• Advanced Photonics Nexus
  • Vol. 3, Issue 1, 016013 (2024)
Tobias Pahl*, Felix Rosenthal, Johannes Breidenbach, Corvin Danzglock..., Sebastian Hagemeier, Xin Xu, Marco Künne and Peter Lehmann|Show fewer author(s)
Author Affiliations
  • University of Kassel, Faculty of Electrical Engineering and Computer Science, Measurement Technology Group, Kassel, Germany
  • show less
    DOI: 10.1117/1.APN.3.1.016013 Cite this Article Set citation alerts
    Tobias Pahl, Felix Rosenthal, Johannes Breidenbach, Corvin Danzglock, Sebastian Hagemeier, Xin Xu, Marco Künne, Peter Lehmann, "Electromagnetic modeling of interference, confocal, and focus variation microscopy," Adv. Photon. Nexus 3, 016013 (2024) Copy Citation Text show less

    Abstract

    We present a unified electromagnetic modeling of coherence scanning interferometry, confocal microscopy, and focus variation microscopy as the most common techniques for surface topography inspection with micro- and nanometer resolution. The model aims at analyzing the instrument response and predicting systematic deviations. Since the main focus lies on the modeling of the microscopes, the light–surface interaction is considered, based on the Kirchhoff approximation extended to vectorial imaging theory. However, it can be replaced by rigorous methods without changing the microscope model. We demonstrate that all of the measuring instruments mentioned above can be modeled using the same theory with some adaption to the respective instrument. For validation, simulated results are confirmed by comparison with measurement results.
    kin=(kin;xkin;ykin;z)=k(sinθincosφinsinθinsinφincosθin)

    View in Article

    ψo;k,θin,φin(x,z)=ψ0R(x,k,θin,φin)ei[qz(h(x)+z)+kin;xx],

    View in Article

    ψo;k,θin,φin(x,z)=eikin;xxn=nminnmaxks;z,nkin;zcnei2πnx/Lxiqz,nz,

    View in Article

    nmin=Lxλ(NA2kin;y2k2kin;xk),

    View in Article

    nmax=Lxλ(NA2kin;y2k2kin;xk)

    View in Article

    Eo;k,θin,φin(x,z)=eikin;xxn=nminnmaxR_T(θs;n,φs;n)T_(θs;n,φs;n)Ps(θs;n,φs;n)ks;z,nkin;zcnei2πnx/Lxiqz,nz,

    View in Article

    T_(θs;n,φs;n)=(cosθmode,nsinθmode,nsinθmode,ncosθmode,n),

    View in Article

    θmode,n=arcsin(kin;xk2kin;y2)arcsin(ks;x,nk2ks;y2)

    View in Article

    cn=1LxLx/2Lx/2dxeiqz,nh(x)ei2πnx/Lx[R;k,θin,φin(x)Ein,;k,θin,φin(x)+R;k,θin,φin(x)Ein,;k,θin,φin(x)]

    View in Article

    u(x)=kin×n(x)|kin×n(x)|andu(x)=kin×(kin×n(x))|kin×(kin×n(x))|.

    View in Article

    Ein,;k,θin,φin=(Ein;k,θin,φin·u)uandEin,;k,θin,φin=(Ein;k,θin,φin·u)u.

    View in Article

    R_(θin,φin)=(cos2φincosθin+sin2φinsinφincosφin(cosθin1)sinφincosφin(cosθin1)sin2φincosθin+cos2φinsinθincosφinsinθinsinφin),

    View in Article

    Ik(x,z)02πdφinθminθmaxdθinPin(θin,φin)2Ik,θin,φin(x,z)sinθincosθin,

    View in Article

    I(x,z)0dkF(k)S(k)Ik(x,z),

    View in Article

    Ein;k,θin,φin(x,z,x0)=eikin;xx0R_(θin,φin)E0eikin·r

    View in Article

    Etot;k(x,z,x0)02πdφin0θmaxdθinEo;k,θin,φin(x,z)Pin(θin,φin)sinθincosθineikin;xx0

    View in Article

    Θ˜(kin;ρ)=2πϱkin;ρMobjJ1(kin;ρϱMobj)

    View in Article

    Ibf;k(x,z)02πdφin0θmaxdθinPin(θin,φin)2Ik,θin,φin(x,z)sinθincosθin,

    View in Article

    Idf;k(x,z)02πdφinθdf,minθdf,maxdθinPin,df(θin,φin)2Ik,θin,φin(x,z)sinθincosθin,

    View in Article

    Tobias Pahl, Felix Rosenthal, Johannes Breidenbach, Corvin Danzglock, Sebastian Hagemeier, Xin Xu, Marco Künne, Peter Lehmann, "Electromagnetic modeling of interference, confocal, and focus variation microscopy," Adv. Photon. Nexus 3, 016013 (2024)
    Download Citation