Method and apparatus for laser control in a two chamber gas discharge laser

1. A laser control system, comprising:

an oscillator gas chamber;

an amplifier gas chamber;

a first voltage input operatively connected to deliver electrical pulses to a first pair of electrodes within the oscillator gas chamber and a second pair of electrodes within the amplifier gas chamber;

an output of the gas chambers is an energy dose calculated by a trapezoidal window;

a control circuit connected to the first voltage input for modifying the first voltage input, wherein a frequency response to a dose operator has at least one zero;

at least one of an energy dither and a timing dither arranged to initiate under one of the zeros; and

a feedback control loop communicating an output of the gas chambers to the control circuit for modifying the first voltage input.

2. The laser control system of claim 1 , wherein the control circuit modifies the first voltage input in accordance with the equation V=Eu 2 /2k, where E is a laser energy, u is a MopaOpPoint, and k is a derivative of MopaOpPoint with respect to a difference in firing time between the gas chambers.

3. The laser control system of claim 1 , wherein the at least one of an energy dither and a timing dither further comprises an energy dither initiated under one of the zeros.

4. The laser control system of claim 3 , wherein a periodic signal from the energy dither is n shots long, has an amplitude A, and satisfies V [k]=A cos(2πn d k/n), where k=0 to n−1 and n d is the number of cosine periods within one full cycle of the dither.

5. The laser control system of claim 1 , wherein the at least one of an energy dither and a timing dither a timing dither is arranged to initiate under one of the zeros.

6. The laser control system of claim 1 , wherein the control circuit further comprises an energy dose feedback circuit calculated as V dose =−K xd, where K is a state feedback vector computed as a solution of a linear quadratic regulator that minimizes a weighted sum of the square of the energy error and the square of the energy dose error and xd is a vector characterizing a state of a dose operator.

7. The laser control system of claim 1 , wherein the control circuit further comprises a function of energy transients, wherein a plurality of repetition rate bins are initialized for a non-zero value.

8. The laser control system of claim 7 , wherein the repetition rate bins are initialized to values of trained bins having a similar repetition rate.

9. The laser control system of claim 1 , wherein the control circuit further comprises a linear quadratic regulator to feed back a state of a filter that approximates a dose operator.

10. A method of controlling a laser system, the method comprising the steps of:

delivering a first voltage input operatively in the form of electrical pulses to a first pair of electrodes within a oscillator gas chamber and a second pair of electrodes within a amplifier gas chamber;

calculating an energy dose of an output of the gas chambers with a trapezoidal window;

modifying the first voltage input with a control circuit, wherein a frequency response to a dose operator has at least one zero;

initiating at least one of an energy dither and a timing dither under one of the zeros; and

communicating an output of the gas chambers to the control circuit with a feedback control loop for modifying the first voltage input.

11. The method of claim 10 , further comprising the step of modifying the first voltage input in accordance with the equation V=Eu 2 /2k, where E is a laser energy, u is a MopaOpPoint, and k is a derivative of MopaOpPoint with respect to time.

12. The method of claim 10 , wherein the step of initiating further comprises initiating the energy dither under one of the zeros.

13. The method of claim 12 , wherein a periodic signal from the energy dither is n shots long, has an amplitude A, and satisfies V [k]=A cos(2πn d k/n), where k=0 to n−1 and n d is the number of cosine periods within one full cycle of the dither.

14. The method of claim 10 , wherein the step of initiating further comprises initiating the timing dither under one of the zeros.

15. The method of claim 10 , the step of modifying further comprising adding to the first voltage input an energy dose feedback calculated as V dose =−K xd, where K is a state feedback vector computed as a solution of a linear quadratic regulator that minimizes a weighted sum of the square of an energy error and the square of an energy dose error and xd is a vector characterizing a state of a dose operator.

16. The method of claim 10 , wherein the control circuit further comprises a function of energy transients, further comprising the step of initializing a plurality of repetition rate bins for non-zero values.

17. The method of claim 16 , wherein the non-zero values further comprise values of trained bins having a similar repetition rate.

18. The method of claim 10 , further comprising the step of feeding back a state of a filter that approximates a dose operator with a linear quadratic regulator.

19. A control system for controlling a laser system, the control system comprising:

means for delivering a first voltage input operatively in the form of electrical pulses within an oscillator gas chamber and an amplifier gas chamber;

means for calculating an energy dose of an output of the gas chambers with a trapezoidal window;

means for modifying the first voltage input with a control circuit, wherein a frequency response to a dose operator has at least one zero;

means for initiating at least one of an energy dither and a timing dither under one of the zeros; and

means for communicating an output of the gas chambers to the control circuit with a feedback control loop for modifying the first voltage input.

20. The control system of claim 19 , wherein the means for initiating further comprises a means for initiating the energy dither, wherein a periodic signal from the energy dither is n shots long, has an amplitude A, and satisfies V [k]=A cos(2πn d k/n), where k=0 to n−1 and n d is the number of cosine periods within one full cycle of the dither.