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Light transport in complex disordered medium, such as white paint, milk, is a fundamental physical phenomenon, and it plays an important role in numerous applications including imaging through turbid layers, and quantum information processes. However, all spatial coherence is lost due to the distorted incident wavefront caused by repeated scattering and interference. Incident coherent light diffuses through the medium and cannot form a geometric focus but a volume speckle field on the imaging plane. In this paper, we propose a four-element division algorithm and experimentally demonstrate that using this algorithm to modulate the incident light, the shaped wavefront can focus through disordered material. At the beginning, we start with four segments on spatial light modulator (SLM), changing the phase of each segment from 0-2πup to search for the optimal phase in terms of the maximal output intensity at a certain field. After the optimal phase of these four segments is found, each of all segments is divided further into four subsegments, so 16 subsegments are formed on the SLM. Just like the first step, the optimal phase is found by cycling the phases of these 16 subsegments. Sequentially, this procedure is repeated several times, so more and more subsegments are obtained. As a result, the modulated input light from SLM can be focused after it has passed through the turbid scattering medium. By employing this approach in the forward scattered experiment, the total pixels of spatial light modulator are divided into 4-4096 segments to shape the incident light. After separately searching for all the optimal phase distributions, we can see that a sharp focusing is gradually achieved. Likewise, in backscattered experiment, 4-1024 segments are used to focus the incident light after passing through the diffuse material. In comparison with stepwise sequential algorithm, the main advantage of our method is that the interference effect of all segments on SLM is taken into consideration, which means that the modulated and the modulating segments are connected with each other. In this way, the signal-to-noise ratio is higher and no iteration is needed. All this experiment shows that the four-element division algorithm can be employed to focus the incident light passing through a disorder material efficiently, which maybe provide a new idea and method in the field of biomedical imaging through scattering medium.
[1] Ishimaru A 1978 Wave Propagation and Scattering in Random Media (New York: Academic Press) pp349-351
[2] Sebbah P 2012 Waves and Imaging through Complex Media (Berlin: Springer Science & Business Media) pp29-53
[3] Tuchin V 2007 Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (Bellingham: SPIE Press) pp3-20
[4] Sebbah P 2010 Waves and Imaging through Complex Media (Netherlands: Kluwer Academic Publishers) pp15-26
[5] Hayakawa C K, Venugopalan V, Krishnamachari V V, Potma E O 2009 Phys. Rev. Lett. 103 043903
[6] Xi S X, Wang X L, Huang S, Chang S J, Lin L 2015 Acta Phys. Sin. 64 114204 (in Chinese) [席思星, 王晓雷, 黄帅, 常胜江, 林列 2015 64 114204]
[7] Zhou Q Q, Xu S W, Lu J F, Zhou Q, Ji X M, Yin J P 2013 Acta Phys. Sin. 62 153701 (in Chinese) [周巧巧, 徐淑武, 陆俊发, 周琦, 纪宪明, 印建平 2013 62 153701]
[8] Li X Q, Wang T, Ji X L 2014 Acta Phys. Sin. 63 134209 (in Chinese) [李晓庆, 王涛, 季小玲 2014 63 134209]
[9] Vellekoop I M, Mosk A P 2007 Opt. Lett. 32 2309
[10] Vellekoop I M, Mosk A P 2008 Phys. Rev. Lett. 101 120601
[11] Yaqoob Z, Psaltis D, Feld M S, Yang C 2008 Nature Photon. 2 110
[12] Cui M, McDowell E J, Yang C 2009 Appl. Phys. Lett. 95 123702
[13] Hillman T, Yamauchi T, Choi W, Dasari R, Yaqoob Z, Park Y 2013 Sci. Rep. 3 1909
[14] Popoff S M, Lerosey G, Carminati R, Fink M, Boccara A C, Gigan S 2010 Phys. Rev. Lett. 104 100601
[15] Yoon J, Lee K R, Park J, Park Y 2015 Opt. Express 23 10158
[16] Cui M 2011 Opt. Lett. 36 870
[17] Conkey D B, Brown A N, Caravaca-Aguirre A M, Piestun R 2012 Opt. Express 20 4840
[18] Vellekoop I M, Mosk A P 2008 Opt. Commun. 281 3071
[19] Goodman J W 2000 Statistical Optics (New York: Wiley) pp30-45
[20] Garcia N, Genack A Z 1989 Phys. Rev. Lett. 63 1678
[21] Webster M A, Gerke T D, Weiner A M, Webb K J 2004 Opt. Lett. 29 1491
[22] Beenakker C W J 1997 Rev. Mod. Phys. 69 731
[23] Conkey D B, Caravaca-Aguirre A M, Piestun R 2012 Opt. Express 20 1733
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[1] Ishimaru A 1978 Wave Propagation and Scattering in Random Media (New York: Academic Press) pp349-351
[2] Sebbah P 2012 Waves and Imaging through Complex Media (Berlin: Springer Science & Business Media) pp29-53
[3] Tuchin V 2007 Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (Bellingham: SPIE Press) pp3-20
[4] Sebbah P 2010 Waves and Imaging through Complex Media (Netherlands: Kluwer Academic Publishers) pp15-26
[5] Hayakawa C K, Venugopalan V, Krishnamachari V V, Potma E O 2009 Phys. Rev. Lett. 103 043903
[6] Xi S X, Wang X L, Huang S, Chang S J, Lin L 2015 Acta Phys. Sin. 64 114204 (in Chinese) [席思星, 王晓雷, 黄帅, 常胜江, 林列 2015 64 114204]
[7] Zhou Q Q, Xu S W, Lu J F, Zhou Q, Ji X M, Yin J P 2013 Acta Phys. Sin. 62 153701 (in Chinese) [周巧巧, 徐淑武, 陆俊发, 周琦, 纪宪明, 印建平 2013 62 153701]
[8] Li X Q, Wang T, Ji X L 2014 Acta Phys. Sin. 63 134209 (in Chinese) [李晓庆, 王涛, 季小玲 2014 63 134209]
[9] Vellekoop I M, Mosk A P 2007 Opt. Lett. 32 2309
[10] Vellekoop I M, Mosk A P 2008 Phys. Rev. Lett. 101 120601
[11] Yaqoob Z, Psaltis D, Feld M S, Yang C 2008 Nature Photon. 2 110
[12] Cui M, McDowell E J, Yang C 2009 Appl. Phys. Lett. 95 123702
[13] Hillman T, Yamauchi T, Choi W, Dasari R, Yaqoob Z, Park Y 2013 Sci. Rep. 3 1909
[14] Popoff S M, Lerosey G, Carminati R, Fink M, Boccara A C, Gigan S 2010 Phys. Rev. Lett. 104 100601
[15] Yoon J, Lee K R, Park J, Park Y 2015 Opt. Express 23 10158
[16] Cui M 2011 Opt. Lett. 36 870
[17] Conkey D B, Brown A N, Caravaca-Aguirre A M, Piestun R 2012 Opt. Express 20 4840
[18] Vellekoop I M, Mosk A P 2008 Opt. Commun. 281 3071
[19] Goodman J W 2000 Statistical Optics (New York: Wiley) pp30-45
[20] Garcia N, Genack A Z 1989 Phys. Rev. Lett. 63 1678
[21] Webster M A, Gerke T D, Weiner A M, Webb K J 2004 Opt. Lett. 29 1491
[22] Beenakker C W J 1997 Rev. Mod. Phys. 69 731
[23] Conkey D B, Caravaca-Aguirre A M, Piestun R 2012 Opt. Express 20 1733
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