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Abstract
An adaptive liquid lens with controllable light intensity is demonstrated, which can modulate both light intensity and beam spot size. The proposed lens consists of a dyed water solution, a transparent oil, and a transparent water solution. The dyed water solution is used to adjust light intensity distribution by varying the liquid-liquid (L-L) interface. The other two liquids are transparent and designed to control the spot size. In this way, two problems can be solved: the inhomogeneous attenuation of light can be achieved through the dyed layer, and a larger optical power tuning range can be achieved through the two L-L interfaces. Our proposed lens can be used for homogenization effects in laser illumination. In the experiment, an optical power tuning range from - 44.03 m−1 ∼ + 39.42 m−1 and an ∼ 89.84% homogenization level are achieved. Our proposed lens may also ease the vignetting problem in imaging systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Liquid photonic devices are gradually becoming the future trend of photonic devices due to the advantages such as simple structure, low cost, and low power consumption. Compared with traditional photonic devices, liquid photonic devices have unique merits such as tunability and adaptability. Liquid photonic devices can be roughly classified as liquid lenses [1–9], liquid optical switches [10–15], liquid prism [16–18], and so on. Recently, these devices have been used to control the beam due to its tunability. For example, liquid lenses achieve the control of beam convergence or divergence by tuning the curvature of the liquid-liquid (L-L) interface [19,20]. However, one L-L interface is inadequate to control the beam well. Fortunately, liquid-lens systems bring a better solution. For example, a zoom microscope objective using electrowetting liquid lenses is proposed, which can also be used to adjust the spot size dynamically [21]. An all-liquid optical zoom system based on two independently controllable liquid lenses is proposed, which is used to zoom as well as adjust spot size [22]. An 8× four-group non-mechanical moving zoom system is proposed using liquid lenses to complete the zoom function. The system can also be used to adjust spot size at different working distances [23]. However, the light intensity is difficult to be adjusted by the liquid-lens system. Another liquid photonic device is more suitable for modulating the light intensity. Liquid optical switches based on dyed liquid are used to attenuate the intensity of the beam. For example, an optical switch based on a deformable liquid droplet is proposed, which controls the shape of the droplet to realize attenuation [24]. Moreover, another optical switch based on the electrowetting effect is proposed which consists of transparent oil and dyed water filled in a cell [25]. In addition, a bidirectional optical switch based on electrowetting is proposed, in which two separated light beams can be controlled by a single droplet. Furthermore, a liquid iris whose aperture can be tuned electrically based on electrowetting is proposed. When a voltage is applied to the liquids, the diameter of the iris is enlarged due to the electrowetting effect [26]. Nevertheless, these optical switches can only control the beam aperture size, however, cannot modulate the light intensity distribution or the beam divergence angle. Currently, no device can modulate both light intensity distribution and beam divergence angle. Therefore, there is an urgent need for new liquid photonic devices capable of controlling light intensity distribution and beam divergence angle to achieve modulation of spot size and intensity distribution and to solve the vignetting problem in imaging systems.
In this paper, we propose an adaptive liquid lens with controllable light intensity, which consists of a dyed water solution, a transparent oil, and a transparent water solution. the dyed water is used to adjust light intensity distribution by varying the L-L interface. The other two transparent liquids are designed to control the spot size. In the experiment, we achieve an optical power range from - 44.03 m−1 ∼ + 39.42 m−1 and an ∼ 89.84% homogenization level. Thus, our liquid lenses can be used for homogenization in laser illumination.
2. Schematic and principle
The principle and operation mechanism of the proposed lens is depicted in Fig. 1. As shown in Fig. 1(a), the proposed lens consists of a lens chamber, two limit rings, and two pieces of window glass. The dyed water solution (Liquid 1) is injected into the bottom of the chamber, and the oil (Liquid 2) is injected into the middle part of the chamber between the two limit rings. The transparent water solution (Liquid 3) is injected into the rest of the space. The refractive index of the oil phase is greater than the two water phases, and the refractive index of the dyed and transparent water phases is almost the same. The densities of the liquids are matched to reduce the gravity effect. The proposed lens has a dyed layer which is a transparent water solution dyed with black pigment to achieve inhomogeneous attenuation of the light beam.
Fig. 1. Device structure and operation mechanism of the proposed lens. (a) Schematic cross-sectional structure. (b) Central decay state I. (c) Central decay state II. (d) Edge decay state I. (e) Edge decay state II. (f)-(g) Homogenization principle.
The proposed lens can work in four states as shown in Figs. 1(b)-(e): Central decay state I, Central decay state II, Edge decay state I, and Edge decay state II. There are two L-L interfaces in the proposed lens. The interface between the dyed water phase and the oil phase is named L-L interface I, and the interface between the oil phase and the transparent water phase is named L-L interface II. The two L-L interfaces work independently by three channels. Two states of the proposed lens for central attenuation of the beam are shown in Figs. 1(b)-(c). When the oil is continuously pumped into the chamber and the transparent water is pumped out of the chamber, the L-L interface I remains motionless while the L-L interface II curvature changes from negative to positive. In the two states, the incident beam with stronger center light intensity can be homogenized as shown in Fig. 1(f). When the transparent water solution is continuously pumped into the chamber and the dyed water solution is pumped out of the chamber, the curvature of L-L interface I and L-L interface II changes simultaneously, and the lens changes from the central attenuation state to the edge attenuation state. In the two states, the incident beam with stronger edge light intensity can also be homogenized as shown in Fig. 1(g). The proposed lens uses a driver to change the interface curvature by pumping in and out the liquid, which is based on the mechanical-wetting effect. The proposed lens has a balance between the applied hydrostatic pressure $\Delta P$ and the Laplace force. It follows the Yang-Laplace law:
where $\gamma $ is the interfacial tension and k is the mean curvature of the L-L interface, which is $1/R$ for a sphere. Following Gibbs’ criterion, the state of the L-L interface position remains stable as long as the contact line remains pinned to the edge. Assuming that the lens liquids are incompressible and the L-L interface is spherical, the liquid volume $\Delta V$ pumped by the actuator is equal to the volume of the spherical interface. At the location of the limit ring, the relationship between the radius of curvature R and the amount of change in the volume of the liquid $\Delta V$ is expressed as follows:The proposed lens can be used in illumination and imaging application. For homogenization purposes, firstly, the L-L interface I is driven to change the face shape to achieve inhomogeneous attenuation from the center to the edge of the lens. Secondly, L-L interface II is driven to compensate for the optical power to achieve the total optical power of the proposed lens. The proposed lens homogenizes a Gaussian beam and outputs a parallel beam for laser manufacturing. For the imaging system, the proposed lens can adjust the local brightness to ease the problem caused by vignetting.
3. Experiment and result
The proposed lens is fabricated using a transparent material to visually demonstrate the movement and deformation behavior of the two L-L interfaces. The lens chamber is made of polymethyl methacrylate (PMMA). The height, outer diameter, and inner diameter of the proposed lens are 15 mm, 24 mm, and 10 mm, respectively. Liquid 1 is a dyed sodium chloride solution with a density of 1.07 g/cm3 and a refractive index of ∼ 1.35. The pigment is Black PN, and the chemical formula is C28H22N5NaO14S4. Liquid 2 is a phenylmethyl silicone oil with a density of 1.07 g/cm3 and a refractive index of ∼ 1.55. Liquid 3 is a sodium chloride solution with a density of 1.07 g/cm3 and a refractive index of ∼ 1.35. The densities of the three liquids are the same to avoid the gravity effect. A stepper motor is used to drive the reservoir piston to precisely control the amount of liquid in the experiment. As the liquid is pumped in and out, the curvature radii of the two L-L interfaces are changed to attenuate the beam and the overall optical power of the lens changes accordingly.
Firstly, we measured the attenuation coefficient of the proposed lens by irradiating the dyed liquid layer using a light source with a constant power of ${I_0}$. For the different thicknesses of the liquid layer ${d_x}$, the output intensity I was measured, and the attenuation coefficient $\alpha $ is calculated according to Eq. (3). The measured results are shown in Table. 1. The attenuation coefficient $\alpha $ of the proposed lens was obtained by averaging the measurement results as 1.520.
Table 1. Measurement of the attenuation coefficient
In the experiment, the object is placed in front of the proposed lens and the distance is ∼ 100 mm. A camera is placed above it to record the image, and the other camera is placed on the side of the proposed lens to record the movement and deformation of the L-L interfaces. The shift and deformation of the L-L interfaces are shown in Fig. 3. The correspondence among changes in aqueous phase volume (Liquid 1 or Liquid 3), shift distance ($d$), and curvature radius ($R$) is plotted in Fig. 3(a). When the volume of the aqueous phase increases, the position of the L-L interface (pink: shift-in distance) keeps rising, while the curvature radius of the liquid interface (Blue: liquid interface curvature) changes from concave to convex shape. The edge detection algorithm was used in Matlab to extract the liquid surface contour from the experimentally captured image, and then the extracted contour was fitted to the liquid surface radius of curvature using the circle curve equation [1], and a good fit is determined if the fit deviation is less than 3%, and then the radius of curvature is solved. The theoretical relationship between the reciprocal of the curvature radius (${C_1}$ and ${C_2}$) and the total optical power of the lens and the experimental data is plotted in Fig. 3(b). The calculated optical power is shown in Fig. 3(b), and the red dots are the experimentally collected data points, which fit well with the theory. The vertex position of the L-L interface can be shifted from +1.59 mm to −3.61 mm, and the measured optical power range of the proposed lens is - 44.03 m−1 ∼ + 39.42 m−1.
Fig. 3. Optical performance of the proposed lens. (a) Shift and deformation of the L-L interface. (b) Theoretical relationship between the reciprocal of the curvature radius (${C_1}$ and ${C_2}$) and the total optical power of the lens and the experimental data fit.
The proposed lens can be used to control the light intensity in the field of view. As shown in Figs. 4(a)-(b), the optical power and the light intensity are changed by varying the L-L interface I. When the L-L interface I is changed from concave to convex shape, the optical power decreases, and the light intensity decreases accordingly. The image of the specimen “B” becomes smaller and darker. In fact, different from the conventional liquid lens and liquid optical switch, the proposed lens can control the light intensity and optical power independently by controlling the two L-L interfaces independently. For example, when the optical power of the L-L interface I is changed from concave to convex shape, the light intensity decreases accordingly. To keep the same optical power, the L-L interface II is adjusted from a convex to a concave shape. Compared with Fig. 4(a), the size of image “B” remains the same as shown in Fig. 4(c). And, the image becomes darker in the center. The same phenomenon is shown in Figs. 4(b) and (d), which show that the proposed lens can achieve different modulations of the incident light at the same optical power. Besides, it also confirms the feasibility of the two L-L interfaces working independently. The vertex position of L-L interface I can be shifted from +1.59 mm to −3.61 mm and the vertex position of L-L interface II can be shifted from −1.6 mm to +3.60 mm. The experiment also proves the proposed lens may ease the vignetting problem in imaging systems because the light intensity in the center and marginal area can be controlled.
Fig. 4. Movement and deformation driving performance of the proposed lens. (a),(b) Experimental results of movement and deformation and imaging at L-L interface I. (c),(d) Experimental results of movement and deformation and imaging at L-L interface II.
The proposed lens can be applied to a vignetting optical system, and we assembled an anti-vignetting imaging system using a fabricated prototype to demonstrate the anti-vignetting capability of the lens. The anti-vignetting system consists of the proposed lens and a vignetting lens. The proposed lens plays a key role as a unique variable in the anti-vignetting system. The proposed lens undertakes anti-vignetting work in the imaging system. The experimental setup is shown in Fig. 5(a), and the assembled zoom system is shown in Fig. 5(b). The image sensor is a 2/3-inch color CMOS (VCXU-25C) with a 1920 × 1200 pixels resolution. In this process, the syringe tubes of the dyed aqueous phase and the transparent aqueous phase were placed on a stepper motor controlled by our syringe pump, while the syringe tube of the oil phase was fixed to one side.
Fig. 5. Anti-vignetting system using the proposed lens. (a) Experimental setup of the anti-vignetting system. (b) Assembled anti-vignetting system.
The simulation of the working process of the proposed lens was carried out in Zemax. In this experiment, the object distance is ∼150 mm and the back working distance is ∼18 mm. The images for vignetting, anti-vignetting, and post-processing are successively recorded in Fig. 6. The simulation process is shown in Figs. 6(a)-(b), and the imaging experimental results are shown in Figs. 6(c)-(e). The initial state of the anti-vignetting system is shown in Fig. 6(a), where the proposed lens is flat and does not contribute to the optical focus of the system. In Fig. 6(b), the working state of the anti-vignetting system is shown, in which the dye layer of the lens is raised, the light attenuation is strong near the optical axis, and the light attenuation is weak part far from the optical axis, and the degree of attenuation decreases from the center to the edge of the lens along the vertical optical axis. In the initial state, the vignetting is obvious, as shown in Fig. 6(c). Then, we modulated the proposed lens according to the characteristics of the vignetting system. The image was taken as shown in Fig. 6(d). We see that the center area becomes darker than the initial state. However, the light intensity on the whole image becomes uniform Finally, we enhanced exposure in CMOS to brighten the image, as shown in Fig. 6(e). The vignetting problem was eased by the proposed lens. It is worth mentioning that the proposed lens can be flexibly applied to different vignetting systems without changing its system focal length.
Fig. 6. Imaging experiment using the proposed lens. (a) Initial state of zoom system based on Zemax simulation. (b) Operating state of zoom system based on Zemax simulation. (c) Captured image in the initial state. (d) Captured image in the operating state. (e) Final result.
The proposed lens can be used in Gaussian beam homogenization systems for adjusting light intensity. In the Gaussian beam homogenization system, the lens performs a flat-topping operation on the laser beam, converting the laser beam spot with Gaussian beam morphology into a laser spot with uniform energy distribution and adjustable spot size. The Gaussian beam homogenization system is shown in Fig. 7, which consists of the proposed lens, a laser (MRL-III-635 L), a laser beam expander, and a Surface array detector (BEAMAGE-3.0). The laser and the laser beam expander are used to create a Gaussian beam. The Surface array detector is used to obtain the energy distribution of the beam spot.
In the first experiment, the Surface array detector is placed ∼ 100 mm away from the proposed lens. In the initial state, the initial shape of the two L-L interfaces is flat. And the beam is a Gaussian beam as shown in Fig. 8(a). When the L-L interface I is changed by syringe pumps. The intensity distribution is changed as shown in Fig. 8(b). To get the homogenized beam, the radius of the L-L interface I $R_1$ is changed to ∼ 28.65 mm, and the radius of the L-L interface II $R_2$ is changed to ∼ 11.24 mm. The final homogenized beam is shown in Fig. 8(c). The light intensity of the spot at different distances from the optical axis for $R_1$=∼28.65 mm and $D$=10 mm is shown in Table. 2, while we calculated the theoretical values of the output light intensity based on Eq. (3). The error analysis is shown in the line graph on the right-hand side of Fig. 8, where $It$ represents the theoretically calculated light intensity value, and $Ir$ represents the experimentally measured light intensity value. And the error is calculated as $\Delta I = {I_t} - {I_r}$, with the specific values indicated in the line diagram. The spot size is ∼ 9.2 mm. The central intensity of the spot before homogenization is 8.2 µw, and the intensity in the marginal area is 5.1 µw. After homogenization by our proposed lens, the intensity in the central area is 5.6 µw and the intensity in the marginal area is 5.0 µw. From the experiment, we can conclude that the proposed lens can achieve a homogenized spot at fixed working distances.
Fig. 8. Homogenization process of Gaussian beam using the proposed lens at D = 10 cm. (a) Initial state. (b) Intermediate state. (c) Final state.
Table 2. Measurement of spotlight intensity after homogenization
In the second experiment, the Surface array detector is placed a different distance away from the proposed lens. The calculation of the homogenization rate is defined as $H = 1 - ({{I_c} - {I_m}} )/{I_c}$, and its root mean square is ${H_{rms}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^N H_i^2}}{N}} = \sqrt {\frac{{H_1^2 + H_2^2 + \cdots + H_N^2}}{N}} $. The results of homogenization at different working distances are shown in Table. 3. We varied the radii of L-L interface I and II to obtain a homogeneous beam for different values of D. For D = 100 mm, we set the radii to ∼ 28.65 mm and ∼ 11.24 mm, respectively. A central intensity of 5.62 µw and a marginal intensity of 5.06 µw are obtained for the homogenized spot, and a homogenization rate reached 90.04%, as shown in Fig. 9(a). For D = 125 mm, we set the radii to ∼ 28.68 mm and ∼ 16.47 mm, respectively. A central intensity of 5.53 µw and a marginal intensity of 4.96 µw are obtained. In this state, the homogenization rate is 89.69%, as shown in Fig. 9(b). For D = 150 mm, we set the radii to ∼ 28.72 mm and ∼ 20.53 mm, respectively. A central intensity of 5.48 µw and a marginal intensity of 4.92 µw are obtained, and homogenization is 89.78%, as shown in Fig. 9(c). In the three states, the spot size is measured to be ∼ 9.20 mm, ∼ 9.22 mm, and ∼ 9.23 mm, respectively. And the RMS homogenization rate ${H_{rms}}$ is ∼ 89.84%. The experiment demonstrates that the proposed lens can achieve a uniform light spot over a wide working distance range.
Fig. 9. Homogenization of the Gaussian beam using the proposed lens at different working distances. (a) D = 100 mm. (b) D = 125 mm. (c) D = 150 mm.
Table 3. Homogenization at different working distances
We note that light loss is unavoidable for the proposed lens. However, several methods can be used to compensate for the light loss. In the vignetting system, an image with proper brightness can be obtained by extending the exposure time. In the laser homogenization systems, the light loss can be compensated by increasing the laser power or extending the laser action time.
4. Conclusion
In this paper, a light intensity controllable liquid lens is demonstrated, which can modulate both light intensity and beam spot size. The proposed lens consists of a dyed water solution, a transparent oil, and a transparent water solution. The dyed water solution is used to adjust light intensity distribution by varying the L-L interface. The other two liquids are transparent and designed to control the spot size. In this way, two problems can be solved: the inhomogeneous attenuation of light can be achieved through the dyed layer, and a larger optical power tuning range can be achieved through the two L-L interfaces. Our proposed liquid lens can solve the vignetting problem in imaging systems, and it can also be used to achieve homogenization effects in laser illumination. In the experiment, we achieve an optical power range from - 44.03 m−1 ∼ + 39.42 m−1 and an ∼ 89.84% homogenization level. Compared with conventional liquid lenses, the proposed lens can modulate both beam intensity distribution and beam spot size which is not available for existing liquid lenses.
Funding
National Natural Science Foundation of China (61975139, 61927809).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data is available from the authors on request.
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