Optical Fingerprint of Flat Substrate Surface and Marker-Free Lateral Displacement Detection with Angstrom-Level Precision

We report that flat substrates such as glass coverslips with surface roughness well below 0.5 nm feature notable speckle patterns when observed with high-sensitivity interference microscopy. We uncover that these speckle patterns unambiguously originate from the subnanometer surface undulations, and develop an intuitive model to illustrate how subnanometer nonresonant dielectric features could generate pronounced interference contrast in the far field. We introduce the concept of optical fingerprint for the deterministic speckle pattern associated with a particular substrate surface area and intentionally enhance the speckle amplitudes for potential applications. We demonstrate such optical fingerprints can be leveraged for reproducible position identification and marker-free lateral displacement detection with an experimental precision of 0.22 nm. The reproducible position identification allows us to detect new nanoscopic features developed during laborious processes performed outside of the microscope. The demonstrated capability for ultrasensitive displacement detection may find applications in the semiconductor industry and superresolution optical microscopy.

Figure 1

(a) Schematic of the experimental setup and the sample consisting of individual GNPs on a glass coverslip. A partial beam block (PBB) could be inserted to the back-focal plane (BFP). (b) Interference contrast image of the sample. Signals of the GNPs are labeled and enlarged on the right. (c) AFM topographic image of the same area of (b) with close-up images of the GNPs on the right. (d) A histogram of measured interference contrasts from 52 GNPs on the same coverslip. The solid and dashed lines denote the relative probability distributions of the calculated contrasts with and without surface roughness considered, respectively. Scale bars: $1\mathrm{\mu }\mathrm{m}$ (black), 100 nm (white).

Figure 2

(a) AFM topographic image and (b) measured interference contrast image for the same coverslip area. (c) AFM image in (a) processed with a low-pass filter. (d) Simulated interference contrast based on (c). (e) Schematics of the induced dipole model and the distribution of the polarizability that is normalized by the absolute value of a 15 nm GNP. (f) Calculated interference contrast image based on the induced dipole model. Scale bar, 500 nm.

Figure 3

Interference contrast images for the same coverslip area (a) before and (b) after spin coating 5 nm GNPs. A PBB is placed at the BFP to amplify the contrast. (c) Normalized cross-correlation between image (a) and image (b) as a function of lateral displacement $(\mathrm{\Delta }x,\mathrm{\Delta }y)$. The white dot and black cross denote zero displacement and a displacement of $(\mathrm{\Delta }{x}_0,\mathrm{\Delta }{y}_0)=(-166.8\mathrm{nm},-90.4\mathrm{nm})$ giving the maximum correlation. (d) Contrast image obtained from subtracting (a) from (b) displaced by $(\mathrm{\Delta }{x}_0,\mathrm{\Delta }{y}_0)$. The dashed circles indicate the point spread function of a 5 nm GNP. Scale bars, 500 nm.

Figure 4

(a) Illustration of the procedure for lateral displacement detection and benchmark (see text). Symbols in the contrast image denote the various regions. (b) Displacements from readings of nanopositioner and from optical fingerprints of the entire area and various regions when the nanopositioner is kept still. (c) Measured displacements when the nanopositioner is actuated to stepwisely (4 nm) move in each direction. Symbols in the solid circles are the close-up views of the data points and the circles have the radii of 0.5 nm.