  Optical transition-edge sensors have shown energy resolution for resolving
the number of incident photons at the telecommunication wavelength. Higher
energy resolution is required for biological imaging and microscope
spectroscopy. In this paper, we report on a Au/Ti (10/20 nm) bilayer TES that
showed high energy resolution. This was achieved by lowering the critical
temperature Tc to 115 mK and the resultant energy resolution was 67 meV full
width at half maximum (FWHM) at 0.8 eV. When Tc was lowered to 115 mK, the
theoretical resolution would scaled up to 30 meV FWHM, considering that the
typical energy resolution of optical TESs is 150 meV and Tc is 300 mK. To
investigate the gap between the theoretical expectation (30 meV) and the
measured value (67 meV), we measured its complex impedance and current noise.
We found excess Johnson noise in the TES and an excess Johnson term M was 1.5
at a bias point where the resistance was 10% of normal resistance. For
reference, the TES was compared with a TES showing typical energy resolution
(156 meV FWHM). We will discuss what improved the energy resolution and what
might have been the limiting factor on it.
