Abstract

Two-Photon Laser-Scanning Microscopy is a powerful tool for exploring biological structure and function due to its ability to optically section through a sample with a tight focus. While it is possible to obtain 3D image stacks by moving a stage, this per-frame imaging process is time consuming. Here, we present a method for an easy-to-implement and inexpensive modification of an existing two-photon microscope to rapidly image in 3D using an electrically tunable lens to create a tessellating scan pattern which repeats with the volume rate. Using appropriate interpolating algorithms, the volumetric imaging rate can be increased by a factor up to four-fold. This capability provides the expansion of the two-photon microscope into the third dimension for faster volumetric imaging capable of visualizing dynamics on timescales not achievable by traditional stage-stack methods.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (4)

2015 (3)

2013 (1)

2012 (2)

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

2011 (1)

2010 (1)

D. Garcia, “Robust smoothing of gridded data in one and higher dimensions with missing values,” Comput. Stat. Data. An. 54(4), 1167–1178 (2010).
[Crossref]

2006 (1)

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref]

2003 (1)

W. B. Amos and J. G. White, “How the Confocal Laser Scanning Microscope entered Biological Research,” Biol. Cell 95(6), 335–342 (2003).
[Crossref]

1997 (2)

A. Bullen, S. S. Patel, and P. Saggau, “High-speed, random-access fluorescence microscopy: I. High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys. J. 73(1), 477–491 (1997).
[Crossref]

J. B. Guild, C. Xu, and W. W. Webb, “Measurement of group delay dispersion of high numerical aperture objective lenses using two-photon excited fluorescence,” Appl. Opt. 36(1), 397–401 (1997).
[Crossref]

1994 (1)

R. M. Williams, D. W. Piston, and W. W. Webb, “Two-photon molecular excitation provides intrinsic 3-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8(11), 804–813 (1994).
[Crossref]

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[Crossref]

1988 (1)

M. Minsky, “Memoir On Inventing The Confocal Scanning Microscope,” Scanning 10(4), 128–138 (1988).
[Crossref]

Abu, S.

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

Ahn, J.

K. Hwang, Y.-H. Seo, J. Ahn, P. Kim, and K.-H. Jeong, “Frequency selection rule for high definition and high frame rate Lissajous scanning,” Sci. Rep. 7(1), 14075 (2017).
[Crossref]

Amos, W. B.

W. B. Amos and J. G. White, “How the Confocal Laser Scanning Microscope entered Biological Research,” Biol. Cell 95(6), 335–342 (2003).
[Crossref]

Angeliki, P.

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

Annibale, P.

Ben-Yakar, A.

Bifano, T.

Bullen, A.

A. Bullen, S. S. Patel, and P. Saggau, “High-speed, random-access fluorescence microscopy: I. High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys. J. 73(1), 477–491 (1997).
[Crossref]

Chen, D.

Chen, S.-C.

Chiovini, B.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[Crossref]

Durr, N. J.

Dvornikov, A.

Fahrbach, F. O.

Garcia, D.

D. Garcia, “Robust smoothing of gridded data in one and higher dimensions with missing values,” Comput. Stat. Data. An. 54(4), 1167–1178 (2010).
[Crossref]

Gengyo-Ando, K.

Goldberg, B. B.

Gratton, E.

Gu, C.

Guild, J. B.

Helmchen, F.

Hillier, D.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Hinsdale, T.

Hoogland, T. M.

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref]

Hoy, C. L.

Huisken, J.

Hwang, K.

K. Hwang, Y.-H. Seo, J. Ahn, P. Kim, and K.-H. Jeong, “Frequency selection rule for high definition and high frame rate Lissajous scanning,” Sci. Rep. 7(1), 14075 (2017).
[Crossref]

Iyer, V.

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref]

Jeong, K.-H.

K. Hwang, Y.-H. Seo, J. Ahn, P. Kim, and K.-H. Jeong, “Frequency selection rule for high definition and high frame rate Lissajous scanning,” Sci. Rep. 7(1), 14075 (2017).
[Crossref]

Jiang, J.

Jo, J. A.

John, L.

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

Kartik, V.

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

Kaszás, A.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Katona, G.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Ke, Y.

Kim, P.

K. Hwang, Y.-H. Seo, J. Ahn, P. Kim, and K.-H. Jeong, “Frequency selection rule for high definition and high frame rate Lissajous scanning,” Sci. Rep. 7(1), 14075 (2017).
[Crossref]

Maák, P.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Maitland, K. C.

Malik, B. H.

Meng, Y.

Mertz, J.

Minsky, M.

M. Minsky, “Memoir On Inventing The Confocal Scanning Microscope,” Scanning 10(4), 128–138 (1988).
[Crossref]

M. Minsky, “Microscopy Apparatus,” (1957).

Motegi, Y.

Nakai, J.

Ohkura, M.

Olsovsky, C.

Patel, S. S.

A. Bullen, S. S. Patel, and P. Saggau, “High-speed, random-access fluorescence microscopy: I. High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys. J. 73(1), 477–491 (1997).
[Crossref]

Piston, D. W.

R. M. Williams, D. W. Piston, and W. W. Webb, “Two-photon molecular excitation provides intrinsic 3-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8(11), 804–813 (1994).
[Crossref]

Roska, B.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Rózsa, B.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Saggau, P.

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref]

A. Bullen, S. S. Patel, and P. Saggau, “High-speed, random-access fluorescence microscopy: I. High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys. J. 73(1), 477–491 (1997).
[Crossref]

Sato, M.

Schmid, B.

Seo, Y.-H.

K. Hwang, Y.-H. Seo, J. Ahn, P. Kim, and K.-H. Jeong, “Frequency selection rule for high definition and high frame rate Lissajous scanning,” Sci. Rep. 7(1), 14075 (2017).
[Crossref]

Shain, W. J.

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[Crossref]

Szalay, G.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Tomas, T.

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

Veress, M.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Vickers, N. A.

Vizi, E. S.

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Voigt, F. F.

Walker, S.

Wang, D.

Webb, W. W.

J. B. Guild, C. Xu, and W. W. Webb, “Measurement of group delay dispersion of high numerical aperture objective lenses using two-photon excited fluorescence,” Appl. Opt. 36(1), 397–401 (1997).
[Crossref]

R. M. Williams, D. W. Piston, and W. W. Webb, “Two-photon molecular excitation provides intrinsic 3-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8(11), 804–813 (1994).
[Crossref]

W. Denk, J. H. Strickler, and W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[Crossref]

White, J. G.

W. B. Amos and J. G. White, “How the Confocal Laser Scanning Microscope entered Biological Research,” Biol. Cell 95(6), 335–342 (2003).
[Crossref]

Williams, R. M.

R. M. Williams, D. W. Piston, and W. W. Webb, “Two-photon molecular excitation provides intrinsic 3-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8(11), 804–813 (1994).
[Crossref]

Xu, C.

Yagi, S.

Yam, Y.

Yung, W. H.

Zhang, D.

Appl. Opt. (2)

Biol. Cell (1)

W. B. Amos and J. G. White, “How the Confocal Laser Scanning Microscope entered Biological Research,” Biol. Cell 95(6), 335–342 (2003).
[Crossref]

Biomed. Opt. Express (2)

Biophys. J. (1)

A. Bullen, S. S. Patel, and P. Saggau, “High-speed, random-access fluorescence microscopy: I. High-resolution optical recording with voltage-sensitive dyes and ion indicators,” Biophys. J. 73(1), 477–491 (1997).
[Crossref]

Chin. Opt. Lett. (1)

Comput. Stat. Data. An. (1)

D. Garcia, “Robust smoothing of gridded data in one and higher dimensions with missing values,” Comput. Stat. Data. An. 54(4), 1167–1178 (2010).
[Crossref]

FASEB J. (1)

R. M. Williams, D. W. Piston, and W. W. Webb, “Two-photon molecular excitation provides intrinsic 3-dimensional resolution for laser-based microscopy and microphotochemistry,” FASEB J. 8(11), 804–813 (1994).
[Crossref]

J. Neurophysiol. (1)

V. Iyer, T. M. Hoogland, and P. Saggau, “Fast Functional Imaging of Single Neurons Using Random-Access Multiphoton (RAMP) Microscopy,” J. Neurophysiol. 95(1), 535–545 (2006).
[Crossref]

Nanotechnology (1)

T. Tomas, L. John, V. Kartik, S. Abu, and P. Angeliki, “High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories,” Nanotechnology 23(18), 185501 (2012).
[Crossref]

Nat. Methods (1)

G. Katona, G. Szalay, P. Maák, A. Kaszás, M. Veress, D. Hillier, B. Chiovini, E. S. Vizi, B. Roska, and B. Rózsa, “Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes,” Nat. Methods 9(2), 201–208 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Scanning (1)

M. Minsky, “Memoir On Inventing The Confocal Scanning Microscope,” Scanning 10(4), 128–138 (1988).
[Crossref]

Sci. Rep. (1)

K. Hwang, Y.-H. Seo, J. Ahn, P. Kim, and K.-H. Jeong, “Frequency selection rule for high definition and high frame rate Lissajous scanning,” Sci. Rep. 7(1), 14075 (2017).
[Crossref]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “Two-Photon Laser Scanning Fluorescence Microscopy,” Science 248(4951), 73–76 (1990).
[Crossref]

Other (1)

M. Minsky, “Microscopy Apparatus,” (1957).

Supplementary Material (2)

NameDescription
» Visualization 1       Real-time imaging of the cells shown in Figure 8 sampled at R = 35 + 7/16 cy/fr. (top left) Raw XY Slice 1 (bottom of volume) at 2.89s or 25% Tvol. The blue voxels are unsampled. (top middle) Interpolated XY Slice 1. (bottom left) Raw XY Slice 8 (mid
» Visualization 2       Visualization 2. 4 µm fluorescent bead diffusing in 50% glycerol captured with 3D-FASTR at an imaging rate of 2.9 sec./vol. (4x speed). Sequence of 28 volumes acquired over 80.9? sec. Left panel shows XY top-down view of bead motion.

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Figures (10)

Fig. 1.
Fig. 1. Comparison between volume scan patterns over time using conventional stage-stack method versus 3D-FASTR. These example volumes are size 512 × 512 × 16 and are shown stretched in Z to a cubic aspect ratio for ease of viewing. (a,c) 3D-view of difference in scan patterns after the first frame-time. While only the lowest image plane has been completely scanned in a conventional stage stack, a triangle wave pattern is apparent with 3D-FASTR, demonstrating sampling across all three axes. (b,d) 3D-view of difference in scan result after the final frame-time, which shows the volume is completely scanned after the passing of 16 frame-times, but the temporal distribution of the scan varies between the two and is color-coded by the frame-time the corresponding voxels were sampled. The axes for (b-d) are the same as those labeled in (a) and are omitted for clarity. (e,f) Cartoon representation of microscope demonstrates YZ scan differences between conventional volumetric acquisition and 3D-FASTR within the span of a single frame-time.
Fig. 2.
Fig. 2. (a) Theoretical relationship between number of Z-translation cycles per frame-time (R), and fill efficiency, demonstrating the effect of pattern timing on volume completion after Tvol. for a simulated volume consisting of Nz = 16 image planes. The effects of R on volume completion are illustrated using the YZ cross-section of the color-coded scan map as seen in Figs. 1(c)–1(d). Here, 3 examples designated by the boxed peaks correspond to (b). global maxima (red), (c). local maxima (yellow), and (d). global minima (green).
Fig. 3.
Fig. 3. Instrument diagram for 3D-FASTR implementation. Beam is split using beamsplitters (BS) and measured by photodiodes (PD). Laser power is analyzed as reference by splitting at BSR and measuring at photodiode (PDR) before focal deflection by the electrically-tunable lens (ETL). Focus is relayed using two lenses (L1/L2) before entering the confocal scanner. The focal range is shifted using L3 before deflection by dichroic mirror (DCM) to objective lens (OL). Emission passes back through DCM to non-descanned detection PMTs.
Fig. 4.
Fig. 4. Detection of real-time ETL focal depth. (a) Principle of photodiode detection scheme shows how two detectors positioned at different distances measure inverse signal levels as a function of ETL focal length. (b) Signal levels for each measurement photodiode as a function of ETL focal power. (c) Relationship between ETL focal power and focal shift in the image plane represented with blue dots scaled in height to match measurement uncertainty. (d, top row) Lateral PSF as measured on 500 nm fluorescent beads for ETL currents of 0 mA (FWHM = 0.71 ± 0.07 µm), 36 mA (FWHM = 0.51 ± 0.11 µm), and 255 mA (FWHM = 0.41 ± 0.15 µm) from left to right. (d, bottom panel) Gaussian-like intensity peak of image stacks at different ETL drive currents (color-coded) show shift in focal depth relative to reference image plane. (e) The signal difference between the two photodiodes shown in blue forms an almost linear relationship as a function of ETL focal power with the final calibration fitting shown in red.
Fig. 5.
Fig. 5. Impact of arbitrary waveform (AWF) creation on efficiency. (a) Polynomial-fit relationship between input/output of input triangle current (TC) waveform (b). Comparison of ETL drive signal over time between TC and AWF. (c). Comparison of resultant focal shift from TC and AWF. The AWF current pattern at ∼4 Hz produces a triangular focal shift which closely matches the model, providing optimum fill efficiency. (d). Bar chart of sampled focal planes across an arbitrary time period evaluates linearity of Z-translation by comparing the total number of voxels sampled in each focal plane. A relative value of 1 corresponds to the theoretical model where each focal plane is sampled equally, illustrated as a dotted red line. The uncorrected TC shows bias to lower image planes, while the AWF’s performance approaches the model. (e) Improvement in scan efficiency with successive iterations of waveform generation at ∼49 Hz ETL frequency.
Fig. 6.
Fig. 6. 3D-FASTR Implementation vs. Theory. (a) Fill efficiency declines with increasing ETL frequency due to decreasing ability to correct ETL waveform, but the result still shows significant improvement compared to an uncorrected sine wave. (b). Low-frequency AWF shows expected pattern timing behavior with respect to R and approaches fill levels of theoretical 3D-FASTR model. The experimentally measured ETL focal displacement (green curve) overlaps with the theoretically predicted 3D-FASTR model (red curve, see also Fig. 2(a)).
Fig. 7.
Fig. 7. The imaging process displayed through a series of 3 image planes (7, 11, 15) from a 16 z-plane volume of live HeLa cells stained with red nucleic acid dye Syto61 and green membrane dye DiA. Volume was acquired using a 3D-FASTR pattern with R = 35–1/16 after 50% Tvol (5.8s/2x speed increase). (a-c) A scan map image showing real intensity of scanned voxels and highlighting unsampled voxels in blue for each image plane. (d-f). Corresponding final interpolated image. (g). Reconstruction of 128 × 128 × 8 µm 3D-FASTR volume from 512 × 512 × 16 voxels. (h). XZ section shows depth profile of sample across line 187.
Fig. 8.
Fig. 8. Trade-offs between imaging speed and fidelity for HeLa cells stained with Syto41 (nucleic acids, green) (a). Full image of bottom plane (depth of −1.25 µm) of volume constructed using 3D-FASTR with crop region outlined in purple. (b). Cropped image at 100% Tvol (11.6s) serves as image quality reference. (c/d). Volume representation of neighboring scanned voxels displayed using the MATLAB function Vol3D developed by Joe Conti [20]. These volumes show the number of scanned neighbors for each voxel position with a shift number of (c). m = 1 vs. (d). m = 7. (e-g). Comparison of scanned voxels and final image quality of images acquired at 50% Tvol (5.8s) for different values of n and m. The left-hand side shows the raw images with unsampled pixels labelled blue. The right-hand side shows the image after interpolation. (h-j). Comparison of scanned voxels and final image quality of images acquired in 25% Tvol (2.9s) for different values of n and m. The left-hand side shows the raw images with unsampled pixels labelled blue. The right-hand side shows the image after interpolation. Orange arrows in (f) and (i) highlight curvature artifacts caused by inadequate sampling at 25% Tvol that is remedied by increasing n from 8 to 35.
Fig. 9.
Fig. 9. Representative frame from Visualization 1 showing the real-time imaging of the cells shown in Fig. 8 sampled at R = 35 + 7/16 cy/fr. (top left) Raw XY Slice 1 (bottom of volume) at 2.89s or 25% Tvol. The blue voxels are unsampled. (top middle) Interpolated XY Slice 1. (bottom left) Raw XY Slice 8 (middle of volume). (bottom middle) Interpolated XY Slice 1. (top right) 3D volumetric image stack generated using Vol3D [20] at 25% Tvol. (bottom right) Map of number of nearest neighbors for each voxel, ranging from 0 to a maximum of 6. The “Fill” bar represents how many voxels in the volume are sampled versus time, with 100% representing a perfect sampling. The green portion is the number of actually sampled voxels, while the red is the theoretical maximum.
Fig. 10.
Fig. 10. Multidimensional dynamics of a 4 µm fluorescent microsphere diffusing through an aqueous solution of 50% glycerol. (a). Maximum intensity projection (MIP) of bead diffusing captured using a conventional stage stack. Motion of bead during acquisition leads to a diagonal, smeared-out appearance. (b) MIP of diffusive bead captured using 3D-FASTR at 25% Tvol (2.9s/4x speed). Because the bead is captured with greater XZ sampling rate and in less time, there is no motion smearing or geometric distortion. (c) Two separately acquired volumes, co-rendered within the image space. The green volume was acquired at 4x speed using 3D-FASTR. The red volume was acquired at 1x speed using a conventional stage-step. The stage stack volume has a visibly tilted and kinked appearance, compared to the mostly-spherical 3D-FASTR volume. (d) Representative frame from Visualization 2 shows diffusive motion of microsphere over time in 3D as captured by 3D-FASTR. Left panel shows XY motion of bead with scalebars. Right panel shows close 3D view during diffusion.

Tables (1)

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Table 1. Sequencing of waveform fits by frequency

Equations (3)

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T v o l = N z F x y
F x y = 1 N x y × P
R = F z F x y = n + m N z

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