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

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.

[1]  Kentaro Uesugi,et al.  Development of large-field high-resolution hard x-ray imaging microscopy and microtomography with Fresnel zone plate objective , 2013, Optics & Photonics - Optical Engineering + Applications.

[2]  Kentaro Uesugi,et al.  Submicrometer tomographic resolution examined using a micro-fabricated test object. , 2010, Micron.

[3]  W. O. Saxton,et al.  The correlation averaging of a regularly arranged bacterial cell envelope protein , 1982, Journal of microscopy.

[4]  M van Heel,et al.  A new generation of the IMAGIC image processing system. , 1996, Journal of structural biology.

[5]  Hstau Y Liao,et al.  Definition and estimation of resolution in single-particle reconstructions. , 2010, Structure.

[6]  Kentaro Uesugi,et al.  X-ray microtomographic imaging of three-dimensional structure of soft tissues. , 2008, Tissue engineering. Part C, Methods.

[7]  O. Bunk,et al.  X-ray ptychographic computed tomography at 16 nm isotropic 3D resolution , 2014, Scientific Reports.

[8]  P Hiselius,et al.  The New Generation , 2019, The Women's Liberation Movement in Russia.

[9]  Peter Modregger,et al.  Spatial resolution in Bragg‐magnified X‐ray images as determined by Fourier analysis , 2007 .

[10]  H. H. Hopkins The frequency response of a defocused optical system , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[11]  Andreas Koch,et al.  X-ray imaging with submicrometer resolution employing transparent luminescent screens , 1998 .

[12]  Wilson K. S. Chiu,et al.  Zone-doubled Fresnel zone plates for high-resolution hard X-ray full-field transmission microscopy , 2012, Journal of synchrotron radiation.

[13]  R. K. Swank Measurement of absorption and noise in an x‐ray image intensifier , 1974 .

[14]  M. van Heel,et al.  Fourier shell correlation threshold criteria. , 2005, Journal of structural biology.

[15]  Kentaro Uesugi,et al.  Hard X-ray imaging microscopy using X-ray guide tube as beam condenser for field illumination , 2013 .

[16]  Kentaro Uesugi,et al.  Three-dimensional microtomographic imaging of human brain cortex , 2008, Brain Research.

[17]  A. Rose,et al.  Vision: human and electronic , 1973 .

[18]  S. H. YÜ,et al.  Determination of Absolute from Relative X-Ray Intensity Data , 1942, Nature.

[19]  Akihisa Takeuchi,et al.  Performance Test of Fresnel Zone Plate with 50 nm Outermost Zone Width in Hard X-ray Region , 2005 .

[20]  Kentaro Uesugi,et al.  Estimation of presampling modulation transfer function in synchrotron radiation microtomography , 2010 .

[21]  M. Heel,et al.  Exact filters for general geometry three dimensional reconstruction , 1986 .