KINEMATICS PATH METHOD FOR LASER-INDUCED BREAKDOWN SPECTROSCOPY

A method for compositional analysis includes providing a sample having a surface and determining with a controller a plurality of equidistant positions along an oscillatory path along the surface. The oscillatory path is sinusoid in at least one orthogonal dimension within a plane approximately parallel to the surface. The method further includes, for each equidistant position of the plurality of equidistant position, moving an ablation point along the oscillatory path to the each equidistant position, pulsing an energy source to provide an electromagnetic energy beam to ablate material at the ablation point, and collecting an emission spectrum with a spectrographic instrument in response to pulsing the energy source. The method also includes analyzing the emission spectrum to determine a composition at the surface.

FIELD OF THE DISCLOSURE

This disclosure in general relates to systems and methods for performing laser-induced breakdown spectroscopy.

BACKGROUND

Elemental analysis techniques aid in determining the elemental composition of a material in various forms. Elemental analysis techniques range from destructive (e.g., material is destroyed in testing) to semi-destructive (e.g., material is sampled or surface damaged) to fully non-destructive (e.g., material is left fully intact). Example techniques can include Inductively Coupled Plasma-Atomic Emission Spectroscopy (e.g. ICP-AES), ICP-Mass Spectrometry (e.g. ICP-MS), Electrothermal Atomization Atomic Absorption Spectroscopy (e.g. ETA-AAS), X-Ray Fluorescence Spectroscopy (e.g. XRF), X-Ray Diffraction (e.g. XRD), and Laser-induced Breakdown Spectroscopy (e.g. LIBS). Elemental analysis may be either qualitative or quantitative and often requires calibration to known standards.

Laser-induced breakdown spectroscopy (LIBS) is an analytical technique used to analyze a large variety of materials, including metals, polymers, glasses, ceramics, and minerals. LIBS can very accurately detect and quantify elements of the periodic table. It can perform analysis of large and small samples, requires little-to-no sample preparation, and can be used for both bulk elemental analysis and microscanning for imaging. LIBS relies on pulsed energy emissions, such as pulsed laser emission, directed toward the sample to ablate, atomize, and ionize matter. The impact of each laser pulse onto the sample's surface creates a plume of plasma, light from which can be analyzed to perform qualitative or quantitative spectroscopy measurements. LIBS can therefore provide an easy to use, rapid, and in-situ chemical analysis with high precision, detection limits, and low cost.

Laser interactions with matter are governed by quantum mechanics which describe how photons are absorbed or emitted by atoms. If an atom absorbs a photon one or more electrons move from a ground state to a higher energy quantum state. Electrons tend to occupy the lowest possible energy levels, and in the cooling/decay process the atom emits a photon to return to a lower energy level. The different energy levels of different atoms produce different photon energies for each kind of atom, with narrowband emissions due to their quantization. These emissions correspond to the spectral emission lines found in LIBS spectra.

There are three basic stages in the plasma lifetime. The first stage is the ignition process which includes the initial bond breaking and plasma formation during the laser pulse. This ignition process is affected by the laser type, laser power, and pulse duration. The second stage in plasma life is the most critical for optimization of LIBS spectral acquisition and measurement because the plasma causes atomic emission during the cooling process. After ignition, the plasma will continue expanding and cooling. At the same time, the electron temperature and density will change. This process depends on ablated mass, spot size, energy coupled to the sample, and environmental conditions (state of the sample, pressure, etc.).

The last stage of the plasma life is less useful for LIBS measurements. A quantity of ablated mass is not excited as vapor or plasma; hence this material is ablated as particles and these particles create condensed vapor, liquid sample ejection, and solid sample exfoliation, which do not emit radiation. Moreover, ablated atoms become cold and create nanoparticles in the recombination process of plasma.

DETAILED DESCRIPTION

In an embodiment, a system for compositional analysis includes an energy source to provide an energy beam directed at an ablation point on a surface of a sample. The energy source can, for example, be a laser. The ablation point can be moved to positions (sample points) on the surface sequentially along an oscillatory path. In an example, the positions can be disposed at equidistance locations along the oscillatory path. In an example, the oscillatory path includes a sinusoidal pattern in at least one orthogonal dimension of the planar dimensions. The system can include a controller that directs the movement of the ablation point to the positions along the oscillatory path. The system can further include lenses and mirrors, or optionally, linear stage platforms to facilitate movement of the ablation point. The energy beam ablates material from the surface of the sample at the ablation point. The ablated material evolves an emission spectrum. The system can include a collection system to collect the emission spectrum. In an example, the collection system includes a collection lens optically connected to a spectral analyzer or spectrograph to determine the wavelengths emitted by the ablated material. The system can use the emission spectrum to determine which elements are present and optionally, in what quantities.

In a further example, a method for compositional analysis includes providing a sample having a surface. At each position (sample point) sequentially along an oscillatory path, material is ablated from the surface at the position, an emission spectrum is collected, and the emission spectrum is analyzed to determine a composition at the surface. Optionally, the emission spectrum is converted to a digital signal for further analysis to determine composition. The compositions can be analyzed, such as through averaging, to determine an average surface composition. In another example, compositions at positions can be used to form an image or map of positionally-resolved compositions.

It has been discovered that conventional scanning methods, particularly when used with irregular shapes, fail to provide quick and distributed coverage of a surface. When averaging composition over a surface, conventional methods tend to over emphasize one region of the surface relative to another region. The systems and methods described herein advantageously provide for uniform coverage and speed of testing, among other benefits.

FIG.1includes a schematic illustration of a system1for performing compositional analysis, for example, through laser-induced breakdown spectroscopy. A sample2is placed on a platform4. An energy source6directs an energy beam8through optical systems, such as lenses10, at an ablation point12positioned on the surface of the sample2. Material is ablated from the surface of the sample2and at least a portion of the ablated material is atomized or ionized, resulting in an emission spectrum14that is collected by a collection lens16optically connected to a spectrometer18, for example, using a fiber-optic cable.

The energy source6can be a laser. In an example, the energy source6is a pulsed laser having a wavelength in a range of 200 nm to 1100 nm, such as 1064 nm, 532 nm, or 266 nm. Further, the energy source6can have a peak power in a range of 0.5 MW/cm2to 2 GW/cm2, such as at least 1 MW/cm2, sufficient for ablating material from a surface of a sample and to probe elemental composition. For example, the laser pulses can have an energy in a range of 100 μJ-100 mJ and a pulse width in the femtosecond, picosecond, or nanosecond regime with a pulse repetition rate of up to the MHz regime. The laser may be a mode-locked or Q-switched laser. For example, the laser may be a passive Q-switched or an active Q-switched laser.

The collection system can include the collection lens16and a spectrometer18. In an example, spectrometer includes an imaging apparatus, such as a charge coupled device (CCD) imaging apparatus. In a further example, the emission spectrum can be directed by one or more mirrors to the spectrometer. In an additional example, the spectrometer can include various optical components such as one or more mirrors, lenses, apertures, gratings, prisms, and emission collection apparatuses. In an example, the emission collection apparatus is a charge coupled device (CCD) apparatus. But in other examples, other emission detectors can be employed.

In particular, the system1includes a controller20. In an example, the controller20can control the relative movement of the ablation point12to positions on the surface of the sample2. For example, the controller20can control a linear stage translation table, such as platform4, to move the sample2relative to a fixed beam8. In another example, mirrors such as galvo mirrors, prisms, or lenses can be used to alter the relative position of the ablation point on a fixed sample. The controller20can control the relative movement of the ablation point12to positions on the surface of the sample2sequentially along an oscillatory path. From the collection of the emission spectrum at each position on the surface of the sample2, it is possible to construct a compositional map of the scanned surface.

The controller20can further control the timing of the laser6to ablate material only at the desired positions on the sample surface. Further, the controller20can control the collection system, such as the spectrometer18, to collect the emission spectrum at a time delayed from the activation of the laser6.

In an example, the controller20can further allow for the selection of a test area on the surface of the sample2. For example, the controller20can use the laser system to detect edges of the surface and select the full surface area. In another example, the controller20can use an optional camera11to detect edges of the surface. In a further example, the controller20can provide an interface to a user that permits the user to select an area of the surface for testing.

As an alternative to a translation table, the system can include a set of one or more fixed mirrors and movable positioning mirrors, such as galvo mirrors, can direct the electromagnetic energy beam through lens to an ablation point on the surface of the sample. In an example, the mirrors, which are motor driven, can be controlled and adjusted automatically to guide the ablation point to positions (sample points) disposed sequentially along the oscillatory path on the surface of the sample2. In an example, the controller20controls the adjustable mirrors to adjust the position (sample points) on the surface of the sample2at which the ablation point12is located. In particular, the controller20is configured to move the ablation point to positions disposed sequentially along the oscillatory path, for example by controlling motors that drive the adjustable mirrors.

The controller20can comprise a computer (not shown): for example, comprising a storage medium, a memory, a processor, one or more interfaces, such as a user output interface, a user input interface and a network interface, which are linked together. The storage medium may be any form of non-volatile data storage device such as one or more of a hard disk drive, a magnetic disc, an optical disc, a ROM, etc. The storage medium may store one or more computer programs for causing the controller20to adjust the position on the surface of the sample2at which the ablation point12is located. The memory may be any random access memory suitable for storing data or computer programs. The processor may be any processing unit suitable for executing one or more computer programs (such as those stored on the storage medium or in the memory). The processor may comprise a single processing unit or multiple processing units operating in parallel, separately or in cooperation with each other. The processor, in carrying out processing operations, may store data to or read data from the storage medium or the memory. An interface may be provided that is any unit for providing an interface between the computer and the movable mirrors or translation platform4and the energy source6. A user input interface may be arranged to receive input from a user or operator. The user may provide this input via one or more input devices of the controller, such as a mouse (or other pointing device) or a keyboard, that are connected to, or in communication with, the user input interface. However, it will be appreciated that the user may provide input to the computer via one or more additional or alternative input devices (such as a touch screen). The computer may store the input received from the input devices via the user input interface in the memory for the processor to subsequently access and process, or may pass it straight to the processor, so that the processor can respond to the user input accordingly. A user output interface may be arranged to provide a graphical/visual output to a user or operator. For example, the emission spectrum collected from the sample may be provided as a graphical/visual output to a user or operator. As such, the processor may be arranged to instruct the user output interface to form an image/video signal representing a desired graphical output, and to provide this signal to a video display unit (VDU) such as a monitor (or screen or display unit) that is connected to the user output interface. It will be appreciated that the computer architecture described above is merely exemplary and that other computer systems with different architectures (for example with fewer components or with additional or alternative components) may be used. As examples, the computer could comprise one or more of: a personal computer; a server computer; a laptop; etc.

FIG.2includes an illustration of a laser-induced breakdown spectroscopy (LIBS) system100that includes a pulsed laser113, a beam expander111, a dual-axis scanning galvo system110, a lens108, a chamber103, one or more mirrors105, associated lenses116, and one or more spectrographs117. A sample101can be positioned on a table including an opening or analysis aperture to expose a surface of the sample to an interior of the chamber103.

The laser source113emits light pulses112, for example, having the wavelength or power as described above in relation toFIG.1. The laser source113can have pulse rates in a range of 1 to 1000 Hz. Each pulse112is directed onto the surface of the sample101, where a plasma102is generated. Light emanating from the plasma102may be collected by mirrors105and directed through lenses116to spectrographs117. The corresponding detection of light intensity can be used to perform qualitative or quantitative spectroscopy, leading to the identification of elements on the surface and potentially composition.

Optionally, a beam expander111is disposed in the path of the laser beam112from the laser source113to increase the diameter of the laser beam112. Expanding the diameter of the laser beam112decreases the power per unit area, avoiding damaging optical components such as mirrors of the galvo system110, and subsequently achieves tighter focusing spots on the sample surface. Thus, the beam112when striking the mirrors110reflects off a larger area109. In an example, the beam expander111includes an entry lens111B and an exit lens111A.

The galvo system110can include two motorized mirrors110A and110B. Such motorized mirrors110A and110B coupled with a lens108, such as an F-theta lens, can direct a beam that follows a mapping on the surface of the sample101. In an example, the lens108can focus the laser beam112to a spot of approximately 10 μm on the sample surface. The laser intensity per unit area on the spot is sufficient to generate a plasma102. Part of the light104emitted by the plasma102is recovered by one or more mirrors105A,105B,105C, or105D and focused through one or more lenses116A,116B,116C, or116D on one or more spectrographs117. Although four mirrors105A,105B,105C and105D and four corresponding lenses116A,116B,116C and116D are shown, it will be appreciated that embodiments can be provided with one or more such mirrors and one or more corresponding lenses.

The spectrograph117splits the light104according to the wavelength using a slit117A, a grating117B, and detects the lights using a linear array sensor117C or single channel sensors117D. The sensor signals from the sensors117C or117D can be used to determine the elemental composition of the sample.

The sample101is coupled with the chamber103to permit a surface of the sample101to be exposed to an interior of the chamber103. The chamber103can otherwise be hermetically sealed. For example, lenses108or116can include o-rings107or115.

The chamber103can be flushed using a gas such as argon, nitrogen, helium, or air. The interior of the chamber103can be maintained at pressure or vacuum. The gas can be injected through an opening106into the chamber103and exit through a second opening114from the chamber103. Optionally, a vacuum pump can be connected to the second opening114, drawing a vacuum in the chamber103as the gas moves through the chamber103. The location of the openings106or114can provide for gas flow across the chamber to reduce dead volumes and evacuate dust generated by the plasma102. When a vacuum pump is connected to the second opening114, dust can be evacuated through the vacuum pump. In particular, the quality and the nature of the plasma102and the resulting emitted light104depends on the environment within the chamber103. As such, a hermetic chamber103with dust management is highly desirable.

As illustrated in the example LIBS system ofFIG.3, a sample table201having an analysis aperture202sits above a chamber210. The sample can be held in place by a sample press209. A laser system207is coupled through a beam expander206via a galvo mirror system to lens205that directs laser pulses to a surface of a sample exposed through the analysis aperture202.

Light emitting from a plasma generated as a result of the laser pulse impinging on the surface of the sample through the analysis aperture202can be collected by mirrors held by the plasma vision mirror supports204A and204B. In an example, light collected by a mirror coupled to the plasma vision mirror support204A is directed to the spectrographic lens208. In another example, light collected by a mirror attached to plasma vision mirror support204B is projected to a spectrograph203.

FIG.4further illustrates details relating to the LIBS system ofFIG.1. A sample press301can secure a sample to a sample table303having an analysis aperture304open to an interior of the chamber313. Laser pulses directed through the beam expander309and the F-theta lens308can impinge on the sample through the analysis aperture304. The F-theta lens308can be supported by an F-theta lens support310. Using a galvo mirror system, such as those illustrated inFIG.2, laser pulses passing through the beam expander309and the F-theta lens308can be mapped onto the surface of the sample exposed through the analysis aperture304.

Light emitted from the resulting plasma can be collected by mirrors307A or307B and can be directed through spectrograph lens302or to a spectrograph311. For example, light collected by the mirror307A can be redirected to the spectrograph311. In another example, light collected by the mirror307B can be directed to the spectrographic lens302. The mirrors307A or307B can be held in place by the plasma vision mirror supports306A or306B, respectively.

In a further example, the chamber313can be configured for gas flow to draw dust particles generated by the plasma away from the sample surface and the sample aperture304. For example, the chamber313may have a gas inlet (not illustrated) disposed proximal to a bottom of the chamber near the lens308. Gas can flow up through the chamber313toward the analysis aperture304. The chamber313can define a flow pipe305or wall. Gas flows over the wall into an annulus connected to an outlet312. Optionally, the outlet312can be connected to a vacuum pump drawing gas through the chamber313, over the flow pipe305, into the annulus, and out of the outlet312.

FIG.5illustrates example paths of light extending through the system. For example, a laser beam410can be directed to motorized mirrors409A or409B of a galvo system and through an F-theta lens408that provides a focused laser beam onto a sample plane401. Upon impinging a sample at the sample plane401, the laser beam generates a plasma404that emits light405. The light405of the plasma404can impinge mirrors406A or406B that direct the collected light405onto a spectrographic lens402or into a spectrograph through entrance403. In an example, the spectrograph, such as the spectrograph illustrated inFIG.1,FIG.2, orFIG.3can collect the spectrum emitted by the plasma and determined elemental composition based on the spectrum.

Each of the systems illustrated inFIG.2,FIG.3,FIG.4, andFIG.5can include the elements and features of each other or of the system illustrated inFIG.1. In an example, each of the systems ofFIG.2,FIG.3,FIG.4, andFIG.5can further include controllers having the form and functionality described in relation toFIG.1. In a further example, each of the systems ofFIG.2,FIG.3,FIG.4, andFIG.5can have a camera as described in relation toFIG.1.

A feature of the system, such as those illustrated inFIGS.1-5, is the oscillatory scanning over the surface of a sample for bulk elemental analysis. In an example, the oscillatory scanning allows for averaging over a large number of sample points to obtain desirable statistics after each measurement. Collection of many sample points over the sample surface under consideration increases the accuracy of the qualitative or quantitative analysis. Collecting measurements from many sample points across the surface is more representative of sample composition compared to a single point. For example, the system can analyze a surface area of 1 mm to 10 mm in diameter, compared to a single point of about 10 μm in diameter.

Without the scanning of the systems described above, the laser would ablate the same portion of the sample at each pulse and, after each pulse, composition of the sample would be analyzed at different depths. Such a measurement technique is limited, as there exists a depth limit after which no further analysis is possible. For example, the plasma digs into a crater to the point that the plasma is shielded by the depth of the crater or the focus of the laser is no longer sufficient to create a reliable plasma. In contrast, the scanning of the present systems increase the number of measurements, while continually detecting the plasma at the focal point of the F-theta lens.

For accurate and representative analysis of the sample surface, it is desirable to have distributed sampling across the surface, for example, using a scanning path that provides distributed sampling of the surface and improved mirror movement with reduced acceleration jumps. In particular, the scanning path can define movement in at least one orthogonal dimension (e.g., x or y dimensions over a surface) as a sinusoidal pattern (e.g., sine or cosine). In an example, the sinusoidal pattern can be a function of time. For example, the sinusoidal pattern can include a periodicity parameter. Further, the sinusoidal pattern can have an amplitude, which may be constant or may be a function of time or position. In general, a first derivative of the sinusoidal pattern is also sinusoidal. For example, the sinusoidal pattern may be a sine or cosine pattern. In an example, when the sinusoidal pattern is a sine pattern, the first derivative is a cosine and the second derivative is a sine. The sinusoidal pattern and the sinusoidal derivatives are favorable for reducing acceleration jumps in the mirror movement and for enabling continuity at the end of the scanning path, such that scans can be run multiple times to increase the number of sampling points and therefore the accuracy of the analytical results.

Sample points can be defined along the sample path, for example, by the sinusoidal pattern. The sample points can be defined equidistant along the path. In an example, the equidistant sample points can be linearly equidistant points or curvilinearly equidistant points. The sinusoidal path and equidistant sample points along the path allow for desirable movement of the mirrors, such that the mirrors can move the beam to a next sample point quickly while remaining stationary at each sample point long enough for the laser to generate the desirable plasma.

FIG.6includes a block flow diagram illustrating an example method600for analyzing a sample. The method600includes inserting a sample, as illustrated at block602. For example, a sample can be inserted into a chamber or placed on a platform in a chamber. In another example, the sample can be placed against a sample table having an analysis aperture exposing a surface of the sample to an interior of a chamber.

As illustrated at block604, the system can determine an oscillatory path defined over the surface of the sample. For example, an analysis aperture can define an area of a sample that is exposed for testing. The oscillatory path can utilize a sinusoidal pattern in at least one dimension over the area exposed on the surface of the sample. Alternatively, an irregular shape can be exposed on the surface or can be selected by a user of the instrument. The system can define an oscillatory path that provides a desirable distribution of sample points across the surface of the irregularly shaped test area. In an example, a controller of the system can utilize a camera, as shown inFIG.1, to determine the shape of the surface and define an appropriate oscillatory path that provides a desirable distribution of sample points across the surface.

In an example, the oscillatory path is sinusoidal along at least one orthogonal dimension of two orthogonal dimensions along the surface of the sample. For example, the oscillatory path can have a sine or cosine pattern along at least one orthogonal dimension of the two orthogonal dimensions. For example, the oscillatory path can have a sine pattern along a height dimension. The sinusoidal pattern can be characterized by a periodicity parameter and an amplitude. The periodicity parameter can be specified to provide a number of oscillations across the surface in one orthogonal dimension. The amplitude may be constant. In another example, the amplitude can be a function of time. In a further example, the amplitude can be a function of position.

In a further example, both orthogonal dimensions are defined by sinusoidal patterns. In an example, the sinusoidal pattern in the first orthogonal dimension can be a sine pattern, while the sinusoidal pattern in a second orthogonal dimension is a cosine pattern. Each pattern can be defined by a periodicity parameter. The periodicity parameter for both patterns along the two orthogonal dimensions can be the same. In another example, the periodicity parameters are different. For example, the ratio of the two periodicity parameters can be an integer. In an example, the ratio is an even number integer. Alternatively, the ratio is an odd number integer. The amplitudes associated with the sinusoidal patterns of the two orthogonal dimensions can be the same. For example, the amplitudes can be the same function of time or the same constant. In another example, the amplitudes for each of the sinusoidal patterns of the two orthogonal dimensions is different. Further, the amplitude for a sinusoidal pattern of the second dimension can be a constant, while the amplitude associated with the sinusoidal pattern of the first orthogonal dimension can be a function of position.

In another example, the oscillatory path having at least one sinusoidal pattern defined along at least one of the orthogonal dimensions can include a non-sinusoidal pattern on the second orthogonal dimension. For example, the sinusoidal pattern in the y-dimension can be a sine pattern having a desired periodicity and amplitude, while the pattern in the x-dimension is linear, such as a linear function of time.

Further, sample points are defined along the oscillatory path. For example, equidistant sample points can be defined sequentially along the oscillatory path. The equidistant ablation points can be linearly equidistant or can be curvilinearly equidistant.

As illustrated at block606, the ablation point of a laser can be directed to a next sample point along the oscillatory path. Redirection of the laser can be accomplished by moving mirrors to direct the ablation point of the laser to the new position. The inertial properties of the galvos may not allow the mirrors to completely stop their movement at each ablation point. Nevertheless, an advantage of using the oscillatory movement presented here is that the rotation of the galvo is kept constant to allow the mirrors to smoothly continue their course. As the laser pulse is several order of magnitude faster than the galvo movements, each pulse impacts as if the mirrors are effectively fixed. This results in each ablation point being directed to the intended location on the sample and without any appreciable distortion of the ablation spot.

The laser is activated, for example, as illustrated at block608. As a result of the activation of the laser, one or more pulses impinge the surface of the sample at the ablation point, causing plasma to form which emits a spectrum characteristic of the composition of the sample at that point along surface.

As illustrated at block610, the emission spectrum is collected. For example, the emission spectrum can be collected by a mirror that directs the collected emission spectrum to a spectrographic lens or a spectrograph. The spectrograph converts the emission spectrum to a signal, as illustrated at block612.

As illustrated at block614, the system can determine whether it has reached the last sample point along the oscillatory path. If the last sample point has not been reached, the system can repeat moving the ablation point along the oscillatory path to a next sample point, as illustrated at block606, activate the laser, as illustrated at block608, collect the emission spectrum as illustrated at block610, and convert the emission spectrum to a signal, as illustrated at block612.

Once the end of the oscillatory path is reached where the last sample point has been tested, the system can analyze the converted signals, as illustrated at block616. For example, the system can analyze signals to determine composition at each point. Further, the system can average the measurements. In an example, the system can determine a mean, median, or mode of the measurements. For example, the system can determine a mean composition measurement across the tested sample points. While analysis is illustrated as occurring after the sampling process is complete, analysis can take place concurrently with the testing of sample points along the oscillatory path.

FIG.7includes a block flow diagram of a further method700for testing a sample. The method700is particular useful when testing a sample having a surface not defined by apertures or other regularly-shaped mechanical features associated with the apparatus. In particular, samples including irregular shaped test areas benefit from the method ofFIG.7.

In an example, the method700includes inserting a sample into the system, as illustrated at block702. For example, inserting the sample can include placing the sample on a table, such as a translation table, or placing the sample above an aperture exposed to a chamber.

A test area is selected on the sample, as illustrated at block704. For example, an image of the sample can be provided to a user to select the desired test area. In another example, the system can determine edges associated with the surface of the sample and select the test area based on the edges of the sample surface. In some examples, the test area can have a regular shape, such as a circle or a rectangle. In other examples, the selected test area can have an irregular shape.

As illustrated at block706, the system can determine a center line and boundary parameters. For example, the system can determine a width of the test area at the center line and a distance to the boundary or edge from the center line.

Oscillatory parameters, for example, periodicity parameters or amplitudes, can be determined to define an oscillatory path, as illustrated block710. For example, the periodicity parameters associated with sinusoidal patterns along one or both orthogonal dimensions along the surface can be defined. Further, amplitude parameters can be determined for one or both patterns along the two orthogonal dimensions.

As illustrated at block712, the system can determine equidistant points along the oscillatory path. For example, the points can be linearly equidistant along the oscillatory path. In another example, the points can be curvilinearly equidistant along the oscillatory path.

The system can test each of the sample points defined along the oscillatory path. For example, the system can move an ablation point of the laser to a next sample point along the oscillatory path, as illustrated at block714. The laser can be pulsed one or more times to generate a plasma, as illustrated at block716.

An emission spectrum emitted by the plasma can be collected, as illustrated at block718. The emission spectrum can then be converted into a signal, as illustrated at block720, for example, by a spectrographic lens or spectrograph.

As illustrated at block722, the system can determine whether it has reached the end of the sample points along the oscillatory path or whether to move to a subsequent sample point along the oscillatory path. Once it has reached the end of the oscillatory path, the system can analyze the converted signals, as illustrated at block724. For example, the system can determine the composition at each of the points along the surface. Further, the system can determine an average composition. In an example, the system can determine a mean, median, or mode of the measurements. The system can average the measurement of the converted signals and determine compositions based on a sum of the signals. Alternatively, the system can determine a composition at each point and average the compositions across the sample points.

Such methods can be used to define patterns providing a desired distribution of sample points across a surface for a variety of shaped test areas. For example, the test area may be circular. In another example, the test area may be rectangular. In a further example, the test area may be irregular.

For example,FIG.8includes an illustration of an example oscillatory path that covers a circular test area. The path follows a spiral pattern. Such a pattern can be generated using sinusoidal patterns in both of the two orthogonal dimensions. In an example, the sinusoidal pattern in a first dimension of the two orthogonal dimensions is a sine pattern, while the sinusoidal pattern in the second orthogonal dimension is a cosine pattern. Each sinusoidal pattern is a function of time. Further, in the illustrated example, the periodicity parameter associated with each of the patterns is equal. The amplitude associated with each of the sinusoidal patterns is the same and is a function of time. For example, the pattern can be generated using the equation below (Eq. 1). As described, the amplitude increases with time (t) until a maximum value is reached at which time the amplitude decreases.

x(t)=r(t)·cos(k·t); and

where tmaxis the time at which the maximum radius (r(t)) is reached and tzerois the time when the radius (r(t)) returns to zero. k and krare constants.FIG.9illustrates a further example of an oscillatory path generated using the sinusoidal pattern in at least one dimension of the two orthogonal dimensions along a surface. For example, the oscillatory path can have a sinusoidal pattern in a y-dimension. The periodicity parameter can be defined to provide a number of oscillations across the surface. The amplitude, a, of the sinusoidal pattern is constant, and kyis a constant.

The second dimension, such as the x-dimension, can be defined using a linear pattern or using a sinusoidal pattern, such as a cosine pattern. In an example, the x-dimension is defined as a linear function that increases with time until an endpoint or full width is reached at which time the pattern reverses direction using the same rate constants (kx).

where txmaxis the time at which x(t) reaches a maximum width and txzerois the time when x(t) returns to zero.

Alternatively, the second dimension can be defined using a sinusoidal pattern, such as a cosine pattern, having a different periodicity than the sine pattern of the first orthogonal dimension. In the illustrated example, the periodicity parameter of the sine pattern is 14 times that of the periodicity parameter of the cosine pattern of the second orthogonal dimension. Thus, the oscillatory path oscillates seven times between boundaries in the y-dimension for each oscillation across the width in the x-dimension.

where β is a constant, and kxis a constant.

WhileFIG.8andFIG.9illustrate oscillatory paths in which the amplitudes are constant or a function of time, the oscillatory path can alternatively be defined using patterns in which the amplitude for at least one dimension is a function of position.

FIG.10illustrates a block flow diagram illustrating a method1000for determining sinusoidal patterns having an amplitude as a function of position. For example, as illustrated at block1002, when a test area is selected, the system can establish a center line. For example, the center line can be defined along one of the orthogonal dimensions, such as, for example, the x-dimension. In particular, the center line can be selected at the maximum width along the x-dimension.

As illustrated at block1004, the system measures the width of the center line. Based on the width of the center line, the desired number of oscillations across the surface, and the desired number of sample points, the system can determine periodicity parameters for the sinusoidal pattern of one or both orthogonal dimensions, as illustrated at block1006. In an example, a ratio of the periodicity parameters is an even number integer. Alternatively, the ratio of periodicity parameters is an odd number integer.

Once the periodicity parameters are determined, a position of each peak in the period of the sinusoidal pattern of at least one of the orthogonal dimensions is known. For example, if a sinusoidal function or pattern is assigned to a y-dimension, based on the linear pattern or sinusoidal pattern in the x-dimension, the x-dimension position of the peaks of the sinusoidal pattern in the y-dimension can be determined.

As illustrated at block1008, a distance from the center line to an edge of the test area at the x-position of each of the peaks of the sinusoidal pattern in the y-dimension can be determined. At block1010, the amplitude parameters of the sinusoidal pattern in the y-dimension can be determined based on the measured distances from the center line at each peak. For example, each time the sinusoidal pattern of the y-dimension passes across the center line, the system can assign a new amplitude parameter to the sinusoidal pattern in the y-dimension.

Once the oscillator path is determined, the system can determine equidistant points along the oscillatory path, as illustrated at block1012. Such equidistant points can be sample points.

For example,FIG.11andFIG.12illustrate an example oscillatory path across a circular test area. In the illustrated example, the oscillatory path has a sinusoidal pattern, such as a sine pattern, in the y-dimension. In a further example, the pattern can include a sinusoidal pattern in the x-dimension, such as a cosine pattern. The periodicity parameter of the sinusoidal pattern in the y-dimension is 14 times that of the periodicity parameter of the sinusoidal pattern in the x-dimension. The amplitude of the cosine pattern in the x-dimension is constant. But the amplitude of the sine pattern in the y-dimension is a function of position. For example, each time the oscillatory path passes through the center line, the amplitude, a, of the sinusoidal function in the y-dimension can be altered based on a distance to the outer edge.

For example, as illustrated inFIG.12, the system can determine a center line that has a width W in the x-dimension. The amplitude for the cosine pattern in the x-dimension can be selected such that the pattern traverses the entire width for each period. The periodicity of the sine pattern associated with the y-dimension can be selected such that the ratio of the periodicity of the sine pattern to the periodicity parameter of the cosine pattern is an integer, such as 14.

Based on the known cosine pattern extending in the x-dimension, the x-position of each of the peaks of the sine pattern in the y-dimension is known. The system can then determine a distance from the center line to an edge at the peaks of the sine pattern and determine the amplitude of the sine pattern based on the distance from the center line to an edge. For example, each time the sine pattern passes down through the center line, a distance to the edge can be determined and the amplitude of the sine pattern determined based on the distance H′. Similarly, when the sine pattern passes up through the center line, the distance H can be determined and the amplitude of the sine pattern determined based on the distance H.

FIG.13andFIG.14include a further illustration, applying such a methodology to an irregular test area. A center line and a width of the center line W can be determined. Based on the determined center line, the pattern associated with the x-dimension can be determined. In an example, the pattern can be linear (e.g., Eq. 3). In another example, the pattern can be sinusoidal, such as a cosine pattern (e.g., Eq. 4).

Based on the desired number of oscillations across the surface during each period of the cosine pattern in the x-dimension, the periodicity parameter of the sinusoidal pattern in the y-dimension can be determined. In the illustrated example, the ratio of the periodicity parameter in the y-dimension relative to the periodicity parameter in the x-dimension is 11. The amplitude in the sinusoidal pattern in the y-dimension can be a function of position (e.g., Eq. 5). For example, for each peak, a distance from the center line H or H′ can be determined. The amplitude can be set based on a crossing of the center line towards a given peak for the sinusoidal pattern in the y-dimension. As such, an irregular pattern can be traversed from edge to edge providing a distribution of samples.

For each of the oscillatory paths, the system can determine equidistant sample points along that path to test using laser ablation of the surface. For example, as illustrated inFIG.15, an oscillatory path can include equidistant sample points. The equidistant sample points can be determined based on the linear distance, as illustrated at1504, (e.g., Eq. 6). Alternatively, the distance can be determined based on a curvilinear distance (e.g., Eq. 7) along the oscillatory path, as illustrated at1506.

When laser pulses are being directed to the surface to generate a plasma, mirrors directing the laser can be stationary. When the laser is being redirected, the laser pulses can be halted. For example, as illustrated inFIG.16, the laser is activated during a period (P) in which the position of the ablation point is stationary at a sample point along the oscillatory path. Once the pulses have ceased, the system can redirect the laser, moving the ablation point during a period (M). The movement during the period (M) when viewed as position versus time can have an s-shape. A first derivative of the s-shaped movement provides a velocity having a triangular shape, and the second derivative provides an acceleration depicted as a square wave. Thus, the oscillatory path with equidistant sample points disposed along the path provides for quick movement between positions and periods in which the system is stationary for testing a point along the oscillatory path.

For example, as illustrated inFIG.17, periods (P), in which one or more pulses are directed at a sample surface, are followed by quick movements during period (M) to redirect the ablation point of the laser to the next sample point. Thus, based on the positioning of points along the path, kinematics between each point can be defined in which in one period, the mirrors are stationary during a lapse of time long enough to allow the laser to generate multiple pulses on the same spot on the sample surface. Such a lapse of time is generally on the order of milliseconds. Such stationary positioning provides a stable and reproducible plasma, improving analytical performance. During the second portion or period of the kinematic movement, the ablation point is moved to the next sample point using an s-profile (displacement as a function of time). Such a profile provides a desired speed between points and an acceleration profile that ensures smooth mirror dynamics. By utilizing both the sinusoidal pattern having equidistant sample points and the kinematics having an s-profile, a system having low scanning error and desirable analytical performance is provided. Moreover, the analysis can be repeated at a desirable rate on the order of kilohertz or more.

In a first embodiment, a method for compositional analysis includes providing a sample having a surface and determining with a controller a plurality of equidistant positions along an oscillatory path along the surface. The oscillatory path is sinusoid in at least one orthogonal dimension within a plane approximately parallel to the surface. For each equidistant position of the plurality of equidistant positions, the method includes moving an ablation point along the oscillatory path to the each equidistant position, pulsing an energy source to provide an electromagnetic energy beam to ablate material at the ablation point, and collecting an emission spectrum with a spectrographic instrument in response to pulsing the energy source. The method further includes analyzing the emission spectrum to determine a composition at the surface.

In an example of the first embodiment, moving the ablation point includes moving the sample using a translation plate.

In another example of the first embodiment and the above examples, moving the ablation point includes positioning mirrors.

In a further example of the first embodiment and the above examples, the plurality of equidistant positions are linearly equidistant along the oscillatory path.

In an additional example of the first embodiment and the above examples, the plurality of equidistant positions are curvilinearly equidistant along the oscillatory path.

In another example of the first embodiment and the above examples, in another orthogonal dimension within the plane, the oscillatory path varies in proportion to time.

In a further example of the first embodiment and the above examples, in another orthogonal dimension within the plane, the oscillatory path is sinusoidal. For example, the oscillatory path is continuously differentiable. In another example, in the at least one orthogonal dimension within the plane, the oscillatory path varies as one of a sine or cosine function of time and, in the another orthogonal dimension within the plane, the oscillatory path varies as the other of the sine or cosine function of time. In a further example, in the at least one orthogonal dimension within the plane, the oscillatory path varies with a first periodicity and, in the another orthogonal dimension within the plane, the oscillatory path varies with a second periodicity, wherein the first periodicity is an integer multiple of the second periodicity. For example, the integer multiple is in a range of 1 to 100, such as in a range of 2 to 20. In an additional example, the integer multiple is 1 and an amplitude of the oscillatory path in both the at least one dimension and the another dimension is proportional to time. In another example, an amplitude of the oscillatory path in the at least one dimension is a function of position in the another orthogonal dimension.

In an additional example of the first embodiment and the above examples, analyzing the emission spectrum includes averaging the composition for each equidistant position of the plurality of equidistant positions.

In another example of the first embodiment and the above examples, the method further includes selecting a test area on the surface of the sample, the oscillatory path being within the test area. For example, the method further includes determining a center line of the test area and determining a width of the center line, the center line extending in another orthogonal dimensions within the plane. In an example, the method further includes, with the controller, determining a distance in the at least one orthogonal dimension from the center line to an edge of the test area at a peak of a sinusoidal oscillation, and adjusting an amplitude of the sinusoidal oscillation based on the distance.

In a second embodiment, a system for laser-induced breakdown spectroscopy includes a table to receive a sample, a laser source to provide a laser beam, and a mirror system to direct the laser beam to a surface of the sample. The laser beam is to ablate a portion of the sample at an ablation point and to initiate a plasma that emits an emission spectrum. The system further includes a spectrographic instrument to receive the spectrum and a controller in communication with the mirror system. The controller is to determine a plurality of equidistant positions along an oscillatory path along the surface. The oscillatory path is sinusoid in at least one orthogonal dimension within a plane approximately parallel to the surface. The controller is to control the mirror system to move the ablation point along the oscillatory path to each equidistant position.

In an example of the second embodiment, the controller is in communication with the laser source, the controller to direct the laser to pulse the laser beam.

In another example of the second embodiment and the above examples, the controller is in communication with the spectrograph, the controller to direct the spectrograph to collect the emission spectrum. For example, the controller is to analyze the emission spectrum to determine a composition at the surface.

In a further example of the second embodiment and the above examples, the system further includes a beam expander in the path of the laser beam prior to the mirror system.

In an additional example of the second embodiment and the above examples, the system further includes an F-theta lens in the path of the laser beam following the mirror system.

In another example of the second embodiment and the above examples, the plurality of equidistant positions are linearly equidistant along the oscillatory path.

In a further example of the second embodiment and the above examples, the plurality of equidistant positions are curvilinearly equidistant along the oscillatory path.

In an additional example of the second embodiment and the above examples, in another orthogonal dimension within the plane, the oscillatory path varies in proportion to time.

In another example of the second embodiment and the above examples, in another orthogonal dimension within the plane, the oscillatory path is sinusoidal. For example, the oscillatory path is continuously differentiable. In another example, in the at least one orthogonal dimension within the plane, the oscillatory path varies as one of a sine or cosine function of time and, in the another orthogonal dimension within the plane, the oscillatory path varies as the other of the sine or cosine function of time. In a further example, in the at least one orthogonal dimension within the plane, the oscillatory path varies with a first periodicity and, in the another orthogonal dimension within the plane, varies with a second periodicity, wherein the first periodicity is an integer multiple of the second periodicity. For example, the integer multiple is in a range of 1 to 100, such as in a range of 2 to 20. In an example, the integer multiple is 1 and an amplitude of the oscillatory path in both the at least one dimension and the another dimension is proportional to time. In an additional example, an amplitude of the oscillatory path in the at least one dimension is a function of position in the another orthogonal dimension.

In a further example of the second embodiment and the above examples, the controller is to analyze the emission spectrum by averaging the composition for each equidistant position of the plurality of equidistant positions.

In an additional example of the second embodiment and the above examples, the controller is to select a test area on the surface of the sample, the oscillatory path being within the test area. For example, the controller is to determine a center line of the test area and to determine a width of the center line, the center line extending in another orthogonal dimensions within the plane. In an example, the controller is to determine a distance in the at least one orthogonal dimension from the center line to an edge of the test area at a peak of a sinusoidal oscillation and to adjust an amplitude of the sinusoidal oscillation based on the distance.

In a third embodiment, a method for compositional analysis includes providing a sample having a surface and determining with a controller a plurality of positions along an oscillatory path along the surface. The oscillatory path is sinusoid in two orthogonal dimensions within a plane approximately parallel to the surface. The oscillatory path varies with time in the two orthogonal dimensions. For each position of the plurality of positions, the method includes moving an ablation point along the oscillatory path to the each position, pulsing an energy source to provide an electromagnetic energy beam to ablate material at the ablation point, and collecting an emission spectrum with a spectrographic instrument in response to pulsing the energy source. The method further includes analyzing the emission spectrum to determine a composition at the surface.

In an example of the third embodiment, the plurality of positions are a plurality of equidistant positions disposed sequentially along the oscillatory path.

In another example of the third embodiment and the above examples, the plurality of equidistant positions are linearly equidistant along the oscillatory path.

In a further example of the third embodiment and the above examples, the plurality of equidistant positions are curvilinearly equidistant along the oscillatory path.

In an additional example of the third embodiment and the above examples, the oscillatory path is continuously differentiable.

In another example of the third embodiment and the above examples, in one orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies as one of a sine or cosine function of time and, in another orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies as the other of the sine or cosine function of time.

In a further example of the third embodiment and the above examples, in one orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies with a first periodicity and, in another orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies with a second periodicity, wherein the first periodicity is an integer multiple of the second periodicity. For example, the integer multiple is in a range of 1 to 100, such as a range of 2 to 20. In an additional example, the integer multiple is 1 and an amplitude of the oscillatory path in both the at least one dimension and the another dimension is proportional to time. In a further example, an amplitude of the oscillatory path in the at least one dimension is a function of position in the another orthogonal dimension.

In an additional example of the third embodiment and the above examples, analyzing the emission spectrum includes averaging the composition for each equidistant position of the plurality of equidistant positions.

In another example of the third embodiment and the above examples, the method includes selecting a test area on the surface of the sample, the oscillatory path being within the test area. For example, the method further includes determining a center line of the test area and determining a width of the center line, the center line extending in another orthogonal dimensions within the plane. In an example, the method further includes, with the controller, determining a distance in the at least one orthogonal dimension from the center line to an edge of the test area at a peak of a sinusoidal oscillation and adjusting an amplitude of the sinusoidal oscillation based on the distance.

In a fourth embodiment, a system for laser-induced breakdown spectroscopy includes a table to receive a sample, a laser source to provide a laser beam, and a mirror system to direct the laser beam to a surface of the sample. The laser beam is to ablate a portion of the sample at an ablation point and is to initiate a plasma that emits an emission spectrum. The system further includes a spectrographic instrument to receive the spectrum and a controller in communication with the mirror system. The controller is to determine a plurality of positions along an oscillatory path along the surface. The oscillatory path is sinusoid in two orthogonal dimensions within a plane approximately parallel to the surface. The oscillatory path varies with time in the two orthogonal dimensions. The controller is to control the mirror system to move the ablation point along the oscillatory path to each position.

In an example of the fourth embodiment, the controller is in communication with the laser source, the controller to direct the laser to pulse the laser beam.

In another example of the fourth embodiment and the above examples, the controller is in communication with the spectrograph, the controller to direct the spectrograph to collect the emission spectrum. For example, the controller is to analyze the emission spectrum to determine a composition at the surface.

In a further example of the fourth embodiment and the above examples, the system further includes a beam expander in the path of the laser beam prior to the mirror system.

In an additional example of the fourth embodiment and the above examples, the system further includes an F-theta lens in the path of the laser beam following the mirror system.

In another example of the fourth embodiment and the above examples, the plurality of positions are a plurality of equidistant positions disposed sequentially along the oscillatory path. For example, the plurality of equidistant positions are linearly equidistant along the oscillatory path. In another example, the plurality of equidistant positions are curvilinearly equidistant along the oscillatory path.

In a further example of the fourth embodiment and the above examples, the oscillatory path is continuously differentiable.

In an additional example of the fourth embodiment and the above examples, in one orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies as one of a sine or cosine function of time and, in another orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies as the other of the sine or cosine function of time.

In another example of the fourth embodiment and the above examples, in one orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies with a first periodicity and, in another orthogonal dimension of the two orthogonal dimensions within the plane, the oscillatory path varies with a second periodicity, wherein the first periodicity is an integer multiple of the second periodicity. For example, the integer multiple is in a range of 1 to 100, such as a range of 2 to 20. In another example, the integer multiple is 1 and an amplitude of the oscillatory path in both the at least one dimension and the another dimension is proportional to time. In a further example, an amplitude of the oscillatory path in the at least one dimension is a function of position in the another orthogonal dimension.

In a further example of the fourth embodiment and the above examples, the controller is to analyze the emission spectrum by averaging the composition for each equidistant position of the plurality of equidistant positions.

In an additional example of the fourth embodiment and the above examples, the controller is to select a test area on the surface of the sample, the oscillatory path being within the test area. For example, the controller is to determine a center line of the test area and to determine a width of the center line, the center line extending in another orthogonal dimensions within the plane. In an example, the controller is to determine a distance in the at least one orthogonal dimension from the center line to an edge of the test area at a peak of a sinusoidal oscillation and to adjust an amplitude of the sinusoidal oscillation based on the distance.