effect of different layer thickness, which is also important as the beam incident on the phase-only SLM is usually linear polarized along the extraordinary direction of the LC layer. Interferometer based methods have also been used to calibrate the phase retardance variation by analyzing the resulting interference fringes [11–13]. However, these methods have a number of limitations including high cost of the optical system, strict optical calibration, high sensitivity to the environment conditions and time-consuming measurement procedure. In addition, the resulting interference fringes are related to not only the phase retardance distortion due to the LCOS SLM, but also the aberration caused by other optical components in the test system. It is challenging to distinguish the portion due to the LCOS SLM itself. Moreover, an accurate compensation at the corners of a square or rectangle shaped SLM is limited due to the circular nature of the Zernike polynomials, on which the general method used for aberration analysis is based [11,12]. A diffraction-based compensation method was also developed using a Fourier diffraction pattern analysis to build a look-up-table (LUT) for the calibration . This method is based on loading binary phase gratings on the LCOS device and measuring the intensities of diffraction orders in the Fourier plane. The phase variation is measured at selected points within the target area and a two-dimensional fitting is performed under the assumption that the phase changes are all non-abrupt. However, because the phase retardance curves of these areas with different liquid crystal thickness are all set to start at the same level, the principle of this method is actually similar to that of the conventional C-P method.
In this paper, we present an efficient and robust method which can fully compensate the phase retardance variation due to both the anisotropic and isotropic nonuniformity in a liquid crystal layer. To begin with, we will expound the measurement and calculation of phase retardance as a function of grey level. This will be followed by a brief explanation about the LC layer thickness calibration process. After that, the theoretical basis of the compensation method will be explained. Finally, the effectiveness of this method will be demonstarted by applying it to compensate the binary phase gratings uploaded on a phase-only LCOS device.
The phase-only LCOS SLM used in this work is a parallel aligned device with 1280 × 720 pixels and a pixel pitch of 15μm . The device is filled with a commercial nematic liquid crystal mixture (Merck BL037) and the average thickness of the liquid crystal layer is 2.5μm.
2.1 Measurement of phase retardance
The phase retardance as a function of the applied voltage is firstly measured with a setup using two crossed polarizers. The director of the nematic liquid crystal is 45° with respect to crossed polarizers in the optical system, and wavelength of incident light is 532nm. The voltage applied to the LC layer over a pixelated electrode is expressed as grey levels, g, using a linear gamma variation:
In this crossed-polarizer setup, the difference in phase retardance between the polarization components along the ordinary and extraordinary directions of the LC layer is referred as the C-P phase retardance, ΔΦLC. It is due to the anisotropic effect in the LC layer and its nonuniformity can be translated into the intensity variation of the outcoming light going through the two crossed polarizers. As the grey level across the device is changed from 0 to 255, the recorded light intensity for a pixel on the LCOS SLM oscillates between its minimum and maximum, as shown in Fig. 1(a). The relationship between the normalized light intensity and the C-P phase retardance is described by Eq. (2), and the corresponding C-P phase retardance can be calculated from Eq. (3). The calculated phase retardance as a function of grey levels is shown in Fig. 1(b) and it is referred as the C-P phase curve.
Since Δn(V) is the difference between n(V) and the ordinary refractive index no, the C-P phase retardance is actually the phase retardance with respect to a reference phase, Φ0, as a result of the anisotropic component of the LC layer. In contrast, the S-P phase retardance describes the full phase retardance as the light goes through an LC layer, including both the anisotropic and isotropic contributions. The relationship between the S-P and C-P phase retardance is described by Eq. (6):
Measurements of the birefringence and refractive index for different wavelengths and temperatures for BL037 are performed and the result shows Δn(0) = 0.282 and no = 1.533 at 532 nm and 30°C. If we know the thickness distribution of the LC layer, the S-P phase retardance as a function of grey levels, referred as the S-P phase curve, can be calculated using Eq. (6) from the corresponding C-P phase retardance.
2.2 Calibration of LC layer thickness
The thickness profile of the LC layer in the LCOS SLM is carried out with the assistance of an LC wedge calibrated by white light spectrum technique. The liquid crystal wedge is assembled with a glass cover plate and an Aluminum-coated silicon backplane, and filled with the same liquid crystal material used in the LCOS SLM. With the LC wedge, a reference LUT for the birefringence color in relation to the LC thickness is generated. Birefringence photos of LCOS devices are taken on the crossed-polarizer setup with a white light source, from which the corresponding thickness distribution can be calculated using the LUT. Figures 2(a) and 2(b) show a typical birefringence photo of the LCOS SLM and the corresponding contour of the LC layer, respectively.
2.3 Compensation theory
The wavefront of a linear polarized uniform light through an LC layer with a nonuniform thickness is shown in Fig. 3 as the uncompensated wavefront. The corresponding wavefront after compensating the nonuniformity of the C-P phase retardance is illustrated as the C-P compensated wavefront which will reach the C-P compensation limit as the applied voltage becomes large. As the C-P phase retardance is only the part of the full phase retardance, the C-P compensation method will only be able to correct the wavefront distortion due to the LC anisotropy, leaving a thickness dependent wavefront distortion related to the LC isotropic part untouched. In order to correct the distorted wavefront fully, we propose to compensate for the nonuniformity of the S-P phase retardance and we refer it as the S-P compensation method.
With a reference C-P phase curve and the thickness distribution of the LC layer, the C-P phase curve for each pixel of the LCOS SLM can be calculated using Eq. (4). As an example, the C-P phase curves for three pixels with different LC layer thicknesses are calculated and plotted in Fig. 4(a). Subsequently, a given phase retardance can be assigned to the corresponding grey level for each pixel, as shown by the dash line in Fig. 4(a).
The S-P compensation method calculates the S-P phase curve for each pixel using Eq. (5). However, as shown in Fig. 4(b), the S-P phase retardance difference between different pixels is much larger than the corresponding C-P phase retardance difference and can be larger than 2π. As a result, it may be impossible to correct the S-P phase variation in the same way as the C-P compensation method. Instead, since the phase retardance has a period of 2π, we can substrate the uncompensated wavefront by 2Nπ (N is an integer) to construct an equivalent uncompensated wavefront as shown in Fig. 3. The phase retardance difference between different equivalent uncompensated wavefronts is within 2π, which makes it possible to compensate the S-P phase retardance variation by applying modified grey levels for each pixel. The equivalent and actual wavefronts as compensated by the S-P method are also shown in Fig. 3. Finally, Fig. 5 shows the distribution of the adjusted grey levels as compensated by the S-P method, which can be load onto the LCOS SLM to generate a planar wavefront.
3. Diffraction Measurement and Results
3.1 Optical system
In order to demonstrate the effectiveness of the proposed S-P compensation methods, a diffraction test system is used to measure the power response of the first diffraction order from the binary phase gratings loaded on the LCOS SLM. Figure 6 shows the schematic of the diffraction test system. A 532nm beam from the laser diode goes through a circular aperture, which blocks the scattered light from the laser diode optics. The beam then passes through a polarizer and becomes linearly polarized, with the polarization direction parallel to the extraordinary direction of the LC layer inside the LCOS SLM. This is followed by a two lens magnification system, which enlarges the beam radius three times, from 1.05 mm (70 pixels) to 3.15mm (210 pixels). The beam radius was measured by the knife-edge method , and the beam profile could be approximated by a Gaussian distribution. After the magnification optics, half of the beam passes through a beam splitter and hits the target zone of the LCOS SLM, while the other half is reflected into a reference photodiode which is used to monitor the fluctuation of input optical power. The light incident on the LCOS SLM is diffracted by the binary phase grating loaded on the device, and the subsequent wavefront is focused by a Fourier transform lens into different diffraction orders. An adjustable aperture is placed in the focal plane of the Fourier transform lens to observe the power response of a specific diffraction order. The size and the positon of the aperture are adjusted with the aid of an imaging system which consists of an imaging lens and a CCD camera. Finally, the optical power of the light passing through the aperture is measured with a power meter placed between the adjustable aperture and the imaging lens.
3.2 Aperture size and dynamic range calibration
In general, the dynamic range is defined as the ratio of the maximum and minimum light intensities. A high dynamic range can bring the benefits of high signal to noise ratio and low crosstalk. In order to maximize dynamic range, a calibration for the aperture size is performed. The aperture is set at the position of + 1st diffraction order of the binary gratings with the beam in the center of the aperture window. Figure 7 shows the intensity variation of 0π, 1π phase depth and the dynamic range with different aperture sizes. The intensity of the 1π phase depth grows with the aperture size and then stabilizes at a certain level, while the intensity of the 0π phase depth increases with aperture size due to the scattered light from LCOS device. The difference between them represents the dynamic range which reaches a maximum of 40 dBm as shown in Fig. 7 when the aperture window size is around 14% of the full opening .
3.3 Diffraction measurement results
The power response of the first diffraction order was measured for three scenarios with different binary phase gratings loaded onto the LCOS SLM being uncompensated, compensated by the C-P method and compensated by the S-P method, respectively. The diffracted power as a function of the phase retardance can be described as:
Figure 8 shows the normalized intensity of the first diffraction order on a log scale against the calculated phase depth. The three curves in Fig. 8 correspond to the above mentioned three scenarios. They all start at around −38 to −39 dB and then increase to their first maximum which is used as the corresponding normalization factor in each cases. The results at the phase depths of 0, 1, 2, 3 and 4π are listed in Table 1. They show that the normalized intensities of the + 1 order for the original uncompensated binary gratings at the phase depth of 2π and 4π are −21.64 dB and −15.37 dB, respectively. The C-P compensation method can lower these minimums to the level of −23dB, while the S-P compensation method can reduce them further by 15 dB to the level of −38dB.
4. Discussions and conclusions
An efficient and versatile compensation method for the phase nonuniformity due to both the anisotropic and isotropic variations in a liquid crystal layer was presented. The conventional crossed-polarizer method compensates only the phase nonuniformity due to the anisotropic contribution and thus manages only a limited enhancement of the dynamic range of the binary phase grating diffraction power by around 8 dB over that of the uncompensated case. The single polarizer method as proposed above compensates the full phase nonuniformity in a liquid crystal layer, which result in a significant enhancement of the dynamic range of the first diffraction order over 23 dB. This method requires no special optical components or experiment settings, thus makes it suitable for automatic measurement and calibration. Moreover, it includes a process of LC layer thickness calibration, which can be used directly for the thickness profiling across a whole LCOS SLM without a time-consuming scanning procedure. It is worth to note that this method is focused on compensating the phase nonuniformity in the liquid crystal layer only and further improvement of the phase uniformity of an LCOS SLM can be achieved by investigating the influence of the thickness variation of the cover glass and the curvature of the silicon back plane, for which an absolute phase reference will be needed.
The authors thank H. Xu and I. Medina-Salazar for their technical support and the helpful comments and suggestions of the reviewers. L. Teng would like to thank the financial support of China Scholarship Council for his visit to University of Cambridge.
References and links
1. I. Underwood, D. G. Vass, R. M. Sillitto, G. Bradford, N. E. Fancey, A. O. Al-Chalabi, M. J. H. Birch, W. A. Crossland, A. P. Sparks, and S. G. Latham, “A high performance spatial light modulator,” Proc. SPIE 1562, 107–115 (1991). [CrossRef]
2. N. Collings, W. A. Crossland, P. J. Ayliffe, D. G. Vass, and I. Underwood, “Evolutionary development of advanced liquid crystal spatial light modulators,” Appl. Opt. 28(22), 4740–4747 (1989). [CrossRef] [PubMed]
3. N. Collings, T. Davey, J. Christmas, D. Chu, and W. A. Crossland, “The applications and technology of phase-only liquid crystal on silicon devices,” J. Disp. Technol. 7(3), 112–119 (2011). [CrossRef]
4. A. A. Cameron, “Optical waveguide technology and its application in head mounted displays,” Proc. SPIE 8383, 83830E (2012). [CrossRef]
5. A. Hermerschmidt, S. Krüger, T. Haist, S. Zwick, M. Warber, and W. Osten, “Holographic optical tweezers with real-time hologram calculation using a phase-only modulating LCOS-based SLM at 1064 nm,” Proc. SPIE 6905, 690508 (2008). [CrossRef]
6. H. C. Lin, N. Collings, M. S. Chen, and Y. H. Lin, “A holographic projection system with an electrically tuning and continuously adjustable optical zoom,” Opt. Express 20(25), 27222–27229 (2012). [CrossRef] [PubMed]
7. N. Wolffer, B. Vinouze, and P. Gravey, “Holographic switching between single mode fibres based on electrically addressed nematic liquid crystal gratings with high deflection accuracy,” Proc. SPIE 3490, 297–300 (1998). [CrossRef]
8. W. A. Crossland, I. G. Manolis, M. M. Redmond, K. L. Tan, T. D. Wilkinson, M. J. Holmes, T. R. Parker, H. H. Chu, J. Croucher, V. A. Handerek, S. T. Warr, B. Robertson, I. G. Bonas, R. Franklin, C. Stace, H. J. White, R. A. Woolley, and G. Henshall, “Holographic optical switching: the ‘ROSES’ demonstrator,” J. Lightwave Technol. 18(12), 1845–1854 (2000). [CrossRef]
9. B. Robertson, H. Yang, M. M. Redmond, N. Collings, J. R. Moore, J. Liu, A. M. Jeziorska-Chapman, M. Pivnenko, S. Lee, A. Wonfor, I. H. White, W. A. Crossland, and D. P. Chu, “Demonstration of multi-casting in a 1 × 9 LCOS wavelength selective switch,” J. Lightwave Technol. 32(3), 402–410 (2014). [CrossRef]
10. D. K. Yang and S. T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006), Chap. 2.
11. J. L. Harriman, A. Linnenberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proc. SPIE 5553, 58–67 (2004). [CrossRef]
12. J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46(23), 5667–5679 (2007). [CrossRef] [PubMed]
14. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. A. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51(17), 3837–3846 (2012). [CrossRef] [PubMed]
15. Z. Zhang, A. M. Jeziorska-Chapman, N. Collings, M. Pivnenko, J. Moore, W. A. Crossland, D. P. Chu, and W. I. Milne, “High quality assembly of phase-only liquid crystal on silicon (LCOS) devices,” J. Disp. Technol. 7(3), 120–126 (2011). [CrossRef]