We report ultra-stable locking of a commercially available extended cavity diode laser to a vibration-insensitive high finesse Fabry-Perot cavity. A servo bandwidth of 2 MHz is demonstrated. The absolute stability of the diode laser after locking is
measured with a three-cornered-hat method. The resulting Allan deviation reaches a level of $2.95times10^{-15}$ at 1 s, corresponding to only 0.93 Hz linewidth, even without vibration isolation of the reference cavity.
We use the three-cornered-hat method to evaluate the absolute frequency stabilities of three different ultrastable reference cavities, one of which has a vibration-insensitive design that does not even require vibration isolation. An Nd:YAG laser and
a diode laser are implemented as light sources. We observe $sim1$ Hz beat note linewidths between all three cavities. The measurement demonstrates that the vibration-insensitive cavity has a good frequency stability over the entire measurement time from 100 $mu$s to 200 s. An absolute, correlation-removed Allan deviation of $1.4times10^{-15}$ at 1 s of this cavity is obtained, giving a frequency uncertainty of only 0.44 Hz.
We demonstrated for the first time the characterization of absolute frequency stability of three reference cavities by cross beating three laser beams which are independently locked to these reference cavities. This method shows the individual featur
e of each reference cavity, while conventional beatnote measurement between two cavities can only provide an upper bound. This method allows for numerous applications such as optimizing the performance of the reference cavity for optical clockwork.
