An energy dispersive spectrometer with a superconducting transition edge sensor (TES) microcalorimeter mounted on a transmission electron microscope (TEM) has been developed to improve the accuracy of nanoscale material analysis. TES microcalorimeters generally have a sensitive surface area on the order of 100 × 100 μm2. Furthermore, because of the magnetic field generated by the TEM objective lens, a TES microcalorimeter cannot be placed in a TEM column. Therefore, a polycapillary lens is used for collecting X-rays emitted by a TEM specimen on the TES microcalorimeter. The X-ray transmission characteristics of the polycapillary lens typically depend on the geometrical arrangements of the optics and the X-ray energy. Energy spectrum measurements were carried out for X-rays transmitted by a polycapillary lens installed in a TEM for evaluating X-ray transmission characteristics of the optics. Values of the focal spot size and the intensity gain were obtained by analyzing the experimental energy spectra in the energy range of 1.0-14.0 keV.