Figure 4
Visualization of the effect of the sample’s micro-structure on the phase-matching condition and emission angle.
The arbitrarily z-structured sample displays only contributions on the kz-axis in reciprocal space. Thus, it can be visualized as a rod which is further convolved with the illumination. The latter is represented by a disc shifted in kz-direction by 2cos(α)kp−kS. Note that this homogeneous disc is a simplification of the kρ-profile arising from the 2D convolution of two identical rings of radius sin(α)kp as analytically displayed by factor 4 in equation (12). As a result of the convolution of sample and illumination the complex emission amplitude can be regarded as “brushed” into kρ-space yielding a stratified structure. The element wise product (Hadamard product) in Fourier space of coherent transfer function with the complex emission amplitude defines which sample Fourier components will observe phase-matching and for which emission angle β the corresponding anti-Stokes emission is expected. Consequently, distinct sample Fourier components contribute to the detected anti-Stokes emission in forward and backward direction. A detection of the collimated anti-Stokes emission in forward direction (f-CARS) is symbolized by a detector plane with green rings. Note that for each gray underlaid element the k-space origin is indicated by a small purple sphere in proximity to the number zero.
