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Contrast and resolution enhanced optical sectioning in scattering tissue using line-scanning two-photon structured illumination microscopy

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Abstract

Optical sectioning imaging with high spatial resolution deep inside scattering samples such as mammalian brain is of great interest in biological study. Conventional two-photon microscopy deteriorates in focus when light scattering increases. Here we develop an optical sectioning enhanced two-photon technique which incorporates structured illumination into line-scanning spatial-temporal focusing microscopy (LTSIM), and generate patterned illumination via laser intensity modulation synchronized with scanning. LTSIM brings scattering background elimination and in-focus contrast enhancement, and realizes nearly 2-fold increase in spatial resolution to ∼208 nm laterally and ∼0.94 µm axially. In addition, the intensity modulated line-scanning implementation of LTSIM enables fast and flexible generation of structured illumination, permitting adjustable spatial frequency profiles to optimize image contrast. The highly qualified optical sectioning ability of our system is demonstrated on samples including tissue phantom, C. elegans and mouse brain at depths over hundreds of microns.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Fluorescence microscopy technique has emerged as a powerful tool for biological applications such as cell biology and neuroscience [1]. Two-photon laser scanning microscopy (TPM) can achieve deep penetration into turbid specimens with highly confined axial resolution, thus being the ideal choice for optical section imaging in thick scattering samples [2, 3]. However, the point-scanning scheme is generally not applicable for rapid acquisition of high throughput information, with one main limitation to be the response speed of scanning devices [4].

Recently, temporal focusing microscopy (TF), a wide-field two-photon technique, has been developed to achieve optical sectioned excitation of 2D planes [5, 6] or scanning lines [7, 8] in the sample via laser pulse duration modulation. This non-scanning or line-scanning scheme is intrinsically superior in rapid acquisition time and access to large field-of-view. Line-scanning modality (LSTF), in which spatial focusing and temporal compression of excitation laser are simultaneously achieved, reveals higher scattering robustness than planar illumination as well as better axial confinement [9,10]. It has been theoretically evaluated that LSTF can achieve axial resolution similar to that of confocal microscopy and penetrate hundreds of microns deep [11]. Taking the above advantages, we design line-scanning two-photon microscopy based on LSTF to guarantee large volume imaging with fine optical sectioning.

Yet more importantly, one limitation of two-photon microscopy is that, as the penetration depth rises, constantly increased light scattering will severely degrade the image resolution and contrast [12]. To address the scattering problem, two approaches have been proposed by researches and successfully implemented in microscopy. One is using adaptive optics (AO) to correct the wavefront aberration and retrieve diffraction-limited focus [13, 14]. However, AO requires time-consuming calculations and is effective only within small regions neighboring the focal spot, holding it from fast imaging in large field-of-view. Structured illumination microscopy (SIM) is a wide-field imaging technique which offers lateral resolution up to 2× beyond the diffraction limit, and more importantly, scattering background suppression under simple and fast operation [15,16]. These properties make SIM an applicable solution to achieve high-resolution optical sectioning in wide-field imaging. Considering the benefits in operation speed and wide-field imaging adaptation, we propose to implement SIM into the line-scanning two-photon temporal focusing (LTSIM) to compensate the scattering-induced resolution and contrast degradation.

Generally used configuration in SIM creates structured illumination by interfering two laser beams diffracted from a ruled grating [17]. Nevertheless, mechanical shifting is required to obtain patterns with different phase profiles, and the frequency of interfered stripes is fixed given the grating groove density. Thus, traditional SIM suffers from low speed and inflexibility. Replacing the grating with a programmable spatial light modulator provides an alternative for fast and flexible switching [18, 19], but works at low photon efficiency. Moreover, the patterned planar illumination is susceptible to scattering, and its aberration might fail the reconstruction. Inspired by the fact that sinusoidal patterns only vary along one dimension, we design a line-scanning SIM configuration which synchronizes sinusoidal intensity modulation of line-shaped excitation laser with orthogonal scanning. Frequency and phase profiles of illumination patterns are determined by the sequential output of a fast electronic-controlled acousto-optical modulator in our setup. Proposed line-scanning SIM design has advantages including higher signal-to-noise ratio and tolerance to scattering compared with wide-field excitation [9, 10], fast and stable performance for phase shifting in an electronic manner, and adjustable modulation frequencies according to scattering properties.

LTSIM takes advantage of capabilities of SIM in superresolution and eliminating scattering aberration, and the robustness and flexibility of line-scanned structured illumination scheme, thus enables highly qualified optical sectioning of thick scattering tissue with enhanced spatial resolution and image contrast. In addition, the line-scanning temporal focusing technique provides potential for rapid imaging with wide field-of-view. We provide implementations of LTSIM with ∼208 nm lateral resolution and ∼0.94 µm axial resolution in scattering samples including tissue-like phantom, C. elegans and mouse brain.

2. Methods

2.1. Optical design of LTSIM

The schematic of line-scanning two-photon structured illumination microscopy is illustrated in Fig. 1. It is based on the design of line-scanning temporal focusing microscopy [9], in which a diffraction grating is imaged onto the focal plane inside the sample through a 4f-system composing a tube lens (TL1) and the objective. Laser beam from an 80 MHz Ti:sapphire oscillator (Coherent, Vitara-T) with the pulse duration of ∼70fs at central wavelength of 800 nm was used for the two-photon excitation. The laser power is controlled by a polarized beam splitter and a half-wave plate. A pair of SF10 prisms are used to compensate the temporal dispersion caused by transmissive optical components of the system. The laser beam is then condensed by two 4f-configured lenses to 1 mm in diameter, and passes through the acousto-optical modulator (Gooch & Housego, AOMO 3080-125). The AOM is controlled by a radio frequency signal and diffracts the first order light off at a diffraction angle of ∼2° at efficiency above 90%. Modulated laser is afterwards expanded by a 4× beam expander (f1 = 50 mm, f2 = 200 mm), polarization-rotated by an HWP, scanned in vertical direction by a one-dimensional galvanometer (Thorlabs) and focused to a thin line by a cylindrical lens (fcyl = 100 mm) at the surface of the diffraction grating (Edmund Optics, 830 lines/mm). A reflection mirror placed between the cylindrical lens and the grating directs the light incident at ∼42° to ensure that the central wavelength of 1st diffracted light is reflected in the original propagation direction. A collimating lens (f = 200 mm) and a 60×, 1.0 NA objective (Olympus, LUMPLFLN60XW) placed in 4f configuration deliver the line-shaped illumination on the grating to the objective focal plane. The length of the temporal focusing focal is around 60µm. For each scanning period, we captured a fluorescent image using an epi-fluorescent setup including a dichroic mirror (Chroma), a lowpass filter (Brightline), a bandpass filter (Brightline), a 200 mm tubelens (Edmund Optics) and an sCMOS (Andor Zyla 4.2 plus, pixel size 6.50µm).

 figure: Fig. 1

Fig. 1 Line-scanning two-photon structured illumination system design. The ultrashort pulsed laser is modulated in intensity by the acousto-optical modulator and provides a line excitation to the sample. Synchronizing the line-scanning and intensity modulation results in a sinusoidal illumination pattern. The fluorescence image is collected by a camera in epifluorescence microscopy scheme. Temporal chirp induced by the grating is first broadened then compressed to the minimum at the objective focus to improve axial confinement. Symbols: HWP, half wave plate; PBS, polarized beam splitter; M, reflective mirror; TL, tube lens; DM, dichroic mirror; BPF, bandpass filter; SPF, shortpass filter.

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The grating disperses the wideband laser in spectrum and introduces temporal chirp to the Fourier transform limited laser pulse. Pulse duration reaches its minimum only at the focal plane of the objective and broadens rapidly along longitude direction [5, 7], resulting in a compressed axial confinement (see Fig. 1(c)). The cylindrical lens converges the light beam into a thin line at the grating surface and the vertically scanning galvanometer mirror reflects the line-shaped laser, leading to a lateral scanning on the specimen. Three-dimensional imaging can be achieved through axial movement of the sample stage.

Hardware synchronization is carried out using a multi-functional DAQ (NI Instrument, USB-6363), with three voltage output channels controlling the response of AOM, galvanometer scanner and camera acquisition respectively. Suppose the angular velocity of galva scanning to be ω, the line-scanning velocity for small angle scanning is approximated as v = ω × fcyl. Given the exposure time texp, we can calculate the height of field-of-view as H = v ×texp. Therefore, to create a structured illumination pattern with spatial frequency of s at the focal plane, the periodicity of sinusoidal stripes should be

N=sMH=sMwfcyltexp,
where M represents the magnification of the lens-objective-composed 4f configuration.

2.2. Structured illumination of LTSIM

We take advantage of structured illumination microscopy and create sinusoidal patterns through intensity-modulated line scanning as illustrated in Fig. 1(b). We use an acousto-optical modulator (AOM) with response time less than 200 ns to rapidly control the excitation intensity in a sine function. To better exploit the benefits of SIM with two-photon excitation, we employ both first and second harmonic spatial frequency components in a nonlinear mode [20], which requires five patterns with equally spaced phases from 0 to 2π to reconstruct one fluorescence image. To generate structured patterns with different frequencies and phases, we simply change the radio frequency input signal of the AOM (the response of AOM was pre-calibrated). We captured example images of structured patterns by illuminating a fluorescent plastic slide (Chroma, 92001) with different frequencies and phases and displayed them in Fig. 2. To numerically evaluate the quality of generated illumination patterns, we fitted the intensity distribution in spatial domain and measured the five frequency components in Fourier domain.

 figure: Fig. 2

Fig. 2 Evaluation of line-scanning structured illumination. (a) shows the 2D excitation of a fluorescent layer captured by the sCMOS through line-scanning with and without intensity modulation, where N denotes the sinusoidal period number in the FOV. (b) shows magnified subregions of structured patterns with different phase profiles (N = 20). Scale-bar = 10 µm. We measured the intensity fluctation on a selected line of the fluorescent image from (b), as illustrated in (c), and calculated the [1 + m cos(kpr)]2 function fitting of discrete sampling points. (d) presents the Fourier transform of the spatial intensity data. We can clearly see the five spatial frequency components in frequency domain. We magnified the 0, +1 and +2 ordered spatial components in (e) and quantified that kp equals to 0.2 µm−1.

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To fully utilize the nonlinear effects of two-photon, we adopt nonlinear structured illumination algorithm. Denoting the excitation light to be

I(r,ϕ)=I0(1+mcos(kpr+ϕ)),
the fluorescent signal can be expressed as
s(r,ϕ)={c(r)I(r,ϕ)2}*h(r)={c(r)I02[1+m22+m(ei(kpr+ϕ)+ei(kpr+ϕ))+m24(ei2(kpr+ϕ)+ei2(kpr+ϕ)]}*h(r),
where c(r) denotes the sample property and h(r) is the point-spreading function of the optical system. We then Fourier transform it and get
S(k,ϕ)={C(k)+m1+m2[C(kkp)eiϕ+C(k+kp)eiϕ]+m24+4m2[C(k2kp)ei2ϕ+C(k+2kp)ei2ϕ]}×H(k).
There are five spatial frequencies, 0, ±kp, ±2kp, in the expression. To retrieve the corresponding frequency components C(klkp), we can capture five images using patterns with different phases ϕl, l = 0, ±1, ±2 and solve a linear function. By recombining the shifted frequency components in frequency domain and conducting inverse Fourier transform, we can obtain the superresolution and scattering-free reconstruction. Commonly, we choose structured illumination patterns with equally-spaced phases (e.g, 0°, 72°, 144°, 216° and 288°) at a fixed kp for one reconstruction. Considering the existing aberrations of spatial frequency and phases, we estimate these parameters by optimizing cross-correlation functions based on the algorithm proposed in [21].

3. Results

3.1. Resolution and contrast improvement in LTSIM

To demonstrate the resolution improvement of LTSIM, we first quantified the spatial resolution by imaging 100 nm-diameter green-labeled fluorescent microspheres (Invitrogen 1807712). The results show a decrease in lateral full width at half maximum (FWHM) from 410 nm to 284 nm and 208 nm after deconvolution, as well as in axial FWHM from 1.61 µm to 1.13 µm and 0.94 µm after deconvolution (Fig. 3). Noted that the lateral FWHM we define here is measured only along the scanning dimension and the resolution on perpendicular dimension should remain unchanged. The structured illumination method nearly doubles the resolution laterally and axially compared to uniform illuminated two-photon imaging. The axial resolution improvement enables thinner excitation plane inside samples.

 figure: Fig. 3

Fig. 3 Measurement of three-dimensional psf for LTSIM (N = 40). (a) shows lateral FWHMs of LT microscopy, LTSIM and LTSIM after deconvolution. (b) shows axial FWHMs of LT microscopy, LTSIM and LTSIM after deconvolution.

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We then studied the contrast and resolution enhancement on biological samples by imaging fixed bovine pulmonary artery endothelial cells (BPAE) whose f-actin structure is stained with Alexa Fluor 488. Fluorescent images captured using uniform illuminated line-scanning TF, LTSIM and LTSIM after deconvolution are presented in Fig. 4. Compared with uniform illuminated LSTF two-photon imaging, our structured illumination modality achieves better performance with high contrast and low background noise. Thin structures blurred in scattering background under uniform illumination imaging is well preserved after SIM. Deconvolution process further improves spatial resolution, allowing a clear visualization of single microtubules and distinguishing of closely distanced microtubules. We magnified a subregion of the cell and measured the intensity fluctuations along indicated lines in all methods. It is noticeable that LTSIM provides a big image contrast enhancement.

 figure: Fig. 4

Fig. 4 Image contrast and resolution enhancement in LTSIM. (a) (b) and (c) are f-actin structures of one same BPAE cell imaged under uniform illuminated LSTF, structure illuminated LTSIM (N = 40) and LTSIM after deconvolution. The insects are magnified views of the squared region, illustrating the imaging performance by LSTF, LTSIM and deconvoluted LTSIM. (d) Intensity along the line-marked region. Scale-bar = 5 µm in (a) (b) and (c) and 2.5 µm in magnified views.

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3.2. Enhanced optical sectioning imaging of scattering sample

Having demonstrated the spatial improvement of LTSIM in thin sample, we then characterized its optical sectioning performance in thick scattering samples. We first imaged tissue-like phantom which contained 1 µm green fluorescent polystyrene beads and 1 µm non-fluorescent polystyrene beads embedded in 1.0% agarose gel at concentration of 3.3 × 109 beads/mL, corresponding to the scattering coefficient µs = 5 mm−1 at 800nm. We recorded images of fluorescent beads at multiple depths up to 500 µm from the coverslip surface, and selected individual beads to measure the signal-to-noise ratio (SNR) and signal-to-background ratio (SBR) in structured illumination and uniform illumination imaging methods. Raw images are captured at the same experimental conditions and the presented fluorescent intensity is normalized. The definitions of SNR and SBR are conducted on a small region C{i} surrounding one single bead of N = 10 × 10 pixels, and a background region B{i} of the same size. SNR is calculated as the ratio of signal intensity to background deviation SNR=iNCi(NiN(Bi1/NiNBi)2), and SBR is calculated as the ratio of signal intensity to background intensity SBR=iNCiiNBi. Figure. 5 illustrates representative beads and calculated SNR and SBR basing on three beads at each depth. Uniform illuminated two-photon imaging can excite bright and sharp signals at depths less than 300 µm but the fluorescent signal degrades as the penetration depth increases. However, LTSIM maintains higher SNR and SBR than uniform illumination at full depth scan, showing the advantage of high image contrast in deep scattering sample. Signal enhancement is mainly attributed to the scattering background subtraction. Moreover, through comparison of single slices between two methods, we also witness an obvious out-of-focus excitation suppression, which demonstrates the improvement of axial confinement in LTSIM.

 figure: Fig. 5

Fig. 5 Optical section imaging in tissue phantom. (a) shows representative image of fluorescence beads excited at different depths by uniform and structure illuminated (N = 20) two-photon microscopy without deconvolution. Scale-bar = 1 µm. (b) and (c) compare the SNR and SBR of fluorescent signals in two methods. Means and standard deviations are calculated from measurements of three beads at each depth.

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To further demonstrate the optical sectioning performance of LTSIM imaging biological specimens, we imaged a whole Caenorhabditis elegans whose actin fiber is stained with Alexa Fluor 488-phalloidin and cell nucleus stained with DAPI (Fig. 6). Taking advantage of the high throughput ability of line-scanning modality, we extended the FOV in the scanning dimension to 60 µm ×150 µm and captured 8 sub-regions in XY plane to visualize a whole C. elegans with body length of about 0.8 mm. Strong fluorescence from the worm body wall was recorded to indicate its appearance. We magnified the structure of the grinder in the worm pharynx and the meiotic germ cells in the pachytene region, and presented optical sectioning images of XY slices at different depths in Figs. 6(b) and 6(d). For uniform illuminated two-photon imaging method, image quality is severely deteriorated due to tissue scattering, as illustrated in Figs. 6(c) and 6(e): fluorescent signals of the grinder actin fiber and the meiotic germ cell nucleus are submerged in the background noise, leading to blurred structure details. Using LTSIM with structured illumination, we can well recover the degradation of image contrast and resolution. Background scattering is largely suppressed to bring a clear view of the cells, and the spatial resolution is significantly improved to enable the identification of thin structures through all image stacks.

 figure: Fig. 6

Fig. 6 Optical section imaging of a whole C. elegans in LTSIM. (a) shows the stitched visualization of the worm at single XY slice of 20 µm depth below the coverslip using LTSIM after deconvolution. (b) (d) are higher magnified views of the squared regions in (a) at indicated axial depths using LTSIM and (c) (e) the counterparts using uniform illumination, proving the high qualified optical section imaging of LTSIM. N = 40. Scale-bar = 50 µm in (a) and 5 µm in (b)–(e).

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3.3. Flexible frequency adjustment to optimize performance

We next analyzed the flexible and fast frequency switching ability of intensity-modulated LTSIM and applied optical section imaging in a highly scattered 50 µm-thick fixed brain slice of CaMKIIα-EGFP transgenic mice [22]. Structured modulation with higher spatial frequencies will theoretically result in larger resolution improvement. On the other hand, densely structured patterns are more scattering-sensitive. For imaging nontransparent sample, scattering-induced pattern distortion and low signal-to-noise ratio may lead to deteriorated reconstruction. To validate this idea, we generated multiple modulation frequencies of the sinusoidal illumination through electronic control of the AOM, and recorded fluorescence images within the same regions of the mouse hippocampus. We illustrated reconstructed slices at two selected depths and compared the image quality related to modulation frequency in Fig. 7. Obvious improvement of image contrast and optical sectioning can be seen in LTSIM, and the performance keeps improving as the modulation frequency rises until sinusoidal period number N reaches 40. If modulated at higher frequencies, however, artifacts from SIM reconstruction would increase and distort the informative signal. This deterioration in image quality is more prominent at larger depths where light scattering increases. Therefore, it is meaningful to adjust the modulation frequency for better adaption to the scattering environment. Benefiting from the flexibility in LTSIM, we can optimize the image contrast and resolution improvement by adjusting and choosing the proper spatial frequencies of structured illumination patterns.

 figure: Fig. 7

Fig. 7 Frequency-switchable structured illumination in LTSIM. (a) (b) are fluorescent images captured at separate depths using uniform illumination and SIM with different modulation frequencies from 10 to 80 cycles within the FOV, indicating the reconstruction performance of structure frequencies related to scattering properties. Scale-bar = 10 µm.

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4. Discussion

Concentrated onto eliminating scattering-induced quality deterioration, we propose a novel line-scanning structured illumination two-photon microscopy and demonstrate its high-qualified optical sectioning in scattering samples. The proposed method is especially suitable for rapidly imaging of scattering samples such as mammalian brain at high resolution within large FOV, when TPM is restricted by slow scanning speed and LSTF is severely affected by the tissue scattering. This approach is mainly based on two techniques: temporal focusing and line-scanning structured illumination.

Temporal focusing techniques provide a solution to realize wide-field two-photon excitation and axial confinement via laser pulse duration manipulation. The high speed of TF is promising to allow dynamic volumetric imaging which is inapplicable for TPM such as recording large-volume neural activities at tens of volume rate [8]. The excitation of large focal spot in our experiments is mainly restricted by the laser power. Using an amplified femtosecond laser source with ~100 Hz repetition rate would enable LTSIM enlarged line excitation to hundreds microns length and extended FOV therefrom with good signal contrast [23].

For non-transparent samples, combining SIM with two-photon microscopy would be a good choice to perform high qualified optical sectioning. Several two-photon SIM methods have been reported these years. One novel structured illumination method, HiLo [17, 18], subtracts scattering background from uniform illuminated image with only one structured illuminated image, but provides limited lateral resolution enhancement due to the discarding of second harmonic frequency components. Our LTSIM employs higher ordered frequency components from nonlinear excitation, thus can extend twice the ability of super-resolution compared with that of linear SIM. Recently, one group claimed an instant SIM by conducting rescanning at the detection side [24]. This detection modulated SIM achieves nearly two-fold lateral super-resolution with no additional acquisition time, but is lack of axial improvement compared to illumination-side modulated configuration such as the proposed LTSIM.

Another novelty of LTSIM is that we generate structured illumination through intensity modulation during line-scanning. The 1D voltage-time input signal of AOM control produces sinusoidal intensity modulation of excitation laser, which is eventually focused in line-shape and vertically swept to create 2D structured patterns at the sample plane. The electronic control has the advantages of rapid and stable response and can generate arbitrary modulation profiles. These ensure the high qualify of generated structured patterns. Nevertheless, two limitations exist. One is that the practical strip patterns are the ideal scanning patterns convolved with the line-width, so the pattern contrast will decrease especially in the case of high modulation frequency. The other problem is that the current system is only capable for one-dimension scanning, which results in asymmetric lateral resolution improvement. To achieve isotropic resolution enhancement, we will need to either rotate the cylindrical lens and grating together or rotate the sample stage to create multiple illumination orientations.

Funding

National Natural Science Foundation of China (NSFC) (No. 61327902, 6172200426, 61631009 and 61771287).

Acknowledgments

The authors thank Xu Zhang, Xue Zhang and Yichang Jia for sample preparation and Hao Xie for critical feedback on the manuscript.

References and links

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Figures (7)

Fig. 1
Fig. 1 Line-scanning two-photon structured illumination system design. The ultrashort pulsed laser is modulated in intensity by the acousto-optical modulator and provides a line excitation to the sample. Synchronizing the line-scanning and intensity modulation results in a sinusoidal illumination pattern. The fluorescence image is collected by a camera in epifluorescence microscopy scheme. Temporal chirp induced by the grating is first broadened then compressed to the minimum at the objective focus to improve axial confinement. Symbols: HWP, half wave plate; PBS, polarized beam splitter; M, reflective mirror; TL, tube lens; DM, dichroic mirror; BPF, bandpass filter; SPF, shortpass filter.
Fig. 2
Fig. 2 Evaluation of line-scanning structured illumination. (a) shows the 2D excitation of a fluorescent layer captured by the sCMOS through line-scanning with and without intensity modulation, where N denotes the sinusoidal period number in the FOV. (b) shows magnified subregions of structured patterns with different phase profiles (N = 20). Scale-bar = 10 µm. We measured the intensity fluctation on a selected line of the fluorescent image from (b), as illustrated in (c), and calculated the [1 + m cos(kpr)]2 function fitting of discrete sampling points. (d) presents the Fourier transform of the spatial intensity data. We can clearly see the five spatial frequency components in frequency domain. We magnified the 0, +1 and +2 ordered spatial components in (e) and quantified that kp equals to 0.2 µm−1.
Fig. 3
Fig. 3 Measurement of three-dimensional psf for LTSIM (N = 40). (a) shows lateral FWHMs of LT microscopy, LTSIM and LTSIM after deconvolution. (b) shows axial FWHMs of LT microscopy, LTSIM and LTSIM after deconvolution.
Fig. 4
Fig. 4 Image contrast and resolution enhancement in LTSIM. (a) (b) and (c) are f-actin structures of one same BPAE cell imaged under uniform illuminated LSTF, structure illuminated LTSIM (N = 40) and LTSIM after deconvolution. The insects are magnified views of the squared region, illustrating the imaging performance by LSTF, LTSIM and deconvoluted LTSIM. (d) Intensity along the line-marked region. Scale-bar = 5 µm in (a) (b) and (c) and 2.5 µm in magnified views.
Fig. 5
Fig. 5 Optical section imaging in tissue phantom. (a) shows representative image of fluorescence beads excited at different depths by uniform and structure illuminated (N = 20) two-photon microscopy without deconvolution. Scale-bar = 1 µm. (b) and (c) compare the SNR and SBR of fluorescent signals in two methods. Means and standard deviations are calculated from measurements of three beads at each depth.
Fig. 6
Fig. 6 Optical section imaging of a whole C. elegans in LTSIM. (a) shows the stitched visualization of the worm at single XY slice of 20 µm depth below the coverslip using LTSIM after deconvolution. (b) (d) are higher magnified views of the squared regions in (a) at indicated axial depths using LTSIM and (c) (e) the counterparts using uniform illumination, proving the high qualified optical section imaging of LTSIM. N = 40. Scale-bar = 50 µm in (a) and 5 µm in (b)–(e).
Fig. 7
Fig. 7 Frequency-switchable structured illumination in LTSIM. (a) (b) are fluorescent images captured at separate depths using uniform illumination and SIM with different modulation frequencies from 10 to 80 cycles within the FOV, indicating the reconstruction performance of structure frequencies related to scattering properties. Scale-bar = 10 µm.

Equations (4)

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N = s M H = s M w f c y l t e x p ,
I ( r , ϕ ) = I 0 ( 1 + m cos ( k p r + ϕ ) ) ,
s ( r , ϕ ) = { c ( r ) I ( r , ϕ ) 2 } * h ( r ) = { c ( r ) I 0 2 [ 1 + m 2 2 + m ( e i ( k p r + ϕ ) + e i ( k p r + ϕ ) ) + m 2 4 ( e i 2 ( k p r + ϕ ) + e i 2 ( k p r + ϕ ) ] } * h ( r ) ,
S ( k , ϕ ) = { C ( k ) + m 1 + m 2 [ C ( k k p ) e i ϕ + C ( k + k p ) e i ϕ ] + m 2 4 + 4 m 2 [ C ( k 2 k p ) e i 2 ϕ + C ( k + 2 k p ) e i 2 ϕ ] } × H ( k ) .
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