Patent Publication Number: US-2022236549-A1

Title: Phase-sensitive single molecule localization microscopy

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of and priority to U.S. Provisional App. No. 63/141,166 filed Jan. 25, 2021. The 63/141,166 provisional application is incorporated herein by reference. 
    
    
     FIELD 
     The present disclosure generally relates to phase-sensitive single molecule localization microscopy. 
     BACKGROUND 
     Unless otherwise indicated herein, the materials described herein are not prior art to the claims in the present application and are not admitted to be prior art by inclusion in this section. 
     Imaging molecular compounds may be facilitated by fluorescence microscopy in which radiation is directed towards a compound of interest, and light emitted by the compound of interest in response to absorbing the radiation, called fluorescent emissions, is observed. Fluorescence microscopy may be helpful for imaging biochemical compounds for applications such as basic research to clinical diagnoses. Some biochemical compounds may exhibit unique fluorescent emissions such that the biochemical compounds may be identified based on their fluorescent behavior. 
     The subject matter claimed in the present disclosure is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one example technology area where some embodiments described in the present disclosure may be practiced. 
     SUMMARY 
     In an example embodiment, a method includes obtaining radiation emitted from a radiation source. The method includes modulating the radiation with a time-varying modulation to generate a time-varying illumination pattern with a known modulation. The illumination pattern includes a time-varying intensity for each of a plurality of spatial locations. The method includes illuminating a target volume with the illumination pattern. The method includes collecting a signal generated by one or more objects within the target volume in response to illumination by the illumination pattern. The method includes estimating a location of each of the one or more objects based on the collected signal and the known modulation. 
     In another example embodiment, a microscopy system includes a radiation source, one or more modulation masks, a sample, one or more photodetectors, and a computing system. The radiation source is configured to emit radiation. The modulation mask is positioned to receive radiation from the radiation source and is configured to modulate the radiation with a time-varying modulation to generate a time-varying illumination pattern with a known modulation. The illumination pattern includes a time-varying intensity for each of a plurality of spatial locations. The sample includes one or more objects in a target volume, such as on a sample slide, and is positioned to receive the time-varying illumination pattern. The photodetector(s) are positioned and configured to collect a signal generated by the objects within the target volume in response to illumination by the illumination pattern. The computing system is coupled to the photodetector(s) and is configured to estimate a location of each of the objects based on the collected signal and the known modulation. 
     Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The features and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. These and other features of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Example embodiments will be described and explained with additional specificity and detail through the accompanying drawings in which: 
         FIG. 1  is a diagram of an example embodiment of a microscope configured for three-dimensional imaging and localization of optically interactive objects using a large quasi-plane wave illumination according to at least one embodiment of the present disclosure. 
         FIG. 2  illustrates a depth of field (DOF) comparison of the DOF generated via a tight focus process and the large quasi-plane wave illumination process according to at least one embodiment of the present disclosure. 
         FIG. 3A  illustrates a first illumination pattern generated at a first time point. 
         FIG. 3B  illustrates a second illumination pattern generated at a second time point. 
         FIG. 3C  illustrates examples of temporal illumination intensity patterns emitted by axially separated fluorophores. 
         FIG. 3D  illustrates a sum of the temporal illumination intensity patterns and a photocurrent signal that contains information identifying positions of the fluorophores based on the summation of the temporal illumination intensity patterns. 
         FIG. 4  is a flowchart of an example method of imaging and localizing molecules using a CHIRPT process according to at least one embodiment of the present disclosure. 
         FIG. 5  illustrates a block diagram of an example computing system that may be used to perform or direct performance of one or more operations described according to at least one implementation of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Existing optical imaging techniques may be capable of resolving spatial features of a sample being imaged. The resolutions achievable by these existing optical imaging techniques may be limited by light diffraction wavelengths, which are defined by the optical wavelength of light in the transverse direction of light propagation. As such, existing optical imaging techniques may resolve spatial features at a spatial resolution limit of approximately 300 nanometers (nm). 
     Super-resolution imaging processes may exceed the light diffraction limits of the above-described existing optical imaging techniques using techniques such as multiplexing spatial-frequency bands, probing near-field electromagnetic disturbances, and/or encoding spatial-frequency details using multiple polarization states. Some examples of super-resolution imaging processes may include photoactivated localization microscopy, stochastic optical reconstruction microscopy, stimulated emission depletion microscopy, and structured illumination microscopy. By exceeding the light diffraction limits, super-resolution imaging processes may facilitate research into new mechanisms of signaling pathways and biochemical interactions cells and/or organisms. However, existing super-resolution imaging processes are currently limited in terms of their abilities to provide super-resolution imaging in an axial direction (i.e., the direction in which light is propagating). Such super-resolution imaging processes typically fail to accurately image tissues and other three-dimensional cell cultures because of strong optical scattering, specimen aberrations, limited imaging volumes, and/or other optical limitations. 
     The present disclosure relates to, among other things, a super-resolution imaging approach that facilitates use of super-resolution imaging in three-dimensional cell cultures and other complex biological environments. A microscope may use time-varying illumination patterns and single-pixel detection methods (e.g., using a photodetector) to improve the spatial imaging resolution of sample objects, such as fluorescent molecules. Additionally or alternatively, absorption spectra, linear scattering, and/or non-linear optical scattering associated with the sample objects based on the time-varying illumination patterns may be used to improve spatial imaging resolution of the sample objects. Additionally or alternatively, encoding phase information and implementing a single-pixel detection strategy as described in the present disclosure may reduce the effects of optical aberrations and optical scattering on imaging the sample objects. 
     Using a super-resolution imaging approach as described in the present disclosure may improve spatial and temporal visualization of interactions between small groups of molecular compounds to a scale of approximately 25 to 50 nm and tens of seconds (or even shorter), respectively. For example, mitotic cell division may be imaged at greater spatial and temporal resolutions such that more insight into a wide range of health ailments may be made. More specifically, how kinetochores of mitotic chromosomes attach to spindle microtubules and how these attachments are regulated to prevent chromosome segregation errors and aneuploidy could improve understanding of birth defects and human cancers. As another example, the super-resolution imaging approach of the present disclosure may improve understanding of disease processes by determining how proteins generate attachment sites for spindle microtubules, how the attachment strength to the microtubules is regulated, and/or how the attachment status is relayed to a spindle assembly checkpoint. 
     Reference will now be made to the drawings to describe various aspects of example embodiments of the invention. It is to be understood that the drawings are diagrammatic and schematic representations of such example embodiments, and are not limiting of the present invention, nor are they necessarily drawn to scale. 
       FIG. 1  is a diagram of an example embodiment of a microscopy system  100  configured for three-dimensional imaging and/or localization of one or more sample objects using large quasi-plane wave illumination according to at least one embodiment of the present disclosure. In some embodiments, the microscopy system  100  may use a single molecule localization microscopy (SMLM) approach in which sparse groups of individual fluorophores relating to a sample object included in a target volume are activated by directing radiation towards the fluorophores. Centroids of point-spread functions for each fluorophore may be collected (e.g., by a photodetector), and the centroids may be used to construct an image with a random distribution of excited fluorophores to represent the sample object. 
     The microscopy system  100  may include or be coupled to a radiation source  102  that emits radiation  105  and a lens  110  of a microscope that may direct the emitted radiation  105  towards one or more modulation masks  120  and/or focus or otherwise reshape the emitted radiation  105 . For example, the lens  110  may focus the emitted radiation  105  on the modulation mask(s)  120  In some embodiments, the radiation  105  may be emitted as a single beam, multiple discrete pulses, or as multiple beams of radiation. In these and other embodiments, the radiation  105  may include electromagnetic waves of various wavelengths, such as infrared radiation, visible light, and/or ultraviolet radiation. For example, the radiation source  102  may include an ytterbium fiber laser oscillator that may produce electromagnetic radiation in ultrashort pulses (e.g., 30 femtosecond (fs) pulses) centered at a particular wavelength (e.g., 1060 nm). Additionally or alternatively, the radiation  105  may include high spatial coherence such that the radiation  105  has highly correlated relationships at different points in space along the electromagnetic waves. In some embodiments, a modal decomposition of radiation with high spatial coherence may contain more than twenty-five coherent modes. 
     In some embodiments, the lens  110  may include a cylindrical or a convex shape to focus the radiation  105  such that the radiation  105  is aimed at a particular area on the modulation mask(s)  120 . Additionally or alternatively, the lens  110  may be configured to generate one or more beams of radiation based on the radiation  105 . For example, the radiation  105  aimed at the lens  110  may include a single beam of radiation, and the lens  110  may split the single beam of radiation into two or more beams. Each radiation beam of the multiple beams of radiation directed from the lens  110  towards the modulation mask(s)  120  may include a respective phase, and two or more of the radiation beams may include different phases such that a spatial phase difference exists between the two or more radiation beams. The spatial phase difference between the two or more radiation beams may be encoded into temporal oscillations associated with emitted fluorescence by fluorophores towards which the radiation beams are directed such that spatial phase disruptions occurring during the imaging process, including sample and microscope aberrations, may be isolated and removed during post-processing. In these and other embodiments, the lens  110  may include a single lens as illustrated in  FIG. 1 , or the lens  110  may refer to multiple lenses configured to operate together or separately to focus, redirect, and/or split the radiation  105 . 
     The modulation mask(s)  120  may receive the radiation  105  from the lens  110  and generate a time-varying illumination pattern  125 . The illumination pattern  125  formed after the radiation  105  passes through the modulation mask(s)  120  may be generated based on a modulation pattern printed, etched, or otherwise formed on or by the modulation mask(s)  120 . The modulation mask(s)  120  may generally include a spatial light modulator (SLM), such as a generally circular (or other shape) amplitude transmission grating with varying groove density as a function of angle, a phase mask, a micro-electro-mechanical-system (MEMS) SLM, a digital light processing (DLP) SLM, a liquid display (LCD) SLM, a phase-only liquid crystal on silicon (LCOS) SLM, two or more deformable mirrors, ferroelectric liquid crystal modulators, or any other system or device that can impart a change in amplitude and/or phase of the radiation  105  in the modulation plane. Because the modulation pattern on the modulation mask(s)  120  is known and the illumination pattern  125  is formed in relation to the known modulation pattern, the illumination pattern  125  may include known time-varying illumination intensities at various spatial locations in a target volume of a sample  150 . In some embodiments, the modulation pattern on the modulation mask(s)  120  may be formed as an amplitude transmission grating with a varying groove density as a function of angle. Each radial position on the modulation mask  120  may include changing on-off intensity modulation such that each transverse spatial position on the modulation mask(s)  120  may be tagged with a modulation frequency different from the modulation frequencies tagged at each other transverse spatial position. In at least one embodiment, for example, the modulation mask(s)  120  may include a maximal density of seventy lines per millimeter with an overall magnification of 77 and a numerical aperture (NA) of 1.05. 
     Additionally or alternatively, the illumination pattern  125  may extend over a volume greater than a depth of field (DOF) of camera-based imaging techniques. The illumination pattern  125  may include different features at one or more points in the target volume on the sample  150  such that intensity and phase information may be jointly used to determine locations of isolated fluorescent emitters using a single-element photodetector  160 . In some embodiments, the time-varying intensity of the illumination pattern  125  may be determined according to the following relationship: 
       I(x,y,z,t)∝I 0 (x,y,z,t)+I 1 (x,y,z,t)cos[Δ ϕ (x,y,z,t)]  (1)
 
     in which a background intensity, I 0 (x, y, z, t), and a product of an envelope of illumination intensity that determines a DOF and/or an imaging volume, I 1 (x, y, z, t), and the cosine of the spatial phase difference, Δϕ(x, y, z; t) are summed to determine the time-varying intensity of the illumination pattern  125 . In Equation (1), x, y, and z are three-dimensional coordinates and t is time. 
     In some embodiments, the illumination pattern  125  may be scanned through one or more spatial filters  130  such that a range of spatial frequencies narrower than a numerical aperture of the radiation  105  is obtained to block a diffracted order and break axial symmetry. Alternatively or additionally, the optics and illumination pattern  125  of the microscopy system  100  may obtain a range of spatial frequencies narrower than the numerical aperture of the radiation  105  to block a diffracted order and break axial symmetry. The numerical aperture may represent an entire range of spatial frequencies of the radiation  105 , and scanning any of the spatial frequencies included in the numerical aperture at any time t may increase a DOF of the illumination pattern  125 . In these and other embodiments, spatial frequencies along the entirety of the numerical aperture may be serially scanned through the spatial filter(s)  130  over a period of time by adjusting the radiation  105  passing through the lens  110 , the illumination pattern  125  passing through the modulation mask  120 , a position or orientation of the spatial filter(s)  130 , or some combination thereof. 
       FIG. 2  illustrates a DOF comparison  200  of a first DOF 1    215  generated via a tight focus process  210  and a second DOF 2    226  generated via a partial pupil illumination process  220  at a particular point in time according to at least one embodiment of the present disclosure. The first DOF 1    215  is an example of a tightly focused DOF formed using the tight focus process  210  associated with existing SMLM techniques. The tight focus process  210  may include affecting coherent interference between various illumination beams over a broad range of spatial frequencies. Because the illumination beams are projected at a broad range of spatial frequencies, some of the illumination beams at the highest spatial frequencies may propagate at extreme angles relative to an optic axis. As such, the first DOF 1    215  is generated at a tight focal spot in which all of the spatial frequencies spatially overlap in a small axial range represented by the first DOF 1    215 . 
     In some embodiments, the second DOF 2    226  may be generated via the partial pupil illumination process  220  as described in relation to one or more embodiments of the present disclosure. The second DOF 2    226  may be determined based on an intersection between a first illumination beam  222  and one or more second illumination beams  224 . The first illumination beam  222  and the second illumination beam  224  may have a phase difference between the two or more illumination beams because the two or more illumination beams may cross at an angle, θ i , relative to one another such that the first illumination beam  222  and the other illumination beams  224  are not parallel to each other. 
     In these and other embodiments, a size of the first DOF 1    215  and/or the second DOF 2    226  may be determined based on the following equations: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       f 
                       x 
                     
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       N 
                       ⁢ 
                       A 
                     
                     λ 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     δ 
                     ⁢ 
                     
                       f 
                       x 
                     
                   
                   = 
                   
                     
                       Δ 
                       ⁢ 
                       
                         f 
                         x 
                       
                     
                     N 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     in which δf x  is a differential of spatial frequency in a small pupil plane resulting from spatial frequency excitation, Δf x  is the change in spatial frequency across the pupil plane, NA is a numerical aperture, λ is a wavelength of radiation illuminating the pupil plane, and N is a large integer, such as 1,000). 
     Assuming a Gaussian model, a spatial frequency distribution may be approximated as: 
     
       
         
           
             
               
                 
                   
                     e 
                     
                       - 
                       
                         
                           ( 
                           
                             
                               f 
                               x 
                             
                             
                               δ 
                               ⁢ 
                               
                                 f 
                                 x 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
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                           ( 
                           
                             π 
                             ⁢ 
                             
                               w 
                               o 
                             
                             ⁢ 
                             
                               f 
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                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     in which w 0  is approximated as: 
     
       
         
           
             
               
                 
                   
                     w 
                     0 
                   
                   ≈ 
                   
                     1 
                     
                       π 
                       ⁢ 
                       δ 
                       ⁢ 
                       
                         f 
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     such that a spatial Gaussian intensity is proportional to: 
     
       
         
           
             
               
                 
                   e 
                   
                     
                       - 
                       2 
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           P 
                           
                             w 
                             ⁡ 
                             ( 
                             z 
                             ) 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     in which: 
     
       
         
           
             
               
                 
                   
                     w 
                     ⁡ 
                     ( 
                     z 
                     ) 
                   
                   = 
                   
                     
                       w 
                       0 
                     
                     ⁢ 
                     
                       
                         1 
                         + 
                         
                           
                             ( 
                             
                               Z 
                               
                                 Z 
                                 R 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Based on Equations (2)-(7), the DOF may be computed according to the following equations: 
     
       
         
           
             
               
                 
                   
                     Z 
                     R 
                   
                   = 
                   
                     
                       
                         π 
                         ⁢ 
                         
                           w 
                           
                             0 
                             2 
                           
                         
                       
                       λ 
                     
                     = 
                     
                       
                         
                           π 
                           λ 
                         
                         ⁢ 
                         
                           
                             ( 
                             
                               1 
                               
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                                 ⁢ 
                                 δ 
                                 ⁢ 
                                 
                                   f 
                                   x 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       = 
                       
                         
                           
                             1 
                             
                               π 
                               ⁢ 
                               λ 
                             
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 N 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                     f 
                                     x 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         = 
                         
                           
                             
                               1 
                               
                                 δ 
                                 ⁢ 
                                 π 
                               
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   
                                     λ 
                                     ⁢ 
                                     N 
                                   
                                   
                                     N 
                                     ⁢ 
                                     A 
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                           = 
                           
                             
                               λ 
                               
                                 4 
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                                 π 
                               
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   N 
                                   
                                     N 
                                     ⁢ 
                                     A 
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   DOF 
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                         z 
                         R 
                       
                     
                     = 
                     
                       
                         λ 
                         
                           2 
                           ⁢ 
                           π 
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             N 
                             
                               N 
                               ⁢ 
                               A 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     As an example, suppose A is 1 micrometer, N is 1,000, and NA is 0.75. In this example, the DOF calculated according to equation (9) is (8/(9π))×10 6  micrometers. 
     Returning to the description of  FIG. 1 , the radiation  105  having the illumination pattern  125  may be passed through a first aperture  142  such that the radiation  105  illuminates the target volume of the sample  150 . Within the target volume on the sample  150 , a sample including one or more objects to be imaged may be illuminated by the radiation  105 . Each of the objects may generate a signal  155  in response to being illuminated by the radiation  105 , and the signals  155  may be directed through a second aperture  144  towards one or more photodetectors  160 . In some embodiments, each of the signals  155  may be generated based on the illumination pattern  125  shone on the target volume of the sample  150  and properties or characteristics of the object being illuminated. By leveraging the illumination pattern  125  modeled according to Equation (1), a precisely known modulation pattern may be applied to the sample  150 , and the time-varying illumination pattern  125  may be matched or correlated with the time-varying fluorescent emissions of signals  155  produced in the sample  150 . In some embodiments, the photodetector(s)  160  and/or other components of the microscopy system  100  may be coupled to a computing system  170  that in some embodiments may be part of the microscopy system  100 . The computing system  170  may perform the matching, correlating, or other processing of, e.g., the output of the photodetector(s)  160  and/or three-dimensional localization of objects in the target volume of the sample  150  based thereon. In general, the computing system  170  may include one or more processors to perform or control performance of one or more of the operations described herein. 
       FIGS. 3A-3D  illustrate examples of spatiotemporally modulated illumination intensities output by a microscopy system  300  via the partial pupil illumination process and corresponding emission intensity patterns and photocurrent signal according to at least one embodiment of the present disclosure. For example,  FIG. 3A  illustrates a first illumination pattern  310  generated at a first time point (i.e., where a spatial filter is positioned and angled at a first orientation), and  FIG. 3B  illustrates a second illumination pattern  320  generated at a second time point (i.e., where the spatial filter is positioned and angled at a second orientation). As illustrated, a first crossing angle, θ(t 1 ), at the first time point, t 1 , and a second crossing angle, θ(t 2 ), at the second time point, t 2 , between the crossing radiation beams may be different because at least one of the radiation beams (e.g., k 1 (t 1 ) at the first time point versus k 1 (t 2 ) at the second time point) may be directed in different directions. There may be many beam crossing angles in some embodiments. 
     Radiation having the first illumination pattern  310 , the second illumination pattern  320 , and any other illumination patterns may be used to illuminate an object. Light emitted by the object in response to being illuminated by the radiation may include temporal illumination intensity patterns that correspond to the illumination patterns of the radiation at the location of the object.  FIG. 3C  illustrates examples of temporal illumination intensity patterns emitted by axially separated fluorophores. A first temporal illumination intensity pattern  332 , β 1 (t), may represent an emission intensity pattern located at a negative z-coordinate (e.g., Δz&lt;0). A second temporal illumination intensity pattern  334 , β 2 (t), may represent an emission intensity pattern located along the z-axis (e.g., Δz=0), and a third temporal illumination intensity pattern  336 , β 3 (t), may represent an emission intensity pattern located at a positive z-coordinate (e.g., Δz&gt;0). As shown in  FIG. 3D , one or more photodetectors  340  may sum the temporal illumination intensity patterns  332 ,  334 ,  336  to generate one or more photocurrent signals  345  that contain information identifying positions of the fluorophores or other object(s) in the sample (based on their induced optical signals, e.g., fluorescence, absorption, or coherent linear or nonlinear scattering signals) that generated the temporal illumination intensity patterns  332 ,  334 ,  336 . In some embodiments, temporal phenomena associated with the fluorophores or other object(s), such as photobleaching and/or blinking, may be observed based on the photocurrent signal(s)  345 . 
     With combined reference to  FIGS. 1 and 3A-3D , the photodetector(s)  160  may be configured to collect the signals  155  at each spatial point in the target volume such that a location of each of the objects may be estimated, e.g., by the computing system  170 , based on the collected signals  155 , or more particularly, based on a photocurrent signal output by each of the photodetector(s)  160  that is representative of the collected signals  155 , and the known modulation pattern that is associated with generation of the signals  155 . As an example, the photocurrent signal output by the photodetector(s)  160  may include the photocurrent signal(s)  345 . The signals  155  generated by the objects may be collected by the photodetector(s)  160  from each spatial point included in the target volume at which the objects are located in a forward or a backward direction. The photodetector(s)  160  may collect light signals that correspond to the illumination pattern  125  from spatial points at which no objects are located in the target volume. In some embodiments, estimating the locations of fluorophores or other objects based on the signals  155  (or more particularly, the photocurrent signal output by the photodetector(s)  160 ) by the computing system  170  may be achieved using a least-squares error (LSE), a maximum likelihood estimation (MLE) optimization strategy, and/or other optimization approach(es). A modeled photocurrent signal for a single example fluorophore of infinitesimal extent may be computed using a Dirac-δ distribution, S δ (t; θ), in which θ={a p , x p , z p } is a parameter vector, a p  is a brightness of the fluorophore, and (x p , z p ) is a location of the fluorophore. The parameter vector θ may be estimated by minimizing an appropriate function using, for example, the Nelder-mead simplex algorithm, or other estimation algorithm. Using a LSE approach, a L 2 -norm of the difference between the measured signal  155  and the Dirac-δ distribution is minimized, and for a MLE approach, a negative log-likelihood function is minimized such that an illumination temporal pattern that is matched to the target object is used to estimate the location of the target object. 
     In some embodiments, aberrations associated with the objects being imaged on the sample  150  and/or with the microscopy system  100  itself may be identified and corrected in a post-processing step. Because spatial phase differences between two or more illumination beams are encoded in the illumination pattern  125 , characteristics relating to spatial phase disruptions (i.e., aberrations), such as pupil phases, systematic misalignment of the microscopy system  100 , and/or specimen aberrations on the sample  150  may inherently be included in the illumination pattern  125 . Some aberrations may be corrected before any signals  155  are collected from the sample  150 , such as adjustment of a correction collar of the objective lens or other aberrations related to the microscopy system  100 . However, specimen aberrations may or may not be known before imaging of the objects included on the sample  150 . In these and other embodiments, post-processing in the CHIRPT process may include extraction of an aberration phase in a local environment of each fluorophore and adding the extracted aberration phases to the illumination pattern  125 . Based on the updated CHIRPT illumination pattern, the locations of the objects may be re-estimated such that the specimen aberrations are accounted for. 
     In some embodiments, deep learning or other machine learning methods may be implemented, e.g., by the computing system  170 , to form initial estimates of locations of multiple objects. The deep learning methods may facilitate handling large numbers of fluorophores or other objects simultaneously. While forming an initial estimate of a single isolated fluorophore or other object may be relatively simple, providing initial estimates of the locations of multiple fluorophores or other objects simultaneously may be difficult due to interference between various fluorophores or other objects caused by holographic-like behavior of the microscopy system  100 . In these and other embodiments, implementing a deep learning method, such as a generative adversarial network, to make these initial location estimates and seed locations for an iterative location estimation approach may improve the accuracy and/or efficiency of simultaneous object location estimations. 
     Modifications, additions, or omissions may be made to the microscopy system  100  without departing from the scope of the present disclosure. For example, the designations of different elements in the manner described is meant to help explain concepts described herein and is not limiting. For instance, in some embodiments, the lens  110 , modulation mask(s)  120 , spatial filter(s)  130 , first aperture  142 , sample  150 , second aperture  144 , photodetector(s)  160 , and computing system  170  are delineated in the specific manner described to help with explaining concepts described herein but such delineation is not meant to be limiting. Further, the microscopy system  100  may include any number of other elements or may be implemented within other systems or contexts than those described. 
       FIG. 4  is a flowchart of an example method  400  of imaging and localizing molecules using a three-dimensional imaging and/or localization of one or more sample objects using large quasi-plane wave illumination process according to at least one embodiment of the present disclosure. The method  400  may be performed by any suitable system, apparatus, or device. For example, the lens  110 , the modulation mask(s)  120 , the spatial filter(s)  130 , the first aperture  142 , the sample  150 , the second aperture  144 , the photodetector(s)  160 , and/or the computing system  170  may perform or control performance of one or more operations associated with the method  400 . Although illustrated with discrete blocks, the steps and operations associated with one or more of the blocks of the method  400  may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the particular implementation. 
     The method  400  may begin at block  410 , where radiation emitted from a radiation source is obtained. As described in relation to  FIG. 1 , the radiation source may emit one or more beams of radiation that includes electromagnetic waves of various wavelengths, such as infrared radiation, visible light, and/or ultraviolet radiation. The emitted radiation may be directed towards a modulation mask, such as the modulation mask(s)  120  of  FIG. 1 . 
     At block  420 , the radiation may be modulated to generate a time-varying illumination pattern in three dimensions. Modulation of the radiation and generation of the time-varying illumination pattern may be facilitated by directing the radiation through the modulation mask(s), which may have a known modulation pattern etched, printed, inscribed, or otherwise provided on or by the modulation mask(s). The modulation pattern of the modulation mask(s) may selectively obstruct portions of the radiation that change over time to generate the time-varying illumination pattern. 
     At block  430 , a target volume may be illuminated by the time-varying illumination pattern. In some embodiments, the target volume may include a volume that includes one or more objects and/or the target volume may be included on a sample (e.g., the sample  150  of  FIG. 1 ). The objects within the target volume may generate signals in response to being illuminated by the time-varying illumination pattern. 
     At block  440 , the signals generated by the objects in the target volume may be collected by one or more optical detectors. In some embodiments, the signals generated by the objects within the target volume in response to the time-varying illumination pattern may be collected by single-element detection sensors, such as the photodetector(s)  160  described in relation to  FIG. 1 . In these and other embodiments, the signals may include electro-luminescence, chemo-luminescence, absorption spectra, or spectral scattering emitted by the objects illuminated by the radiation including the time-varying illumination pattern. 
     At block  450 , a location of each of the objects within the target volume may be estimated as described in relation to  FIGS. 1 and 3A-3D . 
     Optionally (as indicated by the dashed box in  FIG. 4 ) at block  460 , aberrations near each of the estimated locations may be identified. In some embodiments, the aberrations may include optical aberrations associated with the microscopy system used to image the objects. Additionally or alternatively, the aberrations may include specimen-based aberrations. In these and other embodiments, the aberrations relating to the microscopy system may be removed by adjusting one or more aspects of the microscopy system, while the specimen aberrations may be removed in a post-processing step as described elsewhere herein. 
     Optionally (as indicated by the dashed box in  FIG. 4 ) at block  470 , the estimated locations may be adjusted based on the identified aberrations as described elsewhere herein. 
     Modifications, additions, or omissions may be made to the method  400  without departing from the scope of the disclosure. For example, the designations of different elements in the manner described is meant to help explain concepts described herein and is not limiting. Further, the method  400  may include any number of other elements or may be implemented within other systems or contexts than those described. 
       FIG. 5  illustrates a block diagram of an example computing system  500  that may be used to perform or direct performance of one or more operations described according to at least one implementation of the present disclosure. The computing system  500  may include, be included in, or correspond to the computing system  170  of  FIG. 1 . The computing system  500  may include a processor  502 , a memory  504 , and a data storage  506 . The processor  602 , the memory  504 , and the data storage  506  may be communicatively coupled. 
     In general, the processor  502  may include any suitable special-purpose or general-purpose computer, computing entity, or processing device including various computer hardware or software modules and may be configured to execute instructions stored on any applicable computer-readable storage media. For example, the processor  502  may include a microprocessor, a microcontroller, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a Field-Programmable Gate Array (FPGA), or any other digital or analog circuitry configured to interpret and/or to execute computer-executable instructions and/or to process data. Although illustrated as a single processor, the processor  502  may include any number of processors configured to, individually or collectively, perform or direct performance of any number of operations described in the present disclosure. 
     In some implementations, the processor  502  may be configured to interpret and/or execute computer-executable instructions and/or process data stored in the memory  504 , the data storage  506 , or the memory  504  and the data storage  506 . In some implementations, the processor  502  may fetch computer-executable instructions from the data storage  506  and load the computer-executable instructions in the memory  504 . After the computer-executable instructions are loaded into memory  504 , the processor  502  may execute the computer-executable instructions. 
     The memory  504  and the data storage  506  may include computer-readable storage media for carrying or having computer-executable instructions or data structures stored thereon. Such computer-readable storage media may include any available media that may be accessed by a general-purpose or special-purpose computer, such as the processor  502 . By way of example, and not limitation, such computer-readable storage media may include tangible or non-transitory computer-readable storage media including Random Access Memory (RAM), Read-Only Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-Only Memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid state memory devices), or any other storage medium which may be used to carry or store particular program code in the form of computer-executable instructions or data structures and which may be accessed by a general-purpose or special-purpose computer. Combinations of the above may also be included within the scope of computer-readable storage media. Computer-executable instructions may include, for example, instructions and data configured to cause the processor  502  to perform or control performance of a certain operation or group of operations. 
     Some portions of the detailed description refer to different modules or components configured to perform operations. One or more of the modules or components may include code and routines configured to enable a computing system to perform or control performance of one or more of the operations described therewith. Additionally or alternatively, one or more of the modules or components may be implemented using hardware including any number of processors, microprocessors (e.g., to perform or control performance of one or more operations), DSPs, FPGAs, ASICs or any suitable combination of two or more thereof. Alternatively or additionally, one or more of the modules or components may be implemented using a combination of hardware and software. In the present disclosure, operations described as being performed by a particular module or component may include operations that the particular module or component may direct a corresponding system (e.g., a corresponding computing system) to perform. Further, the delineating between the different modules or components is to facilitate explanation of concepts described in the present disclosure and is not limiting. Further, one or more of the modules or components may be configured to perform more, fewer, and/or different operations than those described such that the modules or components may be combined or delineated differently than as described. 
     Some portions of the detailed description are presented in terms of algorithms and symbolic representations of operations within a computer. These algorithmic descriptions and symbolic representations are the means used by those skilled in the data processing arts to convey the essence of their innovations to others skilled in the art. An algorithm is a series of configured operations leading to a desired end state or result. In example implementations, the operations carried out require physical manipulations of tangible quantities for achieving a tangible result. 
     Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout the description, discussions utilizing terms such as detecting, determining, analyzing, identifying, scanning or the like, can include the actions and processes of a computer system or other information processing device (such as the computing systems  170 ,  500 ) that manipulates and transforms data represented as physical (electronic) quantities within the computer system&#39;s registers and memories into other data similarly represented as physical quantities within the computer system&#39;s memories or registers or other information storage, transmission or display devices. 
     Example implementations may also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the required purposes, or it may include one or more general-purpose computers selectively activated or reconfigured by one or more computer programs. Such computer programs may be stored in a computer readable medium, such as a computer-readable storage medium or a computer-readable signal medium. Computer-executable instructions may include, for example, instructions and data which cause a general-purpose computer, special-purpose computer, or special-purpose processing device (e.g., one or more processors) to perform or control performance of a certain function or group of functions. 
     Unless specific arrangements described herein are mutually exclusive with one another, the various implementations described herein can be combined in whole or in part to enhance system functionality and/or to produce complementary functions. Likewise, aspects of the implementations may be implemented in standalone arrangements. Thus, the above description has been given by way of example only and modification in detail may be made within the scope of the present invention. 
     Terms used in the present disclosure and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open terms” (e.g., the term “including” should be interpreted as “including, but not limited to.”). 
     With respect to the use of substantially any plural or singular terms herein, those having skill in the art can translate from the plural to the singular or from the singular to the plural as is appropriate to the context or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity. A reference to an element in the singular is not intended to mean “one and only one” unless specifically stated, but rather “one or more.” Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the above description. 
     Additionally, if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to embodiments containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. 
     In addition, even if a specific number of an introduced claim recitation is expressly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” or “one or more of A, B, and C, etc.” is used, in general such a construction is intended to include A alone, B alone, C alone, A and B together, A and C together, B and C together, or A, B, and C together, etc. 
     Further, any disjunctive word or phrase preceding two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both of the terms. For example, the phrase “A or B” should be understood to include the possibilities of “A” or “B” or “A and B.” 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described implementations are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.