the number of filters in series. Inset (h) shows a triple interferometer with Nb wiring on the SiN$_{\rm x}$. The cross section of each bar was 500 $\times$ 200nm for all devices tested. Note the difference between the interferometers and ring resonators. (g) Scanning Electron Microscopy image of a 1R phononic leg, viewed obliquely.](Figure3.pdf){width="3.37in"}

Figure \[fig:TES\_Images\](a) shows one of our traditional ultra-low-noise devices having long, straight legs ($W =$ 1.5$\mu$m, $L =$ 640$\mu$m). The MoAu bilayer, and bars, can be seen as a small gold-coloured square with lateral bars, and the $\beta$-phase Ta FIR absorber as a large gold-rimmed square. Around the outside of Fig. \[fig:TES\_Images\](a), (b - g), we show a number of the phononic filters fabricated. These comprised single, double and triple interferometers and ring resonators, and all of the features had cross sections of 500 $\times$ 200nm. Table \[tab:TES\_Props\] lists the devices tested, with the path difference $\Delta L$ engineered between the arms of the filters in each phononic leg. Figure \[fig:TES\_Images\](d) shows the Nb wiring, for bias and readout, on one of the 3-element interferometers, with an alignment tolerance of 50nm. Nb is significantly less stiff than SiN$_{\rm x}$ and therefore does not influence the elastic 