Realizing both high temporal and spatial resolution across a large volume is a key challenge for 3D fluorescent imaging. Towards achieving this objective, we introduce an interferometric multifocus microscopy (iMFM) system, a combination of multifocus microscopy (MFM) with two opposing objective lenses. We show that the proposed iMFM is capable of simultaneously producing multiple focal plane interferometry that provides axial super-resolution and hence isotropic 3D resolution with a single exposure. We design and simulate the iMFM microscope by employing two special diffractive optical elements. The point spread function of this new iMFM microscope is simulated and the image formation model is given. For reconstruction, we use the Richardson-Lucy deconvolution algorithm with total variation regularization for 3D extended object recovery, and a maximum likelihood estimator (MLE) for single molecule tracking. A method for determining an initial axial position of the molecule is also proposed to improve the convergence of the MLE. We demonstrate both theoretically and numerically that isotropic 3D nanoscopic localization accuracy is achievable with an axial imaging range of 2um when tracking a fluorescent molecule in three dimensions and that the diffraction limited axial resolution can be improved by 3-4 times in the single shot wide-field 3D extended object recovery. We believe that iMFM will be a useful tool in 3D dynamic event imaging that requires both high temporal and spatial resolution.
"Design and simulation of a snapshot multi-focal interferometric microscope"
Kuan He, Xiang Huang, Xiaolei Wang, Seunghwan Yoo, Pablo Ruiz, Itay Gdor, Nicola J. Ferrier, Norbert Scherer, Mark Hereld, Aggelos K. Katsaggelos, and Oliver Cossairt
Optics Express 26, 27381-27402 (2018) (doi: 10.1364/OE.26.027381)
Proposed iMFM system.
In our iMFM system, two MFGs of opposite focal shifts are employed in the respective Fourier planes of dual objectives before BS, and are capable of producing multifocal interferometry detection on the BS, which is then imaged via a 4f system (lenses L3 and L4) onto the detector in a single exposure.
Comparison of the detection PSF of MFM and the proposed iMFM microscopes.
(a) MFM and (b) iMFM monochromatic PSFs; (c) MFM and (d) iMFM polychromatic PSFs in the presence of chromatic aberration under 10nm bandwidth emission. For each PSF, xy (left), xz (middle left), yz (middle right) cuts and 1D axial profile or each tile’s PSF (right) are shown. Color indicates differently focused tiles.
Comparison of z-derivative between MFM and iMFM PSFs.
xz cuts of the square of z-derivative for MFM monochromatic PSF (left), MFM polychromatic PSF (middle left), iMFM monochromatic PSF (middle right) and iMFM polychromatic PSF (right), respectively. The z-derivative is higher for dual objective iMFM detection due to the steepened axial features of interferometric iMFM PSF.
(Left) Theoretical axial localization precision σz for the proposed iMFM aberrated (cyan) and unaberrated detection scheme (red) in comparison to MFM aberrated (green) and unaberrated detection scheme (blue).
In this simulation, 2500 detected signal photons per objective lens and 10 background photons per pixel are considered for the calculation. (Right) Mean squared error of the z position determined during 50 simulated localizations per individual axial value (black for monochromatic MFM and purple for monochromatic iMFM, respectively) and corresponding theoretical predications (blue for monochromatic MFM and red for monochromatic iMFM, respectively).
An example of determining the initial axial position and range of a single point for the MLE localization algorithm in iMFM.
It is clear that the bottom middle tile (outlined by red rectangle) is most in focus compared with other tiles. According to our MFG design (left), this tile focuses at the focal plane of 3∆z. Therefore, the initial axial position of
a point is set to be 3∆z. Note that the out-of-focus versions of the point source in other
tiles are severely contaminated by the background noise, and therefore are invisible.
Single molecule tracking by MFM and iMFM.
(a) The ground truth trajectory of a single emitter, shown in 3D space along with its projections onto xy, xz and yz planes. (b) MFM and (c) iMFM reconstructed trajectories by MLE with proposed initial value estimations. color indicates time. (d) The histogram of lateral (left) and axial (right) localization error between ground truth (a) and MFM recovery (b). (e) The histogram of lateral (left) and axial (right) localization error between ground truth (a) and iMFM recovery (c). The standard deviation for MFM axial resolution is 48.37nm and standard deviation for
iMFM is 12.12nm, resulting in a 4-fold improvement in axial localization precision.
Snapshot axial super resolution of 3D extended object recovery by the proposed iMFM.
(a) 3D synthetic object of the microtubules. (b) MFM snapshot recovery. (c) iMFM snapshot recovery. (d) Chromatically aberrated iMFM snapshot recovery in the presence of 10nm bandwidth emission. The 3D image is shown in one xy slice (first row), and two xz slices (second and third rows). The fourth row shows comparison of linecuts indicated by red line in the third row. The last row shows the comparison of kz-kx spectra by Fourier transforming the reconstructions. The results clearly demonstrate that both aberrated and unaberrated iMFM can recover higher axial spatial frequencies beyond the detection cut-off
of the single lens MFM.
Biological Systems Science Division, Office of Biological and Environmental Research, Office of Science, U.S. Dept. of Energy, under Contract DE-AC02-06CH11357; NSF CAREER grant IIS-1453192; ONR award N00014-15-1-2735.