KR101742715B1 - Method and apparatus for laser control in a two chamber gas discharge laser - Google Patents

Abstract

The laser control system includes an oscillator gas chamber and an amplified gas chamber. The first voltage input is coupled to deliver electrical pulses to the first pair of electrodes in the oscillator gas chamber and to the second pair of electrodes in the amplifier gas chamber. The output of the gas chamber is the energy dose calculated by the trapezoidal window. The control circuit is coupled to the first voltage input for correcting the first voltage input. The feed control loop transmits the output of the gas chamber to the control circuit to modify the first voltage input.

Description

TECHNICAL FIELD [0001] The present invention relates to a laser control method and apparatus for a two-chamber gas discharge laser,

The present disclosure relates generally to laser systems, and more particularly, to a laser control system for a two-chamber gas discharge laser.

1 is a block diagram of a MOPA (master oscillator / power amplifier) known in the prior art. This MOPA laser system 10 is used, for example, in the area of integrated circuit lithography. In one embodiment of the MOPA laser system 10, a 193 nm ultraviolet laser beam is applied to a lithography machine / scanner 20 such as ASML with an office in the Netherlands or a stepper or scanner machine supplied by Nikon or Canon with offices in Japan Lt; / RTI > The MOPA laser system 10 includes a laser energy control system 4 for controlling the pulse energy of the system and the accumulated dos energy output at a pulse repetition rate of, for example, 4000 Hz or more. The MOPA laser system 10 provides extremely accurate triggering of discharges in two laser chambers for each other with feedback of pulse and dose energy and feedforward control.

The main components of the laser system 4 are often located below the deck / flow 5 where the scanner 2 is installed. However, the MOPA laser system 10 includes a beam delivery unit 6 that provides a closed beam path for delivering a laser beam to the input port of the scanner 2. [ Such a light source may be a seed laser generator such as a master oscillator 11 and a power amplifier 12 as described in more detail below, for example, a power ring oscillator (not shown) Quot; PRA "). ≪ / RTI > For convenience, the seed laser is referred to herein as MO and the amplifier laser may be referred to as a power amplifier or simply PA. This includes intentions to cover other types of laser arrays and amplifier laser arrays, such as a powering amplifier ("PRA ") that is a virtual oscillator that forms a MOPO together, i.e., a power oscillator Unless noted, these terms are so widely defined. This light source also includes a pulse stretcher 22.

The master oscillator 11 and the power amplifier / power oscillator 12 each include a discharge chamber 11A, 12A similar to the discharge chamber of a single-chamber lithography laser system. These chambers 11A and 12A include two electrodes, a laser gas and a tangential to circulate the gas between this electrode and the water-cooled finned heat exchanger. The master oscillator 11 amplifies the first laser beam 14A amplified by two paths through the power amplifier 12 in the PA configuration and by oscillation in the PO / PRA in the PO / PRA configuration And generates a second laser beam 14B as shown in Fig. The master oscillator 11 includes a resonant cavity formed by the output coupler 11C and the line-inwing package 11B. The gain medium for the master oscillator 11C is generated between the two long electrodes included in the master oscillator discharge chamber 11A. The power amplifier 12 is basically a discharge chamber 12A and in the preferred embodiment is almost exactly the same as the master oscillator discharge chamber 11A and this chamber provides a gain medium between the two electrodes. However, unlike the PO / PRA, the power amplifier 12 can not have any resonant cavity. With such a MOPA laser system 10 configuration, the master oscillator 11 can be designed and operated to maximize beam quality parameters such as wavelength stability and ultrasound bandwidth. On the other hand, the power amplifier 12 is designed and operated to maximize the power output. For this reason, the MOPA laser system 10 provides a much higher quality and much higher power laser light source than a single chamber system.

As described above, this portion of the amplifier can be configured for oscillation in a cavity, for example, comprising two beam passages, or an amplifier discharge chamber, that pass through the discharge region of the amplifier discharge chamber, . This beam oscillates in the cavity containing the master oscillation chamber 11A between the output coupler 11C (with a 30 percent reflectivity) of the MO 11 and the LNP 11B, and passes through the LNP 10C So that it deeply falls into the line on the passage. The wavelength of the laser beam emitted from the output coupler 11C is measured by the line center analysis module 7. The wood seed beam into the line is reflected downward by the mirror in the MO wave engineering box (MO WEB) 24 and transmitted to the amplifier chamber 12 through the PA wave engineering box (PA WEB) 26 (for electrode orientation) It is horizontally reflected at the skewed angle. In the back end of the amplifier, the beam reverser 28 retroreflects the beam for oscillation within the PO / PRA chamber, either horizontally, with respect to a second passageway passing through the PA chamber 12, or in line with electrode orientation. The bandwidth of the laser emitted from the discharge chamber 12A is instead measured by the spectrum analysis module 9 although the bandwidth of the laser can be measured by the bandwidth analysis module.

The laser system output beam pulse 14B passes through the beam splitter 16 from the PA / PO chamber 12A. The beam splitter 16 reflects about 60 percent of the power amplifier output beam 14B into the delay path created by the four focusing mirrors 20A, 20B, 20C, and 20D. The 40 percent transmitted portion of each pulse of beam 14B becomes the first hump of the corresponding stretched pulse of output beam pulse 14C. The output beam 14C is directed by a beam splitter 16 to a mirror 20A that focuses the reflected portion to a point 22. Thereafter, this beam is expanded and reflected from the mirror 20B, which converts this extended beam into a parallel beam and directs it to the mirror 20C. This mirror 20C again focuses this beam back to point 22. This beam is then reflected by a mirror 20D which, like the mirror 20B, converts the above-described extended beam into an optical parallel beam and directs it back to the beam splitter 16. [ In this beam splitter 16, about 60 percent of the first reflected light is perfectly matched to the first transmitted portion of this pulse in the output beam 14C so that most of the second hump in the laser system output beam pulse do. 40 percent of this reflected beam exactly follows the path of the first reflected beam that transmits the beam splitter 16 and produces an even less hump in the stretched pulse. Thus, a finished output beam 14C is obtained that is stretched to a pulse length of about 20 ns to about 70 ns. The beam delivery unit BDU transfers the output beam 14C. This BDU may include two beam-pointing mirrors 40A and 40B, and one or both of these mirrors may be controlled to provide tip and tilt correction for variable beam pointing.

Figure 2 is an energy control block diagram 50 for the MOPA / MOPO laser system of Figure 1, in accordance with the prior art. FIG. 2 illustrates various control elements for controlling the voltage source 52 to the MOPA laser system 10. The energy control block diagram 50 includes a static control 54 that provides a basically determined voltage that is expected to achieve the energy target 56 (if no other influences need to be considered). The feedforward block 58 provides voltage adjustment based on the trigger interval 60. The trigger interval 60 is used to calculate the repetition rate, shot number, and duty cycle, which affects the 'voltage input-energy output' relationship. Voltage regulation is calculated as a function of these values. The energy servo 62 adjusts the voltage input 52 based on the calculated voltage error 64 of the previous shot. The dither cancellation 66 adjusts the voltage to offset the energy change caused by the timing dither 68. Finally, the energy dither 70 provides a periodic signal added to the voltage input 52 used to estimate the effect of the voltage on the MO energy, the output energy and the MOPA timing. These five voltage signals are summed together to generate the voltage input 52. When the laser is discharged, the energy 72 is measured. The energy target is subtracted from the measured energy 72 to produce an energy error signal 74 that is scaled by a laser estimate 76 that is a derivative of dV / dE, the voltage to energy. The final voltage error 64 is used to derive an adaptation algorithm 78 that adjusts a portion of the voltage signal in a manner that minimizes energy error, dose error, energy sigma, or some combination.

The MOPA laser system 10 shown in FIG. 1 is superior to a single chamber system by providing greater beam control, beam power, and stability than a single chamber system. However, operation can be significantly improved by eliminating the tone disturbance of such a system and further refining the timing and energy control.

The features of embodiments herein provide a system and method for controlling a laser system. In short, in the structure, the features of one possible embodiment of the system can be implemented as follows. The system includes an oscillator gas chamber and an amplifier gas chamber. The first voltage input is coupled to operate to deliver electrical pulses to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber. The output of the gas chamber is the energy dose calculated by the trapezoidal window. A control circuit is coupled to the first voltage input to modify the first voltage input. The feedback control loop transmits the output of the gas chamber to the control circuit to modify the first voltage input.

It is also a feature of the present invention to provide a method for controlling a laser system. In this regard, one embodiment of this method includes the following steps: a first voltage input in the form of an electrical pulse to a first pair of electrodes in an oscillator gas chamber and a second pair of electrodes in an amplifier gas chamber, ; Calculating an energy dose of the output of the gas chamber through the trapezoidal window; Modifying a first voltage input by a control circuit; And transmitting the output of the gas chamber to a control circuit having a feedback control loop to modify the first voltage input.

Other systems, methods, features and advantages of the subject matter will become apparent to those skilled in the art from the following figures and detailed description. All such additional systems, methods, features, and advantages are intended to be included herein and within the scope of this disclosure and protected by the appended claims.

Many features of the present invention may be better understood with reference to the following drawings. The components of the figures are not to scale to clearly illustrate the principles of the disclosed subject matter. Also, in the drawings, like numerals designate corresponding parts in the various drawings.
1 is a block diagram of a MOPA / MOPRA laser system.
2 is a block diagram of energy control for MOPA / MOPRA of FIG.
3 is a graph illustrating a trapezoidal window of various repetition rates, according to the first embodiment of the present application;
4 is a graph of the frequency response of the DOS operator for the window shown in FIG. 3, according to the first embodiment of the present application;
5 is a block diagram of energy control for the MOPA / MOPRA laser system of FIG. 1, according to the first embodiment of the present application.
FIG. 6 is a flowchart illustrating a method of providing the laser control system of FIG. 5 according to the first embodiment of the present invention.

The element herein is based on the recognition that square windows have been used in the past for energy-dose calculations, but some advantages can be realized by applying them to windows of alternative shapes. 3 is a graph showing trapezoidal windowings of various repetition rates according to the first embodiment of the present application; 4 is a graph of the frequency response of the DOS operator for the window disclosed in FIG. 3, in accordance with a feature of the first embodiment of the present application; It is clear that there is a set of varying zeros for different window widths, but there is a zero for all windows at 20% and 40% of the sample rate. This zero corresponds to zero of the 5-pulse moving average. It can be seen that a trapezoidal window is a convolution of a rectangular window with the same length as a window size smaller than a trailing edge and a 5 pulse rectangular window.

FIG. 5 is an energy control block diagram 150 for the MOPA / MOPRA laser system 10 of FIG. 1, according to a first embodiment of the present application. FIG. 5 illustrates various control elements for controlling the voltage input 152 to the MOPA / MOPRA laser system 10. This energy control block diagram 150 includes a static control 154 that provides a basically determined voltage that is expected to achieve the energy target 156 (if there are no other influences to consider). Part of the purpose of the static control 154 is to create an energy controller responsive to changes in the energy target 156. If the user adjusts the energy target, the first voltage input 152 for the first shot must be calculated to meet the new energy set point. This static control 154 may provide the following voltage signals.

V = (dV / dE) _ref * (E _target - E _ref + e (E _target - E _ref ) ² + V _ref

Here, E _ref is approximately set to the nominal energy of the laser system 10, and V _ref is the voltage required to emit the laser at approximately E _ref .

The feedforward block 158 provides voltage adjustment based on the trigger interval 160. The trigger interval 160 is used to calculate the repetition rate, shot number, and duty cycle that affect the 'voltage input-energy output' relationship. The voltage adjustment for this trigger interval 160 is calculated as a function of these values. More specifically, the voltage signal provided by the feedforward block 158 may be as follows.

_{V = f 0 (D) +} f 1 (R, n)

Where D is the duty cycle, R is the repetition rate, and n is the shot number. It should be noted that the feedforward voltage has two terms. One term, / o, is dependent on the duty cycle and / or the burst interval, and the other term, / i, is dependent on the shot number and the repetition rate. By design, / i is zero for the first shot of each burst. Thus, / o alone determines the feedforward voltage for the first shot of the burst. These terms are usually intended to adjust the laser for changes in efficiency that continue through the burst. The term f ₁ captures the shape of any transient. This equation assumes that the duty cycle or inter burst interval effect only moves the energy-to-shot number up and down by the same amount for all shots in the burst. It is assumed that the shape of the energy transient is dependent only on the repetition rate. / i (R, n) function compensates the shape of the energy transient.

The function / i (R, n) is maintained as a table-to-repeat ratio and a shot number. A simple integrator is used to adjust the bean. In the past, the bean started with zero, which requires multiple bursts before the laser control correctly inverts the transient at the repetition rate.

Instead of initializing this bin to zero, the feedforward bin may be initialized to the value of the nearest trained bin in frequency. By initializing these beans to values closer to the exact value for the shape of the energy transient, the laser control becomes faster and more accurate, inverting the transient at the repetition rate.

The energy servo 162 adjusts the voltage input 152 based on the calculated voltage error 164 of the previous shot in the same burst. Adjustments from this energy servo 162 may be computed in at least one couple of different modes. First, NSqaured feedback is a feedback method known to those skilled in the art. This feedback method feeds back one voltage proportional to the integral of the voltage error (intrinsic gain) and feeds back another voltage proportional to the doubled integral voltage error (I square gain). Numerous sets of gain NSquared filters: Soft; hard; And MO. Soft gain is used in the operating mode when the objective is to minimize the energy error between shot and shot. Soft gain is selected to minimize energy errors. Hard gain is used in DOS and sigma modes. This hard gain is intended to minimize DOS (integrated energy error) and tends to be larger than soft gain. The MO gain is used in the MO energy control mode and is intended to minimize energy errors.

An alternative to HSquared feedback is DOS feedback. Like the HSquared controller with hard gain, the DOS feedback controller is intended to minimize DOS, but it uses a control method that provides better performance with non-orthogonal DOS windows (e.g., trapezoidal DOS windows). The dose feedback is controlled by a vector of the dimming parameters and gain. Such a DOS feedback controller is only useful in DOS and sigma modes and can use a linear quadratic regulator to minimize the square of the energy dose and energy error 172. The use of a linear quadratic regulator instead of 100% integrated feedback has been shown to reduce the energy-dose error by approximately 25%.

As shown in FIG. 5, the effect of the laser system 4 is to convert the voltage input 152 to energy (calculated by the energy measurement 172) through a static gain. There is also a set of disturbances added to the energy signal. Thus, the state of the system may be the same as the disturbance dynamics and the DOS operator. The energy servo 162 is adapted to provide voltage regulation in response to the act of the DOS operator. The energy dose feedback can be calculated as a vector, xd, which characterizes the state of the inner product, k, and the dose operator of the state feedback vector.

Vdose = -Kxd

K is computed as a solution of a linear quadratic regulator that minimizes the weighted sum of the squared energy error and the square of the energy dose error.

The dither cancellation 166 adjusts the voltage to offset the energy change caused by the timing dither 168. The side effect of this cancellation is to estimate the derivative of the voltage for the MOPA / MOPRA timing at a fixed energy, which is the value used to calculate MopaOpPoint (180).
MopaOpPoint 180 is the operating point, u, of the MOPA laser system, which can be defined as:

u = 1 / E * dV / dt (at constant energy)

E is the laser energy, V is the voltage and t is the MOPA timing, i.e. the discharge time difference between the MO and PA chambers. For a particular feature of the timing control, a local slope of the timing for the energy curve is needed. This information is obtained by applying a dither signal to the differential timing commanded to the MO and PA commutator triggers. Since the timing is coupled into the energy, this dither signal produces a matching dither of energy. The dither cancellation algorithm adaptively finds a voltage signal that when applied to a laser accurately cancels the dither in the energy produced by the timing dither signal. Thus, the timing dither no longer appears in the energy signal and thus has no effect on energy sigma or energy dose.

The bi-product of this cancellation algorithm is a derivative of the voltage with respect to timing at a fixed energy. This bi-product is the tilt information applied by the timing dither to identify in the first place. The parameters used in the laser control system for gas control, dMpopdMopa (the derivative of MopaOpPoint for MO and PA chamber discharge time differences), allow the dither cancellation to respond almost immediately to changes in the MOPA timing (MO and PA chamber discharge time differences) . If this parameter is off, for a "large" ¹ (1-2 ns) change at MOPA / MOPRA timing, MopaOpPoint (180: "Mpop") will jump to the new value and then up, You will jump to the shot and drift to a different value. While the MopaOpPoint (180) estimate is converging, some timing dither signals will flow into the energy. If the gas control parameters described above are set correctly, then MopaOpPoint (180) must have a material rediminated drift and remain at the new value after jumping to the new value for the "large" MOPA / MOPPRA timing change.

As described above with respect to FIG. 4 using a trapezoidal window, there is clearly zero for all windows at 20% and 40% of the sample rate (the leading and trailing edges of the trapezoidal window are 5 pulses). Although the amplitude of the dither can usually be set low to reduce the energy dither, the low amplitude delays the calculation of the derivative of the energy dose to the voltage estimate. If the dither is moved below zero of one of the trapezoidal widows, the amplitude may be raised with a weakened negative impact.

Mopop compaction 182 adjusts voltage input 152 to compensate for changes in MOPA timing. This adjustment is primarily to stabilize the energy for changes in DtMopaTarget exceeding about 1 nanosecond. If the laser is working with a bandwidth control enable (ASC) and is currently off resonance, the control system has reduced the delay between the MO and PA triggers to maintain bandwidth. At this point, MopaOpPoint will be a low negative value because DtMopaTarget is below some ns below the value for peak efficiency. Then, the scanner 2 converts the repetition rate to that of the bandwidth resonance. The bandwidth goes up and the bandwidth controller precedes DtMopaTarget by a few ns to compensate. This moves the laser in steps a few nanometers closer to the peak efficiency and energy increase. This step change in energy will affect energy doses until energy servome 162 has a chance to compensate.

On the other hand, the MopaOpPoint compaction 182 conflicts with this effect. It is possible to calculate the amount of voltage needed to change for a given change in Mopa timing, using the same value used to adjust the dither cancellation for the dMpopDMopa, i. e. the change in Mopa timing. When the Mopa timing changes rapidly, the MopaOpPoint compaction 182 can predict what voltage change is needed and provides a voltage signal suitable for the voltage input 152 without waiting for the energy error 174 to appear. The MopaOpPoint compaction 182 can be expressed as follows.

V = Eu ² / 2K

Where E is the laser energy, u is the MopaOpPoint and k is the derivative of MopaOpPoint for the Mopa timing, which is the discharge time difference between dMpopDMopa or the MO and PA chambers.

The disturbance predication 184 adjusts the voltage input 152 based on the prediction of the voltage error, assuming that the disturbance acting on the energy is a multiple of the DC offset plus tone. These tones are at frequencies that are multiples of MO and PA / PO blower speeds. This predicted voltage error is subtracted from the voltage input 152 and thus eliminates the effects described above due to DC offset or blower blade passages.

Finally, the energy dither 170 provides a periodic signal added to the voltage input 152 used to estimate the effect of the voltage on the MO energy, the output energy and the MOPA timing. The periodic signal from the energy dither 170 is the length of n shots and can be expressed by the following equation.

k=0,...,n-1

k = 0, ..., n-1

Where A is the dither amplitude and n _d is the number of cosine periods in one whole cycle of the dither.

The dither signal is reserved for a fixed number of shorts before starting in each burst. This delay is provided so that the dither can not combine with the start of the burst effect to push the laser 4 out of spec. The phase of the dither signal may be randomized to block other signals at or near the dither frequency from interfering with the derivative estimate. Randomization is achieved by randomizing the value of k in the above equation to initiate the dither. For the window shown in FIG. 3, the dither frequency is 1/5 of the repetition rate (5 shots of reading and trailing for each trapezoidal window). This is the core frequency for lasers using trapezoidal windows to compute DOS. For a window with four pulse leading and trailing edges, a repetition rate of 20% is within the zero of the DOS operator. Thus, dithering at this frequency will have no effect on DOS.

These voltage signals are added together to generate voltage input 152. [ When laser is discharged, the energy is measured (172). The energy target is subtracted from the measured energy to produce an energy error signal 174 scaled by dV / dE which is a laser estimate 176, which is a derivative of the voltage to energy. The final voltage error 164 is used to derive an adaptation algorithm 178 that adjusts a portion of the voltage signal in a manner that minimizes energy error, dose error, or energy sigma, or some combination thereof.

FIG. 6 is a flowchart 200 illustrating a method of providing the laser control system 150 of FIG. 5, according to a first embodiment of the present disclosure. It should be understood that any process description or block in the flowchart represents a module, segment, portion or step of a code that includes one or more instructions for implementing a particular logical function in a process, and alternative embodiments may be understood by those skilled in the art It is to be understood that the functions are encompassed within the scope of the invention, which may be practiced out of the order in which the functions are discussed, including substantially simultaneous or reverse order, based on the function involved.

Three alternatives of the first embodiment will now be described with reference to FIG.

In a first alternative, as shown in block 202, a first voltage input is operatively delivered in the form of an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber do. The energy dose of the output of the gas chamber is calculated by a trapezoidal window (block 204). The first voltage input is modified by a control circuit having a frequency response to the dos operator that has at least one zero (block 206). At least one of the energy dither and the timing dither begins below one of the zeros (block 208). The output of the gas chamber is sent to a control circuit having a feedback control loop for modifying the first voltage input (block 210).

In a second alternative, as shown in block 202, a first voltage input is operatively delivered in the form of an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber do. The energy dose of the output of the gas chamber is calculated by a trapezoidal window (block 204). The first voltage input is modified by the control circuit which modifies the first voltage input according to the equation V = Eu ² / 2k. Where E is laser energy, u is MopaOpPoint and k is a derivative of MopaOpPoint with respect to the discharge time difference between gas chambers (block 206). This alternative does not use block 208. [ The output of the gas chamber is transferred to a control circuit having a feedback control loop for modifying the first voltage input.

In a third alternative, as shown by block 202, the first voltage input is operatively coupled to the first pair of electrodes in the oscillator gas chamber and to the second pair of electrodes in the amplifier gas chamber in the form of electric pulses . The energy dose of the output of this gas chamber is calculated by a trapezoidal window (block 204). The first voltage input is modified by the control circuit by adding energy dose feedback calculated as V _dose = -K xd to the first voltage input. Where K is a state feedback vector computed as a solution of a linear quadratic regulator that minimizes the weighted sum of the squared energy error and the squared energy error, and xd is a vector characterizing the state of the dos operator 206). This alternative does not use block 208. [ The output of the gas chamber is sent to a control circuit having a feedback control loop for modifying the first voltage input (block 210).

It should be understood that the above-described embodiments of the invention, particularly the "preferred" embodiments, are merely possible examples for understanding of the principles of the invention. Many variations and modifications may be made to the above-described embodiments of the invention without departing from the spirit and principles of the invention. It is intended that all such modifications and variations be included within the scope of this disclosure and be protected by the following claims.

Claims (27)

An oscillator gas chamber;
Amplifier gas chamber;
A first voltage input coupled to operate to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber;
A control circuit coupled to the first voltage input for modifying the first voltage input, the control circuit having a frequency response to the dos operator having at least one zero;
At least one of an energy dither and a timing dither designed to start by one of the zeros; And
And a feedback control loop for transmitting an output of the gas chamber to a control circuit for modifying the first voltage input,
The output of the gas chambers is an energy dose calculated by a trapezoidal window,
_Wherein the control circuit further comprises an energy dose feedback circuit calculated as V _dose = -K xd, where K is calculated as a solution of a linear quadratic regulator that minimizes the weighted sum of the squared energy error and the square of the energy dose error Xd is a vector characterizing the state of the dos operator. The method of claim 1, wherein the control circuit modifies the first voltage input according to the equation V = Eu ² / 2k, where E is laser energy, u is MopaOpPoint and k is a A laser control system that is a derivative of MopaOpPoint. 2. The laser control system of claim 1, wherein at least one of the energy dither and the timing dither further comprises an energy dither initiated by one of the zeros. 4. The apparatus of claim 3, wherein the periodic signal from the energy dither is a length of n shorts and has an amplitude A,

Wherein k = 0, ..., n-1, and n _d is a number of cosine periods in one full cycle of the energy dither. 2. The laser control system of claim 1, wherein at least one of the energy dither and the timing dither is designed to be initiated by one of the zeros. delete 2. The laser control system of claim 1, wherein the control circuit further comprises a function of an energy transient, and wherein a plurality of repetition rate beans are initialized for a non-zero value. 8. The laser control system of claim 7, wherein the repetition rate bean is initialized to a value of a trained bean having a similar repetition rate. 2. The laser control system of claim 1, wherein the control circuit further comprises a linear quadratic regulator that feeds back the state of the filter approximating the DOS operator. An oscillator gas chamber;
Amplifier gas chamber;
A first voltage input coupled to operate to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and a second pair of electrodes in the amplifier gas chamber;
Wherein a control circuit coupled to the first voltage input to modify the first voltage input, the equation according to V = Eu ² / 2k and modify the first voltage input, E is a laser energy, u is MopaOpPoint k is A control circuit that is a derivative of MopaOpPoint for a discharge time difference between the gas chambers; And
And a feedback control loop for transmitting an output of the gas chambers to the control circuit for modifying the first voltage input,
The output of the gas chambers is an energy dose calculated by a trapezoidal window,
_Wherein the control circuit further comprises an energy dose feedback circuit calculated as V _dose = -K xd, where K is calculated as a solution of a linear quadratic regulator that minimizes the weighted sum of the squared energy error and the square of the energy dose error Xd is a vector characterizing the state of the dos operator. The method of claim 10, wherein the first voltage input _{V = (dV / dE) ref} * (E target - E ref + e (E target - E ref) 2 + V ref as further includes a calculation type from the energy target , Where E _ref is set to the nominal energy of the laser system (10), and V _ref is the voltage required to emit the laser at E _ref . 11. The laser control system of claim 10, wherein the frequency response to the dos operator has at least one zero and the control circuit further comprises an energy dither initiated by one of the zeroes. 13. The method of claim 12 wherein the periodic signal from the energy dither is of length n of n shots and has amplitude A,

Wherein k = 0, ..., n-1, and n _d is a number of cosine periods in one full cycle of the energy dither. 11. The laser control system of claim 10, wherein the frequency response to the dos operator has at least one zero and the timing dither is designed to be initiated by one of the zeroes. delete 11. The laser control system of claim 10, wherein the control circuit further comprises a function of an energy transient, and wherein a plurality of repetition rate beans are initialized for a non-zero value. 17. The laser control system of claim 16, wherein the repetition rate bean is initialized to a value of a training bean having a similar repetition rate. 11. The laser control system of claim 10, wherein the control circuit further comprises a linear quadratic regulator that feeds back the state of the filter that approximates the DOS operator. An oscillator gas chamber;
Amplifier gas chamber;
A first voltage input coupled to deliver an electrical pulse to a first pair of electrodes in the oscillator gas chamber and to a second pair of electrodes in the amplifier gas chamber;
A control circuit coupled to the first voltage input to modify the first voltage input, the control circuit further comprising an energy dose feedback circuit calculated as V _dose = -K xd, where K is the square of the energy error and the square of the energy dose error Xd is a control circuit that is a vector characterizing the state of the dos operator; < RTI ID = 0.0 > a < / RTI > And
And a feedback control loop for transmitting an output of the gas chambers to the control circuit for modifying the first voltage input,
Wherein the output of the gas chambers is an energy dose calculated by a trapezoidal window. 20. The method of claim 19 wherein the control circuit is according to the equation V = Eu ² / 2k and modify the first voltage input, E is laser energy, u is MopaOpPoint k is on the discharge time difference between the gas chamber A laser control system that is a derivative of MopaOpPoint. 20. The laser control system of claim 19, wherein the frequency response to the DOS operator has at least one zero and the control circuit further comprises an energy dither initiated by one of the zeroes. 22. The method of claim 21, wherein the periodic signal from the energy dither has a length of n shots and has an amplitude A,

Wherein k = 0, ..., n-1, and n _d is a number of cosine periods in one full cycle of the energy dither. 20. The laser control system of claim 19, wherein the frequency response for the dos operator has at least one zero and the timing dither is designed to be initiated by one of the zeroes. The method of claim 19, wherein the first voltage input _{V = (dV / dE) ref} * (E target - E ref + G (E target - E ref) 2 + V ref as further includes a calculation type from the energy target , Where E _ref is set to the nominal energy of the laser system (10), and V _ref is the voltage required to emit the laser at E _ref . 20. The laser control system according to claim 19, wherein the control circuit further comprises a function of an energy transient, and wherein a plurality of repetition rate beans are initialized for a non-zero value. 26. The laser control system of claim 25, wherein the repetition rate bean is initialized to a value of a trained bean having a similar repetition rate. 20. The laser control system of claim 19, wherein the control circuit further comprises a linear quadratic regulator that feeds back the state of the filter approximating the DOS operator.

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