1. Introduction

Present day cinema projection systems are in need of a light source with high optical output power directed towards the screen [1], especially in 3D cinema, where a part of the image brightness is always lost in the filtering process that differentiates the images for each eye [1]. Currently, these systems mostly rely on arc-lamp technology [2]. But the output power of these arc-lamps has not increased any further in recent years. Moreover, these components’ performance is known to degrade considerably during their limited lifetime of a few hundred hours, resulting in high operational costs. Laser technology offers a plausible alternative [1,3], with higher output powers, longer lifetimes, less performance degradation and higher optical efficiency, due to its capability to create high-power beams with narrow angular extent. The main drawback of using lasers in cinema projection systems is the presence of speckle in the images. The combination of the beam’s coherence properties and the screen’s roughness leads to a quasi-random interference pattern [4,5], which is observed as a fine granular pattern superposed on the projected image. Luckily, several techniques exist [6–10] to counteract this nuisance for the human cinema audience, i.e. to reduce the speckle contrast to an acceptable level [11, 12]. Speckle reduction occurs when multiple uncorrelated speckle patterns are superposed [4,5]. The speckle contrast will be reduced by a factor $\sqrt{N}$ when N patterns of equal intensity are involved. The independent patterns can be obtained through e.g. polarization, wavelength or angular diversity. The superposition of these patterns can be achieved within the temporal or spatial resolution of the observer. Using a combination of speckle reduction techniques, it is possible to achieve acceptable levels of speckle, but this comes at the expense of a more complex, and thus more costly projection system. This increase in the system cost is even more important for small-scale or hand-held projectors. Therefore, there is still considerable interest in developing and characterizing new methods for speckle reduction.

The technique that we investigate in this paper is based on reducing the coherence of the optical source and using a MicroLens Array (MLA) as screen material to prevent the formation of speckle, thus eliminating the need to reduce it. The use of a MLA as a screen has been demonstrated in [13], but the corresponding speckle properties have not been thoroughly investigated. When using a MLA screen, the fields emitted by the individual microlenses are the interfering fields that form the speckle pattern. By engineering the coherence area at the screen to be small compared to the microlens footprint, we want to prevent these fields from interfering in the plane of the observer and thus prevent the formation of speckle. An additional constraint of this technique is that we will have to avoid resolving the microscopic features of the screen, as this would depreciate the image quality. To this end, the observer’s resolution spot on the screen should be substantially larger than the microlens footprint.

In summary, our approach (as visualized in Fig. 1) requires control over 3 areas : the observer’s on-screen resolution spot area A_res, the microlens footprint area A_fp and the on-screen coherence cell area A_coh. To prevent the fields of different lenses from interfering we want A_coh < A_fp and to avoid imaging the individual lenses we want A_fp < A_res.

 

Fig. 1 Schematic representation of speckle contrast reduction in laser projection systems using a microlens array as screen material.

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To validate this speckle reduction scheme, we characterized the speckle properties of 2 types of MLAs and a paper screen (regular printing paper, a classical diffuser) for comparison. The screens were mounted in a small-scale laser projection setup with a CCD camera replacing a human observer. In Section 2 we elaborate on the calibration and operation of this setup: we explain how we control the coherence area on the screen, how the imaging resolution was determined, how the speckle contrast is extracted from recorded images and how measurement noise is accounted for. We also motivate the choice for the MLA screens under test. In Section 3 we present and interpret the experimental results. We measured how the speckle contrast changes when gradually increasing the coherence area on the screen. Section 4 clarifies what impact the specialized microstructure of the MLA screens and the coherence properties of the beam have on the observed speckle, through the construction of a novel theoretical model that explains the experimental results shown in Section 3. We also explain how the screen’s polarization-scrambling properties, the screen’s roughness and the optical source’s central wavelength and bandwidth influenced the speckle measurements. Finally, our main findings are summarized in Section 5 and we analyze their impact on the future of laser projection systems.

2. Setup and calibration

The speckle measurement setup is schematically illustrated in Fig. 2. The Thorlabs CPS532 optical source is a frequency-doubled diode-pumped solid state laser operating at 532nm, with 4.5mW output power and a divergence angle of 0.5mrad. Next, a single positive lens L₁ with a focal length of 50mm is used to control the beam spot size on the next component, which is a rotating diffuser. This is a ground glass diffuser disk with a diffuser angle of 11 degrees, mounted on a small motor. By moving the focusing lens L₁, mounted on a precision translation stage, we accurately control the distance between the lens and the rotating diffuser. This changes the spot size on the rotating diffuser and thereby alters the coherence properties of the beam propagating towards the screen under test. When the coherent laser beam propagates through the rotating diffuser, it becomes a quasi-homogeneous partially coherent beam with a Gaussian shaped spatial coherence function. To describe the beam’s properties, we have to distinguish between the divergence angle of the intensity θ_int and the divergence angle of the coherence θ_coh. We have [14]

 

Fig. 2 Schematic representation of the speckle measurement setup. From left to right: diode-pumped solid state laser, (L₁) single lens with focal length f = 50mm, (RD) ground plate rotating diffuser, (P) polarizer, (S) screen, (ND) neutral density filter, (L₂) Nikon compound imaging lens and CCD sensor

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A polarizer is inserted between the rotating diffuser and the screen (and oriented for maximal transmission), to ensure that linearly polarized light is incident on the screen. In 3D projection systems, control over the polarization is needed [1]. It is therefore desirable that the used screen maintains the polarization of the incident light.

A speckle pattern will develop on the screen placed behind the rotating diffuser. Depending on the transmissive properties of the screen under test, a neutral density filter is added to the setup to make sure the measured intensity lies within the dynamic range of the sensor. This sensor, a high resolution Spiricon 12-bit CCD camera, model SP620U, is mounted in-line behind the screen. We use a Nikon compound lens, model AF NIKKOR 35-70mm f/3.5 4.5, attached to the sensor to focus onto the screen. The focal length of this zoom lens can be changed continuously from 35mm to 70mm. The f-number can be changed in discrete steps from 3.3 to 22. This means that we have control over the resolution of the imaging system, determined using an USAF-1951 test plate, by changing these settings and/or the distance between the screen under test and the imaging lens. Since we have a digital observer with pixels of finite width, we need to ensure that the speckle spots are large enough. The size of these granular spots is always of the order of the resolution spot size in the plane of the observer [5]. This means that if the resolution spot becomes too small, multiple speckle spots will be present within one pixel of the sensor. Since the sensor cannot make a distinction between different spots in a single pixel, only the average value will be recorded for this pixel, leading to artificial speckle contrast reduction. We will refer to this process as pixel averaging.

The amount of speckle on a uniformly illuminated screen is quantified by the speckle contrast C, defined as the ratio between the standard deviation σ_s of observed intensity fluctuations and the mean intensity I_s on the screen, C = σ_s/I_s. To extract the speckle contrast from a recorded image we first select a region of interest (ROI) in the full image such that only illuminated parts of the screen are considered (see Fig. 3(a)). A first duplicate of this ROI remains unaltered while a second duplicate is ’smoothed’ (see Fig. 3(b)) by replacing each pixel value by the average over m adjacent pixels. The first duplicate is then divided pixel-wise by the smoothed duplicate to compensate for the beam’s intensity profile and (spatially) slowly-varying inhomegeneities in the screen under test. The result is an image with mean intensity equal to 1 (see Fig. 3(c)). The speckle contrast is then obtained by calculating the standard deviation of the intensity fluctuations of this image. The value of m depends on the average speckle spot size, it is chosen large enough (here we use 3 times the average speckle spot width in pixels) such that no speckle features are lost in this filtering procedure.

 

Fig. 3 Recorded and processed images corresponding to consecutive steps in the speckle contrast extraction procedure explained in Section 2.

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It is important to prevent measurement noise as much as possible, as it is difficult to distinguish between speckle and intensity fluctuations due to noise, when processing the recorded images. A first estimate of the speckle contrast C is obtained by dividing the standard deviation σ_s,m of the measured intensity variations in the recorded image by the measured mean intensity I_s,m. However, due to noise, we expect the measured variance ${\sigma }_{s,m}^2$ to be larger than the speckle-induced variance ${\sigma }_s^2$. To limit the contribution of noise to ${\sigma }_{s,m}^2$, we only consider a region with high intensity values (central region in Fig. 3(c)). We avoided ambient light during the experiments, and to correct for electrical noise, we quantified the electronic noise levels (from the CCD sensor itself). To this end, we captured images while all light was blocked from hitting the sensor. The intensity variance in the captured image is then a measure for the electronic noise. This measurement was done using the same settings (video gain, exposure time,) as those used during the actual speckle measurements. We assume that the intensity fluctuations due to speckle and the fluctuations due to electrical noise both have a Gaussian distribution and are fully uncorrelated from one another. We verified experimentally that the intensity histogram of an image recorded without speckle has a Gaussian profile. The speckle induced fluctuations follow a Gaussian distribution when the number of interfering fields exceeds 5 [4]. Under these assumptions the measured intensity variance ${\sigma }_{s,m}^2$ equals the sum of the true speckle contribution ${\sigma }_s^2$ and the electrical noise contribution ${\sigma }_{s,n}^2$. To estimate the true speckle contrast we are then allowed to subtract the measured electrical-noise induced variance from the measured intensity variance.

Two types of MLAs were investigated. The first type, the MLA-S100-f4 Microlens Array by RPC Photonics, has a regular structure with the microlenses arranged in a rectangular grid. These microlenses have a 100 wide square footprint. The second type, the EDS-20-05584 Engineered Diffuser by RPC Photonics, has an irregular structure with varying lens sizes. On average, these microlenses are 120 wide. In the next section, we will discuss and compare the speckle measurements for the different screens.

3. Speckle contrast measurements

This section reveals and compares the speckle measurement results for the different screens. Two types of microlens-array screens are discussed and then compared to a sheet of regular printing paper, in order to validate the proposed MLA-based speckle reduction scheme.

3.1. Irregular MLA

In Fig. 4 we show the measured speckle contrast C on the irregular MLA screen versus the width of the on-screen coherence area L_coh, for 3 different values of the imaging resolution L_res. This resolution is larger than the microlens footprints, L_fp =120, in all experiments. The horizontal axis is normalized by the average width of the microlens footprints in Fig. 4(a), and by the imaging resolution in Fig. 4(b). Remember that the goal is to obtain low speckle contrast. When the coherence is small (L_coh < L_fp; L_coh << L_res), we observe low speckle contrast. At L_coh = L_fp the curves have an upward knee. As the coherence increases, we see the speckle contrast gradually increasing, and eventually saturating when the coherence is large (L_coh >> L_fp, L_res). As the resolution spot size increases, the minimum and maximum of the speckle contrast curve become more pronounced.

 

Fig. 4 Speckle contrast measurement results on irregular MLA screen, for varying sizes of the on-screen coherence area and for 3 different values of the imaging resolution. The two panels show the same experimental data. The horizontal axis has the ratio of the width of the on-screen coherence area L_coh to the width of the a) microlens footprint L_fp b) resolution spot L_res.

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The saturation of the speckle curves to values of C below 100% when the coherence is large, is due to polarization diversity, as will be discussed and modelled in Section 4. Unfortunately, when the coherence is small, the speckle contrast is low but does not reach 0%. The fact that this lower limit of the speckle contrast depends strongly on the imaging resolution L_res indicates that this is due to non-uniformities in the screen, which cause intensity fluctuations in the observed images even when an incoherent light source is used. This occurs when only a few microlenses fit within the imaging resolution and is due to the varying microlens sizes. And although these fluctuations do not constitute a speckle pattern, their impact on the image quality is also detrimental. Also, in the experiment with the smallest on-screen resolution spot L_res =400, the resolution spot on the sensor (in the observer plane) is of approximately the same size as the pixels. Since the sensor cannot distinguish between individual speckle spots within a single pixel, this leads to artificial speckle reduction in this experiment, explaining the lower saturation value for large coherence areas.

These measurement results (see Fig. 4(a)) clearly indicate that low speckle contrast on the irregular MLA is achieved when the coherence area is smaller than the microlens footprints, to avoid speckle, and when the resolution spot is larger than the microlens footprint, to avoid resolving the individual microlenses in the image. Also, these results (see Fig. 4(b)) show the importance of the ratio between the width of the on-screen coherence area L_coh and the width of the resolution spot L_res, as this ratio determines the degree of speckle reduction due to spatial averaging. This mechanism, which causes the smooth transition from low speckle contrast when L_coh << L_res to high speckle contrast when L_coh >> L_res, will be discussed and modelled in Section 4.

3.2. Regular MLA

In Fig. 5 we show the measured speckle contrast C on the regular MLA screen versus the width of the on-screen coherence area L_coh, for 3 different values of the imaging resolution L_res. This resolution is larger than the microlens footprints, L_fp =100, in all experiments. The horizontal axis is normalized by the width of the microlens footprints. When the coherence is small (L_coh < L_fp), we observe low speckle contrast. At L_coh = L_fp the curves have an upward knee. As the coherence becomes larger than the microlens footprint (L_coh > L_fp), we see the speckle contrast sharply increasing, eventually even exceeding 100% in some experiments. When the on-screen coherence area exceeds the microlens footprint, a structured diffraction pattern (instead of a quasi-random interference pattern) forms behind the screen, as can be seen in Fig. 6 where we compare recorded images for the irregular and regular MLA screens.

 

Fig. 5 Speckle contrast measurement results on regular MLA screen, for varying sizes of the on-screen coherence area and for 3 different values of the imaging resolution. The horizontal axis has the ratio of the width of the on-screen coherence area L_coh to the width of the microlens footprint L_fp. The small markers correspond to measurements with a structured diffraction pattern in the recorded image. For these datapoints the estimated speckle contrast C is meaningless. The large markers correspond to valid speckle constrast estimates from measurements where the diffraction pattern had disappeared due to small coherence.

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Fig. 6 Recorded images for the irregular MLA (top row) and the regular MLA (bottom row). For both screens, from left to right, the radius of the coherence area R_coh is equal to 19, 27, 74 and 600. The imaging system resolution is 650.

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The structured diffraction pattern is caused by the regular structure of the MLA and results in quickly increasing but meaningless speckle contrast values extracted from the recorded images (our speckle contrast extraction process is not suited for dealing with structured diffraction patterns). At a distance of L = 1645mm behind the screen, the first and last of 33 consecutive spots in the pattern were separated by D₃₃ = 280mm, corresponding to an angular separation (between 2 consecutive spots) of θ_m = arctan(D₃₃/(32.L)) = 5.32mrad. According to diffraction theory [15], the angular separation of the spots in the far-field diffraction pattern behind a grating with period L_fp depends only on this period and the wavelength (λ = 532nm) according to θ = arcsin(λ/L_fp) = 5.32mrad. So we have verified that we are dealing with a diffraction pattern at a grating structure with pitch 100 (the microlens footprint width). This diffraction is a hindrance when attempting to convey an actual image to the observer. We found that this problem can be overcome by either further reducing the on-screen coherence area to below the microlens footprint (L_coh/L_fp < 1/2, see Fig. 6), or by collimating the beam that is incident on the screen.

These results show that, in accordance with our expectations, low speckle contrast is obtained when the on-screen coherence area is smaller than the microlens footprint. The relative size of the resolution spot with respect to the microlens footprint does not significantly influence these results (within the measured range) because all the lenses have the same shape and size.

3.3. Comparison

In Fig. 7 we compare the experimental results for the different screens when L_res =650. The horizontal axis in this figure is normalized using the imaging resolution L_res.

 

Fig. 7 Speckle contrast measurement results, for varying sizes of the on-screen coherence area and for different screens, imaged with a resolution of 650. The horizontal axis has the ratio of the width of the on-screen coherence area L_coh to the width of the resolution spot L_res.

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Focusing on the region where the coherence area on the MLA screens is smaller than the microlens footprints (L_coh/L_res < 0.15 for regular and L_coh/L_res < 0.18 for irregular MLA), comparison of the measurement results reveals that the irregular MLA screen outperforms the paper screen. This region satisfies the conditions A_coh < A_fp < A_res proposed in the introduction. The average difference in speckle contrast is 3% in this region, with the irregular MLA reaching a minimum of 6.3% speckle contrast. When L_res =1100 the irregular MLA even reaches 4.0% speckle contrast, whereas the disturbance limit is estimated in [12] to lie between 3.2% and 4.1%.

In the next section we construct a model to predict the speckle measurement results. Such a model can be used to find new approaches, i.e. new microstructured surface designs, to improve the results even further in the future.

4. Modelling

This section first introduces a simple model to explain the speckle measurement results from the previous section and then discusses an intuitive approach to improve the model. This model adaptation is inspired by a simple physical insight regarding the coherence properties of the beam and is expressed through straightforward geometric arguments.

4.1. Model construction

In the model, we consider two causes for intensity fluctuations in the recorded images: speckle and screen non-uniformity. We assume that these two mechanisms yield intensity fluctuations with uncorrelated Gaussian distributions. Therefore, to explain the measured variance C² (corrected for electronic noise, see Section 2), we are allowed to sum up the variances of the theoretical speckle contribution $C_{\mathit{theor}}^2$ and the non-uniformity contribution $C_{\mathit{nu}}^2$

The different contributions to this model are:

Table 1. DOP and corresponding reduction factors for different screens

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Table 2. Screen non-uniformity for different screens and different resolutions.

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The model only depends on a set of parameters that we fitted through measurements (independent of the speckle measurements). In the next section we use this model to reproduce the speckle contrast measurement results on the different screens.

 

Fig. 8 Recorded images of polarization measurements on both the irregular and the regular MLA. For these experiments the screens were placed in between two polarizers. The relative angle of the two polarizers for which maximum and minimum transmission is achieved are labeled θ_max and θ_min, respectively. The angles θ_max and θ_min are 90 apart. The measurements on the irregular array show that the amount of polarization rotation is not uniform over the screen.

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4.2. Model validation

The speckle contrast predicted by the model is plotted in Fig. 9(a) together with the experimental data of the irregular MLA and paper screen. We do not include the measurement results on the regular MLA screen due to the presence of structured diffraction patterns in the recorded images (leading to meaningless speckle contrast estimates). The model is well suited to explain the 3 regions in the measurement results, segmented according to the ratio of the width of a coherence cell L_coh to the width of the resolution spot L_res. Firstly, when the coherence is large (L_coh >> L_res) no spatial averaging can occur which means that in our setup only polarization diversity, wavelength diversity and the MLA’s microstructure limit the maximal speckle contrast to (R_λ R_pol R_μ)⁻¹ < 100%. Secondly, when the resolution spot and the coherence area are of the same order of magnitude (O(L_coh) ≈ O(L_res)), spatial averaging will decrease the speckle contrast as the coherence area decreases. Finally, when the coherence area is so small (L_coh << L_res) that the spatial averaging theory predicts nearly 0% speckle contrast, noise and non-uniformities of the screen determine the measurement result, as they too lead to variations in the measured intensity.

 

Fig. 9 Speckle contrast versus the ratio of the width of the on-screen coherence area L_coh to the width of the resolution spot L_res. Markers indicate speckle contrast measurements on paper (blue), and irregular MLA (red) screen, imaged with a resolution of 650μm. The full and dashed lines illustrate the corresponding model predictions, as constructed in a) Section 4.1 b) Section 4.3.

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When comparing this model with the measurement results, it is clear that the model shows the same general trends as observed in the experimental results, but it fails to precisely capture the transition region where the on-screen coherence area and resolution spot area are of the same size. Beyond this point (L_coh >= L_res) the light within the resolution spot is considered fully coherent and the model fixes the reduction factor due to spatial averaging R_N to 1, resulting in a sharp edge in the model. The model for the irregular MLA includes an additional reduction factor R_μ (w.r.t. the paper screen) due to a limited number of interfering fields. This extra reduction factor causes the model to predict a sharp decrease in speckle contrast when the on-screen coherence area becomes smaller than the microlens footprint (L_coh/L_res < 0.18 in Fig. 9(a)). The measured speckle contrast of the irregular array shows the same decline, albeit less pronounced.

The discrepancy (in Fig. 9(a)) between model and measurement results when L_coh ≈ L_res can be qualitatively explained by considering the spatial coherence function γ(r) of the light on the screen. For light passing through a moving (e.g. rotating) diffuser, the magnitude of the complex degree of spatial coherence γ(r) between two points r₁ and r₂ in the beam at the screen only depends on the distance r = |r₂ − r₁| between these points [14] and has a Gaussian shape [14]

 

Fig. 10 Comparison of the spatial coherence described by Eq. (12) with the initial model (see Section 4.1) which models partial coherence only moderately well, and the improved model (see Section 4.3) wich uses an average coherence to mimic partial coherence.

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4.3. Model improvement

To improve the model, we first show why it fails to capture partial coherence in the region where the resolution spot and coherence cell areas are of comparable sizes. The counting procedure associated with the approximation N = A_res/A_coh for determining the degree of spatial averaging is visualized in Fig. 11(a), where we draw a grid of coherence cells and the resolution spot on a part of the screen. We count 9 coherence cells (in green) within the resolution spot (in blue), leading to a speckle reduction factor $R_N^{(a)}=\sqrt{9}=3$. But then we create a different scenario by moving the grid of coherence cells with respect to the resolution spot on the screen without changing their respective areas, as illustrated in Fig. 11(b). Now we count 4 complete and 12 incomplete coherence cells within the resolution spot. We cannot simply calculate the corresponding reduction factor as $R_N^{(b)}=\sqrt{4+12}=4$, since not all 16 coherence cells are fully encapsulated by the resolution spot. Instead, for each scenario, we use an expression for the speckle contrast C_N when N uncorrelated speckle patterns with equal contrast C₁ = σ_n/Ī_n (n = 1 . . . N) are averaged [4]

 

Fig. 11 The size of coherence cells, in green, and the resolution spot, in blue, is the same in both figures, but the grid of coherence cells has shifted with respect to the resolution spot. Within the resolution spot on the screen we count in a) 9 complete and in b) 4 complete and 12 incomplete coherence cells.

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This model effectively mimics partial coherence in an intuitive way. The average coherence function corresponding with this improved model is also plotted in Fig. 10 and corresponds much better with the true coherence function (Gaussian shaped). We used this model to recalculate the speckle contrast predictions, as shown in Fig. 9(b). The correspondence with experimental data is much improved in the region where L_coh ≈ L_res, indicating that the approximation of the coherence function as proposed in Section 4.1 is indeed inadequate, and confirming that the new model correctly captures the relevant speckle reduction mechanisms.

5. Conclusion

In this paper we have measured and modelled the speckle characteristics of microlens-array screens with the goal of being able to design these types of screens such that low speckle contrast and high image quality are attained in laser projection systems. Comparing the speckle contrast measurements with the model we constructed shows that we have good insight in the relevant speckle contrast reduction factors.

Measurement results clearly indicate that, as anticipated, low speckle can be obtained using the MLA screens when the on-screen coherence area is reduced to below the microlens footprint and the resolution spot encompasses multiple microlenses. But the condition on the coherence area can be quite tough to fulfill. Especially in full-frame projection systems, where the laser beam is expanded to illuminate a large screen, it will be hard to sufficiently reduce the coherence area on the screen. It should be less of a problem in point-scan projection systems, where a narrow beam (with a small coherence area) is scanned across the screen.

If one wants to design a projection screen with low speckle and large uniformity, one should start from the resolution spot of the human observer in the projection system at hand. Since the human eye has a fixed angular resolution, the resolution spot on the screen and thus the amount of speckle reduction depend on the distance from the screen. Based on the smallest resolution spot (from observers closest to the screen) and the required level of uniformity, the lens footprint should be made several times smaller. Next, the coherence area on the screen needs to be made smaller than the microlens footprint in order to avoid speckle. The non-uniformity in the observed image due to the lenses’ irregularity can be avoided by using a regular lens array. But then a disturbing diffraction pattern will appear unless the on-screen coherence area is made much smaller than the microlens footprint. Therefore, best results are obtained using an irregular MLA as screen material, reaching the target performance under the right circumstances. Possibly an adjusted design for the irregular MLA with just the right amount of variation in the size, shape and position of the different lenses, could lead to even better performance.