Sparse sampling using a programmatically randomized signal modulating a carrier signal

A method and a system are for sparse sampling utilizing a programmatically randomized signal for modulating a carrier signal. The system includes a compound sparse sampling pattern generator that generates at least one primary carrier signal, and at least one secondary signal. The at least one secondary signal modulates the at least one primary signal in a randomized fashion.

SUMMARY

In one embodiment, a system is provided. The system includes a compound sparse sampling pattern generator that generates at least one primary carrier signal, and at least one secondary signal. The at least one secondary signal modulates the at least one primary signal in a randomized fashion.

In another embodiment, a method is provided. The method includes generating, by a compound sparse sampling pattern generator, at least one primary carrier signal. The method also includes generating, by the compound sparse sampling pattern generator, at least one secondary signal that modulates the at least one primary signal in a randomized fashion.

In yet another embodiment, a scanning probe instrument is provided. The scanning probe instrument includes a compound sparse sampling pattern generator that generates at least one primary carrier signal, and at least one secondary signal that modulates the at least one primary signal in a randomized fashion. The at least one primary carrier signal and the at least one secondary signal are digital signals. The scanning probe instrument also includes a controller communicatively coupled to the compound sparse sampling pattern generator. The scanning probe instrument further includes at least one compound sparse sampling signal converter that receives the digital signals from the controller, converts the digital signals into analog signals; and provides the analog signals to at least one scan input. The analog signals dictate a level of sparsity at which an object is scanned by a scanning probe including the at least one scan input. At least one object signal response converter receives analog scan response signals from at least object response detector that detects a response of the object to scan signals directed at the object by the scanning probe instrument. The at least one object response converter is coupled to the controller and configured to convert the analog scan response signals to digital scan response signals. A sparse sampling reconstruction system is communicatively coupled to the controller. The sparse sampling reconstruction system receives the digital scan response signals from the controller, and responsively reconstructs an amalgamate image of the object scanned by the scanning probe instrument.

Other features and benefits that characterize embodiments of the disclosure will be apparent upon reading the following detailed description and review of the associated drawings.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Embodiments of the disclosure generally relate to sparse sampling applied to analytical instruments which utilize one or more serial scanning systems, or sub-systems, and computational methods applied to reconstruct amalgamate representations of the object being sparsely sensed through interaction with one or more analytical probes and response signals collected by one or more response signal detectors.

Acquisition times for serial scanning analytical instruments can be reduced significantly by application of sparse sampling, sub-sampling or compressed sensing. Such instruments include, by way of example, scanning electron microscopes, electron spectrometers, imaging electron spectrometers, ion microscopes, ion spectrometers, laser confocal microscopes and x-ray spectrometers. An object being sensed may experience reversible modification (e.g., electron or ion charge accumulation) or irreversible modification (e.g., changes in bonding, physical deformation, ion implantation, sputtering) due to interaction with the analytical probe. Detrimental probe-material interactions are reduced through sparse sampling. Sparse sampling and sparse sampling reconstruction benefits from an approach which mitigates artifacts and limitations associated with electro-mechanical scanning systems. Sources of serial scanning artifacts include, by way of example, dynamic hysteresis, slew and non-linear response. Examples of systems subject to one or more artifacts which can influence the quality of sparse sampling and sparse sampling reconstruction include, by way of example, magnetic scan devices, electromagnetic scan devices, electrostatic scan devices, electromagnetic probe blanking systems and electrostatic probe blanking systems.

A sparse sampling approach which mitigates serial scanning artifacts while allowing higher scanning rates benefits the quality of sparse sampling and sparse sampling reconstruction. Constructing sparse sampling scan patterns which are smooth and predominantly continuous on the carrier signal scale while simultaneously invoking statistical randomness at a discrete modulating perturbing signal scale, mitigates typical artifacts in electro-mechanical scanning systems and reduces the performance requirements for, or eliminates the need for, dynamic or high-speed probe blanking. An approach which permits a continuously variable and adaptive degree of sparse sampling enables a higher degree of freedom in the design of scan strategies to probe an object and extract information. Freedom in the degree of sparse sampling and the structure of the carrier signal pattern enables adaptive scan strategies based upon a-priori knowledge of the object being sampled or through information acquired while sensing the object. A-priori knowledge may include geometric information, chemical information and structural information. Information acquired during sparse sampling is derived from the probe-object response function over the governing interaction volume, and in some cases, may permit forward-looking modeling to aid adaptive sparse sampling scan strategies.

In embodiments of the disclosure, a sparse sampling approach employs compound signal convertors. In one embodiment, each element of the compound signal converter includes a primary carrier signal converter modulated by a secondary signal converter wherein the output of the secondary signal converter is referenced to the primary carrier signal converter output. The secondary modulating signal converter is programmatically randomized. One embodiment includes a pair of such “primary-secondary” compound signal converters configured as a programmable X-Y scan pattern generator wherein one “primary-secondary” compound signal converter generates the X coordinate and the second “primary-secondary” compound signal converter generates the Y coordinate, and wherein all outputs are coordinated by a programmable logic controller. Such a compound signal converter configured as an X-Y pattern generator may be programmed to produce an X-Y pattern including a plurality of sequential, ordered and randomized X-Y coordinates, wherein each coordinate is the summation of the primary X-Y carrier signal converters and the secondary X-Y modulating signal converters, wherein the latter acts as a randomizing signal added to the former. In an X-Y scan pattern generator configured in this manner, the X-Y carrier signal pattern can be considered as a “guiding center” path referenced by the programmatically randomized modulating X-Y signal pattern to define the sparse sampling coordinates. The aforementioned configured X-Y scan pattern generator is capable of programming a variety of arbitrarily smooth and arbitrarily continuous X-Y topological curves which include a carrier signal X-Y pattern which is programmatically randomized by the modulating signal X-Y pattern and which, in aggregate, generate a randomized sparse sampling X-Y signal pattern.

Through this approach, the degree of sparsity produced by the aggregate X-Y pattern may be smoothly and continuously regulated in increments of a fractional percent from 0% to greater than 99% sparsity. Statistical randomness is imparted through the randomness programmed into the aggregate X-Y modulated signal pattern. Carrier signal X-Y patterns supported through this approach include, by way of example, continuous space-filling curves, serpentine patterns, fly-back patterns, generalized polygon patterns and custom path coordinates. Compound signal converters configured as a pattern generator capable of conveying a variety of carrier signals which serve as a guiding path perturbed by the action of a modulating signal creating a randomized pattern of coordinates constitutes a versatile and generalized sparse sampling approach applicable to serial scanning probe instruments. This sparse sampling approaches defined herein mitigate artifacts and/or detrimental aspects intrinsic to serial scanning probe instruments. Prior to providing additional details regarding the different embodiments, a description of an illustrative operating environment is provided below.

FIG.1shows an illustrative operating environment in which certain specific embodiments disclosed herein may be incorporated. The operating environment shown inFIG.1is for illustration purposes only. Embodiments of the present disclosure are not limited to any particular operating environment such as the operating environment shown inFIG.1. Embodiments of the present disclosure are illustratively practiced within any number of different types of operating environments.

It will be understood that, when an element is referred to as being “connected,” “coupled,” or “attached” to another element, it can be directly connected, coupled or attached to the other element, or it can be indirectly connected, coupled, or attached to the other element where intervening or intermediate elements may be present. In contrast, if an element is referred to as being “directly connected,” “directly coupled” or “directly attached” to another element, there are no intervening elements present. Drawings illustrating direct connections, couplings or attachments between elements also include embodiments, in which the elements are indirectly connected, coupled or attached to each other.

FIG.1is a diagrammatic illustration of a scanning tool100for obtaining a representation of an object102in which at least some embodiments of the disclosure may be included. As can be seen inFIG.1, system100includes a scanning probe instrument104(e.g., scanning electron microscope, electron spectrometer, imaging electron spectrometer, scanning ion microscope, imaging ion spectrometer, laser confocal microscope, x-ray spectrometer, etc.) that includes scan inputs106for scanning an object such as102.

System100also includes a sparse sampling system108that includes at least one compound signal converter110capable of converting both a primary carrier signal and a secondary modulating signal. Each compound signal converter110may include a carrier signal converter112, and a secondary signal converter114. The secondary signal converter114is configured to modulate the primary carrier signal converter112. An output of the secondary modulating signal converter114is referenced to an output of the primary carrier signal converter112. One embodiment of the compound signal converter110uses a primary signal converter carrier signal with an output range corresponding to the operable (e.g., full scale) scan field of the scanning probe instrument scan inputs106, referenced by a secondary modulating signal converter operating over a reduced range and higher rate. One embodiment of compound signal converter110utilizes one digital-to-analog converter (DAC) to convert the combined signal including the programmable primary carrier signal128and programmable secondary modulating signal130, performing the function of both carrier signal converter112and modulating signal converter114.

Another embodiment of compound signal converter110uses a DAC as the primary carrier signal converter112and a separate DAC as modulating signal converter114, wherein modulating signal DAC114is referenced to the carrier output of carrier signal DAC112. The function of the DACs in all embodiments is to convert digital signals conveyed from a sparse sampling pattern generator119through a controller116into analog signals (e.g., voltages), which are then conveyed across a suitable transmission line (e.g., coaxial cable) to the scan inputs106of the scanning probe instrument104. One embodiment of the sparse sampling system compound signal converter110configures the modulating signal converter114as a DAC which is referenced to a particular bit depth on the carrier signal converter112, configured as a DAC. In one embodiment of compound signal converter110, the modulating signal DAC114is referenced to the bit depth corresponding to a noise floor of the primary carrier signal DAC112. In a particular embodiment of compound signal converter110, secondary modulating signal DAC114is referenced to the least significant bit of a primary carrier signal DAC112. In another embodiment of compound signal converter110, using DACs as signal converters, the secondary modulating signal converter DAC114amplitude is restricted relative to the maximum amplitude of primary carrier signal converter DAC112(e.g., DAC114has a smaller voltage range than DAC112). In one embodiment of compound signal converter110using DACs, the secondary modulating signal converter DAC114has a higher frequency response relative to primary carrier signal converter DAC112(e.g., DAC114is faster than DAC112). In another embodiment of compound signal converter110using DACs, the gain of secondary modulating signal converter DAC114referenced to primary carrier signal converter DAC112output is programmable. In one embodiment of the sparse sampling system108, compound signal converter110is configured as an X-Y pattern generator wherein X includes at least one carrier signal converter112and at least one modulating signal converter114and Y includes at least one primary carrier signal converter112and at least one secondary modulating signal converter114.

In an embodiment of the sparse sampling system108configured as an X-Y sparse sample pattern generator, the carrier signal converter112and modulating signal converter114outputs convey through one transmission line to scanning probe instrument scan inputs106. In another embodiment of the sparse sampling system108configured as an X-Y sparse sample pattern generator, the primary carrier signal converter112and secondary modulating signal converter114outputs convey through separate transmission lines to scanning probe instrument scan inputs106, the actions of which are both synchronized through controller116. For example, the primary carrier signals112could convey to a set of upper deflection coils (not shown) of a scanning transmission electron microscope and the secondary modulating signals compound signal converter114could convey to a lower set of deflection coils (not shown). The sparse sampling system compound signal converter110is extensible to “N” number of signal converter elements. For example, compound signal converter114include a primary, secondary and tertiary signal converter elements. The sparse sampling system108is extensible as a triad of compound signal converters to configure an X-Y-Z pattern generator. One embodiment of the sparse sampling system108configured as an X-Y-Z pattern generator is suitable for three-dimensional scanning probe instruments including, but not limited to, a confocal scanning laser microscope (CSLM).

System100further includes one or more object response signal converters122that convert a “response” signal of the object102from one or more object response detector(s)126. The object response detector(s)126may be of various types, and depend upon the type(s) of response signals collected from the object102(e.g., secondary electrons, backscatter electrons, Auger electrons, secondary ions, X-rays.) One embodiment of object response signal converter122uses an analog-to-digital converter (ADC) signal converter or plurality of ADCs to collect signals from the object response detectors126. One embodiment of object response signal converter122could include a pulse process converter (e.g., to convert x-ray object response detector signals). In one embodiment of the sparse sampling system108, the degree of oversampling from the object response signal converters122, relative to the dwell time used to collect the object response detector(s)126signals induced from the object being sparsely sensed, may be averaged to improve the signal-to-noise ratio (SNR) of the response signals. For example, and assuming a sufficiently high bandwidth object response detector126; a dwell time of one microsecond (1 us) and a sparse sampling system clock rate of 50 MHz (20 nanoseconds), would correspond to an oversampling ratio of 50 and allow a corresponding improvement in SNR of over 7. In one embodiment of the sparse sampling system108, the object response detector(s)126operate continuously or under the control of the scanning probe instrument104. In another embodiment of the sparse sampling system108, the object response detector(s)126are operably triggered through the action of an input-output object response detector(s)126element (e.g., a general purpose input-output, or GPIO). In an alternative embodiment of the sparse sampling system108, the object response detector(s)126transmit a trigger signal to the controller116to initiate and/or increment a scan or scan event action.

A controller116, which may be a part of sparse sampling system108, is operably coupled to the primary carrier signal converter112, the secondary signal converters114and object response signal converter(s)122. Controller116coordinates actions among the signal converters112,114,122as well as, in some embodiments, the object response detector(s)126, as noted above. In one embodiment, the controller116is a programmable logic controller (PLC). In one embodiment, the PLC is configured as a field programmable gate array (FPGA). In a particular embodiment, the FPGA functions as a high-speed data transmission array. In one embodiment of the sparse sampling approach disclosed herein, the sparse sampling X-Y pattern coordinates are synchronized by the PLC with response signal converter data and accessed through an address list which pair the pattern coordinates and the response signals.

In some embodiments, patterns produced by the sparse sampling pattern generator119are adapted to extract information from object102, based upon a-priori knowledge118of the object102being sensed, or to test an expectation of the object102being sensed. A-priori object knowledge118includes, but is not limited to, information of the object102geometry based upon design information such as from computer aided design (CAD) digital content or a graphic design system (GDS) (e.g., a GDSII digital file). A-priori object knowledge118could also be derived from lower resolution and/or larger field of view data which provides knowledge of hierarchical congestion and/or geometric density. Examples of such information include, but are not limited to, optical data or lower resolution data from the same or different scanning probe instrument. In general, a-priori object knowledge118includes structural information about the object102, chemical information about the object102, or any other suitable information.

In a typical operation, the object102is placed in proximity to the scanning probe on support101. In some embodiments, support101is a fixed platen and the scanning probe is moveable in X-Y or X-Y-Z. In an embodiment with a moveable scanning probe, the scanning probe may move step-wise or continuously while the object102being sensed remains fixed and stationary. In other embodiments, support101is a stage which is moveable in X-Y or X-Y-Z. In one embodiment wherein the scanning probe is moveable and the object is placed upon a moveable stage, the sparse sampling approach disclosed herein may be actioned while simultaneously moving a stage or sub-stage during the sparse sampling operations, to allow a continuous or predominantly continuous dynamic sparse sampling pattern to sense the object over an area or volume which may extend to construct a continuous, largely continuous, or a plurality of continuous strips ordered over a one-dimensional, a two-dimensional or a three-dimensional space. In one embodiment of support101, the simultaneously X-Y, or X-Y-Z moving stage is a mechanical piezoelectric stage, a laser interferometric stage, a feedback encoded stage, or an otherwise precision motion stage such that the motion of the object being sensed can be controlled within the aggregate system resolution target. In one embodiment of support101, the simultaneously moving precision stage has a step resolution of 1 nanometer or better, along each axis.

In one embodiment of support101, the simultaneously moving precision stage is a sub-stage affixed permanently or temporarily to an existing primary stage. In some embodiments, the object and/or the scanning probe is in ambient atmosphere. In other embodiments, the object102and/or elements of the scanning probe instrument104are in partial vacuum. The sparse sampling pattern generator119produces a sequential set of patterns which include a primary carrier signal path and a secondary modulating signal path, which are conveyed to the controller116. Where applicable, sparse sampling pattern generator119will define the dwell time for each sparse sampling coordinate of the pattern and convey the dwell time data for each coordinate to the controller116. Typically, a dwell time will significantly exceed the scanning probe instrument104probe transit time between sampling coordinates. In one embodiment of sparse sampling system108, the dwell time is programmable for each discrete sparse sampling pattern element. For example, each pixel element could have a dwell time scaling with the gray scale intensity of a corresponding image pattern. In one embodiment of sparse sampling system108, the programmable dwell time per sample coordinate may be truncated if a threshold signal-to-noise response signal value is attained, as actioned through the controller116. For example, if a programmable threshold pixel intensity value for a back-scattered electron (BSE) object response detector is achieved prior to dwell time programmed for that pixel element; the dwell time will truncate for that pixel through the action of the controller116, and in the process reduce overall sampling time.

The controller116regulates the sequenced timing and distributes the coordinated output signals to the compound signal converter110, which includes a primary carrier signal converter112and secondary modulating signal converter114. While the scanning probe instrument is functioning under nominal operating conditions, the sparse sampling system108conveys output signals from the primary carrier signal converter112and secondary modulating signal converter114to the scan inputs106(e.g., external scan inputs, scan amplifiers circuits or deflection coil circuits of a scanning electron microscope) of the scanning probe instrument104. In one embodiment, the sparse sample system108is an integrated component of the analytical instrument and functions as the primary pattern generator for the scanning probe instrument104. In another embodiment, the sparse sample system108interfaces scan inputs106which are external scan inputs provided by the scanning probe instrument manufacturer. For example, it is common for external scan control inputs to be provided for external scan control on scanning electron microscopes and scanning transmission electron microscopes, as well as other scanning probe instruments for use by third-party pattern generators.

The sequential probe position coordinates are controlled by the sparse sampling system output signals conveyed through the scan inputs106signal interface to position the scanning probe instrument104probe. If the scanning probe instrument104probe is a fixed type, the scan inputs106actions the X-Y or X-Y-Z stage driver interface (not shown) to position the object scan coordinate proximal to the probe. At each scanning probe coordinate the probe induces a response from the object102, e.g., secondary electrons in the case of a scanning electron microscope or an interactive force in the case of an atomic force microscope, over the duration of the dwell time. The induced object response signal at each scan probe coordinate is concurrently sensed by the object response detector126over the duration of the dwell time. The signal stream induced at each scan coordinate position is concurrently conveyed through to the object response signal converter122to the controller116, which correlates the scan probe position signal with the object response signal over the duration of the dwell time. In one embodiment the object response signal converter122signal stream is conveyed in data packets into a memory buffer included in controller116. Controller116conveys an ordered set of data from object response signal converter122to an image reconstruction system120, to reconstruct an amalgamate representation of the sparsely sampled object102.

In one embodiment of the image reconstruction system120, the amalgamate representation of the sparsely sampled object102being sensed may be reconstructed from the object response signal converter122pattern collected through an appropriate object response detector126, using inpainting reconstruction methods. A particular embodiment of an inpainting reconstruction method may be beta process factor analysis (BPFA). In one embodiment of the image reconstruction system120, the amalgamate representation of the sparsely sampled object102being sensed is reconstructed from the object response signal converter pattern collected through an appropriate object response detector using a down sampling method. One embodiment of the down sampling reconstruction method seeks the pixel element nearest to the missing pixel element and assigns the identical value of the nearest element to the missing pixel element. Another particular embodiment of down sampling method to reconstruct the amalgamate representation of the object response signal defines a block of N nearest neighbor pixels (i.e., a block of surrounding pixels where N=8) and, while ignoring the empty pixels in that block, determines the average value of a (??) missing pixel. In another embodiment of the sparse sampling approach disclosed herein, the amalgamate representation of the sensed object is reconstructed from the sparse sampling pattern using methods based upon a Fourier sparse domain.

Examples of how the sparse sampling is carried out are provided below in connection withFIGS.2-9.FIG.2is a graphical representation of one embodiment of a sparse sampling primary carrier signal path produced by sparse sampling pattern generator119. Representation200is scaled for visualization purposes. Scan boundary202encompasses discrete probe position elements defined by grid pattern204. A positional grid pattern in practice may exceed sixty-four million elements. Scan boundary202depicts a square rectilinear boundary but scan boundary202could also encompass a quadrilateral or non-rectilinear boundary. The primary carrier signal path206shown represents a contiguous Hilbert style space-filling curve. Circular markers208overlaid on the primary carrier signal path206represent discrete primary carrier signal values programmatically defined along the path206which act as referential values for the corresponding secondary modulating signal values. In sparse sampling system100, the carrier signal patterns may be constructed from other topological space-filling curves which include, but are not limited to: Hilbert curves, Peano curves, Moore curves, Sierpenski curves, Lissajous curves, and variants thereof.

FIG.3is a graphical representation300of a primary carrier signal path306identical to path206represented inFIG.2, now represented as a dotted line, with the additional representation of a randomized secondary modulating signal path308(solid line). The vertices of each solid line segment308shown inFIG.3represent the X-Y coordinate of a discrete sparse sampling element within an element of the sampling array, as defined by the grid304. It should be noted that the dotted line associated with carrier signal path306and the solid line segments associated with modulating signal path308are virtual expressions for visualization purposes. The set of coordinates identified by the marker type310define the set of sparse sampling coordinates located within elements of grid304. The total number of grid elements defined by grid304determine the size of the array (e.g., 1024×1024, 2048×2048, 4096×4096, 8192×8192) and the corresponding step size expressed in terms of signal amplitude or a resolution spacing.

FIG.4is graphical representation400of one embodiment of discrete sparse sampling coordinates and represented by the circular markers410with scan boundary402and scan grid array404. The collection of points410represent the aggregate sum of the primary carrier path206inFIG.2and the randomized secondary modulating signal path308inFIG.3. Each circular marker410inFIG.4represents a sparse sampling element with programmable dwell time. By choosing a different random seed, or by choosing a different randomizing algorithm, the same primary carrier signal path (e.g., Hilbert style space-filling path inFIG.2) can produce a different set of sparse sampling coordinates with the same, or different, degree of sparsity. The degree of sparsity may be regulated from 0% to greater than 99% in fractional percent sparsity increments through the approach of this disclosure. The distribution of work conveyed to the scanning probe through the action of a primary carrier signal path relative to a secondary modulating pattern may be regulated by adjusting the scale of the primary carrier pattern, in conjunction with the maximum signal amplitude permitted by the secondary modulating signal. For example, in one embodiment of sparse sampling system108, the primary carrier signal has a signal amplitude of ±10V while the maximum amplitude of the secondary modulating signal is ±3 mV. In this embodiment, the secondary modulating signal may deviate up to ±3 mV relative to the concurrent position of the primary carrier signal to which it is referenced. If the maximum permitted secondary modulating signal is ±0.5V, then the secondary modulating signal can contribute a larger fraction of the work to construct the same sparse sampling pattern. The signal amplitude voltage corresponds to a physical deflection on the scanning probe instrument104, a motion of the stage, or both. Varying the maximum secondary modulating signal amplitude, as referenced to the primary carrier signal, and regulating the maximum rate of change of both the primary carrier and secondary modulating signals, allows the sampling rate of the sparse sampling scanning probe system100to be varied to mitigate scanning artifacts including, but not limited to slew, distortion and hysteresis.

A large number of variants are possible in the design of a suitable primary carrier signal path.FIG.5is graphical representation500, of a smoothed Hilbert style space-filling curve path502, superimposed upon unsmoothed Hilbert style space-filling curve path504. The smoothing operation on the smoothed Hilbert style space-filling curve path502represents one variant of a previously described topological curve which may be employed in the embodiments of sparse sampling system108. In one embodiment of the sparse sampling system108, the sparse sampling pattern generator119may be programmed to construct primary carrier patterns which are subsequently smoothed or otherwise modified versions of topological curves and space-filling curves constituting all or part of the primary carrier signals conveyed through to the scanning probe instrument scan inputs106in order to regulate the resulting rate of change of the X-Y or X-Y-Z pattern. Regulating the rate-of-change of the primary carrier pattern is one means to mitigate scanning artifacts such as, but not limited to slew, distortion and hysteresis.

An embodiment of the sparse sampling system108utilizes sparse sample pattern generator119to implement a signal pattern which contains regions of interest (ROIs) with varying sparsity and/or scan grid spacing within a scan boundary.FIG.6is graphical representation600including a scan boundary602encompassing a primary carrier signal path604and a ROI606containing a primary carrier signal path608which is scaled relative to primary carrier path604. ROI606could represent a region related to geometric boundaries wherein a different sample sparsity was desired and/or a different scan grid spacing was desired (e.g., higher pixel density within ROI606). A plurality of ROIs may exist within one scan boundary602. Graphical representation600depicts ROI606as enclosing a primary carrier signal path608constructed using a non-uniformly scaled version of primary carrier signal path604, as a simplified visualization. However, primary carrier signal path608could be constructed from any suitable type of carrier signal path.

FIG.7is a graphical representation700consisting of X-Y sparse sampling embodiment including scan boundary702, serpentine style primary carrier signal path704and a set of randomized sparse sample points defined by the set of plot marker type706. Graphical representation700is useful to illustrate basic features common to the sparse sampling system108. In this example, primary carrier signal path704initiates from location708, transverses along primary carrier signal path704and completes at location710. X-Y coordinate712represents an arbitrary coordinate along the primary carrier signal path704. The area within circular boundary716represents the maximum amplitude of the X-Y secondary modulating signal (not shown), which is referenced to the primary carrier X-Y coordinate712located at the geometric center of circular boundary716along primary carrier signal path704. Sparse sample coordinates may be randomly created within any element of sample grid714located within circular boundary716. The current graphical representation700consists of a two-dimensional X-Y sparse sampling embodiment and therefore, the sparse sampling system108allows two degrees of freedom in defining the possible sparse sample locations within circular area714. Given a three-dimensional X-Y-Z embodiment of the sparse sampling system108, the analogous representation of the two-dimensional circular area714would be a three-dimensional sphere (not shown). In the case of a three-dimensional X-Y-Z embodiment of sparse sampling system108, there are three degrees of freedom in defining the random sparse sampling scan coordinate location. The degrees of freedom afforded by the sparse sampling system108to define sparse sampling coordinates is a significant distinction, as compared to other proposed spare sampling systems.

Further, graphical representation700serves to illustrate that an embodiment of sparse sampling system108operates given an initial set sparse sample coordinates, such as the set of randomized sparse sample points defined by the set of coordinates coincident with marker type706. In an embodiment wherein sparse sampling coordinates are given initially, the sparse sampling pattern generator119constructs primary carrier signal path704and secondary modulating pattern to fit the a-priori set of sparse sampling coordinates.

An identical set of sparse sample coordinates coincident with the set of plot marker type706in graphical representation700may be generated by sparse sampling system108using a variety of primary carrier signal paths. In one embodiment of the sparse sampling system108, a Hilbert style primary carrier signal path is used to generate an identical set sparse sample coordinate coincident with the set of plot marker type706in graphical representation700produced using serpentine primary carrier signal path704. Another very simple alternative primary carrier signal carrier embodiment to produce an identical set of sparse sample coordinates coincident with the set of plot marker type706in graphical representation700is represented by a clockwise or counter clockwise ninety-degree rotation of primary carrier signal path704.

A purpose to invoke a specific primary carrier signal path satisfying a given set of sparse sampling coordinates includes, but is not limited to, mitigation of scanning artifacts related to sample charging, where object102is either insulative or semi-conducting. Both the primary carrier signal path and the degree of sparsity influence sample charging in a charged particle scanning probe instrument and may be tuned using sparse sampling system108.

One embodiment of sparse sampling system108utilizes carrier signal paths created from a sequential set list of X-Y or X-Y-Z coordinates, including a set of X-Y or X-Y-Z coordinates generated by parametric equations.FIG.8is graphical representation800of a continuous X-Y parametric equation to generate primary carrier signal path802. Over-scan boundary804encompasses the entire scan area, and object scan boundary806(dotted line) represents a sub-region of the primary carrier signal path802. It is common practice for pattern generators employed in scanning probe instruments to incorporate an over-scan region defined by the area between the over-scan boundary804and the object scan boundary806, the purpose of which is to exclude regions where the scan pattern may be non-ideal for reasons including, but not limited to, non-linear scan behavior and non-uniform area coverage. The region within the object scan boundary806represents a region of higher uniformity relative to the region between the over-scan boundary804and the object scan boundary806. The primary carrier signal path802in representation800initiates at X-Y coordinate808, follows continuous primary carrier signal path802and terminates at X-Y coordinate810. A particular X-Y parametric equation embodiment to generate space-filling carrier signal path802is a smoothed form of the parametric equation Equation 1:

where, Axand Aydefine the maximum signal amplitudes for X and Y dimensions respectively. The vertical brackets indicate the absolute value of the quantity enclosed. Variable t, is a time increment parameter, a is the X frequency of the primary carrier signal, b is the Y frequency of the primary carrier signal and floor is a mathematical function which takes as input a real number R, and gives as output the greatest integer less than or equal to R. A large family of X-Y and X-Y-Z parametric equations may be utilized by sparse sampling system108in order to produce suitable primary carrier signal paths. Lissajous curves represent yet another particular common family of parametric curves which can be explored as primary carrier signal paths.

In an embodiment of sparse sampling system108employing a continuous space-filling type path, beam blanking may not be required along the scan path, or along parts of the scan path. Beam blanking is a common element in charged particle systems which provides a means to extinguish, or “blank”, the probe interaction with the object. Typically, in charged particle instruments a beam blanking component may include electrostatic deflection plates near the top of the column proximal to a crossover position in the optical path. Action of the beam blanking deflects the probe (beam) into a position which prevents the probe (beam) from transmitting through the optical path to interact with the object. High-speed beam blanking elements are typical options available in a charged particle embodiment of scanning probe instrument104which allow more rapid beam blanking, corresponding to higher resolution definition of the dwell time at each scan coordinate. In another embodiment of sparse sampling system108employing one or more discrete or continuous primary carrier signal paths, beam blanking may be utilized as desired to mitigate scan artifacts and spurious probe interactions with object102.

A large variety of suitable space-filling carrier signals may be utilized by sparse sampling system108. Carrier signal patterns may be programmed to generate any combination of: a continuous and non-overlapping pattern; a continuous and non-intersecting pattern; a continuous and intersecting pattern; or a continuous and overlapping pattern. Sparse sampling system108may utilize carrier signal patterns programmed as discrete segments with arbitrary discontinuity. For example, this approach could be applied to trace and/or fill a plurality of separate, geometric regions or spatial features of the object being sensed. A particular example is a carrier signal path and referenced modulating signal path designed to produce a set of sparse sampling coordinates which trace the path incorporating a neuron in a biological matrix. Similarly, a rectangular, triangular, circular or other geometric pattern on the object being sensed could represent the sparsely sampled domain.

Sparse sampling system108may utilize carrier signal patterns constructed from analytical space-filling curves programmatically modified to adjust the aggregate sparse sampling pattern, and/or the performance of the pattern generator, and/or the interaction with the scanning analytical system. For example, the transmitted carrier signal patterns and referenced secondary modulating signal patterns may be smoothed by software mathematically or by hardware to limit the rate-of-change of the signals in order to not exceed the performance limitations of the scanning probe system in order to avoid scanning artifacts.

FIG.9is diagrammatic illustration900of a dual column scanning probe instrument in which at least some of the embodiments of the disclosure may be included. Scanning electron beam column902and focused ion beam column904are oriented such that a coincidence region exists between the scan areas of electron beam946and ion beam948. Object944surface area is depicted as orthogonal to ion beam948. In one embodiment, object944is affixed to a moveable stage (not shown) that allows X-Y-Z as well as rotation and tilt stage motion with range sufficient to orient object944surface area orthogonal to electron beam946or ion beam948. The scanning electron beam column902depicted includes an electron source906, extraction electrode908, anode910, electromagnetic collimating lens system912, spray aperture914, in-lens object response signal detector916, electromagnetic lens coil body918, outer pole piece920, inner pole piece922, electrostatic objective lens electrodes924and928, and scanning probe coils926. The focused ion column904includes an ion source930, extraction electrode932, condenser lens934, variable aperture936, electrostatic deflection electrodes938and940, and objective lens942.

One embodiment of the sparse sampling system108ofFIG.1is configured with at least two pair of X-Y compound signal converters110to simultaneously drive the scan coils926of scanning electron column902and scan deflection electrodes938and940of focused ion column904. One embodiment of the sparse sampling system108includes an object response detector126configured as a secondary ion detector and an object response detector126configured as a backscatter electron detector which operate simultaneously and concurrently with sparse sampling system108. Additional object response detectors126in dual column scanning probe instrument900may include, but not be limited to, in-lens secondary electron detectors, in-chamber secondary electron detectors, in-chamber backscatter detectors, secondary ion conversion detectors, fluorescence detectors, x-ray detectors, time-of-flight secondary ion mass spectrometers, electrostatic-electromagnetic mass spectrometers, and quadrupole mass spectrometers.

In one embodiment of the sparse sampling system108, a plurality of X-Y discrete layers or thin sections of the object being probed are sparsely sampled. The sparse sampling positions from each layer are programmatically randomized to produce a sparse sampling volume randomized in three dimensions, X-Y-Z. For example, sparse sampling system108drives the scan deflection electrodes938and940to produce an ion milling process by focused ion column904to expose a fresh object944surface layer (e.g., also could be termed a slice or section defined by the interaction volume of the probe and object). Sparse sampling system108drives electron beam column902concurrent with, or subsequent to, the ion milling process to acquire a sparse sampling amalgamate representation of the fresh object944surface region using one or more object response detectors126and wherein each sparse sampling X-Y scan has a unique randomized sparse sampling pattern. The process of using sparse sampling system108to generate a fresh surface with ion beam column904and acquire a sparse sampling with electron beam column902is repeated to generate a stack of X-Y amalgamate representations produced by image reconstruction system120. In this embodiment, the sparse sampling is extended from two dimensions into three dimensions and the maximum percentage of sparsity allowed for successful image reconstruction system120is much higher than the maximum sparsity allowed for a corresponding two-dimensional individual layer. For example, if 90% sparsity is the maximum sparsity which produces an acceptable amalgamate representation using image reconstruction system120for each individual X-Y scan layer; 97% or greater sparsity may produce an acceptable amalgamate representation using image reconstruction system120from the same X-Y scan layers when processed as a randomized three-dimensional X-Y-Z stack. Each depth layer signal pattern includes a programmatically unique randomized X-Y sparse sampling pattern in order to optimize the sparse sampling processed by image reconstruction system120as X-Y-Z layer stack to yield an amalgamate reconstruction with higher sparsity than can be obtained from each layer individually.

In one embodiment of sparse sampling system108, the sparse sampling operation may be repeated successively over the same area using either an identical sparse sampling pattern generated from119for each successive scan, or using a uniquely randomized pattern generated from119for each successive scan pattern, or any combination thereof. This embodiment is utilized, for example, to acquire successive X-Y scans during continuous or semi-continuous sensing of the object102being sparsely sampled.

In one particular embodiment of sparse sampling system108, the entire sparse sampling process from sparse sampling pattern generator119through to image reconstruction system120operates successively and repeatedly as rapidly as combined systems permit. Alternatively, the entire sparse sampling system108operates with discrete time delay. Highest possible operation rate of sparse sampling system108, or discrete delay operation of sparse sampling system108, may be used to continuously, or semi-continuously, observe the object102while it is being sparsely sampled. Observations of the object102being sparsely sampled may include, but not be limited to, changes due to mechanical movement of all or part of the object being sensed (e.g., a clockwork or gear motion), modifications induced through the action of a separate probe (e.g., micromanipulator, laser ablation, focused ion beam, or broad beam ion milling), changes induced by an energy source (e.g., heating, cooling), changes due to chemical interaction with all or part of the object being sensed, or any combination thereof. The benefits of sparse sampling observation of object102during such changes include reduced sensing probe interactions with the object102being sensed (e.g., reduced electron dose, reduced sample charging), and increased object response detector126signal acquisition rate during near real-time observation.

Successive object response signal detector126patterns conveyed through the object response signal converter(s)122during sparse sampling observation of object102are utilized in one embodiment of sparse sampling system108to reconstruct amalgamate representations through image reconstruction system120to provide a record of change over the observation period. For example, image reconstructions resulting from observations while object102is ion milled or mechanically deformed form a three-dimensional volumetric representation from a stack of reconstructed X-Y amalgamate representations. Alternatively, image reconstruction system120may produce a single X-Y-Z volumetric amalgamate representation from either the entire three-dimensional sparse data array, or from one or more three-dimensional array sparse data blocks consisting of subsets of the entire sparse data array. An example embodiment is a tomographic reconstruction of a volume based upon a three-dimensional array of sparse sample data wherein the object response detector126is a back-scattered electron detector used to acquire sparse sample object response signal converter122data obtained from either sequential focused ion beam milling, or during concurrent focused ion beam milling, to generate volumetric object102response signal image data.

In one embodiment of sparse sampling system108, the sparse sampling percentage is adapted to reflect changes in the object102geometry or material property during observation.

One embodiment of the sparse sampling system108utilizes a carrier signal path, a referenced set of modulating signal coordinates and a degree sparsity to suit analytical objectives based upon data from the object response detector126signals induced from object102being sparsely sensed. Analytical objectives may include, but not be limited to, the response signal intensity (e.g., adjusting dwell time) and/or the response signal spatial resolution (e.g., adjusting sparsity).

In one embodiment of the sparse sampling system108, encoding and indexing of the ADC signal data synchronized through the programmable logic controller may be compressed relative to the full sample signal data to save significant digital storage memory by storing data in an ordered list, rather than as an object array.

In one embodiment of the sparse sampling system108, object response signal converter122signals conveyed by the object response detector126signals induced from the object102being sparsely sensed is used to compute a fast Fourier transform (FFT) from the amalgamate representation from the image reconstruction system120. In a further embodiment of the sparse sampling system108, the FFT computed from the amalgamate representation is utilized in an automated focus and/or an automated astigmatism correction method.

One embodiment of sparse sampling system108produces X-Y scan patterns driving the scan deflection electrodes938and940of focused ion beam column904with a sparsity corresponding to an ion dose at or below the static Secondary Ion Mass Spectroscopy limit.

In one embodiment of the sparse sampling system108, sparse sampling pattern generator119incorporates scan distortion corrections to correct scan distortion errors intrinsic to both the scanning probe instrument and the sparse sampling system108. Scan distortion errors resulting from both the scanning probe instrument and the sparse sampling system108are measured using suitable geometric reference standards. Measured scan distortion error corrections are mapped back to sparse sampling pattern generator119to generate signal patterns with minimal scan distortion. Scan distortion errors exhibited by a particular scanning probe instrument104and sparse sampling system119may be compensated in this manner such that corrected scans are output by the sampling scan pattern generator119. A-priori distortion correction as described obviates post-process correction of reconstructed amalgamate representations of object102.

An embodiment of sparse sampling system108includes a point spread function deconvolution (PSFD) operation as part of image reconstruction system120to combinate sparse sampling reconstruction and PSFD. In this embodiment the spatial resolution of the amalgamate representation is improved by inclusion of the PSFD operation and wherein the PSF is a measured or theoretical function corresponding to scanning probe instrument102.