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  • Received: Jun. 22, 2018

    Accepted: Nov. 8, 2018

    Posted: Feb. 18, 2019

    Published Online: Feb. 18, 2019

    The Author Email: Zhao Chengliang (zhaochengliang@suda.edu.cn)

    DOI: 10.1117/1.AP.1.1.016005

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    Xingyuan Lu, Yifeng Shao, Chengliang Zhao, Sander Konijnenberg, Xinlei Zhu, Ying Tang, Yangjian Cai, H. Paul Urbach. Noniterative spatially partially coherent diffractive imaging using pinhole array mask[J]. Advanced Photonics, 2019, 1(1): 016005

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M(r)=δ(r0)+m,nδ(rrm,n),(1)

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I(k)=M(r1)M(r2)*W(r1,r2)exp[i2πk·(r1r2)]d2r1d2r2=W(0,0)+m1,n1m2,n2W(rm1,n1,rm2,n2)exp[i2πk·(rm1,n1rm2,n2)]+m1,n1W(rm1,n1,0)exp(i2πk·rm1,n1)+m2,n2W(0,rm2,n2)exp(+i2πk·rm2,n2),(2)

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F1[I(k)](r)=W(0,0)δ(r0)+m1,n1m2,n2W(rm1,n1,rm2,n2)δ[r(rm1,n1rm2,n2)]+m1,n1W(rm1,n1,0)δ(rrm1,n1)+m2,n2W(0,rm2,n2)δ(r+rm2,n2),(3)

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M(r)=m,nδ(rrm,n).(4)

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W(r1,r2)=O(ρ1)O(ρ2)*W0(ρ1,ρ2)exp[i2π(ρ1·r1ρ2·r2)]d2ρ1d2ρ2,(5)

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W(rm,n,0)=O(ρ1)O(ρ2)*W0(ρ1,ρ2)exp(i2πρ1·rm,n)d2ρ1d2ρ2.(6)

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W(rm,n,0)=T(ρ1)O(ρ1)exp(i2πρ1·rm,n)d2ρ1,(7)

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T(ρ1)=O(ρ2)*W0(ρ1,ρ2)d2ρ2.(8)

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Wδ(rm,n,0)=[O(ρ1)+Cδ(ρ1ρ0)][O(ρ2)+Cδ(ρ2ρ0)]*×W0(ρ1,ρ2)exp(i2πρ1·rm,n)d2ρ1d2ρ2.(9)

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Wδ(rm,n,0)=W(rm,n,0)+|C|2W0(ρ0,ρ0)+Cδ(ρ1ρ0)O(ρ2)*W0(ρ1,ρ2)exp(i2πρ1·rm,n)d2ρ1d2ρ2+O(ρ1)C*δ(ρ2ρ0)W0(ρ1,ρ2)exp(i2πρ1·rm,n)d2ρ1d2ρ2.(10)

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Wδ(rm,n,0)=W(rm,n,0)+|C|2W0(ρ0,ρ0)+[C·O(ρ2)*W0(ρ0,ρ2)d2ρ2]exp(i2πρ0·rm,n)+O(ρ1)C*W0(ρ1,ρ0)exp(i2πρ1·rm,n)d2ρ1.(11)

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F1[Wδ(rm,n,0)W(rm,n,0)]=O(ρ1)C*W0(ρ1,ρ0)+|C|2W0(ρ0,ρ0)δ(ρ0)+[C·O(ρ2)*W0(ρ0,ρ2)d2ρ2]δ(ρρ0).(12)

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W0(ρ1,ρ2)=exp(ρ12+ρ22w02)exp[(ρ1ρ2)22σ2],(13)

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W0(ρ1,ρ2)=exp(ρ12+ρ22w02)exp[(ρ1ρ2)22σ2]Ln0[(ρ1ρ2)22σ2],(14)

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