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Summary A direct technique based on electron energy‐loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM) has been developed to map subcellular distributions of water in frozen‐hydrated biological cryosections. Previously, methods for water determination have been indirect in that they have required the cryosections to be dehydrated first. The new approach makes use of spectrum‐imaging, where EELS data are collected in parallel at each pixel. Several operations are required to process the spectra including: subtraction of the detector dark current, deconvolution by the detector point‐spread function, removal of plural inelastic scattering and correction for the support film. The resulting single scattering distributions are fitted to standard reference spectra at each pixel, and water content can be determined from the fitting coefficients. Although the darkfield or brightfield image from a hydrated cryosection shows minimal structure, the processed EELS image reveals strong contrast due to variations in water content. Reference spectra have been recorded from the major biomolecules (protein, lipid, carbohydrate, nucleic acid) as well as from vitrified water and crystalline ice. It has been found that quantitative results can be obtained for the majority of subcellular compartments by fitting only water and protein reference spectra, and the accuracy of the method for these compartments has been estimated as ± 3·5%. With the present instrumentation the maximum allowed dose of 2 × 103 e/nm2 limits the useful spatial resolution to around 80 nm for ± 5% precision at a single pixel. By averaging pixel intensities a value of 56·8% with a precision of ± 2·0% has been determined for the water content of liver mitochondria. The water mapping technique may prove useful for applications to cell physiology and pathophysiology.

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Calculations of the x-ray optics of four types of doubly curved diffractors are described and the results are compared with similar results for singly curved diffractors (Johann and Johansson geometry). In these calculations the locus of points on a curved diffractor’s surface is determined for a given deviation from the Bragg angle when the diffractor is used at Bragg angles ranging from 15 to 75 degrees. The six cases discussed include cylindrical, spherical, and toroidal geometries. The calculations are used as a basis for comparing the collection efficiency and the spectral resolution when these diffractors are used in scanning monochromators. It is shown that doubly curved diffractors are superior to singly curved ones and that a diffractor with spherical planes and toroidal surface provides the best performance of all of the diffractors considered if a wide range of Bragg angles must be covered.

A general equation is derived for x-ray diffractors with arbitrary toroidally curved surface and planes when used with a point source. This equation, which gives the locus of points on a curved diffractor’s surface for a given deviation from the Bragg angle, is shown to yield the appropriate equations for all of the crystal diffractor geometries that were previously discussed by Wittry and Sun [J. Appl. Phys. 67, 1633 (1990)]. Two examples are given of the use of the general equation to design diffractors with improved collection solid angle over a range of Bragg angles. The x-ray collection solid angle and focusing properties of these two examples are given.