A speckle pattern happens due to the scattering andinterference of highly coherent radiation froma roughsurface. The basic theory of speckle formation, itsstatistical properties, and a detailed review of specklereduction methods is explained in [1]. Considerableeffort has been made to minimize the speckle noisein imaging applications where laser light is used asthe illumination source. In imaging applications, thedetector is an intensity detector with finite spatialand temporal bandwidth. Hence, in such situations,the space-time-integrated intensity speckle is what isperceived by the detector. Different methods havebeen developed to reduce integrated speckle, such asby using amoving randomdiffuser plate placed at theimage plane [2], by a rotating diffractive optical ele-ment in the laser beam [3], by using an ultrasonicpressurewave ina crystal to createa time-varyingdif-fraction grating and passing a laser beam through itto create a traveling interference pattern on thescreen [4], by using multiple non-phase-locked inde-pendent lasers for illumination [5], byusinga rotating
microlens array in the laser illumination path [6], byusing a stationary phase plate based on a Barker orBarker-like binary phase code at an intermediate im-age plane [7–9], by using partially coherent beams[10], by using changing Hadamard phase patternsinside each detector resolution pixel at intermediateimage plane [11,12], and by using a micromirror [13]to introduce angular diversity.
If we use a mechanically vibrating or rotatingelement in the laser beam, such as is used in[2,3,6,11,12], a bulky component is needed to vibrateor rotate at high speed, which may not be very con-venient or reliable. If we use many laser beams forillumination, such as is used in [5,10], we need manyindependent running lasers with a minimum angu-lar separation between them [1] to achieve specklereduction, which may complicate the illuminationoptics. The method presented in [7–9] based on staticphase code is not applicable to full-frame projectors.
In this article, we have used a fast two-dimensionalscanning micromirror to steer the laser beam andachieve angular and spatial diversity. The moving la-ser beam falls on a transmitting random phase plateat different angles and at different spatial positions.Experiments are performedboth for free-space propa-gating geometry as well as imaging geometry. A high
speckle reduction factor is achieved in both configura-tions. In an experiment related to an application in alaser projector, a light pipe is used as a beam homo-genizer, and random phase plates are put both atthe input and at the output face of the light pipe.An object is placed at the output face of the light pipeand is imaged by aCCDcamera.Ahigh speckle reduc-tion factor is achieved using the light pipe geometry,indicating that our scheme is also applicable to full-frame laser display projectors. Speckle contrast mea-surements are done at a different integration time oftheCCDcamera to demonstrate the application of ourtechnique in situations with a human observer, hav-ing an integration time of 30 ms [1].
2. Theoretical Background
The speckle contrast factor C is commonly used tocharacterize a speckled picture. It is defined asfollows [1]:
where hIi and σI are the mean value and the stan-dard deviation of the light intensity in the specklepattern. If we sum N independent speckle patternson an intensity basis, each pattern having the samemean intensity, the speckle contrast C in the inte-grated image is reduced to [1]:
C ¼ 1ffiffiffiffiffiN
p : ð2Þ
The intensity variations in a speckle pattern dependupon the angle of illumination on the rough surfaceand the observation angle of the detector. A detailedtheoretical derivation of the correlation coefficient ofthe speckle field intensity as the illumination or ob-servation angles are changed is given in [1]. A briefsummary of the basic theory is given here for comple-teness. The normalized cross-correlation function μAof the two speckled fields A1 and A2 is given by
μAð~q1;~q2Þ ¼ MhðΔqzÞΨðΔ~qtÞ; ð3Þ
where MhðΔqzÞ is the first-order characteristic func-tion of the surface-height fluctuations h and is deter-mined by the ratio of the surface-height fluctuationsto the wavelength,ΨðΔ~qtÞ represents the translationof the speckle pattern as the illumination or observa-tion angle is changed and is given by
ΨðΔ~qtÞ ¼
R Rþ∞
−∞
Iðα; βÞe−jΔ~qt·~αtdαdβR Rþ∞
−∞
Iðα; βÞdαdβ; ð4Þ
αt ¼ ðα; βÞ being the transverse coordinates in theplane of the scattering surface and~q is the scatteringvector given by
~q ¼~qt þ qz~z ¼~ko −~ki; ð5Þ
where ~qt and qz are the transverse and the perpen-dicular components of the scattering vector~q, respec-tively with respect to the plane of the scatteringsurface,~ki is the incident wave vector on the randomsurface, ~ko is the transmitted wave vector after therandom surface, k ¼ 2π=λ, and λ is the wavelength.The intensity correlation of the two observed specklepatterns is given by [1]:
jμAð~q1;~q2Þj2 ¼ jMhðΔqzÞj2jΨðΔ~qtÞj2: ð6Þ
For a surface with Gaussian surface-height hfluctuations:
jMhðΔqzÞj2 ¼ e−σ2hΔq2z ; ð7Þ
where σh is the root mean square surface height. Ifthe scattering spot is a uniformly bright spot ofdiameter D, then
jΨðΔ~qtÞj2 ¼�2J1ð0:5DΔqtÞ0:5DΔqt
�2; ð8Þ
where J1 is the Bessel’s function of first kind, order 1.For the transmission geometry, as shown in Fig. 2,assuming the observation angle θo ¼ 0°:
For the free-space geometry, the normalized cross-correlation function μA mainly depends upon thetranslation factor ΨðΔ~qtÞ. However, for the imaginggeometry, the normalized cross-correlation functionμA mainly depends upon the surface-height fluctua-tion function MhðΔqzÞ [1] because the speckle trans-lation effect due to ΨðΔ~qtÞ is minimal.
3. Scanning Micromirror
A fast two-axis oscillating micromirror is shown inFig. 1(a). It has a clear aperture of 2 mm, surface re-flectance of 88% in the visible wavelength range, andan oscillating frequency of 1:2 kHz in the fast axisand 0:2 kHz in the slow axis. The micromirror canhandle maximum reflected continuous optical powerof 250 mW, according to the manufacturer’s specifi-cations. The angle of oscillation is�3:5° for both axesas measured experimentally. The applied voltage is asquare waveform at twice the resonant frequency inboth axes. The peak-to-peak applied voltage is 50 Vin the fast axis and 30 V in the slow axis. The two-dimensional Lissajous figure of the laser beam ob-tained by the scanning action of the micromirror isshown in Fig. 1(b). The laser beam retraces its pathafter the oscillating period of 5 ms, and the Lissajous
pattern remains stable when it is projected on ascreen away from the mirror.
4. Experimental Setup and Results
A. Free-Space Geometry
The experimental setup to implement speckle reduc-tion in the free-space propagation (no lens betweenthe random surface and the detector) is shown inFig. 3. The laser is anHe–Newith power 4 mW, beamdivergence angle 1 mrad, and full width at half-maximum diameter of 1 mm. The laser beam has afixed polarization and is passed through polarizer 1
and polarizer 2. Polarizer 1 is rotated to control thebeam intensity, and polarizer 2 maintains a fixed po-larization of the transmitted beam. The laser beam isreflected by the scanningmicromirror. It is imaged bya lens onto a transparent random phase plate withunit magnification. The random phase plate is madefrom BK7 glass by sandblasting with 120 grit, whichhas sand particles of diameter 115 μm. After passingthrough the random phase plate, the beam propa-gates and falls on the CCD detector. The CCD has aresolution of 640 × 480 pixels, and each detector pixelhas a dimension of 5:6 μm × 5:6 μm. The gain andbrightness value of the CCD camera is set to avoidoversaturation or undersaturation of the capturedimage. In addition, polarizer one is also rotated tomaintain a relatively constant mean light intensitylevel of the captured image. The integration time ofthe CCD camera is set manually to the capturedtime-integrated speckle pattern with a different inte-gration time.
As themicromirror oscillates, the spatial position ofthe laser spot on the random screen remains almostfixed and only the illumination angle changes, whichcreates new speckle patterns in time, which are aver-aged by the CCD camera during its integration time.The captured speckle image with and without the os-cillation of the scanmirror are shown in Figs. 4(a) and4(b), respectively. The CCD integration time was31.25ms for these images. The speckle contrast factorC is calculated for these images and results given inTable 1. Please note that due to the depolarization ef-fect of the random plate, there are two independentspeckle patterns due to the x- and y-polarized electricfield, even without the scan motion of the micromir-ror. The number of independent speckle patterns Nestimated fromEq. (2) is also given inTable 1. Speckleimage is also captured with short integration time of
Fig. 1. (a) MEMS two-dimensional micromirror and (b) Lissajousscan pattern of the reflected laser beam after the scanning micro-mirror.
Fig. 2. Random surface transmission geometry.
Fig. 3. Free-space speckle geometry and angle diversity.
0.98ms, and the speckle contrastC andnumberN aregiven in Table 1.
B. Imaging Configuration: Application in Picture Projection
A simple experimental setup, as shown in Fig. 5, isbuilt to demonstrate the application of the scanningmicromirror in reducing speckle in a full-frame pic-ture projection. After passing through the first ran-dom phase plate, the laser beam is scattered andpasses through a rectangular light pipe for beam ho-mogenization. The rectangular light pipe has a cross-sectiondimensionof7 mm × 5 mmandis70 mmlong.At the output face of the light pipe, another randomphase plate is placed to further homogenize the beam.
The letter π is printed by a laser printer on a transpar-ent plastic sheet, and the plastic sheet is placed rightafter the second randomphase plate. TheCCD sensorequipped with a imaging lens of focal length f ¼75 mm and aperture f-number 16 is placed at a dis-tance of approximately 500 mm from the transparentplastic sheet and makes an image of it. As expected,without the scanningmirrormotion, the image is veryspeckled, as shown in Fig. 6(a). As the mirror is oscil-lated, the speckle averaging happens and the image
Fig. 4. Free-space geometry: (a) speckle image with micromirrorstationary and (b) speckle image with micromirror oscillating.
Table 1. Speckle Contrast Factor C and Effective Number of Independent Speckle Patterns N Estimated Experimentallyfor Different Configurations
Configuration CCD Integration Time Speckle Contrast C N ¼ 1=C2
becomes smooth, as shown in Fig. 6(b). The specklecontrast factor C calculated for a uniform region ofthe image (without the letter π) with and withoutthescanmirrormotion isgiven inTable1.Thenumberof independent speckle patterns N introduced by thescan mirror motion is also given in Table 1.
5. Discussion of Results
A. Free-Space Geometry
Without the scanning action of the micromirror, thespeckle contrast factor is nearly 0.684 due to the twoindependent noninterfering speckle patterns createdby the two orthogonal polarizations of light after scat-tering from the random phase plate. The measuredspeckle contrast value is almost equal to the theore-tical value of 0.707 for the sum of two independentspeckle patterns [1]. The exact value of the specklecontrast depends upon the surface roughness andthe statistical properties of the surface-height func-tion [1]. For this article, we are mainly interestedin the speckle reduction with the scanning micromir-ror and not in the absolute value of the speckle con-trast. The random surface is very rough on the opticalwavelength scale, and its scattering angles are sym-metrical in the vertical and horizontal directions. Wemay assume that after scattering from the rough sur-face, the speckle intensity pattern developed by twoorthogonal polarizations is fully developed [1]. Thespeckle contrast value also depends upon the gain,brightness, and nonlinearity of theCCD camera. Dur-ingmeasurements, we adjust the gain and the bright-ness of the CCD camera so that the recorded image iswithin the linear regime of the camera. The nonli-nearity of the CCD camera is expected to be nonexist-ing because its γ value is set to 1 during all themeasurements.
For a perfect monochromatic laser, the speckle con-trast should lie in the range 0.707 to 1. If the diffusercould preserve the original polarization completely,then the speckle contrast should be equal to 1 (onespeckle pattern). With the totally depolarizing diffu-ser, C should be 0.707. We got a speckle contrast of0.687, which is very close to the value 0.707, meaningthat the diffuser is good at depolarizing.
For the free-space propagation geometry after therough surface, the speckle size is approximatelygiven by λz=D, where z is the propagation distanceafter the rough surface and D is the diameter of thescattering spot. In our first experiment for z ¼
75 mm, assuming D ¼ 0:5 mm, the speckle size atthe CCD plane is 94:5 μm, which is big enough tobe faithfully sampled by the CCD pixels of size5:6 μm× 5:6 μm. The spatial averaging of the specklepattern by the CCD pixel can be ignored in this case.As we oscillate the micromirror, the speckle contrastfactor reduces to a very low value of below 4% for acamera integration time of 31.25ms. Such an integra-tion time is typical of that of a human eye [1]. Even fora very short integration time, such as 1 ms, very goodspeckle reduction with speckle contrast value of 5% isachieved. One must also pay attention to the oscillat-ing frequency of the micromirror and its relation tothe integration time of the CCD with regard to thespeckle averaging action. The fast axis of the micro-mirror has one cycle time period of 0.83 ms, and theslow axis has a time period of 5 ms. The incrementalangle Δθ needed to create two completely indepen-dent speckle fields can be calculated from Eq. (3)for the free-space geometry. For example, for a Gaus-sian distributed surface-height function with surfaceroughness σh ¼ 100 μm, scattering spot diameterD ¼0:5 mm, normal incident with θi ¼ 0, and randomtransmissive surface with refractive index n ¼ 1:5,the incremental angle Δθ due to the ΨðΔ~qtÞ factorin Eq. (3) is 0:1° and the incremental angle is Δθ dueto the MhðΔqzÞ factor being 5°. Hence, effectivelyspeaking,ΨðΔ~qtÞ is the dominant factor in determin-ing the incremental angle for speckle reduction infree-space propagation. As the total scanning angleis �3:5° in both oscillating axes, the reflected laserbeam traverses a total angle of �7° in both axes.Hence, in the fast axis, the number of independentspeckle patterns created during half a scan cycle is140. As seen in the Lissajous scan pattern, Fig. 1(b),there is also scanning in the slow axis, which createsits own independent speckle patterns. The number ofindependent nonoverlapping beam tracks visuallycounted in Fig. 1(b) is approximately 10. Hence, inthe slow axis, there is additional speckle reductionand the total number of independent speckle patternscreated during one complete cycle of the Lissajousfigure, which is 5 ms, is the product of fast and slowscan independent speckle patterns.Hence, if theCCDintegration time is equal to or more than 5 ms, itwill accumulate the maximum independent specklepatterns on intensity basic and give a high speckle re-duction factor, as evident from Table 1. If the CCD in-tegration time is shorter, such as 1 ms—as given inTable 1, the total number of accumulated indepen-dent speckle patterns will be fewer and the specklereduction will not be as good. However, as is evidentfromTable 1, even for a short CCD integration time of1 ms, the speckle contrast is 5%, which is quite good.One may also use a microscan mirror with fasteroscillating frequency to accomplish higher speckle re-duction in situations where shorter CCD integrationtime is desired. Nonmechanical beam steering meth-ods, such as given in [14] and the references therein,with a faster scanning rate, larger deflection angle,
Fig. 6. Picture projection geometry: (a) speckle image withmicromirror stationary and (b) speckle image with micromirroroscillating.
and bigger laser beamaperturemay also be used to fitcertain applications as needed.
B. Light Pipe Geometry
For the imaging geometry, the speckle size is approxi-mately given by the resolution size of the imaginglens, that is ð1þmÞλf =Dl [1], where f is the focallength of the imaging lens, Dl is the diameter of theimaging lens, andm is the magnification of the opticsconfiguration. In the imaging configuration, thespeckle size can be controlled by the aperture dia-meter Dl of the imaging lens and the magnificationfactor m. In the light pipe experiment, the apertureof the imaging lens is set to its minimum value of f-number 16 or the lens diameterDl ¼ 4:6875 mm. Theobjectwith letter πwasplacedat adistance of500 mmfrom the CCD camera lens, so the speckle size on theCCD image plane can be estimated to be approxi-mately equal to 11:8 μm,which is about twice the sizeof the CCD pixel dimension. From Fig. 6(a), the effectof the CCD pixel spatial sampling is visible as thespeckle size on the CCD is comparable to the CCDpixel dimension.However, wewere unable to increasethe f-number of the imaging lens as it was the highestf- number allowed by the mechanical aperture insidethe lens. The minimum focus distance from the lightpipe output face to theCCD image planewas500 mm,determined by the C mount of the CCD camera andthe lens construction. Hence, we were not able to re-duce the focus distance and increase the magnifica-tion in a way to increase the speckle size on theCCD pixel. The spatial averaging of the speckle pat-tern by the finite CCD pixel dimension of 5:6 μm ×5:6 μm will create additional speckle reduction [1].It is also evident in Table 1 where for no scan, thespeckle contrast is 0.55 and not 0.7. However, our re-sults are still valid and demonstrate the speckle re-duction achieved by the micromirror scan action.For the second randomphase plate at the output facetof the light pipe, the illuminated area is 7 mm×5 mm. Hence, the incremental angle Δθ needed forcreating new independent speckle pattern is smaller,as evident from Eq. (8). In addition, the laser beam isspatially scanned at different random areas on the in-put random plate, which creates additional specklereduction.
The speckle reduction in this setup happens due totwo factors. First, the scanning laser spot passesthrough different areas of the first random phaseplate and creates new speckle patterns in time, whichare summed by the CCD during its integration time.This method of speckle reduction is similar to themoving diffuser, where the laser beam is not moved;rather, the random phase plate is moved to achieve atime-varying speckle pattern, as explained in [1]. Thescattered laser beam enters the light pipe and getsmultiple reflections from the side walls in a compli-cated manner. As the laser beam is scanned acrossthe input face of the light pipe, its travel path inthe light pipe also changes in time. At the output faceof the light pipe, the beam is spatially homogenized
and it passes through the second randomphase plate.However, as the beam is scanned at the input face ofthe light pipe, the scattered light reaching the secondrandom phase plate also changes its angles of inci-dence and, hence, create additional speckle reductiondue to the angle diversity. So what the CCD capturesis subjective speckle because it is being imaged by theCCD lens (and not free-space propagation and fallingon the CCD surface without the imaging lens). Thespeckle formed in the plane of the CCD sensor inFig. 5 can be described as “speckled speckle” or “com-pound speckle statistics.”We give the following quotefrom p. 53 of [1], “For example, when light passesthrough one diffuser, and the speckled light from thatdiffuser falls on a finite-sized second diffuser, therecan be a compounding of speckle statistics.” Thespeckle contrast for the speckled speckle is C ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN þ K þ 1Þ=ðNKÞp
, according to (3-108) and (6-45)in [1] (we replacedM byN in ourpaper). For very largeK , we obtain C ¼ ffiffiffiffiffiffiffiffiffiffi
1=Np
or N ¼ 1=C2, which we usedin Table 1 in this article.
For the light pipe geometry, the light beam is scat-tered two times from the two random phase plates.Hence, for practical application, the spread of thelight beam after the light pipe must not be more thanallowed by the subsequent optics. For example, if adigital micromirror device (DMD)-based [15] displaychip is to be used for displaying a picture, the max-imum allowed cone angle of the beam falling on theDMD is �9:4° or f- number 3.
In [1], it is stated that the speckle contrast C isequal to
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN þ K � 1Þ=ðNKÞp[see Eqs. (6-41) and
(6-45)], where N is the number of temporal degreesof freedom—that is how many independent specklepatterns are created by the scanning laser beam dur-ing the integration time of the detector—and K is thenumber of spatial degrees of freedom, which is beingdetermined by the ratio of numerical aperture NA ofthe eye to the NA of the projection lens. For N ap-proaching infinity, the contrast is reduced only toffiffiffiffiffiffiffiffiffi
1=Kp
. In our simple setup, we have not used a pro-jection lens to project the image onto a big screen. Inour case, the object transparency is illuminated by atime-varying randomwavefront laser beamand is im-aged by the CCD camera with an imaging lens. So ourexperimental setup is not directly comparable withthe equation
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN þ K � 1Þ=ðNKÞpin Goodman’s book
[1]. Our speckle reduction method is based on a com-bination of spatial and angle diversity, which is ex-plained in Goodman [1] in Chap. 5. We may saythat K is very large in our experiment, so the specklecontrast is 1=
ffiffiffiffiffiN
p, andwehave shown thatN is a large
number in our setup due to the scanning action of thelaser beam over the diffuser surface, so the specklecontrast measured is very low, e.g., 5% in the ex-periment. In the future,wewill do anexperimentwitha projection lens with a certain NA to project amagnified image on a screen, capture the image withthe CCD camera, and calculate the speckle contrastClike Trisnadi did in his papers [11,12]. For his experi-
mental setup, the K was 64, based on the NA of theprojection lens and the imaging optics of the CCDcamera simulating a human eye, so the best specklecontrast obtained was 1=
ffiffiffiffiffiffi64
p ¼ 12:5% due to the mo-tion of the Hadamard diffuser alone. The projectionangle (or NA of the projection optics) can be small,but it should be compared with the NA of the obser-ver’s eye, which gives the value of K in the formulaC ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN þ K � 1Þ=ðNKÞp
. The NA of the observer’seye is normally much smaller than that of the projec-tion optics, as clearly explained by Trisnadi [11,12].
Wehavenotmeasured the energy loss in our experi-ment.Thediffuserplate isnotantireflectioncoated, sothere is someFresnel reflection loss due to the two dif-fuser plates.However this loss can be avoided by anti-reflection coatings on the diffuser plates. The lightfrom the first diffuser is coupled almost 100% intothe light pipe because the diffuser is placed adjacentto the light pipe. The light pipe has some light loss dueto absorption on its internal walls, which is not high.There is some scattering from the second diffuser,which can be the main cause of light power loss in areal DMD- or LCoS-based projector. So the numericalaperture of the projection lens should be large enoughto capture the scattered light after the seconddiffuser.Wemay say that the light loss is not high in our setup.
C. Sources of Error in Experiments
Some possible source of error that can cause discre-pancy between the theoretical and the measuredvalue of speckle contrast are given below.
1. The statistical properties of the surface-heightfunction affect the incremental angle Δθ needed tocreate two independent speckle patterns. Becausewe do not know exactly the random surface profile,it is difficult to theoretically estimate Δθ.
2. The spot size diameter D of the laser beam onthe random surface affects the incremental angle Δθneeded to create two independent speckle patterns.As the laser beam is steered by the micromirror, thespot diameter and its shape falling on the randomphase plate change, hence, the formula in Eq. (8)is oversimplified.
3. The relative linear motion between the laserspot and the random phase plate creates additionalspeckle reduction. It is difficult to estimate the linearmotion of the laser spot due to the scanning action ofthe micromirror after the 1:1 lens in experiment 1.
4. The nonlinear motion of the scanning micro-mirror, especially at the extreme ends of its scan an-gle, creates a nonuniform duration time for eachindependent speckle pattern to be integrated inthe CCD. However, the formula C ¼ 1=
ffiffiffiffiffiN
passumes
equal duration time for all speckle patterns. In addi-tion, the overlapped part of the laser beam travelpath on the Lissajous figure does not create new in-dependent speckle patterns.
5. Some of the laser beam falls outside the clearaperture of the micromirror and creates fixed reflec-tion. This fixed reflection creates a fixed speckle pat-tern that does not change with the scan motion of the
micromirror. The dust particles on the CCD surfacecreate artifacts in the captured image.
6. The electronic noise from the CCD sensor addsextra speckle to the capture images.
7. The gain and the brightness setting of the CCDcamera affect the speckle contrast factor C of thecaptured image.
8. The finite spatial dimension of the CCD pixelas compared to the speckle size creates spatial aver-aging of the captured speckle pattern.
6. Summary and Conclusion
A fast two-axis scanning micromirror is used to intro-ducespatialandangulardiversity into the laserbeam.The time-averaged speckle contrast factor is reducedto a very low value of 5% in the free-space configura-tions with typical integration time of 30ms, similar tothat of a human observer. In a picture projection ap-plication, a light pipe beamhomogenizer is used alongwith two random phase plates to implement specklereduction. A high speckle reduction with a specklecontrast factor 5% is achieved. Our method is simpleto implement with a low-costMEMSmicromirror anddoes not need complicated drive electronics. For thehigher laser power needed for a large display screen,a larger diameter scanning micromirror can be uti-lized. Nonmechanical methods of beam steering mayalso be used to achieve the speckle reduction.
This research work was funded by the ResearchCouncil of Norway under grant BIA-286, projectnumber 182667. The authors are thankful to Projec-tion Design, Fredrikstad, Norway, for providing lightpipes for the experiment.
References1. J. W. Goodman, Speckle Phenomena in Optics: Theory and
Applications (Roberts, 2006).2. S. Lowenthal and D. Joyeux, “Speckle removal by slowly
moving diffuser associated with a motionless diffuser,” J.Opt. Soc. Am. 61, 847–851 (1971).
3. L. Wang, T. Tschudi, T. Halldorsson, and P. R. Petursson,“Speckle reduction in laser projection systems by diffractiveoptical elements,” Appl. Opt. 37, 1770–1775 (1998).
4. L. Wang, T. Tschudi, M. Boeddinghaus, A. Elbert, T.Halldorsson, and P. R. Petursson, “Speckle reduction in laserprojections with ultrasonic waves,” Opt. Eng. 39, 1659–1664(2000).
5. N. George and A. Jain, “Speckle reduction using multipletones of illumination,” Appl. Opt. 12, 1202–1212 (1973).
6. K. Kasazumi, Y. Kitaoka, K. Mizuuchi, and K. Yamamoto, “Apractical laser projectorwithnew illumination optics for reduc-tion of speckle noise,” Jpn. J. Appl. Phys. 43, 5904–5906 (2004).
7. V. Yurlov, A. Lapchuk, S. Yun, J. Song, and H. Yang, “Specklesuppression in scanning laser display,” Appl. Opt. 47, 179–187(2008).
8. V. Yurlov, A. Lapchuk, S. Yun, J. Song, I. Yeo, H. Yang, andS. An, “Speckle suppression in scanning laser displays:aberration and defocusing of the projection system,” Appl.Opt. 48, 80–90 (2009).
9. M. NadeemAkram, V. Kartashov, and Z. Tong, “Speckle reduc-tion in line-scan laser projectors using binary phase codes,”Opt. Lett. 35, 444–446 (2010).
10. S. An, A. Lapchuk, V. Yurlov, J. Song, H. Park, J. Jang, W. Shin,S. Karagpoltsev, and S. Yun, “Speckle suppression in scanning
