A microfocusing experiment for hard X-rays has been performed to evaluate the performance of Fresnel zone plate optics. A tantalum Fresnel zone plate with an outermost zone width of 50 nm and a thickness of 0.5 µm has been fabricated by electron-beam lithography. The focused beam size measured by a knife-edge scan is 58 nm in full-width at half-maximum for the first-order diffraction at an X-ray energy of 8 keV. It can be concluded that this zone plate has nearly diffraction-limited resolution in the hard X-ray region. The measured diffraction efficiency is 5% at 8 keV. The spot size using the third-order focus of the zone plate is measured to be approximately 30 nm.

An x-ray microtomography method combined with hard x-ray imaging microscopy was developed that has a potential spatial resolution of the order of 10–100 nm. The system consists of a high-brilliance undulator source of SPring-8, a beam diffuser plate to reduce the coherence of the illumination, a high-precision rotating sample stage, a Fresnel zone plate objective, and a high-resolution x-ray imaging detector. The three-dimensional images of several samples were observed and successfully reconstructed with a pitch pattern of 0.6 μm.

Microfocusing of 100 keV x ray with a sputtered-sliced Fresnel zone plate (ss-FZP) has been performed at the 250-m-long beamline (20XU) of SPring-8. The ss-FZP with an outermost zone width 0.16 μm which is composed of 70 layers of alternating Cu and Al layers and having thickness ∼180 μm was fabricated and characterized. The minimum focal spot size attained for the first order focal beam was 0.5 μm with a focal distance 900 mm at a photon energy 100 keV. The total flux of the microprobe was ∼2×106 photons s−1 μm−2.

In order to evaluate the 'resonance intensities' and resonance frequencies of piezoelectric transducers driven 'partially', two mathematical methods are considered: One is the evaluation of 'speed of divergence' at the resonance of Mason's equivalent circuit which is applied appropriately using the conventional concept of a distributed-parameter circuit, and the other is a superposition of complex dynamical variable η to form complex infinite geometric series in which |η| 2 corresponds to the stored energy in the transducer and in which the way of superposition reflects the electrical and mechanical boundary conditions of the transducer. The resonance intensity is related to the effective power at the resonance. The 'partial drive' can induce resonance modes other than a set of odd-degree modes, with various resonance intensities due to a nondissipative cause, on appropriate boundary conditions. The calculation results of the two methods agree with each other satisfactorily, and thus suggest the physical reasonableness of both methods.