Chemistry is all about structure–activity relationships. Determining structure is the hard part, especially on the nano scale. Often one is interested in local imperfections rather than the bulk matrix.
A paper by Matthew Bierbaum and colleagues from Cornell University (Ithaca, NY) points out that super-resolution technology has improved feature size dramatically, well beyond the diffraction limit. However, they introduced a general technique called PERI (parameter extraction from reconstructing images) that works with conventional optical and electron microscopes to provide measurements in the single-digit nanometer range or less. The process involves an iterative approach of comparing the observed image with the reconstructed image based upon the spread functions of the imaging instrument and reagents. (See Figure 1 and Bierbaum, M.; Leahy, B.D. et al. Light Microscopy at Maximal Precision. Phys. Rev. 2017, X 7, 041007; doi: 10.1103/PhysRevX.7.041007.)
Figure 1 – Illustration of PERI processing of images from confocal microscope images of a suspension of 1.343-µm-diameter colloidal spheres with volume fraction of 0.135. a) Platonic image of the dye on the sphere’s surface as in conventional microscopy (xy
is the planar image and xz
is the depth image.). ILM: the image obtained from spatially varying illumination. PSF: a bright spot that is the correction by PERI’s point-spread function. b) Top: before PERI; bottom: after PERI. c) Using the fit parameters of PERI facilitates determination of the particle’s radius within 3–4 nm and location accuracy of 1 nm or better than 0.1 pixel. With electron microscopy, locations in the 0.1-pm range are possible.This revolution starts with an image from a conventional microscope. The spread functions of the various steps in image formation are evaluated and measured. For example, starting with a fluorescent microscope, all factors are modeled. The most important factors are: 1) distribution of the fluorescent dye; 2) the dyed sample is illuminated unevenly by the laser; and 3) diffraction effects blur the fluorescence image, and the final image is noisy. The authors created a generative model of the light image formation. For example, Bayesian algorithm examines the noise to give a maximum likelihood model of the original data. Noise is general Gaussian, so a least-squares treatment compares the model to the image. For brightfield optical microscopy of the confocal image, localization accuracy is 1 nm. For TEM, PERI provides localization accuracy of 0.1 pm.
Robert L. Stevenson, Ph.D., is Editor Emeritus, American Laboratory/Labcompare; email: [email protected].
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