Spectral encoding of spatial frequency approach for characterization of nanoscale structures

Abstract

An approach to acquire axial structural information at nanoscale is demonstrated. It is based on spectral encoding of spatial frequency principle to reconstruct the structural information about the axial profile of the three-dimensional (3D) spatial frequency for each image point. This approach overcomes the fundamental limitations of current optical techniques and provides nanoscale accuracy and sensitivity in characterizing axial structures. Numerical simulation and experimental results are presented.

Figure 1

(a) Illustration of the scattering vector. (b) Spatial frequency representation in K-space with different wavelengths (from 400 nm, blue color, to 700 nm, red color). (c) and (d) Collection of spectral data in Fourier and image planes. (e) Intensity distribution in 3D K-space. (f) Spatial frequency vector in image space. (g) and (h) Dependences of (g) absolute value of the 3D scattering vector (dashed lines), axial spatial frequency (solid lines), and (h) maximum uncertainty in determining axial period, on the scattering angles for different wavelengths, at θ = 0.

Figure 2

Numerical simulation of SESF approach: (a) structure of the simulated 3D object, illuminated along Oz axis; the insert is a magnified portion of the object. (b) The SESF image (RGB image) of the simulated object, with profiles of the axial spatial periods for four selected locations. (c) Profile of the axial spatial period averaged over the entire image area. The peak location is identified by locating the zero crossings of the derivative of this profile corresponding to the top three maximum peak strengths. (d) Profiles of the axial spatial period averaged over the entire image area for 250 nm (red) and 251 nm (blue) nanospheres.

Figure 3

The SESF image of experimentally constructed mixed-sized nanosphere aggregate. Scale bar is 10 μm. The axial structural period profiles are presented for four selected areas. The insert is a magnified portion of the selected area within the object.

Figure 4

Experimental results for quantification of the nanoscale structures within the cell nucleus of HeLa cells at different phases of cell cycle. (a) and (b) TEM images for cells arrested at G₁/S and G₂/M phases; (c) spatial period profile extracted from TEM images, nm; (d) axial spatial period profile quantified using SESF, nm.