A method for estimating spatial resolution of real image in the Fourier domain

Abstract

Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high-angle diffraction in reciprocal space. In electron microscopy, correlation in the Fourier domain is used for estimating the resolution. In this paper, we report a method for estimating the spatial resolution of real images from a logarithmic intensity plot in the Fourier domain. The logarithmic intensity plots of test images indicated that the full width at half maximum of a Gaussian point spread function can be estimated from the images. The spatial resolution of imaging X-ray microtomography using Fresnel zone-plate optics was also estimated with this method. A cross section of a test object visualized with the imaging microtomography indicated that square-wave patterns up to 120-nm pitch were resolved. The logarithmic intensity plot was calculated from a tomographic cross section of brain tissue. The full width at half maximum of the point spread function estimated from the plot coincided with the resolution determined from the test object. These results indicated that the logarithmic intensity plot in the Fourier domain provides an alternative measure of the spatial resolution without explicitly defining a noise criterion.

Optical Aberration Correction via Phase Diversity and Deep Learning

“…3 have their origin in erroneous high frequency restitution (see black triangle marker). Using Mizutani's single image resolution estimate [29] we can quantify that improvement further: we find that HUnet deconvolved images have 2-fold wider frequency support than the best focussed input image: 1.99 and 2.34 for fly and zebrafish, respectively. Despite the artefacts mentioned previously, ICTM deconvolution performs well but still underperforms compared to HUnet: 1.52 and 1.89 fold improvement in frequency support for fly and zebrafish, respectively.…”

Cutting‐edge morphological studies of post‐mortem brains of patients with schizophrenia and potential applications of X‐ray nanotomography (nano‐CT)

“…In contrast, X‐ray tomographic analyses, including the clinical CT, are performed by taking images from all directions. They hence visualize the sample with spatially isotropic resolution . Serial‐sectioning electron microscopy has been developed to visualize the 3‐D structure of biological samples, although the tissue sectioning distorts the tissue.…”

“…They hence visualize the sample with spatially isotropic resolution. [60][61][62][63][64] Serial-sectioning electron microscopy has been developed to visualize the 3-D structure of biological samples, 65 although the tissue sectioning distorts the tissue. Reconstruction of 3-D structures from the section images, therefore, requires a distortion-correction procedure, 65,66 which may obscure structural features relevant to the disease.…”

Method for estimating modulation transfer function from sample images

“…A paraffin section of a zebrafish brain stained with the reduced-silver impregnation (Mizutani et al, 2008) was taken with a light microscope (Eclipse80i, Nikon) equipped with a charge-coupled device (CCD) camera (DXM1200F, Nikon), as reported previously (Mizutani et al, 2016), and subjected to 4 × 4 binning. The image dimensions were 500 × 500 pixels.…”

“…In this study, we report a method for estimating the MTF from general sample images independently of the image type. It has been reported that the Gaussian PSF can be identified by plotting the logarithm of the squared norm of the Fourier transform of the image against the squared distance from the origin (Mizutani et al, 2016). A number of test images were generated and analyzed with this plot to extract their PSFs.…”