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Experimental demonstration of Multi Moiré structured illumination microscopy DORON SHTERMAN, Bergin Gjonaj, and Guy Bartal ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b00280 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on April 25, 2018
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Experimental demonstration of Multi Moiré structured illumination microscopy Doron Shterman, † Bergin Gjonaj, † and Guy Bartal †* †
Faculty of Electrical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Supporting Information Placeholder required control over the illumination patterns while introducing high spatial illumination pattern frequencies via a high NA objective as a substitute for the high-index material. Namely, we use the MM-SIM to effectively increase the resolution power of a low NA objective from NA=0.4 up to an equivalent of NA=1.6 without using immersion in the detection system to increase the resolution. This particular setup of MM-SIM is also beneficial for exploiting the benefits of low NA objectives like apparatus simplicity and large field of view without compromising on the resolution. Visual comparison with a secondary high NA diffraction limited measurement provides reference point of view for evaluating the super-resolution reconstruction results. The novelty of the Multi Moiré scheme we demonstrate is based on its ability to introduce a combination of high spatial frequencies in the illumination pattern profile, while preserving the required controllability over the relative illumination patterns phase and amplitude throughout the SIM image acquisition process. Packed into a simple and robust optical setup, the MM-SIM has the potential to be the next practical step for high performance super-resolution fluorescence microscopy realization. Multi Moiré SIM employs illumination patterns consisting of a combination of high and intermediate spatial frequencies which facilitate the reconstruction of continuous broad range of spatial frequencies. One-dimension multi-periodic illumination pattern can be generated by the coherent interference of at least two standing waves U and U :
ABSTRACT: Structured Illumination Microscopy (SIM) improves spatial resolution by folding high frequency spectral components into the optical system passband. Though linear SIM is superior in terms of temporal resolution, living-cells imaging compatibility and overall optical setup simplicity relative to other super-resolution techniques, it is, however, inferior when it comes to spatial resolution enhancement capability. In this letter, we present experimental demonstration of a novel Multi Moiré SIM (MM-SIM) scheme achieving superior lateral resolution enhancement while preserving linear SIM inherent advantages. Using MM-SIM an approximate 4-fold lateral resolution enhancement was achieved, effectively increasing the optical system's NA from 0.4 to 1.6. The MM-SIM scheme is a simple and robust realization of 4-fold resolution enhancement capable of unleashing the full potential of standing-wave TIRF-SIM while preserving SIM inherent advantages. KEYWORDS: super-resolution, fluorescence microscopy, structured illumination microscopy
Structured illumination microscopy (SIM) utilizes illumination of periodic light patterns to allow reconstruction of high spatial frequencies, conventionally doubling1 the microscope’s resolving power, with respect to abbe diffraction limit.2 Though inferior in its spatial resolution to other super-resolution microscopy methods like stimulated emission depletion3,4 and localization-based techniques5,6 SIM stands out7 for its advantage in terms of apparatus simplicity, temporal resolution and compatibility with live samples measurements. The great potential and significant advantages of SIM have driven the motivation to improve its resolution so as to become on par with localization-based techniques. These improvements all rely on generating illumination patterns containing higher spatial frequencies by utilizing high-index materials,8–10 gratings,11 short wavelength plasmonic modes12–15 or non-linear effects.16 However, a simple, robust and highly controllable SIM scheme enabling significant resolution increase of linear SIM by using high-index materials has only recently been proposed.17 Here, we present a first experimental proof of concept (POC) of the Multi Moiré SIM scheme, capable of providing the entire
U = e cos(π f r + φ )
U = e cos(π f r + φ )
( 1) ( 2)
Where θ , f and φ are the amplitude phase, illumination profile spatial frequency and the illumination profile spatial phase respectively. The combined illumination intensity I is given by:
I (r) = |U + U | =
= I 2 + cos 2π f r + 2φ + cos 2π f r + 2φ +
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+ 2cos(∆θ) cos(π(f + f )r + φ + φ ) + + !"(#($ − $ )& + ' − ' ) (,
which were shifted into or originally included within the OTF passband. Similarly to the standard SIM reconstruction process, this can be accomplished by solving a set of nine linear equations, each being eq. (6), with the functions ϕ changing with accordance to the phases φ , φ and ∆φ which were used to obtain I> -*.,= (k) for n = 1, . . . , 9:18
( 3)
Where ∆θ = θ − θ and unity amplitude was taken for simplicity. The Multi Moiré illumination profile I would contain in this case a super position of the two main standing waves with frequencies f and f , which translates into the following 4 distinct frequencies; f , f , ($ − $ )/2, and ($ + $ )/2, as can be seen from eq. (3). Given a fluorophore density distributions (r), the emitted light I*+ (r), in the real domain, can be written as:
I*+ (r) = s(r) ∙ I (r)
( 4)
I-*. (r) = I*+ (r) ⨂ h(r)
( 5)
2 I> -*., (k) D G = DH ⋮ ⋮ 2 I> -*.,F (k)
And light detected by an optical system, I-*. (r), is given by:
⋯ ⋱ ⋯
ϕ∗J, s3(k) h8(k) ⋮ LG M ⋮ N∙ 2 ϕ∗J,F s3(k − π f − f )
( 7)
Inverting the 9X9 phase matrix we retrieve the 9 spectral components s3 that were folded into the diffraction limit observable region. Next, the image Fourier representation is reconstructed by placing each spectral component s3 back into its originated position. This process is then repeated for additional spatial illumination directions where, unlike for the standard SIM, in MM-SIM more than just 3 spatial illumination orientations are used in order to achieve a continues coverage of the spatial frequency domain. For MM-SIM generated with two standing waves interference, demonstrated herein, 6 evenly distributed spatial tions O P 0°, 30°, 60°, 90°, 120°, 150° are required. The POC scheme, presented in Figure 1, enhances the performance of a low NA (0.4) objective in the transmittance channel, i.e. the fluorescence signal collection path, while using a high NA (1.3) objective in the illumination channel to introduce the high frequency illumination pattern profile. This is achieved by generation of Multi Moiré standing waves illumination interference pattern with spectral frequency of up to than 4 times higher than the transmittance channel's maximal NA passband frequency. A spatial light modulator (SLM) is used to generate such pattern in six spatial orientations and to provide the necessary control over the illumination patterns.17 Implementing a dedicated digital mask over the SLM provides full control over the reflected plane-wave phase.19 The pattern we implement on the SLM selectively reflects only a spatially confined portion of the collimated laser beam illuminating the SLM hence, adjusting the mask to reflect only 4 spatially confined locations, as seen in Error! Reference source not found., we create 4 independently controlled laser beams. Each pair creates a single standing-wave, with specific spatial frequency and phase, as they interfere at the objective focal point. In fact, the MM-SIM can be regarded, and also executed, as a linear sum of 4 "standard" independent SIM processes.
Where ⨂ denotes the convolution operator and h(r) is the system point spread function (PSF). In Fourier domain eq. (5) translates to:
I1 3(k) + -*. (k) = I ∙ 2s
+ϕ5 s3(k + 2π f ) + ϕ∗5 s3(k − 2π f ) +
+ϕ7 s3(k + 2π f ) + ϕ∗7 s3(k − 2π f ) +
+ϕ. s3(k + π f + f ) + ϕ∗. s3(k − π f + f ) +
+ϕ- s3(k + π f − f ) + ϕ∗- s3(k − π f − f ) ∙ h8(k),
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( 6)
Where ˜ denotes the Fourier transform, h8(k) is the system optical transfer function (OTF), ϕ where i = q, b, c, d are functions of the phases φ , φ and ∆φ,18 and the superscript ∗ denotes the complex conjugate. Eq. (6) shows eight distinct shifted, and one non-shifted, fluoro1 (k), indicating a spatial phore Fourier spectral component s3 in I-*. frequency range of up to four times larger (relative to uniform illumination) that is being folded into the OTF passband. By taking a set of nine images, while changing each of the phases φ , φ and ∆' independently, one can reconstruct s3 for all frequencies
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Figure 1: Schematics of the experimental MM-SIM setup. Excitation laser is collimated onto a spatial light modulator (SLM) which provides both phase and amplitude control over the reflected laser beam. A set of four spatially separated, and independently controlled, reflected beams are then passed through a polarizer and into the entrance pupil of an Oil Immersion Objective, with relative high-NA (1.3). This objective lens is used for generating the illumination pattern and also provides the reference measurement. The four beams interfere at the focal plane of the objective, coinciding with a fluorescence beads sample, to create "Multi Moiré Illumination" pattern. The illumination pattern excites the fluorescence beads emission response which is than collected with a relative low NA objective (0.4) and imaged with an EMCCD after going through a spectral filter that separates the emission and excitation signals. The performance enhancement is of the low-NA objective lens. The actual scheme we utilized for this demonstration was comprised by a Red HeNe 633 [nm] excitation laser by Newport, "Pluto" 1920X1080 SLM by Holoeye, Nikon Plan Flour 100x Oil immersion objective (NA 1.3), Mitutoyo low-NA objective (NA 0.4) and iXon Ultra EMCCD by Andor. illumination pattern (d). 6 different angles are required for reconstructing the entire 2D spatial domain. The spatial frequency of the standing wave (SW) pattern is governed by the lateral distance between the reflected beams. Here, the reflections represented by the two inner bright spots of the SLM mask generate SW with spatial frequency $ , while those represented by the outer bright spots generate SW with spatial frequency $ . A line cut Fourier decomposition of the horizontal SW pattern (b) is shown in (e) and includes all possible combinations of the SW patterns frequencies as well. The relative modulation depths are also clearly visible in the graph with full compliance to the theory. For this demonstration, we have used a simple iterative approach as the baseline for the image reconstruction process based on a linear extrapolation of the basic SIM reconstruction.1 However, unlike other SIM reconstruction schemes challenges,20–26 the MM-SIM is exceptional in the sense that most parts of the illumination patterns are not accessible with the imaging objective since they contain spatial frequencies lying beyond the optical system passband. Therefore, they cannot be used for evaluating missing reconstruction parameters. We overcome this inherent shortcoming by acquiring an additional single image under uniform illumination conditions, constituting a "pure" DC spectral frequency component, free from any aliasing interference. This DC component is used as the benchmark for the entire reconstruction process. Namely, we use it to "decode" the moiré patterns, where the correlation value of the DC components is used for assessing the relative illumination patterns phases. This allows us next to extract the illumination spatial frequencies, determine the relative modulation factors between adjacent spectral components, and retrieve the Weiner filter and apodization function parameters.27–30 The reconstruction algorithm logic is described in the supplementary section.
Figure 2: Pattern implemented on the SLM and its corresponding Multi Moiré illumination profile. Collimated laser beam is reflected from the SLM mask to create the required Multi Moiré illumination pattern at the high NA objective focal point. (a) a horizontally oriented pattern on the SLM, representing 4 wave-vectors, denoted by the bright spots, (b) the corresponding illumination pattern created in the Fourier plane through a high NA (1.3) objective lens. A slanted pattern on the SLM (c) results in a slanted
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Figure 3: MM-SIM Experimental results. Super-resolution demonstration for fixed fluorescence beads, (Spherotech, Sky Blue, FP-0270-2) utilizing MM-SIM scheme shown in Figure 1. (a) Diffraction limited measurement taken with the low NA (0.4) objective. (b) "Standard" SIM reconstruction results, utilizing a single illumination pattern frequency and a reconstruction algorithm as described in.1 (c) Multi Moiré SIM reconstruction results, utilizing a mix of 4 illumination patterns frequencies and an extended reconstruction algorithm, showing significant resolution increase beyond the "standard" SIM. (d) Single bead FWHM cross-section comparison, from 1.16 [µm] in the diffraction limited system, through 0.7 [µm] accomplished by "standard" SIM process and up to 0.3 [µm] achieved with Multi Moiré SIM. A 3D representation of the fluorescence beads image is shown as well, for the diffraction limited (e), "standard" SIM (f) and Multi Moiré SIM image (g). The peaks in the figures, corresponding to the fluorescence beads in the sample, are clearly more distinguishable in the MM-SIM relative to the standard SIM both in terms of lateral spatial confinement as well as modulation depth. defines the optical system resolution power. While the "standard" SIM process has produced a resolution enhancement of 1.8-fold with respect to the diffraction limited system the MM-SIM has reached a resolution enhancement of ~3.9-fold, as seen in Figure 3Error! Reference source not found.d. The 2D fluorescence image shown in Figure 3Error! Reference source not found.(a)-(c) is however not necessarily sufficient for evaluating and comparing the resolution enhancement since the modulation depth between adjacent peaks in not easily comparable. The 3D representation of the same fluorescence image, shown in Figure 3Error! Reference source not found.(e)(g), provides a clear distinction in terms of the peak to valley modulation depth, eliminating any suspicion for "engineered" image resulting from gray level dynamic range representation.
RESULTS AND DISCUSSION A comparison between diffraction limited image, "standard" SIM reconstructed image and Multi Moiré reconstructed image, produced with the presented POC system, is provided in Figure 3Error! Reference source not found.. For a diffraction limited optical system with NA of 0.4 the "standard" SIM reconstruction shows approximately a 2-fold resolution enhancement while the MM-SIM doubles that to ~4-fold resolution enhancement with full compliance to the theory. In order to quantify the resolution enhancement, we compare the cross-section of a single fluorescence bead between the different imaging schemes. Recalling Abbe's resolution limit, FWHM system response for a point source (single fluorescence bead for example), which is also equivalent to the system PSF FWHM,
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ACS Photonics We ascertain the validity of our method using the reflectance channel in the POC scheme to obtain a ground-truth high resolution reference image, captured with the high NA objective. Visual comparison between the MM-SIM reconstructed image and the high-res reference image, shown in Figure 4, reveals the MM-SIM reconstruction accuracy. It is hence clear that the resolution enhancement is genuine and the smaller detectable features, with respect to the diffraction limited and standard SIM products are not a false attribute of the reconstruction process or postprocessing distortion.
Corresponding Author *E-mail:
[email protected] Funding Sources This work was partially supported by the KAMIN project Number 59006 from the Israel Innovation Authority in Israel's Ministry of Economy.
Notes The authors declare no competing financial interests.
ACKNOWLEDGMENT The authors acknowledge fruitful discussions with Y. Blau S. Dolev and O. Eyal.
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Figure 4: Multi Moiré SIM VS reference image. Comparison between ground-truth high resolution image (a) taken with the high NA objective through the reflection channel described in Figure 1, and the MM-SIM reconstructed image (b). This visual comparison verifies that the reconstructed image does represent the physical reality truthfully.
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CONCLUSION
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We demonstrated experimentally the capability of Multi Moiré SIM to provide 4-fold resolution enhancement beyond the diffraction limit of a given system. While demonstrating a proof of concept on a low-NA system, a platform based on high-index materials, as detailed,17 could potentially provide lateral resolution power better than ~60 [nm] for fluorescence excitation of ~550 [nm] making linear SIM on par with localization-based techniques. Extension of the Multi Moiré scheme for the axial dimension as well is limited however since it is relying on the TIRF mechanism for introducing the high spatial frequency illumination profile. The Multi Moiré SIM is a highly controllable low-loss realization of structure illumination microscopy offering the necessary features for high speed super-resolution microscopy. This combination of resolving power with the known speed, wide-field coverage and low illumination intensity advantages of structured illumination microscopy, has the potential of making MM-SIM highly favorable among other microscopy techniques, especially for exploring living organisms dynamics in the several tens of nanometers scale.
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ASSOCIATED CONTENT Supporting Information
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The Supporting Information is available free of charge via Internet at http://pubs.acs.org Image reconstruction method (PDF)
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For Table of Contents Use Only
"Experimental demonstration of Multi Moiré structured illumination microscopy" Doron Shterman, Bergin Gjonaj, and Guy Bartal
TOC Graphic
The images shown in the TOC graphic are Multi-Moiré illumination patterns implemented and recorded as part of the experimental demonstrations described in the article.
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