Patent Publication Number: US-2023142333-A1

Title: Determination of measurement error in an etalon

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Application No. 63/043,312, filed Jun. 24, 2020 and titled DETERMINATION OF MEASUREMENT ERROR IN AN ETALON, and which is incorporated herein in its entirety by reference. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to determination of measurement error in an etalon. The etalon may be used in a deep ultraviolet (DUV) optical system. 
     BACKGROUND 
     An etalon is an optical cavity made from two partially reflective optical surfaces. The etalon produces an interference pattern and may be used to measure or estimate the wavelength of light that is incident on the etalon. 
     SUMMARY 
     In one aspect, a method includes: accessing information relating to an etalon, the etalon associated with a calibration parameter having a pre-set default value, the etalon configured to produce an interference pattern including a plurality of fringes from a received light beam, and the information relating to the etalon including first spatial information related to a first fringe of the plurality of fringes and second spatial information related to a second fringe of the plurality of fringes; determining a first wavelength value of the received light beam based on the spatial information related to the first fringe and an initial value of the calibration parameter; determining a second wavelength value of the received light beam based on the spatial information related to the second fringe and the initial value of the calibration parameter; and comparing the first wavelength value and the second wavelength value to determine a measurement error value. 
     Implementations may include one or more of the following features. 
     The method may further include determining whether to adjust the pre-set default value of the calibration parameter based on the measurement error value. The measurement error value may include a difference between the first wavelength value and the second wavelength value, and the pre-set default value may be adjusted to a value that causes a magnitude of the measurement error value to be less than a threshold. The pre-set default value may be adjusted to a value that causes the measurement error value to be zero. 
     The calibration parameter may include a focal length of a lens at an output of the etalon, and the measurement error may include a difference between the first wavelength value and the second wavelength value. 
     The first spatial information may include a diameter of the first fringe, and the second spatial information may include a diameter of the second fringe. 
     The method may further include directing a light beam toward the etalon. The first fringe may be produced by a first portion of the light beam, and the second fringe may be produced by a second portion of the light beam. The light beam may include a plurality of pulses, the first portion of the light beam may include a first one of the plurality of pulses, and the second portion of the light beam may include a second one of the plurality of pulses. The light beam may include a continuous-wave light beam, the first portion of the light beam may include a first sample of the light beam, and the second portion of the light beam may include a second sample of the light beam. The method may further include: changing the initial value of the calibration parameter to an updated value of the calibration parameter; actuating an optical element to thereby change the wavelength of the received light beam; determining a first wavelength value of the received light beam based on the spatial information related to the first fringe and the updated value of the calibration parameter; determining a second wavelength value of the received light beam based on the spatial information related to the second fringe and the updated value of the calibration parameter; and comparing the first wavelength value and the second wavelength value to determine a measurement error value based on the updated value of the calibration parameter. The optical element may be actuated to increase the wavelength or to decrease the wavelength prior to determining the second wavelength value. The first wavelength value and the second wavelength value may be determined more than once each time the optical element is actuated. The method may further include determining whether to adjust the pre-set default value of the calibration parameter by comparing the error measurement value determined based on the initial value of the calibration parameter and the error measurement value determined based on the updated value of the calibration parameter. 
     The initial value of the calibration parameter may be the pre-set default value. 
     The first fringe and the second fringe may be in the interference pattern at the same time. 
     In another aspect, a method for calibrating an etalon includes: accessing information relating to the etalon, the etalon associated with a calibration parameter having a pre-set default value, the etalon configured to produce an interference pattern including a plurality of fringes from a received light beam, and the information relating to the etalon including first spatial information related to a first fringe of the plurality of fringes and second spatial information related to a second fringe of the plurality of fringes; determining a measurement error value of the etalon based on the first spatial information, the second spatial information, and an initial value of the calibration parameter; and analyzing the measurement error value to determine whether to adjust the pre-set default value. 
     Implementations may include one or more of the following features. 
     The calibration parameter may include a focal length of a lens at an output of the etalon. The method may further include: determining a first wavelength value based on the first spatial information; and determining a second wavelength value based on the second spatial information. The measurement error may include a difference between the first wavelength value and the second wavelength value. 
     The calibration parameter may include a plurality of initial values. Determining a measurement error value may include simulating a plurality of measurement error values for each of the plurality of initial values. Each measurement error value may be based on the first spatial information, the second spatial information, and one of the plurality of initial values of the calibration parameter. Analyzing the measurement error values may include analyzing the simulated measurement error values. 
     In another aspect, an optical measurement apparatus for a light source includes: an etalon including a focusing lens configured to focus light at an image plane; an optical detector configured to detect an interference pattern produced by the etalon and to produce information related to the etalon; and a control system coupled to the optical detector. The etalon is associated with a calibration parameter related to the focusing lens, and the calibration parameter has a pre-set default value. The information includes first spatial information for a first fringe and second spatial information for a second fringe. The control system is configured to: determine a measurement error value of the etalon based on first spatial information from the detector, the second spatial information, and an initial value of the calibration parameter; and analyze the measurement error value to determine whether to adjust the pre-set default value. 
     Implementations may include one or more of the following features. 
     The light source may include a deep ultraviolet (DUV) light source. 
     In another aspect, a light source includes: a light-generation apparatus; and an optical measurement apparatus. The optical measurement apparatus includes: an etalon including a focusing lens configured to focus light at an image plane; an optical detector configured to detect an interference pattern produced by the etalon and to produce information related to the etalon; and a control system coupled to the optical detector. The etalon is associated with a calibration parameter related to the focusing lens, the calibration parameter having a pre-set default value. The information includes first spatial information for a first fringe and second spatial information for a second fringe. The control system is configured to: determine a measurement error value of the etalon based on first spatial information from the detector, the second spatial information, and an initial value of the calibration parameter; and analyze the measurement error value to determine whether to adjust the pre-set default value. 
     Implementations may include one or more of the following features. 
     The light-generation apparatus may include a deep ultraviolet (DUV) light source. The light-generation apparatus may include a master oscillator. The light generation apparatus may further include a power amplifier. The light-generation apparatus may include a plurality of master-oscillators. 
     The light source may further include an optical element configured to receive light from the light-generation apparatus and to direct light to the etalon. The optical element may be a dispersive optical element. 
     Implementations of any of the techniques described above may include a system, a method, a process, a device, or an apparatus. The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims. 
    
    
     
       DRAWING DESCRIPTION 
         FIG.  1 A  is a block diagram of an example of a system. 
         FIG.  1 B  shows an example of an interference pattern. 
         FIG.  1 C  is a block diagram of an aspect of the system of  FIG.  1 A . 
         FIG.  2 A  is a block diagram of an example of an optical measurement apparatus. 
         FIGS.  2 B and  2 C  relate to another example of an interference pattern. 
         FIGS.  3  and  4    are flow charts of examples of processes for determining measurement error of an etalon. 
         FIG.  5    shows an example plot of measurement error of an etalon. 
         FIG.  6    is a flow chart of an example of a process for determining measurement error of an etalon. 
         FIG.  7    shows an example plot of measurement error of an etalon. 
         FIG.  8 A  shows an example of a deep ultraviolet (DUV) optical system with which an optical measurement apparatus may be used. 
         FIG.  8 B  is an example of a projection optical system. 
         FIG.  9 A  is a block diagram of an example of a spectral adjustment apparatus. 
         FIG.  9 B  shows an example of a prism. 
         FIG.  10    shows an example of a deep ultraviolet (DUV) optical system with which an optical measurement apparatus may be used. 
     
    
    
     DETAILED DESCRIPTION 
       FIG.  1 A  is a block diagram of a system  100 . In  FIG.  1 A , a dashed line between elements represents an optical path along which light travels and a solid line between elements represents a signal path along which information and/or data travels. The system  100  includes a light-generation module  110  that produces a light beam  116 . The light beam  116  propagates on a path  114  to a device  180 . The device  180  is any device that uses the light beam  116 . The device  180  may be an optical lithography apparatus (such as the scanner apparatus  880  of  FIGS.  8 A and  10   ) or a power amplifier such as (the power amplifier  1012 _ 2  of  FIG.  10   ). 
     The system  100  also includes a beam separator  117  that directs a portion  116 ′ of the light beam  116  to an optical measurement apparatus  160 . The beam separator  117  may be, for example, a beam splitter that directs the portion  116 ′ to the optical measurement apparatus  160  while allowing the remaining light in the light beam  116  to continue propagating to the device  180 . The optical measurement apparatus  160  is used to measure the wavelength of the light beam  116 . The optical measurement apparatus  160  includes an etalon  130 , a detector  140 , and a control system  150 . The etalon  130  includes two parallel optical elements  133 A,  133 B, which are separated by a distance  136 , and an output lens  134 . With additional reference to  FIG.  1 C , the output lens  134  has a focal length  163 , and the output lens  134  focuses incident light at an image plane  137 . The image plane  137  coincides with an active region  142  of the detector  140 .  FIG.  1 C  is a block diagram of the active region  142  and the image plane  137 . 
     Referring also to  FIG.  1 B , the output of the etalon  130  is an interference pattern  139  that is focused at the image plane  137 .  FIG.  1 B  shows the interference pattern  139  in the image plane  137 . In the example of  FIG.  1 B , the interference pattern  139  is a plurality of concentric rings that are formed at the image plane  137 . Two fringes  139 _ 1  and  139 _ 2  are shown in  FIG.  1 B . The fringe  139 _ 1  is a first order fringe, and the fringe  139 _ 2  is a second order fringe. The first and second order fringes  139 _ 1 ,  139 _ 2  are two consecutive fringes. The wavelength of the light in the portion  116 ′ is related to the diameter of the fringes in the interference pattern  139  according to Equation 1:  
     
       
         
           
             λ 
             = 
             
               
                 2 
                 N 
                 D 
               
               m 
             
             c 
             o 
             s 
             
               
                 
                   d 
                   
                     F 
                     D 
                   
                 
               
             
           
         
       
     
      where λ is the wavelength of the light incident on the etalon 130 (the portion 116′ in this example), ND is the optical path length between the optical elements 133A, 133B (the distance 136 in this example), m is the order of a particular one of the fringes, d is the diameter of the particular one of the fringes, and FD is the focal length of the output lens 134. The order m of the fringe is an integer number and may be, for example, a relatively large number such as an integer that is equal to or greater than 10,000. 
     The etalon  130  is used to measure the wavelength of the light in the portion  116 ′. The etalon  130  is associated with a measurement error that may be absolute at a specific wavelength or variable as a function of wavelength. One source of measurement error that depends on wavelength may occur when a fixed detector in the image plane  137  (such as the detector  140 ) determines a value for the wavelength using a different order fringe as compared to the prior wavelength determination. In other words, when the wavelength of the same light is measured by different order fringes in the same interference pattern, the measured value of the wavelength based on the first order fringe  139 _ 1  and/or the second order fringe  139 _ 2  may be inaccurate. Specifically, such a measurement error results in the determined value of the wavelength changing artificially between two different measurements even though the true wavelength of the incident light has not changed. 
     The etalon  130  is associated with at least one calibration parameter  131 . The value of FD is a calibration parameter  131 . The value of FD is determined when the etalon  130  is manufactured. However, the value of FD may drift or change over the lifetime of the etalon  130 . The value of FD may change, for example, because of alignment shifts caused by thermal cycling (heating and/r cooling) that may occur during use of the etalon  130 . The alignment shifts may appear as changes in the value of FD. Techniques for determining the value of FD during use and/or during the lifetime of the etalon  130  are discussed below. Details of an example implementation of the optical measurement apparatus  160  are discussed before discussing the techniques related to determining the value of the calibration parameter  131 . 
       FIG.  2 A  is a block diagram of an optical measurement apparatus  260 . The optical measurement apparatus  260  is an example of an implementation of the optical measurement apparatus  160  ( FIG.  1 A ). The optical measurement apparatus  260  includes an input lens  232 , an etalon  230 , an output lens  234  (or focusing lens  234 ), and a detector  240 . The portion  116 ′ is diffused and passes through an aperture  235  of the optical measurement apparatus  260 . The portion  116 ′ may be intentionally diffused by an optical diffuser (not shown) placed at a plane  237 , which is between the beam separator  117  and the aperture  235 . The aperture  235  is at a focal plane of the input lens  232 . The input lens  232  collimates the portion  116 ′ before it enters the etalon  230 . The output lens  234  has a focal length  263  and focuses light to an image plane. The detector  240  is positioned such that an active region  242  of the detector  240  coincides with the image plane. 
     In the example shown in  FIG.  2 A , the etalon  230  includes a pair of partially reflective optical elements  233 A and  233 B. The optical elements  233 A and  233 B are between the input lens  232  and the output lens  234 . The optical elements  233 A and  233 B have respective reflective surfaces  238 A and  238 B that are spaced a distance  236  apart. The distance  236  may be a relatively short distance (for example, millimeters to centimeters) apart. The optical elements  233 A and  233 B are wedged shape to prevent the rear surfaces (the surfaces opposite the surfaces  238 A and  238 B) from producing interference fringes. The rear surfaces may have an anti-reflective coating. Other implementations of the etalon  230  are possible. For example, in other implementations, the optical elements  233 A and  233 B are parallel plates and are not wedge-shaped. In yet another example, the etalon  230  may include only a single plate that has two parallel partially reflecting surfaces. 
     Referring also to  FIG.  2 B , the etalon  230  interacts with the portion  116 ′ and outputs an interference pattern  239 .  FIG.  2 B  shows the interference pattern  239  in the image plane of the lens  234  at an instance in time. The interference pattern  239  includes a plurality of fringes. Two of the plurality of fringes ( 239 _ 1  and  239 _ 2 ) are shown in  FIG.  2 B . The interference pattern  239  includes regions without light created by destructive interference of the portion  116 ′ and regions with light created by constructive interference of the portion  116 ′. The regions of constructive interference are the fringes  239 _ 1  and  239 _ 2 . The regions without light are shown with grey shading and are between the regions of light. The fringes  239 _ 1  and  239 _ 2  are concentric rings of light in the image plane of the output lens  234 . Each ring in the set of fringes is an order (m) of the interference pattern, where m is an integer number equal to or greater than one. The fringe  239 _ 1  is the first order fringe, and the fringe  239 _ 2  is the second order fringe. 
     The interference pattern  239  is sensed at the active region  242  of the detector  240 . The detector  240  is any type of detector capable of sensing the light in the interference pattern  239 . For example, the active region  242  may be a linear photodiode array that includes multiple elements of the same size arranged along a single dimension at an equal spacing in one package. Each element in the photodiode array is sensitive to the wavelength of the portion  116 ′. As another example, the detector  240  may be a two dimensional sensor such as a two-dimensional charged coupled device (CCD) or a two-dimensional complementary metal oxide semiconductor (CMOS) sensor. 
     The detector  240  is connected to a control system  250  via a data connection  254 . The control system  250  includes an electronic processing module  251 , an electronic storage  252 , and an I/O interface  253 . The electronic processing module  251  includes one or more processors suitable for the execution of a computer program such as a general or special purpose microprocessor, and any one or more processors of any kind of digital computer. Generally, an electronic processor receives instructions and data from a read-only memory, a random access memory (RAM), or both. The electronic processing module  251  may include any type of electronic processor. The electronic processor or processors of the electronic processing module  251  execute instructions and access data stored on the electronic storage  252 . The electronic processor or processors are also capable of writing data to the electronic storage  252 . 
     The electronic storage  252  is any type of computer-readable or machine-readable medium. For example, the electronic storage  252  may be volatile memory, such as RAM, or non-volatile memory. In some implementations, and the electronic storage  252  includes non-volatile and volatile portions or components. The electronic storage  252  may store data and information that is used in the operation of the control system  250 . The electronic storage  252  also may store instructions (for example, in the form of a computer program) that cause the control system  250  to interact with the optical measurement apparatus  260 . For example, the instructions may be instructions that cause the electronic processing module  251  to implement the processes discussed with respect to  FIGS.  3 ,  4 , and  6   . The electronic storage  252  also stores information about the etalon  230 , such as an initial value of a pre-defined calibration parameter  231 , or a pre-set value of the calibration parameter  231 . The pre-defined or pre-set value may be a value determined during factory calibration or a value determined using a process such as the processes  300 ,  400 , or  600  discussed below. The calibration parameter  231  may be, for example, a focal length of the lens  234 . In another example, the electronic storage  252  also may store a specification that indicates a range of values or a value related to an acceptable amount of measurement error for the etalon  230 . 
     The I/O interface  253  is any kind of interface that allows the control system  250  to exchange data and signals with an operator, other devices, and/or an automated process running on another electronic device. For example, in implementations in which data or instructions stored on the electronic storage  252  may be edited, the edits may be made through the I/O interface  253 . The I/O interface  253  may include one or more of a visual display, a keyboard, and a communications interface, such as a parallel port, a Universal Serial Bus (USB) connection, and/or any type of network interface, such as, for example, Ethernet. The I/O interface  253  also may allow communication without physical contact through, for example, an IEEE 802.11, Bluetooth, or a near-field communication (NFC) connection. 
     The control system  250  is coupled to various components of the apparatus  260  through a data connection  254 . The data connection  254  is any type of connection that allows transmission of data, signals, and/or information. For example, the data connection  254  may be a physical cable or other physical data conduit (such as a cable that supports transmission of data based IEEE 802.3), a wireless data connection (such as a data connection that provides data via IEEE 802.11 or Bluetooth), or a combination of wired and wireless data connections. 
       FIG.  3    is a flow chart of a process  300 . The process  300  is used to determine a measurement error value. The process  300  may be performed by the control system  250  ( FIG.  2 A ). For example, the process  300  may be performed by one or more electronic processors in the processing module  251 . The process  300  is discussed with respect to the measurement apparatus  260  ( FIG.  2 A ). 
     Information related to the etalon  230  is accessed ( 310 ). The information may be accessed from the electronic storage  252  or through the I/O interface  253 . The information related to the etalon  230  includes first spatial information related to a first fringe and second spatial information related to a second fringe. The first fringe and the second fringes may be two different fringes formed at the same time. For example, the first fringe may be the fringe  239 _ 1  and the second fringe may be the fringe  239 _ 2 . As discussed above, the fringe  239 _ 1  and the fringe  239 _ 2  are two different fringes formed by a single pulse of light or by the same sample of a continuous wave light beam. The process  400  discussed with respect to  FIG.  4    is an example of such an approach. In other implementations, the first fringe is a fringe in an interference pattern formed at a first instance in time, and the second fringe is a fringe in an interference pattern formed at a second instance in time. For example, in these implementations, the first fringe may be a fringe formed by a first pulse of light that is incident on the etalon  230 , and the second fringe may be a fringe formed by a second pulse of light that is incident on the etalon  230  after the first pulse of light. The process  600  discussed with respect to  FIG.  6    is an example of such an approach. The first spatial information may be a diameter of the first fringe. The second spatial information may be a diameter of the second fringe. 
     The information associated with the etalon  230  also includes an initial value of the calibration parameter  231 . The initial value of the calibration parameter  231  may be a factory calibration value that was determined when the etalon  230  was assembled. In some implementations, the initial value of the calibration parameter  231  is a value determined in a previous execution of the process  300 . The pre-set default value of the calibration parameter  231  may be stored on and accessed from the electronic storage  252 . 
     A first wavelength value is determined based on the spatial information related to the first fringe and the initial value of the calibration parameter  231  ( 320 ). A second wavelength value is determined based on the spatial information related to the second fringe and the initial value of the calibration parameter  231  ( 330 ). 
     The first wavelength value and the second wavelength value are compared to determine a measurement error value ( 340 ). The measurement error value is a value that represents the difference between the first wavelength value and the second wavelength value. The measurement error value may be determined, for example, by subtracting the first wavelength value from the second wavelength value, or vice versa. Other implementations are possible. For example, the measurement error value may be a ratio of the first wavelength value to the second wavelength value. 
       FIG.  4    is a flow chart of a process  400 . The process  400  is another example of a process for determining a measurement error value and a value of the calibration parameter  231 . The process  400  is discussed with respect to the interference pattern  239  ( FIGS.  2 B and  2 C ), which is the output of the etalon  230  at an instance in time. The process  400  may be performed by the control system  250 . 
     An initial value of the calibration parameter  231  is accessed ( 410 ). The value of the calibration parameter  231  may be accessed from the electronic storage  252  or provided to the control system  250  via the I/O interface  253 . The calibration parameter  231  is FD in this example. The initial value of the calibration parameter  231  may be a pre-determined and default value that was determined when the etalon  230  was manufactured. The initial value of the calibration parameter  231  may be a value of the calibration parameter that was determined in a prior iteration of the process  400 . 
     The diameter of the first fringe  239 _ 1  (fringe diameter d1) is determined. For example, and referring to  FIGS.  2 B and  2 C , the fringe diameter d1 may be determined based on data produced by the detector  240 . In this example, the fringe diameter d1 may be a count of pixels between two points on opposite sides of the first fringe  239 _ 1  as determined from image data produced by the detector  240 . Other implementations are possible, and the fringe diameters d1 and d2 may be determined in any manner. 
     A first wavelength value (λ1) is determined based on the determined fringe diameter d1 and the initial value of the calibration value ( 420 ). For example, the first wavelength (λ1) may be determined using the initial value of the parameter  231 , the order number (m) of the first fringe  239 _ 1 , the known value of ND, and the fringe diameter d1 in Equation 1. Similarly, the diameter of the second fringe  239 _ 2  (fringe diameter d2) is determined. A second wavelength value (λ2) is determined based on the determined fringe diameter d2 and the initial value of the calibration value ( 430 ). The second wavelength value (λ2) may be determined using the initial value of the parameter  231 , the order number (m) of the second fringe  239 _ 2 , the known value of ND, and the fringe diameter d2 in Equation 1. The first fringe  239 _ 1  and the second fringe  239 _ 2  have consecutive orders. For example, if the order (m) of the first fringe  239 _ 1  is 10,001, the order (m) of the second fringe  239 _ 2  is 10,002. 
     The first wavelength value (λ1) and the second wavelength value (λ2) are compared to determine a measurement error ( 440 ). The measurement error may be determined by finding the difference between the first wavelength value (λ1) and the second wavelength value (λ2). In the absence of measurement error, the first wavelength value and the second wavelength value are the same because the light that was used to create the first fringe  239 _ 1  and the second fringe  239 _ 2  is the same. Thus, the difference between the first wavelength value (λ1) and the second wavelength value (λ2) is a characterization of the measurement error. The difference may be determined by subtracting the first wavelength value (λ1) from the second wavelength value (λ2), or vice versa. Moreover, the measurement error may be an absolute value of the difference. Thus, the measurement error may be a positive number, a negative number, or zero (in the case of no measurement error). 
     The measurement error is compared to a specification to determine whether the calibration parameter  231  (FD in this example), should be adjusted. The specification may be a range of values that includes positive and negative values or a single threshold value that is positive. The measurement error is compared to the specification to determine whether to adjust the value of the calibration parameter  231  ( 450 ). If the value of the calibration parameter  231  is within the specification or less than the threshold value, then the value of the calibration parameter  231  is accurate and the process  400  returns to ( 410 ) to continue monitoring for measurement error. If the value of the calibration parameter  231  is outside of the specification, the value of the calibration parameter  231  is adjusted ( 460 ). The value of the calibration parameter  231  is adjusted until the first wavelength value (λ1) and the second wavelength value (λ2) are within the specification. For example, if the specification is zero, the value of the calibration parameter  231  is adjusted until Equation 1 yields the same wavelength value for the first fringe  239 _ 1  and the second fringe  239 _ 2 . 
     After the value of the calibration parameter  231  has been adjusted, the process  400  returns to ( 410 ) to continue monitoring the measurement error of the etalon, or the process  400  may end. The adjusted value of the calibration parameter  231  may be stored on the electronic storage  252  ( 470 ). In implementations in which the adjusted value of the calibration parameter  231  is stored, the adjusted value of the calibration parameter  231  may be used as the initial value of the calibration parameter  231  in a subsequent performance of the process  400 . In some implementations, the adjusted calibration parameter  231  is not stored and/or is not used in a subsequent performance of the process  400 . In these implementations, the factory determined value of the calibration parameter  231  is always used as the initial value of the calibration parameter  231 . 
       FIG.  5    is a plot of example data that shows measurement error as a function of the value of the calibration parameter  231  (FD). In the example of  FIG.  5   , the measurement error is the difference between the first wavelength value (λ1) determined in ( 420 ) and the second wavelength value (λ2) determined in ( 430 ). The factory determined value of the calibration parameter  231  was 18352 pixels. However, as shown in  FIG.  5   , using the factory determined value of the calibration parameter  231  resulted in a measurement error of about 2.5 femtometers (fm). The value of the calibration parameter  231  was varied through the range of values shown in  FIG.  5   , and the measurement error was determined at the various values of the calibration parameter  231 . As shown in  FIG.  5   , the measurement error was zero when the value of the calibration parameter  231  was 18353 pixels. The value of the calibration parameter  231  is adjusted to be equal to 18353 pixels, and the wavelength of the portion  116 ′ is measured using the interference pattern output by the etalon  130  and Equation 1 (with the updated value of the FD). By adjusting the value of the calibration parameter  231 , the measurement error is removed so that the wavelength value determined from the output of the etalon  230  is accurate. 
       FIG.  6    is a flow chart of a process  600 . The process  600  is another example of a process for determining a measurement error of an etalon (such as the etalon  130  or the etalon  230 ). The process  600  is discussed with respect to the etalon  230  and the control system  250 . 
     An initial value of the calibration parameter  231  is changed to an updated value ( 610 ). The initial value of the calibration parameter  231  may be a factory calibrated value, a value determined during prior operational use of the etalon  230 , a value generated by an automated process (such as a random process), or a value provided by an operator of the control system  250 . The initial value of the calibration parameter  231  may be changed by adding a pre-determined constant amount to the initial value of the calibration parameter  231 . In some implementations, the initial value of the calibration parameter  231  is changed by a specific amount indicated by an operator of the control system  250  or by a pre-programmed recipe or formula. 
     The wavelength of the light in the portion  116 ′ is changed ( 620 ). The wavelength of the light in the portion  116 ′ is changed by a known amount. For example, the wavelength of the light in the portion  116 ′ may be changed by actuating an optical element (such as the prism  922 ,  923 ,  924 , or  925  of  FIG.  9 A ) associated with the light source  110  by a known amount such that the wavelength of light that exits the optical element is changed relative to the light incident on the optical element by a known amount. Next, the process  600  estimates the wavelength value of the light in the portion  116 ′ using one or more instances of the interference pattern  239  output by the etalon  230 , where each of the two instances is output at a different time. For example, the light beam  116  (and the portion  116 ′) may be a pulsed light beam that includes pulses of light, each separated from an adjacent pulse by a finite amount of time during which the light-generation module  110  does not emit light. In this example, the first instance of the interference pattern  239  is produced by irradiating the etalon  230  with a first pulse in the portion  116 ′ and the second instance of the interference pattern  239  is produced by irradiating the etalon  230  with a second pulse in the portion  116 ′. 
     The first wavelength value (λ1) is determined ( 630 ) using a fringe from the first instance of the interference pattern  239 . The first wavelength value (λ1) is determined using Equation 1, with m being the order of the fringe, FD being the updated value of the calibration parameter  231  determined in ( 610 ), and d being the diameter of the fringe. The first wavelength value (λ1) may be determined from more than one instance of the interference pattern  239 . For example, the first wavelength value (λ1) may be determined from 50 or more instances of the interference pattern  239 . The various values of the first wavelength value (λ1) may be averaged together or otherwise filtered to remove or reduce noise, and the averaged or filtered value may be used as the first wavelength value (λ1). 
     The wavelength of the light in the portion  116 ′ is again changed ( 640 ). The wavelength of the light in the portion  116 ′ may be changed by the same known amount as in ( 620 ). The second wavelength value (λ2) is determined ( 650 ) using a fringe from one or more instances of the interference pattern  239 . The second wavelength value (λ2) is determined in the same manner as discussed in ( 630 ), by using Equation 1, with m being the order of the fringe, FD being the updated value of the calibration parameter  231  determined in ( 610 ), and d being the diameter of the fringe. The second wavelength value (λ2) may be determined from more than one instance of the interference pattern  239 . For example, the second wavelength value (λ2) may be determined 10, 50, or 100 times and then averaged to mitigate the effects of noise and mechanical vibrations. 
     A measurement error associated with the updated value of the calibration parameter  231  is determined ( 660 ). The measurement error is the difference between the determined first wavelength value (λ1) and the determined second wavelength value (λ2), taking into account the nominal sensitivity (NS) of the system that controls the actual wavelength of the portion  116 ′ (the actuated optical element in this example). The nominal sensitivity is a constant value and may be determined by the manufacturer and stored on the electronic storage  252 . The nominal sensitivity is the amount of change in wavelength with respect to a unit change in the optical element that determines the wavelength of light incident on the etalon  230 . For example, if the optical element is a prism coupled to a PZT actuator, the nominal sensitivity is the amount of wavelength change for each unit change in the prism position. The measurement error (ME) may be determined from Equation 2: 
     
       
         
           
             M 
             E 
             = 
             
               
                 S 
                 − 
                 N 
                 S 
               
             
             
               
                 O 
                 A 
               
             
           
         
       
     
      where ME is the measurement error, S is the current sensitivity, NS is the nominal sensitivity, and OA is a measure of actuation of the optical element in units of distance. OA may be determined by Equation 3: 
     
       
         
           
             O 
             A 
             = 
             P 
             2 
             − 
             P 
             1 
           
         
       
     
      where P2 is the position of the optical element when light having a second wavelength is provided by the optical element, and P1 is the position of the optical element when light having a first wavelength is provided by the optical element. The current sensitivity (S) is computed based on measured wavelength and change in position of the optical element, and may be determined from Equation 4:  
     
       
         
           
             S 
             = 
             
               
                 
                   
                     λ 
                     2 
                     − 
                     λ 
                     1 
                   
                 
               
               
                 P 
                 2 
                 − 
                 P 
                 1 
               
             
           
         
       
     
      where λ1 is the first wavelength value determined in (630), λ2 is the second wavelength value determined in (650), P2 is the position of the optical actuator when light having the second wavelength value (λ2) is provided to the etalon 230, and P1 is the position of the optical actuator when light having the first wavelength value (λ1) is provided to the etalon 230. Although the above examples related to Equations 2, 3, and 4 discuss the position of the optical element, other distance metrics that are related to the position of the optical element may be used. For example, in implementations in which the relationship between the position of the actuator and the position of the optical element is known, the position of the actuator may be used as the position of the optical element. 
     The measurement error (ME) is stored on the electronic storage  252  or output via the I/O interface  253 . 
     The process  600  may return to ( 610 ) to determine the measurement error (ME) for a different updated value of the calibration parameter  231  using ( 610 )-( 660 ) as discussed above and for another wavelength of the portion  116 ′. For example, the wavelength may be increased or decreased in ( 620 ) as compared to the prior iteration of ( 610 )-( 660 ). In some implementations, a counter is incremented ( 665 ) each time the process  600  returns to ( 610 ) to track how many times the measurement error has been determined. 
     After the measurement error has been determined for more than one value of the calibration parameter  231  or for more than a specified number of values of the calibration parameter  231 , the determined calibration values are analyzed ( 670 ). For example, the absolute value of the measurement errors may be determined, and the minimum error measurement value found from the absolute values. The value of the calibration parameter  231  that is associated with the minimum error measurement is determined. 
     For example,  FIG.  7    shows two sets of determined measurement error values in femtometers (fm) as a function of the updated value of the calibration parameter  231  in pixel values. Each measurement error value in the first set is shown with a solid round symbol. Each measurement error value in the second set is shown with an open round symbol. The first set of measurement error values was determined by performing ( 610 )-( 660 ) for multiple different values of the calibration parameter  231 . Each time the value of the calibration parameter  231  was updated at ( 610 ) to a different value of the calibration parameter  231 , an optical element (such as a prism) was actuated to increase the wavelength of the light in the portion  116 ′, and the measurement error is determined at ( 660 ). The second set is shown as the plot  754 . The second set of measurement error values was determined by performing ( 610 )-( 660 ) for multiple different values of the calibration parameter  231 . Each time the value of the calibration parameter  231  was updated at ( 610 ) to a different value of the calibration parameter  231 , an optical element (such as a prism) was actuated to decrease the wavelength of the light in the portion  116 ′. 
     The first set of measurement values was fit to a linear relationship  753 , and the second set of measurement values was fit to a linear relationship  754 . The value of FD that corresponds to where the linear relationship  753  and the relationship  754  intersect is the minimum measurement error. As shown in  FIG.  7   , the slope of the relationship  753  and the relationship  753  are opposite in magnitude, but also may be different in absolute value. The difference in absolute value may arise from hysteresis in the actuator that moves the optical element. In the example of  FIG.  7   , the actuator was a piezoelectric actuator that was first compressed from its nominal size to actuate the prism to increase the wavelength (to generate the first set of measurement error values) and then expanded back to its nominal size to decrease the wavelength (to generate the second set of measurement error values). The mechanical effects that arise from the compression and expansion resulted in slightly different absolute value fof the slope of the relationship  753  as compared to the absolute value of the slope of the relationship  754 . 
     In the example shown in  FIG.  7   , the value of the calibration parameter  231  that corresponds to the minimum measurement error was about 18369. In contrast, the pre-set, default value of the calibration parameter  231  was about 18362, and is associated with higher measurement errors. 
     The pre-set, default value of the calibration parameter  231  is adjusted if using the default value results in a measurement error that is greater than a specification ( 680 ). In the example of  FIG.  7   , the pre-set default value of the calibration parameter  231  results in a measurement error value that exceeds the specification, and the value of the calibration parameter  231  is adjusted to be the value of the calibration parameter  231  that corresponds to the minimum value of the measurement error ( 690 ). The process  600  then ends. 
       FIGS.  8 A and  10    show examples of deep ultraviolet (DUV) optical systems with which the optical measurement apparatus  160  or  260  may be used. In the examples below, the optical measurement apparatus  260  is shown as used with a DUV optical system. 
     Referring to  FIGS.  8 A and  8 B , a system  800  includes a light-generation module  810  that provides an exposure beam (or output light beam)  816  to a scanner apparatus  880 . The light-generation module  810  and the scanner apparatus  880  are implementations of the light-generation module  110  and the device  180 , respectively ( FIG.  1 A ). 
     The system  800  also includes the beam separator  117 , the optical measurement apparatus  260 , and the control system  250 . The beam separator  117  directs a portion of the exposure beam  816  to the optical measurement apparatus  260  that is used to measure the wavelength of the exposure beam  816 . The control system  250  is coupled to the optical measurement apparatus  260 . In the example of  FIG.  8 A , the control system  250  is also coupled to the light-generation module  810  and to various components associated with the light-generation module  810 . 
     The light-generation module  810  includes an optical oscillator  812 . The optical oscillator  812  generates the output light beam  816 . The optical oscillator  812  includes a discharge chamber  815 , which encloses a cathode  813 - a  and an anode  813 - b . The discharge chamber  815  also contains a gaseous gain medium  819 . A potential difference between the cathode  813 - a  and the anode  813 - b  forms an electric field in the gaseous gain medium  819 . The potential difference may be generated by controlling a voltage source  897  to apply voltage to the cathode  813 - a  and/or the anode  813 - b . The electric field provides energy to the gain medium  819  sufficient to cause a population inversion and to enable generation of a pulse of light via stimulated emission. Repeated creation of such a potential difference forms a train of pulses, which are emitted as the light beam  816 . The repetition rate of the pulsed light beam  816  is determined by the rate at which voltage is applied to the electrodes  813 - a  and  813 - b . 
     The gain medium  819  is pumped by applying of a voltage to the electrodes  813 - a  and  813 - b . The duration and repetition rate of the pulses in the pulsed light beam  816  is determined by the duration and repetition rate of the application of the voltage to the electrodes  813 - a  and  813 - b . The repetition rate of the pulses may range, for example, between about 500 and 6,000 Hz. In some implementations, the repetition rate may be greater than 6,000 Hz, and may be, for example, 12,000 Hz or greater. Each pulse emitted from the optical oscillator  812  may have a pulse energy of, for example, approximately 1 milliJoule (mJ). 
     The gaseous gain medium  819  may be any gas suitable for producing a light beam at the wavelength, energy, and bandwidth required for the application. The gaseous gain medium  819  may include more than one type of gas, and the various gases are referred to as gas components. For an excimer source, the gaseous gain medium  819  may contain a noble gas (rare gas) such as, for example, argon or krypton; or a halogen, such as, for example, fluorine or chlorine. In implementations in which a halogen is the gain medium, the gain medium also includes traces of xenon apart from a buffer gas, such as helium. 
     The gaseous gain medium  819  may be a gain medium that emits light in the deep ultraviolet (DUV) range. DUV light may include wavelengths from, for example, about 100 nanometers (nm) to about 400 nm. Specific examples of the gaseous gain medium  819  include argon fluoride (ArF), which emits light at a wavelength of about 193 nm, krypton fluoride (KrF), which emits light at a wavelength of about 248 nm, or xenon chloride (XeCl), which emits light at a wavelength of about 351 nm. 
     A resonator is formed between a spectral adjustment apparatus  895  on one side of the discharge chamber  815  and an output coupler  896  on a second side of the discharge chamber  815 . The spectral adjustment apparatus  895  may include a diffractive optic such as, for example, a grating and/or a prism, that finely tunes the spectral output of the discharge chamber  815 . The diffractive optic may be reflective or refractive. In some implementations (such as shown in  FIG.  9 A ), the spectral adjustment apparatus  895  includes a plurality of diffractive optical elements. For example, the spectral adjustment apparatus  895  may include four prisms, some of which are configured to control a center wavelength of the light beam  816  and others of which are configured to control a spectral bandwidth of the light beam  816 . 
     Referring also to  FIG.  9 A , a block diagram of a spectral adjustment apparatus  995  is shown. The spectral adjustment apparatus  995  may be used in the light-generation module  810  as the spectral adjustment apparatus  895 . 
     The spectral adjustment apparatus  995  includes a set of optical features or components  921 ,  922 ,  923 ,  924 ,  925  arranged to optically interact with the light beam  816 . The control system  250  is connected to one or more actuation systems  921 A,  922 A,  923 A,  924 A,  925 A that are physically coupled to respective optical components  921 ,  922 ,  923 ,  924 ,  925 . The actuation systems  921 A,  922 A,  923 A,  924 A,  925 A may include shafts (such as a shaft  926 A) that rotate a component coupled to the shaft about an axis parallel to the shaft. The actuation systems  921 A,  922 A,  923 A,  924 A,  925 A also include electronics and mechanical devices such as, for example, motors and electronic interfaces for communicating with the control system  250  and for receiving electrical power. 
     The optical component  921  is a dispersive optical element, for example, a grating or a prism. In the example of  FIG.  9 A , the optical component  921  is a reflective grating that includes a diffractive surface  902 . The optical components  922 ,  923 ,  924 , and  925  are refractive optical elements and may be, for example, prisms. The optical components  922 ,  923 ,  924 , and  925  form a beam expander  901  that has an optical magnification OM  965 . The OM  965  of the light beam  816  through the beam expander  901  is the ratio of the transverse width Wo of the light beam  816  exiting the beam expander  901  to a transverse width Wi of the light beam  816  entering the beam expander  901 . 
     The surface  902  of the grating  921  is made of a material that reflects and diffracts the wavelengths of the light beam  816 . Each of the prisms  922 ,  923 ,  924 , and  925  is a prism that acts to disperse and redirect the light beam  816  as it passes through the body of the prism. Each of the prisms  922 ,  923 ,  924 , and  925  is made of a material that transmits the wavelengths in the light beam  816 . For example, if the light beam  816  is in the DUV range, the prisms  922 ,  923 ,  924 , and  925  are made of a material (such as, for example, calcium fluoride) that transmits light in the DUV range. 
     The prism  925  is positioned farthest from the grating  921 , and the prism  922  is positioned closest to the grating  921 . The light beam  816  enters the spectral adjustment apparatus through an aperture  955 , and then travels through the prism  925 , the prism  924 , the prism  923 , and the prism  922  (in that order). With each passing of the light beam  816  through a consecutive prism  925 ,  924 ,  923 ,  922 , the light beam  816  is optically magnified and redirected (refracted at an angle) toward the next optical component. After passing through the prisms  925 ,  924 ,  923 , and  922 , the light beam  816  reflects off the surface  902 . The light beam  816  then passes through the prism  922 , the prism  923 , the prism  924 , and the prism  925  (in that order). With each passing through the consecutive prisms  922 ,  923 ,  924 ,  925 , the light beam  816  is optically compressed as it travels toward the aperture  955 . After passing through the prisms  922 ,  923 ,  924 , and  925 , the light beam  816  exits the spectral adjustment apparatus  995  through the aperture  955 . After exiting the spectral adjustment apparatus  995 , the light beam  816  passes through the chamber  815  and reflects off of the output coupler  896  to return to the chamber  815  and the spectral adjustment apparatus  995 . 
     The spectral property of the light beam  816  may be adjusted by changing the relative orientations of the optical components  921 ,  922 ,  923 ,  924 , and/or  925 . Referring to  FIG.  9 B , the rotation of a prism P (which can be any one of prisms  922 ,  923 ,  924 , or  925 ) about an axis that is perpendicular to the plane of the page changes an angle of incidence at which the light beam  816  impinges upon the entrance surface H(P) of that rotated prism P. Moreover, two local optical qualities, namely, an optical magnification OM(P) and a beam refraction angle δ(P), of the light beam  816  through that rotated prism P are functions of the angle of incidence of the light beam  816  impinging upon the entrance surface H(P) of that rotated prism P. The optical magnification OM(P) of the light beam  816  through the prism P is the ratio of a transverse width Wo(P) of the light beam  816 A exiting that prism P to a transverse width Wi(P) of the light beam  816  entering that prism P. 
     A change in the local optical magnification OM(P) of the light beam  816  at one or more of the prisms P within the beam expander  901  causes an overall change in the optical magnification OM  965  of the light beam  816  through the beam expander  901 . Additionally, a change in the local beam refraction angle δ(P) through one or more of the prisms P within the beam expander  901  causes an overall change in an angle of incidence  962  ( FIG.  9 A ) of the light beam  816 A at the surface  902  of the grating  921 . The wavelength of the light beam  816  may be adjusted by changing the angle of incidence  962  ( FIG.  9 A ) at which the light beam  816  impinges upon the surface  902  of the grating  921 . The spectral bandwidth of the light beam  816  may be adjusted by changing the optical magnification  965  of the light beam  816 . 
     Accordingly, the spectral properties of the light beam  816  may be changed or adjusted by controlling the orientation of the grating  921  and/or one or more of the prisms  922 ,  923 ,  924 ,  925  via the respective actuators  921 A,  922 A,  923 A,  924 A,  925 A. The actuators  921 A,  922 A,  923 A,  924 A,  925 A may be, for example, piezoelectric actuators that change shape in response to the application of voltage. Other implementations of the spectral adjustment apparatus are possible. 
     Referring again to  FIG.  8 A , the spectral properties of the light beam  816  may be adjusted in other ways. For example, the spectral properties, such as the spectral bandwidth and center wavelength, of the light beam  816  may be adjusted by controlling a pressure and/or gas concentration of the gaseous gain medium of the chamber  815 . For implementations in which the light-generation module  810  is an excimer source, the spectral properties (for example, the spectral bandwidth or the center wavelength) of the light beam  816  may be adjusted by controlling the pressure and/or concentration of, for example, fluorine, chlorine, argon, krypton, xenon, and/or helium in the chamber  815 . 
     The pressure and/or concentration of the gaseous gain medium  819  is controllable with a gas supply system  890 . The gas supply system  890  is fluidly coupled to an interior of the discharge chamber  815  via a fluid conduit  889 . The fluid conduit  889  is any conduit that is capable of transporting a gas or other fluid with no or minimal loss of the fluid. For example, the fluid conduit  889  may be a pipe that is made of or coated with a material that does not react with the fluid or fluids transported in the fluid conduit  889 . The gas supply system  890  includes a chamber  891  that contains and/or is configured to receive a supply of the gas or gasses used in the gain medium  819 . The gas supply system  890  also includes devices (such as pumps, valves, and/or fluid switches) that enable the gas supply system  890  to remove gas from or inject gas into the discharge chamber  815 . The gas supply system  890  is coupled to the control system  250 . 
     The optical oscillator  812  also includes a spectral analysis apparatus  898 . The spectral analysis apparatus  898  is a measurement system that may be used to measure or monitor the wavelength of the light beam  816 . In the example shown in  FIG.  8 A , the spectral analysis apparatus  898  receives light from the output coupler  896 . In some implementations, the spectral analysis apparatus  898  is part of the optical measurement apparatus  260 . 
     The light-generation module  810  may include other components and systems. For example, the light-generation module  810  may include a beam preparation system  899 . The beam preparation system  899  may include a pulse stretcher that stretches each pulse that interacts with the pulse stretcher in time. The beam preparation system also may include other components that are able to act upon light such as, for example, reflective and/or refractive optical elements (such as, for example, lenses and mirrors), and/or filters. In the example shown, the beam preparation system  899  is positioned in the path of the exposure beam  816 . However, the beam preparation system  899  may be placed at other locations within the system  800 . 
     The system  800  also includes the scanner apparatus  880 . The scanner apparatus  880  exposes a wafer  882  with a shaped exposure beam  816 A. The shaped exposure beam  816 A is formed by passing the exposure beam  816  through a projection optical system  881 . The scanner apparatus  880  may be a liquid immersion system or a dry system. The scanner apparatus  880  includes a projection optical system  881  through which the exposure beam  816  passes prior to reaching the wafer  882 , and a sensor system or metrology system  870 . The wafer  882  is held or received on a wafer holder  883 . The scanner apparatus  880  also may include, for example, temperature control devices (such as air conditioning devices and/or heating devices), and/or power supplies for the various electrical components. 
     The metrology system  870  includes a sensor  871 . The sensor  871  may be configured to measure a property of the shaped exposure beam  816 A such as, for example, bandwidth, energy, pulse duration, and/or wavelength. The sensor  871  may be, for example, a camera or other device that is able to capture an image of the shaped exposure beam  816 A at the wafer  882 , or an energy detector that is able to capture data that describes the amount of optical energy at the wafer  882  in the x-y plane. 
     Referring also to  FIG.  8 B , the projection optical system  881  includes a slit  884 , a mask  885 , and a projection objective, which includes a lens system  886 . The lens system  886  includes one or more optical elements. The exposure beam  816  enters the scanner apparatus  880  and impinges on the slit  884 , and at least some of the output light beam  816  passes through the slit  884  to form the shaped exposure beam  816 A. In the example of  FIGS.  8 A and  8 B , the slit  884  is rectangular and shapes the exposure beam  816  into an elongated rectangular shaped light beam, which is the shaped exposure beam  816 A. The mask  885  includes a pattern that determines which portions of the shaped light beam are transmitted by the mask  885  and which are blocked by the mask  885 . Microelectronic features are formed on the wafer  882  by exposing a layer of radiation-sensitive photoresist material on the wafer  882  with the exposure beam  816 A. The design of the pattern on the mask is determined by the specific microelectronic circuit features that are desired. 
     The configuration shown in  FIG.  8 A  is an example of a configuration for a DUV system. Other implementations are possible. For example, the light-generation module  810  may include N instances of the optical oscillator  812 , where N is an integer number greater than one. In these implementations, each optical oscillator  812  is configured to emit a respective light beam toward a beam combiner, which forms the exposure beam  816 . 
       FIG.  10    shows another example configuration of a DUV system.  FIG.  10    is a block diagram of a photolithography system  1000  that includes a light-generation module  1010  that produces a pulsed light beam  1016 , which is provided to the scanner apparatus  880 . The photolithography system  1000  also includes the beam separator  117 , the optical measurement apparatus  260 , and the control system  250 . The control system  250  is coupled to the optical measurement apparatus  260 , various components of the light-generation module  1010 , and the scanner apparatus  1080  to control various operations of the system  1000 . In the example of  FIG.  10   , the beam separator  117  directs a portion of the output light beam  1016  to the optical measurement apparatus  260 . Other implementations are possible. For example, the beam separator  117  may be positioned to interact with a seed light beam  1018 . 
     The light-generation module  1010  is a two-stage laser system that includes a master oscillator (MO)  1012 _ 1  that provides the seed light beam  1018  to a power amplifier (PA)  1012 _ 2 . The PA  1012 _ 2  receives the seed light beam  1018  from the MO  1012 _ 1  and amplifies the seed light beam  1018  to generate the light beam  1016  for use in the scanner apparatus  880 . For example, in some implementations, the MO  1012 _ 1  may emit a pulsed seed light beam, with seed pulse energies of approximately 1 milliJoule (mJ) per pulse, and these seed pulses may be amplified by the PA  1012 _ 2  to about 10 to 15 mJ, but other energies may be used in other examples. 
     The MO  1012 _ 1  includes a discharge chamber  1015 _ 1  having two elongated electrodes  1013   a _ 1  and  1013   b _ 1 , a gain medium  1019 _ 1  that is a gas mixture, and a fan (not shown) for circulating the gas mixture between the electrodes  1013   a _ 1 ,  1013   b _ 1 . A resonator is formed between a line narrowing module  1095  on one side of the discharge chamber  1015 _ 1  and an output coupler  1096  on a second side of the discharge chamber  1015 _ 1 . 
     The discharge chamber  1015 _ 1  includes a first chamber window  1063 _ 1  and a second chamber window  1064 _ 1 . The first and second chamber windows  1063 _ 1  and  1064 _ 1  are on opposite sides of the discharge chamber  1015 _ 1 . The first and second chamber windows  1063 _ 1  and  1064 _ 1  transmit light in the DUV range and allow DUV light to enter and exit the discharge chamber  1015 _ 1 . 
     The line narrowing module  1095  may include a diffractive optic such as a grating that finely tunes the spectral output of the discharge chamber  1015 _ 1 . The light-generation module  1010  also includes a line center analysis module  1068  that receives an output light beam from the output coupler  1096  and a beam coupling optical system  1069 . The line center analysis module  1068  is a measurement system that may be used to measure or monitor the wavelength of the seed light beam  1018 . The line center analysis module  1068  may be placed at other locations in the light-generation module  1010 , or it may be placed at the output of the light-generation module  1010 . 
     The gas mixture that is the gain medium  1019 _ 1  may be any gas suitable for producing a light beam at the wavelength and bandwidth required for the application. For an excimer source, the gas mixture may contain a noble gas (rare gas) such as, for example, argon or krypton, a halogen, such as, for example, fluorine or chlorine and traces of xenon apart from a buffer gas, such as helium. Specific examples of the gas mixture include argon fluoride (ArF), which emits light at a wavelength of about 193 nm, krypton fluoride (KrF), which emits light at a wavelength of about 248 nm, or xenon chloride (XeCl), which emits light at a wavelength of about 351 nm. Thus, the light beams  1016  and  1018  include wavelengths in the DUV range in this implementation. The excimer gain medium (the gas mixture) is pumped with short (for example, nanosecond) current pulses in a high-voltage electric discharge by application of a voltage to the elongated electrodes  1013   a _ 1 ,  1013   b _ 1 . 
     The PA  1012 _ 2  includes a beam coupling optical system  1069  that receives the seed light beam  1018  from the MO  1012 _ 1  and directs the seed light beam  1018  through a discharge chamber  1015 _ 2 , and to a beam turning optical element  1092 , which modifies or changes the direction of the seed light beam  1018  so that it is sent back into the discharge chamber  1015 _ 2 . The beam turning optical element  1092  and the beam coupling optical system  1069  form a circulating and closed loop optical path in which the input into a ring amplifier intersects the output of the ring amplifier at the beam coupling optical system  1069 . 
     The discharge chamber  1015 _ 2  includes a pair of elongated electrodes  1013   a _ 2 ,  1013   b _ 2 , a gain medium  1019 _ 2 , and a fan (not shown) for circulating the gain medium  1019 _ 2  between the electrodes  1013   a _ 2 ,  1013   b _ 2 . The gas mixture that forms the gain medium  1019 _ 2  may be the same as the gas mixture that forms gain medium  1019 _ 1 . 
     The discharge chamber  1015 _ 2  includes a first chamber window  1063 _ 2  and a second chamber window  1064 _ 2 . The first and second chamber windows  1063 _ 2  and  1064 _ 2  are on opposite sides of the discharge chamber  1015 _ 2 . The first and second chamber windows  1063 _ 2  and  1064 _ 2  transmit light in the DUV range and allow DUV light to enter and exit the discharge chamber  1015 _ 2 . 
     When the gain medium  1019 _ 1  or  1019 _ 2  is pumped by applying voltage to the electrodes  1013   a _ 1 ,  1013   b _ 1  or  1013   a _ 2 ,  1013   b _ 2 , respectively, the gain medium  1019 _ 1  and/or  1019 _ 2  emits light. When voltage is applied to the electrodes at regular temporal intervals, the light beam  1016  is pulsed. Thus, the repetition rate of the pulsed light beam  1016  is determined by the rate at which voltage is applied to the electrodes. The repetition rate of the pulses may range between about 500 and 6,000 Hz for various applications. In some implementations, the repetition rate may be greater than 6,000 Hz, and may be, for example, 12,000 Hz or greater, but other repetition rates may be used in other implementations. 
     The output light beam  1016  may be directed through a beam preparation system  1099  prior to reaching the scanner apparatus  880 . The beam preparation system  1099  may include a bandwidth analysis module that measures various parameters (such as the bandwidth or the wavelength) of the beam  1016 . The beam preparation system  1099  also may include a pulse stretcher that stretches each pulse of the output light beam  1016  in time. The beam preparation system  1099  also may include other components that are able to act upon the beam  1016  such as, for example, reflective and/or refractive optical elements (such as, for example, lenses and mirrors), filters, and optical apertures (including automated shutters). 
     The DUV light-generation module  1010  also includes the gas management system  1090 , which is in fluid communication with an interior  1078  of the DUV light-generation module  1010 . 
     Other aspects of the invention are set out in the following numbered clauses.
     1. An optical measurement apparatus for a light source, the optical measurement apparatus comprising: 
   an etalon comprising a focusing lens configured to focus light at an image plane, wherein the etalon is associated with a calibration parameter related to the focusing lens, and the calibration parameter has   a pre-set default value;   an optical detector configured to detect an interference pattern produced by the etalon and to produce information related to the etalon, the information comprising first spatial information for a first fringe and second spatial information for a second fringe; and   a control system coupled to the optical detector, the control system configured to:   determine a measurement error value of the etalon based on first spatial information from the detector, the second spatial information, and an initial value of the calibration parameter; and   analyze the measurement error value to determine whether to adjust the pre-set default value.   
   2. The optical measurement apparatus of clause 1, wherein the light source comprises a deep ultraviolet (DUV) light source.   3. A light source comprising: 
   a light-generation apparatus; and   an optical measurement apparatus comprising:   an etalon comprising a focusing lens configured to focus light at an image plane, the etalon associated with a calibration parameter related to the focusing lens, and the calibration parameter having a pre-set default value;   an optical detector configured to detect an interference pattern produced by the etalon and to produce information related to the etalon, the information comprising first spatial information for a first fringe and second spatial information for a second fringe; and   a control system coupled to the optical detector, the control system configured to:   determine a measurement error value of the etalon based on the first spatial information, the second spatial information, and an initial value of the calibration parameter; and   analyze the measurement error value to determine whether to adjust the pre-set default value.   
   4. The light source of clause 3, wherein the light-generation apparatus comprises a deep ultraviolet (DUV) light source.   5. The light source of clause 4, wherein the light-generation apparatus comprises a master oscillator.   6. The light source of clause 4, wherein the light generation apparatus further comprises a power amplifier.   7. The light source of clause 4, wherein the light-generation apparatus comprises a plurality of master-oscillators.   8. The light source of clause 3, further comprising an optical element configured to receive light from the light-generation apparatus and to direct light to the etalon.   9. The light source of clause 8, wherein the optical element is a dispersive optical element.   10. A method comprising: 
   accessing information relating to an etalon, wherein the etalon is associated with a calibration parameter having a pre-set default value, the etalon is configured to produce an interference pattern comprising a plurality of fringes from a received light beam, and the information relating to the etalon comprises first spatial information related to a first fringe of the plurality of fringes and second spatial information related to a second fringe of the plurality of fringes;   determining a first wavelength value of the received light beam based on the spatial information related to the first fringe and an initial value of the calibration parameter;   determining a second wavelength value of the received light beam based on the spatial information related to the second fringe and the initial value of the calibration parameter; and   comparing the first wavelength value and the second wavelength value to determine a measurement error value.   
   11. The method of clause 10, further comprising determining whether to adjust the pre-set default value of the calibration parameter based on the measurement error value.   12. The method of clause 11, wherein the measurement error value comprises a difference between the first wavelength value and the second wavelength value, and pre-set default value is adjusted to a value that causes a magnitude of the measurement error value to be less than a threshold.   13. The method of clause 12, wherein the pre-set default value is adjusted to a value that causes the measurement error value to be zero.   14. The method of clause 10, wherein the calibration parameter comprises a focal length of a lens at an output of the etalon, and the measurement error comprises a difference between the first wavelength value and the second wavelength value.   15. The method of clause 10, wherein the first spatial information comprises a diameter of the first fringe, and the second spatial information comprises a diameter of the second fringe.   16. The method of clause 10, further comprising directing a light beam toward the etalon; and wherein the first fringe is produced by a first portion of the light beam, and the second fringe is produced by a second portion of the light beam.   17. The method of clause 16, wherein the light beam comprises a plurality of pulses, and the first portion of the light beam comprises a first one of the plurality of pulses, and the second portion of the light beam comprises a second one of the plurality of pulses.   18. The method of clause 16, wherein the light beam comprises a continuous-wave light beam, and the first portion of the light beam comprises a first sample of the light beam, and the second portion of the light beam comprises a second sample of the light beam.   19. The method of clause 16, further comprising: 
   changing the initial value of the calibration parameter to an updated value of the calibration parameter;   actuating an optical element to thereby change the wavelength of the received light beam;   determining a first wavelength value of the received light beam based on the spatial information related to the first fringe and the updated value of the calibration parameter;   determining a second wavelength value of the received light beam based on the spatial information related to the second fringe and the updated value of the calibration parameter; and   comparing the first wavelength value and the second wavelength value to determine a measurement error value based on the updated value of the calibration parameter.   
   20. The method of clause 19, wherein the optical element is actuated to increase the wavelength or to decrease the wavelength prior to determining the second wavelength value.   21. The method of clause 19, wherein the first wavelength value and the second wavelength value are determined more than once each time the optical element is actuated.   22. The method of clause 20, further comprising determining whether to adjust the pre-set default value of the calibration parameter by comparing the error measurement value determined based on the initial value of the calibration parameter and the error measurement value determined based on the updated value of the calibration parameter.   23. The method of clause 10, wherein the initial value of the calibration parameter is the pre-set default value.   24. The method of clause 10, wherein the first fringe and the second fringe are in the interference pattern at the same time.   25. A method for calibrating an etalon, the method comprising: 
   accessing information relating to an etalon, wherein the etalon is associated with a calibration parameter having a pre-set default value, the etalon is configured to produce an interference pattern comprising a plurality of fringes from a received light beam, and the information relating to the etalon comprises first spatial information related to a first fringe of the plurality of fringes and second spatial information related to a second fringe of the plurality of fringes;   determining a measurement error value of the etalon based on the first spatial information, the second spatial information, and an initial value of the calibration parameter; and   analyzing the measurement error value to determine whether to adjust the pre-set default value.   
   26. The method of clause 25, wherein the calibration parameter comprises a focal length of a lens at an output of the etalon.   27. The method of clause 26, further comprising: 
   determining a first wavelength value based on the first spatial information; and   determining a second wavelength value based on the second spatial information, wherein the measurement error comprises a difference between the first wavelength value and the second wavelength value.   
   28. The method of clause 25, wherein 
   the calibration parameter comprises a plurality of initial values;   determining a measurement error value comprises simulating a plurality of measurement error values for each of the plurality of initial values, each measurement error value being based on the first spatial information, the second spatial information, and one of the plurality of initial values of the calibration parameter; and   analyzing the measurement error values comprises analyzing the simulated measurement error values.   
   

     Other implementations are within the scope of the claims.