In Embodiment 18, the subject matter of Embodiment 17 optionally includes wherein determining the beat tone error using quadrature demodulation to includes: mixing, using mixer circuitry, the beat tone with a first signal generated from a local oscillator to create a first mixed signal; mixing, using mixer circuitry, the beat tone with a second signal from the local oscillator, the second signal ninety-degrees out of phase with the first signal; sampling, using an analog to digital converter circuit, the first mixed signal and the second mixed signal to generate a first digital mixed signal and a second digital mixed signal; and determining the beat tone error, using an arctangent 2 circuitry, to perform an arctangent 2 function on the first and second digital mixed signals.

In Embodiment 19, the subject matter of any one or more of Embodiments 16-18 optionally include wherein providing the fast and slow repetition rate control includes: determining an integral-lead loop control using integral-lead circuitry and the beat tone error; determining the fast repetition rate control using fast gain circuitry and frequency-to-voltage converter circuitry; and determining the slow repetition rate control using slow gain circuitry, integration circuitry, and frequency-to-voltage converter circuitry.

In Embodiment 20, the subject matter of any one or more of Embodiments 16-19 optionally include wherein providing the fast and slow carrier envelope offset control includes: determining an integral-lead loop control using integral-lead circuitry and the carrier envelope offset error; determining the fast carrier envelope offset control using fast gain circuitry and frequency-to-voltage converter circuitry; and determining the slow carrier envelope offset control using slow gain circuitry, integration circuitry, and frequency-to-voltage converter circuitry.