A four-pixel-array superconducting transition-edge sensor (TES) microcalorimeter with a mushroom-shaped absorber was fabricated for the energy dispersive spectroscopy performed on a transmission electron microscope. The TES consists of a bilayer of Au/Ti with either a 50-nm or 120-nm thickness. The absorber of 5.0,$mu$m thick is made from a Au layer and its stem is deposited in the center of the TES surface. A Ta$_{2}$O$_{5}$ insulating layer of 100-nm thickness is inserted between the overhang region of the absorber and the TES surface. A selected pixel of the TES microcalorimeter was operated for the detection of Np L X-rays emitted from an $^{241}$Am source. A response of the TES microcalorimeter to L X-rays was obtained by analyzing detection signal pulses with using the optimal filter method. An energy resolution was obtained to be 33,eV of the full width at half maximum value at 17.751,keV of Np L$_{eta 1}$ considering its natural width of 13.4,eV. Response to L X-rays emitted from a mixture source of $^{238}$Pu, $^{239}$Pu and $^{241}$Am was obtained by operating the selected pixel of the TES microcalorimeter. Major L X-ray peaks of progeny elements of $alpha$ decay of Pu and Am isotopes were clearly identified in the obtained energy spectrum. The experimental results demonstrated the separation of $^{241}$Am and plutonium isotopes by L X-ray spectroscopy.

Three-dimensionally assembled TES X-ray microcalorimeter arrays may be utilized for three purposes: (1) to obtain wide X-ray energy coverage of TES microcalorimeters, (2) to distinguish charged particle events from X-ray events, (3) to reconstruct Compton-scattering geometry for hard X-ray Compton cameras. We have designed and fabricated three-dimensionally assembled array of the minimum format i.e. $2 imes 2 imes 2$ array in order to obtain a good energy resolution in a wide energy range of 0.5--20,keV and a high maximum counting rate of 2000,cps for energy dispersive X-ray spectrometer (EDS) system for a transmission electron microscope (TEM). Although we could not obtain required energy resolution because of a problem in the refrigerator system, we confirmed the operation of the three-dimensional array.

In frequency-domain multiplexing (FDM) for TES signals, a magnetic field summation method utilizing a multi-input SQUID has the fundamental merit of small degradation of the signal-to-noise ratio. We formulated shifts of the operation point due to a common impedance and cross talk currents. These effects are evaluated for several FDM methods, and the requirements for the bandwidth and filters are summarized. The design parameters of multi-input SQUIDs and a flux locked loop driving circuits are also presented.