In Embodiment 10, the subject matter of Embodiment 9 optionally includes wherein determining the beat tone error and the carrier envelope offset error includes: mixing the carrier envelope offset out of the first signal using mixing circuitry, the first signal, and the second signal; determining the beat tone error using beat tone digital phase detector circuitry, quadrature demodulation, and the beat tone; determining the carrier envelope offset error using carrier envelope phase detector circuitry, quadrature demodulation, and the carrier envelope offset tone.

In Embodiment 11, the subject matter of Embodiment 10 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 12, the subject matter of any one or more of Embodiments 9-11 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.