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Abstract
Our study proposes a novel method for obtaining speckle-free homogeneous illumination using a combination of a multi-retarder plate, a microlens array, a Fourier lens, and a diffraction optical element (DOE) based on pseudorandom binary sequences. The proof-of-concept multi-retarder plate is introduced to generate multiple uncorrelated laser beams, while a mathematical model was developed to explain the method's mechanism and evaluate its effectiveness. In the DOE passive (stationary) mode, the method was found to reduce speckle contrast to 0.167, 0.108, and 0.053 for red, green, and blue laser diodes, respectively. In active mode, the speckle contrast was further reduced to 0.011, 0.0147, and 0.008. The observed differences in speckle contrast in the stationary mode were attributed to variations in the coherence lengths of the RGB lasers. By implementing the proposed method, we successfully generated a square-shaped illumination spot that was free from interference artifacts. The spot obtained exhibited a slow, weak variation in intensity across the screen, attributable to the multi-retarder plate's suboptimal quality. However, this limitation can be readily addressed in future studies through the adoption of more advanced fabrication techniques.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
Narrow-spectrum light sources such as lasers allow for realizing abundant wide-gamut images [1,2]. Moreover, lasers emit highly efficient, top-quality light beams with low M2 values, rendering them a promising choice for various applications in different branches of research and industry such as illumination (general lighting and decoration lighting), displays (projectors, HD-TV, and cinema, laser shows), communications (visible light communication, satellite communication, underwater communication, and fiber optic communication), automobile (headlight, fog light, and parking sensors), as well as holography, interferometry, and optical metrology [3]. In particular, they can serve as effective light sources for compact and energy-efficient projectors [4]. However, laser-generated images are often affected by coherence noise known as speckle [5] and interference fringes in the light beam homogenizer of an illumination system [6,7]. Both image defects are caused by interference due to the high coherence of the laser beams. In the first case, the interference follows from scattering at the screen, and in the latter – from the interference of light from different parts and elements of the illumination system (for example from different microlenses of a microlens array). Without an acceptable solution to these lighting problems, the widespread use of lasers in projectors and other industries and research will be limited.
Since both effects are caused by interference due to the high coherence of the laser beams, their influence can be significantly diminished to an acceptable level by reducing the coherence of the illuminating laser beams. Therefore, it seems that the solution to one problem can automatically be a solution to another one. However, in the general case, this is not true because the effects are occurred at different locations in the optical system and have varying dependencies on the coherence properties of the laser (such as the angle between decorrelated sub-beams). A solution, which allows the design of a compact and energy-efficient illumination system free of speckle and interference fringes, opens up a wide range of applications for lasers in projectors and other illumination systems.
Speckle contrast C [5] is a commonly used metric to evaluate the level of speckle noise:
where $\sigma$ is the standard deviation of the image intensity of the homogeneously illuminated screen and $\left\langle I \right\rangle$ is the average intensity on the image screen. The effectiveness of the speckle suppression method is convenient to measure by the speckle suppression coefficient k: where ${C_0}$ and C are the speckle contrast before and after a speckle suppression, respectively. The application of active (dynamic) diffractive optical elements (DOEs) or diffusers has been shown to be an effective method for reducing speckles [8–14]. In addition, usage of a dynamic DOE (with electrically controlled gratings) in combination with a static diffuser has been proven to be able to reduce the speckle contrast down to 10% [15]. However, a direct application of this method is limited by the optical system size and requires relatively high DOE speed or electrical switching of the DOE structure. At the same time, methods that use DOEs only offer a solution for the problem of speckle suppression and do not provide homogeneous illumination of the screen with a rectangular spot. Long vibrating light pipes or fibers have been shown to be effective in reducing speckle [16–19], but they have limitations in terms of size and mechanical complexity, making them less suitable for some applications where a compact design is desired. Additionally, they may be sensitive to environmental conditions such as temperature and vibration, which can affect their performance. The vibrating mirror [20] or the diffuser [21] with a long light pipe allows to get a homogeneous light beam without speckles, however, has the same problems as the previous method. The novel refractive optical element with a staircase-like structure has been proposed to be used in combination with a holographic diffuser and a 50 mm long tapered light pipe [22]; however, the achieved subjective speckle contrast of 0.24 is still far above the threshold of the human eye susceptibility (0.03-0.04 typically). A passive method for speckle suppression using low-loss colloidal nanoparticles has been found to be effective, where the Brownian motion and strong light scattering of the nanoparticles result in significant decoherence and speckle suppression [23]. However, this method is not suitable for laser projectors due to issues with the time stability of the colloidal solution and its low optical efficiency. An alternative approach to speckle reduction, which involved static optical fibers and DOEs, was proposed as a fully passive method [24]. However, recent theoretical analysis and experimental findings [25–27] indicate that this method can only achieve acceptable effectiveness when employing optical fibers with a length of at least 15 meters. This limitation renders the approach impractical for compact illumination system applications.In summary, despite numerous efforts and the development of many devices to achieve speckle-free homogeneous illumination, the laser illumination industry still requires improvements in device parameters to enable their widespread application. In this study, we introduce a proof-of-concept multi-retarder plate as an effective method for creating a speckle- and interference fringes-free illumination system.
2. Optical scheme of the laser-based illumination system
The optical scheme of the experimental setup of the laser-based illumination system is shown in Fig. 1. The system consists of a laser RGB module, a beam expander, the multi-retarder (MR), a double microlens array, a Fourier lens, a DOE, an objective lens, an optical modulator, a screen, a 2 mm diameter diaphragm at the camera objective, and a square 3 × 3 mm2 diaphragm after the beam expander in some cases. It should be noted that the optical modulator does not make an influence on the speckle suppression and was included in the principal scheme to indicate the shift of the object plane (optical modulator plane) relative to the DOE plane. To ensure a bright and visible image from a wide angle of view, a laser projector screen should be white, highly reflective, and have a wide scattering angle. A paper screen meets all of these criteria, so it was used in all of our experiments. Furthermore, since the screen is where the objective speckles appear, it was used to measure the intensity.
The multi-retarder (multi-delay plate) is a transparent rectangular plate having a 2D ${M_n} \times {M_m}$ array of rectangular $a \times b$ subareas with plane parallel surfaces (see Fig. 2 where a ${M_3} \times {M_3}$ MR plate is shown). For simplicity, we will assume that $a = b$ and ${M_n} = {M_m}$, i.e. there is a square multi-delay plate with square subareas. The minimum difference $\Delta {H_{ij}}$ between thicknesses of any two adjacent subareas has to be sufficiently large to decorrelate laser sub-beams that pass through different areas, that is $\Delta {H_{ij}} \ge \Delta h = {{{\lambda ^2}} / {[\delta \lambda (n - 1)]}}$, where λ is the laser wavelength and n is the refractive index of the material MR is made of.
Fig. 2. Geometry of 3 × 3 multi-retarder plate: (a) “straight-fabricated” 2D structure; (b) 2D structure composed of two 1D structures. The integer numbers indicate the height of the subarea in units of Δh.
The optical setup also includes two arrays of rectangular microlenses with identical transverse sizes and a Fourier lens to create a rectangular laser spot. Two different implementations of the 3 × 3 multi-retarder plate can be used, as shown in Fig. 2. The first implementation is a pure 2D structure (Fig. 2(a)), which is more difficult to produce. The second implementation is a combination of two 1D structures (Fig. 2(b)), which is more convenient for fabrication. The simplified optical scheme of the illumination system is shown in Fig. 3.
Fig. 3. The principal optical scheme of the laser beam homogenizer based on the microlens array and the multi-retarder plate.
When a collimated light beam passes through the multi-retarder plate, it is split into an array of collimated sub-beams that are uncorrelated with each other and propagate in the same direction. The microlens array and Fourier lens then focus these uncorrelated sub-beams into a rectangular spot, with each sub-beam having a different illumination angle. Square microlenses in the array have linear transverse size d and focal length f, while the Fourier lens has focal length F. The angle $\Delta \varphi $ between sub-beams from neighboring subareas is $\Delta \varphi = d/F$ (see Fig. 8). The number and transverse size of the microlenses of the microlens array should be the same as the number and transverse size of the subareas of the MR. In this way, in our consideration it was assumed that $a = b = d$. The size of the obtained rectangular homogeneous light spot D is determined as $D = d(F/f)$. Since d is small (< 1 mm), the focal length F has to be large (several tens of centimeters) to obtain a relatively large light spot required for illumination systems. Because of small d and large F, the angle $\Delta \varphi $ between sub-beams is significantly smaller ($\Delta \varphi $ ∼ 0.001) than required for the decorrelation of subjective speckles in the eye. Therefore, despite the sub-beam decorrelation, direct use of MR does not result in large speckle suppression.
A binary pseudorandom sequence-based DOE is placed in the Fourier plane of the Fourier lens. The DOE based on the code length N is a 2D periodic structure with a linear period T0 and an element width T ($N = {T_0}/T$) (see Fig. 4). Following the DOE, the optical modulator should be placed as close as possible to the Fourier plane of the Fourier lens. The DOE can be implemented to be either stationary or active (mechanically shifting or electrically switching). The diffraction order angle difference $\Delta \theta = \lambda /{T_0}$ (see Fig. 8) is assumed to be sufficient to create decorrelated speckle patterns by decorrelated sub-beams (≥ twice the eye’s numerical aperture). A 2D DOE based on the pseudorandom binary sequence has $2N \times 2N$ diffraction orders in the main maximum of the envelope function of diffraction order intensity. With an accuracy of about ten percent, we can take into account only these diffraction orders. The full angle width of the main maximum of the envelope function is $2\lambda /T$. For getting strong speckle suppression, one should use a large code length N [10]; therefore, $2\lambda /T$ has to be relatively large (a few tens). It follows from the optical scheme parameters that $\Delta \varphi $ is significantly smaller than $\Delta \theta $.
Fig. 4. One period of the 2D DOE structure composed of two 1D structures based on the M-sequence of length N = 15 stretched in orthogonal directions: (a) side view, (b) facial view, (c) bottom view, and (d) DOE structure on the transparent film.
3. Parameters of the experimental setup
The optical scheme of the experimental setup for analysis of the quality of illumination light and speckle contrast is shown in Fig. 1. The RGB module consists of three laser diodes (parameters of which are presented in Table 1) that produce red, green, and blue collimated beams. The laser module emits the following collimated light beams: red – 1.0 × 1.6 mm2; green – 2.8 × 0.8 mm2; blue – 3.0 × 1.2 mm2, and we have a 3.6 × 3.6 mm2 2D MR structure.
Table 1. Lasers’ parametersa
Therefore, due to the desire to use a laser with high efficiency and the fact that different lasers typically have different beam shapes with irregular intensity distribution along two orthogonal axes, there are three laser beams with different shapes and lateral sizes. This is a common situation. However, there is a large mismatch between the laser beam cross-sections and the size of the multi-retarder plate. Since the goal of the analysis is to evaluate the efficiency of the multi-retarder plate in speckle suppression, it is necessary to reduce this discrepancy. For this purpose, the beam expander was included in the optical scheme. The beam expander consists of a negative lens with a 20 mm focal length and a positive lens with a 45 mm focal length. After the expander, the MR is illuminated by the following laser beams: red – 2.25 × 3.6 mm2; green – 6.3 × 1.8 mm2; and blue – 6.75 × 2.7 mm2. In some experiments, a diaphragm with a 3 × 3 mm2 aperture was introduced to obtain a closer match between the MR size and beam cross-section sizes for the green and blue laser beams. The usage of the diaphragm will be explicitly mentioned in the following text. In addition, we put the DOE exactly in the Fourier plane. The optical modulator was placed at a 5 mm distance from the DOE. This short distance is crucial because the DOE light scattering property enhances the quality of the illumination beam on the optical modulator plane. It will be emphasized in the text below where the objective focus was on the DOE and where on the optical modulator plane.
There was used the 2D DOE structure composed of two-sided 1D DOE [28] based on M-sequences with a code length N of 15 and elementary cell size T of 2 µm (Fig. 4(a,b)). The DOE is fabricated on two sides of a flexible polypropylene film with a structure height h of 510 ± 25 nm (see Fig. 4(c,d)). The optimal structure height h is a slightly smaller than the optimal value, which induces a half-wavelength wavefront shift at the center of the wavelength range (= 530 nm) between the red and blue lasers. The film with the DOE pattern was wrapped in a loop around four rotating poles, and one of the poles was connected to an electromotor that determined the speed of the DOE shifting. The DOE orientation is optimal for speckle suppression in the case of mechanical activation. In active mode, DOE speed is sufficiently large (70-80 mm/s) to decorrelate diffraction orders of light. The objective lens was defocused by 5 mm from the DOE plane (ΔF = 5 mm). The “defocus” here means not DOE shift from the focal plane of the objective, but rather the shift from the objective plane (from the optical modulator plane). This means that the screen and DOE are not located in optically conjugated planes, therefore the image of the DOE will be not formed on the screen.
Laser diodes (LDs) typically have a radiation bandwidth ranging from 1-2 nm, but this value can be affected by the operating current, which can range from the threshold current of a few tens of mA to as high as 240 mA. This variation in the operating current can cause fluctuations in the LD radiation bandwidth. Hence, we based our evaluation of the required thickness differences of the multi-retarder subareas on the typical parameters of the “middle” green LD. The structure should provide an optical pass difference equal to or larger than the decorrelation length of the light beam which is:
Fig. 5. Schematics of the 2D MR plate structure based on two 1D MR structures with six different structure heights (optical path lengths): 1 – plate’s frame, 2 and 3 – 1D MR structures.
Fig. 6. Height profile of the 2D MR based on two 1D MRs with ${M_n} = {M_m} = {M_9}$. The black integer numbers denote plate height differences in 0.6 mm. The 2D structure has a lateral size of 3.6 × 3.6 mm2. The red integer numbers correspond to the optical length difference of the 1D MR structure.
Fig. 7. A photograph of the fabricated 2D MR based on two 1D MRs with six different structure heights. The 2D structure has a lateral size of 3.6 × 3.6 mm2.
It is clear that the structure height differences do not exactly match the design principles since some parts have the same height (optical path difference). Besides, there are multiple beam reflections from the layers and the surface quality is not ideal (especially surfaces of the slits). The same height of a subarea will result in an interference effect that in turns results in an intensity oscillation over the illumination spot. Multiple reflections and not perfect quality also can produce a non-homogeneous intensity distribution of the illumination. The structure produces 13 uncorrelated laser sub-beams with different optical paths (see Fig. 6). Therefore, the passive method (without a DOE movement) should produce a speckle suppression effect with the speckle suppression coefficient k at most of $k < sqrt(13) \approx 3.6$. We used the lens with F = 650 mm as the Fourier lens and a 2-inch diameter lens with F = 55 mm as the objective lens.
4. Speckle suppression in the optical scheme with a passive DOE and multi-retarder plate
In our optical scheme, the Fourier plane is illuminated by decorrelated sub-beams from different MR subareas (see Fig. 8).
Fig. 8. Differences in optical path of two sub-beams from different MR subareas in different diffraction orders.
Each of the MR sub-beams that hits the DOE will diffract into additional $N \times N$ orders. Let consider the speckle patterns created by $nn^{\prime}$-th and $mm^{\prime}$-th sub-beams from the MR, which have a small difference in incident angles to decorrelate subjective speckle on the image screen (as it was assumed before). Without defocusing the field amplitude in the eye from $nn^{\prime}$-th MR sub-beams, the field amplitude of ij-th diffraction order can be rewritten via the field of $00^{\prime}$-th sub-beams of ij-th diffraction order as
In the case of defocusing the amplitude and phase of ij-th diffraction order, field of $nn^{\prime}$-th sub-beam in the focus plane (in the eye) can be written through the amplitude of other $mm^{\prime}$-th sub-beams of ij-th diffraction as:
Let now estimate the smallest range of the phase difference between two sub-beams of the same diffraction order. The estimation will be made with the assumption of a small angles ($m\Delta \varphi < < 1$ and $\lambda /T < < 1$, where $|m|\le M/2$). The smallest range of the phase difference between any two sub-beams of the same diffraction order is for the nearest neighbor sub-beams. The smallest phase difference is for highest negative diffraction order of these sub-beams which can be calculated as:
In Eqs. (7) and (8), only zero and linear term in Taylor series for sin and cos functions are taken into account because of the small arguments. If the range of phase differences for the diffraction orders of any two sub-beams resulting from the MR is larger than 2π, a speckle field of each sub-beam in the eye is the coherent sum of $4{N^2}$ diffraction orders. Since a phase differences between diffraction orders of two sub-beams distributed in a range which is larger than 2π, they will produce weakly correlated speckle patterns due to the oscillation of phases. The speckle patterns of sub-beams are summed incoherently due to the decoherence of two sub-beams. It was shown in [29] that for weakly correlated speckle fields of the same intensity (${k_{mm^{\prime}}} \approx 1$), the speckle suppression coefficient with a small error can be approximated as square root from sub-beams number M, and in our case, this leads to the following expression:
It is clear that the passive mode of the method can provide ${M^2}$ decorrelated speckle pattern only if $M/N \le 1$. To ensure the practical feasibility of the method, the defocus distance must be large enough to get optical path range differences between diffraction orders of the sub-beams larger than 2π. In our case, the smallest optical path range differences for two sub-beams is
5. Quality of the obtained illumination beams
Figure 9 shows (a) red, (b) green, and (c) blue laser spots on the screen for the optical scheme without the diaphragm.
Fig. 9. RGB laser light spot intensity distribution on the screen and horizontal (line 1) and vertical (line 2) cross-sectional distributions along yellow lines that pass through the light spot center. The spots are obtained without the diaphragm before the multi-delay plate, with defocused objective lens by 5 mm away from the DOE plane and with motionless DOE: (a) red laser, exposure time τexp = 78 ms; (b) green laser, exposure time τexp = 94 ms; (c) blue laser, exposure time τexp = 78 ms.
The selection of exposure time values was based on several factors such as laser intensity, camera sensitivity, and the speed of the DOE movement. It is crucial to choose the appropriate image intensity (exposure time) to ensure that the sensor noise is not higher than the intensity, while also avoiding saturation. Additionally, the exposure time difference between experiments and different colors should not be significant. Different color sensitivity of the digital camera’s sensor caused the difference in the exposure time. The cross-section intensity distribution of the light spot formed on the screen is presented along horizontal (line 1) and vertical (line 2) yellow lines that pass through the light spot center. Because there was no aperture to constrain the laser beam size to the 2D MR structure, some of the light passed outside of the 2D MR plate area, leading to suboptimal use of the MR. The rectangular-shaped spots on the screen exhibit a gradual change in intensity, accompanied by high spatial frequency and low amplitude interference modulation. Despite the low amplitude of the high-frequency modulation, it is perceivable by the human eye. The speckle modulation of the image was present, and the DOE remained stationary. However, the speckle contrast is low in spite of motionless DOE. The exposure time τexp was chosen in such a way in order to obtain a high-quality picture because inactive DOE does not influence the speckle suppression efficiency.
Fig. 10 shows photographs of red, green, and blue laser spots on the screen for the optical scheme with the diaphragm having a clear aperture of 3 × 3 mm2. The objective lens was focused on the optical modulator plate (defocused from the DOE by 5 mm). In this case, the MR was used in an optimal way because all light that creates the spot on the screen passes through the 2D MR structure due to the aperture. The spot on the screen has a rectangular shape with only slow intensity variation across the screen. In contrast to the previous optical scheme, the light interference (fast intensity modulation across the spot) of sub-beams was strongly suppressed.
Fig. 10. RGB lasers light spot intensity distribution on the screen and horizontal (line 1) and vertical (line 2) cross-sectional distributions along yellow lines that pass through the light spot center. The spots were obtained with a 3 × 3 mm2 diaphragm before the MR, with the defocused by 5 mm objective lens away from the DOE plane and with motionless DOE: (a) red laser, exposure time τexp = 78 ms; (b) green laser, exposure time τexp = 94 ms; (c) blue laser, exposure time τexp = 78 ms.
The DOE was not moving, and the image is modulated by speckles, although the speckle contrast is low in spite of motionless DOE (virtually invisible for blue laser).
Fig. 11 shows red, green, and blue lasers spot on the screen for the optical scheme with the diaphragm having a clear aperture of 3 × 3 mm2 and moving DOE.
Fig. 11. RGB lasers light spot intensity distribution on the screen and its horizontal (line 1) and vertical (line 2) cross-sectional distributions along yellow lines that pass through the light spot center. The spots were obtained with a 3 × 3 mm2 diaphragm, the objective lens defocused by 5 mm away from the DOE plane, and active DOE: (a) red laser, exposure time τexp = 125 ms; (b) green laser, exposure time τexp = 109 ms; (c) blue laser, exposure time τexp = 110 ms.
The DOE shift length was larger than $N{T_0}$ during the exposure time. The objective lens was focused on the modulator plate (defocused from the DOE plane by 5 mm). All light was passing through the 2D MR plate due to the diaphragm before the MR. The spot on the screen has a rectangular shape with a slow intensity change across the light spot. Speckle noise is virtually invisible for all three lasers in this case.
Fig. 12 shows a white laser spot (the combination of all three RGB lasers light) on the screen for the optical scheme with a diaphragm having the clear aperture of 3 × 3 mm2 and the moving DOE. The objective lens was focused on the optical modulator plate (defocused from the DOE by 5 mm). Used laser module does not allow changing the white light temperature. Therefore, the obtained white illumination beam is dominated by the blue color. However, the color of the whole spot is almost the same across it. This implies that the slow change in light intensity is not caused by coherent interference but rather by the quality of the illumination system's optical components, as previously noted.
Fig. 12. White light laser spot on the screen obtained with a 3 × 3 mm2 diaphragm and with 5 mm defocused objective lens from the plane of the active DOE, and its horizontal (line 1) and vertical (line 2) cross-sectional distributions along yellow lines that pass through the light spot center.
Different exposure time values were used in experiments because of the different laser intensity of different colors and camera sensitivity to different colors. This allowed us to get the best image brightness by avoiding intensity saturation and having small camera noise. The difference in exposure time was not large (< 30%). The proposed method of speckle suppression has only one parameter – a DOE distance shift during the exposure time – that should be larger than $N{T_0}$, which value depends on exposure time. However, the DOE shift speed was chosen sufficiently large to effectively suppress the speckles for all exposure time ranges used in experiments, so from the theoretical point of view this difference is not important for the speckle suppression effect. Experimental results confirmed the theoretical conclusion.
Fig. 13 shows the output plane of the MR plate illuminated by the red laser.
The image displays varying distances between dark lines, indicating unequal widths of the retarder areas with different thicknesses of the MR plate. The face and edges of the layers do not have surfaces of optical quality. In addition, the number of subareas is too small to provide a high-quality homogeneous illumination. Laser beams are thus stretched in the vertical direction, and a smaller number of sub-beams are used in beam homogenization in the horizontal direction. Therefore, the light spot in this direction has a poorer quality. It is well known [6] that number of sub-beams (illuminated lenses in a lens array) has to be large enough in one direction (> 8) to achieve a homogeneous illumination and depends on the initial distribution of intensity in the laser beam. More homogeneous distribution requires the use of more sub-beams. The number of reflections increases from the center to the periphery of the laser beam, as can be seen in Fig. 5. Many reflections due to the multilayer structure of the proposed multi-retarder plate result in the additional decrease in the laser beam intensity from center to periphery. Each layer decreases intensity approximately by 8%, and since there are six layers in the MR, there is a ∼ 48% decrease in intensity at the periphery. Therefore, we assume that it would be feasible to obtain the necessary beam quality for a laser projector by increasing the number of sub-beams, decreasing multireflection (by fabricating the MR structure directly in one layer rather than stacking multiple layers together), and enhancing the surface quality of the MR plate.
6. Speckle contrast obtained with the method
A Nikon CoolPix P7000 RGB digital camera was used for the speckle image recording. This camera has a 7.49 × 5.2 mm2 CCD image sensor containing 9.98 megapixels with 2 µm pixel period. The RAW image format (NRW) was used to study the intensity distribution of the image. We used open-source ImageJ software to calculate the speckle contrast. Before calculation, the image was separated into three color images by ImageJ and only the image of laser color was used for the speckle contrast evaluation (to avoid the noise from two other color channels). The external diaphragm at the camera objective with a clear aperture diameter of 2 mm (that is close to the diameter of the human eye’s pupil) was used for the speckle measurement. The 3 × 3 mm2 square diaphragm before the MR and objective lens focused on the optical modulator plane (defocused from the DOE plane by 5 mm) were used as well. The initial speckle contrast was measured for the laser spot created directly by lasers on the screen without passing through the optical scheme of the proposed illumination system. The measurement was performed for both motionless and active DOE. In the case of active DOE, its speed was sufficiently large to get the full speckle suppression effect of the method, that is, the DOE shift length was larger than $N{T_0}$ during the exposure time. The results of the speckle contrast measurement are shown in Table 2.
Table 2. The speckle contrasts for different illumination conditions
It was shown [30] that the human eye is more sensitive to speckles in still than in moving images and the sensitivity is different for different colors. The human eye is not sensitive to speckle noise the contrast of which is below 7%, 6%, and 5% (in the case of a moving image) and is below 3.6%, 3.2%, and 4.4% (in the case of a still image) for red, green, and blue lasers, respectively. Therefore, the information in Table 2 indicates that the laser projector incorporating a multi-retarder plate, even when the MR structure is not optimal (i.e., not all areas have different optical paths) and a stationary DOE is used, can produce a laser spot with a low speckle contrast that is comparable to the sensitivity of the human eye for blue lasers. However, for green and particularly for red laser, the speckle contrast is much higher than the required value for high-quality imaging without the movement of the DOE. The variations in speckle contrast observed in the stationary mode can be explained by the differences in coherence lengths of the RGB lasers (as shown in Table 1). The red and green LDs have higher coherence lengths, resulting in inadequate decorrelation of laser sub-beams.
In the case of active DOE, the speckle contrast is below 2% for all three lasers, which is lower however than the theoretical prediction. Currently, we lack a thorough understanding of the reason behind the more significant speckle suppression effect we observed compared to the predicted outcome from the theory. One potential reason for this stronger speckle suppression effect than predicted by theory could be the sensitivity of the effect to vibrations in the optical elements induced by environmental factors. From the obtained results it is clear that, with proper optimization and improvement of the multi-retarder plate's design and quality, it may be possible to construct a compact laser illumination system that is speckle-free and has high-quality illumination using a passive speckle suppression mechanism based on the multi-retarder plate and pseudorandom binary DOE.
7. Conclusion
A new design of the laser beam homogenizer utilizing a proof-of-concept multi-retarder (MR) is proposed, which should ensure uniform illumination and a low level of speckle noise. A theoretical model has been developed to explain and evaluate the mechanism of speckle reduction by the MR, an array of microlenses and a diffraction optical element (DOE), when the spatial frequencies created by the multi-retarder plate are significantly lower than those required to create the effect of speckle reduction. At this stage, we have not been able to produce an MR with the optimal structure, high-quality surfaces, and the necessary optical path differences. Therefore, we used the 2D MR with a simplified structure where not all laser sub-beams were decorrelated. The experiment has demonstrated that the idea used for the design is feasible, and the proposed method allows obtaining uniformly illuminated rectangular spots with a low level of speckle noise without the need of using any active optical element. The speckle contrast below the threshold of human speckle sensitivity has been obtained for the blue laser without the use of the active DOE. The observed differences in speckle contrast in the stationary mode were attributed to variations in the coherence lengths of the RGB lasers. The speckle contrast below 2% has been obtained for all RGB lasers using the active DOE. The study was not able to achieve the necessary illumination uniformity (> 95%) for a laser projector, and after analyzing the possible reasons, it was found that the main causes are the manufacturing quality of the MR plate and the insufficient number of laser sub-beams. However, we believe that this limitation can be addressed in future studies by utilizing more advanced fabrication techniques. The proposed approach can lead to the construction of a compact laser illumination system that is speckle-free and has high-quality illumination based on the passive speckle suppression mechanism using the multi-retarder plate and pseudorandom binary DOE.
Funding
Austrian Science Fund (M 2925); National Academy of Sciences of Ukraine (0119U001105); British Academy (RaR\100182).
Acknowledgments
This research was funded in part by the Austrian Science Fund (FWF) through the Lise Meitner Programme (Grant M 2925). AS, IG, and AP acknowledge support from the National Academy of Sciences of Ukraine (Grant 0119U001105). IG acknowledges support from the British Academy through the Researchers at Risk Fellowships Programme (Grant RaR\100182). The authors would like to thank the Armed Forces of Ukraine for providing security to perform this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be obtained from the authors upon request.
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