• Chinese Optics Letters
  • Vol. 13, Issue 7, 070301 (2015)
Myungjin Cho*
Author Affiliations
  • Department of Electrical, Electronic, and Control Engineering, Institute of Information Technology Convergence, Hankyong National University, 327 Chungang-ro, Anseong-si, Kyonggi-do 456-749, Korea
  • show less
    DOI: 10.3788/COL201513.070301 Cite this Article Set citation alerts
    Myungjin Cho. Three-dimensional color photon counting microscopy using Bayesian estimation with adaptive priori information[J]. Chinese Optics Letters, 2015, 13(7): 070301 Copy Citation Text show less

    Abstract

    In this Letter, we propose a novel three-dimensional (3D) color microscopy for microorganisms under photon-starved conditions using photon counting integral imaging and Bayesian estimation with adaptive priori information. In photon counting integral imaging, 3D images can be visualized using maximum likelihood estimation (MLE). However, since MLE does not consider a priori information of objects, the visual quality of 3D images may not be accurate. In addition, the only grayscale image can be reconstructed. Therefore, to enhance the visual quality of 3D images, we propose photon counting microscopy using maximum a posteriori with adaptive priori information. In addition, we consider a wavelength of each basic color channel to reconstruct 3D color images. To verify our proposed method, we carry out optical experiments.
    λ(x)=I(x)x=1NxI(x)(1)

    View in Article

    C(x)|λ(x)Poisson[Npλ(x)],(2)

    View in Article

    N¯c=γcW=ηWhν¯c,(3)

    View in Article

    γc=ηhν¯c,(4)

    View in Article

    L(λ)=k=1K(Npλk)CkeNpλkCk!,(5)

    View in Article

    I(x,zr)=1NpO(x)k=1KCk(x+Δx(k1)),(6)

    View in Article

    Δx=Nxpfcxzr,(7)

    View in Article

    π(λk)=βαΓ(α)λkα1eβλk,λk>0.(8)

    View in Article

    λ˜k(x)=Ck(x)+αkNp(1+βk),Ck(x)>0,(9)

    View in Article

    I˜(x,zr)=1NpO(x)k=1Kλ˜k(x+Δx(k1)).(10)

    View in Article

    μzr(x)=1O(x)k=1Kλk(x+Δx(k1)),(11)

    View in Article

    σzr2(x)=E[λk(x)μzr(x)]2,(12)

    View in Article

    αzr(x)=[μzr(x)]2σzr2(x),(13)

    View in Article

    βzr(x)=μzr(x)σzr2(x),(14)

    View in Article

    λk(x)=Ck(x)+αzr(x)Np(1+βzr(x)),Ck(x)>0,(15)

    View in Article

    I(x,zr)=1NpO(x)k=1Kλk(x+Δx(k1)).(16)

    View in Article

    Myungjin Cho. Three-dimensional color photon counting microscopy using Bayesian estimation with adaptive priori information[J]. Chinese Optics Letters, 2015, 13(7): 070301
    Download Citation