Phase-generating carrier interrogators and related phase-generating carrier investigation methods

Abstract

The phase-generating carrier interrogator comprises a complex multicarrier combiner capable of operating to generate at least a laser-modulated carrier signal for modulating a laser source; a laser power monitor branch capable of operating to measure the power metric of the laser source; a wavelength reference branch including a wavelength reference for wavelength stabilization of the laser source and a wavelength reference detector for measuring the wavelength reference and obtaining a wavelength reference signal; and a signal processing module. The signal processing module is capable of estimating a monitor power-carrier delay that describes the propagation delay of the power monitor signal in the laser power monitor signal path, and using the estimated monitor power-carrier delay, estimating a wavelength reference excess delay that describes the difference between the wavelength reference power-carrier delay and the monitor power-carrier delay that describes the propagation delay of the wavelength reference signal in the wavelength reference branch.

Description

[Technical Field]

[0001] (Cross-reference of related applications)

[0001] This application claims priority to European Patent Application No. 23157591.1, filed on 20 February 2023. This application is incorporated in its entirety by reference.

[0002]

[0002] The present invention relates to an interferometry method, and more particularly to a method and apparatus for investigating phase-generating carriers (PGCs) using an interferometer. [Background technology]

[0003]

[0003] A lithography apparatus is a machine built to apply a desired pattern to a substrate. Lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithography apparatus can project, for example, a pattern (often called a "design layout" or "design") of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer).

[0004]

[0004] As semiconductor manufacturing processes continue to advance, the dimensions of circuit elements are constantly shrinking, while the amount of functional elements, such as transistors, per device has steadily increased over decades, following a trend commonly known as Moore's Law. To keep pace with Moore's Law, the semiconductor industry is seeking technologies that can generate increasingly miniaturized features. To project patterns onto a substrate, lithography equipment can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the features that can be patterned on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Using lithography equipment with extreme ultraviolet (EUV) radiation in the range of 4 nm to 20 nm, for example, with wavelengths of 6.7 nm or 13.5 nm, allows for the formation of smaller features on the substrate than using lithography equipment with, for example, radiation at a wavelength of 193 nm.

[0005]

[0005] In a lithography apparatus, it is important to accurately measure the position of specific components of the lithography apparatus. Such components may include, among other things, one or more wafer (or substrate) stages, reticle (or mask) stages, and / or one or more optical components (e.g., mirrors in the projection system of the lithography apparatus). An interferometer can be used for this purpose, and in particular a multi-axis interferometer can be used. A multi-axis interferometer may include multiple individual interferometers, one for each axis, and each axis is involved in position measurement of a different degree of freedom. In one embodiment, the interferometer may include a 6-axis interferometer for position measurement of 6 degrees of freedom, which are three mutually perpendicular spatial axes conventionally called the x-axis, y-axis, and z-axis, as well as rotations Rx, Ry, and Rz about each of these axes.

[0006]

[0006] It is known that the wavelength of the laser radiation source of such a phase-generating carrier interferometer interrogator can be stabilized using a wavelength reference such as a gas cell reference.

[0007]

[0007] In particular, it is desirable to improve the method of using such a wavelength reference. [Overview of the Initiative]

[0008]

[0008] In a first aspect of the present invention, a phase-generating carrier interrogator is provided. The phase-generating carrier interrogator includes a complex multicarrier combiner capable of operating to generate at least a laser-modulated carrier signal for modulating a laser radiation source; a laser power monitor branch including a power monitor detector and capable of measuring the power metric of the laser radiation source and obtaining a power monitor signal; a wavelength reference branch including a wavelength reference detector for wavelength stabilization and / or control of the laser radiation source and for measuring the wavelength reference and obtaining a wavelength reference signal; and a signal processing module capable of estimating a monitor power-carrier delay describing the propagation delay of the power monitor signal in the laser power monitor signal path, and using the estimated monitor power-carrier delay, estimating a wavelength reference excess delay describing the difference between the wavelength reference power-carrier delay and the monitor power-carrier delay describing the propagation delay of the wavelength reference signal in the wavelength reference branch. It is equipped with.

[0009]

[0009] A second aspect of the present invention provides a method for estimating at least a wavelength reference excess delay related to a wavelength reference. This method includes: measuring the power metric of a laser source to obtain a power monitor signal; stabilizing and / or controlling the wavelength of the laser source using the wavelength reference signal from a wavelength reference; estimating a monitor power-carrier delay that describes the propagation delay of the power monitor signal in the laser power monitor signal path; and using the estimated monitor power-carrier delay to estimate a wavelength reference excess delay that describes the difference between the wavelength reference power-carrier delay and the monitor power-carrier delay that describes the propagation delay of the wavelength reference signal at the wavelength reference branch. [Brief explanation of the drawing]

[0010]

[0010] Hereinafter, an embodiment of the present invention will be described as an example only with reference to the attached schematic diagram.

[0011] [Figure 1] A schematic diagram of a lithography apparatus is shown. [Figure 2] This is a flowchart conceptually illustrating the signal processing method in PGC interferometry according to known methods. [Figure 3] This is a conceptual flowchart illustrating a signal processing method for determining carrier delay in a PGC interferometry setting, according to the first embodiment. [Figure 4] This is a conceptual flowchart illustrating a signal processing method for determining the power monitor carrier delay in a PGC interferometry setting, according to the second embodiment. [Figure 5] This is a conceptual flowchart illustrating a signal processing method for calibrating wavelength-referenced excess carrier delay in a PGC interferometry setting, according to the third embodiment. [Figure 6] This flowchart conceptually illustrates a signal processing method for determining the laser pseudo-delay in a PGC interferometry setting according to the fourth embodiment, and for using each of the calibrated delays shown in Figures 4 to 6 for laser wavelength stabilization. [Figure 7] This flowchart conceptually illustrates a signal processing method for calibrating the interferometer excess carrier delay in a PGC interferometry setting according to the fifth embodiment, and for using each of the calibrated delays shown in Figures 4 to 7 for interferometer signal processing. [Modes for carrying out the invention]

[0012]

[0011] In this specification, the terms “radiation” and “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having wavelengths in the range of about 5 to 100 nm). Interferometers described herein can use radiation having wavelengths greater than 400 nm or greater than 500 nm. More specifically, as an example, the interferometer radiation wavelength can be 633 nm or 1530 nm.

[0013]

[0012] The terms “reticle,” “mask,” or “patterning device,” as used herein, may be broadly interpreted to refer to a general-purpose patterning device that can be used to give an incoming radiation beam a patterned cross-section corresponding to a pattern generated on a target portion of a substrate. The term “light bulb” may also be used in this context. In addition to classic masks (transmissive or reflective masks, binary masks, phase-shift masks, hybrid masks, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0014]

[0013] Figure 1 schematically shows a lithography apparatus LA. The lithography apparatus LA includes an illumination system (also called an illuminator) IL configured to adjust a radiation beam B (e.g., UV radiation, DUV radiation, or EUV radiation), a mask support (e.g., a mask table) MT configured to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to precisely position the patterning device MA according to specific parameters, a substrate support (e.g., a wafer table) WT configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to precisely position the substrate support according to specific parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project the pattern applied to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (e.g., including one or more dies).

[0015]

[0014] During operation, the illumination system IL receives the radiated beam from the radiation source SO, for example, via the beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, and / or other types of optical components, or any combination thereof, for inducing, shaping, and / or controlling the radiation. The illuminator IL can be used to adjust the radiated beam B so that the radiated beam B has a desired spatial and angular intensity distribution within the cross-section on the surface of the patterning device MA.

[0016]

[0015] The term “projection system” PS as used herein should be interpreted broadly and may encompass a variety of projection systems, including refractive optical systems, reflective optical systems, reflective refractive optical systems, anamorphic optical systems, magneto-optical systems, electromagnetic optical systems, and / or electrostatic optical systems, or any combination thereof, depending on the exposure radiation used and / or other factors such as the use of immersion liquid or vacuum. Where the term “projection lens” is used herein, it should be considered synonymous with the more general term “projection system” PS.

[0017]

[0016] The lithography apparatus LA may be of a type that can cover at least a portion of the substrate with a liquid having a relatively high refractive index, such as water, to fill the space between the projection system PS and the substrate W. This is also called immersion lithography. Further information relating to immersion techniques is given in US Patent No. 6952253, which is incorporated herein by reference.

[0018]

[0017] The lithography apparatus LA may also be of a type having two (also called a "dual stage") or more substrate support WTs. In such a "multistage" machine, the substrate support WTs can be used in parallel, and / or, while a substrate W on one substrate support WT is being used to expose a pattern to that substrate W, preparation steps for subsequent exposure can be performed on a substrate W placed on the other substrate support WT.

[0019]

[0018] In addition to the substrate support WT, the lithography apparatus LA may include a measurement stage. The measurement stage is positioned to hold sensors and / or cleaning devices. The sensors may be positioned to measure the characteristics of the projection system PS or the characteristics of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning devices may be positioned to clean parts of the lithography apparatus, such as a part of the projection system PS or a part of the system that provides the immersion fluid. If the substrate support WT is separated from the projection system PS, the measurement stage may move below the projection system PS.

[0020]

[0019] During operation, the radiating beam B is incident on a patterning device, such as a mask MA, which is held on a mask support MT, and a pattern is formed by the pattern (design layout) present on the patterning device MA. After crossing the mask MA, the radiating beam B passes through a projection system PS, which focuses the beam onto a target portion C on the substrate W. Using a second positioner PW and a position measuring system IF, the substrate support WT can be precisely moved to position various target portions C at focused and aligned positions within the path of the radiating beam B, for example. Similarly, the patterning device MA can be precisely positioned relative to the path of the radiating beam B using a first positioner PM and optionally another position sensor (not explicitly shown in Figure 1). The patterning device MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. The substrate alignment marks P1, P2 occupy dedicated target portions as shown, but may be positioned in the space between target portions. When substrate alignment marks P1 and P2 are positioned between target portion C, they are known as scribe line alignment marks.

[0021]

[0020] To clarify the present invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, namely the x-axis, y-axis, and z-axis. Each of the three axes is orthogonal to the other two axes. A rotation about the x-axis is called an Rx rotation. A rotation about the y-axis is called a Ry rotation. A rotation about the z-axis is called an Rz rotation. The x-axis and y-axis define the horizontal plane, and the z-axis is perpendicular. The Cartesian coordinate system is used not to limit the present invention, but solely for the purpose of clarity. Alternatively, the present invention can be clarified using another coordinate system, such as a cylindrical coordinate system. For example, the Cartesian coordinate system may be oriented differently, such as so that the z-axis has a component along the horizontal plane.

[0022]

[0021] The position measurement system PMS may include any type of sensor suitable for determining the position of the substrate support WT. The position measurement system PMS may include any type of sensor suitable for determining the position of the mask support MT. The sensor may be an optical sensor such as an interferometer or an encoder. The position measurement system PMS may include a system that combines an interferometer and an encoder. The sensor may be another type of sensor such as a magnetic sensor, a capacitive sensor, or an inductive sensor. The position measurement system PMS can determine the position relative to a reference such as a metrology frame MF or a projection system PS. The position measurement system PMS can determine the position of the substrate table WT and / or mask support MT by measuring the position or by measuring the time derivative of the position such as velocity or acceleration.

[0023]

[0022] The position measurement system (PMS) may include an interferometer system. An interferometer system is known, for example, by U.S. Patent No. 6,020,964, filed July 13, 1998, which is incorporated herein by reference. The interferometer system may include a beam splitter, mirrors, a reference mirror, and a sensor. The radiating beam is split into a reference beam and a measurement beam by the beam splitter. The measurement beam propagates to the mirrors, is reflected by the mirrors and returns to the beam splitter. The reference beam propagates to the reference mirrors, is reflected by the reference mirrors and returns to the beam splitter. In the beam splitter, the measurement beam and the reference beam are combined to form a combined radiating beam. The combined radiating beam is incident on a sensor. The sensor determines the phase or frequency of the combined radiating beam. The sensor generates a signal based on the phase or frequency. This signal represents the displacement of the mirror. In one embodiment, the mirror is connected to a substrate support WT. The reference mirror may be connected to a metrologic frame MF. In one embodiment, the measurement beam and the reference beam are coupled to a combined emission beam by an additional optical component rather than a beam splitter.

[0024]

[0023] In lithography processes, it is desirable to frequently measure the generated structures, for example, for process control and verification. Tools for performing such measurements are usually called metrologic tools (MT). Various types of metrologic tools (MT) for performing such measurements are known, including scanning electron microscopes and various forms of scattrometer metrologic tools (MT). A scattrometer is a versatile instrument that enables the measurement of parameters of a lithography process, and the measurements are performed by having a sensor on the pupil or conjugate plane of the pupil of the scattrometer's objective system (usually called a pupil-based measurement), or by having a sensor on the image plane or conjugate plane of the image plane (in this case, usually called an image-based or field-based measurement). Such scatorometers and related measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032, or EP1,628,164A, which are incorporated into this application by reference.

[0025]

[0024] Interferometry for position measurement systems of lithography (scanner) or metrology equipment has been proposed to use phase-generating carrier (PGC) interferometry. PGC interferometry requires less interferometer hardware than conventional homodyne or heterodyne investigation techniques, but the required signal processing is more complex.

[0026]

[0025] By using a radiation source or laser source such as a wavelength-modulated laser diode in combination with an unbalanced interferometer (having a non-zero optical path difference OPD), in addition to the target phase φ(t) induced by the object being measured, periodic phase modulation or sinusoidal modulation of the interferometer phase m·sin(ω mod ·t) can be generated. The modulation index m of this modulation is

[0027]

number

[0028] It can be described by: Here,

[0029]

number

[0030] is the laser frequency fluctuation amplitude, and c is the speed of light.

[0031]

[0026] Wavelength modulation can be generated by many different methods. Two of the selectable methods are described below: 1) the emission wavelength of the laser can be changed (this is the lowest cost option), or 2) the laser can be operated at a constant emission frequency and periodic wavelength modulation can be generated by an additional (electro-optic) phase modulator component located downstream of the laser but common to all interferometers. This latter method has advantages over the first method because it avoids modulation of the laser output power, which is a source of inaccuracy.

[0032]

[0027] Figure 2 is a flowchart conceptually showing the signal processing in PGC interferometry. The multicarrier combiner MCS modulates sinusoidal modulation for the laser diode LD of the interferometer sin(ω mod This generates (t). This sinusoidal modulation is either the modulation amplitude or the current excitation amplitude.

[0033]

number

[0034] This is combined with (for example, multiplied by) and further combined with (for example, added by) the bias current BC. This laser current excitation amplitude

[0035]

number

[0036] The following is the laser frequency fluctuation amplitude.

[0037]

Number

[0038]

Number

[0039] Here, η is the current - to - frequency sensitivity of the laser.

[0040]

[0028] The optical power (interferometer signal S IFM (t)) detected by the photodetector PD of the interferometer can be described as follows (ignoring delay for now). S IFM (t)=B + A·cos(φ(t)+m·sin(ω mod ·t)) Here, B is the background power, and A is the amplitude of the power of the interference fringes. The ratio A / B is the interference contrast, and 0≦A / B≦1 is satisfied. Hereafter, the phase - modulation amplitude m is referred to as the modulation index.

[0041]

[0029] This sinusoidal phase modulation functions so as to generate a series of demodulation carrier frequencies or phase - generation carrier frequencies in the detected output power of the interferometer as harmonics of the modulation frequency ω mod . These phase - generation carriers can take the following forms. sin((2k - 1)·ω mod ·t),cos(2k·ω mod ·t) Here, k represents an integer from 1 to infinity for defining the order n.

[0042]

[0030] The amplitude of the odd - order carrier frequencies (carriers) is proportional to the sine of the phase φ(t) induced by the measurement object, and the amplitude of the even - order carrier frequencies (carriers) is proportional to the cosine of the phase φ(t) induced by the measurement object. Also, each carrier of order n has a coefficient J nIt is attenuated by (m), which is the first kind Bessel function of order n (where J0(m) is the DC component of the Fourier series described by the terms enclosed in parentheses). Therefore, the optical power S(t) can be described as follows:

[0043]

number

[0044]

[0031] The time-varying phase φ(t) (and its time derivative) induced by the object being measured cannot be directly used. Instead, this phase φ(t) (object phase) induced by the object being measured can be estimated by a dynamic state estimator SE, also known as a process model (for example, modeling the dynamic state of the object being measured, which could be the instantaneous position of an object such as a stage). This estimation process is phase prediction.

[0045]

number

[0046] The (estimated value of the target phase) can be calculated and compared with the true target-induced phase φ(t) contained in the signal S(t). Phase residuals obtained from this comparison.

[0047]

number

[0048] Using this, the dynamic state predicted by the process model SE can be corrected. In this way, the dynamic state estimator uses the previous state and the aforementioned phase residual.

[0049]

number

[0050] From the aforementioned estimated phase prediction

[0051]

number

[0052] A new state including can be determined. The corrected state is the output of the system. The resulting estimated loop is actually a (digital) phase-locked loop (PLL), which is a Kalman filter.

[0053]

[0032] By properly processing the signal S(t) (for example, within a signal processing module), the desired phase residual is obtained.

[0054]

number

[0055] A complex phasor having as its argument

[0056]

number

[0057] A (phase residual phasor) can be constructed. The necessary signal processing involves three conceptual steps. In the first step, the interferometer signal S(t) is subjected to negative phase prediction.

[0058]

number

[0059] A complex conjugate phasor of magnitude 1 with an argument of 0.

[0060]

number

[0061] Multiply by . This phasor can be constructed using the first lookup table or sine / cosine lookup table LUT1. In the second step, each carrier (i.e., at least one even-order and one odd-order) is considered, so the demodulated component D n (t) or demodulation is formed respectively. Synchronous demodulation is cos(2k·ω) of each carrier. mod ·t),-sin((2k-1)·ω mod This involves multiplication by (t), followed by processing with a low-pass filter (LPF). As a result of these two steps, the following even and odd demodulations are obtained.

[0062]

number

[0063] Here, angle brackets <> indicate time averaging or low-pal filtering. Each demodulation includes two low-pal filtered phasors, i.e., the desired deflection angle.

[0064]

number

[0065] A first phasor including and declination

[0066]

number

[0067] This is an additional phasor having the following characteristics: In situations where the process model closely tracks the desired phase φ(t), the phase residual

[0068]

number

[0069] It is small, and the corresponding first phasor

[0070]

number

[0071] It is always near the real axis or on the real axis. However, additional phasors

[0072]

number

[0073] It rotates at a rate twice the rate of change of the phase φ(t) induced by the object being measured, which can be quite large. Therefore, depending on the rate of change (e.g., velocity), attenuation occurs in this additional phasor due to low-pulse filtering, whereas this does not occur in the desired first phasor.

[0074]

[0033] In the third processing step, the even and odd demodulations are combined by a properly weighted sum in order to remove the additional phasors. In the simplest case, where one even demodulation is combined with one odd demodulation, the appropriate weighting coefficient is the inverse Bessel function.

[0075]

number

[0076]

[0034] It should be noted that the same digital low-pass filter (LPF) acts on both of these demodulations, and therefore the second phasors of each of these demodulations cancel each other out.

[0077]

[0035] As a result of the above three processing steps, the phase residual first phasor

[0078]

number

[0079] This is obtained.

[0080]

number

[0081] That is correct, therefore the phase residual

[0082]

number

[0083] If approaches zero, it is on or near the real axis. Here, the magnitude and phase residual can be separated by inputting this phasor into a Cartesian-to-polar coordinate conversion unit CtP, which can be conveniently implemented as a CORDIC algorithm in an FPGA (or software). For convenience of notation, the phase residual

[0084]

number

[0085] The time dependence of this is quasi-static, so it will be omitted here.

[0086]

[0036] In order to correctly detect various (radix and even-order) carriers of the photodetector signal, it is important to phase-match the demodulated carrier with respect to each carrier signal of the photodetector signal. A carrier phase shift reduces the intensity of the demodulation (cosine-dependent) determined from the demodulated carrier. Therefore, in extreme cases (e.g., absolute phase shift of more than a quarter cycle), the demodulation may become zero or obtain an incorrect sign, which will render the interrogator inoperable. For very small phase shifts, the intensity reduction is a secondary effect.

[0087]

[0037] The wavelength modulation frequency of a laser diode (LD) is typically on the order of several (tens) MHz. This can be achieved by current modulation of a distributed feedback (DFB) laser diode, which results in modulation of the junction temperature and the subsequent emission frequency ν(t) according to the following:

[0088]

number

[0089] Here, θ(ω mod ) is a phase delay that depends on the modulation frequency caused by the thermal process at the laser junction.

[0090]

number

[0091] This represents the amplitude of the laser frequency fluctuation around the average optical frequency ν0.

[0092]

[0038] However, the temperature sensitivity of the wavelength affects the average wavelength, which, if not canceled out, leads to a phase drift (target phase) induced by the object being measured. Therefore, an accurate PGC interrogator must have a laser diode stabilized with respect to a wavelength reference. The wavelength reference can be, for example, a gas cell that provides several candidate absorption lines at a precisely known (e.g., traceable to NIST standards) central wavelength. For the purposes of this specification, the optical transmission characteristics of a gas cell around such a single line center are approximated by a Lorentz profile according to the following.

[0093]

number

[0094] Here, ν c ν is the center frequency, HWHM is the half-width at half maximum, and T minThis is the minimum transmission value at the center of the line.

[0095]

[0039] By constantly adjusting the laser bias current according to an appropriate control residual, the average laser optical frequency can be locked to the center of the absorption line. In principle, the fundamental (modulation) frequency component or other odd frequency components in the gas cell output power can be used as the control residual (any odd frequency component can be used, but the fundamental frequency is the most sensitive). If laser power modulation is assumed to be absent, this component becomes zero because the average wavelength is symmetrical when it is at the center of the line. This mechanism is a variation of the PDH (Pound-Drever-Hall) stabilization scheme. As an example, assuming an optical frequency that stays sufficiently close to the center of the line, the Lorentz transmission characteristics can be further approximated as follows.

[0096]

number

[0097]

[0040] By substituting the time-dependent optical frequency, the following can be obtained.

[0098]

number

[0099]

[0041] Fundamental frequency component

[0100]

number

[0101] ν0=ν c It disappears in this case. This equation means that this component is equal to the average optical frequency ν0 at the line center ν c This demonstrates that it can be used as a control residual to stabilize the system.

[0102]

[0042] However, in reality, laser current modulation causes power modulation at the fundamental modulation frequency. In other words, the laser power P(t) can be written as follows:

[0103]

number

[0104] Here,

[0105]

number

[0106] This represents the amplitude of laser power fluctuations around the average power P0.

[0107]

[0043] Therefore, the optical power P at the output of the gas cell GC (t) is in the following form: P GC (t) = T(ν(t))·P(t)

[0108]

[0044] Laser power modulation at the fundamental frequency adds two extra components to the output power of the gas cell at the fundamental frequency. One of these extra components is due to mixing with the DC component at T(t), and the other is due to mixing with the second harmonic component at T(t). The resulting DC, fundamental frequency, and second harmonic frequency components are given by:

[0109]

number

[0110]

[0045] The two additional components at the fundamental frequency control the average optical frequency ν0 to the line center ν c It deviates from the standard. The most major undesirable term is T minIt is proportional to the amplitude of the desirable term. By making the amplitude of the desirable term equal to the amplitude of the major undesirable term, the worst-case optical frequency error can be roughly estimated.

[0111]

number

[0112]

[0046] This formula is thin (small ν HWHM ), deep (small T min This demonstrates the advantages of using absorption lines and gas cells with high laser power (high P0).

[0113]

number

[0114] Lasers are also beneficial.

[0115]

[0047] However, in order to achieve accurate wavelength stabilization, the power modulation coefficient of the photodetector signal must be compensated. This can be done, for example, by detecting the instantaneous laser power (power metric) using a fiber splitter that branches the fixed portion of the laser power to a dedicated power monitor detector (photodiode or photodetector). The digitized instantaneous signal from the gas cell detector can be power-normalized by dividing it by the digitized instantaneous signal from the power monitor detector. It is also possible to power-normalize the digitized interferometer photodetector signals from (multiple) interferometer axes in this way.

[0116]

[0048] In order to ensure accurate power normalization, the power modulation coefficients of all digitized photodetector signals must be phase-matched to the power modulation term of the normalized monitor signal. This is generally not true without compensation. This is because the length of the fiber through which the gas cell and interferometer axis are interconnected is different from the length of the fiber leading to the power monitor photodetector. These buffer delays are equal and / or common across all axes and do not affect the phase matching with respect to the normalized monitor signal. The (digitized) power monitor signal S obtained from the power monitor photodetector mon This can be described as follows:

[0117]

number

[0118] Here, τ mon η is the associated monitor power-carrier delay of the monitor signal in the monitor signal path, and mon This is the power efficiency of the monitor. Similarly, the gas cell signal S from the gas cell photodetector signal. GC (t) is the gas cell power-carrier delay τ of the gas cell signal in the gas cell signal path. GC It is delayed only by the following, which can be described as follows:

[0119]

number

[0120]

[0049] When the monitor signal is used for power normalization of the gas cell signal, it must be delayed by the difference between the monitor power-carrier delay and the gas power-carrier delay. Thereafter, this is the gas cell excess delay τ GC,ex =τ GC -τ mon It is described as follows: That is, the gas cell signal can be normalized by the following:

[0121]

number

[0122]

[0050] In the ideal case, normalization yields a power-unmodulated signal in the following forms.

[0123]

number

[0124]

[0051] One problem addressed herein is gas cell excess delay τ GC,ex This is an estimate. Once gas cell excess delay estimation

[0125]

number

[0126] Once determined, the monitor signal can be delayed by this estimation before being used to normalize the gas cell signal. Since this estimation is generally not an integer sampling interval, the delay of this monitor signal can be achieved using, for example, a variable non-integer delay filter (frequency transfer function).

[0127]

[0052] Another problem is that the normalized gas cell signal depends on the delayed optical frequency signal.

[0128]

number

[0129]

[0053] For this reason, the gas cell wavelength-carrier delay concept is used in this specification, and the gas cell power-carrier delay τ GC And, the laser pseudo-delay τ is the result of the (sometimes drifting) frequency response of the wavelength-modulated thermal process in the laser. LD (ω mod )=-θ(ω mod ) / ω mod It can be defined as including the sum of the two.

[0130]

[0054] Therefore, in order to ensure that the fundamental frequency component in the (properly) normalized gas cell signal is detected with proper sensitivity and the correct sign by synchronous demodulation, the demodulated carrier must be phase-matched with the fundamental frequency component (which is zero) and maintained in a phase-matched state. In other words, the demodulated carrier is ideally -ω mod ·(τ GC +τ LD (ω mod It can be phase-shifted relative to ))

[0131]

[0055] Laser power modulation causes mixing of even-order and octave-order phase-generating carriers in the interferometer signal, similar to how harmonic mixing occurs in the gas cell signal. This results in periodic errors in phase estimation. Laser phase delay θ(ω mod ) Considering the interferometer signal S IFM (t) takes the following form:

[0132]

number

[0133] Here, φ(t) is the phase induced by the object being measured (target phase), and τ IFM This is another interferometer power-carrier delay that describes the unknown propagation delay and / or time-variable propagation delay of the radiation as it travels from the laser to the interferometer photodetector along two beam paths, including the interferometer. This delay (which may be optionally tracked in some embodiments) will be discussed further later. In other embodiments, it may be ignored.

[0134]

[0056] This can be rewritten as follows using the Jacobi-Anger expansion (a special Fourier series expansion).

[0135]

number

[0136]

[0057] The terms proportional to the power modulation amplitude can be rewritten in a form that clearly shows their distinct frequency components.

[0137]

number

[0138]

[0058] Each carrier frequency n·ω mod In this case, power modulation is (n±1)·ω mod The contributions from neighboring carriers on both sides are added (recognizable by the exponents of the associated Bessel function). The carrier phase of each undesirable component is given by the laser phase delay θ(ω mod The desired carriers are determined by the sum and difference of the Bessel functions of adjacent desirable carriers. Odd-order spurious carriers are proportional to cosφ(t), and even-order spurious carriers are proportional to sinφ(t).

[0139]

[0059] The disclosed method relates to calibrating and / or monitoring one or more of the above-described delays. In particular, the method relates to determining a wavelength-referenced excess delay (hereinafter referred to as gas cell excess delay) which describes the difference between a wavelength-referenced power-carrier delay (hereinafter referred to as gas cell power-carrier delay) and a monitor power-carrier delay. The gas cell power-carrier delay describes the propagation delay of the wavelength-referenced signal (hereinafter referred to as gas cell signal) in the wavelength-referenced (hereinafter referred to as gas cell) signal path, and the monitor power-carrier delay describes the propagation delay of the power monitor signal in the power monitor signal path. The wavelength-referenced excess delay can then be used to delay the power monitor signal and obtain a first delayed power monitor signal which can be used to power normalize the gas cell signal.

[0140]

[0060] Such methods include, for example, monitor power-carrier delay residual

[0141]

number

[0142] Based on determining and setting to zero, monitor power-carrier delay τ mon This may include determining and continuously monitoring and / or tracking. Here,

[0143]

number

[0144] is the estimated monitor power-carrier delay (generally, the tilde represents an estimate in this specification). Monitor power-carrier delay residual

[0145]

number

[0146] This can be determined from the demodulated fundamental component (n=1) in the monitor photodetector signal (ideally, the power monitor signal contains no other harmonic components).

[0147]

[0061] Next, monitor power-carrier delay τ mon Gas cell excess delay τ in the gas cell optical path relative to GC,ex A calibration (for example, only once) can be performed. Here, τ GC,ex =τ GC -τ mon This method is effective when the average laser wavelength is within the region between absorption lines relative to the gas cell, and the gas cell excess delay residual is...

[0148]

number

[0149] This may include setting it to zero. Here,

[0150]

number

[0151] This is the gas cell excess delay estimation. The monitor signal is used to estimate the gas cell excess delay.

[0152]

number

[0153] After delaying by this, this can be applied to normalize the gas cell signal. Alternatively, the reciprocal of the monitor signal can be used as the gas cell overdelay.

[0154]

number

[0155] After delaying, this can be multiplied by the gas cell signal to obtain a normalized gas cell signal. This eliminates the need for a dedicated splitting stage to normalize each photodetector signal, requiring only a single splitting stage for the monitor signal.

[0156]

[0062] In addition, this method has a laser pseudo-delay τ while locked to the absorption line referenced by the gas cell. LD (ω mod )=-θ(ω mod ) / ω mod This may include determining and / or continuously monitoring the estimation of the laser pseudo-delay. The laser pseudo-delay is obtained from the (possibly drifting) frequency response of the wavelength-modulated thermal process in the laser. This laser pseudo-delay τ LD (ω mod ) is the laser pseudo-delay residual, which consists of even-order harmonic components of the gas cell signal.

[0157]

number

[0158] It can be determined from this.

[0159]

[0063] Next, while locked to the absorption line, the laser pseudo-delay τ LD (ω mod ) Estimated, monitor power-carrier delay τ mon , and gas cell excess delay τ GC,ex The sum of these is the wavelength reference wavelength - carrier delay (hereafter, gas cell wavelength - carrier delay) τ LD (ω mod )+τ GC This can be continuously predicted. Using this gas cell wavelength-carrier delay, the demodulated carrier phase or demodulated component phase can be adjusted to match its phase with the fundamental component (or other odd components, if used) of the gas cell signal. That is, when locked to the absorption line of the gas cell, the phase of the demodulated carrier or demodulated component is used to demodulate the (power-normalized) gas cell signal. For this purpose, the effective gas cell carrier delay is used to rotate the complex demodulation of the fundamental frequency component of the (normalized) gas cell signal on the real axis, thereby locking the average optical laser frequency to the center of the absorption line. This is done, for example, by continuously adjusting the laser bias current based on the obtained demodulated wavelength reference signal (e.g., to zero the normalized and phase-matched fundamental frequency component).

[0160]

[0064] This method further involves the interferometer power-carrier delay τ IFM and monitor power - carrier delay τ mon Interferometer excess delay τ is defined as the difference IFM,ex This may include determining or calibrating the interferometer's excess delay τ. IFM,ex The monitor signal or its reciprocal can be delayed (to obtain a second delayed (e.g., reciprocal) power monitor signal), and then the (e.g., reciprocal) monitor signal can be used to power normalize each interferometer signal.

[0161]

[0065] Interferometer excess delay τ IFM,ex Monitor power - carrier delay τ mon , and laser pseudo-delay τ LD (ω modFrom the sum of (e.g., for each interferometer), the interferometer wavelength - carrier delay τ can be predicted. For example, τ = τ IFM,ex + τ mon + τ LD (ω mod ). Using this interferometer wavelength - carrier delay prediction, each partial demodulation carrier phase or demodulation component phase can be adjusted to phase - match the partial demodulation component with each carrier signal of the interferometer signal.

[0162]

[0066] In summary, the estimated delay amounts that can be maintained and / or calibrated are the monitor power - carrier delay τ mon , the gas cell excess delay τ GC,ex , the laser pseudo - delay τ LD (ω mod ), and the interferometer excess delay τ IFM,ex (for each individual interferometer axis). The monitor power - carrier delay τ mon and the laser pseudo - delay τ LD (ω mod ) are associated with the active components and thus may drift. Therefore, it is proposed to continuously update their estimated values. The excess delay amounts represent the optical propagation delays of the passive components and their estimations, so frequent updates are not necessary but calibration (e.g., only once) should be required.

[0163]

[0067] Using the excess delay estimation of (the gas cell and, where appropriate, the interferometer axis), the monitor signal (e.g., the reciprocal) can be delayed and then used to normalize each photodetector signal. Each of the carrier delay predictions is an absolute delay (not relative), and using this, the complex demodulation obtained from the demodulation by the complex phasor is rotated to the real axis of the complex plane. Then, the real part of the rotated demodulation becomes the signed amplitude of the corresponding component in the photodetector signal.

[0164]

[0068] FIG. 3 is a flowchart showing the basic principle of how at least some of these delay estimations can be improved by determining the corresponding delay residuals. Each of these delay residuals can be extracted as a phase residual from the complex demodulation stage. In FIG. 3 and the corresponding description, a general-purpose delay τ is described, which can be any of the delays determined herein. The estimation of this delay is

[0165]

Number

[0166] represented by, and thus the residual is

[0167]

Number

[0168] represented as. If the features of this method are the same as those shown in FIG. 2, these features are not necessarily described again.

[0169]

[0069] In the complex demodulation stage, the real delay signal component (nth harmonic) of the form A·cos(n·ω mod ·(t - τ)) is multiplied by a synchronous complex demodulation carrier of the form

[0170]

Number

[0171] (e.g., generated by a complex multi-carrier synthesizer CMCS), giving the following product.

[0172]

Number

[0173] This contains two complex phaser components. The following low-pass filter process LPF, which is hereafter denoted by the chevron <>, rejects the (rapidly rotating) second component and leaves the (static) first component as useful / desirable demodulation.

[0174]

Number

[0175]

[0070] This phaser generates an angle of -n·ω·τ with respect to the real axis of the complex plane. Carrier delay prediction can be applied to this phaser to rotate the demodulation to the real axis. mod This involves multiplying by the phaser to produce a phaser product.

[0176]

Number

[0177] This can be applied. This involves multiplying by the phaser to produce a phaser product.

[0178]

Number

[0179] This involves multiplying by the phaser to produce a phaser product.

[0180]

Number

[0181]

[0071] The argument (phase) of this rotated phaser is the delay residual, and the modulation angular frequency is ω.

[0182]

Number

[0183] This is the delay residual, and the modulation angular frequency is ω. modAnd it is scaled by the harmonic order n. Therefore, the phasor is supplied to the CORDIC unit CtP (conversion from Cartesian coordinates to polar coordinates) to obtain the deflection angle, and this deflection angle is (n·ω mod ) -1 By multiplying by this, the delayed residual can be conveniently extracted. Next, the delayed residual

[0184]

number

[0185] Using the delay estimate maintained by the delay tracker DT

[0186]

number

[0187] This can be improved. This improvement is a scaled-down version of the negate residual. The scaling factor L < 1 determines the bandwidth of the delay tracker.

[0188]

[0072] The range of the delay residual, and therefore the convergence range of the delay estimator, is the nth harmonic component f mod This corresponds to a + / - half-cycle. That is, as follows:

[0189]

number

[0190]

[0073] This approach is extremely easy to implement. The demodulation phasors themselves do not phase shift (individually) and can therefore be distributed across many channels (monitor, gas cell, multiple interferometer axes), while the demodulation rotation occurs at a much lower sampling rate, allowing these (e.g., FPGA-based) resources to be shared (pipelined) among these channels at the expense of only a small additional FPGA clock cycle latency.

[0191]

[0074] Figure 4 is a flowchart showing the basic configuration of FIG. 3 in a situation where the monitor carrier delay τ mon is determined and monitored using the monitor carrier delay tracker MDT. Through the monitor analog-to-digital converter Mon ADC and the buffer Bf, the (delayed) monitor signal S mon (t) is acquired and measured by a monitor photodetector (not shown). Each of the monitor ADC, the buffer, and the signal carrier can contribute to the unknown delay of the monitor signal S mon (t). During normal operation, the monitor signal S mon (t) contains only a (large) DC component and a small component at the fundamental modulation frequency. The fundamental component is due only to power modulation. To obtain the monitor carrier delay residual

[0192]

Number

[0193] it is proposed to demodulate the fundamental component (n = 1) in the monitor photodetector signal. ​​​​​​​​​​​​​​

[0077] As mentioned above, a monitor power-carrier delay phasor has an angle of deviation proportional to the monitor power-carrier delay prediction.

[0197]

number

[0198] The complex demodulation is rotated by (in each figure, a general-purpose τ is used for the deflection angle of each phasor, and the actual delay is evident in the context) to bring the demodulation toward or near the real axis (i.e., phase-matched with the fundamental frequency component). As a result, the power-carrier delay residual is monitored.

[0199]

number

[0200] Having a phase angle proportional to,

[0201]

number

[0202] A monitor power-carrier delay residual phasor proportional to this is obtained.

[0203]

[0078] Figure 5 shows the gas cell excess delay τ GC,ex =τ GC -τ mon This is a flowchart of the proposed method for performing the calibration. This calibration can be performed as a one-time calibration. This method and diagram are related to the monitor carrier delay prediction described in Figure 4.

[0204]

number

[0205] This method is built upon and uses gas cell excess delay estimation.

[0206]

number

[0207] It can generate [this].

[0208]

[0079] In this calibration, the laser wavelength must be kept somewhere within a relatively wide regime between two adjacent absorption lines of the wavelength reference. In such a regime, gas cell transmission has extremely low wavelength sensitivity. Thus, optical frequency modulation is not a coefficient, and the modulation of the gas cell output power is determined overall from the input power modulation at the fundamental modulation frequency. By keeping the average laser wavelength in the region between absorption lines, the gas cell carrier delay estimation no longer fits normal operation. Thus, this delay cannot be tracked continuously. Fortunately, this excess delay is due only to the excess optical path length in the gas cell channel, which does not change significantly with environmental influences, so continuous tracking is not necessary. Thus, a one-time calibration at startup is sufficient.

[0209]

[0080] The calibration wavelength reference signal or calibration gas cell signal S is transmitted via the gas cell analog-to-digital converter GC (ADC) and buffer Bf. GCc (t) is acquired (and consequently delayed), but this signal is measured by a gas cell photodetector (not shown) when the average laser wavelength is within the region between absorption lines. Gas cell carrier delay residual

[0210]

number

[0211] To obtain the gas cell photodetector signal S GC It is proposed to demodulate the fundamental frequency component (n=1) in (t) (but any odd-order frequency component may be used). During this calibration, power normalization of the gas cell signal may be temporarily interrupted. Complex demodulation is used for phasor prediction.

[0212]

number

[0213] This rotates it, bringing it closer to the real axis. As a result, the gas cell excess delayed residual

[0214]

number

[0215] and monitor power - carrier delay residual

[0216]

number

[0217] The argument is proportional to the sum of the values.

[0218]

number

[0219] A phasor proportional to this is obtained. Monitor power - Carrier delay residual

[0220]

number

[0221] Since this is already controlled to zero by the monitor power-carrier delay tracker MDT (already explained), it is essentially the gas cell excess delay residual.

[0222]

number

[0223] Only this remains. The gas cell excess delay tracker / estimator GCDE is used for gas cell excess delay estimation.

[0224]

number

[0225] To calibrate this, (only in this calibration stage) it works to control this residual to zero.

[0226]

[0081] Figure 6 is a flowchart describing how the following can be performed using the aforementioned delay: (1) delay-compensated gas cell power normalization using a partially delayed FDF reciprocal monitor signal, (2) laser pseudo-delay tracking based on second harmonic components in the signal from a locked gas cell, and (3) laser average wavelength control based on the delay-compensated fundamental frequency component of the gas cell signal.

[0227]

[0082] The gas cell excess delay tracker and its residual determination loop are no longer available in this operating mode and are therefore no longer part of this scheme. Instead, the calibrated gas cell excess delay estimate is used.

[0228]

number

[0229] This is used as a static value. Once gas cell excess delay τ GC,ex Once calibrated, gas cell power normalization can be resumed (gas cell excess delay τ GC,ex Since this can be accurately estimated at this point, gas cell power-carrier delay prediction

[0230]

number

[0231] At this point, the signal becomes accurate for the first time, and a lock on the absorption line can be achieved (for example, by slowly scanning the laser temperature). A successful lock can be detected from a sufficiently strong second harmonic amplitude combined with the zero fundamental frequency component.

[0232]

[0083] When locked to the center of the absorption line, the normalized gas cell signal no longer has fundamental frequency (or other odd-order harmonic) components. Therefore, the laser pseudo-delay residual is derived from even-order (e.g., second-order) harmonic components.

[0233]

number

[0234] It is proposed to construct a small frequency fluctuation amplitude (relative to the absorption linewidth) of the target.

[0235]

number

[0236] Therefore, the second harmonic is dominant. This second harmonic is demodulated by the complex demodulation stage. In this demodulation, phasors (e.g., generated by a complex multicarrier combiner CMCS)

[0237]

number

[0238] Multiplication is performed, followed by a low-pass filter (LPF) using an FIR decimation filter, similar to that used in the fundamental frequency complex demodulation stage.

[0239]

[0084] Rotation of quadratic complex demodulation by phasor prediction:

[0240]

number

[0241] This requires bringing the demodulation closer to the real axis. This phasor is the predicted gas cell wavelength-carrier delay.

[0242]

number

[0243] It has a phase angle proportional to (note that τ GC =τ GC,ex +τ mon This results in phasors proportional to the following:

[0244]

number

[0245] This is the laser pseudo-delay residual.

[0246]

number

[0247] , gas cell excess delayed residual

[0248]

number

[0249] , and monitor power-carrier delay residual

[0250]

number

[0251] The deviation is proportional to the sum of the two. The monitor power-carrier delay residual is controlled to zero by the monitor delay tracker MDT, and the gas cell excess delay residual has already been calibrated to zero, so the laser pseudo-delay residual

[0252]

number

[0253] Only this remains. This residual is the laser pseudo-delay estimation.

[0254]

number

[0255] To determine this, it can be controlled to zero by a laser pseudo-delay residual tracker / estimator (LDpD).

[0256]

[0085] By using this approach, the fundamental frequency component of the normalized gas cell signal can be rotated correctly even when the average laser frequency is controlled to zero to lock it to the center of the absorption line. By combining monitor power-carrier delay estimation, gas cell excess delay estimation, and laser pseudo-delay estimation, a gas cell wavelength-carrier delay estimation is obtained, i.e., a (predicted) gas cell wavelength-carrier delay phasor based on the combination of gas cell power-carrier delay estimation and estimated laser pseudo-delay.

[0257]

number

[0258] This can be constructed. Therefore, the complex demodulation of the fundamental frequency is this gas cell wavelength-carrier delay phasor.

[0259]

number

[0260] This can be rotated by . This stabilizes the sensitivity of the fundamental frequency complex demodulation component to the deviation of the average wavelength from the absorption line center, and makes it possible to use this as a residual for controlling the average wavelength, for example, by controlling the laser bias current BC via the laser bias control LBC.

[0261]

[0086] Figure 7 is a flowchart describing another embodiment that takes into account the measured and delayed interferometer signals. As described above, the cause of the carrier phase shift is the unknown propagation delay and / or time-variable propagation delay of the radiation as it travels from the laser to the photodetector signal along two beam paths including the interferometer.

[0262]

[0087] Delayed interferometer photodetector signal S IFM (t) can be modeled as follows: S IFM (t) = B + A·cos(φ(t) + m·sin(ω mod ·(t-τ))) Here, delay τ describes the interferometer wavelength-carrier delay, and interferometer power-carrier delay τ IFM and laser pseudo-delay τ LD (ω mod It is similar to the gas cell wavelength-carrier delay described above in that it includes the sum of ). Also, similar to the gas cell excess delay, the interferometer excess delay τ IFM,ex This is the interferometer power-carrier delay τ IFM and monitor power - carrier delay τ mon It can be defined as the difference between τ. That is, τ IDM,ex =τ IFM -τ mon Therefore, the interferometer wavelength-carrier delay τ is equal to the interferometer excess delay τ. IFM,ex Monitor power - carrier delay τ mon , and laser pseudo-delay τ LD (ω mod It can be determined from the sum of (for example, for each interferometer). For example, τ = τ IFM,ex +τ mon +τ LD (ω mod This interferometer wavelength-carrier delay describes the propagation delay of the carrier signal used to modulate the laser emission wavelength.

[0263]

[0088] The extension of the interferometer signal to the phase generating carrier is expressed as follows:

[0264]

number

[0265]

[0089] In this embodiment, interferometer excess delay estimation

[0266]

number

[0267] This can be calibrated. In one embodiment, interferometer over-delay estimation

[0268]

number

[0269] Since it is generally static, it can be estimated in a calibration step (e.g., only once), and the calibrated value can be used in combination with (e.g., continuously tracked) monitor power-carrier delay and laser pseudo-delay to determine the interferometer wavelength carrier delay.

[0270]

[0090] Once calibrated, this interferometer over-delay estimate can be combined with the monitor power-carrier delay estimate and the laser pseudo-delay estimate to determine the interferometer wavelength-carrier delay prediction. This interferometer wavelength-carrier delay prediction can then be used to correct the estimated target phases determined from each interferometer signal. This correction can be performed, for example, by rotating the partial demodulated components of the interferometer signal by each angle determined from the aforementioned interferometer wavelength-carrier delay prediction to place the partial demodulated components on the real axis (i.e., phase-matching the partial demodulated components with each carrier signal of the interferometer signal).

[0271]

[0091] Interferometer excess delay estimation

[0272]

number

[0273] Using this method, the monitor signal (for example, by its reciprocal) can be delayed, and then the interferometer signal can be power-normalized using the monitor signal (for example, by its reciprocal).

[0274]

[0092] In one embodiment, the interferometer excess delay estimation is obtained from the interferometer wavelength-carrier delay residual obtained from a weighted combination of the imaginary parts of the rotated partial demodulation components.

[0275]

number

[0276] This can be determined based on the construction.

[0277]

number

[0278] This is the laser pseudo-delay residual.

[0279]

number

[0280] Interferometer excess delay residual

[0281]

number

[0282] , and monitor power-carrier delay residual

[0283]

number

[0284] It has a deflection angle proportional to the sum of the two. The monitor power-carrier delay residual is controlled to zero by the monitor power-carrier delay tracker MDT, and the laser pseudo-delay residual

[0285]

number

[0286] Since it is controlled to zero by the laser pseudo-delay residual tracker / estimator LDpD, the interferometer excess delay residual

[0287]

number

[0288] Only this remains. This interferometer excess delay residual is made zero by the interferometer excess delay tracker IFM EDT, and the interferometer excess delay

[0289]

number

[0290] It is possible to make a decision.

[0291]

[0093] In this embodiment, the (real) carriers in the photodetector signal are not real demodulation carriers that must be phase-shifted (as in the conventional example in Figure 2), but rather complex demodulation carriers or complex demodulation phasors.

[0292]

number

[0293] Demodulation can be performed using this method. As a result, two complex partial demodulation components or demodulations are obtained for each carrier (not a single actual demodulation). These two complex partial demodulations are DR n and DI n This is represented by the partial demodulation DR. n This involves a complex demodulation phasor and a detection signal S. IFM (t) and complex conjugate phasor prediction

[0294]

number

[0295] Includes combinations or products (e.g., low-pass filtered) with the real part, and partial demodulation DI n This involves a complex demodulation phasor and a detection signal S. IFM (t) and complex conjugate phasor prediction

[0296]

number

[0297] This may include combinations or products (e.g., low-pal filtered) with the imaginary part of the complex conjugate phasor prediction. The complexity resulting from the complex conjugate phasor prediction is temporarily interrupted by separating the complex conjugate phasor prediction into its two constituent real representations, where the complex demodulation phasor

[0298]

number

[0299] The detected signal S IFM A new complexity is introduced to describe the demodulation process of (t). Therefore, even and odd partial demodulations are formed as follows:

[0300]

number

[0301]

[0094] τ-delayed photodetector signal S IFM Substituting the formula into (t), we obtain the following:

number

[0302]

[0095] This means that these partial demodulations are in the complex plane with respect to the real axis at an angle of -2k·ω mod·τ and -(2k-1)·ω mod • Indicates that it is directed toward τ. In this specification, each angle

[0303]

number

[0304] These partial demodulations are performed by each delay-compensated phasor.

[0305]

number

[0306] It is proposed to rotate it on the real axis by multiplication with . Both of these phasors are interferometer wavelength-carrier delay prediction

[0307]

number

[0308] (Interferometer excess delay estimation)

[0309]

number

[0310] Monitor power - Carrier delay estimation

[0311]

number

[0312] , and laser pseudo-delay estimation

[0313]

number

[0314] It can be constructed from (determined by the sum of ). The rotational motion and its result are given by the following:

[0315]

number

[0316]

[0096] Interferometer wavelength-carrier delay prediction

[0317]

number

[0318] If this is correct, these rotated partial demodulations lie on the real axis. Therefore, by combining the real parts of the rotated partial demodulations, the full demodulation D is obtained. n (Including those complexities) can be obtained. This can be achieved, for example, as follows:

[0319]

number

[0320]

[0097] This is evaluated against the following formula.

[0321]

number

[0322] This appears similar to what would be obtained by directly demodulating with unshifted real carriers, but differs in that the intensity reduction coefficient is a function of the interferometer wavelength-carrier delay residual, rather than the true interferometer wavelength-carrier delay. Therefore, it is a correct prediction of the interferometer wavelength-carrier delay.

[0323]

number

[0324] If this is maintained, it is possible to eliminate the decrease in intensity and avoid operational problems and periodic errors caused by delays.

[0325]

[0098] If the interferometer wavelength-carrier delay prediction is accurate, the rotated partial demodulation lies on the real axis of the complex plane. Therefore, the non-zero imaginary part of the rotated partial demodulation indicates an inaccurate delay prediction.

[0326]

[0099] Here, the imaginary part of the rotated partial demodulation is taken from the interferometer wavelength-carrier delay residual.

[0327]

number

[0328] This explains how to construct a fully demodulated D. n When determining this, similar to the method of combining the real part described above, the imaginary part can be combined, for example, as follows.

[0329]

number

[0330] These combinations are interferometer wavelength-carrier delay residuals

[0331]

number

[0332] It is proportional to the sine function of ω, and the modulation frequency ω mod These are scaled by PGC orders 2k and 2k-1, respectively. For small values ​​of the interferometer wavelength-carrier delay residual, these sine functions can be approximated by each deflection angle. Furthermore, these combinations are used for demodulation D 2k and D 2k-1 The complex phasor coefficients shared with

[0333]

number

[0334] It includes. Therefore, from these combinations, form

[0335]

number

[0336] The phasor can be constructed (for example by weighted addition), which is then multiplied by the conjugate (and normalized) C / N phase residual phasor to obtain the (scaled) interferometer wavelength-carrier delay residual.

[0337]

number

[0338] To make it possible.

[0339]

number

[0340]

[0100] Therefore, small interferometer wavelength-carrier delay residual

[0341]

number

[0342] Then, the desired form of phasor can be obtained by constructing a first weighted combination or first weighted addition of the imaginary parts of the rotated partial demodulation according to the following:

[0343]

number

[0344] Here, modulation index estimation

[0345]

number

[0346] The first weighted coefficient that depends on

[0347]

number

[0348] A set of the first weighting coefficients can be defined.

[0349]

number

[0350] The requirements for can be found by substituting the form of the evaluated combination and replacing its sine function with its arguments. This gives the following:

[0351]

number

[0352]

[0101] This is the phase residual.

[0353]

number

[0354]

number

[0355]

[0102] The latter two of these requirements impose a single constraint on the even-order and odd-order weighting coefficients. In a real-world configuration where N≧2 even-order and N>2 odd-order PGCs are considered, this leaves at least one degree of freedom in the selection of coefficients. This degree of freedom can be used to optimize the noise performance of the interferometer wavelength-carrier delay residual construction. When the noise of the photodetector signal S(t) is white, the optimal noise performance is obtained when the following vector is:

[0356]

number

[0357] This is the case when the vectors are parallel to each of the following vectors.

[0358]

number

[0359]

[0103] This is the case when the first weighting coefficient is selected according to the following:

[0360]

number

[0361]

[0104] In one embodiment, these first weighting coefficients K n (m sp ) is the selected modulation index setting point m sp This can be calculated in advance (and stored as a design constant for the FPGA). Therefore, the selection of the first weighting coefficient K is determined by the modulation index m sp The setpoint value, for example, the modulation index, can be controlled and therefore based on an assumed value. In such an embodiment, the reference to the modulation index in the above equation is the modulation index m sp It must be read as the setpoint value. Also, the lookup table LUT2 is the Bessel function J n(m) (or the second weighting coefficient G in the following embodiments) n (m) may be included.

[0362]

[0105] In another embodiment, instead of controlling the modulation index to a predetermined value, each measurement axis may have a modulation index that can fluctuate individually over time, as the OPD of that axis fluctuates (due to changes in the object being measured). Then, each of these modulation indices is estimated, and each measurement signal is demodulated from that axis using the estimated value for each axis. In such an embodiment, the reference to the modulation index in the above equation is the estimated modulation index.

[0363]

number

[0364] It can be read as follows.

[0365]

[0106] Next,

[0366]

number

[0367] Using the estimated modulation index represented by , a second set of weighting coefficients

[0368]

number

[0369] This can be defined (for example, by a second weighting coefficient lookup table which may be identical to the first weighting coefficient lookup table, such as LUT2). These coefficients are a phase residual first phasor of a constant magnitude.

[0370]

number

[0371] Therefore, phase residual

[0372]

number

[0373] It is expected that the corresponding demodulated carrier amplitudes will be made equal in order to obtain the desired result.

[0374]

[0107] In one embodiment, the second weighted combination or addition of demodulation may include the following:

[0375]

number

[0376]

[0108] In the example where the noise spectral density of signal S(t) is white, demodulation D n This includes independent, additive noise with equal variance. This means that, for example, the weighted root-mean-square (rms) noise of the sum can be calculated as one of the demodulated rms noises and amplified by each coefficient, as shown below.

[0377]

number

[0378]

[0109] These coefficients can be recognized as the lengths of each vector.

[0379]

number

[0380]

[0110] Therefore, the smallest vector G that satisfies the constraints given above. even and G odd Thus, minimum noise amplification is achieved. Furthermore, these constraints can be interpreted as the dot product of the vectors of even-order and odd-order Bessel functions.

[0381]

number

[0382]

[0111] Therefore, each vector J even and J odd The smallest vector G that generates the unit dot product even and G odd This is what is required. In other words, vector G even and G odd is vector J even and J odd We must select parallel values ​​for each and normalize them to the squared length.

[0383]

number

[0384]

[0112] Therefore, the noise optimization coefficient is as follows:

[0385]

number

[0386] It is found.

[0387]

number

[0388]

[0113] These weighting coefficients are pre-calculated for the expected range of the estimated modulation index and can be stored in a lookup table LUT2 (for example, within an FPGA containing an algorithm that embodies the proposed method). If it is known that the noise of the detected signal S(t) has a specific non-white spectral density, the calculation of the coefficients described above can be modified by first applying a noise-whitening virtual gain to each demodulation. The calculation of the G coefficients is then conceptually identical. The stored coefficients are then determined as the product of each noise-whitening gain calculated after applying the noise-whitening gain to the demodulation and the corresponding G coefficient.

[0389]

[0114] As already mentioned, in order to perform accurate instantaneous power normalization, the monitor signal can be delayed (e.g., by its reciprocal) using the interferometer over-delay estimation (e.g., using a non-integer delay filter). Therefore, when the interferometer over-delay calibration is first started, the power normalization is not yet accurate. Also, each PGC demodulation experiences some degree of "crosstalk" from its surroundings, which affects the accuracy of the wavelength carrier delay residual construction. As a result of this effect, a (small) reduction in the convergence range occurs. However, as the interferometer over-delay estimation converges, this crosstalk gradually decreases, and there is no remaining effect of the interferometer over-delay on the final accuracy.

[0390]

[0115] The monitor power-carrier delay is the only absolute delay among the maintained delay estimates. The other delay estimates are relative delays. Therefore, the monitor delay is overwhelmingly the largest of the four delay contributions described above. This includes all the delays the fundamental frequency experiences, i.e., starting at the carrier combiner (e.g., FPGA), through the laser signal FIFO buffer, laser DAC, laser driver, laser, optical fiber path, photodetector and amplifier, ADC, photodetector signal FIFO buffer, and ending at the demodulator stage (e.g., after FPGA). This delay estimate serves as a common base for delays observed in other photodetector channels. This is because a) the number of sample delays in the digital signal processing stages of different photodetector signals can easily be made the same, b) the path from the combiner to the fiber splitter is common to all channels, and c) the path from the fiber splitter branch to the monitor photodetector is the shortest among all optical channels.

[0391]

[0116] To ensure rapid and reliable convergence of the delay estimator at system startup, the initial delay estimate can be pre-set to an appropriate nominal value (e.g., known from design parameters and experience). However, depending on the initial uncertainty of various delay items and the modulation frequency used, the convergence range of the delay estimator may not be sufficiently large. The initial delay uncertainty must not exceed ±1 / 2 of the cycle duration of the harmonic frequency used. To expand the convergence range, the system can use (much) lower modulation frequencies at startup. Furthermore, since the laser pseudo-delay is not a pure delay but a frequency-dependent delay, it is also possible to use various intermediate modulation frequencies to ensure reliable re-convergence of the pseudo-delay estimate at the next higher modulation frequency.

[0392]

[0117] Furthermore, since this laser pseudo-delay is a (strong) function of the modulation frequency, it has a large initial uncertainty. The convergence range (acceptable initial delay uncertainty) of this method is ±1 / -2 of the period of the second harmonic frequency. This guaranteed large convergence range means that interferometer over-delay calibration can be performed anywhere within the operating range of the interferometer. This is because the convergence range only needs to address the initial uncertainty of the interferometer over-delay (related to fiber length) and not the laser pseudo-delay.

[0393]

[0118] The proposed signal processing method (e.g., an algorithm that embodies the method and associated lookup tables) can be implemented in software or firmware (e.g., in a programmable firmware component such as a field-programmable gate array (FPGA)).

[0394]

[0119] Also disclosed is a phase-generating carrier interferometer interlogger including at least one interferometer that is operable to process (e.g., demodulate) the detected interferometer signal by performing any of the methods disclosed herein. The phase-generating carrier interferometer interlogger may include, for example, a multi-interferometer or multi-axis phase-generating carrier interferometer interlogger using a common laser (e.g., laser diode) for each interferometer / axis.

[0395]

[0120] Also disclosed is a position measuring system for measuring the position of a component of a machine such as a lithography apparatus (e.g., a scanner), which includes at least one interferometer and is operable to process (e.g., demodulate) the detected interferometer signal by performing one of the methods disclosed herein. The position measuring system may include the above-described (e.g., multi-axis) phase-generating carrier interferometer interlogger. The component may include, for example, a stage of a lithography apparatus (e.g., a wafer stage or a reticle stage), or any other arbitrary component such as a projection component of a projection system of a lithography apparatus (e.g., an EUV lithography apparatus) (e.g., a steering mirror or a beam delivery mirror). The position measuring system may be operable to measure any two or more axes, each of which relates to each degree of freedom of the component being measured. In a particular example, the position measuring system may be operable to measure six axes, namely three spatial axes x, y, z, and rotations Rx, Ry, Rz about each of these axes.

[0396]

[0121] Also disclosed is a lithography apparatus that includes at least one such position measuring system for measuring the position of components of the lithography apparatus.

[0397]

[0122] Although this text specifically refers to the use of lithography equipment in the manufacture of ICs, it should be understood that the lithography equipment described herein has other applications. Other possible applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memory, flat panel displays, liquid crystal displays (LCDs), thin-film magnetic heads, and the like.

[0398]

[0123] Although embodiments of the present invention are specifically referred to in the context of lithography apparatus in this text, embodiments of the present invention may also be used in other apparatuses. Embodiments of the present invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus for measuring or processing objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatuses may generally be referred to as lithography tools. Such lithography tools may operate under vacuum conditions or ambient (non-vacuum) conditions.

[0399]

[0124] Although the embodiments of the present invention have been specifically referred to above in the context of photolithography, it will be acknowledged that the present invention is not limited to photolithography and may be used in other applications such as imprint lithography, where permitted by context.

[0400]

[0125] Where permitted by context, embodiments of the present invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present invention may also be implemented as instructions stored in a machine-readable medium that can be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read-only memory (ROM), random access memory (RAM), magnetic storage media, optical storage media, flash memory devices, the electrical, optical, acoustic, or other forms of propagating signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Furthermore, firmware, software, routines, and / or instructions may be described herein as performing a particular action. However, such descriptions are merely for convenience, and it will be acknowledged that such actions are actually obtained as a result of a computing device, processor, controller, or other device executing firmware, software, routines, instructions, etc., and causing an actuator or other device to interact with the material world at runtime.

[0401]

[0126] Although specific embodiments of the present invention have been described above, it will be acknowledged that the present invention can be carried out in ways other than those described. The above description is intended to be illustrative and not limiting. Accordingly, it will be apparent to those skilled in the art that the described invention can be modified without departing from the claims set forth below. Other aspects of the present invention are described in the following numbered clauses.

[0402] 1. A complex multicarrier combiner capable of generating at least a laser modulated carrier signal for modulating a laser radiation source, A laser power monitor branch, which includes a power monitor detector and is operable to measure the power metric of a laser radiation source and acquire a power monitor signal, A wavelength reference branch including a wavelength reference detector for wavelength stabilization and / or control of a laser radiation source, and for measuring the wavelength reference and obtaining a wavelength reference signal. A signal processing module, We estimate the monitor power-carrier delay, which describes the propagation delay of the power monitor signal in the laser power monitor signal path. Using the estimated monitor power-carrier delay, we estimate the wavelength-referenced excess delay, which describes the difference between the wavelength-referenced power-carrier delay (which describes the propagation delay of the wavelength-referenced signal at the wavelength-referenced branch) and the monitor power-carrier delay. A signal processing module capable of operating in this manner, A phase-generating carrier interrupter equipped with the following features. 2. The signal processing module further, The fundamental frequency component in the power monitor signal is complex demodulated, From the complex demodulated fundamental frequency components, the monitor power-carrier delay residual, which describes the error in the estimated monitor power-carrier delay, is determined. Monitor power-carrier delay is continuously tracked based on the monitor power-carrier delay residual. A phase-generating carrier interrupter as described in Clause 1, capable of operating in this manner. 3. The phase-generating carrier interlogger described in Clause 2 is operable to determine the monitor power-carrier delay residual by rotating the complex demodulated fundamental frequency component of the power monitor signal by an angle proportional to the monitor power-carrier delay estimate determined from either a previous iteration or an initial estimate. 4. The signal processing module is capable of estimating the wavelength-referenced excess delay in the first calibration, and the first calibration is, Acquiring a calibration wavelength reference signal while the wavelength of the laser emission is maintained between two adjacent absorption lines of the wavelength reference, Complex demodulation of the odd-order harmonic frequency components of the calibration wavelength reference signal, To zero out the wavelength-referenced excess delay residual, which describes the error in the estimation of the wavelength-referenced excess delay determined from the complex demodulation of the odd-order harmonic frequency components of the calibration wavelength-referenced signal, A phase-generating carrier interrupter as described in any of clauses 1 to 3, including the one described in any of clauses 1 to 3. 5. The phase-generating carrier interrupter described in Clause 4, wherein the odd-order harmonic frequency components of the calibration wavelength reference signal include the fundamental frequency components of the calibration wavelength reference signal. 6. A phase-generating carrier interlogger as described in either Clause 4 or 5, wherein the signal processing module is operable to determine the wavelength-referenced excess delay residual by rotating the complex demodulation of the odd-order harmonic frequency components of the calibrated wavelength-referenced signal by an angle proportional to the sum of the estimated monitor power-carrier delay and the estimated wavelength-referenced excess delay, which is determined from either a previous iteration or an initial estimation. 7. The signal processing module is A first delayed power monitor signal is obtained by delaying the power monitor signal or its reciprocal by a determined wavelength-referenced excess carrier delay. The wavelength reference signal is power-normalized using the first delayed power monitor signal. A phase-generating carrier interrupter as described in any of clauses 1 to 6, which is capable of operating in this manner. 8. The signal processing module is The phase-generating carrier interlogger described in Clause 7 is capable of estimating and / or continuously monitoring the laser pseudo-delay while locked to a wavelength-referenced absorption line, the laser pseudo-delay describing the phase delay of the laser wavelength-modulated carrier relative to the associated laser power-modulated carrier, and resulting from the drift of the laser's thermal time constant. 9. The signal processing module is Complex demodulation of even-order harmonic frequency components of a wavelength reference signal, and To zero out the laser pseudo-delay residual, which describes the error in the estimation of the laser pseudo-delay determined from the even-order harmonic frequency components of the wavelength reference signal. A phase-generating carrier interlogger as described in Clause 8, which is operable to perform estimation and / or continuous monitoring of laser pseudo-delay. 10. The phase-generating carrier interlogger described in Clause 9 is operable to determine the laser pseudo-delay residual by rotating the complex demodulation of the even-harmonic frequency components of the wavelength reference signal by an angle proportional to the sum of the estimated monitor power-carrier delay, estimated wavelength reference excess delay, and estimated laser pseudo-delay, which are determined from either previous iterations or initial estimations. 11. A phase-generating carrier interrogator as described in Clause 9 or 10, wherein the even-order harmonic frequency components of the wavelength reference signal include the second-order harmonic frequency components of the wavelength reference signal. 12. The signal processing module is A phase-generating carrier interlogger according to any of clauses 8 to 11, which is operable to estimate the wavelength-referenced wavelength-carrier delay as the sum of the estimated laser pseudo-delay, the estimated monitor power-carrier delay, and the estimated wavelength-referenced excess delay while locked to a wavelength-referenced absorption line. 13. The signal processing module is The odd-order harmonic frequency components of the wavelength reference signal are complex demodulated, The complex demodulation of odd-order harmonic frequency components is rotated only by the wavelength-based wavelength-carrier delay estimation. The average wavelength of the laser emission source is controlled using the real part of the rotated complex demodulation of odd-order harmonic frequency components. A phase-generating carrier interrupter as described in Clause 12, capable of operating in this manner. 14. Controlling the average wavelength of a laser radiation source using the real part of a rotated complex demodulation of odd-order harmonic frequency components includes controlling the bias current of a laser radiation source using the real part of a rotated complex demodulation of odd-order harmonic frequency components, as described in Clause 13. 15. Controlling the average wavelength of a laser radiation source using the real part of the rotated complex demodulation of odd-order harmonic frequency components includes controlling the laser radiation source to zero out the real part of the rotated complex demodulation of odd-order harmonic frequency components, as described in Clause 13 or 14. 16. A phase-generating carrier interrupter as described in Clauses 13, 14, or 15, wherein odd-order harmonic frequency components include the fundamental frequency component. 17. One or more interferometers, each of which is operable to receive modulated radiation from a laser radiation source and generate an interferometer signal that includes a target phase induced by the object being measured, and each interferometer signal also includes periodic phase modulation induced by the modulated radiation, At least one detector capable of detecting each interferometer signal, Furthermore, the complex multicarrier combiner is capable of operating to generate a complex demodulation phasor for each interferometer signal. The signal processing module, for each of one or more interferometers, Determine at least two partial complex demodulations from the complex demodulation phasor and each interferometer signal. A phase-generating carrier interlogger as described in any of clauses 8 to 16, capable of estimating an interferometer excess delay that describes the difference between the interferometer power-carrier delay and the monitor power-carrier delay from at least two partial complex demodulations. 18. The signal processing module is A second delayed power monitor signal is obtained by delaying the power monitor signal or its reciprocal by the determined interferometer excess delay. Before the demodulation step, each interferometer signal is power-normalized using a second delayed power monitor signal. A phase-generating carrier interrupter as described in Clause 17, capable of operating in this manner. 19. The signal processing module is The interferometer wavelength-carrier delay is predicted from the sum of the estimated interferometer excess delay, estimated monitor power-carrier delay, and estimated laser pseudo-delay. Using the predicted interferometer wavelength-carrier delay, at least two partial complex demodulations corresponding to each interferometer signal are corrected to obtain the corrected partial complex modulation. A phase-generating carrier interrupter as described in Clause 17 or 18, which is capable of operating in this manner. 20. The phase-generating carrier interrogator as described in Clause 19, wherein the correction step includes rotating each of at least two partial complex demodulations by an angle proportional to the interferometer wavelength-carrier delay prediction. 21. The signal processing module is operable to estimate the interferometer excess delay based on the interferometer excess delay residual determined from a first weighted combination of the imaginary parts of the corrected partial complex demodulation, the first weighted combination comprising weighting by a first set of weighting coefficients, each of which depends on each modulation exponent estimation of one or more interferometers, the modulation exponent describing the amplitude of periodic phase modulation, as described in any of clauses 19 to 20. 22. The interferometer excess delay is estimated in the second calibration, using the phase-generating carrier interrogator described in Clause 21. 23. The first weighted combination of the imaginary parts of the corrected partial complex demodulation is the phase-generating carrier interrupter described in Clause 22, which includes the first weighted sum of the imaginary parts of the corrected partial complex demodulation. 24. The signal processing module shall, for each of one or more interferometers, The full demodulation is determined from the real part of the corrected partial complex demodulation. A phase-generating carrier interrupter according to any one of clauses 21 to 23, which is capable of estimating the target phase from the total demodulation. 25. The signal processing module further, Estimate the modulation index of one or more interferometers, obtain the estimated modulation index of each of the one or more interferometers, Determine a first weighting coefficient from each estimated modulation index of one or more interferometers. A phase-generating carrier interrupter as described in Clause 24 is capable of operating in this manner. 26. The signal processing module is operable to define a second set of weighting coefficients for full demodulation using the estimated modulation index of each of one or more interferometers, the second set of weighting coefficients, the second set of weighting coefficients, the second set of weighted combinations of full demodulation including the weighting by the second set of weighting coefficients, the second set of weighted combinations of full demodulation, the second set of weighting coefficients 27. A phase-generating carrier interlogger as described in Clause 25 or 26, wherein the signal processing module is operable to estimate the modulation index of each of one or more interferometers by repeatedly updating the estimated modulation index based on the modulation index residual, which represents the error of the estimated modulation index. 28. The signal processing module is capable of determining the phase residual, which represents the error in the estimated value of the target phase. The signal processing module further includes a phase-generating carrier interlogger as described in any of clauses 19 to 27, which includes a dynamic state estimator capable of determining a new state, including an estimate of the target phase, from the previous state and phase residuals. 29. A phase-generating carrier interrogator as described in any of clauses 1 to 28, including a programmable firmware component programmed to perform a signal processing module. 30. A phase-generating carrier interrogator as described in any of clauses 1 to 29, further comprising multiple interferometers. 31. A phase-generating carrier interlogger as described in Clause 30, further comprising a common radiation source for generating radiation that is modulated to acquire modulated radiation for each of the multiple interferometers. 32. A multi-axis position measuring system comprising a phase-generating carrier interlogger as described in Clause 30 or 31, which measures each axis of the multi-axis position measuring system using each of a plurality of interferometers. 33. The multi-axis position measurement system is the multi-axis position measurement system according to Clause 32, which includes at least three axes for measuring three rigid body position coordinates related to the object being measured. 34. The multi-axis position measurement system according to Clause 32, comprising at least six axes for measuring three rigid body position coordinates and three rigid body attitude coordinates related to the object being measured. 35. A lithography apparatus comprising a multi-axis positioning system according to any one of clauses 32 to 34, wherein the multi-axis positioning system is operable to measure the position coordinates and / or orientation coordinates of the components of the lithography apparatus. 36. A metrology apparatus comprising a multi-axis position measuring system according to any one of clauses 32 to 34, wherein the multi-axis position measuring system is operable to measure the position coordinates and / or orientation coordinates of the components of the metrology apparatus. 37. A method for estimating at least wavelength-referenced excess delay related to a wavelength reference, This involves measuring the power metric of the laser radiation source and obtaining a power monitor signal, Stabilizing and / or controlling the wavelength of a laser radiation source using a wavelength reference signal from a wavelength reference, To estimate the monitor power-carrier delay, which describes the propagation delay of the power monitor signal in the laser power monitor signal path, Using the estimated monitor power-carrier delay, we estimate the wavelength-referenced excess delay, which describes the difference between the wavelength-referenced power-carrier delay (which describes the propagation delay of the wavelength-referenced signal at the wavelength-referenced branch) and the monitor power-carrier delay. A method that includes this. 38. Complex demodulation of the fundamental frequency component in the power monitor signal, From the complex demodulated fundamental frequency component, we determine the monitor power-carrier delay residual, which describes the error in the estimated monitor power-carrier delay, and Continuously tracking monitor power-carrier delay based on monitor power-carrier delay residual, The method described in Article 37, including the method described in Article 37. 39. The method of Clause 38, comprising determining the monitor power-carrier delay residual by rotating the complex demodulated fundamental frequency component by an angle proportional to the monitor power-carrier delay determined from either a previous repetition or an initial estimation. 40. The first calibration includes estimating the wavelength-referenced excess delay, and the first calibration is: Acquiring a calibration wavelength reference signal while the wavelength of the laser emission is maintained between two adjacent absorption lines of the wavelength reference, Complex demodulation of the odd-order harmonic frequency components of the calibration wavelength reference signal, To zero out the wavelength-referenced excess delay residual, which describes the error in the estimation of the wavelength-referenced excess delay determined from the complex demodulation of the odd-order harmonic frequency components of the calibration wavelength-referenced signal, The method described in any of clauses 37 to 39, including the method described in any of clauses 37 to 39. 41. The method according to clause 40, wherein odd-order harmonic frequency components include the fundamental frequency component. 42. The method according to Clause 40 or 41, comprising determining the wavelength-referenced excess delay residual by rotating the complex demodulation of odd-order harmonic frequency components by an angle proportional to the sum of the estimated monitor power-carrier delay and the estimated wavelength-referenced excess delay, which are determined from either previous iterations or initial estimations. 43. Obtaining a first delayed power monitor signal by delaying the power monitor signal or its reciprocal by a determined wavelength-referenced excess carrier delay, The wavelength reference signal is power-normalized using the first delayed power monitor signal, The method described in any of the clauses 37 to 42, including the method described in any of the clauses 37 to 42. 44. The method according to Clause 43, comprising estimating and / or continuously tracking a laser pseudodelay while locked to a wavelength-referenced absorption line, wherein the laser pseudodelay describes the phase delay of the laser wavelength-modulated carrier relative to the associated laser power-modulated carrier and arises from the drift of the laser's thermal time constant. 45. Complex demodulation of even-order harmonic frequency components of a power-normalized wavelength reference signal, and To zero out the laser pseudo-delay residual, which describes the error in the estimation of the laser pseudo-delay determined from the complex demodulation of even-order harmonic frequency components. The method according to Clause 44, which includes performing estimation and / or continuous tracking of the laser pseudo-delay. 46. ​​The method of Clause 45, comprising determining the laser pseudo-delay residual by rotating the complex demodulation of even-order harmonic frequency components by an angle proportional to the sum of an estimated monitor power-carrier delay, an estimated wavelength-referenced excess delay, and an estimated laser pseudo-delay, which are determined from either a previous iteration or an initial estimate. 47. The method according to clause 45 or 46, wherein even-order harmonic frequency components include second-order harmonic frequency components. 48. The method of any one of the clauses 44 to 47, which includes determining the wavelength-referenced wavelength-carrier delay as the sum of the estimated laser pseudo-delay, the estimated monitor power-carrier delay, and the estimated wavelength-referenced excess delay while locked to a wavelength-referenced absorption line. 49. Complex demodulation of the odd-order harmonic frequency components of the power-normalized wavelength reference signal, The complex demodulation of odd-order harmonic frequency components is rotated by the wavelength-carrier delay, Controlling the wavelength of the laser emission source using the real part of the rotated complex demodulation, The method described in Article 48, including the method described in Article 48. 50. The method according to Clause 49, wherein controlling the wavelength of a laser emission source using the real part of a rotated complex demodulation includes controlling the bias current of a laser emission source using the real part of a rotated complex demodulation. 51. The method according to Clause 49 or 50, wherein controlling the average wavelength of a laser emission source using the real part of a rotated complex demodulation includes controlling the laser emission source to zero out the real part of a rotated complex demodulation. 52. The method according to clauses 49, 50, or 51, wherein odd-order harmonic frequency components include the fundamental frequency component. 53. Generating a carrier signal, To generate a complex demodulation phasor, The radiation from a laser source is modulated by a carrier signal, and periodic phase modulation is applied to each of one or more interferometers. The method involves detecting each interferometer signal from one or more interferometers, wherein each interferometer signal includes a target phase induced by the object being measured in addition to periodic phase modulation. To determine at least two partial complex demodulations from the complex demodulation phasor and interferometer signals, To estimate the interferometer excess delay, which describes the difference between the interferometer power-carrier delay and the monitor power-carrier delay, from at least two partial demodulation components, The method described in any of the clauses 44 to 52, including the method described in any of the clauses 44 to 52. 54. Obtain a second delayed power monitor signal by delaying the power monitor signal or its reciprocal by the determined interferometer excess delay, Before the demodulation step, each interferometer signal is power-normalized using a second delayed power monitor signal, The method described in Article 53, including the method described in Article 53. 55. Predicting the interferometer wavelength-carrier delay from the sum of the estimated interferometer excess delay, estimated monitor power-carrier delay, and estimated laser pseudo-delay, Using the predicted interferometer wavelength-carrier delay, at least two partial complex demodulations corresponding to each interferometer signal are corrected to obtain the corrected partial complex modulation, The method described in Article 53 or 54, including the method described in Article 53 or 54. 56. The method according to Clause 55, wherein the correction step includes rotating each of at least two partial complex demodulations by an angle proportional to the interferometer wavelength-carrier delay prediction. 57. The method of either clause 55 or 56, comprising estimating the interferometer excess delay based on the interferometer excess delay residual determined from a first weighted combination of the imaginary parts of the corrected partial complex demodulation, wherein the first weighted combination comprises weighting by a first set of weighting coefficients, each of which depends on each modulation exponent estimation of one or more interferometers, and the modulation exponent describes the amplitude of the periodic phase modulation. 58. Interferometer excess delay is estimated in the second calibration, as described in Clause 57. 59. The method of Clause 58, wherein the first weighted combination of the imaginary parts of the corrected partial complex demodulation includes the first weighted sum of the imaginary parts of the corrected partial complex demodulation. 60. For each of the one or more interferometers, Determining the full demodulation from the real part of the corrected partial complex demodulation, Determining the target phase from the total demodulation, and The method described in any of the clauses 57 to 59, including the method described in any of the clauses 57 to 59. 61. Estimate the modulation index of one or more interferometers and obtain the estimated modulation index of one or more interferometers, Determining a first weighting coefficient from each estimated modulation index of one or more interferometers, The method described in Clause 60, including the method described in Clause 60. The method according to Clause 61, comprising defining a second set of weighting coefficients for full demodulation using each estimated modulation index of one or more interferometers, wherein the second weighting coefficients are defined such that the second weighted combination of full demodulation, including the weighting by the second weighting coefficients, produces a phase residual phasor whose phase residual has an angle representing the error of the estimated value of the target phase. 63. The method of Clause 61 or 62, comprising estimating the modulation index of each of one or more interferometers by repeatedly updating the estimated modulation index based on the modulation index residual, which represents the error of the estimated modulation index. 64. Determine the phase residual, which represents the error in the estimated value of the target phase, Determining a new state, including an estimated value of the target phase, from the previous state and phase residuals, The method described in any of clauses 55 to 63, including the method described in any of clauses 55 to 63. 65. The method according to any one of the clauses 53 to 64, comprising processing each interferometer signal from each of a plurality of interferometers, wherein the plurality of interferometers use a common laser radiation source. 66. The method of any one of the clauses 53 to 65, comprising determining each position value that describes the position coordinates of the machine's components for each of the estimated values ​​of the target phase. 67. The machine, including a lithography apparatus, as described in Clause 66. 68. The machine includes a metrology device, as described in Clause 66. 69. A computer program containing computer-readable instructions that are capable of performing any of the methods described in any of the clauses 38 to 66. 70. A programmable firmware component programmed to perform any of the methods described in clauses 38 to 66.

Claims

1. A complex multicarrier combiner capable of operating to generate at least a laser modulated carrier signal for modulating a laser radiation source, A laser power monitor branch, which includes a power monitor detector and is operable to measure the power metric of the laser radiation source and acquire a power monitor signal, A wavelength reference branch including a wavelength reference for wavelength stabilization and / or control of the laser radiation source, and a wavelength reference detector for measuring the wavelength reference and obtaining a wavelength reference signal, It is a signal processing module, The monitor power-carrier delay, which describes the propagation delay of the power monitor signal in the laser power monitor signal path, is estimated. Using the estimated monitor power-carrier delay, the wavelength-referenced excess delay is estimated, which describes the difference between the wavelength-referenced power-carrier delay that describes the propagation delay of the wavelength-referenced signal at the wavelength-referenced branch and the monitor power-carrier delay. A signal processing module capable of operating in this manner, A phase-generating carrier interrupter equipped with the following features.

2. The signal processing module further, The fundamental frequency component of the power monitor signal is complex demodulated, From the aforementioned complex demodulated fundamental frequency component, the monitor power-carrier delay residual, which describes the error in the estimated monitor power-carrier delay, is determined. The monitor power-carrier delay is continuously tracked based on the monitor power-carrier delay residual. A phase-generating carrier interrupter according to claim 1, which is capable of operating in this manner.

3. The phase-generating carrier interlogger according to claim 2, wherein the signal processing module is operable to determine the monitor power-carrier delay residual by rotating the complex demodulated fundamental frequency component of the power monitor signal by an angle proportional to the monitor power-carrier delay estimate determined from either a previous iteration or an initial estimate.

4. The signal processing module is operable to estimate wavelength-referenced excess delay in the first calibration, and the first calibration is Acquiring a calibration wavelength reference signal while the wavelength of the laser radiation is maintained between two adjacent absorption lines of the wavelength reference, The odd-order harmonic frequency components of the calibration wavelength reference signal are to be complex demodulated, To set the wavelength-referenced excess delay residual, which describes the error in the estimation of the wavelength-referenced excess delay, determined from the complex demodulation of the odd-order harmonic frequency components of the calibration wavelength-referenced signal, to zero, A phase-generating carrier interrupter according to any one of claims 1 to 3, including the above.

5. The phase-generating carrier interrupter according to claim 4, wherein the odd-order harmonic frequency components of the calibration wavelength reference signal include the fundamental frequency components of the calibration wavelength reference signal.

6. The phase-generating carrier interlogger according to claim 4 or 5, wherein the signal processing module is operable to determine the wavelength-referenced excess delay residual by rotating the complex demodulation of the odd-order harmonic frequency components of the calibration wavelength reference signal by an angle proportional to the sum of the estimated monitor power-carrier delay and the estimated wavelength-referenced excess delay, which is determined from either a previous iteration or an initial estimation.

7. The aforementioned signal processing module is The power monitor signal or its reciprocal is delayed by the determined wavelength-referenced excess carrier delay to obtain a first delayed power monitor signal. The wavelength reference signal is power-normalized using the first delayed power monitor signal. A phase-generating carrier interrupter according to any one of claims 1 to 6, which is operable in such a manner.

8. A method for estimating at least wavelength-referenced excess delay related to a wavelength reference, This involves measuring the power metric of the laser radiation source and obtaining a power monitor signal, Stabilizing and / or controlling the wavelength of the laser radiation source using a wavelength reference signal from a wavelength reference, To estimate the monitor power-carrier delay that describes the propagation delay of the power monitor signal in the laser power monitor signal path, Using the estimated monitor power-carrier delay, estimate the wavelength-referenced excess delay, which describes the difference between the wavelength-referenced power-carrier delay describing the propagation delay of the wavelength-referenced signal at the wavelength-referenced branch and the monitor power-carrier delay. A method that includes this.

9. The fundamental frequency component of the power monitor signal is to be complex demodulated, From the aforementioned complex demodulated fundamental frequency component, the monitor power-carrier delay residual, which describes the error in the estimated monitor power-carrier delay, is determined. The monitor power-carrier delay is continuously tracked based on the monitor power-carrier delay residual, The method according to claim 8, including the method described in claim 8.

10. The method according to claim 9, comprising determining the monitor power-carrier delay residual by rotating the complex demodulated fundamental frequency component by an angle proportional to the monitor power-carrier delay determined from either a previous iteration or an initial estimation.

11. The first calibration includes estimating a wavelength-referenced excess delay, and the first calibration is: Acquiring a calibration wavelength reference signal while the wavelength of the laser radiation is maintained between two adjacent absorption lines of the wavelength reference, The odd-order harmonic frequency components of the calibration wavelength reference signal are to be complex demodulated, To set the wavelength-referenced excess delay residual, which describes the error in the estimation of the wavelength-referenced excess delay, determined from the complex demodulation of the odd-order harmonic frequency components of the calibration wavelength-referenced signal, to zero, The method according to any one of claims 8 to 10, including the method described above.

12. The method according to claim 11, wherein the odd-order harmonic frequency components include the fundamental frequency component.

13. The method according to claim 11 or 12, comprising determining the wavelength-referenced excess delay residual by rotating the complex demodulation of the odd-order harmonic frequency components by an angle proportional to the sum of the estimated monitor power-carrier delay and the estimated wavelength-referenced excess delay, which are determined from either previous iterations or initial estimations.

14. A computer program comprising computer-readable instructions operable to perform the method described in any one of claims 8 to 13.

15. A programmable firmware component programmed to carry out the method described in any one of claims 8 to 13.

Images