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• W3195622969 abstract "•Nyquist figure-of-merit is introduced to characterize laser-scanning MPM digitization•Maximum aliasing-free FOV and cross-over excitation wavelength are formulated•High repetition-rate laser can enable high-speed large-FOV high-resolution MPM imaging•Up-to 1.6 mm-wide non-aliased FOV and ∼400 nm digital resolution at 8 kHz line-rate The Nyquist-Shannon criterion has never been realized in a laser-scanning mesoscopic multiphoton microscope (MPM) with a large field-of-view (FOV)-resolution ratio, especially when employing a high-frequency resonant-raster-scanning. With a high optical resolution nature, a current mesoscopic-MPM either neglects the criterion and degrades the digital resolution to twice the pixel size, or reduces the FOV and/or the raster-scanning speed to avoid aliasing. We introduce a Nyquist figure-of-merit (NFOM) parameter to characterize a laser-scanning MPM in terms of its optical-resolution retrieving ability. Based on NFOM, we define the maximum aliasing-free FOV, and subsequently, a cross-over excitation wavelength, below which the FOV becomes NFOM-constrained irrespective of an optimized optical design. We validate our idea in a custom-built mesoscopic-MPM with millimeter-scale FOV yielding an ultra-high FOV-resolution ratio of >3,000, while securing up-to a 1.6 mm Nyquist-satisfied aliasing-free FOV, a ∼400 nm lateral resolution, and a 70 M/s effective voxel-sampling rate, all at the same time. The Nyquist-Shannon criterion has never been realized in a laser-scanning mesoscopic multiphoton microscope (MPM) with a large field-of-view (FOV)-resolution ratio, especially when employing a high-frequency resonant-raster-scanning. With a high optical resolution nature, a current mesoscopic-MPM either neglects the criterion and degrades the digital resolution to twice the pixel size, or reduces the FOV and/or the raster-scanning speed to avoid aliasing. We introduce a Nyquist figure-of-merit (NFOM) parameter to characterize a laser-scanning MPM in terms of its optical-resolution retrieving ability. Based on NFOM, we define the maximum aliasing-free FOV, and subsequently, a cross-over excitation wavelength, below which the FOV becomes NFOM-constrained irrespective of an optimized optical design. We validate our idea in a custom-built mesoscopic-MPM with millimeter-scale FOV yielding an ultra-high FOV-resolution ratio of >3,000, while securing up-to a 1.6 mm Nyquist-satisfied aliasing-free FOV, a ∼400 nm lateral resolution, and a 70 M/s effective voxel-sampling rate, all at the same time. IntroductionCompared to single-photon and camera-based imaging systems, with a better penetration capability due to the use of near-infrared (NIR) excitation spectrum and excitation localization of nonlinear optical absorption, a laser-scanning multiphoton microscope (MPM) becomes a promising candidate for deep intact tissue imaging while maintaining high enough three-dimensional (3D)-resolution (Denk et al., 1990Denk W. Strickler J.H. Webb W.W. Two-photon laser scanning fluorescence microscopy.Science. 1990; 248: 73-76Crossref PubMed Scopus (8189) Google Scholar; Helmchen and Denk, 2005Helmchen F. Denk W. Deep tissue two-photon microscopy.Nat. Methods. 2005; 2: 932-940Crossref PubMed Scopus (3106) Google Scholar; Theer et al., 2003Theer P. Hasan M.T. Denk W. Two-photon imaging to a depth of 1000 μm in living brains by use of a Ti:Al2O3 regenerative amplifier.Opt. Lett. 2003; 28: 1022-1024Crossref PubMed Scopus (559) Google Scholar; Ntziachristos, 2010Ntziachristos V. Going deeper than microscopy: the optical imaging frontier in biology.Nat. Methods. 2010; 7: 603-614Crossref PubMed Scopus (1292) Google Scholar; Jacques, 2013Jacques S.L. Optical properties of biological tissues: a review.Phys. Med. Biol. 2013; 58: 37-61Crossref PubMed Scopus (2235) Google Scholar; Kobat et al., 2009Kobat D. Durst M.E. Nishimura N. Wong A.W. Schaffer C.B. Xu C. Deep tissue multiphoton microscopy using longer wavelength excitation.Opt. Express. 2009; 17: 13354-13364Crossref PubMed Scopus (462) Google Scholar; Horton et al., 2013Horton N.G. Wang K. Kobat D. Clark C.G. Wise F.W. Schaffer C.B. Xu C. In vivo three-photon microscopy of subcortical structures within an intact mouse brain.Nat. Photon. 2013; 7: 205-209Crossref Scopus (1032) Google Scholar; Horton and Xu, 2015Horton N.G. Xu C. Dispersion compensation in three-photon fluorescence microscopy at 1,700 nm.Biomed. Opt. Express. 2015; 6: 1392-1397Crossref PubMed Scopus (40) Google Scholar; Rosenegger et al., 2014Rosenegger D.G. Tran C.H.T. LeDue J. Zhou N. Gordon G.R. A high performance, cost-effective, open-source microscope for scanning two-photon microscopy that is modular and readily adaptable.PLoS One. 2014; 9: e110475Crossref PubMed Scopus (47) Google Scholar; Chakraborty et al., 2019Chakraborty S. Lee S.Y. Lee J.C. Yen C.T. Sun C.K. Saturated two-photon excitation fluorescence microscopy for the visualization of cerebral neural networks at millimeters deep depth.J. Biophotonics. 2019; 12: e201800136Crossref PubMed Scopus (3) Google Scholar). To accomplish a high-speed laser-raster-scanning of a mesoscale volumetric tissue-sample with a reduced necessity of digital-image-stitching operations, an extended FOV becomes an imperative requirement. Nevertheless, the FOV of a traditional MPM is typically limited to <1 mm2 while preserving a submicron optical resolution. It is however important to note that with the advent of a wide variety of moderate or low magnification objective lenses with moderate numerical apertures (NAs), it is becoming feasible to extend an MPM FOV up-to several millimeters while still preserving an adequate optical resolution. Being a digital microscopy system however, an adequate digitization facility becomes another important aspect to retrieve such high optical resolution over the extended FOV under observation. That is to say, an adequate number of pixels on the digitized image is essential. While to secure the same yet maintaining a fast raster-scanning, a high enough effective voxel-sampling rate is required to satisfy or even exceed the respective Nyquist-Shannon criterion (Nyquist, 1928Nyquist H. Certain topics in telegraph transmission theory.Trans. AIEE. 1928; 47: 617-644Google Scholar; Shannon, 1949Shannon C.E. Communications in the presence of noise.Proc. IRE. 1949; 37: 10-21Crossref Scopus (4858) Google Scholar), which demands the digitized size of each sampling pixel to be at least half of the smallest resolvable spacing in order to prevent the phenomenon of aliasing, which essentially converts the optics-limited high spatial frequencies of the objects into low spatial frequencies in the final image by the Moiré effect (Pawley, 2006Pawley J.B. Pawley J.B. Handbook of Biological Confocal Microscopy. Springer, 2006: 59-79Crossref Scopus (67) Google Scholar; Heintzmann and Sheppard, 2007Heintzmann R. Sheppard C.J.R. The sampling limit in fluorescence microscopy.Micron. 2007; 38: 145-149Crossref PubMed Scopus (11) Google Scholar). An effective voxel-sampling rate, in this case, can be realized as an image-pixel-sampling rate, i.e., the number of pixels on the digitized image acquired in a unit second. A laser-scanning MPM typically uses a pulsed laser source for an efficient nonlinear excitation, where each digitized voxel or image-pixel is expected to correspond to at least one optical pulse. Thus, an MPM can reach a sampling rate as high as the repetition-rate of the laser while employing a pulse-synchronized digitization (Prevedel et al., 2016Prevedel R. Verhoef A.J. Pernía A.J. Weisenburger S. Huang B.S. Nöbauer T. Fernández A. Delcour J.E. Golshani P. Baltuska A. Vaziri A. Fast volumetric calcium imaging across multiple cortical layers using sculpted light.Nat. Methods. 2016; 13: 1021-1028Crossref PubMed Scopus (97) Google Scholar; Weisenburger et al., 2019Weisenburger S. Tejera F. Demas J. Chen B. Manley J. Sparks F.T. Traub F.M. Daigle T. Zeng H. Losonczy A. Vaziri A. Volumetric Ca2+ imaging in the mouse brain using hybrid multiplexed sculpted light microscopy.Cell. 2019; 177: 1050-1066Abstract Full Text Full Text PDF PubMed Scopus (93) Google Scholar). Following the same, it becomes feasible to enable a high sampling rate in an MPM simply by opting to a high-repetition-rate laser source. However, despite securing a high sampling rate, a subsequent downscaling operation to the digitized dataset typically in an attempt to improve signal-to-noise ratio (SNR) by means of an interpolation and/or pixel-binning method might lead to aliasing and thus might degrade the digital resolution. As a matter of fact, in such a digital microscopy system, the effective digital resolution not only depends on the objective's NA and excitation wavelength, but also gets affected by the associated digitization and image-formation strategies. Remarkably, an ultra-high effective voxel-sampling rate becomes necessary when one simultaneously targets an extended FOV, a high digital resolution, and a fast resonant-raster-scanning. In such a scenario, overcoming the Nyquist-restriction in a laser-scanning MPM becomes challenging, as the maximum effective voxel-sampling rate is essentially limited by the laser repetition-rate. Note that an undersampling-induced aliasing in such a case essentially degrades the effective digital resolution of the system to twice the effective pixel size, and enforces one to reduce the raster-scanning speed and/or the imaging area to retrieve the best optical resolution.Over the past several years, quite a few researchers have successfully addressed various design challenges to extend the FOV of a laser-scanning MPM, and demonstrated their ultra-large FOVs up-to several square millimeters (Tsai et al., 2015Tsai P.S. Mateo C. Field J.J. Schaffer C.B. Anderson M.E. Kleinfeld D. Ultra-large field-of-view two-photon microscopy.Opt. Express. 2015; 23: 13833-13847Crossref PubMed Scopus (79) Google Scholar; Bumstead et al., 2018Bumstead J.R. Park J.J. Rosen I.A. Kraft A.W. Wright P.W. Reisman M.D. Côté D.C. Culver J.P. Designing a large field-of-view two-photon microscope using optical invariant analysis.Neurophoton. 2018; 5: 025001Crossref PubMed Scopus (36) Google Scholar; Terada et al., 2018Terada S.I. Kobayashi K. Ohkura M. Nakai J. Matsuzaki M. Super-wide-field two-photon imaging with a micro-optical device moving in post-objective space.Nat. Commun. 2018; 9: 3550Crossref PubMed Scopus (29) Google Scholar; Stirman et al., 2016Stirman J.N. Smith I.T. Kudenov M.W. Smith S.L. Wide field-of-view, multi-region, two-photon imaging of neuronal activity in the mammalian brain.Nat. Biotechnol. 2016; 34: 857-862Crossref PubMed Scopus (191) Google Scholar; Balu et al., 2016Balu M. Mikami H. Hou J. Potma E.O. Tromberg B.J. Rapid mesoscale multiphoton microscopy of human skin.Biomed. Opt. Express. 2016; 7: 4375-4387Crossref PubMed Scopus (27) Google Scholar; Sofroniew et al., 2016Sofroniew N.J. Flickinger D. King J. Svoboda K. A large field of view two-photon mesoscope with subcellular resolution for in vivo imaging.eLife. 2016; 5: e14472Crossref PubMed Scopus (299) Google Scholar). Remarkably, by means of moderate- or high-NA objective lenses, the prior arts successfully preserved high enough optical resolutions over their extended-FOVs as per their experimental requirements or specific research goals. Most of such prior arts thus secured substantial improvement to the FOV-resolution ratios, as being enlisted in Table 1. In addition, several of these prior arts employed high-frequency resonant-mirrors to avail a fast-enough raster-scanning. Despite such substantial improvements being contributed to the mesoscopic-MPM modality, to the best of our knowledge, the significance of the Nyquist-Shannon sampling theorem to correlate its direct consequences over the maximum aliasing-free FOV is not yet well-explored to date. Especially for an MPM with an ultra-high FOV-resolution ratio, the issue of aliased digitization is indeed an important aspect to deal with, to unlock a large aliasing-free FOV with a submicron effective digital resolution while simultaneously preserving a fast resonant-raster-scanning.Table 1A comparison of a few of the state-of-the-art large-FOV high-lateral-resolution MPMsLiteratureFast-axis scanner typeNumerical aperture (NA)Axial resolution (μm) (optical; reported)Reported extended FOV (approx.)Estimated pixel size (fast-axis) (μm)Lateral resolution (μm) (optical; reported)Lateral resolution (μm) (digital; limited by Nyquist-Shannon sampling theory)Reported fast-axis FOV/reported resolutionEstimated effective voxel-sampling rate (M/s)Estimated NFOM (using reported resolution)Tsai et al., 2015Tsai P.S. Mateo C. Field J.J. Schaffer C.B. Anderson M.E. Kleinfeld D. Ultra-large field-of-view two-photon microscopy.Opt. Express. 2015; 23: 13833-13847Crossref PubMed Scopus (79) Google Scholar)Galvanometric0.28148 × 10 mm24188000<10.13Bumstead et al., 2018Bumstead J.R. Park J.J. Rosen I.A. Kraft A.W. Wright P.W. Reisman M.D. Côté D.C. Culver J.P. Designing a large field-of-view two-photon microscope using optical invariant analysis.Neurophoton. 2018; 5: 025001Crossref PubMed Scopus (36) Google Scholar)Galvanometric0.22284.95 × 4.95 mm24.951.79.92912<10.17Balu et al., 2016Balu M. Mikami H. Hou J. Potma E.O. Tromberg B.J. Rapid mesoscale multiphoton microscopy of human skin.Biomed. Opt. Express. 2016; 7: 4375-4387Crossref PubMed Scopus (27) Google Scholar)Resonant (4 kHz)1.053.30.8 × 0.8 mm20.50.51160012.80.5Stirman et al., 2016Stirman J.N. Smith I.T. Kudenov M.W. Smith S.L. Wide field-of-view, multi-region, two-photon imaging of neuronal activity in the mammalian brain.Nat. Biotechnol. 2016; 34: 857-862Crossref PubMed Scopus (191) Google Scholar)Resonant (4 kHz)0.4312.13.5 mm (width)1.711.23.42291716.40.35Terada et al., 2018Terada S.I. Kobayashi K. Ohkura M. Nakai J. Matsuzaki M. Super-wide-field two-photon imaging with a micro-optical device moving in post-objective space.Nat. Commun. 2018; 9: 3550Crossref PubMed Scopus (29) Google Scholar)Resonant (8 kHz)0.69.961.2 × 3.5 mm22.341.264.699528.20.27This reportResonant (4 kHz)0.952 @1070 nm1.6 × 1.6 mm20.180.48 @1070 nm0.48 @1070 nm>3000 (above λc)70≥11.6 × 1.6 mm20.180.41 @919 nm0.41 @919 nm>3800 (near λc)1.42 × 1.42 mm20.160.37 @824 nm0.37 @824 nm>3800 (below λc)Note: The NFOMs (would be discussed in following sections) in this table were calculated considering reported optical resolutions, following, NFOM = 0.5 ropt/Ps; where, ropt and Ps are reported optical lateral resolution and estimated fast-axis pixel size, respectively. Parameters cited/estimated in this table are based on the reported results in each case, to the best of our knowledge. Open table in a new tab In this paper, based on the Nyquist-Shannon sampling theorem we first formulate the minimum required repetition-rate of a pulsed laser source to fulfill the Nyquist-Shannon criterion for a given laser-scanning MPM with a specific FOV. To characterize such an MPM in terms of its reliable digitization capability, we formulate a Nyquist figure-of-merit (NFOM) parameter which indicates whether or not the system is capable of retrieving the best optical resolution. For the digitization to be aliasing-free, the value of NFOM must be greater than or at least equal to one. Taking NFOM into account, we then derive the maximum allowed FOV for a given laser repetition-rate, fast-axis scanner frequency, excitation wavelength, and objective's NA. Beyond this theoretical limit, the FOV will get aliased and the effective resolution will tend to degrade regardless of its superior optical design. For an MPM with an optimized optical FOV design, we further study the cross-over excitation wavelength, below which the FOV gets constrained by the respective NFOM and becomes wavelength dependent. Based on our derivation, we justify that in order to maximize the FOV while neither compromising the digital resolution nor the raster-scanning speed, the key solution is to enable an ultra-high voxel-sampling rate by means of a high-repetition-rate pulsed laser source, where a one-pulse-per-voxel synchronized acquisition is assumed for the optimum case. Our derivation further remarks that for a laser-scanning MPM with a high-NA objective lens but using a low-repetition-rate pulsed laser, it is not feasible to achieve a large millimeter-scale FOV without getting aliased unless the raster-scanning speed is greatly slowed down.To validate our derivation experimentally, a design-optimized mesoscopic MPM was custom-built (Borah et al., 2020Borah B.J. Chi H.-H. Yen C.-T. Sun C.-K. Super-speed multiphoton microscopy for mesoscopic volume imaging with ultra-dense sampling beyond Nyquist Limit.in: Proc. SPIE 11245, Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XXVII. 2020: 1124515Crossref Scopus (3) Google Scholar; Sun and Borah, 2019Sun C.-K. Borah B.J. Large-angle Optical Raster Scanning System for Deep Tissue Imaging. U.S. Patent Application No. 20210173189(A1). U.S. Patent and Trademark Office, 2019Google Scholar) (refer to STAR Methods) to yield an optics-limited FOV of up-to 1.6 × 1.6 mm2 whereas preserving a submicron lateral resolution with a 0.95 NA objective lens. By implementing a regular 70 MHz femtosecond laser following our design guideline, we successfully achieved aliasing-free MPM imaging, i.e., NFOM≥1, with an FOV-resolution ratio of more than 3,000. To validate the optical-zoom-free submicron resolution retrievability, we performed two-photon imaging of biological tissue samples with fine enough structures, and reliably retrieved them without shrinking down the 1.6 × 1.6 mm2 imaging area if the excitation wavelength is longer than 912 nm. Our experimental study further confirms the Nyquist-Shannon sampling theorem in a laser-scanning MPM, as well as the derived cross-over excitation wavelength. By shifting the excitation wavelength down to around 919 nm which is close to this cross-over wavelength, a resolution-optimized mesoscopic MPM was also demonstrated with the 1.6 × 1.6 mm2 FOV, while maintaining NFOM = 1 and ∼400 nm lateral resolution with a maximized FOV-resolution ratio of more than 3,800. Whereas, our study further confirmed that with an excitation shorter than this cross-over wavelength, we had to shrink down the FOV to rescue an NFOM of at least 1, i.e., the aliasing-free FOV in this regime is wavelength-dependent and is limited by Nyquist-Shannon criterion rather than the optical system design. Our study and demonstration of the mesoscopic MPM with an ultra-high FOV-resolution ratio can serve as a guideline to eliminate the final MPM barrier of aliased digitization and to enable deep-tissue volumetric MPM imaging with simultaneously an ultra-large aliasing-free FOV and a submicron digital resolution without compromising the raster-scanning speed.ResultsFormulation of Nyquist figure-of-merit (NFOM)To properly digitize the smallest optically resolvable spacing in a digital imaging system, the pixel size must be at least half of this smallest resolvable spacing, called the Nyquist-Shannon criterion (Nyquist, 1928Nyquist H. Certain topics in telegraph transmission theory.Trans. AIEE. 1928; 47: 617-644Google Scholar; Shannon, 1949Shannon C.E. Communications in the presence of noise.Proc. IRE. 1949; 37: 10-21Crossref Scopus (4858) Google Scholar; Pawley, 2006Pawley J.B. Pawley J.B. Handbook of Biological Confocal Microscopy. Springer, 2006: 59-79Crossref Scopus (67) Google Scholar; Heintzmann and Sheppard, 2007Heintzmann R. Sheppard C.J.R. The sampling limit in fluorescence microscopy.Micron. 2007; 38: 145-149Crossref PubMed Scopus (11) Google Scholar), which must be satisfied to avoid the phenomenon of aliasing. For an objective lens with a specific value of NA, its smallest resolvable lateral spacing, i.e., the lateral resolution can be estimated by the full width half maximum (FWHM) of the lateral cross section obtained by imaging a small enough structure. Theoretically, for a high-NA (>0.7) objective lens, the lateral resolution (FWHM) for multiphoton fluorescence can be described as (Zipfel et al., 2003Zipfel W.R. Williams R.M. Webb W.W. Nonlinear magic: multiphoton microscopy in the biosciences.Nat. Biotechnol. 2003; 21: 1369-1377Crossref PubMed Scopus (3108) Google Scholar; Sheppard and Gu, 1990Sheppard C. Gu M. Image formation in two-photon fluorescence microscopy.Optik. 1990; 86: 104-106Google Scholar)rFWHM=0.541λexcnNA0.91,(Equation 1) where λexc and n stand for excitation wavelength and order of the multiphoton process, respectively. In a pulsed-laser based point scanning MPM, fulfilling/exceeding the Nyquist-Shannon criterion for an aliasing-free maximum fast-axis field of view of FOVmax with a specific lateral resolution of rFWHM requires the repetition-rate (R) of the pulsed laser source to beR≥Vmin N, and Vmin=4fFOVmaxrFWHM;(Equation 2) where Vmin is the minimum voxel-sampling rate required to fulfill the Nyquist-Shannon criterion, N (≥1) is an integer signifying number of optical pulse(s) per voxel, and f is the fast-axis frequency for either a resonant or a galvanometer-based scanner. Using Equation (1), Vmin can be redefined for an MPM with a high-NA (>0.7) objective lens asVmin=7.3937nNA0.91fFOVmaxλexc.(Equation 3) As Vmin is directly proportional to f and FOVmax, and inversely proportional to λexc, for a given value of Vmin, to extend the aliasing-free FOV while imaging with a high-NA objective lens, one must either decrease the fast-axis scanning frequency sacrificing the imaging speed, and/or increase the excitation wavelength sacrificing the resolution. Therefore, the only way left to neither compromise speed nor resolution is to enhance the voxel-sampling rate sufficiently. For the optimized condition, following N = 1 in Equation (2) inequality, the lowest required repetition-rate of the laser would thus be equal to the minimum voxel-sampling rate, i.e., Rmin=Vmin. Thus, for a given MPM, the required value of Rmin can be estimated from Equation (3) based on desired FOVmax and choices of NA, f, and λexc. For instance, if one employs an 8 kHz fast-axis scanner and a 1.0 NA objective lens for two-photon imaging at 920 nm excitation, for achieving a 2 mm-wide fast-axis FOV, the minimum required voxel-sampling rate will be ∼181.86 M/s, and hence the laser repetition-rate must be at least ∼181.86 MHz. This requirement can be of course relaxed to ∼90.9 MHz with a 4 kHz fast-axis scanner.Considering Equations (2) and (3), for a straightforward assessment of the optical-resolution retrieving capability of a laser-scanning MPM, we formulate a Nyquist figure-of-merit (NFOM) parameter as followsNFOM=0.1353RλexcnN f NA0.91 FOVmax.(Equation 4) Formulation of maximum achievable aliasing-free field of view (FOVmax) and cross-over excitation wavelengthFor the digitization to be aliasing-free, NFOM must be greater than or at least equal to 1. For a given λexc, an attempt to enhance the FOVmax with a high-f and/or a high-NA configuration will tend to degrade the NFOM to be less than 1, which must be rescued by means of a high-R laser. Incorporating an even higher-NA objective lens, and/or even lower λexc will demand an even higher value of R to maintain a specific FOVmax. For instance, a ∼1.4 times higher value of R will be required when NA is enhanced from 1.0 to 1.45; likewise, lowering λexc from 1,070 nm to 760 nm, will require a ∼1.4 times higher R, the remaining parameters kept unchanged in each case.For the optimized case with NFOM = 1 and N = 1, the aliasing-free FOVmax for a specified set of laser, fast-axis scanner, and objective lens can be thus estimated asFOVmax=0.1353RλexcnfNA0.91.(Equation 5) Figure 1A plots the maximum aliasing-free field of view, FOVmax from Equation (5) as a function of R for the fixed values of NA=0.95 and N=1. As depicted by the data points, to achieve an aliasing-free FOVmax of 1 mm to be operated up-to a minimum λexc of 920 nm, the laser repetition-rate must be at least 43.4 MHz for a 4 kHz scanner, and at least 86.8 MHz for an 8 kHz scanner. This essentially justifies that for a high-NA objective lens employed with a high-frequency fast-axis scanner, the only way to extend the aliasing-free FOVmax beyond ∼1 mm is to opt for a pulsed laser source with high enough repetition-rate (R) to enable an ultra-high effective voxel-sampling rate (V).Based on Equation (5), Figure 1B plots the FOVmax as a function of λexc for two high-NA MPM settings each with NFOM≥1, where the blue-dashed line corresponds to the experimental parameters of a prior report by Jaepel et al., 2017Jaepel J. Hübener M. Bonhoeffer T. Rose T. Lateral geniculate neurons projecting to primary visual cortex show ocular dominance plasticity in adult mice.Nat. Neurosci. 2017; 20: 1708-1714Crossref PubMed Scopus (48) Google Scholar. In this case, although an 80 MHz pulsed laser was employed for excitation, the previously reported aliasing-free FOV is ∼19 times lower than our idealized theoretical value FOVmax with N = 1 (blue-dashed line). Part of the discrepancy can be attributed to the low effective voxel-sampling rate of 8.2 M/s. On the other hand, our report studied the case of a femtosecond laser with a 70 MHz repetition-rate, which is on the same order or slightly lower than most commercial femtosecond lasers. As shown in the green-dashed line, which represents FOVmax with NA=0.95, N=1, and f=4 kHz, with a maximized effective voxel-sampling rate of 70 M/s, this report predicts the possibility to achieve an aliasing-free FOVmax much greater than 1 mm across the excitation wavelengths between 700 and 1,100 nm while digitally preserving the diffraction-limited nonlinear optical resolution. Our calculation also justifies the impact of true/effective voxel-sampling rate (V) and hence the laser repetition-rate (R) for a large-FOV aliasing-free imaging.For a conventional laser-scanning system (Chun et al., 2013Chun W. Do D. Gweon D.G. Design and demonstration of multimodal optical scanning microscopy for confocal and two-photon imaging.Rev. Sci. Instrum. 2013; 84: 013701Crossref PubMed Scopus (5) Google Scholar) with an optics-limited field of view of FOVOL (Equation (S11)), we can redefine the minimum effective voxel-sampling rate, and hence the minimum laser repetition-rate required for a given laser-scanning MPM to be aliasing-free. Following Equations (3) and (S11), and considering FOVmax=FOVOL, we obtainVmin=Rmin=14.7874n NA0.91ftan|θ±|fofsλexcft,(Equation 6) where, θ± is the fast-axis scan-angle by the scanning mirror with respect to the optical axis, fo, fs, and ft are the effective focal lengths (EFLs) of the objective lens, scan lens, and tube lens, respectively.From Equation (5), for a laser-scanning MPM with FOVOL≤FOVmax, a cross-over excitation wavelength λc can be further estimated as follows. When λexc is longer than λc, the FOV of the system remains limited by the relevant optics. However, as λexc becomes shorter than λc, the FOV is rather constrained by the NFOM of the respective system. For an optics-limited resolution-optimized FOV, λexc∼λc is expected withλc=7.3937nfNA0.91 FOVOLR.(Equation 7) Experimental demonstration and validation of the proposed theory and hypothesisTo validate our theory and hypothesis, we constructed a mesoscopic MPM utilizing off-the-shelf optomechanical components. Following Equation (6), we chose fo, fs, and ft of 9 mm, 110 mm, and 166.7 mm, so that θ±∼±7.70 can provide up-to an FOVOL of ∼1.6 mm. Combining a high (0.95) NA objective lens with 9 mm EFL preserved not only a high spatial resolution, but also resulted in a large FOV-resolution ratio greater than 3,000. For two-photon imaging we further chose λexc=1070nm and f=4kHz, thus obtaining Vmin= Rmin=59.7 MHz, which is lower than most of the commercially available femtosecond oscillators and is easily achievable. For demonstration, a femtosecond laser source with R=70 MHz and λexc≈1070 nm was first chosen. Following Equation (2), the value of N, being an integer, is not allowed to be more than 1 in this case, enforcing a one-pulse-per-voxel acquisition. Therefore, following Equation (5), we obtain FOVmax=1.87 mm (>FOVOL) for N=1 case. From Equation (4), NFOM=1.17>1; thus, the optics-limited FOV is guaranteed to be aliasing-free. In this case, from Equation (7), the cross-over excitation wavelength, λc was estimated to be around 912 nm.To experimentally validate the fulfillment of the Nyquist-Shannon criterion, we performed two-photon imaging of a coronal section from the medulla of a Nav1.8-tdTomato mouse across a volume size of ∼1.6 × 1.6 × 0.4 mm3 preserving a voxel size of 0.182 × 0.182 × 0.3 μm3. With λexc≈1070 nm>λc, the FOV was optics-limited in this case. Figure 2A depicts the stitch-free 3D-rendered volume (using Amira software, Mercury Computer Systems, USA) in an inclined view. The 3D region of interest (ROI) R1 is cropped and enlarged in Figure 2B, and its top view is presented in Figure 2C. Red, green, and cyan colored axes represent X, Y, and Z axes, respectively. Figure 2D shows a two-dimensional (2D) representation of the acquired volume with color-coded depth information, processed using ImageJ software (National Institutes of Health, USA) and OpenCV (an open-source computer vision library). No stitching/mosaicking was applied. Figure 2E shows a 3× digitally enlarged ROI R2 with 2,933 × 2,933 pixels maintaining a ∼182 nm pixel size, presenting the color-coded fine fibers. With a 26× digital zoom to the original image, the ROIs R3 and R4 marked in Figure 2E are enlarged in Figures 2F and 2G, respectively, each with a pixel number of 333 × 333, with 182 nm pixel size. The red arrows in Figures 2F and 2G mark two submicron fibers. Figures 2H and 2I respectively show the intensity profiles across the fibers in Figures 2F and" @default.
• W3195622969 created "2021-08-30" @default.
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• W3195622969 date "2021-09-01" @default.
• W3195622969 modified "2023-10-18" @default.
• W3195622969 title "Nyquist-exceeding high voxel rate acquisition in mesoscopic multiphoton microscopy for full-field submicron resolution resolvability" @default.
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• W3195622969 doi "https://doi.org/10.1016/j.isci.2021.103041" @default.
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