The primary error occurred during the simulation of the Zerodur coiled HCF. We mistakenly input the Young's modulus in COMSOL as 9.03 GPa instead of the correct value of 90.3 GPa, as stated in the text. After re-simulating the results, we found that this error did not influence other findings except for Fig. 1 below (Fig. 6 in our original paper [1]). Previously, we reported that “Further tuning can be achieved by drilling a hole in the center of the spool, as this reduces its stiffness. This is shown in Fig. 1, where a coiled HCF thermal sensitivity of -0.02 ppm/K for a homogenous Zerodur spool with CTE = -0.05 ppm/K and R = 55 mm is tuned to zero sensitivity when a hole of 46 mm is drilled in the middle of the spool.” However, our updated simulation results revealed that the thermal sensitivity of the Zerodur coiled HCF does not change significantly with the size of the hole. The corrected results are presented below:

 

Fig. 1. Thermal sensitivity of coiled HCF on spool with CTE of -0.05 ppm/oC with respect to the central hole radius for spool with R = 90 mm.

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“We also investigated the influence of Zerodur thickness, for instance, by drilling a hole in the Zerodur cylinder, on the spool coiled HCF. The updated results are shown in the following figure. Here, a coiled HCF thermal sensitivity of -0.0025 ppm/K for a homogenous Zerodur spool with CTE = -0.05 ppm/K and R = 90 mm is tuned to zero sensitivity when a hole of 87 mm is drilled in the middle of the spool. This means that the Zerodur cylinder is only 1.5 mm thick, which may be difficult to achieve using drilling. These results, however, demonstrate that the Zerodur spool can be made reasonably thin (e.g., 5 mm wall thickness) without reducing the Zerodur’s effect, which would significantly reduce its weight, of interest in many weight-sensitive applications.”

We apologize for any inconvenience this error may have caused and appreciate the opportunity to correct the scientific record.