Despite of much effort and significant progress in recent years, speckle removal is still a challenge for laser projection technology. In this paper, speckle reduction by dynamic deformable mirror was investigated. Time varying independent speckle patterns were generated due to the angle diversity introduced by the dynamic mirror, and these speckle patterns were averaged out by the camera or human eyes, thus reducing speckle contrast in the final image. The speckle reduction by the wavelength diversity of the lasers was also studied. Both broadband lasers and narrowband laser were used for experiment. It is experimentally shown that speckle suppression can be attained by the widening of the spectrum of the lasers. Lower speckle contrast reduction was attained by the wavelength diversity for narrowband laser compared to the broadband lasers. This method of speckle reduction is suitable in laser projectors for wide screen applications where high power laser illumination is needed.
© 2014 Optical Society of America
Projection technology plays an important role in modern life. The applications of projection technology can be seen everywhere such as rear-projection televisions, conference room projectors, home theatre projectors, cinema projectors and micro projectors. With the advancement of the technology, the customers expect higher image quality from the projector such as better resolution, higher brightness, more displayed colors and longer life-time without the need to replace the light source as well. Laser is a good candidate as an illumination light source for the projection technology. Lasers offer a number of advantages compared to thermal sources or light emitting diodes (LED). Lasers provide wider color gamut, better electrical-to-optical conversion efficiency, brightness and contrast of the images and longer life-time [1, 2]. However, an obstacle of lasers in imaging applications is speckle which is a consequence of the high coherence intrinsic property of the lasers. Speckle is caused by the interference of the reflective coherent laser beam from the screen which is rough on the scale of optical wavelength. Speckle introduces granular noise superimposed on to the intended images, and therefore it significantly degrades the observed images quality . For practical application of laser light in projectors, it is imperative that speckle noise should be reduced below the human perception limit. If the contrast is less than 4%, human eyes would not be able to recognize the speckle noise on the images .
A number of speckle reduction technologies have been developed in recent years. Low spatial coherence can be generated by passing laser light through multimode optical fiber [5, 6]. However, coupling laser beam into the fiber is a challenge with significant light loss. Spatial coherence of the lasers can be also modified by tailoring structure of single laser [7, 8] or of the laser array . These techniques cannot be applied for an arbitrary laser. Speckle can also be reduced by moving Hadamard phase patterns [10, 11] or by binary phase code . The most common method is to generate time varying independent speckle patterns by moving of a diffractive optical element [13–16], by phase spatial light modulator , by fast scanning mirrors  or by Micro-Electro-Mechanical Systems (MEMS) devices [19, 20]. Speckle contrast can also be suppressed by using broadband lasers . The output of laser projection applications is up to 100000lm which requires the input power of a combined red green blue (RGB) lasers up to 800W by assuming optimized RGB primaries and good throughput . Thus, high power lasers are required for wide screen laser projection applications. The objective of this paper is to study of speckle contrast reduction with the combination of the use of broadband lasers and the generation of time-varying speckle patterns by deformable mirrors. These two methods are practical for laser projection applications.
A commercial phase-randomizing deformable mirror for anti-speckle technology was used for the study [2, 23]. It comprises of continuous surface of mirrors array that can be individually deformed and actuated up to hundreds of KHz. Inactive deformable mirror is shown in Fig. 1(a). The active area of the mirror is elliptical with major axis lengths 40mm and 50mm. The mirror is coated with Silflex that can provide 97.5% of reflection efficiency over the range of visible wavelengths . The mirror can tolerate up to 70W of optical power and of power density. Figure 1(b) shows the active deformable mirror with randomly distributed surface deformation. Due to the randomly distributed deformation at high frequency, many uncorrelated speckle patterns is produced. This leads to the reduction of speckle contrast in the projected image. The maximum divergence angle of the light beam after reflection from the mirror is 2 degrees when it is activated. One advantage of such a mirror as compared to a random diffuser is that its surface is relatively smooth, which results much less light scattering into higher angles. Thus it does not cause much light loss as stray light effects in projector is minimized.
2. Theoretical background
Speckle is characterized by the speckle contrast parameter , which is defined as the ratio between the standard deviationand the mean valueof the light intensity in a speckle patterns 
Forindependent speckle patterns with equal mean intensities, the expression of speckle contrast is
We define a scattering vector as a function of illumination wave-vector and observation wave-vector as in 
The scattering vector can also be expressed in terms of the transverse component and the normal component
The normalized intensity correlation of the two speckle fieldsandis
The speckle reduction mechanism of the dynamic mirror is based on the difference in illumination angles when it is actuated. The Eq. (5) becomes
By the activation of the mirror, the angle scattering of the two vectors and become larger and decreases. Hence, the two speckle patterns are uncorrelated to each other. Consequently, the number of temporal degree of freedom increases and the speckle contrast reduces. The speckle contrast is also affected the spectrum width of the laser. For normal incident light and normal observation, the difference of normal component of scattering vector is
The broadening of laser spectrum increases the and therefore the correlation function decreases. This leads to the reduction of speckle contrast due to the rise of the number. While the increase of number of temporal degree of freedom is introduced by the deformable mirror and the broadening of laser spectrum, the spatial degree of freedom depends on the speckle size and the area of the integration of the detector. For the case of the average of speckle pattern is larger than the measurement area, approximately equals to 1.
We define the weighting function which represents the distribution of the detector’s photosensitivity over space
The area of the detector is given by
The case of the detection area larger compared with the average size of a speckle pattern is considered. In this case, the effective measurement area is
With a uniform sensitive detector, the effective measurement area is the same as the area of the detector. The correlation area of the speckle intensity is defined as a function of the autocovariance function of intensity
The parameter therefore can be expressed in terms of effective measurement area and the correlation area of the speckle intensity
Thus in the limit of a large measurement area compared with the speckle size, the value of is proportional to the ratio.
3. Experiment setup
The experiment setup is shown in Fig. 2. The laser diodes were driven in continuous mode (CW). Since the temperature has effect on the spectrum of the lasers. In order to have an accurate measurement, the lasers were mounted on a Peltier stage with a constant temperatureduring measurements. An absorptive neutral density filter was used to attenuate the transmittance light so that it does not saturate the charge-coupled device (CCD) camera. After passing through the filter, the initial laser beam was split into two equivalent intensity beams by a non-polarizing beam splitter. The reflected beam was steered to a spectrometer. The transmitted beam propagated to a deformable mirror. In order to avoid the damage of the mirror by high power density, the laser beam was extended by a lens. The spot size of the laser beam on the mirror was approximately 20mm × 6mm. The reflected beam from the mirror was focused and imaged on to the first diffuser. The scattered laser beam passed through a 6mm × 4mm cross-section rectangular light pipe for beam homogenization. The light pipe has 70mm length. A second diffuser was placed at the output face of the light pipe for further homogenization of the beam. A CCD camera without imaging lens was used to capture the speckle images for the free space geometry. The camera has 1600 × 1200 pixels and the pixel size is 4.4µm × 4.4µm. For imaging geometry, the camera was equipped with an imaging lens. The imaging lens has focal length f of 50mm. It is shown that the aperture number of the camera lens influences the speckle size which is represented by the correlation area of the speckle intensity . Thus, the number has an influence on the measured speckle contrast. Therefore, the number of the lens was fixed at constant value 8 for all measurements, resulting in speckle size much bigger than the pixel size and avoiding any spatial averaging effect on the measured speckle contrast. For speckle contrast calculation, ten pictures were captured in one minute with the same experimental conditions.
4. Speckle reduction
Red and blue broad-area Fabry Perot semiconductor lasers with a relatively broad emission spectrum, and green frequency-doubled laser with a narrow emission spectrum were used for the comparison.
4.1 Blue laser
A collimated blue laser diode Nichia NUB802T was used for the investigation. This laser produces blue laser beam with typical output power of 2.3W at current 2A. The measurement was done both for the free space and the imaging geometry. Speckle contrast was measured with inactive and active mirror. Figure 3 shows the measurement results. When the mirror is inactive, the initial unsuppressed speckle contrast values are and for the free space and the imaging geometry at the laser drive current of 220mA. Then the speckle contrast reduces with the increase of the driving current. At the driving current of 2A, the speckle contrast values are and for the free space and the imaging geometry respectively. When the mirror is activated, speckle contrast drops down to for the free space geometry and to for the imaging geometry at the laser drive current of 220mA. The values of speckle contrast are the same for both geometries at 2A of the driving current. By changing the driving current from 220mA to 2A, 82.6% and 81.3% of speckle contrast reduction from its initial value are achieved with the free space and the imaging geometries. Speckle contrast reduction by the deformable mirror is easier to observe at low driving current than at high driving current. 83.8% and 86.3% of speckle reduction from its initial value for the free space and the imaging geometries can be obtained by the activation of the mirror at 220mA. These values are 59.6% and 65.2% for free space and imaging geometries respectively at 2A drive current. The images of speckle for the imaging geometry at current 2A are shown in Fig. 4. Speckle is reduced with the active mirror in Fig. 4(b) compare to the inactive mirror Fig. 4(a).
4.2 Red laser
A red broad area laser Mitsubishi ML501P73 was used for the experiment. The laser provides 0.5W CW of output power at 650mA. A separate collimating lens with focal length of 3.3mm was used to make the laser beam parallel. A plot of speckle contrast for the two different geometries for both inactive mirror and active mirror is shown in Fig. 5. There is a small difference in speckle contrast for the free space and the imaging geometries. With inactive mirror at 200mA driving current, the speckle contrast values are for free space geometry and for imaging geometry. These values go down to for free space geometry and to for imaging geometry at 650mA driving current. With the active mirror at 200mA drive current, speckle contrast for free space and imaging geometries are and. At driving current 650mA, the speckle contrast is for free space geometry and for imaging geometry. It shows 53.3% and 55.3% of speckle reduction from its initial value for the free space and for the imaging geometries with the change of driving condition from threshold current 200mA to 650mA. Up to 79.5% of speckle reduction can be achieved with imaging geometry at 200mA with the mirror active, while this value is 70% at 650mA driving current. Speckle images for the imaging geometry at driving current 650mA are shown in Fig. 6. It can be seen that there is speckle reduction with active mirror Fig. 6(b) compare to speckle image with inactive mirror Fig. 6(a).
4.3 Green laser
Solid state frequency-doubled green laser MGL-H532 was used for the experiment. It has optical output power of 600mW and the spectrum width less than 0.1nm. A plot of measured speckle contrast is shown in Fig. 7. For the free space geometry setup, speckle contrast at 300mA of driving current is for inactive mirror and for the active mirror. At driving current of 965mA, the speckle contrast is for inactive mirror and for active mirror. Speckle contrast is higher for the imaging geometry than free space geometry. For the inactive mirror, speckle contrast is at 300mA and at 965mA. When the mirror is active, there is a relatively small change in the speckle contrast with the driving current. For the imaging geometry, speckle contrast is nearly the same at 300mA and at 965mA driving current. For the free space geometry, this value is. By changing the driving current from 300mA to 965mA, speckle contrast is reduced from its initial value by 26.5% and 26% for free space and for imaging geometries. For the free space geometry, speckle contrast is reduced by 82.8% at 300mA and 81% at 965mA by the deformable mirror. For the imaging geometry, 77.1% and 69.1% of speckle reduction is attained at 300mA and at 965mA respectively. Figure 8 shows the speckle images for imaging geometry at 965mA with inactive mirror Fig. 8(a) and with active mirror Fig. 8(b).
Speckle contrast is susceptible to spatial averaging which reduces the measured speckle contrast from its true value. When the size of speckle pattern is comparable to the size of CCD camera pixel, speckle contrast is significantly reduced . As the speckle contrast is a statistical calculation, the speckle size needs to be big enough so that the true statistics of the speckle patterns is faithfully calculated. It is shown that the minimum speckle size for faithful calculation should be at least 7 × 7 pixels [28, 29]. For the free space geometry, the speckle size is approximately given by Eq. (14), the speckle size of the blue laser is 59.7µm. The speckle size is 68.7µm for the green laser and 82.4µm for the red laser. Hence the speckle size is much bigger than the CCD pixel size, and no spatial averaging happens.
For the imaging geometry, a portion of the scattered light is collected by an imaging lens and that light is then brought to the sensor of the CCD camera. In the imaging geometry, the speckle size of blue laser is 132µm. Speckle size for the green and the red lasers are 167.2µm and 176µm. Size of the speckle patterns for the free space and imaging geometry are listed in Table 1. The speckle size is big compared to the CCD pixel size which is. Hence, the spatial averaging of the speckle pattern by the CCD pixel can be ignored.
For both imaging and the free space geometries, the effective measurement which is expressed in Eq. (11) is the same. However since the size of speckle patterns are different in the two geometries setup, the correlation area of speckle intensity in Eq. (12) is different. Because speckle size of the free space geometry is smaller than the speckle size of imaging geometry, the correlation area value of free space geometry is less than the value of correlation area of imaging geometry. From Eq. (13), the spatial degree of freedom for the free space geometry is more than the spatial degree of freedom for the imaging geometry . It is shown in Eq. (2) that the speckle contrast is inversely proportional to the. As a consequence, the speckle contrast of the imaging geometry is higher than the speckle contrast of the free space geometry as can be seen in the experimental result for the blue, red and green lasers.
If independent speckle patterns with equal mean intensity are averaged, speckle contrast reduces from 1 to. Speckle reduction methods provide the change in temporal degree of freedom. For analysis, a reduction factor is defined as
In this experiment, three different methods for speckle reduction have been applied. The first method is the polarization diversity which gives polarization reduction factor. The second method of speckle reduction is the angle diversity which is provided by the deformable mirror. Finally is the wavelength diversity method which is given by the spectrum widening of the lasers. The two speckle reduction factors and are provided by angle diversity and the wavelength diversity respectively. The maximum speckle reduction factor for the system is 
The free space geometry configuration is selected for the calculation of speckle reduction factors and number of independent speckle patterns. The spatial degree of freedom is much larger than temporal degree of freedom in the free space geometry. Hence, the number of independent speckle patterns is dominated by
5.1 Speckle reduction by the polarization diversity
The diffusers scattered the light in the two orthogonal polarizations. The amount of speckle reduction depends on the degree of polarization of the light in the speckle patterns. For a fully depolarized speckle, the temporal degree of freedom that is achieved by the polarization diversity is. Therefore, an automatic of speckle reduction is obtained. In this case, the polarization reduction factor . The calculation is shown in Table 2. The degree of freedom of the polarization diversityis determined in term of the speckle contrast at the threshold current when the mirror is inactive. From the experimental result, the speckle contrast at the minimum driving current is used for the calculation of
The calculated is 2.9 for the blue laser, 2.7 for the green laser and 4.5 for the red laser. These experimental values are higher than the theoretical value . The reason for this is the lasers do have some spectrum width broadening even at the minimum driving current. The minimum driving current is slightly higher than the threshold current. Therefore, a number of independent speckle patterns are introduced by the wavelength diversity due to the finite spectrum width of the laser.
5.2 Speckle reduction by the angle diversity with the deformable mirror
Speckle contrast is reduced by the deformable mirror approach by the generation of time varying phase patterns which will effectively destroy the spatial coherence. The reduction of speckle contrast due to the diversity of illumination angle can be calculated as shown in . However, the theoretical calculation cannot be done in this case due to the random excitation of the array of piezo actuators under the thin deformable mirror surface. The piezo actuators were actuated with random voltage signals at high frequency up to many KHz range. This creates ripples on the surface of the thin flat deformable mirror causing the light to diffract. The reflected light has no single well-defined angle in this case and it does not have a plane wavefront. Moreover, a light pipe was also used in the experimental setup to homogenize the beam, and the light made multiple reflections inside the light pipe making it difficult to have only a single angle emerging after the lightpipe. So the theoretical calculation as shown in  cannot be directly applied in this case. The degree of freedom of the angle diversity is the ratio between of speckle contrast when the deformable mirror was inactive and active at the same driving current 
Therefore, the speckle contrast reduction factor can be expressed as
For the blue laser, the speckle reduction factor at the minimum current is and at the maximum current. For the red laser, these values are and. It can be seen that there are differences in speckle reduction factor by angle diversity at maximum current and minimum current for the blue and the red lasers. The mirror provides a higher at low current than at high current. For the green laser, there is just a small change of speckle reduction factor with the driving current. At the minimum driving current, the speckle reduction factor is. At the maximum driving current, the speckle reduction factor is. All of the values of the speckle reduction factor by angle diversity are given in Table 2.
5.3 Speckle reduction by the wavelength diversity
Speckle contrast depends on the spectrum width of the illuminating light source. For a broadband laser, more modes are excited in the laser with higher driving current [32, 33]. These different modes propagate independently and therefore cause the incoherence of the laser beam. Due to the incoherence of the laser beam at the high current driving regime, the speckle contrast is reduced as shown in the experiment.
The degree of freedom provided by wavelength diversity is calculated in terms of the ratio between speckle contrast at minimum driving current and maximum driving current
And the speckle reduction factor by the wavelength diversity is expressed as
By adjusting the driving current from the threshold to the maximum, the speckle reduction factor by wavelength diversity with the inactive mirror is estimated for the blue laser. The number of independent speckle patterns increases from 2.9 at the threshold current to 102 at the maximum current. When the mirror is active, the speckle reduction factor by wavelength diversity goes down to 2.4. Lower speckle reduction factor is achieved by the red laser. The value of speckle reduction factor with the inactive mirror for the red laser is 2.1. The number of independent speckle patterns at the minimum driving current is 4.5 for the red laser while this number rises to 20 at the maximum driving current.
The blue laser has higher power than the red laser. Hence, the blue laser can be driven at higher current than the red laser. More modes are excited in the blue laser at higher current and this leads to the more widening of the spectrum. For a laser source has frequency bandwidth which is much smaller than the central frequency , the speckle contrast is Eq. (23) indicates that the wider spectrum width , the lower of speckle contrast value is. A plot of the spectrum width at 20% of the maximum light intensity for the blue and the red laser with the logarithm scale current is shown in Fig. 9. The 20% of maximum light intensity was chosen for spectrum width calculation in order to take into account the modes that have low intensity. The spectrum width of the blue laser at minimum driving current 220mA is 0.2nm. The width of the spectrum increases up to 2.02nm at the maximum driving current 2000mA. The spectrum width of the red laser at 200mA driving current is 0.665nm. At maximum driving current 650mA, the spectrum width is 1.06nm. It can be seen that the spectrum at maximum driving current of the blue laser is wider than that of the red laser. As a consequence, higher speckle reduction by wavelength diversity was attained with the blue laser than the red laser.
The green laser that was used for the experiment is a frequency doubled laser. Less than 0.1nm bandwidth is indicated in the specification of the laser. Therefore, the speckle reduction by wavelength diversity for the green laser is closed to 1. In Table 2, the number of independent speckle patterns at maximum driving current with inactive mirror is 5 compare to 2.7 at minimum driving current. The value of speckle reduction factor by wavelength diversity when the mirror is inactive is 1.4. When the mirror is active, speckle reduction factor is 1.2. Although the change in the driving current of the green laser is larger than the red laser, better speckle reduction by wavelength diversity is attained with the red laser. This can be explained by the widening bandwidth of the laser spectrum. Since the green laser is a narrowband laser, the spectrum width does not increase with the driving current. Consequently, low speckle reduction can be attained for the green laser with wavelength diversity.
Although the driving temperature of the Peltier stage was fixed at for the blue and the red lasers, only the temperature at the mounting surface was controlled. The heat was induced in the lasers p-n junction by Joule heating when they were in operation. For semiconducting laser, the lasing wavelength shifts toward the longer wavelength as the operation temperature increases due to reduction in the band gap of the semiconducting material at higher temperature . The spectrum of the blue and the red lasers with different currents are shown in Fig. 10. It can be seen that the spectrum of the lasers shift towards longer wavelength with the increase of the current. The light intensity of the emission light is also higher and the spectrum width becomes broader with higher driving current. In Fig. 10(a), the central emission wavelength of the blue laser at 300mA is 463.5nm. The central emission wavelength shifts to 465.5nm at 1100mA and to 467.5nm at 2000mA. In Fig. 10(b), the light from the red laser has central wavelength of 636nm at 200mA driving current. The central wavelength of laser beam shifts to 636.9nm at 400mA of driving current and to 637.8nm at 650mA. For the variation of driving current from minimum to maximum, the approximate shift wavelength is 4nm for the blue laser and 1.8nm for the red laser.
Following , the increase of the wavelength has two effects. The first effect is the diffraction angles are proportional to the wavelength. Hence, the increase of the wavelength leads to the reduction of speckle. The second effect is that the phase shift is proportional to the ratio of root mean square surface roughness and the wavelength. The increase of the wavelength causes the reduction of phase shift and therefore the speckle contrast increases. Since the shift of wavelength has two contrary effects on speckle contrast value, it provides a minor effect on the speckle reduction.
Speckle reduction for single laser using dynamic deformable mirror is studied in this paper. It is also shown that the speckle contrast depends on the spectrum bandwidth of the laser. Both broadband lasers and narrowband laser were used for the study. Speckle contrast measurement was done for the free space and the imaging geometries at different driving current of the lasers. It was shown that speckle contrast can be reduced by the driving current due to the wavelength diversity. For the broadband blue laser Nichia NUB802T, up to 82.6% and 81.3% of speckle contrast reduction can be attained from its initial value for the free space and the imaging geometry by increasing the driving current from 220mA to 2A. The reduction is due to the widening of the band width from 0.2nm to 2.02nm. Speckle contrast is further reduced by deformable mirror based on the angle diversity. At 2A of driving current, speckle contrast goes down to 0.04 for both free space and imaging geometry with the dynamic mirror activated. The spectrum width of red laser Mitsubishi ML501P73 increased from 0.665nm to 1.06nm by changing the driving current from 200mA to 650mA. The spectrum widening and the wavelength shift of the red laser are smaller than the blue laser. As a consequence, only 53.3% and 55.3% of speckle reduction for the free space geometry and the imaging geometry was attained by the change of driving condition for the red laser. Speckle contrast reduces to 0.063 for the free space and 0.066 for the imaging geometry by activating the deformable mirror. The solid state green laser MGL-H532 has a narrow bandwidth. Therefore, only 26% of speckle contrast can be reduced by the change of the current from 300mA to 965mA. Speckle contrast was brought down to 0.09 for the free space geometry by activating the mirror for the green laser. This method of speckle reduction is practical for laser projectors where high laser power is needed to display a picture on a big screen. The deformable mirror can be placed before the light pipe homogenizer in the optical path. Even further speckle reduction can be achieved by using an array of red and blue lasers.
The authors would like to thank Professor Einar Halvorsen for his valuable discussion. The authors would like to acknowledge the financial support from Education Department of Norway (KD) for the Ph.D. stipend and Norwegian Research Council LasePro project.
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