Correction of nonlinear lateral distortions of scanning probe microscopy images

An accuracy improvement method for the topology measurement of an atomic force microscope using a 2D wavelet transform

The topology image is constructed from the 2D matrix (XY directions) of heights Z captured from the force-feedback loop controller. For small height variations, nonlinear effects such as hysteresis or creep of the PZT-driven Z nano scanner can be neglected and its calibration is quite straightforward. For large height variations, the linear approximation of the PZT-driven Z nano scanner fail and nonlinear behaviors must be considered because this would cause inaccuracies in the measurement image. In order to avoid such inaccuracies, an additional strain gauge sensor is used to directly measure displacement of the PZT-driven Z nano scanner. However, this approach also has a disadvantage in its relatively low precision. In order to obtain high precision data with good linearity, we propose a method of overcoming the low precision problem of the strain gauge while its feature of good linearity is maintained. We expect that the topology image obtained from the strain gauge sensor showing significant noise at high frequencies. On the other hand, the topology image obtained from the controller output showing low noise at high frequencies. If the low and high frequency signals are separable from both topology images, the image can be constructed so that it is represented with high accuracy and low noise. In order to separate the low frequencies from high frequencies, a 2D Haar wavelet transform is used. Our proposed method use the 2D wavelet transform for obtaining good linearity from strain gauge sensor and good precision from controller output. The advantages of the proposed method are experimentally validated by using topology images.

Single-Cell Optical Distortion Correction and Label-Free 3D Cell Shape Reconstruction on Lattices of Nanostructures

Imaging techniques can be compromised by aberrations. Especially when imaging through biological specimens, sample-induced distortions can limit localization accuracy. In particular, this phenomenon affects localization microscopy, traction force measurements, and single-particle tracking, which offer high-resolution insights into biological tissue. Here we present a method for quantifying and correcting the optical distortions induced by single, adherent, living cells. The technique uses periodically patterned gold nanostructures as a reference framework to quantify optically induced displacements with micrometer-scale sampling density and an accuracy of a few nanometers. The 3D cell shape and a simplified geometrical optics approach are then utilized to remap the microscope image. Our experiments reveal displacements of up to several hundred nanometers, and in corrected images these distortions are reduced by a factor of 3. Conversely, the relationship between cell shape and distortion provides a novel method of 3D cell shape reconstruction from a single image, enabling label-free 3D cell analysis.