Suppression of laser speckle contrast using negative dielectric anisotropy nematic liquid crystal doped with an ionic medium

ABSTRACT A liquid crystal (LC) with negative dielectric anisotropy called N-(4-Methoxybenzylidene)-4-Butylaniline (MBBA) doped with the ionic agent cetyltrimethylammonium bromide (CTAB) has been investigated as a speckle suppression device to reduce the laser’s speckle contrast. The electrohydrodynamic instabilities (EHDI) effect in LC is exploited to reduce speckle contrast. The EHDI effect causes chaotic turbulence in LC, resulting in dynamic scattering of the incident light beam. In order to investigate the electro-optic properties and frequency region for optimal performance, optical measurements and dielectric spectroscopy of the pristine and doped LC are performed. The dielectric characteristics of the LC demonstrate that the frequency range to produce the EHDI effect in the LC cell is broadened as the ionic agent is doped. The inclusion of ions also enhances the ion density, mobility, and conductivity in LC. The increase in ion density and mobility enhances the turbulence in the LC at a faster rate; as a result, the dynamic scattering becomes more rapid. When measured with a charge-coupled device (CCD) camera, the faster dynamic scattering provides higher suppression in the laser’s speckle contrast. This method can be used to reduce the speckle contrast in laser source-based imaging and projection displays. Graphical abstract


Introduction
The use of a coherent light source such as a laser for the display and imaging application has been very challenging because the image quality is degraded by an optical phenomenon called speckle.Speckles appear when a coherent light beam passes through a stationary optical medium with rough surfaces or variable refractive indices or is reflected from the rough surfaces [1,2].When a coherent light beam passes through optically rough surfaces with the roughness of the order of an optical wavelength [3] or via an optical medium with varying refractive indices [4,5], each point in these media can be considered as a secondary light source, producing scattered light.A stationary detector will detect a granular pattern with a strong contrast on the scattering spot.The term 'speckle' refers to this type of granular intensity profile [1].
Speckle can be quantified in terms of speckle contrast C; which is expressed as [1,2]: where σ I and I are defined as the standard deviation and intensity of the independent pixels, respectively.� I is average intensity.A fully formed speckle has a speckle contrast value of 1, whereas an image with no speckle pattern has a speckle contrast value of 0.
The speckle contrast represents the fluctuation of individual pixel intensity with respect to the average of pixels' intensity.It is difficult to separate information from a picture that has been taken from a highly coherent light beam because of the speckle pattern.
There are two types of speckle patterns: objective and subjective speckle.In the objective speckle, the speckle distribution is collected on the optical sensor plane without the use of imaging optics.Whereas in subjective speckle, imaging optics are used to record speckle patterns on an optical sensor [6].
Several approaches have been explored to reduce the speckle contrast value from a high-coherence light source in imaging and laser projection systems [6,7].To reduce speckle contrast, a rotating ground glass diffuser [8], a moving diffuser [9], a vibrating diffractive beam shaper [10], a vibrating light pipe [11], and a rotating ball lens [12] have been utilised.The rotating ground glass diffuser [8] demonstrates the technique for speckle contrast suppression.Using the moving diffuser [9], speckle contrast is reduced to 0.1.The speckle contrast in these works is given in the % values [10][11][12].Speckle contrast is lowered to 5.5% via vibrating beam shaping [10].It is lowered to 4% when employing a vibrating light pipe [11] and reduced to less than 4% when utilising a spinning ball lens [12].The speckle contrast value is significantly suppressed to being undetectable by the human eye using these devices.However, these devices are required to be upgraded to eliminate the bulky setup and expensive optical components as well as to provide an alternative without mechanical vibrations in many applications.
To offer a vibration-free, portable, and inexpensive alternative, devices based on liquid crystal (LC) have been developed to provide reduced speckle contrast.Over the past few years, several researchers have used the electro-optic characteristics of various types of LC to lessen the speckle contrast [13][14][15][16][17][18][19].When considering the ferroelectric LC cell combined with the wedge cell, the substantially altered speckle pattern is produced by modulating the polarisation of light; around 40% of the speckle contrast is suppressed [13].In polymerdispersed liquid crystals using optical diffusion properties and the reorientation of LC molecules in the presence of an electrical field, 25% of the speckle is reduced [14].By the utilisation of chiral nematic LC doped with the ionic substance, electrohydrodynamic instabilities (EHDI) are induced into the LC to produce statistically independent speckle pattern in a finite period of time, resulting in about 80% reduction in speckle contrast [15].A polymerstabilised liquid crystal system's ability for light scattering offers a nearly 55% reduction in speckle contrast [16].Recently, in the chiral nematic LC, lowering the pitch resulted in a 75% reduction of speckle contrast [17], and by doping the redox reagent in chiral nematic LC, the speckle contrast suppression is nearly 83% [18].Similar to introducing the EHDI effect in a chiral LC, the speckle contrast suppression of nearly 90% is achieved by introducing the EHDI effect in the nanoparticle-doped nematic LC with homogeneous alignment [19], and 62% reduction using the mixture of negative dielectric anisotropy LC and photoinitiator [20].Although the LCbased devices' suppression of speckle contrast is very promising, further development is still required to prevent human eye detection of speckles in the image.The speckle contrast value should be smaller than 0.04 [15].However, the method proposed utilising liquid crystals reduces the speckle contrast value for a coherent laser source, which is close to 0.1.Considering the devices reported based on the liquid crystal, further development is required to reduce the speckle contrast below 0.1 [17].Additionally, the ferroelectric-based devices are restricted in their functionality because the polariser is needed to reduce the speckle contrast via polarisation diversity.In contrast, chiral nematic-based devices require a high operational voltage.
Here, we employ the EHDI effect in the negative dielectric anisotropic LC to create dynamic scattering and develop a continuous sequence of independent speckle patterns over a finite duration in order to reduce the speckle contrast.The introduction of the dynamic scattering using the EHDI effect by dispersion of ionic dopant in nematic LCs is mainly used for the information display and smart windows [21][22][23][24].The EHDI effect is created when an external electric field acting on an LC has an amplitude greater than the threshold value and a low operational frequency.The oscillation of ions or charge carriers and the reorientation of anisotropic LC molecules under an electric field causes chaotic turbulence, which is known as the EHDI effect [15][16][17][18][19][20][21].The LC director orients arbitrarily as a result of this EHDI phenomenon, which also leads to strong dynamic scattering.
For our experiment, we have used the negative dielectric anisotropic LC N-(4-Methoxybenzylidene)-4-butylaniline (MBBA) doped with the cetyltrimethylammonium bromide (CTAB).We used the objective speckle measurement approach to investigate the speckle pattern, which is according to the IEC standard 62906-1-2:2015 [16,25,26].We have used objective speckle measurement to effectively demonstrate how dynamic scattering resulting from the electrohydrodynamic effect in the negative dielectric anisotropic nematic liquid crystal can be used to reduce speckles.The dynamic light scattering effect is used to reduce the speckle contrast of the coherent laser light source on the rough surface of the screen.
The inclusion of an external ionic medium improves the EHDI effect in the LC and increases ion density and mobility, enhancing conductivity and broadening the frequency response region for the EHDI.The LC-based device described is simple, vibration-free, electrically controllable, cost-effective, compact, and portable, lowering the speckle contrast value up to 0.05.In comparison to prior study results, the operational voltage (in V rms ) required to reduce the speckle contrast value by around 90% is also low.

Material and fabrication
The negative dielectric anisotropic LC N-(4-Methoxybenzylidene)-4-butylaniline (MBBA) having ε k ¼ 4:7; ε ?¼ 5:4 and Δε ¼ À 0:7 [27] and an ionic agent, cetyltrimethylammonium bromide (CTAB), are used in this work.Both materials were purchased from TCI Chemicals (India) Pvt. Ltd. and used without further purification.The nematic-to-isotropic transition temperature of MBBA LC (T N-I ) is 45°C.Several concentrations of CTAB ranging from 0 to 0.3 wt % into MBBA are used.The suitable weight ratios of MBBA and CTAB are mixed with chloroform to make a homogenous solution.The solution is ultrasonicated in an ultrasonic cleaner (make Labman Model LMUC-3) for 30 min and shaken in a vortex mixer (make Labman Model LMVM 20) for 5 min.This homogeneous solution is kept at 55°C for 1 h and then at room temperature for 24 h for the complete evaporation of chloroform.After completely removing the solvent from the mixture, the mixture is again shaken on a vortex mixture for 5 min to avoid any possible segregation in the mixture.The solution was filled in the LC cell having a homeotropic alignment layer.The used LC cells (Instec, USA) are made from transparent glass coated with Indium Tin Oxide (ITO) layers with a cell gap of 9 µm and an overlapped electrode area of 1 cm 2 .

Experimental details
The Olympus BX51Polarizing optical microscope (POM) attached with a Charge-Coupled Device (CCD) camera is used to observe the LC cells' optical texture.The LC cell was kept between the crossed positions of the polariser and the analyser.The inbuilt camera captured the optical texture of the LC cell with a change in the amplitude and frequency of the applied field to LC cell.The temperature of the LC cell is controlled by placing it in an Instec HSC 300 hot-stage connected to a mK-1000 temperature controller.The LC cells are mounted inside the hot stage, which is connected to a temperature controller.The dielectric spectroscopy of the LC cells is done using the Agilent E4980A Precision LCR meter in the range of 20 Hz to 2 MHz.
For the speckle contrast measurement, another CCD camera Lumenera infinity2-5C is used.The exposure time of the CCD camera is set at 50 msec by considering the temporal integration time of the human eye [15,17].The pixel size of the CCD camera is 3.45 µm × 3.45 µm.The camera is used in monochrome mode with a resolution of 1224 × 1024 (binning 2 × 2).When imaging with monochromatic light, to further maximise the resolution, the CCD camera is used in monochrome mode [15,28].The sample's speckle contrast was measured using the IEC standard 62906-1-2:2015.In the setup shown in Figure 1, the distance between the He-Ne laser (make REO Precision optical solution, Model 30993, λ = 633 m, spot size = 2 mm) and the ND filter is 9.5 cm, the hot stage is 19 cm away from the ND filter, and the screen is 23 cm away from the hot stage.The CCD is positioned at a 30° angle, 18 cm away from the screen.Screen is made out of white paper.An optimal value of the intensity distribution is selected in our experiments in such a way that the camera pixel does not saturate for an exposure time of 50 msec of the CCD camera.The experiment is performed on an optical bench in a dark environment to avoid the effect of optical alignment disturbance and ambient lightning.
The speckle patterns are directly recorded on the CCD sensor plane without imaging optics.The hot stage and controller used in texture analysis are applied to control the temperature of the LC cell.To provide the square waveform electric field to the LC cell, the function generator (Tektronix AFG 1062) is used.The digital storage oscilloscope (DSO Tektronix, TPS 2024) is used to continuously verify the output from the homemade voltage amplifier.The image of 0.1 wt % CTAB-doped LC cell with and without the applied electric field is shown in Figure 2. In the configuration shown in Figure 1, in order to observe how the applied electric field's amplitude and frequency affect the optical transmission, the ND filter is removed, and the screen is replaced with the photodiode (Gentec EO PH100-Si-HA-OD1-D0) attached with a power meter to record the optical transmission.

Optical texture
The CTAB ion is doped in the negative dielectric anisotropic material MBBA at concentrations of 0.1, 0.2, and 0.3 wt %.POM analyzes the optical texture of LC cells with homeotropic alignment.From the photographs of 0.1 wt % CTAB-doped MBBA LC cell in Figure 2, in the off state, the LC director is initially aligned in a homeotropic manner, and the cell looks transparent.When an external, low-frequency alternating electric field is applied, the LC director begins to align in a direction perpendicular to the applied electric field, and ions begin to oscillate in the field direction.The ions in the LC are influenced by the applied alternating electric field, which generates the EHDI effect in the LC cell.The turbulence created by the EHDI effect leads to a random change in the refractive index in the LC cell [21].As a result, the EHDI effect produces dynamic scattering of the incident light, and the LC cell appears opaque.The voltage at which the EHDI effect starts in the LC cells with different concentrations of CTAB is given in Table 1.The POM textures of 0.1 wt % CTAB-doped MBBA LC cell for various frequencies and applied voltages are shown in Figure 3.The applied Voltage amplitude for different operating frequencies at which the LC cells begin to exhibit EHDI effects is shown in Table 1.The POM texture of the CTAB-doped MBBA LC cells for different applied voltages of square waveform shows that when the CTAB concentration is higher, the LC cell's response to the applied field for producing the EHDI effect shifts to the high-frequency region.The agglomeration of the CTAB is seen when its concentration is 0.2 and 0.3 wt %.

Optical transmission
Initially, in the off state, the LC cell is transparent, and the light is directly transmitted.In the pure and CTABdoped MBBA LC, when an electric field is applied across the LC cell, the ions inside the LC cell respond to the field at a low frequency and begin to reorient.For 50 Hz operational frequency, as the voltage amplitude of the applied electric field increases above 21 Vpp (peak-topeak), the ions in the LC produce chaotic disturbance, which arises from the flow of oscillating ions and the orientation of anisotropic LC molecules.As a result of  the LC molecule's disturbance, the LC director begins to orient randomly.This is revealed by the optical texture for the 0.1 wt% CTAB-doped MBBA LC cell.It is given in  The threshold voltage required to produce EHDI increases with an increase in the applied frequency of the electric field, as can be observed from the POM texture in Figure 3 for 0.1 wt% CTAB-doped LC cell.The effect of CTAB ion concentration and operating frequency on the EHDI effect is discussed in detail in a later section.Furthermore, the direct optical transmission measurement confirms the impact of the applied electric field's frequency on the threshold voltage to produce EHDI.For the 50 Hz frequency for all LC cells, the change in the optical transmission starts after 21 Vpp and is nearly the same at the higher voltage, as shown in Figure 4(a).As the applied electric field's frequency increases, the ions fail to respond to the change in the polarity of the alternating electric field [29] and does not produce the EHDI effect and is unable to provide any significant change in the transmission as shown in Figure 4  transmission is very low and is only due to a change in the orientation of LC director from homeotropic to homogeneous alignment.The applied electric field's frequency and amplitude can be adjusted to alter how dynamically the LC cell scatters the incident beam.This is the characteristic of LC-based dynamic scattering devices [29,30].

Speckle contrast measurement
EHDI effect in the LC cell provides a time-varying phase modulation of the scattered light.When this scattered light is recorded using the CCD camera over an exposure time, and the exposure time of the camera is large enough for the phase modulation time due to dynamic scattering, the independent speckle pattern is superimposed.This provides an image with average exposure intensity.It has been reported that adding N statistically independent speckle patterns together reduces the speckle contrast by a factor of 1⁄√N [1].The steps used to analyse the speckle contrast after the recording of the data are given in Figure 5 in the flow chart.To calculate the σ I and � I of the recorded CCD image, the inbuilt function Analyze, followed by the Measure function of ImageJ is used.
The speckle contrast measurement graph for different frequencies and applied field amplitude is given in Figure 6.The exposure time or integration time of the CCD camera is 50 msec.The speckle contrast of the pure and CTAB-doped sample is given in graph (a) of Figure 6.
The colour map in Figure 6(a,b) represents the speckle contrast graph for the LC cells.The measurement graph of the speckle contrast for LC cells corresponding to frequencie 50 Hz and different applied voltages of the square waveform is shown in Figure 6(a).Additionally, the impact of operating frequency on the speckle contrast is also examined; Figure 6(b) shows the speckle contrast for a 0.1 wt % CTAB-doped LC cell corresponding to different frequencies.
The influence of doping concentration on the EHDI effect in the LC and the speckle contrast of the laser light is described using dielectric spectroscopy.The EHDI effect is predominantly due to the ions present in the LC [21].The dielectric spectroscopy data in the dielectric spectroscopy measurement (Figure 10(a)) show that at T = 27°C, the frequencies at which loss tangent is maximum correspond to different LC cells are nearly 34 Hz for the pure LC and 50 Hz, 71 Hz, and 80 Hz for the 0.1 wt %, 0.2 wt % and 0.3 wt % CTAB-doped LC, respectively.When the applied electric field frequency is 50 Hz, the laser speckle contrast for the 0.1 wt% CTAB-doped MBBA LC cell is reduced at the lower voltage amplitude than that of the other LC cell, Figure 6(a).It indicates a significant effect of ion doping on laser speckle contrast suppression of the device.The voltage amplitude of the applied electric field is quite large at higher frequencies to produce the EHDI effect in the LC cell.For higher operating frequency, the ions do not follow the change in polarity very effectively with the applied electric field, and thus to move the ions at a faster rate, high voltage is required.As a result, ions do not produce effective instabilities at high frequencies in the LC, resulting in weak dynamic scattering when compared to dynamic scattering for the same LC cell at a lower frequency of the applied electric field.The speckle contrast values for the 0.1 wt % CTAB-doped LC cell corresponding to the different voltage amplitude and frequency of the applied electric field are given in graph (b) of Figure 6.
In Figure 7(a), the speckle contrast observed from the pristine MBBA LC and 0.1 wt % CTAB-doped MBBA LC cell for different frequencies at 60 Vpp voltage amplitude is shown.It confirms that the 0.1 wt % CTAB-doped LC cell has a broad frequency range for the EHDI effect compared to the undoped.The effect of CCD camera integration time on the speckle contrast is investigated for 0.1 wt % CTABdoped sample, as shown in Figure 7(b).As the camera integration time increases, the number of captured speckle patterns increases and more independent speckle patterns are averaged, which results in the suppression of the speckle contrast.The movies for the 0.1 wt% CTAB-doped MBBA LC cell with and without an electric field are also included as supplementary material to validate the results.

Intensity profile of the speckle images
The line intensity profile corresponds to the central horizontal line for a sample doped with CTAB at 0.1 wt.% is shown in Figure 8.For 0.1 wt % CTAB-doped LC cell, initially, in the off state, for a central horizontal line, the intensity corresponding to the pixels is highly fluctuating.At f = 50 Hz, when the applied external field amplitude is 32 Vpp, the fluctuation is immensely suppressed and further reduced with the increase in the amplitude of the field.The speckle contrast reduction performance of 0.1 wt % CTAB-doped sample over a period of 14 days is monitored.The applied voltage and the operating frequency were Vpp = 60 V and f = 50 Hz, respectively.There is a slight variation in the speckle contrast over the period of 14 days, as shown in Figure 9.This variation may be due to the oxidation of the LC in the cell and the accumulation of the ion near the alignment layer over time [18,21,31].

Dielectric spectroscopy
The dielectric spectroscopy is performed for all the samples in the 20 Hz to 2 MHz frequency (f) range to analyse the effect of the doped ions on the LC for various frequencies of the applied field.The real ε´(f) and imaginary part ε´´(f) of the dielectric constant corresponding to the studied frequency range are given in Figure 10(a).The dielectric loss tangent or dissipation factor, tan(δ) with respect to the frequency, is also given in Figure 10(a).It is observed that ε´(f) and ε´´(f) decreases with the increase in frequency.The ionic concentration (n), diffusion constant (D), and ac conductivity (σ ac ) of the LC with a higher doping concentration of CTAB ions are calculated by fitting dielectric spectroscopy data.The value of ε´(f) and ε´´(f) increases with decreasing frequency in the f range of 20 Hz to 1 kHz due to space charge polarisation in the LC [29].In the LC, ion responds to changes in the polarity of the applied alternating electric field.The shift in ε´(f) and ε ´´(f) to the higher frequency region suggests that ion transport gets faster with the doping of the CTAB.The frequency value that relates to the maximum value of tan(δ) is termed as the relaxation frequency (f R ), and the frequency at which the contribution of molecular orientation starts in the ε´(f) and behaves like a constant; this is the higher limit of frequency (f H ). The n and D of the  LC are calculated by fitting the ε´(f) and ε´´(f) into the Equations ( 2) and (3) [32][33][34] In the above two equations, n is the ionic concentration, q is the electric charge, d is the cell thickness, D is the diffusion constant, ε 0 is the free space permittivity, k B is the Boltzmann constant, T is the absolute temperature and ε 0 b is the intrinsic dielectric constant of the bulk LC.The dielectric permittivity ε´(f) and ε´´(f) are fitted between the frequency range f R and f H where they follow the relation f −3/2 and f À 1 , respectively [29,32].The frequency range from f R and f H is not same for all studied samples because there is a shift in the ε´(f) and ε´´(f) in the direction of the higher frequency region with doping of CTAB and also with increasing the temperature.The fitted graph of 0.1 wt % CTABdoped MBBA LC at 27°C is shown in Figure 10(b).Following the fitting with Equations ( 2) and ( 3) the obtained values of f R and f H are 50.23 Hz and 447.74 Hz, respectively.The parameter R 2 ≈0.99, indicates high-quality fit with the experimental observations.The values of f R and f H for different doping concentrations of CTAB in MBBA LC are given in Table 2.
Figure 10(c) shows the values of ionic concentration and diffusion constant as a function of the doped CTAB concentration.The ionic concentration (m −3 ) in the pure MBBA LC is 4:50 � 0:14 ð Þ � 10 19 and it increases for the 0.1 wt % and 0.2 wt %.For 0.1 wt %, it is 5:21 � 0:16 ð Þ � 10 19 and 5:76 � 0:18 ð Þ � 10 19 for 0.2 wt % CTAB-doped MBBA LC.The increase in the concentration of ions increases with the higher doping of the CTAB.When the CTAB concentration is increased to 0.3 wt%, the ionic concentration in the LC decreases to 5:31 � 0:16 ð Þ � 10 19 , which is low compared to the 0.2 wt % CTAB-doped MBBA LC.This may be due to some agglomeration of the ions in the LC at higher doping concentration.
The diffusion constant (m 2 s −1 ) increases monotonically with the increasing CTAB concentration.For the pure MBBA LC, it is 1:18 � 0:03 ð Þ � 10 À 10 and 2:86 � 0:08 ð Þ � 10 À 10 for 0.3 wt % doped LC.For a given temperature T, the increase in ion diffusion constant with the higher doping indicates that the ion diffuses effectively with the doping of the ion in this LC.
The shifting in the dielectric data is explained by the ion mobility.This can be determined using Einstein's electrical mobility equation [35] For a given temperature, ion mobility (µ) is proportional to the diffusion constant D. From the ion mobility graph in Figure 11(c), the value of µ increases with the doping of the CTAB ion in the LC.The shift in f R and f H towards higher values with a doping concentration of CTAB can be understood from the ion mobility in the LC.
The dielectric loss ε´´(f) does not properly follow with f À 1 when the frequency is lower than f R .For the ions, the time to follow the polarity change of the applied electric field gets longer, resulting in an ion accumulation effect near the electrodes.The accumulation of ions near the electrodes for the lower frequencies of the applied electric field acts as the counteracting field, which leads to a decrease in the conductivity, and as a result, large amplitude of the applied field will be required for the EHDI effect.
When the operating frequency is near the relaxation frequency (f R ), ions follow the polarity inversion of the applied electric field very effectively, and they efficiently diffuse in the LC.The voltage required to produce the EHDI effect is lower for this operating frequency.When the operating frequency is much higher f > 3f R , the ions do not follow the polarity change of the applied electric field effectively, and the high amplitude of the field is required to move the ions.
The conductivity is calculated from the ε´´(f) with the following equation [35] The ac conductivity graph is shown in Figure 10(d).For a given temperature, conductivity increases with the doping of the CTAB ion in the LC.The variation in the ac conductivity with frequency is due to the polarisation effect.At lower frequency values, the ac conductivity has lower values due to the electrode polarisation, and then it is nearly constant and gives dc conductivity because in this region electric field polarity inversion becomes fast, and the ion does not follow this periodic reversal effectively.At a very high frequency, the conductivity of the LC increases with the frequency [36,37].The effect of temperature on the ion density and diffusion constant is shown in Figure 11(b).The ion density of the LC is nearly constant as temperature increases, but the diffusion constant increases because the viscosity of the nematic LC reduces with temperature [38].As the temperature rises, the ion accumulates more kinetic energy and becomes more energetic, resulting in higher ion diffusion and ion mobility against the low LC fluid resistance, as shown in Figure 11(b,d).
As a result, the doping of the CTAB ion in the MBBA LC demonstrates that the relaxation frequency may be adequately adjusted with the appropriate doping concentration of the ionic agent.In comparison to other operating frequency values of the applied field, the LC provides the speckle suppression at a lower voltage when the frequency is nearer to the dielectric relaxation frequency.This device can be used in real-time applications such as laser projection displays.The reported device offers a compact, simple, inexpensive, vibrationfree alternative to mechanical methods.
The speckle contrast can be suppressed below 0.05 as a future scope and improvement of this work.By optimising the MBBA LC with some other ionic agent, the relaxation frequencies of the LC can be shifted to much higher values.Thus, causing the ions to oscillate at a higher rate and the electrohydrodynamic instabilities (EHDI) will be induced at a faster rate.A faster EHDI effect creates more independent speckle patterns within an exposure time of the charge-coupled device (CCD) camera, resulting in a further reduction in the speckle contrast.Additionally, by investigating the electrohydrodynamic instabilities (EHDI) in various types of LC with a suitable ionic agent, further reduction in the speckle contrast values below 0.05 is possible.The speckle contrast of the reported device changes only slightly over the period of 2 weeks as shown in Figure 9.To make a more stable device, a study based on an improved stable LC and suitable ionic agents which can enhance ion density and mobility are required.

Conclusion
In conclusion, the dielectric and electro-optic properties of the CTAB-doped MBBA LC are investigated.The doping of the CTAB ions provides the shift in the relaxation frequency of MBBA LC to the high-frequency region.The ions, diffusion constant, and electrical mobility of the LC are calculated by fitting the dielectric data.The electro-optic measurement confirms the electrohydrodynamic effect in the LC cell.The introduction of the electrohydrodynamic effect in the LC cell leads to the dynamic scattering of the incident laser light.The EHDI effect in the MBBA LC is studied by varying the concentration of ionic dopant CTAB.Negative dielectric anisotropic LC MBBA with CTAB as an ionic dopant is explored as the speckle suppression device.For 0.1 wt % CTAB-doped MBBA LC cell, nearly 90% speckle contrast suppression of laser light incident on a paper screen is achieved at 50 Hz frequency for 60 Vpp square waveform.These investigations indicate that it is a promising candidate for laser projection display and imaging applications because it provides reduced speckle contrast without requiring a complicated setup.

Figure 2 .
Figure 2. (Colour online) Photograph of 0.1 wt % CTAB-doped MBBA LC cell (a).without external voltage, (b).for Vpp = 60 Volt at f = 50 Hz.The square dashed area is the electrode region of the cell.The length of the scale bar in figure (a) is 1 cm.

Figure 3 ,
which corresponds to the various operating frequencies and voltage amplitudes of the applied electric field.The random fluctuation of the LC molecule's director produces dynamic scattering for the incident light beam.As a result of the dynamic scattering from the LC cell, the direct transmission of the incident laser beam starts to reduce and light transmits in the diffused form, as shown in Figure4(a,b).

Figure 4 (
c) shows the schematic diagram of the laser light transmission (i) when the LC cell does not produce the EHDI effect and (ii) when the EHDI effect is produced in the LC cell.When the applied voltage amplitude further increases, it promotes the LC director fluctuation at a faster speed (Figure3for Vpp ≥30 V), which enhances the dynamic scattering of the incident light beam.
(b) for 500 Hz frequency.The optical transmission graph corresponding to the different frequency and amplitude of the applied electric field is shown in Figure 4(b) for 0.1 wt% CTAB-doped MBBA LC cell.In Figure 4(b), for f = 500 Hz, the change in the

Figure 3 .
Figure 3. (Colour online) POM texture image of 0.1 wt % CTAB-doped MBBA LC cell corresponding to different applied voltage and frequency of the applied square waveform.The polarizer (P) and analyzer(A) are in a cross position for all the images.It is shown only corresponding to Vpp = 0 for each frequency.The spherical dot in the images is the spacer beads present in the cell.

Figure 4 .
Figure 4. (Colour online) (a) Direct transmittance of the LC cells for 50 Hz operating frequency, and (b).for 0.1 wt % CTAB-doped LC cell for different frequency and voltage.(c).schematic diagram when the laser beam passes through the LC cell (i) without and (ii) with the application of an electric field to produce the EHDI effect in the LC cell.

Figure 5 .
Figure 5. (Colour online) Flow chart of the steps for post-processing data.

Figure 6 .
Figure 6.(Colour online) (a).The color map of the speckle contrast corresponds to the different amplitude of the applied voltage for f = 50 Hz of the CTAB-doped LC cells (b).Color map of speckle contrast for 0.1 wt % CTAB-doped MBBA LC cell corresponding to different frequencies.

Figure 8 .
Figure 8. (Colour online) CCD image of the 0.1 wt % CTAB-doped MBBA LC cell at the different applied voltage for f = 50 Hz at 27°C, and line profile of intensity across the horizontal central line.

Figure 7 .
Figure 7. (Colour online) (a) Speckle contrast of 0 and 0.1 wt % CTAB-doped LC cell at different frequency, (b) Speckle contrast of 0.1 wt % CTAB-doped LC cell with different exposure time of the CCD camera.

Figure 9 .
Figure 9. (Colour online) Speckle contrast value of 0.1 wt % CTAB-doped LC cell over the number of days.The measurement's temperature value is T = 27°C.

Figure 10 .
Figure 10.(Colour online) (a,b) Dielectric spectroscopy, (c) ion density and diffusion constant, and (d) ac conductivity of the LC cells at 27°C.

Table 1 .
Minimum voltage (peak-to-peak in Volt) to start the EHDI effect for different frequencies.

Table 2 .
Ion density, diffusion constant, and ion mobility of the LC at 27°C.