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Abstract
Current static speckle suppression methods have an extremely large system size and unsatisfactory performance. This study proposes a device called beam-splitting cavity (BSC) and establishes a model of speckle suppression based on the combination of BSC and a liquid-core fiber. Subsequently, a passive static speckle suppression system is constructed and the key factors affecting the speckle contrast are studied. Consequently, the speckle contrast was reduced from 30.2% to 3.1%, which is below the human-eye speckle-discrimination limit (<4%). The scheme consists entirely of passive optical elements, which are more applicable to projectors than the traditional static and dynamic speckle-suppression methods.
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1. Introduction
Three types of light sources are commonly used in projectors: traditional light sources, such as halogen lamps, light-emitting diode (LED), and lasers. Traditional light sources are bright and inexpensive; however, they have a short lifetime, which is typically thousands of hours. LED have high energy efficiency, a long lifetime, and a wider color gamut than traditional light sources; however, they have low brightness and are more suitable to be used in the situations where the ambient light is low. Lasers based on stimulated emission have the advantages of high brightness, long lifetime, low energy costs, and a further increase in the color gamut compared to LED [1]. However, the high coherence of laser causes speckle, which is a random granular noise pattern that is observed when the laser is diffusely reflected at a surface with a rough structure, such as a display screen, or a metallic surface. It seriously degrades image quality and limits the use of lasers as a projection light source [2].
Laser speckle not only degrades the image quality of projectors but can also cause discomfort to viewers. The effect of laser speckles on image quality has become the most significant challenge in the application of laser projection technology. Laser speckle suppression has been extensively studied in recent years [3].
The speckle contrast $C = \sigma /\bar{I}$ is generally used to measure the magnitude of a laser speckle [4], which is defined as the ratio of light intensity standard deviation (σ) to the light intensity average ($\bar{I}$). Many innovative speckle-suppression methods have been proposed, which can be divided into several types. For optical systems with or without active elements, speckle suppression methods can be categorized as dynamic, static, or a combination of dynamic and static methods. The reported dynamic suppression methods can be classified into two main types. One type uses temporal averaging generated by moving phase-modulated optical elements. The most popular method uses a moving diffuser plate [5–9], where the laser beam scatters at each point on the diffuser surface. The speckle pattern can be superimposed on an intensity basis by the displacement of the diffuser plate. The speckle can be suppressed by time averaging. Similar methods include the use of vibrating multimode fibers [10–13], moving apertures [14], laser through a time-variable ultrasonic grating [15–17] or a coded time-variable diffractive optical element (DOE) [18–22], a mechanically scanned micro-electro-mechanical system (MEMS) device [23,24], a rotating array of microlenses [25], and a dynamic deformable mirror [26–28]. In another type of dynamic suppression method, the element itself does not move, but the particles within it do. Speckles can be suppressed by dynamically scattering the laser light by moving these particles in the element. Examples include the dynamic scattering of colloidal particles in a colloidal solution [29–31] and the dynamic scattering of molecules in a liquid-core fiber [32]. Static-suppression methods can be classified into two types. The first type uses static devices with electro-optical, magneto-optical, and acousto-optic modulations, which generate a time-varying speckle pattern using electronic control. For example, methods using the electro-optical modulation effect of liquid crystals created a time-varying phase distribution of the laser to suppress speckles [33–46]. Another type involves creating a certain optical path difference using passive optical elements to reduce the coherence of the laser. For example, a study suppressed speckles using the intermode dispersion of a multimode fiber [12,47–50] or optical retardation [51–53], as well as ultra-wideband or random lasers [54–58]. The combination of static and dynamic methods typically generates a time-varying phase distribution of the laser beam using a dynamic element and amplifies this time-varying effect using another static element. Therefore, the amplitude of mechanical motion in this method is significantly smaller than that in a simple dynamic method. For example, speckle noise can be reduced by combining a vibrating multimode fiber and a diffuser [12], or using a rotating lens array with a rod integrator [59].
The current methods for speckle suppression have a few disadvantages. Dynamic methods using mobile devices require a relatively violent mechanical motion to achieve a satisfactory suppression effect, which is not ideal for practical applications. Moreover, the dynamic method using dynamic scattering from particles in a solution has relatively weak dynamic scattering and generally requires a longer optical path through the solution or an increase in the density of the solution. An increase in the speckle-suppression effect causes a severe weakening of the transmittance, which is not ideal for laser-display applications. Moreover, static speckle-suppression methods using electro-optic, magneto-optic, or acousto-optic modulation require an additional power supply, and the speckle-suppression effect is relatively limited for achieving a large speckle-suppression ratio. In addition, the method of using a multimode fiber requires an unreasonably long fiber to achieve strong speckle reduction, which significantly limits its application in an actual laser projector. The use of static elements, such as optical retardation, to suppress speckles is limited by the number of superimposed decoherent beams that can be utilized to achieve sufficient speckle suppression. The advantage of the combined method is that speckle suppression is generally effective and mechanical vibrations are relatively weak compared to the dynamic method. However, it is still influenced by mechanical vibrations and usually involves a more complex optical system, resulting in a bulky system.
In this study, we developed a device called the beam-splitting cavity (BSC), which can introduce a larger optical path difference and produce a greater number of decoherent sub-beams compared to optical retardation. Subsequently, we propose a speckle-suppression scheme that superimposes these decoherent sub-beams by coupling them to a liquid-core fiber. Each sub-beam exiting the BSC produces a decoherence by the liquid-core fiber. Therefore, the coherence of the laser was further reduced, and the sub-beams were superimposed by the bulk scattering of the liquid. We established a theoretical model for analyzing and determining the key factors that affect the speckle-suppression efficiency, including the beam-splitting ratio, length of the BSC, and number of sub-beams. Subsequently, we assembled an experimental system to investigate and obtain the ideal settings for these three factors. Finally, the speckle-suppression efficiency was experimentally verified using the proposed scheme with the BSC and liquid-core fiber, and the speckle contrast was reduced from 30.2% to 3.1%, which is markedly lower than the human-eye speckle-discrimination limit (4%).
2. Principle of the proposed optical scheme
2.1 Fundamental theory of speckle suppression
Trisnadi [53] analyzed the factors causing speckle reduction in a laser projection display system and concluded that the speckle-reduction efficiency of a system, R, is the product of three speckle-reduction factors:
where ${R_\lambda }\; $, $\textrm{}{R_\sigma }$, and ${R_\Omega }$ are the speckle reduction factor by wavelength, polarization, and angular diversities, respectively. Moreover, ${R_\lambda }$ can be written as where $\Delta d$ is the average surface-profile height variation of a projection screen, and ${L_c}$ is the coherence length of the light source. Therefore, ${R_\lambda }$ depends on the characteristics of the light source and roughness of the screen.A previous study [60] summarized the effect of polarization diversity as follows: when a polarization-preserving screen is used, there is no suppression of speckles by polarization diversity; when a completely depolarized screen is used, the factor due to polarization diversity is between $\sqrt 2 $ and 2. If the incident light is polarized, there are two uncorrelated speckle patterns due to the depolarization of the screen, and ${R_\sigma }$ is $\sqrt 2 $. If the incident light is unpolarized, two uncorrelated speckle patterns are formed for each polarization state after screen scattering. Therefore, there are four uncorrelated speckle patterns, and ${R_\sigma }$ is 2.
The reduction factor by the angular diversity, ${R_\Omega }$, is given by:
2.2 Proposed optical scheme
In this study, the BSC (Fig. 1) comprises of a reflector and beam splitter, which produces numerous decoherent sub-beams. The device introduces a large optical path difference between two adjacent sub-beams. Many sub-beams with extremely large differences in the optical path can be achieved by the BSC.
A liquid-core fiber was introduced for effective superimposition of the speckle patterns produced by the sub-beams from the BSC. Compared to ordinary multimode fibers, a liquid-core fiber has a larger numerical aperture and better uniformity of emitted light. Owing to the effects of intermodal dispersion and bulk scattering of the liquid-core fiber, the spatial coherence of the incident light can also be reduced. However, the effect of speckle suppression is restricted when only a liquid-core fiber is used. With an increase in the length of the liquid-core fiber, the speckle contrast gradually approaches a constant value. Consequently, the speckle contrast cannot be suppressed to a low degree using only the liquid-core fiber.
Combining the BSC with the liquid-core fiber not only solves the difficulty of superimposing sub-beams from the BSC, but also further reduces the coherence of the laser by involving in further angular diversity and achieves a significantly lower speckle contrast. To achieve the optimized speckle-suppression effect, we must analyze and optimize the key parameters of the proposed scheme based on a combination of the BSC and liquid-core fiber.
To study the key factors affecting the speckle-suppression effect of the proposed scheme, the mechanism of speckle suppression in the scheme was first studied. The key function of this scheme is to reduce the coherence of the laser. As illustrated in Fig. 1, a BSC splits a laser beam into a series of sub-beams with a constant and large optical path difference between adjacent sub-beams. The sub-beams exiting the BSC were then coupled to a liquid-core fiber. With intermodal dispersion and bulk scattering of the liquid-core fiber, the sub-beams are temporally spread and superimposed. Notably, the effect on the reduction in coherence is greatly diluted when the optical path difference between the sub-beams introduced by the BSC is small. Therefore, the length of the BSC is the first key factor influencing the speckle-suppression effect and must be sufficiently large. With a sufficiently large BSC length and a sufficient angle difference between sub-beams, the speckle patterns from each sub-beam were independently uncorrelated. The relationship between the ratio of speckle suppression to the intensity of the independent speckle pattern can be written as:
In summary, three key factors affect the speckle-suppression effect of the proposed scheme: the beam-splitting ratio of the beam splitter, the length of the BSC, and the number of sub-beams to be superimposed. Therefore, we investigated the effects of the beam-splitting ratio, number of sub-beams, and length of the BSC on the speckle suppression performance.
3. Experiments and discussion
To determine the optimal parameters to achieve the best possible speckle suppression performance, a series of experiments were conducted to test the variation in the speckle-suppression effect under different parameters.
The BSC used in the experiment consisted of a silver-plated beam splitter and broadband dielectric reflector. The beam splitter measured 50 mm × 50 mm × 0.7 mm, with a transmittance-to-reflectance ratio of 5/95. The broadband dielectric reflector had a diameter of 50 mm and has a high reflectance for light from 400 to 700 nm. The liquid-core fiber (LUMATEC Series380) used in the experiments had a diameter of 8 mm and a length of 1.5 m.
The Thorlabs semiconductor laser (OSRAM PL 520B1) used in the experiment has a central wavelength of 520 nm and Δλ = 2 nm, the decorrelation length therefore is around 135.2 µm. As shown in Fig. 2, the laser has an initial speckle contrast of C0 = 30.2%.
Fig. 2. (a) Measured light spot of the laser, (b) One-dimensional intensity distribution of the light spot along the yellow line in (a).
The experimental setup is illustrated in Fig. 3:
Fig. 3. Optical scheme for speckle suppression experiments with a BSC, where S1 = 40 mm, S2 = 70 mm, S3 = F1 = 100 mm, S4 = 50 mm, S5 = S6 = 1 m, S7 = F3 = 25 mm, D1 = 5 mm, D2 = 50.8 mm, D3 = 8 mm, D4 = 50.8 mm and L = 1.5 m.
The collimated laser beam was incident on the BSC with a length of S1, and sub-beams with specific optical path differences were generated. Next, the sub-beams from the BSC were coupled to the liquid-core fiber using a coupling lens and were transmitted and superimposed within the liquid-core fiber. The light emitted at the distal end of the fiber was projected onto the screen using a projection lens. Finally, an image of the screen was captured using a camera. The focal lengths of the coupling lens, projection lens, and camera lens were F1 = 100, F2 = 60 mm, and F3 = 25 mm, respectively.
3.1 Effect of beam-splitting ratio
The intensity distribution of sub-beams is a key factor in speckle suppression and it is determined by the beam-splitting ratio of the beam splitter and reflection loss of the reflector. To obtain an optimal beam-splitting ratio that supports a large speckle suppression ratio as well as low light intensity loss, the loss caused by reflection was measured in the experiments.
The light spots were recorded using a camera (Thorlabs DCC3260M), and the intensity distribution of the light spots was analyzed using Image J software. We used a group of 10 sub-beams, sequentially recorded the speckle patterns for different number of sub-beams, and analyzed and determined the intensity of each sub-beam. Because the splitting ratio and reflection loss are insensitive to the angle, the measured intensity of each sub-beam can be fitted with an exponential function, which indicates the change in intensity of the speckle pattern of each sub-beam. The curves of the spot intensity variations are depicted in Fig. 4.
Figure 4 illustrates the fitting curve of the spot intensity of each sub-beam from the group of 10 sub-beams. It reveals the declining tendency of the sub-beam intensity with an increase in the order of the sub-beams. By analyzing the measured intensity of the sub-beams and eliminating the singularities, we can express the fitting curve of the light-spot intensity variation as
where x is the order of the sub-beam, and y is its average optical intensity. The fitted exponential function reveals that the intensity of the sub-beam decreases with the order, and the ratio of the two adjacent sub-beams is 0.9333. Therefore, when light travels within the BSC for one cycle, its intensity decreases by 0.0667, which comprises both sub-beam transmission and reflection loss. In addition, the measured original average intensity of the laser spot (I0) was 1160.01, and the optical intensity of the first sub-beam spot was 58.55. Therefore, the beam-splitter transmittance T = 58.55/1160.01 = 0.0505, and the reflection loss of a sub-beam passing through the BSC was 0.0162.Because the difference in the reflection loss between the beam splitters was very small, we analyzed the best beam-splitting ratio at a reflection loss of 0.0162. In previous experiments, we placed the beam splitter parallel to the reflector, and only ten sub-beams were generated due to the size limitations of the reflector and beam splitter. The number of sub-beams can be further increased by marginally varying the reflector angle relative to the beam splitter. In addition, because the liquid-core fiber has a large aperture and good homogenization properties, several sub-beams can be coupled into the liquid-core fiber and superimposed to reduce the loss of light intensity and increase speckle suppression.
In the experiments, the beam diameter was set to 4 mm, the cavity length of the BSC to 40 mm, and the diameters of both the beam splitter and reflector to 50 mm. First, we placed the beam splitter parallel to the reflector and obtained ten sub-beams. The number of sub-beams can be further increased to 22 by subtly changing the reflector angle of ∼0.29° relative to the beam splitter. Twenty-two has been demonstrated to be the maximum number of sub-beams that can be coupled to the liquid-core fiber for speckle pattern superposition as the fiber has a limited numerical aperture (NA). With a reflection loss of 0.0162 and a maximum of 22 sub-beams, the speckle suppression ratio and optical transmission efficiency can be calculated for different splitting ratios using Eq. (4) for the proposed optical scheme. The results are shown in Fig. 5.
Fig. 5. Curves of speckle suppression ratio and light transmission efficiency at different splitting ratios.
As illustrated in Fig. 5, when the splitting ratio is small, the speckle-suppression ratio decreases and light transmission efficiency increases; when it is excessively large, the suppression ratio increases and transmission efficiency decreases simultaneously. Because laser displays require high suppression and efficiency, a beam splitting ratio of 0.05 was chosen. At this splitting ratio, a high speckle suppression ratio can be achieved with a higher light-transmission efficiency.
3.2 Effect of BSC length
The optical path difference, which is primarily determined by the BSC length, is also a determining factor in speckle suppression. The effect of the optical path difference between sub-beams on the speckle suppression ratio was investigated by varying the BSC length.
In the experiments, a 1.5-m liquid-core fiber was employed together with the BSC for measuring speckle contrast. Our previous study showed that the speckle contrast saturates when only a liquid-core fiber is used [32]. The fiber length corresponding to the saturation value of speckle contrast was approximately 1.5 m; therefore, a 1.5-m liquid-core fiber was used in the proposed scheme. The speckle contrast was measured with different number of sub-beams and BSC lengths, and the results are depicted in Fig. 6.
As observed in Fig. 6, the speckle contrast rapidly decreases with an increasing number of sub-beams. When the number of sub-beams is one, only the liquid-core fiber affects the speckle suppression. In addition, we can see from Fig. 6 that when the number of sub-beams is less than 7, the four curves with BSC length of 40mm-70 mm are almost coincide. Once the number of sub-beams is greater than 7, there are certain discrepancy between the four curves, which is because the calculation of speckle contrast actually includes the local speckle noise and the global background light intensity change. As the speckle contrast continues to be reduced, the influence of uneven background light intensity on the calculated speckle contrast gradually become obvious, resulting in a deviation in the curve change. However, the overall change trend for the four curves is still consistent with our theory. We can still conclude that the curves of speckle contrast were similar when the BSC length was greater than 40 mm. Therefore, the minimum BSC length should be 40 mm to achieve the complete decoherence of the sub-beams. Considering the smaller system size, a BSC length of 40 mm and a liquid-core fiber of 1.5 m were set as the optimal parameters for the proposed optical scheme.
3.3 Effect of number of sub-beams
The number of sub-beams is another key factor related to the speckle-suppression effect. According to Eq. (4), an increasing number of sub-beams resulted in better speckle suppression. Therefore, we analyzed the variation in speckle contrast with different numbers of sub-beams at an optical path difference of 80 mm. The theoretical speckle contrasts were then calculated for different number of fully decoherent sub-beams using Eq. (4) and compared with the experimental results (Fig. 7).
As observed in Fig. 7, the experimental speckle contrast decreases as the number of sub-beams increases, which is consistent with the theoretical results. With only the 1.5-m liquid-core fiber, the speckle contrast was C = 11.72%; with the combination of the 40-mm length BSC and 1.5-m liquid-core fiber, the speckle contrast was further reduced from 11.72% to 4.28%, with a speckle suppression ratio of 2.74. Moreover, the experimental speckle contrast nearly converged to the theoretical speckle contrast, indicating that the sub-beams were fully decoherent. The experimental results verified the theoretical prediction model, and the speckle contrast was further reduced by increasing the number of sub-beams.
3.4 Laser projection experiments
After determining the optimal parameters of the two factors, the BSC length (S1 = 40 mm), and splitting ratio of the beam splitter (T = 0.05), we marginally adjusted the angle between the beam splitter and the reflector and increased the number of sub-beams to 22. We then used the optical system shown in Fig. 3 to record the speckle patterns in three scenarios: with a combination of the BSC and liquid-core fiber, with only the liquid-core fiber, and without any optical device for speckle suppression. The measurement results are displayed in Fig. 8.
Fig. 8. Light spot and one-dimensional intensity distribution of the laser projection system with (a) a combination of BSC and liquid-core fiber, (b) only liquid-core fiber, (c) without any optical device.
The original speckle contrast (without any optical device for speckle suppression) was measured at 30.2%. With the addition of a 1.5-m liquid-core fiber, it was reduced to 11.72%. With the addition of the BSC, the speckle contrast was further reduced from 11.72% to 3.1%, with a speckle suppression ratio of 3.78. Hence, the proposed scheme was demonstrated to reduce the speckle contrast from 30.2% to 3.1%, which is significantly lower than the sensitivity limit of the human eye. In addition, with a further increase in the number of sub-beams, the effect of speckle suppression was saturated. This is because the value of M in Eq. (3), which represents the degrees of freedom related to the time-integrated speckle dependence, is excessively large, and Eq. (3) can be approximated as:
In this case, the speckle contrast was determined by $K = {\Omega _{proj}}/{\Omega _{det}}$, which is the ratio of the stereo angles of the projection and camera lenses. In this experiment, the diameter of the projection lens was 50 mm, and the distance between the projection lens and the screen was 1 m. The F-number of the camera was 16, the distance between the camera and the screen was 1 m, and the focal length of the camera lens was 25 mm. Therefore, the diaphragm diameter of the camera lens was 1.5625 mm. Based on $K = {\Omega _{proj}}/{\Omega _{det}}$, we calculated that K ≈ 1,024. With Eq. (6), the minimum speckle contrast can be calculated as 3.125%, which fits well with the lowest limit of the speckle contrast obtained in our experiments. Therefore, we confirmed that the number of sub-beams generated by the proposed BSC was sufficient for speckle-free imaging.
4. Conclusions
In this study, we proposed the BSC and established a model of speckle suppression based on the combination of a BSC and a liquid-core fiber. Then, we constructed a static passive speckle-suppression system and studied the key factors affecting the speckle contrast, successfully reducing the speckle contrast from 30.2% to 3.1%, which is below the limit of the human eye speckle discrimination (< 4%). The scheme consisted entirely of passive optical elements, which are more applicable to projectors than the traditional static and dynamic speckle suppression methods.
In summary, by passing a laser through a BSC, we generated numerous sub-beams with extremely large optical path differences. Thus, we significantly increased the angular diversity of the decoherent sub-beams and produced a better speckle-suppression effect than the extant static speckle-suppression methods. However, this setup has a few limitations, such as the size of the system being larger than that of the static suppression method with only a multimode or liquid-core fiber. We also discovered that the coherence (related to M) generated by the proposed scheme had already saturated; therefore, a shorter liquid-core fiber can be chosen for superimposing sub-beams in sub-sequent applications.
Funding
National Natural Science Foundation of China (61975183).
Disclosures
The authors declare no conflicts of interest.
Data availability
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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