Simultaneous multi‐plane, multi‐colour microscopy imaging using quadratically distorted (QD) grating and grisms
Authors: Feng Yan , Liu Yuewei , Liu Zhengkun 
Published: December 2016

The recent emergence of super‐resolution microscopy imaging techniques has surpassed the diffraction limit to improve image resolution. Contrary to the breakthroughs of spatial resolution, high temporal resolution remains a challenge. By introducing a detour phase term, a quadratically distorted (QD) grating, which imparts an equal but opposing focal power in the positive and negative diffracted orders, can provide a simple, versatile avenue for simultaneous multi‐plane microscopy imaging when combined with a lens [1]. As Fig. 1 illustrated, objects A, B and C located at different distances from QD grating are imaged simultaneously and spatially separated on a single image plane, and the biological images on the right side are, for example, the partial views of a stage 8 drosophila egg chamber (Δz~7.3µm). This narrowband multi‐plane bioimaging work was in collaboration with Prof. Ilan Davis of Oxford University.
However, QD gratings are dispersive and the multi‐colour images may be chromatically smeared if the dispersion is not corrected. A correction scheme based on grism, which is a combination of blazed grating and prism, has been demonstrated earlier [2]. In principle, utilizing the inherent non‐periodic chirps of QD grating, identical diffraction angles with respect to different wavelengths could be obtained, thus correcting the chromatic dispersion (Fig. 2a). Therefore a collimated beam in which the spectral components are laterally displaced has been created by a pair of grisms (Fig. 2b). The lateral shear between the polychrome components in the output beam is controlled by varying the separation between the grisms. Due to the various errors in alignment of the long optical path (>1 metre in reference [2]) and the defects in the fabrication of grisms and their mounts, the grism‐based approach we proposed before is also limiting, which is only applicable for optical tests rather than the real microscopy imaging [2].

We have recently customized a new pair of grisms and their mounts, and optimized the design of QD grating with practicable parameters, such that the optical system can be effectively improved and hence available for simultaneous multi‐plane, multi‐colour microscopy imaging. Fabricated from Schott B270 glass, a 17.5° wedge/blazed angle was designed, and a transmission grating of 300 grooves/mm was cemented to one side of the prism, thus forming a grism with an un‐deviated wavelength of 527.3nm. The grism pair was mounted between two 250mm achromatic lenses for qualitatively evaluating the wide‐range chromatic correction capability. The achromats were spaced 200mm apart, and the QD grating (a nominal axial period of 50μm, a curvature
W
20
of 50 waves and radius of 10mm) was placed 208mm from the second principal plane of the compound achromats system, thus equal magnification images can be obtained in each diffraction order. Then a simulated 3D imaging of eGFP fluorophore was implemented — a high power fibre continuum source (Fianium SC450‐PP‐HE) filtered by a set of 20nm bandpass filters (Thorlabs) with central wavelengths from 480nm to 600nm in 20nm steps was applied, and the system was focused for the central wavelength of ~532nm in 0
th
order, with and without grism correction. The combined greyscale image of all the 7 wavebands (simulated from bandpass weighting) demonstrate that the chromatic smearing of first‐order images can be effectively corrected (Fig. 3). The grism and thus the optical system can also be designed for broadband simultaneous multi‐plane imaging of various fluorophores/wavebands.

This technique can be realised with a simple optical attachment fully compatible with commercial microscopes and standard camera systems, and has direct applications for studies of rapidly‐changing objects in cell‐biology, fluid‐flow and high‐speed, 3D tracking. A few biological applications are still in process, and the details of which may be published in the near future.