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Abstract
Phase flickers in the digital liquid crystal on silicon (LCOS) devices employing the pulse width modulation (PWM) driving scheme have a detrimental effect on optical performances, especially in the non-display applications. This paper investigated the relationship between the PWM waveform and the corresponding phase flicker in digital LCOS devices. It has been identified that the magnitude of the phase flicker depends on the pulse patterns in the driving waveform as well as the dynamic response of the liquid crystal molecules at different tilting angles. A simple but generic method has been developed based on these findings, which is able to accurately predict the temporal phase response of the liquid crystal to any PWM waveforms. This method is further used for rapid identifications of low-flicker PWM waveforms, without the need for increasing the complexity of the driving circuitry. The peak-to-peak phase flicker in the LCOS device under our investigation has been reduced by >80% from ∼0.16pi to ∼0.03pi when operating at 30°C.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid crystal on silicon (LCOS) technology [1–3] has the unique capability of spatially modulating the wavefront of an optical beam in a reconfigurable fashion. Although originally developed for the information display applications [4–6], this technology has also been widely used in the optical tweezers [7], laser pulse shaping [8], optical coherence tomography [9], mask-less lithography [10], 3D printing [11] and telecom wavelength selective switches (WSSs) [12].
A typical LCOS device consists of a liquid crystal (LC) layer sandwiched between a glass coverplate and a piece of silicon backplane based on the complementary metal-oxide-semiconductor (CMOS) technology. The silicon backplane has millions of individually addressable reflective electrodes, i.e. pixels. By applying voltage to the pixels, the effective refractive index of the LC molecules can be controlled electrically to spatially modulate the input optical beam, either in its phase [13] or amplitude [14], depending on the LC configuration. In recent years, LCOS devices that only modulate the phase of the input optical beam has become the mainstream option in both display and non-display applications due to its high efficiency [15]. Such devices are referred to as the phase-only LCOS devices.
The LCOS devices can be classified into two categories based on the driving mechanisms. In the analogue LCOS devices [16,17], digital to analogue converters (DACs) are used to generate various voltage levels to individual pixel electrodes to control the LC molecules. The digital LCOS devices [18] utilise the pulse width modulation (PWM) scheme to generate various root-mean-square (RMS) voltage levels, although the pixels electrodes can only generate binary waveforms. The analogue LCOS devices are traditionally associated with higher optical performances, especially in terms of the phase stability [19,20] for the phase-only LCOS devices, whereas the digital LCOS devices have the better scalability towards higher pixel resolutions and frame rates due to the relative simplicity in the driving circuitry [21]. In addition, the digital LCOS devices also have the advantages of lower power consumption and costs [22].
In display applications, the phase flicker can be filtered out by human eye and brain as long as the its frequency is beyond a certain frequency [23], although it might affect the contrast ratio of the displayed images to a certain degree depending on the optical system designs. In non-display applications, however, the negative impact of the phase flicker is more serious. Take the telecom WSSs for example, the phase flicker in the LCOS device imposes a further modulation on the optical signals and introduces crosstalks [24,25], both of which reduce the optical signal to noise ratio (OSNR) and therefore shorten the transmission distance in the fibre networks. In the laser pulse shaping systems based on the LCOS technology, the phase flicker will negatively affect the consistency in pulse shapes [26].
Previous research on the phase flickers in the LCOS devices mainly focuses on the characterisation methods, including the averaged Stokes polarimetric method [27], the diffractive method [28] and the two beam interference method [28]. Characterisation results for some of the commercial LCOS devices have been presented in [29–31]. The reported peak-to-peak phase flicker ranges from 0.2pi to 0.5pi. It has been demonstrated in [24,30,31] the phase flicker can be reduced by cooling the LCOS device to 0 degree or even lower. This is because the LC material usually has high viscosity at lower temperature [32]. However, such low operating temperature significantly increases the response time of the LCOS device. More importantly, it restricts the use of LCOS devices in many applications. Cooling also is also associated high power consumption.
In order to address this problem, this paper will introduce a diffractive method to investigate the relationship between the PWM waveforms and the LC phase response, which can help to identify the origin of the phase flicker in the digital LCOS devices. As a result, a simple and generic method will be proposed to accurately predict the temporal response of the LC molecules to any PWM driving waveforms. This enables a rapid identification of PWM waveforms that can deliver low phase flicker for the room temperature operation. The results will be presented and compared with the default waveforms from the LCOS supplier.
2. Optical system for phase flicker measurement
The diffractive behaviour of the binary gratings was used to evaluate the phase flickers in the LCOS device in this work. In the optical system shown in Fig. 1(a), the input laser (Thorlabs S3FC1550) beam was placed at the front focal plane of the collimating lens (L1) and on its optical axis. The LCOS device was placed on the back focal plane of L1. The beam covers ∼80×80 pixels on the LCOS device. The LCOS would display a series of binary grating phase patterns with a fixed period of T but variable peak-to-valley phase depth (Δ(t)), as shown in Fig. 1(b). In this case, the input beam would be diffracted into the + 1st and −1st diffraction orders equally. The positions of these diffraction orders would remain the same during the measurement as they only depend on the grating period. Their diffraction efficiency would change with respect to the peak-to-valley phase depth (Δ(t)) [33]. The relationship for the ± 1st diffraction orders can be described by Eq. 1.
where Po equals the maximum power possible for the ± 1st diffraction orders, which is 40.5% of the input power in the ideal case. This relationship was also plotted in Fig. 1(c). A high-speed photo-detector (Thorlabs PDA50B2) can be placed at the position of either the + 1st or −1st diffraction order to measure the average power and the temporal power fluctuation. The measurement results can be used to deduce the average phase depth and the phase flickers based on Eq. 1.
Fig. 1. (a) a diffractive optical system for measuring the phase flickers in the LCOS device; (b) the cross-section of the binary grating; (c) the power response of the ± 1st diffraction order to the peak-to-valley phase depth in the binary grating.
This diffractive method for the phase depth and flicker measurement is flexible and easy to align. Unlike the polarimetric method [27], the photo-detector in this system would always receive no power when the voltage is not applied to the LC. This makes the data processing more straightforward. However, it should be noted that the calculated phase flickers can be artificially high in this case when the peak-to-valley phase depth is between 0.8pi and 1.2pi, i.e. when the power curve for the ± 1st diffraction orders turns. This is because a small power fluctuation can be translated into a relative larger phase variation in those conditions. The noise from the high-speed photo-detectors would play a significant role as a result. Nevertheless, the polarimetric method also has such problem albeit at a different phase range, depending on the birefringence of the LC material and the LC cell thickness.
The LCOS device under investigation in this work is based on a JDC SP55 digital backplane [34]. The backplane and its driving circuitry operate at 60 frames per second and allows up to 128 bitplanes within a frame. In other words, the PWM driving waveforms can be divided into 128 time slots, each of which can have either on state or off state. The nematic LC in the device is parallel-aligned for the phase-only operation. The LC alignment layer is made of rubbed polyimide. The LC material has a birefringence of ∼0.2 at 1550 nm. The LC cell thickness is 6 µm, which aims to achieve >2pi phase modulation at 1550 nm wavelength. All the experiments described in this paper was carried out when the LCOS device is operating at 30°C.
3. Origin of the phase flicker
In order to identify the origin of the phase flicker in the digital LCOS device, a series of PWM driving waveforms with variable duty cycles at a fixed frequency of 120 Hz (equals the duration of 64 bitplanes) were applied to the peak area of the binary grating, while a constant off-state voltage is applied to the valley area of the binary. The on-state voltage in the PWM waveform was set as 2.5 V while the off-state voltage was 0.5 V, which was just below the threshold voltage of the LC. Since a constant voltage was applied to the valley area, the LC molecules can be viewed as static in this case. Therefore, the temporal power fluctuation of the + 1st diffraction order can reflect the phase flicker under the specific test PWM waveform.
In our experiment, the duty cycle of the waveform was increased from 0% (0 bitplanes) to 50% (32 bitplanes) in a step of 1.5625% (1 bitplane). Figure 2 gives the examples of the phase responses of the LCOS devices when the duty cycle was at 20.3125% (13 bitplanes) and 32.8125% (21 bitplanes), respectively. It can be seen from Fig. 2 that the phase depth increased in the presence of an on-state pulse. Immediately after the pulse was off, the phase depth continued to increase for a very short period of time (∼0.1 ms) before it started to decrease. The phase depth kept decreasing until the start of the next pulse. Figure 3 plots the relationship between the duty cycle in the test waveforms and the duration (tr) of the phase depth increase due to on-state pulse. The linear relationship observed in Fig. 3 indicates the difference between tr and the pulse duration (ton) stays constant at ∼0.1 ms. Since the duty cycle in the test waveform decides its RMS voltage level, it can also be concluded that the difference between tr and ton is independent of the average phase depth that the LCOS device is operating at.
Fig. 3. The relationship between the duty cycle in the test waveforms and duration (tr) of phase depth increase due to an on-state pulse.
In the two examples given in Fig. 2, the LCOS device was operating at different phase depths. The speed of the temporal phase increase (vr) in the presence of an on-state pulse was faster in the second example shown in the Fig. 2(b), when its average phase depth was higher. The speed of phase decrease (vd) during the off-state pulse was also faster in the second example. The measured values of vr and vd for most of the test driving waveforms are plotted in Fig. 4. It should be noted that the results when the phase depth is between 0.8pi and 1.2pi are not plotted in Fig. 4 due to the uncertainty introduced by the noise from the high-speed photo-detector as explained in the previous section. It can be seen from Fig. 4 that the speed of phase change initially increases with the phase depth that the LCOS device is operating at. This is consistent with our previous work [35,36], which showed the LC molecules responded faster to the change of the electrical field when operating at higher phase depth. As the phase depth increases, however, the resulted phase change introduced by the same amount of angular tilting change of the LC director decreases due to the birefringent nature of the LC molecule. This contributes to the decrease in the vr when the LCOS device is operating at a phase depth >1.2pi. The value of vd seems to be stable under those circumstances. The absolute value of vd is smaller than that of vr, which means the force introduced by the external electrical field is stronger than that from the LC relaxation.
Fig. 4. The speed of phase increase in the presence of an on-state pulse and the speed of phase decrease during an off-state pulse when the LCOS device is operating at different phase depth.
It can be concluded that the RMS voltage levels of a PWM waveform determines the average phase depth that the LCOS device operates at. This average phase depth further influences the temporal phase response to an on-state or off-state pulse. Therefore, the duration of a pulse and the corresponding phase response speed together decides the magnitude of the phase flicker. At lower phase depth, when the LC’s response to a pulse is slow, a long pulse might not cause large flicker. At certain phase depth, however, the temporal phase response can be very sensitive to long pulses and therefore short-pulse sequence is required for low phase flicker operation. These need to be taken into consideration when designing the optimal PWM waveforms.
4. Phase flicker prediction
The temporal phase responses to on/off-state pulses at different phase depths plotted in Fig. 4 can be used to predict the phase flicker caused by PWM driving waveform. The prediction process can be summarised in the following the steps:
- 1. Calculate the RMS voltage level of the PWM driving waveform under investigation.
- 2. Use the calculated RMS voltage level to predict the average phase depth that the LCOS device is going to operate at.
- 3. During an on-state pulse, the phase depth will increase at the corresponding speed measured in Fig. 4.
- 4. When the pulse switches to the off-state, the phase depth will continue to increase at the same speed for 0.1 ms. Then the phase depth will start to decrease at the corresponding speed measured in Fig. 4.
- 5. Repeat Steps 3 and 4 until the last pulse in the PWM waveform under investigation.
Fig. 5. (a)-(e) the predicted and experimentally measured temporal phase responses under test driving waveforms with different frequencies; (f) comparison between the predicted and experimentally measured phase flicker under test driving waveforms with different frequencies. See enlarged view in Visualization 1.
It can also be seen from Fig. 5(f) that the phase flicker decreased as the driving frequency increases. Shorter pulses limit the period of time, during which the LC molecules can oscillate. This ultimately limits the magnitude of the peak-to-peak phase flicker. When the driving frequency increased to 3840 Hz for a PWM waveform with 50% duty cycle, the peak-to-peak phase flick can be reduced to <0.01pi. In order to achieve such phase flicker for multiple unique phase levels, the clock rate need to be significantly higher. If the target is 256 unique phase levels for example, at least eight bitplanes is required during the period of 1/3840 second. This requires the LCOS driving circuitry to be able to support 1024 bitplanes during a frame. The duration for each bitplane is 1/30720 second. Considering the number of pixels that need to be addressed on a LCOS backplane, this requires complicated high-speed driving circuitry with large buffering memories. The power consumption and the cost of the driving circuitry will be significantly increased as well.
5. Waveform optimisation
This work aims to optimise the PWM driving waveform within the constraints of the current driving circuitry, i.e. 128 bitplanes per frame and a frame rate of 60 Hz.
Firstly, a customised bitplane configuration was proposed. This bitplane configuration as shown in Fig. 6 has 128 bitplanes with a uniform duration. Therefore, each of them lasts 1/60/128 second. Taking into account the findings in the previous section, each bitplane has a fixed sub-section that is permanently assigned to either the on-state or off-state. This would prevent the presence of long on-state or off-state pulses. The sub-sections that are permanently assigned to the on-state are shown as white colour in Fig. 6 while those assigned to the off-state are shown as the black colour. It can be seen that most of those sub-sections are permanently assigned to the off-state. Because a long on-state pulse will have bigger impact on the phase flicker due to difference between the absolute values of vr and vd shown in Fig. 4. The grey areas in Fig. 6 corresponds to the sub-sections within the bitplanes that can be switched to either on-state or off-state. The duration of these switchable sub-section varies between each bitplane. This would help fine tune the RMS voltage levels of the PWM waveforms.
128 bitplanes are able to generate 2^128 unique PWM waveforms. It would take extremely long time to experimentally verify all of them and select the ones with low phase flicker. However, the phase flicker prediction method described in the previous section enables rapid identification of PWM waveforms with low phase flicker through computer simulation. By using this method, 256 optimised PWM waveforms were selected to generate unique phase levels between 0 and 2pi in this work. The RMS voltage levels of these 256 PWM waveforms are linearly spaced between 0.67 V and 2.12 V. This voltage range can be adjusted by changing the on-pulse and off-pulse voltage levels. In this work, they are set at 2.5 V and 0.5 V, respectively. The phase responses of these 256 PWM waveforms were measured using the binary diffractive method described in Section 2. Figure 7 shows the relationship between the power of + 1st diffraction order and the phase levels. The actual phase values at different phase levels were derived based on this curve and plotted in Fig. 7 as well. It can be seen that the LCOS is able to achieve 256 unique phase levels between 0 and 2.2pi. It is unsurprising that the phase response is not linear given the RMS voltage levels of the PWM waveforms are linearly spaced. The non-linear response of the LCOS device can be corrected by the software during the hologram generation process. Further work could be done to achieve a linear phase response. Based on our experience, the linearization of the phase response would only yield marginal improvement in the performance for the telecom application.
Fig. 7. The relationship between the phase level and the power of + 1st diffraction order of the test binary grating pattern as well as the LCOS phase response, respectively.
The maximum phase change between the neighbouring phase levels is 0.05pi. Therefore, the LCOS device should be able to deliver phase response that is accurate enough for most applications.
Figure 8 gives some examples of the optimised PWM waveforms and their corresponding temporal phase responses. It can be seen that the predicted temporal phase responses have a good match with the experimental results. This shows that the proposed phase flicker prediction method can work accurately for complicated PWM waveforms, which further validates the method. It can also be seen that the optimised waveforms give the maximum peak-to-peak phase flicker of ∼0.03pi.
Figure 9 compares the phase flickers due to default waveforms and our optimised waveforms at different phase levels. It should be noted that results that corresponds to phase depths between 0.8pi and 1.2pi are not plotted due to the uncertainty caused by the noise in the high-speed photo-detector system. However, the phase flickers in this region should be in line with its neighbouring regions. It can be seen that the optimised waveforms in this work successfully reduced the peak-to-peak phase flicker in the digital LCOS device by ∼80%. The worst-case peak-to-peak phase flicker measured in our work is just above 0.03pi. These results obtained at 30°C are significantly better than previously reported results [30,31] achieved at 25°C. It is expected that the level of phase flicker can be further reduced when the operating temperature of the LCOS device is reduced. It is also worth noting that level of phase flicker across the whole phase range is at least as good as the level observed in many analogue LCOS devices [19], if not better.
Fig. 9. The phase flicker comparison between the default PWM waveforms and the optimised waveforms at different phase depths.
6. Conclusions
Phase flickers in digital LCOS devices are one of key problems for its wider applications, especially in the non-display systems. This paper presented an optimisation process that is able to achieve low flicker operation at room temperature for the digital phase-only LCOS device, based on a commercially available driving circuitry.
A series of waveforms with a fixed frequency but variable duty cycles were used to investigate the LC’s temporal response to on-state or off-state pulses when the it operates at different phase depths. It has been found that the LC responses to a pulse with different speed when it operates at different phase depths. This is related to the rotational behaviour of the LC molecule and its birefringent nature. In addition, the response to an on-state pulse is generally much faster than that to an off-state pulse. Such LC behaviour in conjunction with the pulse pattern within a PWM waveform determine the magnitude of the phase flicker.
Based on these experimental results, a method is established to accurately predict the LCOS device’s temporal phase response to any PWM waveforms. The predicted temporal responses have an excellent match with the experimental results in our verification process. Initial results also indicate that high-frequency pulse patterns can help reduce the phase flicker in the LCOS device. However, this requires complicated high-speed driving circuitry in order to achieve required number of unique phase levels. It also has cost and power consumption implications, which would compromise the key advantages of the digital LCOS devices.
A 128-bit bitplane configuration was proposed, with an aim to prevent the presence of long on-state or off-state pulses in the PWM waveforms. This configuration is compatible with existing driving circuitry without the need for further increasing the driving frequency. The phase flicker prediction method developed in this work was used to rapidly identification of the ideal waveforms for the low-flicker operation across the whole phase range. Compared with the default waveforms, the optimised waveforms were demonstrated to reduce the peak-to-peak phase flicker from ∼0.16pi to ∼0.03pi across the whole phase range. Such level of phase flicker is as good as that observed in many analogue LCOS devices, if not better. This makes the digital LCOS devices suitable for applications that are sensitive to phase flickers, e.g. optical switches in the telecom fibre networks.
The optimisation process based on the phase flicker prediction method could be further used to optimise the bitplane configurations, which may result in further reduction in the phase flickers. The process is also generic and independent of the LCOS device and its digital driving circuitry. The same principle can be applied to any digital driving circuitry to identify the best PWM waveforms possible. When the driving circuitry with higher speed becomes available, it is expected that the phase flicker can be further reduced in this way.
Funding
Fundamental Research Funds for the Central Universities (2242019k1G001).
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