Glow discharge optical emission coded aperture spectroscopy

Abstract

The invention relates to a glow discharge optical emission spectroscopy (GDOES) apparatus that includes a spectral filter mask with a plurality of slits that are each operable to receive optical radiation emitted from a sample. The apparatus also includes a processor operable to analyze a sample's emitted optical radiation from the plurality of slits of the spectral filter mask. The invention also relates to methods of analyzing a sample by utilizing the aforementioned apparatus.

Description

TITLEGLOW DISCHARGE OPTICAL EMISSION CODED APERTURE SPECTROSCOPYSTATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was made with government support under CHE-2108359 and PHY-2206769, awarded by the National Science Foundation. The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 710,350, filed on October 22, 2024. The entirety of the aforementioned application is incorporated herein by reference.BACKGROUND

[0003] Current methods and systems for analyzing samples have numerous limitations. Embodiments of the present disclosure aim to address the aforementioned limitations.SUMMARY

[0004] In some embodiments, the present disclosure pertains to a glow discharge optical emission spectroscopy (GDOES) apparatus. In some embodiments, the apparatus includes a spectral filter mask with a plurality of slits that are each operable to receive optical radiation emitted from a sample. In some embodiments, the apparatus also includes a processor operable to analyze a sample’s emitted optical radiation from the plurality of slits of the spectral filter mask.

[0005] Additional embodiments of the present disclosure pertain to methods of analyzing a sample by utilizing the apparatus of the present disclosure. In some embodiments, the methods of the present disclosure include: (1) placing a sample on an apparatus of the present disclosure: (2) applying a glow discharge plasma to the sample such that the sample emits optical radiation; (3) receiving in each slit of the spectral filter mask optical radiation emitted from the sample; and (4) utilizing the apparatus processor to analyze the sample’s emitted optical radiation from the plurality of slits to determine the elemental composition of the sample.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. 1A provides a schematic of a glow discharge optical emission spectroscopy (GDOES) apparatus in accordance with various embodiments of the present disclosure.

[0007] FIG. IB provides an illustration of a method of analyzing a sample in accordance with various embodiments of the present disclosure.

[0008] FIG. 1C provides another schematic of a glow discharge optical emission spectroscopy (GDOES) apparatus in accordance with various embodiments of the present disclosure. The schematic illustrates a glow discharge optical emission coded aperture spectrometry (GOCAS) instrument setup, where the emitted light from a glow discharge (GD) lamp is encoded by a coded aperture on a digital micromirror device (DMD) and dispersed by a spectrograph onto an intensified charge-coupled device (ICCD) camera.

[0009] FIG. ID provides GOCAS data processing from encoded overlapping images of the GD optical emission of Cr I 521.45 nm, 521.60 nm, and 521.84 nm, from a nimonic alloy 90 standard reference material (B7009). The reconstruction / deconvolution of the spectra in the full field of view is achieved with the measured coded aperture / mask illuminated with a flat-field (Ag HCL, Ag I 520.91 nm) and using compressed sensing algorithms.

[0010] FIGS. 2A-2D provide the effects of coded aperture element size (FIGS. 2A-2B) and transmittance (FIGS. 2C-2D) on spectra reconstruction fidelity PSNR and Pearson’s Correlation with different CS algorithms: TwIST (A), ADMM-TV ( ), SeSCIcpu W, and SeSCIcipu («). The respective measured coded apertures are displayed as inserts in the Pearson’s Correlation plots.

[0011] FIG. 3 provides the effect of coded aperture width a number of elements in x / X dimension on spectral reconstruction fidelity as PSNR ( ) or Pearson’s Correlation (♦).

[0012] FIGS. 4A-4B provide fidelity characterization, in terms of spectral PSNR (dB) (FIG.4A) and Pearson’s Correlation (FIG. 4B), which were studied for different detector noise levels with several algortihms: TwIST (A), ADMM-TV (<). SeSCIcpu (M). and SeSCIcpu (»)•

[0013] FIGS. 5A-5E provide GDOES single slit spectra and GOCAS spectra for SRM BNF B7009 (FIG.5A) and BNF E3918 (FIG. 5B). The GDOES single slit spectrum multiplied xlO is displayed in the insert for better comparison of the S / N. GDOES single slit (^) and GOCAS ( ) calibration curves with low alloy steel SRMs for Cr I lines at 520.45 nm (FIG. 5C), 520.60 nm (FIG. 5D), and 520.85 nm (FIG. 5E).DETAILED DESCRIPTION

[0014] It is to be understood that both the foregoing general description and the following detailed description are illustrative and explanatory, and are not restrictive of the subject matter, as claimed. In this application, the use of the singular includes the plural, the word “a” or “an” means “at least one”, and the use of “or” means “and / or”, unless specifically stated otherwise. Furthermore, the use of the term “including”, as well as other forms, such as “includes” and “included”, is not limiting. Also, terms such as “element” or “component” encompass both elements or components comprising one unit and elements or components that include more than one unit unless specifically stated otherwise.

[0015] The section headings used herein are for organizational purposes and are not to be constmed as limiting the subject matter described. All documents, or portions of documents, cited in this application, including, but not limited to, patents, patent applications, articles, books, and treatises, are hereby expressly incorporated herein by reference in their entirety for any purpose. In the event that one or more of the incorporated literature and similar materials defines a term in a manner that contradicts the definition of that term in this application, this application controls.

[0016] Glow discharge optical emission spectrometry (GDOES) is a technique that relies on cathodic-sputtering sampling to allow fast and direct multi-elemental analysis of solids with little-to-no sample preparation. Other advantages of GDOES include excellent depth resolution (~nm), broad dynamic range, and limits of detection (LOD) down to the single ppm.

[0017] Thus, GDOES is widely used in metallurgy and material sciences, including semiconductors, optics, photonics, and biomedical applications, as well as characterization of thin films (TFs) and ultra-TFs. Nevertheless, the best LODs reported are for bulk analysis, where longer acquisition time is used toward signal averaging to achieve the best signal to noise ratio.

[0018] In the case of TF analysis and depth profiling, GD operating conditions are optimized to obtain the flattest-bottom craters that are best for depth resolution, but not best for LODs. In addition, the fast sputter- sampling in GD results in very fast transient signals from materials with nanoscale changing features in depth, like ultra-TFs, such that it requires the shortest acquisition time, which severely limits signal averaging, S / N, and further compromises the LOD’s to restrict depth analysis mainly to major components.

[0019] GDOES commercial instruments have slit-based wavelength selection systems (polychromators, monochromators, and recently ccd array spectrographs) designed to favor high spectral resolution with a very thin slit. The width of the slit, however, is one of the main parameters that determines the light throughput, such that a very thin slit greatly limits light collection power.

[0020] Other wavelength selection devices feature multiplexing schemes that allow high light throughput without comprising spectral resolution. For example, several researchers have used Fourier Transform (FT) interferometry approaches coupled to GDOES for fundamental studies and building a spectral library. While these approaches have several advantages, one of the disadvantages is that all wavelengths in the spectral window interfere with each other, which means that there is a very high probability of incurring multiplex disadvantage when source noise is dominant, thus resulting in poorer S / N ratio for weak spectral features.

[0021] Compressed sensing (CS) is a sampling paradigm that makes use of the natural sparsity of a signal in a suitable domain to enable its acquisition using only a small fraction of the samples required by the Shannon-Nyquist theorem. Thus. CS enables more efficient and significantly faster data acquisition and has been shown to overcome limitations of traditional molecular spectral imaging systems.

[0022] Moreover, operating conditions for best LODs are compromised in lieu of best sputtering crater shapes for depth resolution. In addition, the fast transient signals from ultra-TFs do not permit the optimal sampling statistics of bulk analysis, such that LODs are further compromised. Furthermore, commercial GDOES instruments rely on slit-based light dispersion that favors high spectral resolution at the expense of light throughput.

[0023] As such, a need exists for more effective methods and systems for GDOES-based analysis of samples. In particular, there is a need for techniques that can enhance all aspects of GDOES techniques without sacrificing any other parameters. Numerous embodiments of the present disclosure aim to address the aforementioned need.

[0024] In some embodiments, the present disclosure pertains to a glow discharge optical emission spectroscopy (GDOES) apparatus. With reference to apparatus 10 in FIG. 1A for illustrative purposes, the apparatus of the present disclosure generally includes a spectral filter mask 18 with a plurality of slits 20 that are each operable to receive optical radiation emitted from a sample. In some embodiments, apparatus 10 also includes a processor 22 operable to analyze a sample’s emitted optical radiation from the plurality of slits 22 of the spectral filter mask 18. In some embodiments, processor 22 may also include a camera 24.

[0025] In some embodiments, apparatus 10 also includes a light source 12 operable to generate a glow discharge plasma for application to the sample. Apparatus 10 may also include a glow discharge chamber 14 operable to hold a sample and receive light from a light source 12. In some embodiments, apparatus 10 may also include one or more lenses 13 operable to modify a glow discharge plasma or an emitted optical radiation. In some embodiments, apparatus 10 may also include one or more mirrors 15 operable to reflect a glow discharge plasma or an emitted optical radiation. In some embodiments, apparatus 10 may also include a power supply operable to generate a glow discharge plasma from a sample.

[0026] Additional embodiments of the present disclosure pertain to methods of analyzing a sample. With reference to FIGS. 1A and IB for illustrative purposes, such methods may include: placing a sample on a glow discharge optical emission spectroscopy (GDOES) apparatus 10 (FIG. IB, step 30); applying a glow discharge plasma to the sample (FIG. IB, step 32) such that the sample emits optical radiation (FIG. IB, step 34); receiving in each slit 20 of spectral filter mask 18 optical radiation emitted from the sample (FIG. IB, step 36); and utilizing processor 22 to analyze the sample’s emitted optical radiation from the plurality of slits 20 (FIG. IB, step 38) to determine the elemental composition of the sample (FIG. IB, step 40). In some embodiments illustrated in FIG. 1A, one or more lenses 13 of apparatus 10 may modify a glow discharge plasma and / or an emitted optical radiation. In some embodiments, one or more mirrors 15 of apparatus 10 may reflect a glow discharge plasma or an emitted optical radiation.

[0027] As set forth in more detail herein, the apparatus and methods of the present disclosure may include numerous embodiments. Additionally, the apparatus and methods of the present disclosure may include numerous applications.

[0028] Light sources

[0029] The apparatus of the present disclosure may include various light sources. Moreover, the methods of the present disclosure may utilize various light sources. For instance, in some embodiments, the light source is operable to generate a glow discharge plasma for application to a sample. In some embodiments, the light source includes a glow discharge (GD) lamp.

[0030] Spectral filter masks

[0031] The spectral filter masks of the present disclosure generally include a plurality of slits that are each operable to receive optical radiation emitted from a sample. The apparatus of the present disclosure may include various spectral filter masks. Moreover, the methods of the present disclosure may utilize various spectral filter masks. For instance, in some embodiments, the spectral filter masks of the present disclosure may be operable to reflect a sample’s emitted optical radiation from each of the plurality of slits (e.g., slits 20 in FIG. 1A) onto a processor (e.g., processor 22 in FIG. 1A).

[0032] In some embodiments, the spectral filter masks of the present disclosure are in the form of a digital micromirror device (DMD). In some embodiments, the spectral filter masks of the present disclosure are in the form of a coded aperture. In some embodiments, the spectral filter masks may be in the form of a spatial light modulator, such as a liquid crystal device. In some embodiments, the spectral filter masks may be in the form of a solid plate with holes / slits of different shapes, sizes, and distribution.

[0033] The spectral filter masks of the present disclosure may include various numbers of slits in various arrangements. For instance, in some embodiments, the spectral filter masks of the present disclosure include at least 5 slits. In some embodiments, the spectral filter masks of the present disclosure include at least 10 slits. In some embodiments, the spectral filter masks of the present disclosure include at least 25 slits. In some embodiments, the spectral filter masks of the present disclosure include at least 50 slits.

[0034] In some embodiments, the slits of the spectral filter masks of the present disclosure are in the form of an array. In some embodiments, the slits of the spectral filter masks of the present disclosure are in the form of an array of rectangles, squares, circles, and / or ellipses.

[0035] The slits of the present disclosure may include various widths. For instance, in some embodiments, the slits include a width ranging from about 10 pm to about 10 mm. In some embodiments, the slits include a width ranging from about 100 pm to about 1 mm. In some embodiments, the slits include a width ranging from about 100 pm to about 500 pm.

[0036] The slits of the present disclosure may include various depths. For instance, in some embodiments, the slits include a depth ranging from about 10 pm to about 10 mm. In some embodiments, the slits include a depth ranging from about 100 pm to about 1 mm. In some embodiments, the slits include a depth ranging from about 100 pm to about 500 pm.

[0037] Processor

[0038] The apparatus of the present disclosure may include various processors. Moreover, the methods of the present disclosure may utilize various processors to analyze samples. For instance, in some embodiments, the processor includes an optical spectrometer. In some embodiments, the optical spectrometer includes, without limitation, a spectrograph, an optical detector, a camera, or combinations thereof.

[0039] In some embodiments, the optical spectrometer includes a camera (e.g., camera 24 in FIG.1A). In some embodiments, the camera includes, without limitation, an intensified charge-coupled device (ICCD) camera, an encoded camera, or combinations thereof.

[0040] In some embodiments, the processor includes: an optical spectrometer; and an algorithm in electronic communication with the optical spectrometer. In some embodiments, the algorithm is operable to analyze the sample’s emitted optical radiation from the plurality of slits of the spectral filter mask to identify elemental compositions of the sample. In some embodiments, the algorithm includes programming instructions for: (a) receiving a sample’s emitted optical radiation from the plurality of slits of the spectral filter mask; (b) analyzing the emitted optical radiation to identify elemental compositions of the sample; and (c) generating a report of the identified elemental compositions of the sample.

[0041] In some embodiments, the algorithm includes a compressed sensing algorithm. In some embodiments, the compressed sensing algorithm is operable to analyze a deconvoluted spectrum from a full field of view. In some embodiments, the algorithm is operable to perform wavelengthspecific detection to identify specific elements based on their emission spectra. In some embodiments, the compressed sensing algorithm is operable to analyze a spectrum from each of the plurality of slits of the spectral filter mask.

[0042] In some embodiments, the algorithm utilizes convex optimization to recover a full field of view from an image. In some embodiments, the algorithm utilizes convex optimization to converge onto an optimal solution for a cost function. In some embodiments, the convex optimization enforces a sparsity constraint by iteratively minimizing the error between a reconstructed image and a measurement In some embodiments, the reconstruction algorithm may be of different types, including iterative threshold, non-convex, convex relaxation, greedy, combinatorial, and / or Bregman iterative. In some embodiments, the reconstruction algorithm may incorporate deep leaming / machine learning strategies.

[0043] Samples

[0044] The methods and apparatus of the present disclosure may be utilized to analyze various samples. For instance, in some embodiments, the sample includes a solid. In some embodiments, the sample includes thin films and ultra-thin films. In some embodiments, the sample includes a bulk material with different compositional profile along its depth. In some embodiments, the sample includes nanoscale materials, such as nanoparticles and nanowires. In some embodiments, the sample includes microscale materials, such as microparticles. In some embodiments, the sample includes biological materials, such as dried physiological fluids, cell cultures, and plant tissues.

[0045] In some embodiments, a sample may act as a cathode in an argon glow discharge. Energetic Ar ions may then strike a sample and sputter atoms and molecules off a sample surface and into the plasma. In some embodiments, sputtering may be carefully controlled to erode the material for depth profiling. Atoms sputtered from the surface are excited by collisions with electrons in the plasma. These atoms emit characteristic radiation as they relax. Elements are identified and quantified by the resultant optical emission spectra.

[0046] Applications and Advantages

[0047] In some embodiments, the methods and apparatus of the present disclosure overcome limitations associated with GDOES-based devices by enabling significant improvements in signal-to-noise ratio and detection limits at fast acquisition times (e.g., fractions of a ms). For instance, in some embodiments, the apparatus and methods of the present disclosure take advantage of coded apertures and compressed sensing reconstruction algorithms to enable significantly better detection limits at the fastest acquisition times. Moreover, the apparatus and methods of the present disclosure can easily be implemented on commercial instruments that feature array detectors by replacing an entrance slit with a filter mask of the present disclosure.

[0048] As such, the apparatus and methods of the present disclosure can have numerous advantageous applications. For instance, in some embodiments, the applications of the apparatus and methods of the present disclosure may include, without limitation: (1) a potential to achieve faster GDOES measurement times; (2) the ability to enable new types of studies of minor elements via lower detection limits; (3) the ability to expand and enhance the information obtainable from thin film analyses; (4) the ability to utilize a coded aperture mask compatible with existing GDOES instruments with spectral array detectors; and (5) the ability to analyze depth profiling of samples, such as nanoscale materials.

[0049] In some embodiments, the methods and apparatus of the present disclosure may be used for multi-elemental analysis of solids. In some embodiments, the methods and apparatus of the present disclosure may be used for depth profiling of a sample. In some embodiments, the methods and apparatus of the present disclosure may be utilized to perform a depth profile analysis to determine the distribution of elements across different layers of the sample.

[0050] Additional Embodiments

[0051] Reference will now be made to more specific embodiments of the present disclosure and experimental results that provide support for such embodiments. However, Applicant notes that the disclosure below is for illustrative purposes only and is not intended to limit the scope of the claimed subject matter in any way.

[0052] Example 1. Glow Discharge Optical Emission Coded Aperture Spectroscopy

[0053] In this Example, Applicant presents a new technique called glow discharge optical emission coded aperture spectrometry (GOCAS), which is shown to allow both higher spectral resolution and higher light throughput by using a coded aperture (CA) with multiple thin slits at the spectrograph’s entrance to measure the convoluted spectra and increasing light throughput without compromising high spectral resolution, and compressed sensing (CS) algorithms to recover the deconvoluted spectra from the full field of view. The effects of CA characteristics on spectral reconstruction fidelity were studied and showed best fidelity for smaller slits, 50% transmittance, and wider CA with higher number of slits.

[0054] In addition, Shearlet Enhanced Snapshot Compressive Imaging (SeSCI)cpu showed the best performance of the CS algorithms studied, including SeSCIcpu, Two-Steps Iterative Shrinkage / Thresholding (TwIST), and Alternating Direction Method of Multipliers Total Variation Minimization (ADMM-TV). Moreover, GOCAS is shown to be very robust against increasing detector Gaussian noise. Finally, standard reference materials are used to show up to ~ 30x improved S / N, and order of magnitude improved LODs, at the fastest acquisition times (fraction of a ms), which has the potential to be transformative for depth profiling of nano structured materials.

[0055] The added advantage of CA approaches is that multiplexing overlap is only limited to adjacent wavelength channels, such that the possibility of multiplex disadvantage is limited. The effect of CA parameters on spectral reconstruction fidelity was studied, including transmittance, slit size, and number of slits in the dispersion dimension. In addition, the performance of several CS reconstruction algorithms was also studied. Optimum conditions were used to characterize quantitative figures of merit from calibration curves. GOCAS has the potential to substantially impact depth profiling applications of nanostructured materials, including ultra-TFs and nanoparticles, by opening the possibility of characterizing minor components.

[0056] Example 1.1. Instrumentation

[0057] The GOCAS instrument layout is presented in FIG. 1C. The GD lamp previously described was adapted with an extended Grimm-type anode with an inner diameter of 7 mm. The GD was operated under UHP Ar gas at 5-8 torr, controlled using a roughing pump (Edwards, RV12) and mass flow controller (Apex, AX-MC-1SLPM-D / 5M), and monitored using a pressure gauge (MKS,901P-11040). The RF power supply (Dressier, Cesar 1350) for GD lamp was externally pulsed (frequency - 1 kHz, pulse duration - 200 ps to 500 ps, RF forward power - 400 Wforwaid, RF reflected power - 50 Wrefiected) and synchronized to an ICCD camera (ANDOR DH734-18U-03 iStar, gate delay - 25 ps . gain - 0 / 255, binning - 1x1, exposure - 0.4 ms to 1 s, ~4 full frames per second readout) using an oscilloscope (Agilent Technologies, DSO-X 3034A). The de bias voltage (Vac) was measured at the cathode (sample) with a high voltage probe (Tektronix P6015A).

[0058] A chiller (Thermo Scientific, Neslab Merlin M25) was used to cool the RF power supply and backing electrode. The light emitted by the GD is collimated and focused with lenses (50 mm diameter, 200 mm focal length, UV-VIS Coated, Near UV Achromatic Lens) onto a Digital Micromirror Device (DMD) that displays the coded aperture. Two different Texas Instruments DMDs were tested: (1) DLP 300 Light Crafter EVM, 608 x 684 mirrors, 6.5718 mm w. x 3.699 mm h. dimensions, designed for side illumination (micromirror pixel diagonal is along the width of the chip), only 2 mm w. x 3 mm h. area used for studies of CA transmittance and element size, as well as the effect of noise; and (2) DLP9500 DMD evaluation board, 1920x1080 mirrors, 20.736 mm w. x 11.664 mm h. dimensions, designed for comer illumination (micromirror pixel side along the width of the chip) so it had to be rotated 45 degrees to fit the optical path of our instrument, only 3 mm w. x 4 mm h. area used to study effect of number of apertures / slits in the dispersion dimension, and for characterization of quantitative figures of merit.

[0059] The GD light reflected from the DMD CA is collimated and focused onto the entrance of a “slit-less” (slit completely open to 3 mm w. x 7 mm h.) spectrograph (24001 / mm, 0.320 m focal length, Teledyne-Princeton Instruments. IsoPlane SCT320) where light is dispersed and captured on the ICCD. The spectral resolution under these conditions is ~60 pm, which is comparable to some commercially available GDOES instruments. The reconstruction station has the following specifications: Intel(R) Core (TM) i7-7700HQ CPU @ 2.80GHz, 64-bit operating system, x64-based processor, RAM 16.0 GB.

[0060] Example 1.2, Coded apertures

[0061] The coded apertures consisted of a pseudo-random binary matrix with a Bernoulli distribution (‘binomd’ function, MATLAB R2020b), using ‘0’ and ‘1’ values, where 0 corresponds to a closed aperture / slit and 1 to an open aperture / slit. This CA matrix was projected on the DMD. A flat field at the position of the GD cathode / sample was used for studying the effect of CA parameters and different CS algorithms on the spectral reconstruction fidelity. The flat field was produced by a set of diffusers transmitting the optical emission from a hollow cathode lamp (HCL, Westinghouse VWR), operated at ~15mA and ~1.2 kV.

[0062] The effect of CA parameters was measured with an ICCD exposure of 100 ms. Studies of the effect of CA element size and transmittance were performed for spectra from a Cu HCL, featuring a single peak of Cui at 520.82 nm. The effects of CA element size were studied by setting the transmittance to 50% and varying the size of each element in terms of DMD pixels from 7 X 14 (75.6 pm X 75.6 pm), 9 X 18 (97.2 pm X 97.2 pm), 11 X 22 (118.8 pm X 118.8 pm), to 15 X 30 (162 pm X 162 pm), which accounts for DMD pixel pitch in the x dimension being twice as long as the y dimension.

[0063] Measured CA are shown in corresponding figures as inserts for reference. Also, the effects of CA percent transmittance (number of elements closed / total mask elements * 100) were studied by setting the element size to 7 x 14 (75.6 pm X75.6 pm) and varying the transmittance from 40%, 50%, 60%, to 70%. In addition, the reconstruction fidelity for more complex spectra was also studied by using an Fe HCL (Fe I lines at 516.74 nm and 517.15 nm) and a Cr HCL (Cr I lines at 520.45 nm, 520.60 nm, and 520.84 nm). Furthermore, the effect of CA width, or number of apertures / slits on the dispersion dimension, on reconstruction fidelity was also studied, where the number of elements in the x-axis of each CA was varied from 35. 45. to 58. Moreover, the effect of detector noise was studied at several levels (xl, xlO, xlOO) of added gaussian white noise. The original noise level was determined from the standard deviation of the background of ICCD image under dark conditions (no GD or HCL emission). The standard deviation value was used in MATLAB as a multiplier in the ‘randn’ function, and the positive tail was adjusted to the level of interest and added to encoded spectral images.

[0064] Example 1.3. CS reconstruction

[0065] The 1 s and 0s coded aperture matrix was not used directly for decoding / CS reconstruction. Instead, the ICCD measured coded aperture projected on the DMD from a flat field at a singlewavelength channel for a well-resolved peak from an HCL (10 images. 1 s exposure; CA parameter studies: Cu I 515.32 nm; Quantitative figures of merit from Cr standards: Ag I 520.91 nm) was used for reconstruction (FIG. ID middle), which enables considering all the system aberrations. The CS reconstruction software requires the dimensions to be the same for the convoluted CA spectral image (FIG. ID left) and the measured single-wavelength coded aperture, which is achieved by padding the single-wavelength CA image with zeros to fit the width of the ICCD window. In addition, spectral reconstruction is achieved by using the measured single-wavelength CA for deconvolution at each wavelength channel, such that a different matrix for each wavelength channel is produced where the measured CA is shifted across the spectral dimension from wavelength to wavelength (pixel by pixel).

[0066] Thus, the CS reconstructed hyperspectral data cube shows the recovered image at each subsequent wavelength shifted as per the dispersion in the original convoluted CA spectral image. Finally, the pixels with padded zeros are removed at each wavelength channel to obtain the finished reconstructed hyperspectral data cube.

[0067] In this Example, Applicant compared the performance of several CS reconstruction algorithms, including Two-Steps Iterative Shrinkage / Thresholding (TwIST), Alternating Direction Method of Multipliers Total Variation Minimization (ADMM-TV) and two variants of Shearlet Enhanced Snapshot Compressive Imaging (SeSCI) - SeSCIcpu and SCSCIGPU. All these algorithms use convex optimization to converge onto an optimal solution for a cost function, which enforces a sparsity constraint, by iteratively minimizing the error between the reconstructed image and the measurement. Based on previous studies, certain parameter value ranges were considered: SeSCIcpu - lambda (-0.005-25), step size (-10-150) and number of iterations (-10-300); SCSCIGPU - sigma (-0.005-25), lambda (-0.005-25), step size (-10-150) and number of iterations(~10-300); TwIST- number of iterations (-10-500), Tau (-0.01-5), TV iterations (~4-60); ADMM-TV-number of iterations (-50-500), Eta (-0.01-10). lambda(~0.01-10), TV weight (-0.1-20). Plots and details for optimization are provided in supporting information.

[0068] Example 1.4, Reconstruction fidelity assessment

[0069] A traditional single-slit spectra was measured to have as a standard to assess reconstruction fidelity under each set of experimental conditions tested. Peak signal-to-noise ratio (PSNR) and Pearson’s correlation coefficient (PCC) were used to quantify the spectral reconstruction fidelity by comparing the reconstructed GOCAS spectra to the single-slit spectra. PSNR is a widely accepted metric in the field of signal / image processing that calculates the mean squared error, through a pixel-to-pixel comparison between the test signal and the standard signal, weighed by the maximum possible pixel value and expressed in decibels. Higher PSNR values indicate better reconstruction meaning reconstructed signal is more representative of the standard signal. PCC measures the linear correlation between the reconstructed signal and the standard signal, by calculating the ratio between their covariance and the product of their standard deviations. PCC values closer to 1 represent a strong correlation. Normalized spectra were used for comparison to put the major focus on the shape and relative intensities.

[0070] Example 1.5. Quantitative figures of merit

[0071] GOCAS performance was determined in terms of S / N for Cr I (520.45 nm, 520.60 nm and 520.84 nm) by using two nickel-base alloys standard reference materials (SRMs), BNF B7009 (Nimonic alloy 90, Cr: 19.65 wt.%) and BNF E3918 (Nimonic alloy 75, Cr: 19.4 wt.%). Operating conditions include pressure at 8 torr, flow rate of Ar: 0.2 SLPM, Wappiied: 350, GD pulse duration of 200 ps at 1 kHz, total pulses integrated per exposure: 2 (BNF E3918), and 10 (BNF B7009).

[0072] In addition, calibration curves were constructed to determine LCDs for Cr in low alloy steel SRMs, including NIST 1226 (Cr: 0.467 wt.%), NIST 1761A (Cr: 0.222 wt.%), BCS / SS 406 / 1 (Cr: 2.10 wt.%), BCS / SS 407 / 1 (Cr: 2.95 wt.%), BCS / SS 408 / 1 (Cr: 0.102 wt.%), BCS / SS 409 / 1 (Cr: 0.94 wt.%), BCS / SS 410 / 1 (Cr: 1.34 wt.%). Experimental conditions were 350 Wappiied, 50Wreflected, 7 torr, Ar flow rate at 0.2 SLPM, GD pulse duration of 500 ps at 1 kHz, and 200 GD pulses integrated per acquisition. The coded aperture mask (50% T, aperture / slit size 5 DMD pixels) was measured using an Ag HCL at the Ag I 520.91 nm and the image cropped to final dimensions of 250 x 280 (Y and X ICCD pixels, respectively).

[0073] For reconstruction, datasets were normilized to ‘1’ by dividing it by the maximum value. To plot the calibration curve, the reconstruted datasets were un-normalized back to the original scale by multiplying by the original maximum value. For comparison between single-slit vs GOCAS, the spectra at a single spatial position were used. SeSCIcpu was the CS algorithm used for recovering all the quantitative figures of merit. Hyperparameters for SeSCIcpu were optimized for SRM NIST 1761 A and kept constant for all other samples since different parameter values can converge to a different solution and introduce error in calibation curve.

[0074] The optical signal intensity of each SRM was normalized to its measured Vdc during analysis for inclusion in the calibration. Calibration curves take into account sputtering rates of each SRM under the same experimental conditions but operated for a long enough time to produce easily measurable craters by optical profilometry (applied power WappUcd: 350 watts, pressure at 7 torr, Ar flow rate 0.2 SLPM, GD pulse duration of 500 ps at 1 kHz, in a burst of 2000 pulses, and a total 2000 bursts). The SRM full crater topography was measured using a chromatic confocal sensor (Chrocodile C sensor, Precitec, P / N - 5009277, depth dynamic range of 500 pm) integrated into an automated profilometry system (3D Profiler), and the data processed using TrueMAP 6 (TrueGage). The crater volume and SRM density were used to calculate the sputtering rates. Relative sputtering rates (RSR) were obtained by normalizing to the sputtering rate for the standard SS 407 / 1. because a standard for pure iron was not available. The LODs were determined as 3o / S, where c is the standard error of the intercept is divided by the slope of the calibration curve.

[0075] Example 1.6. Effects of coded aperture characteristics

[0076] The spatial encoding of the light collected from the source is a critical step in the GOCAS measurement, such that it is very important to study the effects of the coded aperture characteristics on the spectral reconstruction fidelity. The first study looks at the effect of CA element size, while maintaining the transmittance at 50%, and the measured CAs (insert FIG. 2B) show how the size of the element can change its appearance. For a relevant comparison, the width of the slit in the single-slit spectra used as a standard in the reconstruction fidelity comparison was adjusted to match the CA element size.

[0077] It should also be noted that the standard deviation of the plotted values in all results shown yield error bars smaller than the marker size (< 0.5 PSNR; < 0.005 Pearson’s correlation). The performance of four CS reconstruction algorithms was compared by individually optimizing the respective hyperparameters (supporting information). Only the results for the spectral reconstruction with the optimum parameters for each algorithm are plotted in FIGS.2A-2D. The results indicate a general and significant decrease in spectral reconstruction performance with an increase CA element size, which is more evident in the PSNR (FIG. 2A).

[0078] It is also worth noting that the number of CA elements decreased with the increase in element size, given that the CA width was kept constant. Thus, the larger number of elements that can be fit into the CA for smaller element sizes translate into more coded information, which may be responsible for the better reconstruction performance. It is also evident that the optimized SeSCIcpu outperformed the other reconstruction algorithms throughout the CA element size studies, with SeSCIcpu a close second. TwIST performed well at smaller CA element size but showed significantly decreased performance at larger CA element size.

[0079] The second study looks at the effect of CA transmittance on reconstruction fidelity. The measured CAs (FIG. 2D insert) show a clear change in their brightness going from 40% to 70% transmittance. Overall, the spectral reconstruction fidelity increases from 40% to 50% transmittance, where it peaks, and it decreases at 60% and again at 70% transmittance. SeSCIcpu showed the best performance and SeSCIcpu was a close second. TwIST showed the most significant effect of the CA mask transmittance on reconstruction fidelity with a range >9 dB in the PSNR.ADMM-TV SeSCICtjlPIL1SeSCICPUTwISTIterations: 70 Iterations: 30 Iterations: 75 Iterations: 50Eta: I Step size: 20 Lambda: 0.5 TV iterations: 30TV weight: 10 Sigma:5 Step size: 120 Tau: 2Lambda: 1.5 Lambda: 5Reconst, time: 5 min Reconst, time: 4 min Reconst, time: 7 min Reconst, time: 15 minTable 1. Optimized hyperspectral parameters and reconstruction time for each reconstruction algorithm for simple spectra GOCAS data set at optimum CA transmittance of 50% and optimum / smallest CA element size.

[0080] Table 1 summarizes the hyperparameter values used for the highest fidelity reconstruction of each algorithm, as well as the reconstruction time required. It is clear that SCSCIGPU not only gives the best fidelity but also the fastest reconstruction time. TwIST showed slightly lower performance compared to SCSCIGPU under optimum CA element size and transmittance, but it required significantly longer time for reconstruction (x3.75). ADMM-TV was the second fastest algorithm, but it consistently showed the worst reconstruction fidelity.

[0081] It is also crucial to study the effects of increasing complexity of the spectral features on the reconstruction fidelity. In this case, instead of using simple spectra with clean peaks, such as above with Cu I at 520.82 nm, the spectra were taken from sources where the wavelength of the lines of interest are adjacent to each other, such that dispersion of the CA resulted in partial overlap on the camera. This was achieved with HCL sources for iron (Fe I 516.74 nm and Fe I 517.15 nm) and chromium (520.45 nm, 520.60 nm, and 520.84 nm). The spectral reconstruction fidelity does decrease several dB compared to the simple spectra results, but it is still sufficient. In addition, the SeSCI algorithm still outperforms the others.

[0082] Given the correlation observed in the CA element size study, where smaller element sizes with higher number of elements per CA lead to improved spectral fidelity, the next step was to only change the number of CA elements while maintaining the optimum / smallest size. Thus, the width of the CA was varied from 35, 45, to 58 elements as can be observed in the measured CAs (FIG. 3 inserts). It is evident that increasing the CA width in terms of # elements improved the reconstruction fidelity significantly from 27.7 dB all the way up to 32.3 dB.

[0083] During the measurement, the spectral dimension is convoluted with the x-spatial dimension, i.e. the spectra from apertures / slits in the same row will overlap with each other. Increasing the CA width results in an increase in the number of open elements (slits / apertures) which will yield an improved light throughput and multiplexed measurements that are likely leading to improved fidelity. It is important to note that the absolute fidelity values are not directly comparable with the ones discussed above because the different studies were performed with different DMD models to enable a wider CA to be projected. However, the DMD pixel size is different, which may account for the differences.

[0084] Nonetheless, the effect of the CA width (# of elements) was successfully demonstrated. Additionally, the optimum number of iterations required by the reconstruction algorithm increased with larger CA (Table 2), which is likely due to the larger number of pixels with non-zero values in the data set matrices that leads to longer reconstruction time.CA I (35 elements) CA II (45 elements) CA III (58 elements)Iterations: 10 Iterations: 20 Iterations: 30Step size: 50 Step size: 10 Step size: 20Sigma: 5 Sigma: 2 Sigma: 5Lambda: 0.005 Lambda: 0.005 Lambda: 5Reconst, time: 1.5 min Reconst, time: 2.5 min Reconst, time: 4 minTable 2. Optimized hyperspectral parameters and reconstruction time for each CA width size and SeSCIGpureconstruction algorithm.

[0085] It is also important to understand the effect of detector noise on the spectral reconstruction fidelity. This was studied by adding the standard deviation of the ICCD dark noise at three different levels (xl, xlO, xlOO) onto the measured convoluted GOCAS image before reconstruction. It is evident from FIGS. 4A-4B that all reconstruction algorithms are very robust against this type of noise from xl to xlO, as demonstrated by very small decreases in the fidelity values (<1 dB in PSNR overall).

[0086] In the case of the xlOO noise level, a larger decrease in reconstruction fidelity of up to 2 dB to 2.6 dB was observed for TwIST, SeSCIcpu, and ADMM-TV. As in the results presented above, SeSCIcpu showed the best performance and robustness with respect to detector noise with only ~ 1 dB lower fidelity at the xlOO level. The notable robustness against detector noise is likely due to several factors, including the sparsifying / compressive nature of CS that results in denoising.

[0087] Additionally, in this case, the added noise spatial frequency is higher (single ICCD pixel) compared to the size of the CA element (>5 ICCD pixels), which enables disentangling the signal from the noise. Finally, the higher robustness against noise of the SeSCI algorithm is likely due to its unique feature of a Shearlet transform that is implemented in the frequency domain, such that it is preceded by a Fourier transform.ADMM-TV SeSCIrPTTSeSCICPUTwIST Iterations: 300 Iterations: 50 Iterations: 100 Iterations: 500 Eta: 1 Step size: 25 Lambda: 10 TV iterations: 4 TV weight: 5 Sigma:0.02 Step size: 45 Tau: 1 Lambda: 5 Lambda: 5Reconst, time: 8 min Reconst, time: 5 min Reconst, time: 8 min Reconst, time: 30 min Table 3. Optimized hyperspectral parameters and reconstruction time for each reconstruction algorithm for simple spectra GOCAS data set at the highest noise level (xlOO).

[0088] Table 3 shows that the highest noise level required an increased number of iterations for all reconstruction algorithms but significantly higher for TwIST, compared to experiments with no additional noise (Table 1). This led to longer reconstruction time that was only 25% more for SeSCIcpu, for 5 min total, but 100% for TwIST, for 30 min total.

[0089] Example 1.7. Quantitative figures of merit

[0090] SCSCIGPU showed the best overall spectral fidelity performance compared to other reconstraction algorithms, so it was chosen to determine the quantitative figures of merit for GOCAS and evaluate them with respect to traditional single-slit GDOES. The significantly increased light throughput feature of GOCAS may be most advantageous for samples, such as nanostructured materials and ultra-thin films, where very fast transient signals can only be captured with few acquisitions having very short exposure times.

[0091] Thus, these are the conditions used for determining the figures of merit. First, the spectra from standard reference materials featuring Cr I peaks were captured with a total camera exposure of 2 ms (BNF B7009; FIG. 5A) or 0.4 ms (BNF E3918; FIG. 5B). At the same intensity scale, it is difficult to observe the peaks in the GDOES single-slit spectra. The GDOES single-slit spectra must be multiplied xlO to allow visual comparison with the GOCAS. At first sight, it is evident that the signal-to-noise ratio is much higher for the GOCAS spectra, and this is confirmed by the calculated values which are significantly higher for GOCAS by xl8 (E3918) or x33 (B7009). It is important to consider that the Cr content in these standards is ~20 wt.%. The combination of experimental conditions here was intentionally used to collect spectra with poor S / N for single-slit GDOES to demonstrate the S / N enhancement with GOCAS under the same conditions (except for the introduction of the CA and CS reconstruction). As such, these results indicate that, even when ideal GDOES experimental conditions are used, atomic emission lines showing poor S / N (due to low emission efficiency, low sample matrix sputtering rate, low element concentration, etc.) from fast transient sputtered layers that could be significantly enhanced by GOCAS at the fastest acquisition time.

[0092] It is also instructive to consider another way to recover the encoded spectra, such as Hadamard Transform (HT), with the caveat that one could not reconstruct the full field of view, as opposed to GOCAS. but only recover the under-sampled hyperspectral data cube. i.e. with spectral images missing the blocked sections from the mask. In HT spectroscopy, the theoretical S / N improvement for a single slit = (Order of the Hadamard matrix / 2). Thus, if the same number of elements were utilized with HTS, a theoretical improvement of x5.4 in S / N would be expected, which is significantly lower than the one obtained by GOCAS. It is also important to consider that this HTS best case scenario is typically affected by optical system aberrations of the nominally completely open or completely closed CA elements and the complexities of taking them into account. In contrast, GOCAS can fully account for CA aberrations by the system using the experimentally measured CA and the capability of CS recovery to handle half-tone (between 0, completely closed, and 1, completely open) CA elements. In addition, the S / N improvement with GOCAS goes beyond the increased aperture partly due to the sparsifying nature of CS that results in denoising.

[0093] The GOCAS signal-to-noise ratio improvements vs single-slit GDOES are very encouraging, but the limits of detection must be determined to obtain a more definitive performance measure. In this case, calibration curves were constructed for Cr I lines using low alloy steel certified reference materials.

[0094] For GOCAS, the optimized SCSCIGPU hyperparameter values for the reconstruction of the spectra of the NIST 1761 A SRM were kept constant for the reconstruction of all other SRMs to minimize reconstruction fidelity variability. It is evident that the slopes for the GOCAS calibration curves are significantly steeper compared to the single-slit GDOES (FIGS. 5C-5E). In addition, the fitted line correlation coefficient values, R2, are also improved for GOCAS. The determined LODs for GOCAS (0.210 RSR*wt.%, Cr I 520.45 nm; 0.297 RSR*wt.%, Cr I 520.60 nm; 0.255 RSR*wt.%, Cr I 520.84 nm) were up to an order of magnitude better (xl0.4, Cr I 520.45 nm; x 6.5, Cr 1520.60 nm; x 7.9, Cr 1520.84 nm) compared to the single-slit GDOES (2.19 RSR*wt.%, Cr I 520.45 nm; 1.95 RSR*wt.%, Cr 1520.60 nm; 2.03 RSR*wt.%, Cr I 520.84 nm). The GOCAS LODs improvements are not as high as the S / N, which may be due to some spectral reconstruction fidelity variations between the standards that would contribute to the error of the linear fit. Nevertheless, an improvement of an order of magnitude in LODs demonstrates that GOCAS has the potential to be transformative for ultra-thin films and nanostructured materials analysis. While adsorbed atmospheric gases may cause matrix effects at the topmost surface in some samples and hinder depth profiling at nm scale, in situ plasma cleaning can be implemented to remove adsorbed contaminants and enable the analysis.

[0095] Furthermore, the GOCAS accuracy was assessed by removing a standard from the calibration curves (NIST 1761a, 0.222 +- 0.006 Cr wt.%) and treating it as an unknown sample. The GOCAS determined Cr content was 0.223 wt.% at 520.84 nm (relative error 0.5 %), 0.222 wt. % at 520.60 nm (relative error 0%), and 0.210 wt. % at 520.45 nm (relative error -5.4 %). Accuracy for major elements in GDOES can be 1 % - 2 % such that GOCAS accuracy here is very good considering that the relative standard deviation of the NIST 1761a certified value is 2.7 %, and that Cr is not a major component (>1 wt.%) but a minor component (0.1 wt.% - 1 wt.%) in the standard.

[0096] Finally, it is worth noting that compressed sensing recovery of coded aperture spectra has been demonstrated for a variety of spectral features and X windows. Thus, even though the GOCAS proof-of-concept is demonstrated here for a relatively small window, it is expected that it will be applicable for a significantly larger X window, such as that featured by some GDOES commercial instruments that measure spectra over hundreds of nm simultaneously. GOCAS can be implemented on an instrument with such capabilities to enable multi-matrix calibration approaches for analysis at the highest depth resolution.

[0097] Example 1.8. Conclusion

[0098] The concept of glow discharge optical emission coded aperture spectroscopy is presented for the first time. GOCAS enables significantly higher light throughput while achieving higher spectral resolution, as opposed to commercial GDOES instruments. In addition, instrumentation was designed and developed to successfully demonstrate the novel GOCAS technique proof-of-concept. Furthermore, a study of the coded aperture characteristics on the spectral reconstruction fidelity showed the best performance at 50% transmittance, as well as improvements with decreasing CA element size, and increasing CA width in terms of number of elements. Moreover, the performance of several different compressed sensing iterative reconstruction algorithms was studied and SCSCIGPU consistently showed significantly better spectral reconstruction fidelity, the fastest reconstraction time, and robustness toward detector noise. Finally, GOCAS quantitative performance is shown to be significantly better compared to single- slit GDOES at the shortest acquisition time, down to a fraction of a millisecond, by more than an order of magnitude in terms of S / N and up to an order of magnitude in LODs. Thus, GOCAS has significant potential to be transformative for analysis of nano structured materials and ultra-thin films.

[0099] Without further elaboration, it is believed that one skilled in the art can, using the description herein, utilize the present disclosure to its fullest extent. The embodiments described herein are to be construed as illustrative and not as constraining the remainder of the disclosure in any way whatsoever. While the embodiments have been shown and described, many variations and modifications thereof can be made by one skilled in the art without departing from the spirit and teachings of the invention. Accordingly, the scope of protection is not limited by the description set out above, but is only limited by the claims, including all equivalents of the subject matter of the claims. The disclosures of all patents, patent applications and publications cited herein are hereby incorporated herein by reference, to the extent that they provide procedural or other details consistent with and supplementary to those set forth herein.

Claims

WHAT IS CLAIMED IS:

1. A glow discharge optical emission spectroscopy (GDOES) apparatus comprising:a spectral filter mask comprising a plurality of slits, wherein each slit is operable to receive optical radiation emitted from a sample; anda processor operable to analyze the sample’s emitted optical radiation from the plurality of slits of the spectral filter mask.

2. The apparatus of claim 1, further comprising a light source operable to generate a glow discharge plasma for application to the sample.

3. The apparatus of claim 2, wherein the light source comprises a glow discharge (GD) lamp.

4. The apparatus of claim 1, further comprising a glow discharge chamber operable to hold the sample and receive light from a light source.

5. The apparatus of claim 1, wherein the spectral filter mask is operable to reflect the sample’s emitted optical radiation from each of the plurality of slits onto the processor.

6. The apparatus of claim 1, wherein the spectral filter mask is in the form of a digital micromirror device (DMD).

7. The apparatus of claim 1, wherein the spectral filter mask is in the form of a coded aperture.

8. The apparatus of claim 1, wherein the slits are in the form of an array, wherein each of the slits comprises a width ranging from about 10 pm to about 10 mm, and wherein each of the slits comprises a depth ranging from about 10 pm to about 10 mm.

9. The apparatus of claim 1, wherein the processor comprises an optical spectrometer.

10. The apparatus of claim 9, wherein the optical spectrometer comprises a camera.

11. The apparatus of claim 1, wherein the processor comprises:an optical spectrometer; andan algorithm in electronic communication with the optical spectrometer, wherein the algorithm is operable to analyze the sample’ s emitted optical radiation from the plurality of slits of the spectral filter mask to identify elemental compositions of the sample.

12. The apparatus of claim 11, wherein the algorithm comprises programming instructions for:(a) receiving the sample’s emitted optical radiation from the plurality of slits of the spectral filter mask;(b) analyzing the emitted optical radiation to identify elemental compositions of the sample; and(c) generating a report of the identified elemental compositions of the sample.

13. The apparatus of claim 11, wherein the algorithm comprises a compressed sensing algorithm operable to analyze a spectrum from each of the plurality of slits of the spectral filter mask.

14. A method of analyzing a sample, said method comprising:placing the sample on a glow discharge optical emission spectroscopy (GDOES) apparatus, wherein the apparatus comprises:a spectral filter mask comprising a plurality of slits, anda processor;applying a glow discharge plasma to the sample such that the sample emits optical radiation;receiving in each slit optical radiation emitted from the sample;utilizing the processor to analyze the sample’s emitted optical radiation from the plurality of slits to determine the elemental composition of the sample.

15. The method of claim 14, wherein the spectral filter mask reflects the sample’s emitted optical radiation from each of the plurality of slits onto the processor.

16. The method of claim 14, wherein the spectral filter mask is in the form of a digital micromirror device (DMD).

17. The method of claim 14, wherein the processor comprises:an optical spectrometer; andan algorithm in electronic communication with the optical spectrometer, wherein the algorithm analyzes the sample’s emitted optical radiation from the plurality of slits of the spectral filter mask to identify elemental compositions of the sample.

18. The method of claim 17, wherein the algorithm(a) receives the sample’s emitted optical radiation from the plurality of slits of the spectral filter mask;(b) analyzes the emitted optical radiation to identify elemental compositions of the sample; and(c) generates a report of the identified elemental compositions of the sample.

19. The method of claim 17, wherein the algorithm comprises a compressed sensing algorithm, wherein the algorithm is operable to analyze a spectrum from each of the plurality of slits of the spectral filter mask.

20. The method of claim 14, wherein the sample comprises a solid.

21. The method of claim 14, wherein the method is used for multi-elemental analysis of solids.

22. The method of claim 14, wherein the method is used for depth profiling of the sample.

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