Active vibration cancellation and control for scanning probe microscopy.

Abstract

Various embodiments include systems, methods, architectures, mechanisms, and apparatus for processing images containing distortions induced by the presence of acoustic noise and / or ground vibrations during image generation by a sensitive imaging device, such as an atomic force microscopy (AFM) device. The initial filtered image is generated by filtering an image noise signal captured simultaneously with the image. [Equation 1] TIFF2025530300000304.tif9170 A finite impulse response (FIR) filter configured to process [Equation 2] TIFF2025530300000305.tif7114 can be obtained using

Description

[Technical Field]

[0001] government subsidies This invention was made with government support under grant numbers CMMI-1663055, CMMI-1851907, and IIBR-1952823 awarded by the NSF. The government has certain rights in the invention.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 63 / 396,754, entitled ACTIVE NOISE CANCELLATION FOR SCANNING PROBE MICROSCOPE IMAGERY (Attorney Docket No. RU-2022-144), filed August 10, 2022, and U.S. Provisional Patent Application No. 63 / 448,132, entitled ACTIVE VIBRATION CANCELLATION AND CONTROL FOR SCANNING PROBE MICROSCOPY (Attorney Docket No. RU-2023-072), filed February 24, 2023, which applications are incorporated herein by reference in their entireties.

[0003] The present disclosure relates generally to image processing, and more particularly to minimizing scanning probe microscope (SPM) imaging distortions associated with acoustic sources and ground vibrations. [Background technology]

[0004] This section is intended to introduce the reader to various aspects of the art that may be related to various aspects of the present invention, which are described and / or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

[0005] Atomic force microscopy (AFM) is sensitive to disturbances such as acoustic noise, which can cause distortions in AFM images. Although some of the effects of disturbances can be reduced by conventional passive methods, residual noise distortions remain, resulting in loss of image quality.

[0006] Filtering distortions caused by acoustic noise in AFM images presents challenges. Traditional frequency-domain filtering approaches (e.g., low-pass, band-pass filtering) are ineffective because acoustic noise contributions are primarily random and broadband and do not decay with increasing frequency. As a result, using these filters can significantly distort the sample topography or remove it altogether.

[0007] Traditionally, the state-of-the-art in acoustic noise reduction in the AFM industry has been to use acoustic noise enclosures (acoustic hoods) to isolate and absorb environmental acoustic noise from entering the local measurement environment of the AFM scanner. However, acoustic hoods are not only bulky and expensive, but also unable to reduce acoustic noise to the levels required for applications such as cleanroom nanometrology in the semiconductor industry. Furthermore, hoods cannot be installed when AFMs are integrated with other instruments, such as optical microscopes and environmental control chambers, for measuring live biological samples in biomedical and biological research and development. Summary of the Invention

[0008] Various deficiencies in the prior art are addressed by a system, method, architecture, mechanism, and apparatus for processing images containing distortions induced by the presence of acoustic noise and / or ground vibrations during image generation by a sensitive imaging device, such as an atomic force microscopy (AFM) device. An initial filtered image is generated by filtering an image noise signal captured simultaneously with the image.

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[0009] According to one embodiment, a method for processing an image including distortions induced by the presence of acoustic noise during generation of the image includes: receiving acoustic noise data from each of a plurality of microphones proximate to the imaging device during operation of the imaging device to generate an image; determining acoustic noise source locations using the acoustic noise data; using a dictionary-based method to estimate a primary acoustic dynamic (PAD) of the acoustic noise based on the determined locations of the acoustic noise sources; using a dictionary-based method to estimate an acoustic noise signal; obtaining an initial filtered image using the estimated PAD and the estimated noise signal; and optimizing a filter using adaptive coherence minimization to thereby obtain the filtered image. The initial filtered image is an image noise signal.

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[0010] The microphones in proximity to the imaging device are three microphones M placed at known locations a, b, and c. A , M B , and M C where the acoustic noise source location is estimated in terms of the sensor-source distance calculated using the acoustic noise data and the known locations of the three microphones.

[0011] The method is to estimate the PAD of acoustic noise using a dictionary-based method, where the location is selected according to the following equation:

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[0033] The method may further include constructing a dictionary of frequency responses of the PAD measured at:

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[0012] The method estimates the acoustic noise signal by using a dictionary-based method, where the location is selected according to the following equation:

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[0013] According to one embodiment, a method for processing an image including distortions induced by the presence of vibrations during generation of the image includes receiving vibration data from each of at least one vibration sensor proximate to an imaging device during operation of the imaging device to generate an image; and using the vibration data to generate an estimated noise signal.

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[0014] Additional objects, advantages, and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.

[0015] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present invention and, together with the general description of the invention given above and the detailed description of the embodiments given below, serve to explain the principles of the invention. [Brief explanation of the drawings]

[0016] [Figure 1] 1 depicts an AFM system that can benefit from various embodiments. [Figure 2A] 1 depicts AFM images of a silicon waver acquired with and without induced environmental acoustic noise. [Figure 2B] 1 depicts AFM images of a silicon waver acquired with and without induced environmental acoustic noise. [Figure 3] 2 is a spectral diagram illustrating an example frequency response (magnitude part) of a primary acoustic dynamics (PAD) such as a noise source as described above with respect to the AFM system of FIG. 1. [Figure 4] FIG. 1 is a schematic diagram of acoustic source localization using time delay measurements. [Figure 5] FIG. 1 is a schematic diagram of the construction of a dictionary of primary acoustic dynamics (PAD). [Figure 6] 1 depicts a pseudo-code representation of a method for offline acoustic noise filtering, according to one embodiment. [Figure 7]1 depicts a flow diagram of a method according to one embodiment. [Figure 8] 1 depicts a high-level block diagram of a noise reduction mode (NRM) process according to one embodiment. [Figure 9] 1 depicts an AFM system that can benefit from various embodiments. [Figure 10] 1 depicts a pseudo-code representation of a method for vibration filtering according to one embodiment. [Figure 11] 1 depicts a flow diagram of a method according to one embodiment.

[0017] It should be understood that the accompanying drawings are not necessarily to scale and that they represent somewhat simplified representations of various features illustrating the basic principles of the invention. Specific design features of the sequences of operations disclosed herein, including, for example, the specific dimensions, orientations, locations, and shapes of the various illustrated components, will be determined, in part, by the particular intended application and use environment. Certain features of the illustrated embodiments may be enlarged or distorted relative to others to facilitate visualization and clear understanding. In particular, for example, thin features may be depicted in bold for clarity or illustrative purposes. DETAILED DESCRIPTION OF THE INVENTION

[0018] The following description and drawings merely illustrate the principles of the invention. Thus, it will be understood that those skilled in the art can devise various arrangements not explicitly described or shown herein, but which embody the principles of the invention and are within the scope of the invention. Furthermore, all examples cited herein are expressly intended solely for educational purposes to primarily aid the reader in understanding the principles of the invention and concepts provided by the inventor(s) to further the art, and should not be construed as being limited to such specifically recited examples and conditions. Furthermore, the term "or" as used herein refers to a non-exclusive or (e.g., "or otherwise" or "or alternatively") unless otherwise indicated. Furthermore, the various embodiments described herein are not necessarily mutually exclusive, as some embodiments may be combined with one or more other embodiments to form new embodiments.

[0019] Many of the innovative teachings of the present application will be described with particular reference to presently preferred exemplary embodiments. However, it should be understood that such embodiments provide only a few examples of the many advantageous uses of the innovative teachings herein. In general, statements made in the specification of the present application do not necessarily limit any of the various claimed inventions. Moreover, some statements may apply to certain inventive features but not to other inventive features. Those skilled in the art, and informed by the teachings herein, will recognize that the present invention is applicable to a variety of other technical fields or embodiments.

[0020] Various embodiments provide systems, methods, architectures, mechanisms, and apparatus for mitigating image distortions associated with acoustic noise, such as those associated with atomic force microscopy (AFM) and other processes sensitive to acoustic noise and similar disturbances.

[0021] Various embodiments contemplate a data-driven, dictionary-based filtering approach to remove AFM image distortions caused by acoustic noise from unknown locations. Specifically, a filter is designed directly as a finite impulse response (FIR) representation of the underlying primary acoustic dynamics (PAD) response. To consider the influence of unknown noise locations on the PAD, the unknown noise source is identified based on a time-delay measurement method. A dictionary-based approach is proposed to estimate the corresponding PAD based on the estimated noise location. To minimize the acoustically induced image distortions through coherence minimization, an acoustic dynamics modulator is introduced into the estimated PAD. In particular, the modulator is found via a gradient-based iterative method that iteratively minimizes the coherence between the acoustic noise and the residual acoustically induced image distortion. The approach of minimizing the coherence between the acoustic noise and the noise-distorted AFM image signal is newly applied herein, and a gradient-based algorithm is created to minimize the coherence and optimize the filter (i.e., the acoustic dynamics model). The proposed filtering scheme is implemented on an example AFM image, and experimental results show that image distortions are significantly reduced.

[0022] For example, various embodiments use a time delay measurement method to estimate the location of the noise source, thereby providing an estimated noise signal. The acoustic dynamics modulator then minimizes the corresponding image distortion by minimizing the coherence between the acoustic noise and the filtered acoustic noise-affected image through gradient-based optimization.

[0023] Various embodiments contemplate online active noise reduction mode (NRM) imaging for processing cantilever probe vibrations induced by acoustic noise during AFM imaging. A prefilter for online adjustment of the setpoint of the feedback loop for topography tracking to make the AFM system robust to environmental acoustic noise. A feedforward controller based on a PAD model of the acoustic noise effect on the AFM system is augmented to counter noise-induced vibrations.

[0024] Various embodiments provide active noise control / cancellation suitable for use in AFM imaging applications, etc., to reduce or eliminate image distortion caused by acoustic noise. Some embodiments provide active noise control / cancellation during the SPM imaging or image acquisition process, while other embodiments provide active noise cancellation later through post-imaging processes.

[0025] Various embodiments provide a dictionary-based approach integrated with time delay measurements to identify acoustic noise source(s) and estimate the corresponding acoustic dynamics in AFM imaging.

[0026] A noise-image coherence minimization approach is presented that minimizes acoustically induced image distortions via gradient-based optimization.

[0027] A noise reduction mode (NRM) is provided to reduce / eliminate disturbances caused by acoustic noise on the AFM cantilever probe during the imaging process, the set point of the feedback loop for tracking the sample topography is adjusted online to make the AFM system robust to environmental noise, and the feedforward controller is augmented to counter vibrations caused by acoustic noise in the feedback loop.

[0028] Various embodiments advantageously provide a data-driven approach to capturing and using acoustic noise dynamics. Acoustic noise dynamics tend to be complex and time-varying. By using a data-driven approach, acoustic noise dynamics can be directly captured by a finite impulse response (FIR) sequence without losing robustness through a dictionary-based finite impulse response-based approach. Furthermore, various embodiments introduce a modulator that further enhances the captured acoustic noise dynamics, and optimizes the modulator using a coherence minimization approach. Illustratively, a gradient-based coherence minimization algorithm can be used to eliminate distortions caused by acoustic noise in AFM images. Additionally, a denoising mode adapted for AFM imaging is also provided, consisting of both adaptive adjustment of a feedback loop (via a prefilter) and feedforward noise cancellation. The noise reduction performance of the denoising mode is further enhanced using a Wiener filter.

[0029] The modulator-enhanced FIR filter can be used independently without the use of an acoustic dynamics dictionary to compensate for the effects of unknown noise source locations on acoustic noise dynamics measurements, thereby directly canceling acoustically induced AFM image distortion. Thus, various embodiments provide modulation of one or more filters, such as modulation of an acoustic noise filter, to thereby optimize a filter configured to minimize acoustic noise induced distortion in the AFM image.

[0030] Figure 1 depicts an AFM system that can benefit from various embodiments. Specifically, Figure 1 depicts an AFM 110 that includes an AFM head 112 configured to cause the AFM probe 112 to scan a sample surface (not shown). An AFM controller 116 is configured to manage various control and input / output functions of the AFM 110, including providing AFM image data to an image processor 140. The image processor 140 is configured to process the AFM image data in accordance with various embodiments, as described below.

[0031] FIG. 1 also exemplarily shows a microphone M A , M B , and M C 1 depicts microphone array 120 including three microphones, designated as (collectively microphones M of array 120). Acoustic information, such as sound / vibrations, proximate to AFM 110, such as from acoustic noise source 105, is received by microphone M, which provides a corresponding acoustic information signal that is provided to image processor 140, optionally via signal amplification / conditioning circuitry 130. Note that sound / vibrations proximate to AFM 110, such as from acoustic noise source 105, are also "received" by AFM probe 114, either directly from noise source 105 (or an acoustic transmission medium therebetween) or indirectly via other parts of AFM 110 that are also affected by or perturbed by the sound / vibrations proximate to AFM 110 and that mechanically cooperate with the AFM probe to transmit the sound / vibrations to the AFM probe.

[0032] The impact of acoustic noise is to degrade AFM imaging quality. For example, in Tapping Mode (TM) imaging, the cantilever tip is excited (typically using a small piezo stack actuator called a dither piezo) to tap on the sample surface; as the tip scans across the surface, the tapping amplitude is maintained near a preselected constant level under feedback control. Sample topography images are then acquired from the (vertical) displacement of the cantilever. However, in the presence of environmental acoustic noise, the mechanical structure of the AFM (to which the cantilever is attached) can be excited into vibration, resulting in undesired cantilever vibration relative to the sample and, therefore, image distortion.

[0033] 2A and 2B depict AFM images of a silicon wafer acquired with and without induced environmental acoustic noise, respectively. Specifically, while FIGS. 2A and 2B depict images of a silicon wafer acquired under environmental acoustic noise (e.g., as discussed herein with respect to FIG. 1), it can be seen that there is significant image distortion in the presence of the induced noise (FIG. 2A) compared to the lower image distortion in the image acquired without the induced noise (FIG. 2B).

[0034] Eliminating distortions caused by such acoustic noise in AFM images is difficult. Conventional filtering techniques based on frequency-domain separation (e.g., low-pass, band-pass, or notch filters) are ineffective because the noise-induced distortions are primarily coupled to the sample topography in the acquired image. These techniques will remove and blur sample topography features. A further challenge arises because acoustic noise dynamics are primarily random and broadband, and do not decay with increasing frequency, as depicted in the spectral diagram of FIG. 3 , which illustrates an example frequency response (magnitude portion) of the primary acoustic dynamics (PAD) from the noise source 105 of the AFM system in FIG. 1 to the piezoelectric actuator for tracking the sample topography (e.g., the AFM head 115 in FIG. 1 ).

[0035] Of particular interest is the scenario where the acoustic noise comes from an arbitrary, unknown, but fixed location behind the sensor (whose location is fixed and known), as illustrated, for example, in FIG.

[0036] FIG. 4 is a schematic diagram of acoustic source localization using time delay measurements, where a, b, and c represent the locations of three microphones, the solid and dashed lines are hyperbolic curves on which potential noise source locations are located, and e(n) and f(n) represent the location of noise source n, respectively.

[0037] Referring to FIG. 4, three microphones M are placed at known locations a, b, and c. A , M B , and M C The location of noise source n (105) with respect to can be determined to be at one of two intersection points of two hyperbolas, one with foci at a and b and the other with foci at b and c.

[0038] The hyperbola with foci at a and b (solid line in Figure 4) is given by the following equation:

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[0039] Similarly, the hyperbola with foci at locations b and c (dashed line in FIG. 4) is given by the following equation:

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[0040] The noise source location n is the sensor-source distance difference in equations (1) and (2).

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[0041] (distance difference)

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[0042] Distance difference

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[0043] Figure 5 is a schematic diagram of the construction of a dictionary of primary acoustic dynamics (PAD), where the receiver (e.g., the AFM scanner in this work) is located at the origin, the dots on the semicircular grid are the locations where PAD in the dictionary was measured, and dots B, C, D, and E, respectively, represent PAD locations that are estimated using the dictionary and then used to estimate PAD at location "A" (dot A is between dots B and C), where there is an unknown noise source.

[0044] A dictionary of frequency responses of primary acoustic dynamics (PAD) measured at selected locations TIFF2025530300000027.tif10114 is constructed as follows:

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[0045] That is,

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[0046] PAD at unknown locations can be calculated using a dictionary, e.g. via linear interpolation.

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[0047] The dynamics at location A can then be estimated via linear interpolation of the radical directions as follows:

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[0048] Alternatively,

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[0049] The influence of unknown noise locations on noise measurements can also be accounted for via a data-driven dictionary-based approach: a dictionary of noise propagation dynamics (NPD) measured at selected locations

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[0050] NPD at any unknown location A

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[0051] Using the above estimated NPD, the noise at location A during the targeted imaging process can be calculated by multiplying the measured noise by

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[0052] The above estimated PAD and NPD in non-parametric finite impulse response form are calculated based on the noise-induced image distortion (i.e., the image noise signal JPEG2025530300000066.jpg14114 ) can be used directly to quantify:

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[0053] Dynamic Modulator

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[0054] Virtually optimal modulator

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[0055] The minimization of equation (22) is based on the acoustic noise n[k] and the true sample topography Z T [k], R nt Based on the fact that there is zero correlation between [j] and the measured noise and the filtered image signal Z F It is transformed to minimize the coherence between [k]:

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[0056] If the noise is completely removed:

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[0057] Minimize

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[0058] The above cost function in equation (28) can be expressed in the frequency domain as follows:

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[0059] The above correlation minimization in equation (29) can be rewritten as follows:

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[0060] Coherence

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[0061] The minimization in equation (30) is further modified as follows:

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[0062] Figure 6 depicts a pseudo-code representation of a method for offline acoustic noise filtering, according to one embodiment. Specifically, a methodology according to an embodiment for implementing offline acoustic noise filtering is summarized in Figure 6 and Algorithm 1, as presented below. Figure 7 depicts a flow diagram of a method following the method of Figure 6, according to one embodiment. Note that the descriptions of Figures 6 and 7 are similar and therefore presented together.

[0063] The embodiments of Figures 6 and 7 provide methods for processing images that contain distortions induced by the presence of acoustic noise during generation of images by imaging devices that are sensitive to such acoustic noise, such as atomic force microscopy (AFM) devices as described above.

[0064] 7, in step 710, acoustic noise data is received from each of a plurality of microphones, such as in a microphone array, proximate to the imaging device and active during operation of the imaging device to generate an image. Referring to box 715, and as depicted with respect to FIG. 1 and other examples above, the acoustic noise data may include data from three microphones proximate to the AFM device and having known locations relative to the AFM device during operation of the AFM device, thereby providing an image file or image data that includes distortions induced by the presence of acoustic noise during generation of the image file or image data by the AFM device.

[0065] In step 720 of method 700 of FIG. 7 (step 602 of method 600 of FIG. 6), the received acoustic noise data is used to determine acoustic noise source location(s).

[0066] 7 (step 603 of method 600 of FIG. 6), a dictionary-based method for estimating the primary acoustic dynamic (PAD) of the acoustic noise based on the determined locations of the acoustic noise sources. Prior to performing step 730, a PAD dictionary is constructed, such as according to step 601 of method 600 of FIG. 6.

[0067] Step 740 of method 700 of Figure 7 (step 604 of method 600 of Figure 6) uses a dictionary-based method to estimate the acoustic noise signal. Prior to performing step 740, a noise propagation dynamics (NPD) dictionary is constructed, such as according to step 601 of method 600 of Figure 6.

[0068] In optional step 750 of method 700 of FIG. 7, the measured noise signal is subjected to Wiener filter-based optimization filtering, as described herein, to improve the SNR of the measured noise signal.

[0069] In step 760 of method 700 of FIG. 7 (step 605 of method 600 of FIG. 6), the estimated PAD and estimated noise signal are used to obtain an initial filtered image.

[0070] In step 770 of method 700 of FIG. 7 (steps 606-612 of method 600 of FIG. 6), the filter associated with the initial filtered image is optimized using adaptive coherence minimization, thereby obtaining a final filtered image.

[0071] The above-described embodiments are described primarily within the context of post-processing (i.e., after image capture) image data that includes distortions induced by the presence of acoustic noise during image data capture. That is, data related to the acoustic noise is captured simultaneously with the image data distorted or affected thereby, and once image data for substantially the entire image is captured, various embodiments simultaneously process the image using the acoustic noise data to remove or at least reduce the distorting effects of the acoustic noise present at the time of image data capture.

[0072] Various other embodiments are directed to online active noise control during the capture of image data that is susceptible to acoustic noise distortion. Online active noise control embodiments will now be described in more detail.

[0073] 8 depicts a high-level block diagram of a noise reduction mode (NRM) process / processor according to one embodiment. Specifically, the NRM processor 800 of FIG. 8 is configured to reduce the effects of acoustic noise n(z) within the context of AFM imaging.

[0074] Specifically, in the presence of acoustic noise n(z), the AFM cantilever deflection during the imaging process can be given as:

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[0075] In equation (46),

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[0076] Feedforward controller configured to eliminate acoustic noise effects on cantilever deflection

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[0077] Under this feedforward controller 815, the cantilever deflection is given by:

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[0078] The set value given to the input noise signal n(z)

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[0079] Thus, the cantilever deflection induced by acoustic noise is reflected by the feedback error signal, as shown in Figure 8.

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[0080] Prefilter in equation (50)

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[0081] Feedforward controller for acoustic noise cancellation during the imaging process

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[0082] A time-domain inversion-based iterative control (TDIIC) algorithm 850 is optionally applied to improve topography tracking performance, as follows:

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[0083] In the presence of acoustic noise,

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[0084] Iterative Gain

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[0085] An inner-outer feedback loop was introduced to regulate the averaged (vertical) position of the cantilever oscillation (i.e., TM-deflection), and the outer loop was to adjust the TM-deflection setpoint through the following PID-type control (see Figure 8):

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[0086] Initially, the outer loop dTM_d setpoint is set to the average TM deflection at the start of the imaging process.

[0087] Each in equation (60)

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[0088] The autocorrelation signal in the above equations (67) and (68)

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[0089] Cross-correlation

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[0090] In various embodiments, the acoustic noise measurement n m A Wiener filter-based algorithm is provided to improve the signal-to-noise ratio (SNR) of the image signal z[k] (acoustic noise n m [k]) using the Wiener filter

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[0091] Wiener filter

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[0092] Therefore, various embodiments may be implemented to reduce the acoustic noise measurement error n e We present a Wiener filter that improves the effective SNR of acoustic noise measurements by minimizing the cross-covariance between [k] and the acoustically affected AFM image signal z[k].

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[0093] Additional embodiments further enhance the effective SNR of the acoustic noise measurement through the modulator via the coherence minimization described above. Note that the modulator-enhanced FIR filter can be used independently without the use of an acoustic dynamics dictionary to compensate for the effect of unknown noise source locations on the acoustic noise dynamics measurement, thereby directly canceling acoustically induced AFM image distortion. Thus, various embodiments provide for modulation of one or more filters, such as modulation of an acoustic noise filter, thereby optimizing a filter configured to minimize acoustic noise induced distortion in the AFM image.

[0094] Vibration & vibration + noise reduction embodiment The various embodiments discussed above are primarily directed to reducing image distortions associated with acoustic noise experienced by equipment associated with atomic force microscopy (AFM) and other processes sensitive to acoustic noise and similar disturbances.

[0095] Additional embodiments may be directed to reducing image distortions associated with vibrations or a combination of vibrations and acoustic noise experienced by equipment associated with AFMs and other processes that are sensitive to vibrations and similar disturbances.

[0096] Various embodiments are discussed herein within the context of modulator-based signal-to-noise ratio optimization via coherence maximization. Specifically, various embodiments are discussed herein within the context of active ground vibration cancellation using accelerometers, active acoustic noise and ground vibration cancellation by combining accelerometers and microphones together, and methodologies for fusion of multiple sensor signals to optimize signal-to-noise ratio, such as atomic force microscopes (AFMs) and other precision instruments (e.g., scanning electron microscopes, confocal microscopes, and / or other precision instruments).

[0097] Figure 9 depicts an AFM system that can benefit from various embodiments. Specifically, Figure 9 depicts an AFM system 900 that is similar to AFM system 100 described above with respect to Figure 1, but that has been further modified to reduce image distortion associated with vibration alone or a combination of vibration and acoustic noise.

[0098] 9 (similar to FIG. 1) depicts an AFM 110 comprising an AFM head 112 configured to cause the AFM probe 112 to scan a sample surface (not shown). An AFM controller 116 is configured to manage various control and input / output functions of the AFM 110, including providing AFM image data to an image processor 140. The image processor 140 is configured to process the AFM image data according to various embodiments, as described below.

[0099] 9 is configured similarly to AFM system 100 of FIG. 1, i.e., configured to include a microphone array 120 that illustratively includes three microphones, designated as microphones MA, MB, and MC (collectively microphones M of array 120), and optional microphone signal amplification / conditioning circuitry 130. Acoustic information, such as sound / vibration, proximate AFM 110, such as from acoustic noise source 105, is received by microphone M, which provides a corresponding acoustic information signal, optionally via microphone signal amplification / conditioning circuitry 130, that is provided to image processor 140. It should be noted that sound / vibrations proximate to the AFM 110, such as from the acoustic noise source 105, are also "received" by the AFM probe 114, either directly from the noise source 105 (or the acoustic transmission medium therebetween), or indirectly via other parts of the AFM 110 that are also affected or perturbed by the sound / vibrations proximate to the AFM 110 and that mechanically cooperate with the AFM probe 114 to transmit the sound / vibrations to the AFM probe.

[0100] In an embodiment that mitigates vibration-related image distortion, the AFM system 900 of FIG. 9 may include an accelerometer A, which is directly connected to or located on the AFM 110 or a portion thereof (e.g., the housing or chassis of the AFM 110, the AFM head 112, or some other location). A , A B , A C , and A D(collectively accelerometer A), as well as optional accelerometer signal amplification / conditioning circuitry 135. Vibration information experienced by AFM 110, or a portion thereof, such as from vibration source 106, is sensed by accelerometer A, which generates a corresponding vibration information signal that is provided to image processor 140, optionally via signal amplification / conditioning circuitry 136. It should be noted that vibrations proximate AFM 110, such as from acoustic noise source 106, are also "received" by AFM probe 114, either directly from vibration source 106 (or a vibration transmission medium therebetween), or indirectly via other parts of AFM 110 that are impacted or perturbed by the vibrations proximate AFM 110 and mechanically cooperate with AFM probe 114 to transmit the vibrations to the AFM probe.

[0101] The effects of acoustic noise and / or vibrations can degrade AFM imaging quality. For example, in Tapping Mode (TM) imaging, the cantilever tip is excited (usually using a small piezo stack actuator called a dither piezo) to tap on the sample surface, and the tapping amplitude is maintained near a preselected constant level under feedback control as the tip scans across the surface. A sample topography image is then acquired from the (vertical) displacement of the cantilever. In the presence of environmental acoustic noise and / or vibrations, the mechanical structure of the AFM (to which the cantilever is attached) can be excited into vibration, resulting in undesired cantilever vibration relative to the sample and thereby image distortion.

[0102] FIG. 9 shows a first pair of accelerometers (AFMs) mounted on the AFM system 110. C and A D ) (e.g., a chassis or other vibration conduit), as well as a second pair of accelerometers (A A and A B) is illustratively depicted. Note that fewer or more accelerometers A may be attached to AFM system 110 or portions thereof. Also, note that a single accelerometer A attached to only one or portion of AFM system 110 may also be used in various embodiments.

[0103] Whether one accelerometer A or multiple accelerometers A are used, each accelerometer A is configured to sense or measure ground vibrations, etc., that are transmitted to the AFM system, which vibrations may result in extraneous cantilever vibrations and subsequent image errors or distortions.

[0104] In particular, sensor / accelerometer A is configured to measure vibration-indicative displacements of the AFM system or portions thereof, such as cantilever deflection signals, which measurements are used to process acquired images, such as with filtering and / or vibration cancellation algorithms described below. Using this algorithm-based method, optical tables currently used in AFM systems can be replaced or further enhanced for vibration isolation (e.g., by combining the vibration processing techniques described below with the noise processing techniques described above).

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[0106] In the above equations (72-74),

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[0107] In various embodiments, the optimal coefficient

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[0108] The coefficients obtained after each iteration are normalized before the next iteration:

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[0109] For example, the above correlation minimization in equation (74) can be reduced to:

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[0110] Coherence

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[0111] In various embodiments, coherence

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[0112] In various embodiments, the minimization in equation (78) is further modified as follows:

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[0113] With the above modifications, the calculations in equations (79) to (85) become

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[0114] Image distortion caused by vibration is due to the coherence between the vibration and the residual vibration-induced image distortion.

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[0115] Various embodiments contemplate online active acoustic rejection mode (ARM) imaging to address cantilever probe vibrations caused by acoustic noise during AFM imaging, active vibration rejection mode (VRM) imaging to address cantilever probe vibrations caused by vibrations during AFM imaging, or active vibration acoustic rejection mode (VARM) imaging to address cantilever probe vibrations caused by vibrations and caused by acoustic noise during AFM imaging.

[0116] A pre-filter may be provided to online adjust the set point of the feedback loop for topography tracking to make the AFM, VRM, or VARM system robust to environmental vibrations or acoustic noise. Additionally, a feed-forward controller based on a PAD model of acoustic noise effects on the AFM system may be augmented to counter noise-induced vibrations, as described above.

[0117] Various embodiments provide active vibration and / or noise control / cancellation suitable for use in AFM imaging applications, etc., to reduce or eliminate image distortion caused by vibration and / or acoustic noise. Some embodiments provide active vibration and / or noise control / cancellation during the SPM imaging or image acquisition process, while other embodiments provide active vibration and / or noise cancellation later through post-imaging processes.

[0118] Figure 10 depicts a pseudo-code representation of a method for vibration filtering, according to one embodiment. Specifically, a methodology according to an embodiment for implementing vibration filtering is summarized in Figure 10 and Algorithm 2, as presented below. Figure 11 depicts a flow diagram of a method following the method of Figure 10, according to one embodiment. Note that the descriptions of Figures 10 and 11 are similar and therefore presented together.

[0119] Briefly, Algorithm 2 of FIG. 10 and method 1100 of FIG. 11 calculate the measured total image signal

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[0120] In step 1120 (step 1001 of method 1000 of FIG. 10), the vibration / noise data is converted into a noise signal or ground vibration signal (estimated noise signal ) as described above with respect to at least Equations 72-73.

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[0121] In step 1130 (steps 1002-1006 of method 1000 of FIG. 10), the estimated noise signal

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[0122] In step 1140 (steps 1007-1008 of method 1000 of FIG. 10), coherence

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[0123] In step 1150, the obtained optimal noise and / or ground signals are used to generate a filtered image, such as via an online active noise reduction mode (NRM) or control process and / or an offline noise filtering process, both of which are described above with respect to various embodiments.

[0124] Various computing and / or processing functions as described herein may be implemented using standard computing techniques, such as via a special-purpose or general-purpose computer configured to perform the computing and / or processing functions and including processing, memory, and input / output (I / O) circuitry. For example, a controller or processor may be configured to perform various computing and / or processing functions in response to computer instructions stored in non-transitory computer-readable memory. Thus, the various functions depicted and described herein may be implemented in hardware or a combination of software and hardware, elements or portions thereof, such as by using a general-purpose computer, one or more application-specific integrated circuits (ASICs), or any other hardware equivalents or combinations thereof. In various embodiments, computer instructions associated with the functions of the elements or portions thereof are loaded into respective memories and executed by respective processors to implement the respective functions as described herein. Thus, the various functions, elements, and / or modules described herein, or portions thereof, may be implemented as a computer program product, where the computer instructions, when processed by a computing device, adapt the operation of the computing device such that methods or techniques described herein are invoked or otherwise provided. The instructions for invoking the methods of the present invention may be stored on a tangible and non-transitory computer-readable medium, such as a fixed or removable medium or memory, or may be stored in memory within a computing device that operates according to the instructions.

[0125] While various embodiments incorporating the teachings of the present invention have been shown and described in detail herein, those skilled in the art can readily devise many other various embodiments which still incorporate these teachings. Thus, while the foregoing is directed to various embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof.

Claims

1. 1. A method for processing an image containing distortions induced by the presence of vibrations during the generation of said image, comprising: receiving vibration data from each of at least one vibration sensor proximate to the imaging device during operation of the imaging device to generate the image; Using the vibration data, an estimated noise signal [Equation 1] and determining Iteratively minimize the coherence between the vibration noise and the image distortion caused by the residual vibration to obtain an updated noise signal [Equation 2] and coherence [Equation 3] and the updated noise signal [Equation 4] and coherence [Equation 5] and generating filtered image data using the

2. The method of claim 1 , wherein the filtered image data is generated using image data for the entire captured image.

3. The method of claim 1 , wherein the filtered image data is generated using image data of a partially captured image.

4. The method of claim 1 , wherein the imaging device comprises an atomic force microscopy (AFM) device.

5. The method of claim 1 , wherein the vibration sensor comprises an accelerometer.

6. The method of claim 2 , wherein at least one vibration sensor is mounted directly to a portion of the AFM device and comprises an accelerometer.

7. Using a Wiener filter, the acoustic noise measurement error n ｅ 2. The method of claim 1, further comprising minimizing the cross-covariance between the acoustically affected AFM image signal z[k] and the acoustically affected AFM image signal z[k].

8. the image further includes distortions induced by the presence of acoustic noise during the generation of the image; receiving acoustic noise data from each of a plurality of microphones proximate to the imaging device during operation of the imaging device to generate the image; determining acoustic noise source locations using the acoustic noise data; and using a dictionary-based method to estimate a primary acoustic dynamic (PAD) of the acoustic noise based on the determined location of the acoustic noise source; using a dictionary-based method for estimating the acoustic noise signal; obtaining an initial filtered image using the estimated PAD and the estimated noise signal; and optimizing the filter using adaptive coherence minimization to thereby obtain a filtered image.

9. The plurality of microphones in proximity to the imaging device are three microphones M located at known locations a, b, and c. Ａ , M Ｂ , and M Ｃ 9. The method of claim 8, comprising: wherein the acoustic noise source location is estimated in terms of a sensor-to-source distance calculated using the acoustic noise data and known locations of the three microphones.

10. 1. A method for processing an image containing distortions induced by the presence of acoustic noise during the generation of said image, comprising: receiving acoustic noise data from each of a plurality of microphones proximate to the imaging device during operation of the imaging device to generate the image; determining acoustic noise source locations using the acoustic noise data; and using a dictionary-based method to estimate a primary acoustic dynamic (PAD) of the acoustic noise based on the determined location of the acoustic noise source; using a dictionary-based method for estimating the acoustic noise signal; obtaining an initial filtered image using the estimated PAD and the estimated noise signal; optimizing the filter using adaptive coherence minimization to thereby obtain a filtered image.

11. The method of claim 10 , wherein the imaging device comprises an atomic force microscopy (AFM) device.

12. The plurality of microphones in proximity to the imaging device are three microphones M located at known locations a, b, and c. Ａ , M Ｂ , and M Ｃ 11. The method of claim 10, comprising: wherein the acoustic noise source location is estimated in terms of a sensor-to-source distance calculated using the acoustic noise data and known locations of the three microphones.

13. A dictionary of frequency responses of the PAD measured at selected locations for use in the dictionary-based method of estimating the PAD of the acoustic noise according to the following equation: [Equation 6] 11. The method of claim 10, further comprising constructing: [Equation 7]

14. A dictionary of noise propagation dynamics (NPD) measured at selected locations for use in the dictionary-based method of estimating the acoustic noise signal according to the following equation: [Equation 8] 11. The method of claim 10, further comprising constructing: [Equation 9] 。

15. The initial filtered image is an image noise signal [Equation 10] a finite impulse response (FIR) filter configured to process [0011] The method of claim 10, wherein the signal is obtained using

16. the image further includes distortions induced by the presence of acoustic noise during the generation of the image; receiving acoustic noise data from each of a plurality of microphones proximate to the imaging device during operation of the imaging device to generate the image; determining acoustic noise source locations using the acoustic noise data; and using a dictionary-based method to estimate a primary acoustic dynamic (PAD) of the acoustic noise based on the determined location of the acoustic noise source; using a dictionary-based method for estimating the acoustic noise signal; obtaining an initial filtered image using the estimated PAD and the estimated noise signal; and optimizing the filter using adaptive coherence minimization to thereby obtain a filtered image.

17. The plurality of microphones in proximity to the imaging device are three microphones M located at known locations a, b, and c. Ａ , M Ｂ , and M Ｃ 17. The method of claim 16, comprising: wherein the acoustic noise source location is estimated in terms of a sensor-to-source distance calculated using the acoustic noise data and known locations of the three microphones.

18. 1. A method of processing image data representative of an atomic force microscopy (AFM) system, the image processor being configured to cooperate with the AFM system to process image data provided thereto, the AFM system being configured to scan a sample surface with an AFM probe to thereby generate image data, the AFM system further comprising at least one vibration sensor configured to sense vibrations imparted to the AFM to thereby generate vibration data, the image processor processing image data representative of the image including distortions induced by the presence of vibrations during generation of the image, the method comprising: receiving vibration data from each of at least one vibration sensor proximate to the AFM system during operation of the AFM system to generate the image; Using the vibration data, an estimated noise signal [0012] and determining Iteratively minimize the coherence between the vibration noise and the image distortion caused by the residual vibration to obtain an updated noise signal [0013] and coherence [0014] and the updated noise signal [Equation 15] and coherence [0016] and generating filtered image data using the image processor.

19. 20. The image processor of claim 18, wherein at least one vibration sensor is mounted directly to a portion of the AFM device and includes an accelerometer.

20. The method uses a Wiener filter to calculate the acoustic noise measurement error n ｅ 20. The image processor of claim 18, further comprising minimizing cross-covariance between [k] and the acoustically affected AFM image signal z[k].

21. a plurality of microphones proximate the AFM system each configured to generate respective data indicative of acoustic noise sensed thereat, the method comprising: receiving acoustic noise data from each of the plurality of microphones proximate to the AFM system during operation of the AFM system to generate an image; determining acoustic noise source locations using the acoustic noise data; and using a dictionary-based method to estimate a primary acoustic dynamic (PAD) of the acoustic noise based on the determined location of the acoustic noise source; using a dictionary-based method for estimating the acoustic noise signal; obtaining an initial filtered image using the estimated PAD and the estimated noise signal; 20. The image processor of claim 18, further comprising optimizing the filter using adaptive coherence minimization to thereby obtain a filtered image.

22. The plurality of microphones in proximity to the AFM system includes three microphones M located at known locations a, b, and c. Ａ , M Ｂ , and M Ｃ 20. The image processor of claim 18, wherein the acoustic noise source location is estimated in terms of a sensor-to-source distance calculated using the acoustic noise data and known locations of the three microphones.

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