Volume scattering diffusers (VSDs) with different thicknesses were fabricated for speckle reduction investigation in a two-diffuser system. The VSDs were obtained by spin-coating the mixture of SiO2 microspheres and SU-8 photoresist, where the monodispersed SiO2 microspheres were synthesized by the Stöber method with an average diameter of 1.43 µm. The Mie scattering effect of the VSDs was observed owing to the refractive index difference between the SiO2 microspheres and the SU-8 photoresist. The speckle reduction effect of the two-diffuser system comprising cascaded stationary and moving VSDs was experimentally studied. The result can be used in designing more effective speckle reduction techniques in laser displays.
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Lasers are widely used in projection displays because they can produce a high luminance, have a wide color gamut, and have long lifetimes. When a highly coherent laser illuminates a rough surface such as a projection screen, bright and dark grainy light distributions called speckles are formed . In laser displays, speckles significantly restrain the ability of audiences to extract details in projected images, and thus, speckles must be suppressed .
Currently, several speckle reduction approaches, such as ensuring wavelength diversity , angle diversity , and polarization diversity  and moving a diffuser or screen [6–8], have been proposed for implementation in laser projection systems to improve the image quality. Among those, a moving diffuser is a simple yet effective speckle suppression method. The mechanism of moving diffusers in speckle reduction involves the temporal averaging of different speckle patterns during the detector integration time. There are two types of systems for moving diffusers: a single-diffuser system and a two-diffuser system. The single-diffuser system achieves speckle reduction by moving a diffuser and recording speckles formed on the diffuser . The two-diffuser system is composed of a stationary diffuser and a moving diffuser. A two-diffuser system has been theoretically discussed, wherein the speckle reduction effect of the two-diffuser system was related to the motion of the moving diffuser and the properties of the stationary and moving diffusers [2,7]. Li et al. analyzed the effect of diffuser motion on speckle reduction, and the results showed that the rotations of the two diffusers in opposite directions could achieve improved speckle reduction performance than the rotation of a single diffuser . Although the effect of the diffuser motion on speckle reduction in two-diffuser systems has been comprehensively discussed theoretically and experimentally, there have been only a few experimental investigations on the effects of diffuser characteristics on speckle reduction [9,10].
Moreover, light scattering is a phenomenon based on the change of light travelling direction in a medium. Light scattering occurs when light is incident on a rough surface, when it travels in an optically inhomogeneous medium with a varying refractive index or from one optically homogeneous medium into another homogeneous medium of different refractive indexes, or when photons encounter scattering particles in the medium . The scattering phenomena that produce speckle can be broadly divided into two classes: surface scattering and volume scattering . For surface diffusers, the scattering process can be generated by an incident light passing through the rough surface of the diffuser. Conventional surface diffusers consist of opal and ground glass plates . In addition, Sant et al. developed a method of replicating randomly rough surfaces fabricated in photoresist by exposing the coated substrates to speckle patterns and rinsing the plates in a developer, thereby fabricating a one-dimensional, randomly rough surface . For the volume scattering diffuser (VSD), the scattering process is generated by the inhomogeneous material of the diffuser. A commonly used method involves mixing the scattering particles with the matrix to fabricate the VSD. The scattering ability of VSDs can be modified by controlling the size, volume fractions, and refractive index of the scattering particles, as well as the thickness of the VSD. For example, in order to determine the relationship between VSD and the variation of the correlated color temperature of white light, Ma et al. fabricated a prototype VSD with various mass fractions of scattering particles, by pouring the solution mixture of epoxy and polymethyl methacrylate into a plastic mold and solidifying it . Moreover, Liu et al. presented an approach for fabricating polymethyl methacrylate/polyethylene terephthalate light scattering materials by melt blending and compression molding using polymethyl methacrylate as the matrix and polyethylene terephthalate as dispersed particles . The above-mentioned methods require a mold for the fabrication of the diffuser. However, the mold manufacturing process is complicated, and the precision of the mold to control the thickness of the diffuser cannot meet the requirement. Favorably, spin coating is a simple and speedy procedure that is used to apply uniform thin films of organic materials on flat substrates, and the thicknesses of the thin films can be precisely controlled [16,17].
In this study, we have fabricated VSDs with different thicknesses by the spin coating method using SU-8 photoresist as the matrix and SiO2 microspheres as the scattering particles. The scattering effect is generated by the refractive index difference between SiO2 microspheres and SU-8 photoresist. We experimentally studied the effect of the diffuser thickness on speckle reduction in a two-diffuser system consisting of a stationary VSD and a moving VSD. Subjective speckle contrasts of the two-diffuser system were obtained by using a high-coherence HeNe laser and a low-coherence multimode laser diode (LD), and by driving the moving VSD at different speeds. Experimental results indicate that thicker VSDs under low-coherence multimode LD illumination are the most effective in reducing speckles. Therefore, our work complements the speckle reduction investigation achieved by two-diffuser systems, and aids the engineering of similar potential techniques to reduce speckles more effectively in laser displays.
2. Fabrication of VSDs with different thicknesses
The VSDs are fabricated by mixing monodispersed SiO2 microspheres with an SU-8 photoresist and spin coating the mixture on glass substrates. Figure 1 shows the fabrication process of the VSDs that includes four steps: synthesis of SiO2 microspheres, dispersion of SiO2 microspheres, mixing of SiO2 microspheres and SU-8 photoresist, and spin coating and soft bake.
The methods of synthesizing SiO2 microspheres include microemulsion, precipitated silica, Stöber method, and biomimetic sol-gel . The Stöber method is commonly used because of its simple reaction process, easy operation, low reaction cost, and high monodispersity of the obtained SiO2 microspheres . The sizes of SiO2 microspheres synthesized by the Stöber method range from 0.05 µm to 2 µm in diameter. According to the wavelength dependence of the scattering cross-section at the value of δ = λ/d, where λ and d are the wavelength of the incident light and the diameter of the microspheres, respectively, when δ ≥ 10, the light scattering behavior can be classified as Rayleigh scattering; when 10−2 ≤ δ ≤ 10, the light scattering behavior can be classified as Mie scattering . Strong Mie scattering decreases the reflectivity of incident light at the front interfaces of the VSDs, thereby improving the light utilization efficiency of the optical system . In laser displays, the laser sources are visible (wavelength: 400-700 nm). To generate Mie scattering by the VSDs, the size of the SiO2 microspheres should be greater than 0.04 µm according to the formula δ = λ/d. Therefore, we synthesized SiO2 microspheres with a diameter of 1-2 µm via the Stöber method. The reactant included two solutions: solution I containing 0.015 g of KCl (Aladdin, analytical grade, purity: 99.5%), 60 mL of ethanol (Aladdin, analytical grade, purity: ≥ 99.7%), 7 mL of deionized water (resistivity: 18.25 MΩ · cm), and 9 mL of NH3·H2O (Aladdin, analytical grade, purity: 25-28%) was added to a 250-mL four-necked flask, and solution II, containing 35 mL of ethanol and 6.04 g of tetraethyl orthosilicate (Sinopharm Chemical Reagent Co., Ltd, analytical grade) was mixed by a magnetic stirrer for 20 minutes and subsequently added into the four-necked flask using a syringe pump at a supply rate of 0.1 mL/min. The reaction was conducted at 25 °C with mechanical stirring at 200 rpm using an agitator blade. In general, SiO2 microspheres are prone to aggregation because the number of hydroxyl groups present in their large specific surface area can easily condense a molecule of water . Silane coupling agents, such as γ-methacryloxy propyl trimethoxy silane, can be used to change the surface properties of SiO2 microspheres by covalent bonds . We added 0.188 mL of γ-methacryloxy propyl trimethoxy silane to the reaction system using a pipette to modify the surface properties of the SiO2 microspheres. After further reaction for 12 hours, modified micro-sized monodispersed SiO2 microspheres in suspension were obtained. To remove the excess reactant from the surface of the SiO2 microspheres, the obtained SiO2 microspheres were purified by centrifugation and ultrasonic cleaning using ethanol for three times and subsequently dried under vacuum at 40 °C for 5 hours. Figure 2 shows the morphology of the SiO2 microspheres using scanning electron microscope (SEM). The size distribution of the obtained SiO2 microspheres (Fig. 2) was measured by the Nano Measurer software. The average diameter of the SiO2 microspheres was 1.43 µm with a polymer dispersity index of 1.08%.
In a colloidal system, microspheres maintain their individuality but lose their mobility either partially or entirely . In other words, it is difficult to uniformly disperse SiO2 microspheres in the SU-8 photoresist because of the high viscosity of SU-8. The low-viscosity organic solvent, cyclopentanone (thinner for the SU-8 photoresist), was employed to disperse SiO2 microspheres before they were added to SU-8 . The dosage of cyclopentanone was obtained by calculating the mass difference of SU-8 2150 before and after dilution, where the diluted mass of SU-8 photoresist is equal to the mass of SU-8 2150 multiplied by the ratio of the solid content of SU-8 2150 before and after dilution. The solid content of SU-8 2150 was 76.75%, and the solid content of the diluted SU-8 photoresist was approximately equal to that of SU-8 2025 (68.55%). The amount of SiO2 microspheres can be calculated based on the fact that the VSD is fabricated by mixing SU-8 photoresist and SiO2 microspheres at a mass fraction of 85:15. After SiO2 microspheres were dispersed into cyclopentanone, a two-step dispersion process was introduced: magnetic stirring for 5 minutes and ultrasonic deagglomeration for 10 minutes.
Next, a suspension of cyclopentanone and SiO2 microspheres was poured into SU-8 2150. The suspension and SU-8 2150 were mixed by Vaccum Rev-Rot Gravity Mixer (VM300SA2, SINOMIX, Mianyang, China). The mixing is performed in two steps: the first step is to mix at 1780 rpm for 120 seconds, and the second step is to mix at 300 rpm for 180 seconds. The mixing process was repeated five times. The obtained mixture was used to fabricate the VSDs.
VSDs were fabricated by spin coating on glass substrates. Before spin coating, the two-inch glass substrates were cleaned using acetone and ethanol successively in an ultrasonic environment, followed by rinsing with deionized water. The cleaned glass substrates were heated at 80 °C for 1 hour to dehydrate. The spin coating program consists of two steps: a spin speed of 500 rpm for 20 seconds at an acceleration of 100 rpm/s, followed by a spin speed of 4500 rpm for 60 seconds at an acceleration of 800 rpm/s. To obtain VSDs with different thicknesses, we changed the spin speed of the second step to 1800 rpm, 1200 rpm and 1100 rpm, respectively . Soft bake was implemented with the help of a contact hotplate. To ensure that the SU-8 photoresist was fully cured, the bake condition for the VSD obtained by spin coating at 4500 rpm was 65 °C for 3 minutes and 95 °C for 6 minutes; for the other thicker VSDs, the bake conditions were modified to 65 °C for 5 minutes and 95 °C for 10 minutes. Figure 3 shows the SEM images of the cross-sections of the fabricated VSDs.
According to the SEM images shown in Fig. 3, the thicknesses of the fabricated VSDs are 25 µm at 4500 rpm (Fig. 3(a)), 41 µm at 1800 rpm (Fig. 3(b)), 62 µm at 1200 rpm (Fig. 3(c)), and 89 µm at 1100 rpm (Fig. 3(d)). It can be seen from Fig. 3 that the scattering particles of SiO2 microspheres are dispersed in the matrix SU-8 photoresist. Under constant mass fraction of the scattering particles and the matrix, obviously, thicker VSDs contain more scattering particles and scatter light more significantly. The scattering angles (full width at half maximum) of the VSDs are measured, which are approximately < 2°, 52°, 68°, and 100° for the VSDs with thicknesses of 25 µm, 41 µm, 62 µm, and 89 µm, respectively. The optical losses of the VSDs are mainly caused by the reflections existing in the air/VSD/air interfaces, which are about 60%.
3. Experiments and discussions
3.1 Experimental setup
Figure 4 schematically shows the two-diffuser speckle reduction system consisting of stationary and moving VSDs. We used a high-coherence HeNe laser and a low-coherence multimode LD as the light source. The HeNe laser has a Gaussian spectral profile with the central wavelength of λHeNe = 632.8 nm and the spectral width (full width half maximum) of ΔλHeNe ≈ 0.03 nm; the multimode LD has a multiline spectrum profile with the central wavelength of λLD = 525.2 nm, the longitudinal mode spacing of ΔλLD ≈ 0.08 nm, and the overall bandwidth of about 1.5 nm . The driving current of the LD was 150 mA, and the working temperature of the LD was stabilized at 20 °C using a temperature-controlled mount. The laser beam was expanded by a 20 × beam expander. A rotatable linear polarizer was employed to adjust the light intensity of the laser beam. The aperture of the laser beam was redefined by an iris with a diameter of Ф = 10 mm. Cascaded VSDs were placed after the iris. The first VSD was fixed on a motorized linear translation stage (Thorlabs, maximum traveling distance: 50 mm, resolution: 0.05 µm) driven by a stepper motor actuator, and the second VSD was fixed on the optical table. The distance between the two VSDs was approximately 1 mm. Subjective speckles formed on the cascaded VSDs were recorded using a charge-coupled device (CCD) camera with a mounted imaging lens. The aperture of the mounted imaging lens is about 1 mm in diameter. The exposure time of the CCD camera was set to 300 ms. The distance between the cascaded VSDs and the CCD camera was 120 mm. During the experiment, we rotated the linear polarizer to maintain the CCD camera working in its linear region. The driving speed of the motor, that is, the speed of the moving VSD, was changed from 0 to 0.05 mm/s with an increasing interval of 0.005 mm/s.
3.2 Results and discussions
Subjective speckle contrasts C were obtained by calculating the ratios between the standard deviations and the mean values of the speckle intensities. Figure 5(a) shows the relationship between the subjective speckle contrast and the driving speed of the motorized linear translation stage when the high-coherence HeNe laser and the low-coherence multimode LD are employed. Figure 5(b) shows subjective speckle images when the driving speeds of the motorized linear translation stage are minimum (0 mm/s) and maximum (0.05 mm/s). The first to fourth columns correspond to the cascaded VSDs with 25 µm, 41 µm, 62 µm, and 89 µm thicknesses, respectively. The first and second rows are the conditions when the driving speeds of the motorized linear translation stage are minimum and maximum, respectively, where the high-coherence HeNe laser is used as light source. The third and fourth rows are the conditions that the driving speed of the motor is minimum and maximum, respectively, where the low-coherence multimode LD is used as the light source.
When the same laser source is used, as shown in Fig. 5(a), the subjective speckle contrast C decreases with an increase in the thickness of the cascaded VSDs. With increasing thickness of the cascaded VSDs, both the arrival time of the photon spread in the cascaded VSDs and the variance of the path length increase . When the laser beam transmits through the cascaded VSDs, the spatial coherence of the laser is destroyed by the optical path length differences caused by the cascaded VSDs with different thicknesses. As expected, with increasing thickness of the cascaded VSDs, the speckles are eventually washed out, where the standard deviation of the speckle intensity becomes zero in the ideal limit. Therefore, we can conclude that speckles can be suppressed by cascaded VSDs in the stationary state, and the speckle reduction effect becomes better as the thickness of the VSD increases. Compared with surface diffuser, VSD is more effective in speckle reduction. This is confirmed by the experimental results shown in Fig. 5(b). When the HeNe laser is used as the laser source, the subjective speckle contrast C of the cascaded VSDs with thicknesses of 25 µm, 41 µm, 62 µm, and 89 µm are 0.92, 0.85, 0.8, and 0.72, respectively (first row in Fig. 5(b)), while these values are 0.47, 0.35, 0.31, and 0.19, respectively, for the multimode LD (third row in Fig. 5(b)).
In addition to the influence of VSD thickness on speckle reduction, Figs. 5(a) and 5(b) show that speckles are reduced more effectively when the laser source is the multimode LD than the HeNe laser, when the same thick cascaded VSDs are used. For example, as shown in Fig. 5(b), for the cascaded VSDs with the thickness of 25 µm, the subjective speckle contrast C is 0.47 (the first column of the third row in Fig. 5(b)) when the multimode LD is used as the laser source; the value is 0.92 (the first column of the first row in Fig. 5(b)) when the HeNe laser is used as the laser source. This is because the equivalent linewidth of the multimode LD is larger than that of the HeNe laser . Thus, the coherence length of the HeNe laser is much larger than that of the multimode LD. The spatial coherence of the low-coherence multimode LD is more easily destroyed than that of the high-coherence HeNe laser under the same optical path length difference.
When the cascaded VSDs are actuated, a speckle reduction mechanism by temporal averaging of different speckle patterns in the integration time of the camera is introduced. In this situation, for speckle reduction, we assume that the VSDs operate in a manner similar to that in surface scattering, and the speckle contrast is given by 
From Fig. 5(a), we observe that the subjective speckle contrast C decreases with an increase in the driving speed of the motor. When the driving speed of motor v increases, the temporal correlation coefficient μA(τ) of the cascaded VSDs decreases . After substituting μA(τ) into Eq. (1), the subjective speckle contrast C decreases with an increase in the driving speed of the motor. Under high-speed motor driving, the subjective speckle contrast C in Fig. 5(a) tends to be saturated. The saturation of subjective speckle contrasts can also be explained by the relationship between the temporal correlation coefficient μA(τ) of the cascaded VSDs and the driving speed of the motor. When the driving speed of the motor is high, subjective speckle contrasts become saturated because of the saturation trend of the temporal correlation coefficient μA(τ) of the cascaded VSDs . When the driving speed of the motor increases from 0 to 0.05 mm/s, the subjective speckle contrast C decreases from 0.92, 0.85, 0.8, and 0.72 (first row in Fig. 5(b)) to 0.24, 0.19, 0.17, and 0.14 (second row in Fig. 5(b)) respectively, when the HeNe laser is used as the laser source, where the thicknesses of the cascaded VSDs are 25 µm, 41 µm, 62 µm, and 89 µm, respectively. When the multimode LD is used as the laser source, the subjective speckle contrast C decreases from 0.47, 0.35, 0.31, and 0.19 (third row in Fig. 5(b)) to 0.15, 0.11, 0.09, and 0.07 (fourth row in Fig. 5(b)) respectively, when the thicknesses of the cascaded VSDs are 25 µm, 41 µm, 62 µm, and 89 µm, respectively.
Generally, there are tradeoffs between speckle reduction and the performance of the optical system in laser display. Comparing with a single-diffuser system, the introduction of two-diffuser system reduces speckle more effectively. Imaging blurring is the first consequence for the two-diffuser system. The scatterings caused by the first VSD result in the overlaps of nearby pixels on the second VSD. As thicker VSDs are introduced, image blurring becomes worse. Another consequence is optical loss by the two-diffuser system because light is scattered more seriously and the existence of reflections among the air/VSD/air interfaces. In some laser display cases where a small-size screen and low image brightness are preferred, such as laser TVs, the two-diffuser system are applicable.
In conclusion, we have fabricated VSDs by spin coating a mixture of SiO2 microspheres and SU-8 photoresist, where the SiO2 microspheres were synthesized and modified by the Stöber method. The VSDs with the thicknesses of 25 µm, 41 µm, 62 µm, and 89 µm were used to investigate the speckle reduction effect of a two-diffuser system. When the photon transmitted through the VSDs, it will undergo multiple scattering, resulting in random optical path differences and the destruction of the laser spatial coherence. When one of the VSDs is moving, the temporal correlation of the VSDs decreases with an increase in the driving speed of the motor. Therefore, by combining these speckle reduction mechanisms, thicker VSDs driven at high speeds under low-coherence LD illumination reduce speckles more effectively. The experimental results presented here help the understanding of the speckle reduction theory of a moving two-diffuser system under the modification of the thicknesses of the VSDs. Thus, the results could facilitate the designing of similar speckle reduction techniques with greater efficiency in laser displays. By using other fabrication technologies, such as an electrospray technique, low-cost VSD can be fabricated for mass production .
National Key Research and Development Program of China (2016YFB0401903); Natural Science Foundation of Shanxi Province (201901D111024); Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (IRT_17R70); State Key Program of National Natural Science of China (11434007); 111 Project (D18001); Fund for Shanxi “1331 Project” Key Subjects Construction.
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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