Lens Free Super-Resolution Microscopy

Distributed Aperture Illumination Allows Large Working Distances

  • Fig. 1: Principle of Distributed Aperture Illumination Microscopy. Blue discs: Individual sources S1, S2,…SK,.. SN of coherent, collimated light at positions (xK,yK,zK) with defined phase and polarization relations emitting the light in defined directions (purple, one indicated by a white arrow); the red “spot” indicates the joint focal illumination distribution (i.e. the “focal volume” or the “observation volume of the illumination spot”) produced by the constructive interference of the collimated waves. Altogether, the sources span a solid angle Ω = 2π (1-cosθ), corresponding to the numerical aperture (NA) of a conventional objective lens with half opening angle θ. Published in Scientific Reports under the Creative Commons Attribution License (CC-BY) [15]by Birk et al. [7].Fig. 1: Principle of Distributed Aperture Illumination Microscopy. Blue discs: Individual sources S1, S2,…SK,.. SN of coherent, collimated light at positions (xK,yK,zK) with defined phase and polarization relations emitting the light in defined directions (purple, one indicated by a white arrow); the red “spot” indicates the joint focal illumination distribution (i.e. the “focal volume” or the “observation volume of the illumination spot”) produced by the constructive interference of the collimated waves. Altogether, the sources span a solid angle Ω = 2π (1-cosθ), corresponding to the numerical aperture (NA) of a conventional objective lens with half opening angle θ. Published in Scientific Reports under the Creative Commons Attribution License (CC-BY) [15]by Birk et al. [7].
  • Fig. 1: Principle of Distributed Aperture Illumination Microscopy. Blue discs: Individual sources S1, S2,…SK,.. SN of coherent, collimated light at positions (xK,yK,zK) with defined phase and polarization relations emitting the light in defined directions (purple, one indicated by a white arrow); the red “spot” indicates the joint focal illumination distribution (i.e. the “focal volume” or the “observation volume of the illumination spot”) produced by the constructive interference of the collimated waves. Altogether, the sources span a solid angle Ω = 2π (1-cosθ), corresponding to the numerical aperture (NA) of a conventional objective lens with half opening angle θ. Published in Scientific Reports under the Creative Commons Attribution License (CC-BY) [15]by Birk et al. [7].
  • Fig. 2: Focal spot for sources covering a solid angle of Ω = 1.25π. Intensity distribution calculated for 6,580 sources distributed over Ω = 2π (1-cosθ) = 1.25π (this corresponds to an objective lens with NA =1.4). In this calculation, the refractive index at the position of the focus is given by n = 1.518. (a) Lateral distribution of the focal intensity F(x,y). (b) Profile across the lateral focus intensity distribution along the x- or y-axis. (c) x-z-section through the focus intensity distribution. (d) Shows the corresponding axial profile Fx=y=0(z). In principle, the light sources may be positioned at arbitrary large distances from the focal region. Published in Scientific Reports under the Creative Commons Attribution License (CC-BY) [15] by Birk et al. [7].
  • Fig. 3: Implementation of Stimulated Emission Depletion (STED)/MINFLUX mode. Left: z-projection of the arrangement of N = 6,576 coherent light sources (e.g. glass fibers with low numerical aperture) directed towards the origin. Sources are distributed within a solid angle of Ω = 2π(1-cosθ) = 1.25π (This corresponds to an objective lens with NA =1.4). Center: y-z section across the intensity distribution around the origin. The STED beam width given (axial: 378 nm, lateral: 293 nm) refers to the FWHMs of the respective minima (z; x,y). Right: x-y section across the intensity distribution around the origin. For STED-type illumination, half of the sources in the center were phase-delayed by π. In principle, the STED producing light sources may be positioned at arbitrary large distances from the focal region. Instead of using the donut structure at high illumination intensities for STED, it may be used also in the low illumination “Minflux” mode for enhancing the optical resolution down to the nm range. Published in Scientific Reports under the Creative Commons Attribution License (CC-BY) [15] by Birk et al. [7].
High-resolution microscopy methods typically use objective lenses with large numerical apertures, i.e. low working distances (WD) in the range of 0.2 mm. This impedes its application to thick transparent specimens, or to objects with large topographical differences. To extend high-resolution microscopy also to whole tissues and to the material sciences, lens free microscope systems allowing WDs up to the multicentimeter range and an optical resolution down to the nanometer range may be constructed.
 
Light Microscopy is one of the most important optical methods in biology and medicine, as well as in the material sciences. In combination with super-resolution microscopy (SRM) approaches [1,2] it allows an optical resolution down to the few nanometer scale. Its application in the high-resolution range, however, is substantially limited by the small working distance of ca. 0.2 mm, due to the use of high numerical aperture (NA) objective lenses. With light in the visible spectrum, according to the Abbe/Rayleigh criteria lateral resolution values around 200 nm are attained for high numerical apertures (NA ~ 1.30), and around 400 - 500 nm for moderate apertures (e.g. NA ~ 0.60) for imaging of objects with long distance objective lenses (mm range). Since optical microscopy inside a medium with refractive index n provides a depth of focus L = n λ/NA2, for low NAs required to realize large working distances (WD), the focal depth may increase to the multi-micrometer range (e.g. L = 91 μm for NA = 0.1, λ = 600 nm, n = 1.515). To enhance the resolution at larger WDs, Structured Illumination Microscopy (SIM) may be used [3,4]. In the linear (low illumination intensity) mode, the achievable enhancement of resolution is about 2x when illuminating through the objective lens. The above mentioned resolution criteria together with the 2-fold enhancement by SIM yield a lateral resolution around 360 nm and an axial resolution of about 2.2 µm (λ = 500 nm, n = 1.515) for a long working distance objective lens (WD = 2 cm, NA = 0.42). Experimentally, such a SIM enhanced resolution and contrast with low NA objective lenses has been realized [5]. By using an innovative spot illumination pattern instead of grid lines, Lattice SIM [6] overcomes some of the limitations of classic SIM regarding deep imaging with higher contrast and robustness for image processing.

In the following, it is described an alternative approach based on a “lens free” illumination concept to combine high/enhanced resolution with very large working distances; this approach could lead to the development of “lens free” super-resolution microscopy.

 
Distributed Aperture Microscopy (DAM)
Since the axial resolution deteriorates with the square of the NA value, a 3D resolution of a biological object (e.g. a cell) in the range of a few hundred nm is possible with high NA only, i.e. at relatively low working distances (typically far below 1 mm). This excludes larger objects, such as cell spheroids, embryos, or tissues to be imaged at such a high 3D resolution.
These limits may be eliminated, however, using an illumination device with multiple collimated laser beams (“Distributed Aperture Illumination”, DAI) directed constructively to a given object region (“Distributed Aperture Microscopy”, DAM [7]). This allows to realize high NAs for the imaging optics at arbitrary large working distances [8]). Here it shall be discussed an approach using DAM in the confocal laser scanning mode [9], assuming for simplicity of argument stage scanning. DAM is based on the idea that an illumination pattern for high-resolution imaging may be realized also by combining multiple collimated laser beams characterized by appropriate incidence angles and phase relations between each other. To achieve this, various technical solutions are possible. Here it will be only discussed the general concept.
Figure 1 shows schematically the general arrangement to realize the multi-beam illumination concept of DAM.
As an example, figure 2 shows the result of detailed numerical calculations approximating the scanning focus of a high aperture objective lens by a distributed array of such phase matched laser beams. Using an appropriate array of multiple collimated laser beams with a total aperture corresponding to a high NA lens, an illumination focus with a Full-Width-at-half-Maximum (FWHM) around 160 nm in the object plane (x,y) and ca. 470 nm along the optical axis (z) can be produced (λ = 488 nm; n = 1.518) in a homogeneous, transparent medium. Using a “4π” arrangement [8], an isotropic FWHM of about 150 nm may be obtained [7]. Since each of the coherent light beams is collimated, the distance of the sources is in principle arbitrary, i.e. this distance can be varied within large limits (e.g. up to several cm or more); this, however, is equivalent to the possibility to realize a joint ‘focal spot’ for scanning based imaging. The joint ‘focal spot’ can be made substantially smaller than possible with low aperture objective lenses appropriate to realize the same large working distance; hence an enhanced resolution will be obtained compared with a lens-based system at the same large working distance. Since the position information for the fluorescence intensity of a given target site is obtained by the localization of the DAI focused laser beams given e.g. by the stage coordinates, the fluorescence can be detected as the joint signal of e.g. a number of small low aperture lenses at large WDs in the emission path. Numerical simulations using the same algorithms as in figures 2 have shown that an efficient focusing can be obtained already with a few hundred collimated beams; hence for detection a large WD/low NA detection lens could alternatively be inserted between the excitation laser beams.
The concept of the distributed aperture illumination (DAI) can also be implemented into various super-resolution microscopy approaches. For example, by reduction of the effective aperture of the DAI arrangement, the focal diameter may be broadened to allow Single Molecule Localization Microscopy (SMLM) at a given small region of interest; or the DAI patterns may be generated in such a way that in addition to a diffraction limited focused beam, the generation of a depletion focus similar to that implemented in a Stimulated Emission Depletion (STED) microscope [10] is possible; or a low intensity donut illumination pattern may be used to allow super-resolution based on the “Minflux” concept [11]. The results of such numerical calculations for the STED/Minflux modus are depicted in figure 3. If such a DAI based donut distribution is applied to a previously excited ensemble of fluorophores, the concept of fluorescence depletion in the vicinity of the origin can be realized at arbitrarily large working distances, without requiring depletion intensities significantly higher than usually applied e.g. in commercial STED systems. In this way, a STED resolution down to few tens of nm may be realized at working distances up to the multi-centimeter range. In the Minflux modus (using a low intensity donut without the central focused excitation beam), a resolution enhancement down to the 1 nm range appears to become feasible at similarly large working distances. Instead, also other structured illumination patterns may be used in a way similar to the Minflux concept [12-14] to enhance the localization precision of single molecules (and hence the optical resolution) at low photon emission.
In addition to point scanning modes (including STED and Minflux related approaches), DAM might also be applied to allow pattern-based scanning modes like structured illumination (SIM) and light sheet microscopy (LSM) [5]). A decisive additional advantage of DAM in this respect is the possibility to program the DAI in such a way that the switching between different imaging modes can be done very fast.
 
Discussion
Focusing to larger depths within a sample requires long working distances at low or moderate aperture of objective lenses. This limits the resolution and increases the depth of focus.
Distributed aperture microscopy (DAM) offers completely new possibilities for 3D/Deep view imaging. DAM may permit to produce a very small focal diameter for point-by-point-scanning of the object at arbitrarily large working distances, and to efficiently detect the generated signal as a function of the “spot” position (e.g. fluorescence or scattering). Furthermore, it should be possible to perform STED/Minflux based super-resolution at a substantially larger working distance than possible with conventional objective lenses. Biomedical application examples are 3D microscopy of small model organisms, of cell spheroids in developmental biology, cancer research and pharmacology, neuronal “micro brains”/brain tissues in neurobiology, or entire organs, made suitably transparent by “tissue clearing” methods. In the material sciences, DAM is expected to allow high resolution analyses of samples with large topographical differences, such as narrow but deep cracks in rough surfaces; the high-resolution analysis of the surface of allergenic pollen; or the inspection of electronic circuits.
 
Acknowledgments
We thank H. Schneckenburger (Aalen/Ulm), S. Ritz and M. Gelleri (Mainz), and F. Schock (Heidelberg) for valuable comments.

 

Authors
Christoph Cremer1,2, Johann von Hase2, Udo Birk3

Affiliation
1Kirchhoff Institute for Physics (KIP), University Heidelberg, Germany, and Institute of Molecular Biology, Mainz, Germany
2Institute of Pharmacy & Molecular Biotechnology, University Heidelberg, Germany
3Institute for Photonics and ICT, University of Applied Sciences (FHGR), Chur, Switzerland

 

Contact
Prof. Dr. Christoph Cremer

Kirchhoff Institute for Physics (KIP)
Institute of Pharmacy & Molecular Biotechnology
University Heidelberg, Germany
cremer@kip.uni-heidelberg.de
Institute of Molecular Biology
Mainz, Germany
c.cremer@imb-mainz.de

References
[1] Christoph Cremer and Barry R. Masters: Resolution enhancement techniques in microscopy. Eur. Phys. J. H 38: 281–344 (2013) doi: 10.1140/epjh/e2012-20060-1
[2] Udo Birk: Super-Resolution Microscopy: A Practical Guide. Wiley-VCH (2017) doi: 10.1002/anie.201804434
[3] Mats G. Gustafsson: Extended resolution fluorescence microscopy. Curr. Opinion Struct. Biol. 9: 627-634 (1999) doi: 10.1016/s0959-440x(99)00016-0
[4] Rainer Heintzmann and Christoph Cremer: Lateral modulated excitation microscopy: Improvement of resolution by using a diffraction grating. Proc. SPIE 3568: 185-196 (1999) doi: 10.1117/12.336833
[5] Herbert Schneckenburger, Verena Richter, Marton Gelleri, Sandra Ritz, Renata Vaz Pandolfo, Florian Schock, Johann v. Hase, Udo Birk, and Christoph Cremer: High Resolution Deep View Microscopy of Cells and Tissues. Quantum Electronics, submitted Sept 2019
[6] Eric Betzig: Excitation strategies for optical lattice microscopy, Optics Express 13: 3021-3036 (2005) doi: 10.1364/OPEX.13.003021
[7] Udo Birk, U., Johann von Hase, J., and Christoph Cremer: Super-resolution microscopy with very large working distance by means of distributed aperture illumination. Sci. Rep. 7:3685 (2017) doi: 10.1038/s41598-017-03743-4
[8] Christoph Cremer and Thomas Cremer: Considerations on a Laser-Scanning-Microscope with high resolution and depth of field. Microsc. Acta 81: 31 – 44 (1978)
[9] James Pawley: Handbook of Biological Confocal Microscopy, 3rd ed., Springer: Boston, MA, USA (1990) 10.1007/978-0-387-45524-2
[10] Stefan W. Hell and Jan Wichmann. 1994. Breaking the diffraction resolution limit by stimulated-emission-depletion fluorescence microscopy. Optics Letters 19: 780- 782 (1994) doi: 10.1364/OL.19.000780
[11] Francisco Balzarotti, Yvan Eilers, Klaus C. Gwosch, Arvid H. Gynnå, Volker Westphal, Fernando D. Stefani, Johan Elf, and Stefan W. Hell: Nanometer resolution imaging and tracking of fluorescent molecules with minimal photon fluxes. Science 355, 606–612 (2017) doi: 10.1126/science.aak9913
[12] Benno Albrecht, A. Virgilio Failla, Rainer Heintzmann, and Christoph Cremer: Spatially modulated illumination microscopy: online visualization of intensity distribution and prediction of nanometer precision of axial distance measurements by computer simulations, Journal of Biomedical Optics 6: 292–299 (2001) doi: 10.1117/1.1383293
[13] Gerrit Best, Christoph Cremer, Sabrina Rossberger, and Stefan Dithmar: Method and apparatus for combination of localization microscopy and structured illumination microscopy. US Patent 9 , 874 , 737 B2, filed May 7 , 2014 (granted Jan 23, 2018)
[14] Jelmer Cnossen, Taylor Hinsdale, Rasmus Ø. Thorsen, Florian Schueder, Ralf Jungmann,Carlas S. Smith, Bernd Rieger, and Sjoerd Stallinga: Localization microscopy at doubled precision with patterned illumination. bioRxiv preprint (2019) doi: 10.1101/554337
[15] Creative Commons – Attribution International – CC BY 4.0, https://creativecommons.org/licenses/by/4.0/

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