Scanning transmission X-ray microscopy is a powerful method for mapping chemical phases in nano-materials. The point spread function (PSF) of a conventional zone-plate-based microscope limits the achievable spatial resolution and also results in spatially resolved spectra that do not accurately reflect the spatial heterogeneity of the samples when the scale of the detail approaches the probe size. X-ray ptychography, a coherent-scattering-based imaging scheme that effectively removes the probe from the image data, returns accurate spectra from regions smaller than the probe size. We show through simulation how the long tails on the PSF of an x-ray optic can cause spectral distortion near a boundary between two spectrally distinct regions. The resulting apparent point spectra can appear mixed, with the species on one side of the boundary seeming to be present on the other even at a distance from the boundary equal to several times the spatial resolution. We further demonstrate the effect experimentally and show that ptychographic microscopy can return the expected spectra from a model system, whereas conventional microscopy does not.

Point spread function (PSF) deconvolution is an attractive software-based technique for resolution improvement in the scanning electron microscope (SEM) because it can restore information which has been blurred by challenging operating conditions. In Part 1, we studied a modern PSF determination method for SEM and explored how various parameters affected the method's ability to accurately estimate the PSF. In Part 2, we extend this exploration to PSF deconvolution for image restoration. The parameters include reference particle size, PSF smoothing (K), background correction, and restoration denoising (λ). Image quality was assessed by visual inspection and Fourier analysis. Overall, PSF deconvolution improved image quality. Low λ enhanced image sharpness at the cost of noise, while high λ created smoother restorations with less detail. λ should be chosen to balance feature preservation and denoising based on the application. Reference particle size within ±0.9 nm and K within a reasonable range had little effect on restoration quality. Restorations using background-corrected PSFs had superior quality compared with using no background correction, but if the correction was too high, the PSF was cut off causing blurrier restorations. Future efforts to automatically determine parameters would remove user guesswork, improve this method's consistency, and maximize interpretability of outputs.

The point spread function (PSF) of the scanning electron microscope (SEM) can be determined using a recently developed nanoparticle calibration method. Many parameters are involved in PSF determination and introduce a previously unstudied amount of uncertainty into the PSF size and shape. Signal type, support material thickness, reference particle size, PSF smoothing (K), and background correction were investigated regarding their effect on the PSF. Experimental data were complemented by CASINO simulations. Differences in detector position between the observed particles and the method's simulated reference particles caused shifting between secondary electron PSFs and backscattered electron PSFs. Support material thickness did not have a practical effect on the PSF at the tested voltages. Uncertainty in reference particle size varied the PSF full width at half maximum (FWHM) within ±0.7 nm at 2σ, with virtually no uncertainty in some cases. K and background correction within a reasonable range of values resulted in PSF FWHM differences within ±0.9 nm, except at 2 kV for K with an upper bound of ±1.9 nm due to increased noise. Tailoring K and background correction case-by-case would result in smaller differences. The interconnection of these parameters may help in future efforts to calculate their best selection.

Routine system checks are essential for supervising the performance of an advanced light microscope. Recording and evaluating the point spread function (PSF) of a given system provides information about the resolution and imaging. We compared the performance of fluorescent and gold beads for PSF recordings. We then combined the open-source evaluation software PSFj with a newly developed KNIME pipeline named PSFtracker to create a standardized workflow to track a system's performance over several measurements and thus over long time periods. PSFtracker produces example images of recorded PSFs, plots full-width-half-maximum (FWHM) measurements over time and creates an html file which embeds the images and plots, together with a table of results. Changes of the PSF over time are thus easily spotted, either in FWHM plots or in the time series of bead images which allows recognition of aberrations in the shape of the PSF. The html file, viewed in a local browser or uploaded on the web, therefore provides intuitive visualization of the state of the PSF over time. In addition, uploading of the html file on the web allows other microscopists to compare such data with their own.

A method is presented to determine the spatial distribution of electrons in the focused beam of a scanning electron microscope (SEM). Knowledge of the electron distribution is valuable for characterizing and monitoring SEM performance, as well as for modeling and simulation in computational scanning electron microscopy. Specifically, it can be used to characterize astigmatism as well as study the relationship between beam energy, beam current, working distance, and beam shape and size. In addition, knowledge of the distribution of electrons in the beam can be utilized with deconvolution methods to improve the resolution and quality of backscattered, secondary, and transmitted electron images obtained with thermionic, FEG, or Schottky source instruments. The proposed method represents an improvement over previous methods for determining the spatial distribution of electrons in an SEM beam. Several practical applications are presented.

Light microscopy is a powerful tool that allows for many types of samples to be examined in a rapid, easy, and nondestructive manner. Subsequent image analysis, however, is compromised by distortion of signal by instrument optics. Deconvolution of images prior to analysis allows for the recovery of lost information by procedures that utilize either a theoretically or experimentally calculated point spread function (PSF). Using a laser scanning confocal microscope (LSCM), we have imaged whole impact tracks of comet particles captured in silica aerogel, a low density, porous SiO2 solid, by the NASA Stardust mission. In order to understand the dynamical interactions between the particles and the aerogel, precise grain location and track volume measurement are required. We report a method for measuring an experimental PSF suitable for three-dimensional deconvolution of imaged particles in aerogel. Using fluorescent beads manufactured into Stardust flight-grade aerogel, we have applied a deconvolution technique standard in the biological sciences to confocal images of whole Stardust tracks. The incorporation of an experimentally measured PSF allows for better quantitative measurements of the size and location of single grains in aerogel and more accurate measurements of track morphology.

The charge-coupled devices used in electron microscopy are coated with a scintillating crystal that gives rise to a severe modulation transfer function (MTF). Exact knowledge of the MTF is imperative for a good correspondence between image simulation and experiment. We present a practical method to measure the MTF above the Nyquist frequency from the beam blocker's shadow image. The image processing has been fully automated and the program is made public. The method is successfully tested on three cameras with various beam blocker shapes.

Most theoretical studies of image processing employ discrete image models. While that might be a good approximation to digital analysis, it severely restricts the class of tractable models for the blur component of image degradation, and concentrates excessive attention on specialized features of the pixel lattice. It is analogous to modelling all real statistical data using discrete distributions, which is clearly unnecessary. In this paper we study a continuous model for image analysis, in the presence of systematic degradation via a point spread function and stochastic degradation by a second-order stationary random field. Thus, we depart from the restrictive white-noise models which are commonly used in the theory of image analysis. We establish a general result which describes the performance of optimal image processing methods when the noise process has short-range dependence. Concise limits to resolution are derived, depending on image type, point spread function and noise correlation. These results are developed in important special cases, giving explicit formulae for optimal smoothing sets and convergence rates.