We present a method for reducing the phase flicker originated by the pulsed modulation of a Liquid Crystal on Silicon (LCoS) Spatial Light Modulator (SLM). It consists in reducing the temperature of the LCoS in a controlled way, in order to increase the viscosity of the liquid crystal. By doing this, we increase the time response of the liquid crystal, and thus reduce the amplitude of phase fluctuations. We evaluate the efficacy of this method quantifying the temporal evolution of phase shift using an experiment that is insensitive to optical polarization fluctuations. Additionally, we determine the effect of the temperature reduction on the effective phase modulation capability of the LCoS. We demonstrate that a reduction of up to 80% of the flicker initial value can be achieved when the LCoS is brought to −8 °C.
© 2012 OSA
The Liquid Crystal (LC) Spatial Light Modulators (SLM) are widely used for their capability to control light beams. Such devices are used in several applications like the encoding of arbitrary complex fields , optical metrology [2,3], optical tweezers , and pulse shaping , to mention only a handful of applications. Recently, it has been suggested their use for synthetic superresolving pupils . More applications are found in literature, mainly due to their high spatial resolution, the high light efficiency, and from a metrological point of view, its convenient depth of modulation or stroke that goes up to 2π. However, in some cases the SLMs do not satisfy the requirements of experimentalists due to temporally fluctuations in phase also known as flicker [5,7,8]. The typical frequency of flicker is 120 Hz . These temporal-phase fluctuations can introduce a non-uniform instantaneous deviation greater than λ/5, and should be considered when phase modulation is required. The large excursions in phase inhibit the use of LC-SLM for applications where time-averaging is not feasible. Therefore, the flicker characterization and reduction has been an active research field, in order to understand and overcome its effects. Some authors have tried to minimize the flicker effects by limiting the stroke to a fractional extent of its capacity . Despite advances, the time-fluctuations of phase are still present in Parallel Aligned Liquid Crystal on Silicon (PALCoS) devices as recently reported . Additionally, a polarization state generator configured to reduce the degree of depolarization (of approximately 10%) on the light beam reflected by LCoS and diattenuation has been reported [12–15]. This referred technique reduces phase fluctuations but a remaining amount is still present.
The origin of flicker is attributed to the electric polarization of the LC by pulse modulation (PM) [16,17]. This type of electric polarization contrasts with the predecessor analog technology that had a smooth temporal response. As explained in , the analog devices use a storage capacitor, which provide a memory voltage to the pixels, having the advantage of reducing the low frequency flicker of the line-addressed arrays. The advantage of PM is that the LC is driven between threshold and saturation voltages by multiplexing pixels , avoiding in this way the slow response of charging capacitors.
The main motivation to carry on this work is found in the possibility to use this device to synthesize either phase-only pupils or complex pupils [20–23], in order to push the limits of resolution in microscopy. It has been shown that a narrowed point spread function can be achieved by the interferometric superposition of two phase pupils . These pupils can be synthesized by a pair of LCoS, taking advantage of the inherent flexibility of these devices. When used for superresolution pupil engineering applications, the LCoS-SLMs operate under the most stringent conditions, in order to achieve the flattest possible wavefront, as well as accurately reproduce phase and amplitude modulation. Unfortunately, the temporal-phase fluctuations are an obstacle to achieve the desired pupils. Moreover, when two independent devices are simultaneously used on the same arrangement, a strong beating effect is observable. In addition to the behavior just described, temporal fluctuations on the polarization of light reflected by the LCoS are also present. Both fluctuations are coupled, because phase and polarization modulation is achieved through the same physical process of the LC. Therefore, their undesirable effects could be observed simultaneously. For example, when performing interferometric experiments, phase flicker results in periodic fringe displacement, while polarization flicker results in oscillating fringe contrast. In this manuscript, we propose a method for phase flicker reduction, based on the viscosity modification of the LC by means of temperature reduction. We evaluate the efficacy of this method on a commercial LCoS-SLM (Holoeye LC-2500). By using a specially designed experimental procedure that is insensitive to polarization fluctuations, we quantify the effective phase flicker reduction. Additionally, we evaluate the effect of the temperature reduction on the effective phase modulation capability of the LCoS.
The Holoeye LC-R2500 is an optical modulator based on the X97c3A0 monochrome reflective liquid crystal on silicon (LCoS) display fabricated by Phillips. The X97c3A0 device is a 0.97” XGA display designed originally for projection applications. This device consists of pixels arranged in 1032 columns by 776 rows. The imager uses 45° twisted nematic liquid crystal type. The modulator is operated using a personal computer through the digital video interface as a conventional display. Then, gray levels displayed by the computer are translated to voltage applied to the LC pixels. The electric polarization of each pixel is supplied by an 8-bit pulse-accumulation modulation scheme. The X97c3A0 display does not incorporate the polarizer required for light intensity modulation, thus the dependence of the birefringence of the LC on the electric polarization can be used to configure the device as an optical phase-mostly modulator. The LCoS SLM model LC-R 2500 has a resolution of 8 bits, which correspond to 256 gray levels, covering a phase shift interval of 2π in the visible spectrum.
As described by the manufacturer, when the LCoS is used for its primarily application, the imager produces a gray level by providing a pulse accumulation modulated signal whose RMS voltage corresponds to the desired gray level to be displayed. The exact algorithm is described as complex by the manufacturer and it is not disclosed . Each pixel is biased by a periodic function. Each bias cycle is divided into a positive and a negative half cycles. During the first bias half cycle, the positive version of the pulse modulated signal is driven onto the display while the common terminal (ITO) is held at ground by a polarization transistor. For the second half cycle, the pixel modulation data pattern is inverted and the common terminal is connected to the positive voltage source by a complementary transistor. This inversion provides for liquid crystal de-biasing, thus preventing the liquid crystal’s physical deterioration. The observed modulation period is as long as 8.3 ms. The average mechanical orientation of the LC molecules responds to the RMS voltage applied to each cell. As the polarization voltage applied to the LCoS is not constant but pulsed, the LC can be seen, from a physical point of view, as composed by molecules periodically oscillating around an orientation value that corresponds to the RMS value of the polarization voltage. The response time of the LC claimed by the manufacturer is 16 ms at ambient temperature of 25 °C. The relatively long modulation period, compared to the fast time response of the LC results in significant fluctuations of the LC molecules orientation around the average position. The effect of these fluctuations is not apparent to the naked eye, but results in severe beating when two LCoS are used on the same interferometric arrangement −and thus disturbing the interference. The magnitude of the fluctuations could be reduced by increasing the modulation frequency, but this functionality depends on the construction of the LCoS device and it is not under control of the user of the Holoeye LC-R2500.
The influence of viscosity on the time response is analog to the damping on a second order linear dynamic system . By increasing the damping, the time response of the system can be increased. This results in a reduction of the magnitude of the LC molecules oscillation due to the pulsed modulation, and thus the reduction of the periodic phase fluctuations. The viscosity of the LC at ambient temperature is out of control of the user. Nevertheless, we found possible to increase the viscosity by decreasing the temperature of the device. In order to achieve this purpose, we designed and implemented a temperature controlled mount for the LCoS. The cooling system consists of a Peltier cooler module attached to the mechanical frame hosting the LCoS. The cooler is located in between the LCoS and a tip and tilt mount that is used to align the beam in the optical system. The heat from the hot face of the Peltier cooler is extracted by a heat exchanger based on an open-circuit liquid refrigerating system. A closed-loop electronic temperature control module has been developed to gradually decrease the temperature of the LCoS and stabilize it at repeatable values. The cooling liquid pump is activated on demand, in order to provide vibration free operation during the interferometric experiments. The cooling system is capable of setting the temperature of the LCoS as low as −15 °C. In order to avoid condensation upon the device, the cooling system (comprising the LCoS device, the Peltier cooler, and the liquid cooler heat exchanger, in Fig. 1 ) is located into a semi-hermetic enclosure. The cavity is partially filled with desiccant pellets, in order to decrease the relative humidity. An optical window of interferometric quality allows the optical access to the LCoS.
Cooling LCoS-SLM is a known procedure and has been used to avoid damages caused by high power lasers  or when the device is deployed in a hot environment . Nevertheless, the effect of cooling on flicker has not been previously reported. In low optical power applications, the heat generated by the LCoS can be dissipated by natural convection. The manufacturer reports that the internal panel temperature increases about 5 °C at a room temperature of 25 °C. The change in viscosity, and thus flicker, due to this temperature increment is not noticeable. Nonetheless, the self-heating effect was observable at our interferometric arrangement, where the interferograms remained unstable until reaching thermal equilibrium, as a result of the thermal expansion.
It has been previously shown that polarization flicker results from the LCoS operation due to partial depolarization of light . In this work, we want to characterize and minimize the flicker due exclusively to the temporal phase fluctuations, while being insensitive to the polarization fluctuations. The experiment is designed to characterize phase fluctuations as a function of time that results from the electrical polarization −i. e. the pulse accumulation modulation− of the LCoS. This quantification of phase fluctuations is not affected by the changes of the state of polarization that are also induced by the LCoS [12,14].
The phase modulation performance of the LCoS has been previously tested by the implementation of a single path interferometer . While this approach provides high stability and low vibration sensitivity, the phase modulation is measured as the relative phase shift between two regions of the same LCoS device. Therefore, the observed flicker results from the combined effect of phase fluctuations of both regions. In order to compare the phase fluctuation as a function of time against an absolute reference, we implemented a Twyman-Green interferometer with an LCoS-SLM in one arm and a high quality reference mirror in the second arm. The reference mirror is aligned by means of a precision gimbal mount. The beam from a linearly polarized He-Ne laser is filtered using a spatial filter and collimated by a positive lens. A diaphragm limits the diameter of the expanded beam to the height of the LCoS. A plate beam splitter with an uncoated second surface is used (Fig. 1). Phase fluctuations due to LCoS electric polarization are not evident to the naked eye, as they occur at a frequency of 120 Hz. Therefore, a high-speed CCD camera is used to capture the temporal evolution of the interferogram.
We choose a slightly wedged beam splitter aligned to the vertical axis. Therefore, the reflections from the uncoated surface induce high frequency vertical fringes that are not visible to the naked eye, but are registered by the CCD. We adjust the tilt of the reference mirror to introduce horizontal fringes of approximately the same spatial frequency as those due to the beam splitter. The resulting interferogram is a pattern of bright spots periodically arranged, as shown in the Fig. 2 −see the video sequence. As the size of the CCD is smaller than the diameter of the beam, the image shows only the central part of the interferogram. When the optical length of one arm of the interferometer is modified, the effect is observed as the vertical displacement of the spots. Therefore, by tracking the spatial position of the spots at each frame of the high speed video, we are able to quantify the time evolution of the phase.
The frame rate of the camera is limited by the computer link bandwidth. We configured the image size as 80 by 112 pixels in order to achieve a rate of 2,300 frames per second, it means almost 20 times faster than the phase fluctuations. The tilt of the reference mirror is adjusted to obtain approximately 20 horizontal fringes across the height of the image, matching the fixed frequency of the vertical fringes. Therefore, a phase shift of 2π rad is observed as a small displacement of the spots of approximately 7 pixels long. In order to achieve high resolution in phase shift quantification, we developed a spot tracking algorithm that determines the position of the spots as a function of time with sub-pixel resolution. This algorithm resulted from the combination of spot tracking by correlation and center of mass calculation.
We quantify phase fluctuation due to the LCoS by displaying uniform gray level images on it, and acquiring and analyzing the high speed videos. The length of each video is approximately 130 ms or 310 frames. We have found that the phase shift from the LCoS fluctuates simultaneously with the same amplitude across the surface when a uniform gray level image is displayed. Therefore, we quantify the phase fluctuation averaging the displacement of several spots at each frame and calculating the RMS value.
2.1 Phase fluctuation at room temperature
We characterized the phase fluctuation as a function of time for different gray level values. For this evaluation, we have displayed uniform images of constant gray level value. We have found that phase fluctuation shows dependence on the gray level value applied to the LCoS. It tends to be lower for gray values close to zero or 255 because the duty cycle of the pulse modulation is near to zero and 100% respectively. Moreover, we found that the repeated measurements of phase shift for the same gray level value show different RMS values of phase fluctuation. In Fig. 3 we show two waveforms of phase fluctuation as a function of time for two different measurements of uniform gray level of 130. The average value of phase shift was subtracted, and only the variation of phase as a function of time is shown. These measurements were registered within a time span of 10 minutes, and the LCoS was operated at room temperature.
The experiment was executed performing the following sequence. First, the uniform gray level value of 130 was displayed at the LCoS and maintained for two minutes. The first measurement was taken. Then, two images of uniform gray level values of zero and 255 where displayed at the LCoS, maintaining each one for 2 minutes. Finally, the image of gray level value of 130 was displayed again, and the second measurement was registered. It can be observed at Fig. 3 that temporal evolution of phase shift is different for each measurement, and the RMS value of phase fluctuation resulted in different values. In all cases, the phase fluctuation shows a main component of 120 Hz, as revealed by the Fourier analysis. From these measurements, we infer that the pulse modulation patterns applied by the LCoS were different on each case, but equivalent in RMS value. As previously mentioned, the algorithm used to generate the pulse modulation pattern is not disclosed by the manufacturer, but it is known to be designed to reduce current peaks . As this modulation pattern is variable for each gray level value and these results in non constant RMS value of phase fluctuation, we express the dependence of phase fluctuation as a function of a gray level as a band, as shown in Fig. 4 . The high and low limits were obtained by repeated measurements of phase fluctuation for different gray level values. Even when an RMS flicker value of 0.4 rad could be interpreted as small, it represents an uncertainty equivalent to λ/5 or even worst, depending on the used wavelength.
2.2 Phase fluctuation as a function of temperature
We characterized the phase reduction of phase fluctuation as a function of temperature. We calculated the RMS value of phase fluctuation for distinct temperatures from 25 °C (ambient temperature) to −8 °C, being this near to the lowest practical temperature achieved by our cooled mount. The manufacturer published 0 °C as the minimum operating temperature of the panel, and – 20 °C as the absolute minimum temperature for storage. We operated the device beyond the recommended limits in order to improve the fluctuation reduction, but never exceeded the minimum storage in order to avoid any damage to the device. The temperature decrement was carefully controlled by a slow ramp, reducing the probability of thermal stress on the panel. We started the evaluation at room temperature and decreased until reaching the lowest temperature. As our experiment is performed using an inteferometric arrangement, the cooling liquid pump is temporarily disabled while registering the measurements. At intermediate temperature points, we measured a representative group of gray level values and calculated the maximum and minimum observed RMS value of phase fluctuation. We use these values to present the dependence of phase fluctuation as a function of temperature as shown in Fig. 5 .
The phase fluctuation for any gray level value at a given temperature is expected to be found between the maximum and the minimum limits given by the band. The phase fluctuation was effectively reduced by the decrement of the temperature. For some critical gray level values, i. e. 200, we found that the phase was reduced to less than 20% of their original value, as shown in Fig. 6 . For some other gray level values that show a low fluctuation at room temperature, as those near to 255, the proportional reduction was much lower. Actually, when reducing the temperature to −8 °C, the phase fluctuation of all gray level values converges to 0.05 rad. The Fourier analysis of the waveforms shows that the 120 Hz component is strongly reduced as temperature decreases, while the lower frequency component at 60 Hz is relatively increased. This is consistent with the expected behavior if the LC viscosity is increased while the temperature is decreased.
2.3 Phase modulation capability at low temperature
We implemented an experimental setup based on the previously described arrangement in order to quantify the reduction in phase shift modulation interval due to the decrement of temperature. This experiment uses the previously described interferometer, but incorporates a long focal distance positive lens to reduce the beam diameter from 14.6 to 3.6 mm (heights of the LCoS and CCD respectively). After this, the beam impinging the complete surface of the LCoS is imaged completely by the camera. The exposure time is set to a multiple of 1/120 [1/Hz], in order to minimize the effect of phase flicker. The reference mirror is tilted to induce low frequency horizontal fringes. The relative phase shift induced by the LCoS when displaying uniform images is observed as a vertical displacement of the fringes.
In order to quantify the phase shift, we sequentially display two images, labeled as (a) and (c) in Fig. 7 . The image (a) is the reference image and it presents a uniform gray level value of zero. The phase shift is measured as a relative value to this image. The second image is composed by two patches. The right half of the image is a uniform zero and it is used to verify and compensate for mechanically induced phase shifts. The left part of image (c) presents a uniform gray level value of 200 and it is used to quantify phase shift. While displaying the images (a) and (c), we register the interferograms (b) and (d), respectively.
These measurements were repeated at 26 °C and −5 °C, resulting in one pair of interferograms for each temperature. The pair or interferograms obtained at room temperature are shown in Fig. 7.
For each pair of interferograms, we extract the information of column 250. (shown in green color). We simultaneously graph the gray level information as a function of row of each interferogram in order to compare them and asses the achieved phase shift, as shown in Fig. 8 . The phase difference of the gray level waveforms for a given column between interferograms (b) and (d) corresponds to the relative optical phase shift obtained while displaying images (a) and (c). While no mechanical phase shifting is induced, both quasi-sinusoidal waveforms from column 250 are almost identical and no wave displacement is visible. Then, we extract the information of column 80 (shown in red) and compare it in the same way. The phase difference between the waveforms represents the relative phase shift induced by the LCoS while displaying zero and 200 gray level values. Several methods for phase shift calculation can be found in [28,29]. We implemented a modified algorithm that is not sensitive to the decreasing period of the waveforms. Comparing the measurements performed at 25 °C and −5 °C, we have found that the relative phase shifting is reduced by 30% due to LCoS cooling. In contrast, the achieved flicker reduction value is up to 80%, as shown in section 2.2. Therefore, the ratio between the remaining phase modulation capability and the remaining flicker is almost 4:1. This ratio indicates an important improvement over the previously documented alternative, where the operative gray level interval of the LCoS has to be limited in order to reduce flicker .
We have described a method to reduce the temporal phase fluctuations (flicker) by means of controlled liquid crystal cooling. By doing this, we increase the LC viscosity in order to increase the time response of the device, and thus reduce the flicker originated by the electric pulse modulation. We evaluated the efficacy of this technique implementing an experiment specially designed to be insensitive to the polarization fluctuations that are also present. The flicker has been measured with respect to an absolute reference, the mirror of a Twyman-Green interferometer. We found that the phase fluctuation is uniform and synchronized across the surface of the LCoS under test when displaying uniform gray level images. By characterizing the flicker in the range from 25° Celsius to −8° Celsius, we have found that fluctuations can be reduced down to the 18% of their initial value. Below −5° Celsius the amount of the flicker reduction follows an asymptote (Fig. 5). The increment of viscosity attenuates, in fact, the main 120 Hz component of flicker. We have also quantified the effect of temperature reduction upon the phase modulation capability of the LCoS. We demonstrated that 70% of the phase shift capability of the LCoS is preserved while more than 80% of the temporal phase fluctuations have been abated.
The authors want to thanks the reviewers for their fruitful comments as well as Drs. A. Dávila, N. Alcalá and J. E. A. Landgrave for their support. A. González-Vega and J. García-Márquez also acknowledge the grant PROMEP/103.5/10/4684.
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