Lapchuk et al.
Vol. 30, No. 11 / November 2013 / J. Opt. Soc. Am. A
2253
Experimental evaluation of speckle suppression efficiency using a moving 2D Barker code DOE A. Lapchuk,1,* O. V. Shyhovets,1 A. Kryuchyn,1 V. Petrov,1 G. A. Pashkevich,2 O. V. Bogdan,2 A. Kononov,3 and A. Klymenko4 1 2
Institute for Information Recording of NAS of Ukraine, Shpak Str. 2, Kiev 03113, Ukraine Kyiv Polytechnic Institute, Research Institute for Applied Electronics, Kiev 03056, Ukraine 3 Specialized Enterprise Holography Ltd., Lenin Str. 64, Kiev 02088, Ukraine 4 National Aviation University, Cosmonaut Komarov Pr., Kiev 03058, Ukraine *Corresponding author:
[email protected] Received July 8, 2013; revised August 27, 2013; accepted September 17, 2013; posted September 18, 2013 (Doc. ID 193384); published October 11, 2013
This paper reports the findings from an experimental evaluation of speckle suppression efficiency using a method based on a moving 2D Barker code diffractive optical element (DOE). The optical setup and the optical scheme parameters of the method are presented. A speckle contrast of ∼4.4–5.3% and speckle suppression coefficient (coefficient of speckle contrast reduction) of k> 8 was obtained in experiments. However, the experimentally obtained speckle suppression coefficient was approximately 1.5 times smaller than the theoretical prediction. It is speculated that the discrepancy between the theoretical and the experimental data is due to an inexact match between the optical setup and the optimal optical parameters of the method. Analysis of the experimental data revealed that once the optical scheme is optimized, it will be possible to obtain a speckle suppression that is closer to the theoretical prediction. © 2013 Optical Society of America OCIS codes: (110.6150) Speckle imaging; (110.1650) Coherence imaging. http://dx.doi.org/10.1364/JOSAA.30.002253
p C α1∕N 2;
1. INTRODUCTION Laser illumination helps in achieving compact devices, large optical efficiency, and high color saturation. Therefore, it is the optimal solution for many optical devices [1–6]. However, the quality of images created using coherent laser illumination severely deteriorates because of granular modulation caused by speckle phenomena [7,8]. The speckle noise is the main factor that constrains extensive implementation of laser illumination in technical devices [7,8]. The speckle contrast C, which determines the depth of light intensity modulation due to speckles, is the most important parameter for determining speckle noise: C σ I ∕hIi;
(1)
where σ I and hIi are the standard deviation and the mean light intensity on the screen, respectively. Speckle suppression methods are based on speckle pattern averaging using the wavelength, angle, or polarization diversity of a laser beam [8]. One of the most effective methods of speckle suppression is the speckle averaging mechanism that is based on a vibrating random diffuser or a regular diffractive optical element (DOE) [9–16]. In our previous publication, we proposed a method of a speckle suppression based on Barker code and M-sequence DOEs and worked out its mathematical model [17–20]. This method is based on 2D phase modulation of light passed through a DOE based on Barker code or M-sequences. The mathematical model of this method gives the speckle contrast of the method as [17–19]: 1084-7529/13/112253-06$15.00/0
(2)
where N is the Barker code length and α is a coefficient (whose value is close to unity) that depends on the parameters of the optical scheme. The Eq. (2) reveals the possibility of decreasing speckle contrast below human eye sensitivity (below 5%) using this method. This occurs in the case of N 13 Barker code DOEs or DOEs based on M-sequences of lengths N ≥ 13. It was proved that this method has a large waveband range and as a result, one Barker code DOE can be used for red, green, and blue laser beams [17,19]. It was also shown that this method can be implemented using two 1D Barker code DOEs moving in orthogonal directions [17] or one 2D Barker code DOE moving with a specified linear velocity and direction [18,20]. This method can also use liquid crystals, micro-electro-mechanical systems (MEMS), and mixed realizations [19]. In the cases of liquid crystals, MEMS, and mixed realizations, this method does not require any mechanical vibration. The previous results [17–19] were obtained from a theoretical model without experimental validation. In this study, we present the experimental evaluation of speckle suppression and optical efficiency of a 2D Barker code DOE moving mechanically with constant velocity.
2. EXPERIMENTAL SETUP The optical scheme of the method used in the experiment is shown in Fig. 1. The DOE is placed at the object plane in the present experimental setup. However, in general, the DOE can be situated at any plane conjugate to the object plane [19]. The © 2013 Optical Society of America
2254
J. Opt. Soc. Am. A / Vol. 30, No. 11 / November 2013
Lapchuk et al.
Fig. 1. (a) Principal optical scheme and (b) scheme of the DOE movement in the method. The DOE structure is shown schematically (without a structure of one DOE period).
Barker code DOE is placed on the carriage of a plotter. The method requires the DOE to be inclined at a particular angle relative to the direction of movement to get the best speckle suppression effect. The angle, φ, can be calculated from the equation tan φ 1∕MN [see Fig. 1(b)]. The carriage of the plotter moves with only three predetermined velocities. Therefore, we constructed the optical scheme in such a manner that two of the speeds of the plotter carriage were close to the speed required to achieve a maximum speckle suppression effect. The speckle suppression efficiency of the method is maximized if the input (NA1in ) and output (NA1out ) numerical apertures of the projector, input (NA2in ) and output (NA2out ) numerical apertures of the camera (or eye), Barker code element grating width (T), and its velocity (vd ) satisfy the following five conditions [17–19]: (1) (2) (3) (4) (5)
NA1in d1 ∕2s1 > λ∕T; NA1out d1 ∕2s2 > N NA2in N d2 ∕2s3 ; λ∕2 NA2in > MT 0 ; λ∕2 NA2out > 3Δ; vd Δt K · M · NT;
where (see Fig. 1) λ is the laser radiation wavelength; d1 , the aperture diameter of the objective lens of the projector; s1 , the distance from object plane to the objective lens; s2 , the distance from the objective lens to the screen; d2 the aperture diameter of the camera objective; M, the projector magnification; Δ, the width of one photodetector of the camera;
T 0 NT; Δt, the exposure time; and K, any positive integer. The first condition is required for a maximized speckle suppression effect and large optical efficiency since almost all the spatial frequencies of diffracted light will be used for image creation and speckle averaging in this case. The second and third conditions follow from the fact that the optimal speckle suppression can be obtained only when the eye (or camera) fails to resolve one image period of the DOE grating on the screen (MT0 ). The fourth condition is required to avoid speckle averaging in the measuring system due to the finite size of the camera’s photodiode. The fifth condition is important for exact speckle averaging during the exposure time of the camera. Since the plotter carriage velocity and the exposure time of the camera have a finite number of discrete values, only an approximate implementation of the fifth condition is possible in our experiment. A 2D Barker code DOE of length 13 with an element width of T 6 μm and a period of T 0 78 μm was fabricated using electron beam lithography (to produce photomask) and photolithography (to produce DOE from photomask). The depth of relief was chosen to accomplish a half-wave phase shift for a wavelength of 532 nm. A green laser pointer with a wavelength of 532 nm and output light power of ∼10 mW was used as a source of coherent light. The optical system of the pointer was not perfect since the laser beam inside the pointer is strongly scattered by the walls of the pointer, and this results in the creation of fringes on the screen. This effect caused an overestimation of speckle contrast in our experiment. Therefore, the speckle contrast was evaluated as follows. First, the speckle contrast of the small homogeneously illuminated parts of the screen (large enough to have a large number of speckle decorrelated areas in one part) was evaluated. The overall speckle contrast was calculated by averaging the speckle contrast obtained from these smaller screen parts. The speckle image was taken using a camera with an aperture diameter of 1.5–2 mm. The digital camera used was a Canon PowerShot A630 with an 8.0-megapixel CCD imaging sensor. The DOE speed and exposure time were 0.0018 m∕s and 0.6 s, respectively. Thus, during the exposure, the DOE shift was ΔL 13.8 T 0 , and it was a little higher than ΔL 13 T 0 (at almost the width of one grating element T), which is the condition for optimal speckle suppression. Since the eye resolution time is 0.04 s (approximately 15 times shorter than camera exposure time), the speed of the DOE in the projector should be 15 times higher (∼0.027 m∕s). The reduction of the DOE period allows the proportional decrease of the DOE speed. All the parameters of the experimental setup are presented in Table 1. The first row presents parameters used for the first experiment and the second row presents parameters used for the second experiment. From the data in Table 1, it is easy to see that almost all the optical parameters were within the desired range for speckle suppression using the proposed method.
Table 1. Parameters of the Experimental Setup Used for Evaluation of Speckle Suppression Efficiency for the Method M
S 1 mm
D1 mm
S 2 mm
D2 mm
S 3 mm
N
M
NA1in
NA1out
NA2in
λ∕2 NA2in mm
1 2
56 60
20 20
280 260
2 1.6
1100 1150
13 13
5 4.7
0.17 0.11
0.0357 0.038
0.0009 0.0065
0.29 0.41
Lapchuk et al.
Vol. 30, No. 11 / November 2013 / J. Opt. Soc. Am. A
2255
Fig. 2. Barker code DOE: (a) photograph of the Barker code DOE, (b) photograph of the intensity of green collimated laser beam diffracted on the Barker code DOE, and (c) cross-section of the intensity distribution in diffracted order.
3. RESULTS AND DISCUSSION Figure 2 shows a photograph of the fabricated Barker code DOE [Fig. 2(a)] and the intensity distribution of light in the Fourier plane of the collimated green laser beam diffracted by the DOE [Figs. 2(b) and 2(c)]. Figure 2(b) shows the 2D intensity distribution of light in the Fourier plane and Fig. 2(c) shows the cross-section of the intensity distribution of light in the horizontal direction along the central row of diffraction orders. The intensity measurement in Fig. 2 was obtained by taking an image from the screen using the digital camera and therefore, the intensity distribution was strongly modulated by speckle noise. In spite of the strong speckle noise, one can see that the intensity distribution in the Fourier plane (the envelope function of the diffraction grating) has the shape of a Sinc function with the width of the central maximum determined by the width of one grating element, T. This intensity distribution in the Fourier plane is in good agreement with theory and hence, we confirm that the DOE was fabricated correctly and had the required optimal parameters. Figures 3 and 4 show a photograph and a cross section of intensity distribution, respectively, of a green laser beam projected on a screen without [Figs. 3(a) and 4(a)] and with [Figs. 3(b) and 4(b)] the moving Barker code DOE (parameters of the experimental setup are shown in the first row of Table 1). The images data was taken from green photodiodes of the camera. Without speckle suppression [Figs. 3(a) and 4(a)], the intensity of the beam spot on screen was strongly modulated by speckles and it was practically impossible to see the fine characteristics of the intensity distribution of light on the screen. In contrast, in the image of the laser spot obtained with the use of the moving Barker code DOE [Fig. 3(b) and 4(b)], the speckle noise was strongly suppressed and the fine structure of the intensity distribution was clearly seen. Although the intensity modulation by speckles was
significantly decreased, the weak modulation of light intensity by speckles was still visible in Fig. 3(b). Table 2 presents the speckle contrasts measured from different small parts of the screen and mean speckle contrast (average over all the screen parts) for two cases (first experiment): without and with the moving Barker code DOE. The initial speckle contrast without DOE was smaller (C without 0.45) than that predicted by the theory (C 0.707; k 0.707∕0.45 1.57). Hence, an initial speckle contrast averaging exists in our method of speckle contract measurement. This initial speckle averaging effect could be due to the finite size of the camera’s photodiode or due to the finite wavelength range for laser illumination. The data in Table 2 indicate that the speckle contrast decreased from 0.45 to 0.054 with a speckle suppression coefficient k C without ∕C with 8.3 1.5. Although we obtained large speckle suppression, the speckle suppression coefficient predicted by the theory is more than 1.6 times larger [17–19]. There are several reasons for this discrepancy including: (1) error in the speed of the DOE movement because vΔt 13.7T 0 instead of 13 T 0 , (2) error in the angle of inclination of the DOE structure because tan φ 17∕200 1∕11.76 instead of tan φ 1∕13, (3) vibration of the DOE in the vertical direction due to vibration of the plotter carriage, and (4) speckle averaging due to partial pixelization (spatial resolution of the camera was only slightly larger than the width of photodiode). All the four factors influenced the speckle contrast significantly. Hence, they can substantially decrease the speckle suppression efficiency of the method. From the data in Table 2, it is clear that the speckle contrast reveals a significant variation from area to area. This can be explained by the small value of the area (a large error due to a small number of decorrelated areas within one sample) and by the fact that the light on the screen was also modulated by the
2256
J. Opt. Soc. Am. A / Vol. 30, No. 11 / November 2013
Lapchuk et al.
Fig. 4. Green laser light intensity distribution at the screen along a vertical line close to the spot center: (a) without the Barker code DOE and (b) with the moving Barker code DOE.
Fig. 3. Photograph of the green light beam intensity distribution projected on a screen (a) with and (b) without the moving Barker code DOE.
fringes arising from the scattering of light by the side walls of the green laser pointer. It is clear that the fringes on the screen increase the speckle contrast stronger (in relative units) for the illumination with the use of the Barker code DOE because in this case, the intensity modulation by the speckles was small, but the intensity modulation by the fringes was the same. Therefore, the real value of the decrease in speckle contrast due to the method was, to some extent, larger than that obtained in the experimental evaluation. On comparing the light intensity without and with the Barker code DOE, we observed that the differences between the two were negligible and can be considered to be measurement errors. Hence, practically all the diffracted light was gathered by the objective lens of the projector and optical efficiency in this case was close to 100%, if we neglect the light reflected from the DOE plate. We performed the optimization of optical parameters of the experimental setup in second experiment to improve speckle suppression efficiency (second row of Table 1). The inclination angle of the DOE was placed as close as possible to
optimal value. The aperture of the camera was decreased from 2 to 1.5 mm and distance from the camera to the screen was increased from 1100 to 1150 mm. Our camera has a relatively high noise level for low light intensity and relatively low sensitivity. Therefore, in the new experiment, we reduced the camera magnification approximately twice to compensate for light power flow decreases due to numerical aperture reduction and increases in distance to the screen. The results of the new experiment are presented in Fig. 5. In the new experiment, we obtained a speckle contrast of 0.044 (initial value 0.42) and a speckle suppression coefficient of ∼9.5. This was significantly better than in the first experiment, but it was still sufficiently lower than the theoretical prediction. We assumed that the discrepancy between the theoretical Table 2. Speckle Contrast Measurement Without and With Moving 2D Barker Code DOE of Length N 13 M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Mean Standard deviation
Without
With
0.41 0.49 0.52 0.41 0.45 0.52 0.39 0.41 0.40 0.50 0.40 0.51 0.435 0.44 0.49 0.45 0.047
0.049 0.056 0.063 0.05 0.07 0.047 0.06 0.045 0.066 0.055 0.044 0.048 0.053 0.055 0.060 0.054 0.0076
Lapchuk et al.
Vol. 30, No. 11 / November 2013 / J. Opt. Soc. Am. A
2257
I/I0 1.8 1.4 1.0 0.6 0.2 10
30
70
50
pix. numb.
(b)
(a) I/I0
0.8 0.6 0.4 0.2
10
30
(c)
50
70 pix. numb.
(d)
Fig. 5. Green light intensity distribution at the screen along a vertical line close to the spot center: (a) and (b) without the Barker code DOE, (c) and (d) with the moving Barker code DOE, (a) and (c) 2D distribution, and (b) and (d) distribution along vertical line; C without 0.42; C with 0.044; k C without ∕C with 9.5.
and experimental results can be explained by not having an accurate DOE speed (we did not optimize DOE speed) and by fringes of the laser beam, which impose additional modulations on the laser beam intensity. However, at the present stage, further methods for optimization are beyond our technical capabilities.
4. CONCLUSIONS The speckle contrast from the method based on moving 2D Barker code DOE of length N 13 was successfully evaluated. A high speckle suppression coefficient k C without ∕C with > 8 as well as a high optical efficiency (close to 100%) was achieved in the experiment. However, we were not successful in satisfying all the conditions required for optimal speckle suppression efficiency in the experimental setup. The conditions that were left unsatisfied included the movement speed, the carriage vibration, and the quality of the laser beam. We speculate that the speckle suppression efficiency obtained in the experiment was smaller than that of theoretical predictions by a factor of approximately 1.5 because of these improper conditions. However, additional experimentation with the optimal projector parameters will be required in order to prove these speculations.
ACKNOWLEDGMENT We are grateful for the support of the National Academy of Sciences of Ukraine (Grant No. 0110U002090).
REFERENCES 1. J. I. Trisnadi, C. B. Carlisle, and V. Monteverde, “Overview and applications of Grating Light Valve based optical write engines for high-speed digital imaging,” Proc. SPIE 5348, 52–64 (2004). 2. M. W. Kowarz, J. C. Brazas, and J. G. Phalen, “Conformal grating electromechanical system (GEMS) for high-speed digital light modulation,” in 15th IEEE International Conference on Micro Electro Mechanical Systems (IEEE, 2002), pp. 568–573. 3. R. Sprague, M. Champion, M. Brown, D. Brown, M. Freeman, and M. Niesten, “Mobile projectors using scanned beam displays,” in Mobile Displays, Technology and Applications, K. Bhowmik, Z. Li, and P. J. Bos, eds. (Wiley, 2008), pp. 565–588. 4. W. O. Davis, R. Sprague, and J. Miller, “MEMS-based picoprojector display,” in IEEE/LEOS International Conference on Optical MEMS and Nanophotonics (IEEE, 2008), pp. 31–32. 5. S. K. Yun, J. H. Song, I. J. Yeo, Y. J. Choi, V. I. Yurlov, S. D. An, H. W. Park, H. S. Yang, Y. G. Lee, K. B. Han, I. Shyshkin, A. S. Lapchuk, K. Y. Oh, S. W. Ryu, J. W. Jang, C. S. Park, C. G. Kim, S. K. Kim, E. J. Kim, K. S. Woo, J. S. Yang, E. J. Kim, J. H. Kim, S. H. Byun, S. W. Lee, O. K. Lim, J. P. Cheong, Y. N. Hwang, G. Y. Byun, J. H. Kyoung, S. K. Yoon, J. K. Lee, T. W. Lee, S. K. Hong, Y. S. Hong, D. H. Park, J. C. Kang, W. C. Shin, S. I. Lee, S. K. Oh, B. K. Song, H. Y. Kim, C. M. Koh, Y. H. Ryu, H. K. Lee, and Y. K. Raek, “Spatial optical modulator (SOM): high density diffractive laser projection display,” Proc. SPIE 6487, 648710 (2007). 6. S. K. Yun, J. H. Song, S. D. An, I. J. Yeo, Y. J. Cho, Y. G. Lee, H. W. Park, K. B. Han, H. S. Yang, V. Yurlov, I. Shyshkin, A. Lapchuk, H. Y. Kim, J. W. Jang, J. H. Kyoung, J. S. Yang, S. K. Yoon, Ch. S. Park, J. P. Cheong, Y. N. Hwang, K. S. Woo, S. W. Ryu, S. W. Lee, Ch. M. Koh, Y. K. Baek, D. H. Bae, H. K. Lee, J. H. Lee, Y. H. Ryu, H. Y. Hwang, Ch. M. Yang, O. K. Lim, D. H. Park, S. H. An, J. H. Bae, S. M. Cho, B. S. Go, S. K. Hong, H. Ph. Jung, S. J. Kim, K. U. Lee, J. H. Park, J. H. Yang, G. Y. Byun, S. H. Byun, Y. J. Cho, Ch. G. Kim, J. H. Kim, S. K. Kim, S. I. Lee, W. H. Lee, K. Y. Oh, S. K. Oh, W. Ch. Shin, B. K. Song, and E. M. Bourim,
2258
7. 8. 9.
10. 11.
12. 13. 14.
J. Opt. Soc. Am. A / Vol. 30, No. 11 / November 2013 “A novel diffractive micro-optical modulator for mobile display applications,” Proc. SPIE 6887, 688702 (2008). K. V. Chellappan, E. Erden, and H. Urey, “Laser-based displays,” Appl. Opt. 49, F79–F98 (2010). J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Roberts, 2006). D. S. Mehta, D. N. Naik, R. K. Singh, and M. Takeda, “Laser speckle reduction by multimode optical fiber bundle with combined temporal, spatial, and angular diversity,” Appl. Opt. 51, 1894–1904 (2012). P. Janssens and K. Malfait, “Future prospects of high-end laser projectors,” Proc. SPIE 7232, 72320Y (2009). L. Wang, T. Tschudi, T. Halldorsson, and P. R. Pétursson, “Speckle reduction in laser projection systems by diffractive optical elements,” Appl. Opt. 37, 1770–1775 (1998). Sh. Kubota and J. W. Goodman, “Very efficient speckle contrast reduction realized by moving diffuser device,” Appl. Opt. 49, 4385–4391 (2010). J. I. Trisnadi, “Hadamard speckle contrast reduction,” Opt. Lett. 29, 11–13 (2004). W. Gao, Zh. Tong, V. Kartashov, M. N. Akram, and X. Chen, “Replacing two-dimensional binary phase matrix by a pair of
Lapchuk et al.
15. 16. 17.
18.
19.
20.
one-dimensional dynamic phase matrices for laser speckle reduction,” J. Display Technol. 8, 291–295 (2012). V. Yurlov, A. Lapchuk, S.-K. Yun, J.-H. Song, and H.-S. Yang, “Speckle suppression in scanning laser display,” Appl. Opt. 47, 179–187 (2008). M. N. Akram, V. Kartashov, and Zh. Tong, “Speckle reduction in line-scan laser projectors using binary phase codes,” Opt. Lett. 35, 444–445 (2010). A. Lapchuk, A. Kryuchyn, V. Petrov, V. Yurlov, and V. Klymenko, “Full speckle suppression in laser projectors using two Barker code-type optical diffractive elements,” J. Opt. Soc. Am. A 30, 22–31 (2013). A. Lapchuk, A. Kryuchyn, V. Petrov, and V. Klymenko, “Optimal speckle suppression in laser projectors using a single two-dimensional Barker code diffractive optical element,” J. Opt. Soc. Am. A 30, 227–232 (2013). A. Lapchuk, A. Kryuchyn, V. Petrov, O. V. Shyhovets, G. A. Pashkevich, O. V. Bogdan, A. Kononov, and V. Klymenko, “Optical schemes for speckle suppression by Barker code diffractive optical elements,” J. Opt. Soc. Am. A 30, 1760–1767 (2013). A. Lapchuk, V. Petrov, I. Beliak, and A. Kryuchyn, “The method of decreasing speckle noise in laser projector system,” Ukraine patent application No. a 2013 04828 (April 16, 2013).
