Patent Publication Number: US-2021194202-A1

Title: Metrology for a body of a gas discharge stage

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Application No. 62/730,428, filed Sep. 12, 2018 and titled METROLOGY FOR A BODY OF A GAS DISCHARGE STAGE, which is incorporated herein in its entirety by reference. 
    
    
     TECHNICAL FIELD 
     The disclosed subject matter relates to controlling a position or alignment of a body of a gas discharge stage to improve performance of the gas discharge stage. 
     BACKGROUND 
     In semiconductor lithography (or photolithography), the fabrication of an integrated circuit (IC) requires a variety of physical and chemical processes performed on a semiconductor (for example, silicon) substrate (which is also referred to as a wafer). A lithography exposure apparatus (which is also referred to as a scanner) is a machine that applies a desired pattern onto a target region of the substrate. The substrate is fixed to a stage so that the substrate generally extends along an image plane defined by orthogonal X L  and Y L  directions of the scanner. The substrate is irradiated by a light beam, which has a wavelength in the ultraviolet range, somewhere between visible light and x-rays, and thus has a wavelength between about 10 nanometers (nm) to about 400 nm. Thus, the light beam can have a wavelength in the deep ultraviolet (DUV) range, for example, with a wavelength that can fall from about 100 nm to about 400 nm or a wavelength in the extreme ultraviolet (EUV) range, with a wavelength between about 10 nm and about 100 nm. These wavelength ranges are not exact, and there can be overlap between whether light is considered as being DUV or EUV. 
     The light beam travels along an axial direction, which corresponds with the Z L  direction of the scanner. The Z L  direction of the scanner is orthogonal to the image plane (X L -Y L ). The light beam is passed through a beam delivery unit, filtered through a reticle (or mask), and then projected onto a prepared substrate. The relative position between the substrate and the light beam is moved in the image plane and the process is repeated at each target region of the substrate. In this way, a chip design is patterned onto a photoresist that is then etched and cleaned, and then the process repeats. 
     SUMMARY 
     In some general aspects, a light source apparatus includes: a gas discharge stage including a three-dimensional body defining a cavity that is configured to interact with an energy source, the body including at least two ports that are transmissive to a light beam having a wavelength in the ultraviolet range; a sensor system comprising a plurality of sensors, each sensor is configured to measure a physical aspect of a respective distinct region of the body of the gas discharge stage relative to that sensor; and a control apparatus in communication with the sensor system. The control apparatus is configured to analyze the measured physical aspects from the sensors to thereby determine a position of the body of the gas discharge stage in an XYZ coordinate system defined by an X axis, wherein the X axis is defined by the geometry of the gas discharge stage. 
     Implementations can include one or more of the following features. For example, the light source apparatus can also include a measurement system configured to measure one or more performance parameters of a light beam that is generated from the gas discharge stage. 
     The control apparatus can be in communication with the measurement system. The control apparatus can be configured to: analyze both the position of the body of the gas discharge stage in the XYZ coordinate system and the one or more measured performance parameters of the light beam; and determine whether a modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters. The light source apparatus can include an actuation system physically coupled to the body of the gas discharge stage, and configured to adjust a position of the body of the gas discharge stage. The control apparatus can be in communication with the actuation system. The control apparatus can be configured to provide a signal to the actuation system based on the determination regarding whether the position of the body of the gas discharge stage should be modified. The actuation system can include a plurality of actuators, each actuator configured to be in physical communication with a region of the body of the gas discharge stage. Each actuator can include one or more of an electro-mechanical device, a servomechanism, an electrical servomechanism, a hydraulic servomechanism, and/or a pneumatic servomechanism. 
     The control apparatus can be configured to determine the position of the body of the gas discharge stage in the XYZ coordinate system by determining a translation of the body of the gas discharge stage from the X axis or a rotation of the body of the gas discharge stage from the X axis. The translation of the body of the gas discharge stage from the X axis can include one or more of: a translation of the body of the gas discharge stage along the X axis, a translation of the body of the gas discharge stage along a Y axis that is perpendicular with the X axis, and/or a translation of the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. The rotation of the body of the gas discharge stage from the X axis can include one or more of: a rotation of the body of the gas discharge stage about the X axis, a rotation of the body of the gas discharge stage about a Y axis that is perpendicular with the X axis, and/or a rotation of the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. 
     Each sensor can be configured to measure as the physical aspect of the body of the gas discharge stage relative to that sensor a distance from the sensor to the body of the gas discharge stage. 
     The gas discharge stage can include a beam turning device at a first end of the body and a beam coupler at a second end of the body, the beam turning device and the beam coupler intersecting the X axis such that a light beam produced in the gas discharge stage interacts with the beam coupler and the beam turning device. When the body of the gas discharge stage is within a range of acceptable positions, the energy source can supply energy to the cavity of the body, and the beam tuning device and beam coupler can be aligned, the light beam is generated. The light beam can be an amplified light beam having a wavelength in the ultraviolet range. The beam turning device can be an optical module that includes a plurality of optics for selecting and adjusting a wavelength of the light beam and the beam coupler includes a partially reflecting mirror. The beam turning device can include an arrangement of optics that is configured to receive the light beam exiting the body of the gas discharge stage through a first port and changing a direction of the light beam so that the light beam re-enters the body of the gas discharge stage through the first port. The gas discharge stage can also include a beam expander configured to interact with the light beam as it travels between the beam coupler and the cavity. 
     Each sensor can be configured to be fixedly mounted relative to the body of the gas discharge stage. Each sensor can be configured to be fixed at a distance from the other sensor when it is fixedly mounted relative to the body of the gas discharge stage. 
     The light source apparatus can also include: a second gas discharge stage that is optically in series with the gas discharge stage and a second plurality of sensors. The second gas discharge stage includes a second three-dimensional body defining a second cavity that is configured to interact with an energy source, the second body including at least two ports that are transmissive to a light beam having a wavelength in the ultraviolet range. Each sensor in the second plurality can be configured to measure a physical aspect of a respective distinct region of the second body relative to that sensor. The control apparatus can be in communication with the second plurality of sensors, and can be configured to analyze the measured physical aspects from the sensors of the second plurality to thereby determine a position of the second body relative to a second XYZ coordinate system defined by a second X axis that passes through the at least two ports of the second body. 
     Each sensor can include a displacement sensor. The displacement sensor can be an optical displacement sensor, a linear proximity sensor, an electromagnetic sensor, and/or an ultrasonic displacement sensor. Each sensor can include a contact-less sensor. 
     The X axis can be defined by a beam turning device at a first end of the body and optically coupled with a first port and a beam coupler at a second end of the body and optically coupled with a second port. 
     In other general aspects, a metrology apparatus includes: a sensor system including a plurality of sensors, each sensor is configured to measure a physical aspect of a body of a gas discharge stage relative to that sensor; a measurement system configured to measure one or more performance parameters of a light beam that is generated from the gas discharge stage; an actuation system including a plurality of actuators, each actuator configured to be physically coupled to a distinct region of the body of the gas discharge stage, the plurality of actuators working together to adjust a position of the body of the gas discharge stage; and a control apparatus in communication with the sensor system, the measurement system, and the actuation system. The control apparatus is configured to: analyze the measured physical aspects from the sensors to thereby determine a position of the body of the gas discharge stage in an XYZ coordinate system defined by an X axis that is defined by the gas discharge stage; analyze the position of the body of the gas discharge stage; analyze the one or more measured performance parameters; and provide a signal to the actuation system to modify the position of the body of the gas discharge stage based on the analyses of the position of the body of the gas discharge stage and the one or more measured performance parameters. 
     Implementations can include one or more of the following features. For example, the sensors can be positioned apart from each other and relative to the body of the gas discharge stage. 
     The control apparatus can be configured to provide the signal to the actuation system to modify the position of the body of the gas discharge stage based on the analyses of the position of the body of the gas discharge stage and the one or more measured performance parameters by determining a position of the body of the gas discharge stage that optimizes a plurality of the performance parameters of the light beam. 
     The X axis can be defined by a beam turning device at a first end of the body and optically coupled with a first port and a beam coupler at a second end of the body and optically coupled with a second port. 
     In other general aspects, a method includes: measuring, at each of a plurality of distinct regions of a body of a gas discharge stage of a light source, a physical aspect of the body at that region; measuring one or more performance parameters of a light beam that is generated from the gas discharge stage; analyzing the measured physical aspects to thereby determine a position of the body in an XYZ coordinate system defined by an X axis, wherein the X axis is defined by a plurality of apertures associated with the gas discharge stage; analyzing the determined position of the body of the gas discharge stage; analyzing the one or more measured performance parameters; determining whether a modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters; and, if it is determined that a modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters, then modifying the position of the body of the gas discharge stage. 
     Implementations can include one or more of the following features. For example, the position of the body of the gas discharge stage can be modified based on the analysis of the determined position of the body of the gas discharge stage. 
     The position of the body of the gas discharge stage can be determined by determining one or more of a translation of the body of the gas discharge stage from the X axis and/or a rotation of the body of the gas discharge stage from the X axis. The body of the gas discharge stage can be translated from or along the X axis by one or more of: translating the body of the gas discharge stage along the X axis, translating the body of the gas discharge stage along a Y axis that is perpendicular with the X axis, and/or translating the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. The body of the gas discharge stage can be rotated from or about the X axis by one or more of: rotating the body of the gas discharge stage about the X axis, rotating the body of the gas discharge stage about a Y axis that is perpendicular with the X axis, and/or rotating the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. 
     The physical aspect of the body can be measured by measuring a distance from the sensor to the region of the body of the gas discharge stage. 
     Determining whether the modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters can include determining a position of the body of the gas discharge stage that optimizes a plurality of measured performance parameters. 
     The method can also include generating the light beam from the gas discharge stage including forming a resonator defined by a beam coupler at one side of the body and a beam turning device at another side of the body, the beam coupler and the beam turning device defining the X axis and generating energy within a gain medium in a cavity defined by the body. 
     The one or more performance parameters of the light beam can be measured by measuring a plurality of performance parameters. The plurality of performance parameters can be measured by measuring two or more of a repetition rate of a pulsed light beam produced by the light source, an energy of the pulsed light beam, a duty cycle of the pulsed light beam, and/or a spectral feature of the pulsed light beam. The method can also include: determining an optimal position of the body of the gas discharge stage that provides an optimal set of values of the performance parameters of the light beam; and modifying the position of the body of the gas discharge stage to be at the optimal position. 
     In other general aspects, a metrology kit includes: a sensor system including a plurality of sensors, each sensor is configured to measure a physical aspect of a three-dimensional body relative to that sensor; a measurement system including a plurality of measurement devices, each measurement device configured to measure a performance parameter of a light beam; an actuation system including a plurality of actuators configured to physically couple to the three-dimensional body; and a control apparatus configured to be in communication with the sensor system, the measurement system, and the actuation system. The control apparatus includes: a sensor processing module configured to interface with the sensor system and receive sensor information from the sensor system; a measurement processing module configured to interface with the measurement system and receive measurement information from the measurement system; an actuator processing module configured to interface with the actuation system; and a light source processing module configured to interface with a gas discharge stage having a three-dimensional body. 
     Implementations can include one or more of the following features. For example, the control apparatus can include an analysis processing module in communication with the sensor processing module, the measurement processing module, the actuator processing module, and the light source processing module. The analysis processing module can be configured to, in use, instruct the light source processing module to adjust one or more characteristics of the gas discharge stage and analyze the sensor information and the measurement information and determine an instruction to the actuator processing module based on the adjusted characteristics of the gas discharge stage. 
     The metrology kit can be modular such that it is configured to be operably connected and disconnected from one or more gas discharge stages, each gas discharge stage including a respective three-dimensional body defining a cavity that generates a respective light beam. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram of an apparatus configured to determine a position of a three-dimensional body in an XYZ coordinate system of a gas discharge stage, the apparatus including a sensor system; 
         FIG. 2A  is a perspective view of the apparatus of  FIG. 1 ; 
         FIG. 2B  is a perspective view of the body from the apparatus of  FIG. 2A , in which a longitudinal axis of the body is aligned with the X axis of the XYZ coordinate system; 
         FIG. 3A  is a perspective view of the body from the apparatus of  FIG. 2A , in which the longitudinal axis of the body is misaligned with the X axis of the XYZ coordinate system by a rotation of the body about a Y axis of the XYZ coordinate system; 
         FIG. 3B  is a perspective view of the body from the apparatus of  FIG. 2A , in which the longitudinal axis of the body is misaligned with the X axis of the XYZ coordinate system by a rotation of the body about a Z axis of the XYZ coordinate system; 
         FIG. 3C  is a perspective view of the body from the apparatus of  FIG. 2A , in which the longitudinal axis of the body is misaligned with the X axis of the XYZ coordinate system by a rotation of the body about a X axis of the XYZ coordinate system; 
         FIG. 3D  is a perspective view of the body from the apparatus of  FIG. 2A , in which the longitudinal axis of the body is misaligned with the X axis of the XYZ coordinate system by a translation of the body along the Y axis of the XYZ coordinate system; 
         FIG. 3E  is a perspective view of the body from the apparatus of  FIG. 2A , in which the longitudinal axis of the body is misaligned with the X axis of the XYZ coordinate system by a translation of the body along the Z axis of the XYZ coordinate system; 
         FIG. 3F  is a perspective view of the body from the apparatus of  FIG. 2A , in which the longitudinal axis of the body is misaligned with the X axis of the XYZ coordinate system by a translation of the body along the X axis of the XYZ coordinate system; 
         FIG. 4  is a perspective view of the body and the apparatus of  FIGS. 1-2B , showing an implementation of a sensor system and a control apparatus; 
         FIG. 5  is a side cross-sectional view taken along the YZ plane of the body and apparatus of  FIG. 4 ; 
         FIG. 6  is a plan view of the XY plane showing the body and an example of how the sensor system of the apparatus of  FIGS. 1-2A  measures a position of the body; 
         FIG. 7  is a perspective view of an apparatus configured to measure a position of the body similar to the design of  FIG. 2A , except that the apparatus of  FIG. 7  further includes an actuation system configured to adjust a position of the body (and therefore also adjust the longitudinal direction of the body) relative to the X axis of the XYZ coordinate system; 
         FIG. 8  is a perspective view of the body and the apparatus of  FIG. 7 , showing an implementation of a sensor system, a control apparatus, and an actuation system; 
         FIG. 9  is a perspective view of an apparatus configured to measure a position of the body and to adjust the position of the body similar to the design of  FIG. 7 , except that the apparatus of  FIG. 9  further includes a measurement system configured to measure or monitor performance or performance characteristics of the gas discharge stage; 
         FIG. 10  is a perspective view of the body and the apparatus of  FIG. 9 , showing an implementation of a sensor system, a control apparatus, an actuation system, and a measurement system; 
         FIG. 11  is a graph of an implementation of an alignment feedback control process in which an optimum energy of a light beam output from the gas discharge stage is determined as the position of the body is rotated about the Z axis and translated along the Y axis; 
         FIG. 12  is a block diagram of a dual-stage light source including two gas discharge stages, either or both of which can include the apparatus of  FIG. 2A, 7 , or  9 ; 
         FIG. 13  is a block diagram of a metrology kit that includes the components that make up the apparatus of  FIG. 9 ; 
         FIG. 14  is a flow chart of a procedure performed by the apparatus of  FIG. 1, 2A, 7 , or  9 ; and 
         FIG. 15  is a block diagram of a light source that includes the apparatus of  FIG. 1, 2A, 7 , or  9 . 
     
    
    
     DESCRIPTION 
     Referring to  FIGS. 1 and 2A , an apparatus  100  is designed to determine a position of a three-dimensional body  102  in an XYZ coordinate system  104  relative to an X axis  106  of the coordinate system  104 . The body  102  is a part of gas discharge stage  108  that is configured to produce a light beam  110  that has a wavelength in the ultraviolet range. The body  102  defines a cavity  112  that is configured to interact with an energy source  114 , which can include a pair of electrodes. The energy source  114  can be fixed to the body  102 , as discussed in greater detail below. 
     The gas discharge stage  108  includes the body  102  plus other optical components (such as components  140 ,  142 ) for producing the light beam  110 . The gas discharge stage  108  can include other components not shown in  FIGS. 1 and 2A . The representation of the gas discharge stage  108  as a cuboid in  FIG. 2A  does not necessarily correspond to physical walls and is shown this way to point out that it could include other components not shown. The gas discharge stage  108  can simply correspond to a platform on which all the optical components (including the body  102 ) are placed. The light beam  110  output from the gas discharge stage  108  can be used in an apparatus such as a lithography exposure apparatus (as discussed below with reference to  FIG. 15 ) for patterning of a substrate W or it can be subjected to further processing before being used in the apparatus. 
     The body  102  is movable relative to the components of the gas discharge stage  108 . During operation, the position of the body  102  in the XYZ coordinate system  104  can change due to factors that are external to the body  102 . For example, pressure and temperature variations within the gas discharge stage  108  can cause the body  102  to move in the XYZ coordinate system  104 . Another reason for misalignment is an internal change inside the body  102  that leads to a change in the alignment. This can happen, for example, as the electrodes of the energy source  114  age and change shape over the course of their use. Additionally, the wear on the electrodes as well as the geometric modification to the electrodes of the energy source  114  is one reason for having to exchange the body  102  with a new body. Moreover, the body  102  becomes misaligned when it is replaced with a new body  102 . In this case, the new body  102  needs to be properly aligned with the X axis  106 . 
     In the example of  FIGS. 1 and 2A , the body  102  is aligned with the X axis  106 . Alignment between the body  102  and the X axis  106  can be determined based on how well a longitudinal axis Ab of the body  102  is aligned with the X axis  106 . The longitudinal axis Ab of the body  102  is shown in  FIG. 2B . This longitudinal axis Ab can be defined as that axis that intersects two ports  118 ,  120  at ends of the body  102 . The ports  118 ,  120  are transmissive to a light beam  122  (that will form the light beam  110 ) having a wavelength in the ultraviolet range. 
     Referring to  FIGS. 3A-3F , the body  102  of the gas discharge stage  108  can be misaligned relative to the X axis  106  in one or more manners. For example, in  FIG. 3A , the body  102  is rotated out of alignment about the Y axis and its longitudinal axis Ab is not aligned with the X axis  106 . In  FIG. 3B , the body  102  is rotated out of alignment about the Z axis and its longitudinal axis Ab is not aligned with the X axis  106 . And, in  FIG. 3C , the body  102  is rotated out of alignment about the X axis. In this case, the longitudinal axis Ab is shifted along the X axis  106 . If the body  102  is configured to rest on a platform, then it is being held up by gravity and the plane of the earth is the XY plane. In this situation, a common misalignment is that shown in  FIG. 3B  in which the body  102  is rotated out of alignment about the Z axis. 
     In  FIG. 3D , the body  102  is translated out of alignment along the Y axis, and the longitudinal axis Ab is shifted from the X axis  106  along the Y axis. In  FIG. 3E , the body  102  is translated out of alignment along the Z axis, and the longitudinal axis Ab is shifted from the X axis  106  along the Z axis. And in  FIG. 3F , the body  102  is translated out of alignment along the X axis  106 , and the longitudinal axis Ab is shifted along the X axis  106 . If the body  102  is configured to rest on the platform, and is being held up by gravity and the plane of the earth is the XY plane, then a common misalignment that has a relatively larger impact on efficiency of the gas discharge stage  108  is that shown in  FIG. 3D  in which the body  102  is translated along the Y axis. 
     It is possible for the body  102  to be misaligned in more than one way, and thus it could be both translated and rotated, translated along more than one axes, or rotated about more than one axes. 
     Certain misalignments to the body  102  can have a different impact on the efficiency and operation of the gas discharge stage  108 . Moreover, some adjustments may be more accessible or feasible to modify. For example, translation along the Y axis (shown in  FIG. 3D ) and rotation about the Z axis (shown in  FIG. 3B ) can be performed relatively easily and thus, their impact on the efficiency and operation of the gas discharge stage  108  can be tracked. Thus, in this example, the apparatus  100  determines a translation of the body  102  along the Y axis and determines a rotational value (angle) of the body  102  about the Z axis. It is possible for the apparatus  100  to determine a translation of the body  102  along either or both of the other two axes and a rotational value about either or both of the other two axes. 
     The position of the body  102  or misalignment of the body  102  relative to the X axis  106  has an impact on the efficiency at which the gas discharge stage  108  operates. If the body  102  is misaligned relative to the X axis  106 , this can lead to inefficiency in the operation of the gas discharge stage  108 , and this can result in reduced quality in the light beam  110 . For example, the path of the light beam  110  coincides with the X axis  106 , and the X axis  106  is determined based on apertures associated with optical components  140 ,  142 . The energy source  114  (which includes the electrodes) that is fixed to the body  102  supplies the energy to the cavity  112  to pump the gas with an electric discharge. The pumping of the gas with the energy source  114  produces a plasma state of the gas. Moreover, when this plasma state aligns with the X axis  106  (which occurs when the body  102  is properly aligned with the X axis  106 ), there is efficient coupling between the resonator cavity (which is formed by the components  140 ,  142  and defined along the X axis  106 ) and the plasma state, and the light beam  110  parameters are improved. On the other hand, when this plasma state is misaligned from the X axis  106  (which occurs when the body  102  is misaligned from the X axis  106 ), there is inefficient coupling between the resonator cavity and the plasma state, and the light beam  110  parameters suffer. For example, the efficiency of operation of the gas discharge stage  108  drops. In this scenario, then more energy is needed to supply to the body  102  (for example, by way of an energy source  114 ) in order to maintain performance parameters of the light beam  110 . 
     As another example, in a dual-stage design that is discussed below with respect to  FIG. 12 , misalignment of the body  102  in a first gas discharge stage  1272  results in lower efficiency of that first gas discharge stage  1272 , which leads to a reduced performance in a second gas discharge stage  1273  that receives the light beam  1273  output from the first gas discharge stage  1272 . This, in turn, causes the operation of the second gas discharge stage  1273  to suffer unless changes are made to operate the second gas discharge stage  1273 . 
     The apparatus  100  provides a quantifiable metrology for this alignment, as well as a fast and accurate direct measure of the position of the body  102  relative to the X axis  106  not previously provided. Moreover, the apparatus  100  determines the position of the body  102  relative to the X axis  106  without having to rely on slow and inaccurate measures of the performance of the gas discharge stage  108 . 
     In particular, the apparatus  100  determines the position of the body  102  relative to the XYZ coordinate system  104  using a plurality of direct measurements of the body  102 , as discussed next. 
     In some implementations, the apparatus  100  can operate to determine the position of the body  102  during use of the gas discharge stage  108  in which the light beam  110  is being produced. In other implementations, the apparatus  100  can operate to determine the position of the body  102  after the body  102  is initially installed in the system, but before it is used to produce the light beam  110  for use by the apparatus. 
     The apparatus  100  includes a sensor system  124 , the output of which is used to determine the position of the body  102  relative to the X axis  106 . The sensor system  124  includes at least two sensors  124   a  and  124   b  that provide for the direction measurements of the body  102 . While two sensors  124   a  and  124   b  are shown in  FIG. 1 , it is possible for the sensor system  124  to have more than two sensors. Each sensor  124   a ,  124   b  is configured to measure a physical aspect of a respective distinct region  126   a ,  126   b  of the body  102  of the gas discharge stage  108  relative to that sensor  124   a ,  124   b.    
     The apparatus  100  includes a control apparatus  128  in communication with each of the sensors  124   a ,  124   b  of the sensor system  124 . The control apparatus  128  is configured to analyze the measured physical aspects from the sensors  124   a ,  124   b  to thereby determine a position of the body  102  of the gas discharge stage  108  relative to the X axis  106 . 
     The body  102  can be any shape configured to house, within the cavity  112 , a gas mixture that includes a gain medium. Optical amplification occurs in the gain medium when enough energy is provided by the energy source  114  to form the plasma state. The gas mixture can be any suitable gas mixture configured to produce an amplified light beam (or laser beam) around the required wavelengths and bandwidth. For example, the gas mixture can include argon fluoride (ArF), which emits light at a wavelength of about 193 nm, or krypton fluoride (KrF), which emits light at a wavelength of about 248 nm. 
     Moreover, an optical feedback mechanism can be arranged or configured relative to the body  102  to provide an optical resonator, as discussed in detail below. 
     The energy source  114  can include two elongated electrodes that extend in the cavity  112  and are fixed to the body  102 . Current supplied to the electrodes causes an electromagnetic field to generate within the cavity  112 , the electromagnetic field providing the energy needed to the gain medium to form the plasma state in which optical amplification occurs. The body  102  can also house a fan that circulates the gas mixture between the electrodes. 
     The body  102  is made of a rigid and non-reactive material such as a metal alloy (stainless steel). The body  102  can be of any suitable geometry, and the geometry is determined by the arrangement of the electrodes as well as the ports  118 ,  120 . The body  102  can have a cuboid shape or a cube shape. As shown in  FIG. 2A , the body  102  has a cuboid shape with two flat parallel surfaces  130   x ,  131   x  that are intersected by the X axis  106  and four flat surfaces  132   z ,  133   z ,  134   y ,  135   y  extending between the flat surfaces  130   x ,  131   x . The surfaces  132   z ,  133   z  are parallel with each other and are intersected by the Z axis and the surfaces  134   y ,  135   y  are parallel with each other and are intersected by the Y axis. In this example, the regions  126   a ,  126   b  are on the surface  134   y . In other implementations, the regions  126   a ,  126   b  could be on other surfaces or several different surfaces of the body  102 . 
     The ports  118 ,  120  on the body  102  are transmissive to the light beam  122  that forms the light beam  110 . Thus, the ports  118 ,  120  are transmissive to light having a wavelength in the ultraviolet range. The ports  118 ,  120  can be made of a rigid substrate such as fused silica or calcium fluoride that can be coated with anti-reflective material. The ports  118 ,  120  can have flat surfaces that interact with the light beam  122 . Because the cavity  112  of the body  102  holds or retains the gas mixture, the body  102  needs to be enclosed or sealed, and it can be hermetically sealed. Thus, the ports  118 ,  120  are also hermetically sealed in respective openings of the body  102  to ensure that gas mixture does not leak out of the body  102  at the seam between a port and the body  102 . 
     In some implementations, the X axis  106  and the XYZ coordinate system  104  are defined by the design of the gas discharge stage  108 . In particular, the X axis  106  is defined as that line that passes through two apertures within the gas discharge stage  108 . These two apertures can be positioned adjacent respective optical components  140 ,  142  that interact with the body  102  in the gas discharge stage  108 . In this way, the optical components  140 ,  142  and their apertures define the X axis  106  (and therefore the XYZ coordinate system  104 ). Moreover, these optical components  140 ,  142  define the optical resonator for forming the light beam  110 . 
     In some implementations, the optical components  140 ,  142  can form the optical feedback mechanism to provide an optical resonator and thereby output the light beam  110  from the light beam  122 . Thus, when the body  102  of the gas discharge stage  108  is within a range of acceptable positions, the energy source  114  supplies energy to the cavity  112  of the body  102 , and the optical components  140 ,  142  are aligned, the light beam  122  is generated. 
     In some implementations, the optical component  140  can be a spectral feature apparatus that receives a pre-cursor light beam  121  and enables fine tuning of spectral features of the light beam  122  by adjusting the spectral features of the pre-cursor light beam  121 . Spectral features that can be tuned using a spectral feature apparatus include the center wavelength and the bandwidth of the light beam  122 . The spectral feature apparatus includes a set of optical features or components arranged to optically interact with the pre-cursor light beam  121 . The optical components of the spectral feature apparatus include, for example, a dispersive optical element, which can be a grating, and a beam expander made of a set of refractive optical elements, which can be prisms. The optical component  142  can be an output coupler that allows the extraction of the light beam  122  from the intracavity beam. The output coupler can include a partially reflective mirror, allowing a certain portion of the intracavity beam to transmit through as the light beam  122 . The gas discharge stage  108  can also include a beam expander configured to interact with the light beam  122  as it travels between the output coupler (the optical component  142 ) and the cavity  112 . 
     In other implementations, the optical component  140  can be beam turning device and the optical component  142  can be a beam coupler. The beam turning device includes an arrangement of optics that is configured to receive the pre-cursor light beam  121  exiting the body  102  of the gas discharge stage  108  through the port  118  and changing a direction of the light beam  121  so that the light beam  121  re-enters the body of the gas discharge stage through the first port  118 . 
     As discussed above, each sensor  124   a ,  124   b  in the sensor system  124  is configured to measure a physical aspect of the body  102  of the gas discharge stage  108  relative to that sensor  124   a ,  124   b . Each sensor  124   a ,  124   b  can measure, as the physical aspect of the body  102 , a distance from the sensor  124   a ,  124   b  to the body  102  of the gas discharge stage  108 . 
     In various implementations, the sensors  124   a ,  124   b  are mounted to a mechanically stable structure of the gas discharge stage  108 , where the structure holds the sensors  124   a ,  124   b  in fixed positions relative to each other and to components that define the X axis  106 , or that define the XYZ coordinate system  104 . For example, the sensors  124   a ,  124   b  can be mounted on an optical table or on to other stable mechanical mounts that are rigidly coupled to optical elements (for example, optical elements  140 ,  142 ) that delineate the X axis  106 , which is the optical axis of the system. 
     For example, each sensor  124   a ,  124   b  is configured to be fixedly mounted relative to XYZ coordinate system  104 . Thus, during measurements, the sensors  124   a ,  124   b  are fixed relative to the XYZ coordinate system  104 . Additionally, each sensor  124   a ,  124   b  is configured to be fixed at a distance from the other sensor  124   b ,  124   a  when it is fixedly mounted relative to the XYZ coordinate system  104 . Thus, the distance d(ss) between the sensors  124   a ,  124   b  is fixed during operation and measurements. The distance d(ss) between the sensors  124   a ,  124   b  is great enough along the X axis  106  so that it is possible for the control apparatus  128  to determine a rotation about the Z axis ( FIG. 3B ) based on the output from the sensors  124   a ,  124   b . In particular, relative changes between the output from each of the sensors  124   a ,  124   b  can be used to determine the rotation about the Z axis ( FIG. 3B ). The sensors  124   a ,  124   b  have a measurement resolution that is fast enough for enabling alignment. For example, a temporal resolution of 1 second (s) can be fast enough; or a temporal resolution less than 1 s (for example, 0.1 s) can be fast enough. 
     In some implementations, each sensor  124   a ,  124   b  includes a displacement sensor. The displacement sensor can be an optical displacement sensor, a linear proximity sensor, an electromagnetic sensor, or an ultrasonic displacement sensor. 
     Each sensor  124   a ,  124   b  can be a contact-less sensor, which means that it does not make contact with the body  102 . In such a design in which the sensor  124   a ,  124   b  is contact-less, the measurement itself does not noticeably (for example, greater than 1μ) displace the body  102 , because any such displacement could impact the performance of the gas discharge stage  108 . 
     Any contact-less metrology with a suitable resolution (for example, a resolution that is better than 10 μm (that is, less than 10 μm)) is suitable for this application. One example of a contact-less sensor is a laser displacement sensor, which is an off-the-shelf product that includes a laser light source and a photodiode array. The laser light source of each sensor  124   a ,  124   b  shines light on the surface  134   y  of the body  102 ; the light is reflected back toward the respective sensor  124   a ,  124   b ; and the location on the diode array at which the reflected light lands corresponds to a displacement of surface  134   y  of the body  102 . 
     In other implementations, the sensors  124   a ,  124   b  are contact sensors, which come into minimal contact with the body  102  at the respective regions  126   a ,  126   b . For example, the sensors can be electromechanical devices used to convert mechanical motion of the body  102  into a variable electrical current, voltage, or electric signals. An example of such a sensor is a linear variable displacement transducer (LVDT), which is a device that provides a voltage output quantity related to the characteristic (position) being measured. 
     The control apparatus  128  includes one or more of digital electronic circuitry, computer hardware, firmware, and software. The control apparatus  128  includes memory, which can be read-only memory and/or random-access memory. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including, by way of example, semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. The control apparatus  128  can also include one or more input devices (such as a keyboard, touch screen, microphone, mouse, hand-held input device, etc.) and one or more output devices (such as a speaker or a monitor). 
     The control apparatus  128  includes one or more programmable processors, and one or more computer program products tangibly embodied in a machine-readable storage device for execution by a programmable processor. The one or more programmable processors can each execute a program of instructions to perform desired functions by operating on input data and generating appropriate output. Generally, the processor receives instructions and data from memory. Any of the foregoing may be supplemented by, or incorporated in, specially designed ASICs (application-specific integrated circuits). 
     The control apparatus  128  includes a set of modules, with each module including a set of computer program products executed by one or more processors such as the processors. Moreover, any of the modules can access data stored within the memory. Each module can receive data from other components and then analyze such data as needed. Each module can be in communication with one or more other modules. 
     Although the control apparatus  128  is represented as a box (in which all of its components can be co-located), it is possible for the control apparatus  128  to be made up of components that are physically remote from each other. For example, a particular module can be physically co-located with the sensor system  124  or a particular module can be physically co-located with another component. 
     Referring to  FIG. 4 , in some implementations, the sensors  124   a ,  124   b  are arranged to interact with the surface  134   y . In these implementations, the sensors  124   a ,  124   b  are mounted on a platform  144 , which supports the weight of and maintains the stability of the sensors  124   a ,  124   b . In  FIG. 4 , the platform  144  is a three-legged frame or stand.  FIG. 5  shows a side cross-sectional view of the arrangement. In  FIG. 5 , the platform  144  is a basic platform base  544  on which the sensors  124   a ,  124   b  are placed. The platform base  544  can be integrated into a frame or other component fixed within the gas discharge stage  108 . The sensors  124   a ,  124   b  can be repositionable; that is, the sensors  124   a ,  124   b  can be placed at any location relative to any two regions of the body  102  and then moved to another location relative to two other regions of the body  102 . 
     As shown in  FIG. 5 , the energy source  114  is a pair of electrodes  514 A,  514 B arranged in the cavity  112 . The electrodes  514 A,  514 B extend along the X axis  106 . 
     Referring also to  FIG. 6 , each sensor  124   a ,  124   b  measures a distance or displacement from the respective region  126   a ,  126   b  of the surface  134   y  of the body  102 . For example, the sensor  124   a  measures a displacement d(a) from the sensor  124   a  to the region  126   a  of the surface  134   y  and the sensor  124   b  measures a displacement d(b) from the sensor  124   b  to the region  126   b  of the surface  134   y . Additionally, the calculation performed by the control apparatus  128  requires a set of reference displacements, D(a) and D(b). The reference displacements D(a) and D(b) are measurements taken by respective sensors  124   a ,  124   b  during a time when the body  102  is properly aligned with the X axis  106  and the XYZ coordinate system  104  (this is shown by the dashed line box labeled as  102 _ ref . In some implementations, proper alignment between the body  102  and the X axis  106  can be assumed to occur when the gas discharge stage  108  is operating at its highest efficiency (for example, when the most energy input by way of the energy source  114  is converted into an energy in the light beam  110 ). 
     The values of the displacement d(a) and d(b) output from the respective sensors  124   a ,  124   b  are not necessarily linearly independent of each other. This means that the displacement of one, such as d(a), can be written in terms of the other, such as d(b). It is possible to transform such linearly dependent values into linearly independent values with the use of additional information. In this case, the distance L taken along the X axis  106  between the regions  126   a ,  126   b  when the body  102  is aligned with the X axis  106  can be used to provide this transformation. Specifically, the distance L, along with d(a), and d(b) can be used to determine the relative position of the center of the body  102  (given by R) and the relative angular orientation θ of the body about the Z axis, as discussed next. 
     The relative displacements d′(a) and d′(b) are given by: 
         d ′( a )= D ( a )− d ( a ); and
 
         d ′( b )= D ( b )− d ( b ).
 
     And, the relative displacement R of the body  102  is defined as half the sum of the relative displacements d′(a) and d′(b), as follows: 
     
       
         
           
             R 
             = 
             
               
                 
                   
                     
                       d 
                       ′ 
                     
                      
                     
                       ( 
                       a 
                       ) 
                     
                   
                   + 
                   
                     
                       d 
                       ′ 
                     
                      
                     
                       ( 
                       b 
                       ) 
                     
                   
                 
                 2 
               
               . 
             
           
         
       
     
     The relative angular orientation θ can be approximated as a ratio of the difference between the relative displacements d′(a) and d′(b) and the distance L, as follows: 
     
       
         
           
             θ 
             ∼ 
             
               
                 
                   
                     
                       d 
                       ′ 
                     
                      
                     
                       ( 
                       a 
                       ) 
                     
                   
                   - 
                   
                     
                       d 
                       ′ 
                     
                      
                     
                       ( 
                       b 
                       ) 
                     
                   
                 
                 L 
               
               . 
             
           
         
       
     
     The small angle approximation is invoked because L&gt;&gt;|d′(a)−d′(b)|. For example, L is on the order of hundreds of millimeters (mm) (for example, 0.5-0.7 meters) while |d′(a)−d′(b)| is on the order of a mm. 
     Referring to  FIG. 7 , in some implementations, an apparatus  700  is designed to not only determine the position of the three-dimensional body  102 , but also to move the body  102  in the XYZ coordinate system  104 . To this end, the apparatus  700  is substantially similar to the apparatus  100 , and includes all of the components detailed above and shown in  FIG. 1  and a discussion of those components is not repeated here. 
     The apparatus  700  further includes an actuation system  754  physically coupled to the body  102  of the gas discharge stage  108 , the actuation system  754  being configured to adjust a position of the body  102  of the gas discharge stage  108  within the XYZ coordinate system  104 . The control apparatus  128  is in communication with the actuation system  754  and is configured to provide a signal to the actuation system  754  based on the output from the sensor system  124 . In particular, the control apparatus  128  determines whether the position of the body  102  of the gas discharge stage  108  should be modified based on the output from the sensor system  124  and the control apparatus  128  determines how to adjust one or more signals to the actuation system  754  based on this determination. 
     The actuation system  754  includes a plurality of actuators  754   a ,  754   b , etc., with each actuator configured to be in physical communication with a respective region  756   a ,  756   b , etc. of the body  102  of the gas discharge stage  108 . While the actuation system  754  is shown as being in physical communication with the surface  134   y , it is possible for the actuation system  754  to include one or more actuators that are in physical communication with one or more other surfaces of the body  102 . Moreover, it is not necessary for the actuation system  754  to be in physical communication with the same surface or surfaces that are measured by the sensor system  124 . 
     Each actuator  754   a ,  754   b  can include one or more of an electro-mechanical device, a servomechanism, an electrical servomechanism, a hydraulic servomechanism, and/or a pneumatic servomechanism. The various motions imparted to the regions  756   a ,  756   b  are used to adjust the position of the body  102  along any of the rotational directions detailed above with respect to  FIGS. 3A-3C  and any of the translational directions detailed above with respect to  FIGS. 3D-3F . 
     Referring to  FIG. 8 , in some implementations, each respective region  756   a ,  756   b  is associated with a rotational mount  857   a ,  857   b  attached to the surface  134   y . The rotational mount  857   a ,  857   b  is actuated by rotation, and the rotation is converted into a translational motion. Thus, for example, rotation of the mount  857   a  in a clockwise direction translates a rod that is fixed to the region  756   a  along the −Y direction (which causes the region  756   a  to translate along the −Y direction). And, while rotation of the mount  857   a  in a counterclockwise direction translates the rod that is fixed to the region  756   a  along the Y direction (which causes the region  756   a  to translate along the Y direction). By rotating both rotational mounts  857   a ,  857   b  at the same time and synchronously (in the same direction), the body  102  is translated along the Y axis, as shown in  FIG. 3D . Rotation of the mounts  857   a ,  857   b  at the same time and asynchronously (in opposite directions) causes the body  102  to be rotated about the Z axis, as shown in  FIG. 3B . For example, rotating one mount  857   a  clockwise while rotating the other mount  857   b  counterclockwise causes the region  756   a  to be translated along the −Y direction and the region  756   b  to be translated along the Y direction and this causes the rotation of the body  102  about the Z axis. It is possible to do both a synchronous and an asynchronous rotation of the mounts  857   a ,  857   b  to impart both a translation along the Y axis and a rotation about the Z axis to the body  102 . In this example, the rotational mount  857   a ,  857   b  at the respective region  756   a ,  756   b  is controlled, respectively, by the actuator  754   a ,  754   b . The actuator  754   a ,  754   b  can be any device that rotates the mount respective mount  857   a ,  857   b . Moreover, the rotation of the mount  857   a ,  857   b  can be in incremental steps. 
     Referring to  FIG. 9 , in some implementations, an apparatus  900  is designed to not only determine the position of the three-dimensional body  102  (using the sensor system  124 ), and to adjust a position of the body  102  (using the actuation system  754 ), but also to measure or monitor performance or performance characteristics of the gas discharge stage  108 . As discussed above, the alignment of the body  102  impacts or changes the performance of the gas discharge stage  108 , and thus, it is expected that the misalignment of the body  102  will reduce the performance. To this end, the apparatus  900  is substantially similar to the apparatus  700 , and includes all of the components detailed above and shown in  FIG. 1  and a discussion of those components is not repeated here. 
     The apparatus  900  further includes a measurement system  960  arranged to measure performance parameters of the light beam  110 . Examples of performance parameters include energy E of the light beam  110 , a spectral feature such as bandwidth or wavelength of the light beam  110 , and a dose of the light beam  110  at the apparatus (such as the lithography exposure apparatus). The control apparatus  128  is in communication with the measurement system  960 . In this way, the control apparatus  128  can find the best or improved position or alignment of the body  102  that provides the best or improved performance parameter or parameters. Because the performance of the gas discharge stage  108  is measured based on many different parameters, a parameter space that includes a plurality of parameters can be considered by the control apparatus  128  in making the determination. For example, the control apparatus  128  could perform an adaptive control for adjusting the position of the body  102  that provides a set of performance parameters of the light beam  110  that fall within acceptable ranges. 
     The measurement system  960  can include one or more measurement devices, with each measurement device positioned relative to the light beam  110  and to measure a specific performance parameter. The measurement system  960  can include as measurement device, an energy monitor for measuring the energy of the light beam  110 . The measurement system  960  can include as a measurement device, a spectral feature analysis device configured to measure the spectral feature (bandwidth or wavelength) of the light beam  110 . In these cases, the measurement devices can be devices that are already included in the gas discharge stage  108  or are a part of an analysis module that is already present to measures these aspects of the light beam  110 . For example, an analysis module can include a wavemeter and a bandwidth meter that includes, among other components, an etalon with an imaging lens, as well as beam homogenization optics. The analysis module can also include a photodetector module (PDM) that monitors the energy of the light beam  110 , and provides a fast photodiode signal for diagnostic and timing purposes. In some implementation, one or more energy sensors can be placed anywhere along the path of the light beam  110 . The control apparatus  128  can estimate an efficiency of the gas discharge stage  108  based on a ratio of this measured energy to an energy input through the energy source  114  (which can be a voltage applied to the electrodes of the energy source  114 ). 
     The measurement devices can be associated with diagnostics within a spectral feature adjuster (such as spectral feature adjuster  1275  shown in  FIG. 12 ). The spectral feature adjuster  1275  receives a pre-cursor light beam  1276  from body  102  of the gas discharge stage  1272  to enable fine tuning of spectral parameters such as the center wavelength and the bandwidth of the light beam  1274  at relatively low output pulse energies. It is possible to monitor the beam expansion optics within the spectral feature adjuster  1272  to track the spectral feature (such as the bandwidth) of the light beam  110  because the beam expansion within the spectral feature adjuster  1275  directly correlates to the bandwidth of the light beam  1274  (and therefore the light beam  110 ). 
     The measurement system  960  can include a measurement device configured to measure the dose of the light beam  110  at the lithography exposure apparatus. The measurement system  960  can include a measurement device configured to measure the repetition rate at which the pulses of the light beam  110  are produced. The measurement system  960  can include a measurement device configured to measure the duty cycle of the light beam  110 . These measurement devices can include a laser energy detector (such as a photodetector). In this example, the dose can be estimated as the sum of the energy over a fixed number of pulses detected by the laser energy detector; the repetition rate can be estimated as an inverse of the time between any two pulses (usually fixed) detected by the laser energy detector; and the duty cycle can be arbitrarily defined as the number of pulses fired in a time frame (such as the most recent two minutes) divided by a maximum repetition rate times the time that passed in the time frame (for example, two minutes). The measurement devices can also include a timer in order for the control apparatus  128  to compute the repetition rate and the duty cycle from the output. 
     The control apparatus  128  can send independent signals to actuators  754   a ,  754   b , read independent measurements from each of the sensors  124   a ,  124   b , and read independent measurements from each of the measurement devices in the measurement system  960 . 
     In operation, the control apparatus  128  analyzes both the position of the body  102  of the gas discharge stage  108  (it receives from the sensor system  124 ) and the one or more measured performance parameters of the light beam  110  (it receives from the measurement system  960 . The control apparatus  128  determines whether a modification to the position of the body  102  of the gas discharge stage  108  would improve one or more of the measured performance parameters. The control apparatus  128  can perform a process that maps the position space and determines an optimal position that achieves the best performance parameter (or parameters). 
     Referring to  FIG. 11 , an example of an alignment feedback control process is shown in a topographic map  1162  in which the position of the body  102  can be rotated about the Z axis ( FIG. 3B ), translated along the Y axis ( FIG. 3D ), or both. The map  1162  shows a value of a performance parameter (such as energy) relative to values of the rotation about the Z axis ( 1162 Z) and values of the translation along the Y axis ( 1162 Y). Because the map is a topographic map, the value of the energy is listed on each line. The shape of the three dimensional surface that corresponds to the map  1162  is depicted by these contour lines, and the relative spacing of the lines indicating the relative slope of the three dimensional surface. 
     In this example, the control apparatus  128  receives positions measured by sensors  124   a ,  124   b  while controlling the actuators  754   a ,  754   b , in order to generate the map  1162  of the energy of the light beam  110 . Higher values of the energy represent more efficient energy values. Thus, a value of the position of the body  102  along the Y axis and a rotational angle of the body  102  about the Z axis is determined that provides the most efficient energy value of the light beam  110 . In some implementations, the feedback control process can be configured to intelligently find the peak of the map (and therefore the peak of the energy) without mapping the entire space. For example, the search path  1164  shows one specific way to modify the position of the body  102  along the Y axis and to rotate the body  102  about the Z axis to obtain the most efficient energy value of the light beam  110 . 
     The feedback control process can be a non-linear optimization problem that finds the best solution (the peak of the map or peak of the energy) from all feasible solutions. For example, the process can be a gradient ascent, which is a first-order iterative optimization algorithm for finding the maximum of a function. 
     Referring to  FIG. 12 , in some implementations, the gas discharge stage  108  can be incorporated into a dual-stage light source  1270 . The light source  1270  is designed as a pulsed light source that produces an amplified light beam  1271  of optical pulses. The light source  1270  includes a first gas discharge stage  1272  and a second gas discharge stage  1273 . The second gas discharge stage  1273  is optically in series with the first gas discharge stage  1272 . In general, the first stage  1272  includes a first gas discharge chamber housing an energy source and containing a gas mixture that includes a first gain medium. The second gas discharge stage  1273  includes a second gas discharge chamber housing an energy source and containing a gas mixture that includes a second gain medium. 
     The first stage  1272  includes a master oscillator (MO) and the second stage  1273  includes a power amplifier (PA). The MO provides a seed light beam  1274  to the PA. The master oscillator typically includes a gain medium in which amplification occurs and an optical feedback mechanism such as an optical resonator. The power amplifier typically includes a gain medium in which amplification occurs when seeded with the seed light beam  1274  from the master oscillator. If the power amplifier is designed as a regenerative ring resonator then it is described as a power ring amplifier (PRA) and in this case, enough optical feedback can be provided from the ring design. 
     A spectral feature adjuster  1275  receives a pre-cursor light beam  1276  from the master oscillator of the first stage  1272  to enable fine tuning of spectral parameters such as the center wavelength and the bandwidth of the light beam  1274  at relatively low output pulse energies. The power amplifier receives the light beam  1274  from the master oscillator and amplifies this output to attain the necessary power for output to use in photolithography by the lithography exposure apparatus. 
     The master oscillator includes a discharge chamber having two elongated electrodes, a laser gas that serves as the gain medium, and a fan circulating the gas between the electrodes. A laser resonator is formed between the spectral feature adjuster  1275  on one side of the discharge chamber, and an output coupler  1277  on a second side of the discharge chamber to output the seed light beam  1274  to the power amplifier. 
     The power amplifier includes a power amplifier discharge chamber, and if it is a regenerative ring amplifier, the power amplifier also includes a beam reflector or beam turning device that reflects the light beam back into the discharge chamber to form a circulating path. The power amplifier discharge chamber includes a pair of elongated electrodes, a laser gas that serves as the gain medium, and a fan for circulating the gas between the electrodes. The seed light beam  1274  is amplified by repeatedly passing through the power amplifier. The second stage  1273  can include a beam modification optical system that provides both a way (for example, a partially-reflecting mirror) to in-couple the seed light beam  1274  and to out-couple a portion of the amplified radiation from the power amplifier to form the amplified light beam  1271 . 
     The laser gas used in the discharge chambers of the master oscillator and the power amplifier can be any suitable gas for producing a laser beam around the required wavelengths and bandwidth. For example, the laser gas can be argon fluoride (ArF), which emits light at a wavelength of about 193 nm, or krypton fluoride (KrF), which emits light at a wavelength of about 248 nm. 
     In general, the light source  1270  can also include a control system  1278  in communication with the first stage  1272  and the second stage  1273 . The control system  1278  includes one or more of digital electronic circuitry, computer hardware, firmware, and software. The control system  1278  includes memory, which can be read-only memory and/or random-access memory. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including, by way of example, semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks. The control system  1278  can also include one or more input devices (such as a keyboard, touch screen, microphone, mouse, hand-held input device, etc.) and one or more output devices (such as a speaker or a monitor). 
     The control system  1278  includes one or more programmable processors, and one or more computer program products tangibly embodied in a machine-readable storage device for execution by a programmable processor. The one or more programmable processors can each execute a program of instructions to perform desired functions by operating on input data and generating appropriate output. Generally, the processor receives instructions and data from memory. Any of the foregoing may be supplemented by, or incorporated in, specially designed ASICs (application-specific integrated circuits). 
     The control system  1278  includes a set of modules, with each module including a set of computer program products executed by one or more processors such as the processors. Moreover, any of the modules can access data stored within the memory. Each module can receive data from other components and then analyze such data as needed. Each module can be in communication with one or more other modules. 
     Although the control system  1278  is represented as a box (in which all of its components can be co-located), it is possible for the control system  1278  to be made up of components that are physically remote from each other. For example, a particular module can be physically co-located with the light source  1270  or a particular module can be physically co-located with the spectral feature adjuster  1275 . Moreover, the control system  1278  can be a module incorporated into the control apparatus  128 . 
     The first gas discharge stage  1272  can correspond to the gas discharge stage  108 . The second gas discharge stage  1273  can correspond to the gas discharge stage  108 . Or, each of the first gas discharge stage  1272  and the second gas discharge stage  1273  can correspond to the gas discharge stage  108 . Thus, the apparatus  100 ,  700 , or  900  described above can be designed to determine a position of a body in the first gas discharge stage  1272 ; to adjust a position of the body in the first gas discharge stage  1272 ; and to base the adjustment on the position on monitored performance parameters associated with the first gas discharge stage  1272 . Additionally, or alternatively, the apparatus  100 ,  700 , or  900  described above can be designed to determine a position of a body in the second gas discharge stage  1273 ; to adjust a position of the body in the second gas discharge stage  1273 ; and to base the adjustment on the position on monitored performance parameters associated with the second gas discharge stage  1273 . The adjustment and optimization of the position of the body in the second gas discharge stage  1273  can be performed simultaneously with the adjustment and optimization of the position of the body in the first gas discharge stage  1272 . Moreover, the performance parameters associated with the first gas discharge stage  1272  can be measured by measuring performance parameters of the seed light beam  1274  or of the amplified light beam  1271  (which is produced from the seed light beam  1273 ). The performance parameters associated with the second gas discharge stage  1273  can be measured by measuring performance parameters of the amplified light beam  1271 . 
     If both the first gas discharge stage  1272  and the second gas discharge stage  1273  are under the control of the apparatus  100 ,  700 , or  900 , then a single control apparatus  128  can be configured to communicate with both sensor systems  124 , both actuation systems  754 , and both measurement systems  960 . 
     Referring to  FIG. 13 , a metrology kit  1380  includes the components that make up the apparatus (such as the apparatus  900 ). A metrology kit  1380  is useful because it does not need to be fixed or associated with a single gas discharge stage  108  and can be moved from one gas discharge stage  108  to another. Moreover, because of this, it is possible to use the metrology kit  1380  for more than one gas discharge stage  108  instead of setting up an apparatus  900  for each gas discharge stage  108 , which is more costly. 
     The metrology kit  1380  includes a sensor system  1324  including a plurality of sensors  1324   a ,  1324   b , . . .  1324   i  (where i is any integer greater than 1). Each sensor  1324   a ,  1324   b ,  1324   i  is configured to measure a physical aspect of a three-dimensional body  102  relative to that sensor. The metrology kit  1380  includes a measurement system  1360  including at least one measurement device  1360   a ,  1360   b , . . .  1360   j  (where j is any integer). Each measurement device  1360   a ,  1360   b , . . .  1360   j  is configured to measure a performance parameter of the light beam  110 . The metrology kit  1380  includes an actuation system  1354  including a plurality of actuators  1354   a ,  1354   b , . . .  1354   k  configured to physically couple to the body  102 . 
     The metrology kit  1380  includes a control apparatus  1328  configured to be in communication with the sensor system  1324 , the measurement system  1360 , and the actuation system  1354 . The control apparatus  1328  includes a sensor processing module  1381  configured to interface with the sensor system  1324  and receive sensor information from the sensor system  1324 . The control apparatus  1328  includes a measurement processing module  1382  configured to interface with the measurement system  1360  and receive measurement information from the measurement system  1360 . The control apparatus  1329  includes an actuator processing module  1383  configured to interface with the actuation system  1354 . 
     The control apparatus  1328  can also include a light source processing module  1384  configured to interface with the gas discharge stage  108  having the three-dimensional body  102 . 
     The control apparatus  1328  can also include an analysis processing module  1385  in communication with the sensor processing module  1381 , the measurement processing module  1382 , the actuator processing module  1383 , and the light source processing module  1384 . The analysis processing module  1385  is configured to, in use, instruct the light source processing module  1384  to adjust one or more characteristics of the gas discharge stage  108  and analyze the sensor information (from the sensor system  1324 ) and the measurement information (from the measurement system  1360 ) and determine an instruction to the actuator processing module  1383  based on the adjusted characteristics of the gas discharge stage  108 . 
     The metrology kit  1380  is modular such that it is configured to be operably connected and disconnected from one or more gas discharge stages  108 . Each gas discharge stage  108  includes a respective three-dimensional body  102  defining a cavity  112  that generates a respective light beam  110 . Thus, when the position of the body  102  needs to be optimized, the metrology kit  1380  can be installed to the gas discharge chamber  108 . For example, the sensors  1324   a ,  1324   b , . . .  1324   i  can be mounted at respective locations relative to their respective region of the body  102 . The measurement devices  1360   a ,  1360   b , . . .  1360   j  can be placed at locations to measure the performance parameters of the light beam  110 . The actuators  1354   a ,  1354   b , . . .  1354   k  can be physically coupled to the respective regions of the body  102 . And, the sensor system  1324 , the measurement system  1360 , and the actuation system  1354  can be connected to or placed in communication with the control apparatus  1328 . After the body  102  has been optimized, the reverse steps for disconnection can be performed. 
     In some implementations, the measurement system  1360  includes, in place of one or more of the measurement devices, one or more measurement interfaces. Each measurement interface is able to be connected to a measurement device that is fixed within the gas discharge stage  108  and also to be connected to the control apparatus  128  in the kit  1380 . 
     Referring to  FIG. 14 , a procedure  1487  is performed by the apparatus  900 . The procedure  1487  can be performed any time a component of the gas discharge stage  108  is moved or replaced, or any time an efficiency of the gas discharge stage  108  drops below an acceptable range. The procedure  1487  is generally performed while the gas discharge stage  108  is offline from the lithography exposure apparatus. 
     The efficiency of the gas discharge stage  108  can be represented by one or more performance parameters of the light beam  110 . Moreover, a set of plural performance parameters can be considered as the parameter space. The parameter space therefore includes a plurality of performance parameters. The procedure  1487  strives to optimize the parameter space. Optimization of the parameter space does not necessarily mean that a particular performance parameter is optimized or that each performance parameter is optimized. Rather, the set or plurality of performance parameters are determined that provide the most efficient operation of the gas discharge stage  108 . As discussed above, examples of performance parameters include the energy E of the light beam  110 , a spectral feature such as the bandwidth or the wavelength of the light beam  110 , the dose of the light beam  110  at the apparatus (such as the lithography exposure apparatus), a repetition rate at which the pulses of the light beam  110  are produced, and a duty cycle of the light beam  110 . 
     The procedure  1487  includes measuring, at each of the plurality of distinct regions  126   a ,  126   b , etc. of the body  102  of the gas discharge stage  108 , a physical aspect of the body  102  at that region ( 1488 ). For example, the sensor system  124  (and in particular, the sensors  124   a ,  124   b , etc.) can measure the physical aspect at each distinct region  126   a ,  126   b , etc. 
     The procedure  1487  includes measuring one or more performance parameters of the light beam  110  that is generated from the gas discharge stage  108  ( 1489 ). For example, the measurement system  960  can measure the one or more performance parameters of the light beam  110 . It is possible for the measurement system  960  to measure only one performance parameter as a representation of the efficiency of the gas discharge stage  108 . Moreover, it is also possible that the measurement system  960  measures a plurality of performance parameters in order to represent the efficiency of the gas discharge stage  108 . Examples of performance parameters that can be measured include the repetition rate of the pulsed light beam  110 , the energy of the pulsed light beam  110 , the duty cycle of the pulsed light beam  110 , and/or a spectral feature of the pulsed light beam  110 . 
     The procedure  1487  includes analyzing the measured physical aspects ( 1490 ) to thereby determine a position of the body in the XYZ coordinate system  104  defined by the X axis  106  defined by the plurality of apertures determined by the optical components  140 ,  142  of the gas discharge stage  108  ( 1491 ). The procedure  1487  also includes analyzing the determined position of the body  102  of the gas discharge stage  108  ( 1492 ) and analyzing the one or more measured performance parameters ( 1493 ). The control apparatus  128  performs the analyses  1490 ,  1492 ,  1493  after receiving the outputs from the measurements  1488  and  1489  and after determining the position of the body  1491 . 
     The procedure  1487  includes determining whether a modification to the position of the body  102  of the gas discharge stage  108  would improve one or more of the measured performance parameters ( 1494 ) and, if it is determined that the modification to the position of the body  102  of the gas discharge stage  108  would improve one or more of the measured performance parameters, then modifying the position of the body  102  of the gas discharge stage  108  ( 1495 ). For an example in which the performance parameter is the energy E of the light beam  110 , the control apparatus  128  can use feedback control, such as what is shown in  FIG. 11 , and make incremental adjustments to the position of the body  102 , then re-measure the performance parameter at  1489  to determine if that adjustment improved the performance parameter ( 1494 ). 
     If it is determined that no modification to the position of the body  102  would improve the one or more measured performance parameters ( 1494 ), then the procedure  1487  ends. In particular, the procedure  1487  has determined the position of the body  102  of the gas discharge stage  108  that optimizes the plurality of measured performance parameters. The optimal position of the body  102  of the gas discharge stage  108  provides an optimal set of values of the performance parameters of the light beam  110 , and the procedure  1487  operates to modify the position of the body  102  of the gas discharge stage  108  to be at this optimal position. 
     The position of the body  102  of the gas discharge stage  108  can be modified ( 1495 ) based on the analysis of the determined position of the body  102  of the gas discharge stage  108  at  1492 . The position of the body  102  of the gas discharge stage  108  can be determined ( 1491 ) by determining one or more of a translation of the body  102  of the gas discharge stage  108  from the X axis  106  and a rotation of the body  102  of the gas discharge stage  108  from the X axis  106 . An example of this determination is described above with reference to  FIG. 6 . 
     As discussed above, the physical aspect of the body  102  at a distinct region of the body  102  can be measured ( 1488 ) by measuring a distance from the corresponding sensor to that region of the body  102 . 
     The procedure  1487  can also include generating the light beam  110  from the gas discharge stage  108  by forming a resonator defined by a beam coupler (such as optical component  142 ) at one side of the body  102  and a beam turning device (such as optical component  140 ) at another side of the body  102 , and generating energy within the gain medium in the cavity  112 . The beam coupler and the beam turning device can also define the X axis  106 . 
     As discussed above, and with reference to  FIG. 15 , the light beam  110  can be used in an apparatus such as a lithography exposure apparatus EX for patterning of a substrate W. In this case, the apparatus  100 ,  700 , or  900  is incorporated into a light source LS that provides an amplified and pulsed light beam LB to the lithography exposure apparatus EX. The light beam LB can correspond to the light beam  110  output from the gas discharge stage  108 . Or, the light beam LB can correspond to a light beam that is formed from the light beam  110  output from the gas discharge stage  108 . Moreover, as discussed above, the gas discharge stage  108  and the apparatus  100 ,  700 , or  900  can be incorporated into a dual-stage light source LS. 
     For example, although connections between the control apparatus  128  and other components of the apparatuses  100 ,  700 ,  900  are shown as lines, the connections between the control apparatus  128  and the other components can be wired connections or wireless connections. 
     The implementations may further be described using the following clauses: 
     1. A light source apparatus comprising: 
     a gas discharge stage including a three-dimensional body defining a cavity that is configured to interact with an energy source, the body including at least two ports that are transmissive to a light beam having a wavelength in the ultraviolet range; 
     a sensor system comprising a plurality of sensors, each sensor is configured to measure a physical aspect of a respective distinct region of the body of the gas discharge stage relative to that sensor; and 
     a control apparatus in communication with the sensor system, and configured to analyze the measured physical aspects from the sensors to thereby determine a position of the body of the gas discharge stage in an XYZ coordinate system defined by an X axis, wherein the X axis is defined by the geometry of the gas discharge stage. 
     2. The light source apparatus of clause  1 , further comprising a measurement system configured to measure one or more performance parameters of a light beam that is generated from the gas discharge stage. 
     3. The light source apparatus of clause  2 , wherein the control apparatus is in communication with the measurement system, and is further configured to: 
     analyze both the position of the body of the gas discharge stage in the XYZ coordinate system and the one or more measured performance parameters of the light beam; and 
     determine whether a modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters. 
     4. The light source apparatus of clause  3 , further comprising an actuation system physically coupled to the body of the gas discharge stage, and configured to adjust a position of the body of the gas discharge stage. 
     5. The light source apparatus of clause  4 , wherein the control apparatus is in communication with the actuation system and is configured to provide a signal to the actuation system based on the determination regarding whether the position of the body of the gas discharge stage should be modified. 
     6. The light source apparatus of clause  5 , wherein the actuation system includes a plurality of actuators, each actuator configured to be in physical communication with a region of the body of the gas discharge stage. 
     7. The light source apparatus of clause  6 , wherein each actuator includes one or more of an electro-mechanical device, a servomechanism, an electrical servomechanism, a hydraulic servomechanism, and/or a pneumatic servomechanism. 
     8. The light source apparatus of clause  1 , wherein the control apparatus is configured to determine the position of the body of the gas discharge stage in the XYZ coordinate system by determining a translation of the body of the gas discharge stage from the X axis or a rotation of the body of the gas discharge stage from the X axis. 
     9. The light source apparatus of clause  8 , wherein the translation of the body of the gas discharge stage from the X axis includes one or more of a translation of the body of the gas discharge stage along the X axis, a translation of the body of the gas discharge stage along a Y axis that is perpendicular with the X axis, and/or a translation of the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. 
     10. The light source apparatus of clause  8 , wherein the rotation of the body of the gas discharge stage from the X axis includes one or more of a rotation of the body of the gas discharge stage about the X axis, a rotation of the body of the gas discharge stage about a Y axis that is perpendicular with the X axis, and/or a rotation of the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. 
     11. The light source apparatus of clause  1 , wherein each sensor is configured to measure as the physical aspect of the body of the gas discharge stage relative to that sensor a distance from the sensor to the body of the gas discharge stage. 
     12. The light source apparatus of clause  1 , wherein the gas discharge stage includes a beam turning device at a first end of the body and a beam coupler at a second end of the body, the beam turning device and the beam coupler intersecting the X axis such that a light beam produced in the gas discharge stage interacts with the beam coupler and the beam turning device. 
     13. The light source apparatus of clause  12 , wherein, when the body of the gas discharge stage is within a range of acceptable positions, the energy source supplies energy to the cavity of the body, and the beam tuning device and beam coupler are aligned, the light beam is generated. 
     14. The light source apparatus of clause  13 , wherein the light beam is an amplified light beam having a wavelength in the ultraviolet range. 
     15. The light source apparatus of clause  12 , wherein the beam turning device is an optical module that includes a plurality of optics for selecting and adjusting a wavelength of the light beam and the beam coupler includes a partially reflecting mirror. 
     16. The light source apparatus of clause  12 , wherein the beam turning device includes an arrangement of optics that is configured to receive the light beam exiting the body of the gas discharge stage through a first port and changing a direction of the light beam so that the light beam re-enters the body of the gas discharge stage through the first port. 
     17. The light source apparatus of clause  12 , wherein the gas discharge stage also includes a beam expander configured to interact with the light beam as it travels between the beam coupler and the cavity. 
     18. The light source apparatus of clause  1 , wherein each sensor is configured to be fixedly mounted relative to the body of the gas discharge stage. 
     19. The light source apparatus of clause  18 , wherein each sensor is configured to be fixed at a distance from the other sensor when it is fixedly mounted relative to the body of the gas discharge stage. 
     20. The light source apparatus of clause  1 , further comprising: 
     a second gas discharge stage that is optically in series with the gas discharge stage, the second gas discharge stage having a second three-dimensional body defining a second cavity that is configured to interact with an energy source, the second body including at least two ports that are transmissive to a light beam having a wavelength in the ultraviolet range; and 
     a second plurality of sensors, each sensor in the second plurality configured to measure a physical aspect of a respective distinct region of the second body relative to that sensor; 
     wherein the control apparatus is in communication with the second plurality of sensors, and configured to analyze the measured physical aspects from the sensors of the second plurality to thereby determine a position of the second body relative to a second XYZ coordinate system defined by a second X axis that passes through the at least two ports of the second body. 
     21. The light source apparatus of clause  1 , wherein each sensor includes a displacement sensor. 
     22. The light source apparatus of clause  21 , wherein a displacement sensor is an optical displacement sensor, a linear proximity sensor, an electromagnetic sensor, or an ultrasonic displacement sensor. 
     23. The light source apparatus of clause  1 , wherein each sensor includes a contact-less sensor. 
     24. The light source apparatus of clause  1 , wherein the X axis is defined by a beam turning device at a first end of the body and optically coupled with a first port and a beam coupler at a second end of the body and optically coupled with a second port. 
     25. A metrology apparatus comprising: 
     a sensor system including a plurality of sensors, each sensor is configured to measure a physical aspect of a body of a gas discharge stage relative to that sensor; 
     a measurement system configured to measure one or more performance parameters of a light beam that is generated from the gas discharge stage; 
     an actuation system including a plurality of actuators, each actuator configured to be physically coupled to a distinct region of the body of the gas discharge stage, the plurality of actuators working together to adjust a position of the body of the gas discharge stage; and 
     a control apparatus in communication with the sensor system, the measurement system, and the actuation system, and configured to:
         analyze the measured physical aspects from the sensors to thereby determine a position of the body of the gas discharge stage in an XYZ coordinate system defined by an X axis that is defined by the gas discharge stage;   analyze the position of the body of the gas discharge stage;   analyze the one or more measured performance parameters; and   provide a signal to the actuation system to modify the position of the body of the gas discharge stage based on the analyses of the position of the body of the gas discharge stage and the one or more measured performance parameters.       

     26. The metrology apparatus of clause  25 , wherein the sensors are positioned apart from each other and relative to the body of the gas discharge stage. 
     27. The metrology apparatus of clause  25 , wherein the control apparatus is configured to provide the signal to the actuation system to modify the position of the body of the gas discharge stage based on the analyses of the position of the body of the gas discharge stage and the one or more measured performance parameters by determining a position of the body of the gas discharge stage that optimizes a plurality of the performance parameters of the light beam. 
     28. The metrology apparatus of clause  25 , wherein the X axis is defined by a beam turning device at a first end of the body and optically coupled with a first port and a beam coupler at a second end of the body and optically coupled with a second port. 
     29. A method comprising: 
     measuring, at each of a plurality of distinct regions of a body of a gas discharge stage of a light source, a physical aspect of the body at that region; 
     measuring one or more performance parameters of a light beam that is generated from the gas discharge stage; 
     analyzing the measured physical aspects to thereby determine a position of the body in an XYZ coordinate system defined by an X axis, wherein the X axis is defined by a plurality of apertures associated with the gas discharge stage; 
     analyzing the determined position of the body of the gas discharge stage; 
     analyzing the one or more measured performance parameters; 
     determining whether a modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters; and 
     if it is determined that a modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters, then modifying the position of the body of the gas discharge stage. 
     30. The method of clause  29 , wherein modifying the position of the body of the gas discharge stage is based on the analysis of the determined position of the body of the gas discharge stage. 
     31. The method of clause  29 , wherein determining the position of the body of the gas discharge stage includes determining one or more of a translation of the body of the gas discharge stage from the X axis and a rotation of the body of the gas discharge stage from the X axis. 
     32. The method of clause  31 , wherein translating the body of the gas discharge stage from the X axis includes one or more of translating the body of the gas discharge stage along the X axis, translating the body of the gas discharge stage along a Y axis that is perpendicular with the X axis, and translating the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. 
     33. The method of clause  31 , wherein rotating the body of the gas discharge stage from the X axis includes one or more of rotating the body of the gas discharge stage about the X axis, rotating the body of the gas discharge stage about a Y axis that is perpendicular with the X axis, and/or rotating the body of the gas discharge stage along a Z axis that is perpendicular with the X axis and the Y axis. 
     34. The method of clause  29 , wherein measuring a physical aspect of the body at that region comprises measuring a distance from the sensor to the region of the body of the gas discharge stage. 
     35. The method of clause  29 , wherein determining whether the modification to the position of the body of the gas discharge stage would improve one or more of the measured performance parameters comprises determining a position of the body of the gas discharge stage that optimizes a plurality of measured performance parameters. 
     36. The method of clause  29 , further comprising generating the light beam from the gas discharge stage including forming a resonator defined by a beam coupler at one side of the body and a beam turning device at another side of the body, the beam coupler and the beam turning device defining the X axis and generating energy within a gain medium in a cavity defined by the body. 
     37. The method of clause  29 , wherein measuring one or more performance parameters of the light beam comprises measuring a plurality of performance parameters. 
     38. The method of clause  37 , wherein measuring the plurality of performance parameters comprises measuring two or more of a repetition rate of a pulsed light beam produced by the light source, an energy of the pulsed light beam, a duty cycle of the pulsed light beam, and/or a spectral feature of the pulsed light beam. 
     39. The method of clause  37 , further comprising: 
     determining an optimal position of the body of the gas discharge stage that provides an optimal set of values of the performance parameters of the light beam; and 
     modifying the position of the body of the gas discharge stage to be at the optimal position. 
     40. A metrology kit comprising: 
     a sensor system including a plurality of sensors, each sensor is configured to measure a physical aspect of a three-dimensional body relative to that sensor; 
     a measurement system including a plurality of measurement devices, each measurement device configured to measure a performance parameter of a light beam; 
     an actuation system including a plurality of actuators configured to physically couple to the three-dimensional body; and 
     a control apparatus configured to be in communication with the sensor system, the measurement system, and the actuation system, the control apparatus including:
         a sensor processing module configured to interface with the sensor system and receive sensor information from the sensor system;   a measurement processing module configured to interface with the measurement system and receive measurement information from the measurement system;   an actuator processing module configured to interface with the actuation system; and   a light source processing module configured to interface with a gas discharge stage having a three-dimensional body.       

     41. The metrology kit of clause  40 , wherein the control apparatus includes an analysis processing module in communication with the sensor processing module, the measurement processing module, the actuator processing module, and the light source processing module, and configured to, in use, instruct the light source processing module to adjust one or more characteristics of the gas discharge stage and analyze the sensor information and the measurement information and determine an instruction to the actuator processing module based on the adjusted characteristics of the gas discharge stage. 
     42. The metrology kit of clause  40 , wherein the metrology kit is modular such that it is configured to be operably connected and disconnected from one or more gas discharge stages, each gas discharge stage including a respective three-dimensional body defining a cavity that generates a respective light beam. 
     Other implementations are within the scope of the following claims.