System and method for surface profile estimation via optical coherence tomography

Abstract

An optical coherence tomography (OCT) system comprises an interferometer configured to split incident light into a reference beam and an inspection beam and to interfere the inspection beam reflected from a sample with the reference beam reflected from a reference mirror to generate an interference pattern. The OCT system also comprises a spectrometer configured to analyze spectral components of the interference pattern at non-uniformly sampled frequencies. The computer-readable memory of the OCT system is configured to store a measurement model having elements weighted with weights derived from the power spectral density (PSD) of the incident light for corresponding frequencies, connecting different depth values to different non-uniformly sampled frequencies. The OCT system further comprises a processor configured to obtain a profilometry measurement of the sample as a maximum likelihood estimate of the sample surface depth by back-projecting the measured intensity in the measurement model.

Description

[Technical Field]

[0001] This disclosure relates in general to imaging, and more specifically to optical coherence tomography (OCT) systems and methods for generating profilometry measurements of a sample. [Background technology]

[0002] Profilometry is a technique used to extract topographic data from a surface. This can be a single-point, line scan, or even a full three-dimensional scan. The purpose of profilometry is to obtain surface morphology, step height, and surface roughness. In many applications, electromagnetic sensing is used to obtain information about the surface or subsurface of a particular sample for profilometric measurements. One such technique is tomography. Tomography can be used in a variety of applications, such as radiology, biology, materials science, manufacturing, quality assurance, and quality control. Several types of tomography include, for example, optical coherence tomography (OCT), X-ray tomography, positron emission tomography, and optical projection tomography.

[0003] OCT is a technique used to perform high-resolution cross-sectional imaging. It is often applied to image biological tissue structures, such as the human eye, in real time, for example, at a microscopic scale. Light waves are reflected from an object or sample, and a computer generates a cross-sectional or three-dimensional volumetric rendering image of the sample by using information about how the light waves change in the reflection.

[0004] Optical Coherence Tomography (OCT) is an interferometer-based imaging technique that coherently mixes an optical signal from a target with a reference signal. OCT provides non-invasive, non-contact, label-free imaging of a sample with micron-scale resolution in three dimensions. Due to OCT's ability to achieve micron-scale resolution, it is used across a variety of technological fields, including factory automation processes that check the integrity of assembly or manufacturing operations, as well as in various medical specialties, including ophthalmology and cardiology.

[0005] OCT can be performed based on time-domain processing (time-domain OCT or TD-OCT) or Fourier-domain processing (Fourier-domain OCT or FD-OCT). In time-domain OCT (TD-OCT), the path length difference between the light returning from the sample and the reference light is transformed longitudinally in time to recover depth information within the sample. In frequency-domain or Fourier-domain OCT (FD-OCT), broadband interference between the reflected sample light and the reference light is acquired in the frequency domain, and depth information is recovered using the Fourier transform. [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] The sensitivity advantages of FD-OCT over TD-OCT are well established. However, FD-OCT is still plagued by measurement noise and may require extra computation and subsampling methods to improve the accuracy of profilometry estimations. See, for example, U.S. Patent 10502544. [Means for solving the problem]

[0007] The objective of some embodiments is to provide optical coherence tomography (OCT) systems and methods for generating profilometry measurements of a sample. In addition, or alternatively, the objective of some embodiments is to provide systems and methods for Fourier-domain OCT (FD-OCT) with an improved signal-to-noise ratio (SNR) of recovered depth information. In addition, or alternatively, the objective of some embodiments is to overcome the aforementioned drawbacks of the FD-OCT method.

[0008] OCT uses the interference of two light beams to measure the difference in optical path length. The beat frequency of the interfered light is much lower than the oscillation frequency of the light, allowing OCT to achieve fine depth resolution without high-bandwidth electronics. FD-OCT profilometry utilizes Fast Fourier Transform (FFT) based processing over the wavenumber values ​​of the interfered signal. Applying the Fourier Transform to an interfered signal that is uniformly sampled at wavenumber should result in sharp peaks in the depth domain. However, OCT systems typically sample the interfered light at a uniform wavelength λ, which means that the samples are non-uniformly spaced at wavenumber k = 2π / λ. The processor in an FD-OCT system can interpolate the data and resample it uniformly at wavenumber k so that the measurements can be processed using the Inverse Fast Fourier Transform (IFFT). However, the interpolation process also propagates noise to the non-sampled wavenumbers, which reduces robustness to noise, especially for higher frequency interference patterns corresponding to the deepest features of the sample.

[0009] Some embodiments are based on the understanding that depth can be recovered from a back projection of the measurement, instead of using an FFT to recover depth for a single reflector. Back projection reverses the mapping from the depth region to the measurement region through a model of the measurement system. Back projection is not suitable for recovering depth for multiple reflectors because it is not equivalent to reversing this mapping. Therefore, an FFT with an interpolated wavenumber is usually more advantageous than back projection due to the calculation of the reciprocal of the approximation. Thus, it is not surprising that, to the extent of available knowledge, back projection is not used for profilometric measurements. However, some embodiments are based on the understanding that, under certain conditions, back projection can be adapted to outperform the FFT.

[0010] Various embodiments adapt the back projection by modifying the structure of the measurement matrix and the reconstructed data. Specifically, in some embodiments, the back projection f=M *y generates a vector f from the measured value y using the measurement matrix M. For opaque surface measurements, the largest element of vector f can be obtained as an approximate maximum likelihood estimate for a single surface depth, avoiding interpolation of the back-projected input.

[0011] In addition, some embodiments are based on an understanding of the nature of profilometry measurements using an interferometer. The interferometer generates an interference pattern of beat signals, which is analyzed to measure the intensity of wavelengths uniformly sampled in the interference pattern. This uniform sampling of wavelengths is due to the nature of the physical properties of diffraction. However, there is a nonlinear relationship between wavenumber and wavelength. n = 2π / λ n There is a correlation between the intensity of uniformly sampled wavelengths and the non-uniformly sampled wavenumbers.

[0012] In contrast to FFT, which requires uniformly sampled wavenumbers, the measurement matrix can be directly defined for heterogeneously sampled wavenumbers corresponding to uniformly sampled wavelengths of the interference pattern. Furthermore, for the target depth range, it is possible to derive a measurement model in which different depth values ​​are connected to different heterogeneously sampled wavenumbers corresponding to uniformly sampled wavelengths. In this way, interpolation within the back projection can also be avoided.

[0013] Furthermore, in contrast to FFT, the measurement matrix in some embodiments is not only depth and wavenumber, but also different wavenumbers k n The power spectral density (PSD) S(k) is required for this. n This also includes the amplitude envelope multiplied by the measured values.

[0014] The PSD in the measurement matrix explains the weight each element of the data should receive in the backprojection. In this way, the PSD increases the robustness of the backprojection by becoming more strongly dependent on samples with higher envelope amplitudes.

[0015] Furthermore, some embodiments allow for a possible depth z m The measurement matrix M is explicitly defined for a set of (m=0,...,M-1). These possible depths can be selected with any coarse or fine resolution as desired, and over any range of depths involved. For example, OCT measurements are typically taken with respect to a reference depth z=0. The sample is kept entirely above or below the reference depth, otherwise ambiguity arises. Thus, it is possible to reconstruct depth values ​​that are positive only (or negative only).

[0016] Several exemplary embodiments may be implemented for process monitoring in manufacturing. For example, but not limited to, some exemplary embodiments may include manufacturing machines, electrical discharge machines (EDMs), wire EDMs, and other computer numerical control (CNC) machines.

[0017] To achieve the aforementioned objectives and advantages, several exemplary embodiments provide systems, methods, and programs for profilometry measurements of samples.

[0018] For example, some embodiments provide an OCT system for measuring the profilometry of a sample. The OCT system includes an interferometer configured to split incident light into a reference beam and an inspection beam, and to interfere the inspection beam reflected from the sample with the reference beam reflected from a reference mirror to generate an interference pattern. The OCT system also includes a spectrometer configured to analyze the spectral components of the interference pattern at non-uniformly sampled wavenumbers. The computer-readable memory of the OCT system is configured to store a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumbers, with different depth values ​​linked to different non-uniformly sampled wavenumbers. The OCT system further includes a processor configured to obtain the profilometry measurement of the sample as a maximum likelihood estimate of the sample surface depth by back-projecting the measured intensity in the measurement model.

[0019] Some exemplary embodiments also provide a method for obtaining profilometry measurements of a sample in an OCT system. This method includes an interferometer splitting incident light into a reference beam and an inspection beam, and interfering the inspection beam reflected from the sample with the reference beam reflected from a reference mirror to generate an interference pattern. This method further includes a spectrometer analyzing the spectral components of the interference pattern at heterogeneously sampled wavenumbers. The computer-readable memory of the OCT system connects different depth values ​​to different heterogeneously sampled wavenumbers and stores a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumbers. This method further includes obtaining the profilometry measurements of the sample as the maximum likelihood estimate of the sample's surface depth by back-projecting the measured intensities in the measurement model.

[0020] Some exemplary embodiments also provide a non-temporary computer-readable medium storing computer-executable instructions, which, when executed by a computer, cause the computer to perform a method for profilometry measurements of a sample in an OCT system. The method includes an interferometer splitting incident light into a reference beam and an inspection beam, and interfering the inspection beam reflected from the sample with the reference beam reflected from a reference mirror to generate an interference pattern. The method further includes a spectrometer analyzing the spectral components of the interference pattern at heterogeneously sampled wavenumbers. The computer-readable memory of the OCT system connects different depth values ​​to different heterogeneously sampled wavenumbers and stores a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumbers. The method further includes obtaining the profilometry measurements of the sample as the maximum likelihood estimate of the sample's surface depth by back-projecting the measured intensities in the measurement model.

[0021] According to some embodiments, depth values are uniformly sampled from the depth measurement range at the resolution of the OCT system. The depth values may be relative values with respect to a reference depth selected outside the depth measurement range.

[0022] As part of the method, each profilometry measurement may be estimated by performing a maximum likelihood estimator (MLE) The process of seeking to generate an argument of the maximum likelihood estimate of the non-zero elements in the corresponding reflectivity vector. Further, each argument of the reflectivity vector corresponds to one of the depth values in the measurement model. Further, the MLE may be an approximate MLE, and the approximate MLE The process of seeking includes back-projecting a data vector through a measurement matrix. The MLE may be the depth value corresponding to the element of the largest magnitude in the back-projection.

[0023] According to some exemplary embodiments, the MLE may be an exact MLE, and the exact MLE The process of seeking includes refining the approximate MLE by maximizing the maximum likelihood objective function using a gradient-free optimization method.

[0024] Embodiments of the present disclosure will be described below with reference to the following drawings. The drawings shown are not necessarily to scale; instead, emphasis is generally placed on explaining the principles of the embodiments of the present disclosure.

Brief Description of the Drawings

[0025] [Figure 1A] A method 100A for profilometry measurements of a sample in an optical coherence tomography (OCT) system according to some exemplary embodiments is shown. [Figure 1B] A schematic diagram of an OCT system for generating profilometry measurements of a sample from measurements non-uniformly sampled in frequency according to some exemplary embodiments is shown. [Figure 1C] A detailed schematic diagram of an OCT system for generating profilometry measurements of a sample according to some exemplary embodiments is shown. [Figure 2A] This figure shows the process of obtaining the maximum likelihood estimator (MLE) for the depth of a sample surface, according to several exemplary embodiments. [Figure 2B] This figure shows the process of obtaining the maximum likelihood estimator (MLE) for the depth of a sample surface via back projection, according to several exemplary embodiments. [Figure 2C] This figure shows one exemplary structure of a measurement matrix used to obtain the maximum likelihood estimator (MLE) for the depth of a sample surface, according to several exemplary embodiments. [Figure 2D] This figure shows the process of obtaining the maximum likelihood estimator (MLE) for the depth of a sample surface by refining the back projection estimate, according to several exemplary embodiments. [Figure 3] This figure shows exemplary scenarios illustrating the sampling of interference signals to samples that are non-uniformly spaced in wavenumber, according to several exemplary embodiments. [Figure 4] This figure shows an exemplary scenario illustrating how, by placing the sample on one side of the reference plane, it becomes unnecessary to calculate both positive and negative depths, according to several exemplary embodiments. [Figure 5] A schematic diagram of wavelength calibration using an additional optical spectral analyzer to determine the wavelength associated with each detector pixel of a detector array is shown, according to several exemplary embodiments. [Figure 6A] Several exemplary embodiments of wavenumber calibration methods are shown. [Figure 6B] This figure shows the LED source spectrum as the spectral bandwidth of the calibration measurement according to several exemplary embodiments. [Figure 6C] This figure shows a reference mirror spectrum as the spectral bandwidth of a reference measurement, according to several exemplary embodiments. [Figure 6D] Figure 6B shows interpolation and resampling of the LED source spectrum for the wavelength calibration method by spectral alignment shown in Figure 6A, according to several exemplary embodiments. [Figure 6E]The cross-correlation between the LED spectrum and the reference mirror spectrum is shown for the wavelength calibration method by spectral alignment in several exemplary embodiments, as shown in Figure 6A. [Figure 7] This section provides a schematic comparison of experimental results obtained by applying maximum likelihood estimators to simulated data of OCT surface measurements using several exemplary embodiments. [Figure 8] This document presents a performance comparison between several surface depth estimation methods using several exemplary embodiments. [Figure 9] A block diagram of a system for implementing OCT in several exemplary embodiments is shown. [Modes for carrying out the invention]

[0026] While the drawings identified above illustrate embodiments of the present disclosure, other embodiments are contemplated, as discussed. The present disclosure presents exemplary embodiments as representative, not limiting, examples. Those skilled in the art can devise numerous other modifications and embodiments that fall within the scope and spirit of the principles of the embodiments of the present disclosure. [Description of Embodiments]

[0027] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the following description of exemplary embodiments provides a practicable description for realizing one or more exemplary embodiments. The intent is to describe various modifications that may be made to the function and configuration of the elements without departing from the spirit and scope of the subject matter disclosed as described in the claims.

[0028] The following description provides specific details for a complete understanding of the embodiments. However, those skilled in the art will understand that embodiments may be carried out without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in the form of block diagrams so as not to obscure the embodiments with unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, similar reference numbers and names in different drawings refer to similar elements.

[0029] Furthermore, individual embodiments may be described as processes shown as flowcharts, flow diagrams, data flow diagrams, structural diagrams, or block diagrams. While flowcharts may describe operations as sequential processes, many operations can be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may terminate when its operations are complete, but it may have additional steps that are not discussed or included in the diagrams. Moreover, not all operations in any particular process described may occur in all embodiments. A process may correspond to a method, function, procedure, subroutine, subprogram, etc. When a process corresponds to a function, the termination of the function may correspond to a return to the calling function or the main function.

[0030] Furthermore, embodiments of the disclosed subject matter may be implemented at least partially manually or automatically. Manual or automatic implementations may be performed, or at least assisted, by the use of a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. If implemented in software, firmware, middleware, or microcode, program code or code segments for performing the required tasks may be stored in a machine-readable medium. The required tasks may be performed by a processor.

[0031] To measure the surface profile of a material surface, quantified measurements of the material surface are required. This can be done by profilometry, in which a mechanical (contact) or optical (non-contact) probe traverses the surface. The probe follows the contour at each point on the surface, the probe height at each point is recorded, and the resulting 1D scan or 2D map is analyzed. To quantify roughness, parameters such as the arithmetic mean (Ra) of the absolute values ​​of all points in the profile and the mean square (Rq) of the total height around the mean are often used. The profilometer generates an image of the surface height. The size of the measured area and the size of the probe set upper and lower limits on the size of the features that can be characterized. The properties of the probe limit the range of surfaces that can be investigated by these techniques. In this regard, optical techniques are more suitable for relatively soft materials.

[0032] Optical profilometry is a more recent, modern technique that has been developed to improve accuracy. Simply put, it involves scanning the sample surface using a light source and focusing the diffracted light beam onto a mirror. The resulting image is the displacement of the light beam on the mirror. Theoretically, this technique can evaluate roughness as low as the nanometer scale.

[0033] Optical profilometry is a rapid, non-destructive, and non-contact surface measurement technique. An optical profiler is a type of microscope where light from a lamp is split into two paths by a beam splitter. One path directs the light to the surface under inspection, and the other directs the light to a reference mirror. The reflections from the two surfaces are recombined and projected onto an array detector. Interference can occur if the path difference between the recombined beams is on the order of a few wavelengths or less. This interference contains information about the surface contour of the surface under inspection. Vertical resolution can be on the order of a few angstroms, while lateral resolution depends on the purpose and is typically in the range of a few microns.

[0034] In many applications, electromagnetic sensing is used for profilometric measurements to obtain information about the surface or subsurface of a particular sample. One such technique is tomography. Several types of tomography include, for example, optical coherence tomography (OCT), X-ray tomography, positron emission tomography, and optical projection tomography. OCT is a technique used to perform high-resolution cross-sectional imaging. It is often applied to image biological tissue structures, such as the human eye, in real time, for example, at a microscopic scale. Light waves are reflected from the object or sample, and a computer generates a cross-sectional or three-dimensional volumetric rendering image of the sample by using information about how the light waves change in the reflection.

[0035] OCT uses the interference of two light beams to measure the difference in optical path length. The beat frequency of the interfered light is much lower than the oscillation frequency of the light, which reduces the need for high-bandwidth electronics. FD-OCT profilometry utilizes Fast Fourier Transform (FFT) based processing over the wavenumber values ​​of the interfered signal. Applying the Fourier Transform to an interfered signal that is uniformly sampled at wavenumber should yield sharp peaks in the depth domain. However, OCT systems typically sample the interfered light at a uniform wavelength λ, which means that the samples are non-uniformly spaced at wavenumber k = 2π / λ. The processor in an FD-OCT system can interpolate the data and resample it uniformly at wavenumber k so that the measurements can be processed using the Inverse Fast Fourier Transform (IFFT). However, the interpolation process also propagates noise to the non-sampled wavenumber, which reduces robustness to noise, especially for higher frequency interference patterns corresponding to the deepest features of the sample.

[0036] Figure 1A shows Method 100A for profilometry measurement of a sample in an OCT system according to several exemplary embodiments. Method 100A may be performed by some or all components of an OCT system, which will be described in detail later with reference to Figure 1B. Profilometry measurement method 100A includes step 3, which splits the incident light beam into a reference beam and an inspection beam. This can be performed by the interferometer 104 of the OCT system. According to some embodiments, a beam splitter may be used in this regard. In step 5, Method 100A includes interfering the inspection beam reflected from the sample with the reference beam reflected from a reference mirror to generate an interference pattern.

[0037] In step 7, the method includes analyzing the spectral components of the interference pattern at non-uniformly sampled wavenumbers. In step 9, the OCT system's processor 110 uses the computer-readable memory 112 to obtain the profilometry measurement of the sample as the maximum likelihood estimate of the sample surface depth by back-projecting the measured intensity in the measurement model. The OCT system's computer-readable memory 112 connects different depth values ​​to different non-uniformly sampled wavenumbers and stores a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumbers.

[0038] According to some embodiments, depth values ​​are sampled uniformly from the depth measurement range at the resolution of the OCT system. In some exemplary embodiments, the depth values ​​are relative to a reference depth selected outside the depth measurement range. Profilometry measurements thus obtained by the processor 110 can be output via the interface 120 of the OCT system (11).

[0039] One or more components, such as the interferometer 104, the spectrometer 106, the interface 120, and / or the memory 112, may be communicatively coupled to the processor 110. The processor 110 may be additionally coupled to one or more additional processing circuits to perform additional processing. The processor 110 can perform one or more operations, such as communication operations, read / write operations, and / or control operations, of the one or more components described above. The profilometry measurement method includes several modules, which are described in detail below. Firstly, in order to understand the components and elements used to realize the OCT system, an overview of the OCT system is provided with reference to Figures 1B and 1C.

[0040] Figure 1B shows a schematic diagram of an OCT system 100B that generates depth estimates 116 of a sample 118 from measurements 108 made at non-uniformly sampled wavenumbers 114. The OCT system 100B comprises a light source 102 (also called an illumination source), an interferometer 104, a spectrometer 106, a processor 110, and memory 112. In some exemplary embodiments, the sample 118 may be opaque or may have a single visible surface.

[0041] The light source 102 may comprise any suitable illumination source that supplies a light beam or electromagnetic beam for investigating the sample. The choice of illumination source may depend on the sample under investigation and / or the intended use of the OCT system. For example, but not limited to, the light source 102 may comprise one or more of the following: a tunable laser, an LED array, an incandescent light source, a rare gas lamp, an X-ray generator, a photon emitter, a positron emitter, and so on. According to some exemplary embodiments, the light source 102 comprises one or a combination of a laser, a superluminescent diode (SLD), or a light-emitting diode (LED).

[0042] In some exemplary embodiments, the light source 102 may be configured to utilize a planar shape, a fan beam shape, point illumination, or any combination thereof. Point illumination may be provided by any beam steering mirror-like device such as electromechanical, optoelectronic, acousto-optics, all optical systems, liquid crystal mirrors, and any other such devices.

[0043] The beam originating from the light source 102 may include coaxial, orthogonally polarized and / or light having different optical frequencies. The beam is split by a beam splitter in the interferometer 104. In some exemplary embodiments, the interferometer 104 may be a Michelson interferometer. In some exemplary embodiments, the interferometer 104 may be a Linnik interferometer. According to some embodiments, the beam splitter may be a partially reflective mirror. In some exemplary embodiments, the beam splitter may be an unpolarized beam splitter. The beam splitter can split the beam into reference illumination transmitted to a reference mirror and sample illumination transmitted to the sample 118.

[0044] According to some embodiments, the beam splitter may optionally comprise a series of beam splitters and / or polarizers. Sample illumination is incident on the sample 118, and all or part of the sample illumination may be reflected from the sample toward the beam splitter. The reflected signal from the sample 118 may be split by the beam splitter, and at least a portion thereof is combined with the reflected reference illumination and directed toward the detector array of the spectrometer 106 for further analysis and detection. The detector array of the spectrometer 106 may comprise a suitable imaging device such as a charge-coupled camera. The detector array can provide one or more detection signals corresponding to the recombination of the reflected signal and the reference signal.

[0045] The sample illumination may include an electromagnetic two-dimensional (2D) field directed by the interferometer 104 to form an axial scan of the sample 118 such that the measured intensity of the interference pattern includes measurements corresponding to a sequence of points on the line of the sample 118. In some exemplary embodiments, the OCT system 100B may also include one or more actuators for directing the incident light to another line parallel to the line of the previous scan.

[0046] The processor 110 can extract a sequence of intensities corresponding to a sequence of points on a line of the sample 118. In addition, the processor 110 can process the intensities of different points simultaneously to generate a profilometry measurement for the sequence of points. In some exemplary embodiments, the OCT system 100B may include one or more processing circuits for generating profilometry measurements for at least some points in the sequence of points in parallel, or additionally coupled thereto. One or more processing circuits may include suitable processing means such as a processor and memory.

[0047] According to some exemplary embodiments, the OCT system 100B may further include a line field generator comprising an expanded light source with an angular size greater than the lateral resolution over the profilometry measurement; a lens positioned on the path of the light emitted by the expanded light source to focus the light into an expanded line field light with a width greater than the lateral resolution; and a filter positioned at the focal plane of the lens to spatially filter the incident light into a line field with a width equal to the lateral resolution.

[0048]

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[0049]

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[0050]

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[0051] The preprocessing and depth estimation steps may be performed by the processor 110 of the computer system 150. The DC component is removed from the measured value 108. In some exemplary embodiments, the DC component is removed by subtracting the scaled PSD from the raw measured value, as follows:

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[0052] In some exemplary embodiments, the DC component is removed by applying a high-pass filter to the raw measurements. The resulting interference data vector y has the following values ​​for element n:

number

[0053] As described above, the spectrometer 106 includes a diffraction grating 140 and a detector array 142. The detector array 142 may have detection elements arranged at different diffraction angles to measure the intensity of different beams corresponding to the intensity of wavelengths uniformly sampled in the interference pattern. The detection elements of the detector array 142 are calibrated to map each index of the detection elements in the detector array to the corresponding wavelength.

[0054] Figure 2A shows the process 200 for obtaining the maximum likelihood estimate (MLE) 214 for the depth of the sample surface 118, given the data vector 202, wavenumber calibration 204, power spectral density calibration 206, and a set of candidate depths 208. Assuming the noise is Gaussian noise, the likelihood of observing the data y is as follows:

number

[0055]

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[0056] Figure 2B shows a detailed process leading to the rough estimation step 210 in Figure 2A, according to several exemplary embodiments. For the rough step, in some embodiments, the slowly changing PSD is MLE

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[0057] The advantage of this approximation is that it can be efficiently evaluated via matrix-vector multiplication over a discrete set of candidate depths.

[0058]

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[0059]

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[0060]

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[0061] The accurate depth MLE minimizes the negative log-likelihood and maximizes the value of z that maximizes F(z), i.e.,

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[0062]

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[0063] According to some embodiments, the processor 110 in Figures 1B and 1C calculates the maximum likelihood estimator (MLE). The process of seeking Each profilometry measurement may be estimated by performing the following to generate arguments for the maximum likelihood estimate of the non-zero elements in the corresponding reflectance vector. Each argument in the reflectance vector corresponds to one of the depth values ​​in the measurement model. The MLE may be an approximate MLE or an exact MLE. In some exemplary embodiments where the MLE is an approximate MLE, The process of seeking This involves backprojecting the data vector through the measurement matrix, where MLE is the depth value corresponding to the largest element in the backprojection. In some exemplary embodiments, the MLE is the exact MLE. The process of seeking This involves refining the approximate MLE by maximizing the maximum likelihood objective function using a gradient-free optimization method such as Brent's minimization method or golden ratio search.

[0064] A common technique for OCT-based surface estimation is to compute the Fourier transform of the data and find the peaks. However, the Fast Fourier Transform (FFT) algorithm cannot be directly applied to the data vector y because the FFT requires that the samples of y be uniformly spaced at wavenumber. In spectral-domain OCT (SDOCT) systems, dispersive elements such as the diffraction grating 140 cause an almost linear change in angle as a function of wavelength. As a result, referring to Figure 3, the detector array 142 uniformly samples the interference signal at wavelength 300, resulting in a non-uniform sample at wavenumber 304.

[0065] In sweep-source OCT (SSOCT) systems, existing methods for achieving uniform wavenumber samples require additional complex hardware. These involve determining a nonlinear sweep of the drive current that would produce time-uniform time samples, or using an arbitrary drive current and additional criteria (e.g., a k-clock based on an etalon or Michelson interferometer) to determine when to sample non-uniformly in relation to uniform wavenumber samples. Instead of using these complex methods, uniform wavenumber spacing is typically achieved through software post-processing. Measurements are performed at non-uniform wavenumber samples, and the signals are interpolated and resampled so that the sample spacing is uniform at wavenumber 302 (i.e., uniform k-spacing), as shown in Figure 3.

[0066] A second approach for OCT-based surface estimation attempts to invert the measurement y using M and sparse recovery methods, applying the assumption that there are few surfaces. However, sparse solvers are too common in typical scenarios, as they assume that a single surface may exist, and therefore these solvers are much slower than FFT methods.

[0067] The ML method has the following advantages compared to the FFT method. Firstly, the ML method avoids interpolation: the measurement matrix M is determined by the measured wavenumber k, regardless of the sample distribution. nIt is explicitly defined in. On the other hand, in the fast Fourier transform (FFT), it is necessary to uniformly sample the measured values at the frequencies. FIG. 3 shows how a sample that is uniform at a wavelength of 300 reaches a sample that is non-uniform at a frequency of 304. The measured values taken at the non-uniform frequency 310 must be interpolated and resampled at a uniform frequency 312 before the FFT can be applied, and interpolation is undesirable because it also interpolates noise.

[0068] Second, the ML method identifies the useful measurement range: The measurement matrix M is explicitly defined for a set of possible depths z from m = 0,..., M - 1 m These z m can be selected at that resolution and over that range of depths, regardless of what coarse or fine resolution is desired. For example, OCT measurements are typically measured with respect to a reference depth z = 0. According to some exemplary embodiments, as shown in FIG. 4, the sample surface 404 is held entirely on one side of the reference plane 400 so that there is no ambiguity. That is, no calculations are required for negative depths 402. Therefore, it is easy to reconstruct only positive depth values. On the other hand, the FFT automatically calculates depth profiles for both positive and negative depths, which adds unnecessary calculations. Furthermore, the FFT resolution is inversely proportional to the length of the data vector. For a finer depth resolution, the measured values are usually zero-padded to increase its length, which also increases the calculation time.

[0069] Third, the ML method includes all available information: The measurement matrix includes not only depth and frequency, but also the power spectral density (PSD) S(k n ). This is equivalent to the amplitude envelope that multiplies the measured values. Including the PSD in M appropriately accounts for the weights that each element of the data should receive in backprojection. The FFT does not include the PSD. As a result, the depth region is convolved with the Fourier transform of the PSD, the peaks spread, and it becomes more difficult to identify the true peaks.

[0070] Compared to sparse recovery methods, ML estimation has the additional advantage that ML methods have fast implementation: back projection multiplies the data by the trivial adjoint measurement matrix M*, which is computed (transpose and conjugate). More general sparse reconstruction methods require regularized least squares solutions, which are iterative and much slower. Modified SS-OCT system

[0071] In a certain SS-OCT configuration, the illumination source sweeps one wavelength at a time. Since the wavelengths are temporally separated, the spectrometer is a single-pixel detector that measures the intensity of the coupled light over time samples n=0,...,N-1 that cover the wavelength sweep of the light source. Some implementations use a balanced detector to remove the DC component of the measurement in hardware. Calibration Procedure

[0072] The measurement taken by the detector array 142 is I D [n] can be given as such, but the data required for estimation may require the conversion of measurements to the form given by Equation 4(a). The detector measurements have a linear index n, but k is needed to accurately recover the absolute depth. nThe actual value of is needed. Figure 5 shows a schematic diagram of wavelength calibration for determining the wavelength associated with each detector pixel of the detector array 142 according to several exemplary embodiments. The illumination source 102, interferometer 104, spectrometer 106, and computer system 150 may be the same as those described with reference to Figure 1C and may operate as described with reference to Figure 1C. As shown in Figure 5, in some exemplary embodiments, a “reference only” measurement 504 is performed in the detector array 142 by blocking the sample arm 506. For example, the sample may be masked by a non-reflective surface to block the sample arm. In this case, the intensity in the detector 142 is attributable only to the reference arm reflected from the reference mirror 132, and therefore it includes the power spectral density but does not include any interference terms. In some embodiments, the spectrometer 106 has a diffraction grating 140 that causes linear dispersion as a function of wavelength. In such a scenario, the only light reaching the detector array 142 is from the reference arm. In that case, the intensity in the detector is as follows:

number

[0073] According to some exemplary embodiments, the OCT system 100B may further include a PSD calibrator for blocking the sample arm of the interferometer 104, where the measured values ​​include only light from a reference beam propagating within the reference arm of the interferometer 104, and the measured intensity of the interference pattern is a function of the PSD of the incident light to the corresponding wavenumber scaled by the responsiveness of the spectrometer 106 and the reflectance of the reference arm. During the execution of the PSD calibrator, the processor 110 is configured to calibrate the PSD of the incident light so that the wavenumber corresponding to each pixel of the spectrometer 106 is estimated.

[0074] The reference measurement has index n and associated wavevalue k nThis is unknown. These associated wave values ​​are necessary to accurately recover the absolute depth. The method for determining the associated wave values ​​is based on the wavelength calibration procedure described below.

[0075] The wavenumber calibration procedure, shown in Figures 6A to 6E, involves aligning two PSD measurements, one performed with a standard inspection device and the other with the OCT system 50. The light source spectrum is expressed as a function of wavelength, with respect to illumination intensity I GT (λ) is measured using an optical spectrum analyzer (OSA) 500. In that case, I GT (λ) is used to find a fit between measurements that allows the pixel index to be directly mapped to the wavelength, using the reference measurement I. C It is rescaled and aligned for [n].

[0076]

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[0077] Figure 6A shows wavenumber calibration methods according to several exemplary embodiments. Figure 6A is described in relation to Figure 5. The optical spectral analyzer 500 in Figure 5 provides calibration measurement values ​​502, and the detector array 142 provides reference measurement values ​​504 in the manner described above.

number

[0078] Referring back to Figure 6A, the calibration measurement is interpolated and resampled based on the spectral bandwidth of the reference measurement (606). In particular, as shown in Figure 6D, the LED source spectrum 650A has a uniform wavelength sample interval.

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[0079] The resampled calibration measurement 650C and the reference mirror spectrum (i.e., reference measurement 650B) are then cross-correlated to find a shift that maximizes the overlap between spectra 650C and 650B (608). The cross-correlation between the LED spectrum and the reference mirror spectrum 6555 is shown in Figure 6E. Wavelength calibration is finally achieved by aligning the two spectra 650C and 650B (610) to generate a direct mapping 657 between the wavelength from the calibration wavelength and the reference measurement index, which is used to assign the detector index along with its true wavelength (612).

[0080] Figure 7 shows a schematic comparison of experimental results applying the maximum likelihood estimator to simulated data of OCT surface measurements. Note that the comparison shown in Figure 7 is non-restrictive and for illustrative purposes only, and it is intended that experimental values ​​for various parameters may be set to different sets of values. The illumination source may be set to have a Gaussian spectrum with a center wavelength of approximately 550 nm and an FWHM bandwidth of 100 nm. The sample shown in 700 is a one-dimensional linear lamp with a depth from approximately 10–23 μm. The reflectance at each pixel may be set to a constant value of 0.05, and a phase shift is randomly and uniformly added over [0, 2π). Measurement 702 is performed at wavelength 500, and the reconstruction is calculated for a depth resolution of 25 nm and a maximum depth of 25 μm. Additive white Gaussian noise is added so that the measurement has a signal-to-noise ratio (SNR) of -10 dB.

[0081] For 704, the conventional method (IFFT) is applied, which uses linear interpolation of the measurement 702 to obtain a uniform wavenumber sample and inverts it via the FFT algorithm. The error between the FFT estimate 704 and the ground truth 700 is 712, which indicates a significant error in surface depth estimation. For 706, another conventional method (IDFT) is applied, which uses linear interpolation of the measurement 702 to obtain a uniform wavenumber sample, but the inversion is performed instead by explicitly specifying a partial inverse discrete Fourier transform matrix for a small range of positive depth values ​​only. The error between the FFT estimate 706 and the ground truth 700 is 714, which is the same as 712, indicating a significant error in surface depth estimation.

[0082] At 708, a coarse step (back projection) of the proposed maximum likelihood estimator (ML grid: depth MLE on a discrete grid) is applied directly to the measurement 702 without interpolation. The surface estimation error between the coarse ML estimate 708 and the ground truth 700 is 716, which is significantly smaller than that of 712 and 714. At 710, a step of fine ML estimation (ML-iter: depth MLE with iterative refinement) is applied directly to the measurement 702, using the result from the coarse step 708 as initialization. The error between the fine ML estimate 710 and the ground truth 700 is 718, which is significantly smaller than that of 712. Thus, exemplary embodiments based on the ML fine estimation method offer several advantages over conventional available solutions.

[0083] Figure 8 shows a performance comparison between surface depth estimation methods. Note that the comparison shown in Figure 7 is non-restrictive and for illustrative purposes only; it is intended that experimental values ​​for various parameters may be set to different sets of values. In 800, the root mean square error (RMSE) of the depth estimation is plotted against the SNR averaged over 10 trials. The RMSE is compared to the square root of the Cramer-Rao lower bound (CRLB), which gives a lower bound to the range accuracy for the unbiased estimator. The expected RMSE limits for the discrete estimators are also plotted. The backprojection, FFT, and DFT methods use a grid spacing δ. z Since we are limited to discrete grids having , the root mean square error (RMSE), assuming a uniformly distributed depth,

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[0084] ML coarse estimators (back projection) are faster than inverse DFT matrices because they avoid the wavenumber interpolation step. Both ML coarse estimators and inverse DFT methods using explicitly defined matrices are faster than inverse FFT algorithms, which perform unnecessary calculations for negative and out-of-range depth values. ML fine estimators require exactly twice the execution time of conventional FFT-based methods.

[0085] Figure 9 shows a block diagram of a system for realizing OCT according to an embodiment of the present disclosure. The computer 911 includes a processor 940, computer-readable memory 912, storage 958, and a user interface 949 with a display 952 and a keyboard 951, which are connected via a bus 956. For example, the user interface 949, which communicates with the processor 940 and the computer-readable memory 912, receives input from the user from the surface of the user interface 957 and the keyboard 953, and acquires image data to store in the computer-readable memory 912.

[0086] The computer 911 may include a power supply 954 depending on the application, and the power supply 954 may optionally be located outside the computer 911. A user input interface 957 adapted to connect to a display device 948 can be linked via bus 956, and the display device 948 may include, among other things, a computer monitor, camera, television, projector, or mobile device. A network interface controller (NIC) 934 adapted to connect to a network 936 via bus 956 can, among other things, render image data or other data onto a third-party display device, third-party imaging device, and / or third-party printing device outside the computer 911.

[0087] Referring further to Figure 9, in particular, image data or other data may be transmitted via a communication channel of network 936 and / or stored in a storage system 958 for storage and / or further processing. Furthermore, time-series data or other data may be received wirelessly or via wire from receiver 946 (or external receiver 938) or transmitted wirelessly or via wire from transmitter 947 (or external transmitter 939), both of which are connected via bus 956. Computer 911 may be connected via input interface 908 to external sensing devices 944 and external input / output devices 941. For example, external sensing device 904 may include sensors that collect data before, during, and after collected time-series data of a machine. Computer 911 may be connected to another external computer 942. Output interface 909 may be used to output data processed by processor 940. It should be noted that the user interface 949, which communicates with the processor 940 and the non-temporary computer-readable storage medium 912, acquires area data and stores it in the non-temporary computer-readable storage medium 912 when it receives input from the user from the surface of the user interface 949.

[0088] The above description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments provides a practicable description for carrying out one or more exemplary embodiments for those skilled in the art. Various modifications that may be made in the function and arrangement of the elements are contemplated without departing from the spirit and scope of the subject matter disclosed as described in the claims.

[0089] The following description provides specific details for a complete understanding of the embodiments. However, those skilled in the art will understand that embodiments may be carried out without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in the form of block diagrams so as not to obscure the embodiments with unnecessary details. In other cases, well-known processes, structures, and techniques may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, similar reference numbers and names in various drawings indicate similar elements. Also, individual embodiments may be described as processes shown as flowcharts, flow diagrams, data flow diagrams, structural diagrams, or block diagrams. While flowcharts may describe operations as sequential processes, many operations may be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may terminate when its operations are complete, but it may have additional steps that are not discussed or included in the diagrams. Furthermore, not all operations in any particular process described may occur in all embodiments. A process may correspond to a method, function, procedure, subroutine, subprogram, etc. When a process corresponds to a function, the termination of that function can correspond to a return to the calling function or the main function.

[0090] Furthermore, embodiments of the disclosed subject matter may be implemented at least partially manually or automatically. Manual or automatic implementations may be performed, or at least assisted, through the use of a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. When implemented in software, firmware, middleware, or microcode, program code or code segments for performing the required tasks may be stored in a machine-readable medium. The required tasks can be performed by a processor. Various methods or processes outlined herein may be coded as software executable on one or more processors using any one of various operating systems or platforms. In addition, such software may be written using any of several preferred programming languages ​​and / or programming or scripting tools, and may be compiled as executable machine language code or intermediate code that runs on a framework or virtual machine. Typically, the functionality of program modules may be combined or distributed as desired in various embodiments.

[0091] Embodiments of this disclosure may be embodied as the examples provided. The actions performed as part of the method may be ordered in any preferred manner. Accordingly, embodiments may be constructed in which the actions are performed in a different order than the examples, including performing several actions shown as sequential actions in the exemplary embodiments simultaneously. Furthermore, the use of ordinal terms such as “first,” “second,” etc., to modify elements of a claim in a claim does not in itself imply that the priority, precedence, or order of one element of a claim exceeds that of another element of a claim, or the chronological order in which the actions of the method are performed, but is simply used as a label to distinguish one element of a claim having a certain name from another element having the same name (but for which ordinal terms are used). While this disclosure has been described with reference to certain preferred embodiments, it should be understood that various other adaptations and modifications may be made within the spirit and scope of this disclosure. Accordingly, the aspects of the claims encompass all such variations and modifications that fall within the true spirit and scope of this disclosure.

Claims

1. An optical coherence tomography (OCT) system for profilometry measurements of a sample, An interferometer that splits incident light into a reference beam and an inspection beam, and generates an interference pattern by interfering the inspection beam reflected from the sample with the reference beam reflected from a reference mirror, A spectrometer configured to analyze the spectral components of the interference pattern at non-uniformly sampled wavenumbers, A computer-readable memory configured to store a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumber, with different depth values ​​connected to different non-uniformly sampled wavenumbers, An OCT system comprising a processor configured to obtain the profilometry measurement value of the sample as the maximum likelihood estimate of the surface depth of the sample by back-projecting the intensity measured in the measurement model.

2. The OCT system according to claim 1, wherein the depth value is sampled uniformly from the depth measurement range with the resolution of the OCT system, and the depth value is a relative value to a reference depth selected outside the depth measurement range.

3. The OCT system according to claim 1, wherein the processor is configured to estimate each profilometry measurement by performing a process to obtain a maximum likelihood estimator (MLE) and generating arguments for the maximum likelihood estimator of non-zero elements in the corresponding reflectance vector, each argument of the reflectance vector corresponding to one of the depth values ​​in the measurement model.

4. The OCT system according to claim 3, wherein the MLE is an approximate MLE, and the process of determining the approximate MLE includes backprojecting the data vector through a measurement matrix, and the MLE is a depth value corresponding to the largest element in the backprojection.

5. The OCT system according to claim 3, wherein the MLE is an accurate MLE, and the process of obtaining the accurate MLE includes refining the approximate MLE by maximizing the maximum likelihood objective function using a gradient-free optimization method.

6. The aforementioned spectrometer, A diffraction grating configured to diffract beams of different wavelengths that form the aforementioned interference pattern to different diffraction angles, The OCT system according to claim 1, further comprising a detector array having detection elements arranged at different diffraction angles for measuring the intensity of different beams corresponding to the intensity of uniformly sampled wavelengths in the interference pattern.

7. The OCT system according to claim 6, wherein the detection elements of the detector array are calibrated to map each index of the detection elements in the detector array to a corresponding wavelength.

8. The incident light includes an electromagnetic two-dimensional (2D) field directed by the interferometer to form an axial scan of the sample such that the measured intensity of the interference pattern includes measurements corresponding to a series of points along the line of the sample, and the processor further, It is configured to extract a sequence of intensity corresponding to the sequence of points, The OCT system according to claim 1, configured to process the intensity of different points simultaneously to generate a profilometric measurement of the sequence of points.

9. The OCT system according to claim 8, further comprising the processor, and a plurality of processing circuits for generating the profilometry measurements in parallel for at least some points in the sequence of points.

10. The OCT system according to claim 8, further comprising an actuator for directing the incident light to another line parallel to the line of the previous scan.

11. The OCT system according to claim 1, further comprising an illumination source for generating the incident light, wherein the illumination source includes one or a combination of a laser, a superluminescent diode (SLD), or a light-emitting diode (LED).

12. The OCT system according to claim 1, further comprising: an expanded light source with an angular size greater than the lateral resolution over the profilometry measurement; a lens positioned on the path of light emitted by the expanded light source for focusing the light into an expanded line field light having a width greater than the lateral resolution; and a line field generator positioned at the focal plane of the lens for spatially filtering the expanded line field light into the incident light with a line field having a width equal to the lateral resolution.

13. The OCT system according to claim 1, wherein the interferometer is a Michelson interferometer or a Linnik interferometer.

14. The OCT system according to claim 1, further comprising a PSD calibrator configured to block the sample arm of the interferometer, wherein the light reaching the spectrometer includes only light from the reference beam propagating within the reference arm of the interferometer, the measured intensity of the interference pattern is a function of the PSD of the incident light to the corresponding wavenumber scaled by the responsiveness of the spectrometer and the reflectance of the reference arm, and during the execution of the PSD calibrator, the processor is configured to calibrate the PSD of the incident light such that the wavenumber corresponding to each pixel of the spectrometer is estimated.

15. A method for profilometry measurement of a sample in an optical coherence tomography (OCT) system, The interferometer splits the incident light into a reference beam and an inspection beam, and generates an interference pattern by interfering the inspection beam reflected from the sample with the reference beam reflected from the reference mirror. The spectrometer includes analyzing the spectral components of the interference pattern at non-uniformly sampled wavenumbers, The computer-readable memory of the OCT system connects different depth values ​​to different non-uniformly sampled wavenumbers and stores a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumbers, and the method further, A method comprising obtaining the profilometry measurement of the sample as the maximum likelihood estimate of the surface depth of the sample by back-projecting the intensity measured in the measurement model.

16. The method according to claim 15, wherein the depth value is sampled uniformly from the depth measurement range with the resolution of the OCT system, and the depth value is a relative value to a reference depth selected outside the depth measurement range.

17. The method according to claim 15, further comprising estimating each profilometry measurement by performing a process to obtain a maximum likelihood estimator (MLE) and generating arguments for the maximum likelihood estimator of non-zero elements in the corresponding reflectance vector, wherein each argument of the reflectance vector corresponds to one of the depth values ​​in the measurement model.

18. The method according to claim 17, wherein the MLE is an approximate MLE, and the process of determining the approximate MLE includes backprojecting a data vector through a measurement matrix, wherein the MLE is a depth value corresponding to the largest element in the backprojection.

19. The method according to claim 17, wherein the MLE is an exact MLE, and the process of obtaining the exact MLE includes refining the approximate MLE by maximizing the maximum likelihood objective function using a gradient-free optimization method.

20. A non-temporary computer-readable medium storing computer-executable instructions that, when executed by a computer, cause the computer to perform a method for measuring the profilometry of a sample in an optical coherence tomography (OCT) system, wherein the method is The interferometer splits the incident light into a reference beam and an inspection beam, and generates an interference pattern by interfering the inspection beam reflected from the sample with the reference beam reflected from the reference mirror. The spectrometer includes analyzing the spectral components of the interference pattern at non-uniformly sampled wavenumbers, The computer-readable memory of the OCT system connects different depth values ​​to different non-uniformly sampled wavenumbers and stores a measurement model having elements weighted by weights derived from the power spectral density (PSD) of the incident light for the corresponding wavenumbers, and the method further, A non-temporary computer-readable medium, which includes obtaining the profilometry measurement of the sample as the maximum likelihood estimate of the surface depth of the sample by back-projecting the intensity measured in the measurement model.

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