We propose a structured illumination differential interference contrast (SI-DIC) microscopy, breaking the diffraction resolution limit of differential interference contrast (DIC) microscopy. SI-DIC extends the bandwidth of coherent transfer function of the DIC imaging system, thus the resolution is improved. With 0.8 numerical aperture condenser and objective, the reconstructed SI-DIC image of 53 nm polystyrene beads reveals lateral resolution of approximately 190 nm, doubling that of the conventional DIC image. We also demonstrate biological observations of label-free cells with improved spatial resolution. The SI-DIC microscopy can provide sub-diffraction resolution and high contrast images with marker-free specimens, and has the potential for achieving sub-diffraction resolution quantitative phase imaging.
©2013 Optical Society of America
In biological and medical research, cells in their nature living state, which can be assumed as phase objects, are generally transparent and thus rarely visible under the conventional light microscopy. Therefore, a wealth of development of microscopic techniques has been focused on enhancing the contrast, which can be broadly grouped into two categories: exogenous contrast and intrinsic contrast . The first category, exogenous contrast, is based on adding chemical compounds (e.g. dyes, fluorophores, etc.), to obtain excellent contrast. One drawback of the exogenous contrast method is the fact that the preparation of the specimen with dyes or fluorophores can also bring in undesired effects, such as photo-bleaching and photo-toxicity . The second category, intrinsic contrast, was developed by utilizing the phase change information arisen from the light passing through the transparent specimen. The intrinsic contrast methods are valuable owing to the non-invasive and label-free features that allow us to observe untreated ‘native’ samples.
Differential interference contrast (DIC) microscopy, one type of the intrinsic contrast imaging methods, has been one of the most widely used techniques and gained broad application in the biomedical community [3–7]. The DIC converts the variations of phase gradients in the specimen into intensity variations, and produces the first-order derivative of the phase by the interference of two identical but laterally displaced beams. Compared to other intrinsic contrast imaging techniques, such as phase contrast (PhC)  microscopy, DIC has several benefits, including high spatial resolution owing to the full numerical aperture utilization, free of halo and shade-off artifacts and optical sectioning capability . However, since DIC microscopy is one kind of lens-based far-field light microscopy, its spatial resolution is limited by the law of diffraction. This makes many biological structures smaller than the diffraction limit unresolvable. Therefore, the enhancement of spatial resolution below the classical diffraction limit is critically important to reveal the finer structures for an increasing understanding of their functions.
Motivated by obtaining high resolution DIC images, Allen et al.  have proposed the Allen video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy. They obtained sub-diffraction resolution images by enhancing the imaging contrast and detecting the movement of the edges of the specimen. Nevertheless, the technique is not ‘really’ beyond the diffraction resolution limit, as it only records the edges of the specimen and the edges are not limited by diffraction. Moreover, AVEC-DIC microscopy depends strongly on the performance of the devices and requires complicated protocols , which hamper its wide application.
On the other hand, many attempts to break the diffraction limit and achieve super-resolution have found tremendous success in fluorescent imaging. These super-resolution techniques, such as stimulated emission depletion (STED), structured illumination microscopy (SIM), stochastic optical reconstruction microscopy (STORM) and photoactivated localization microscopy (PALM), have been developed based on pattern illumination or single molecular location [12–15]. Nevertheless, all these super-resolution techniques are based on fluorescence emission properties, and thus dyes or fluorophores must be added to the specimen, which may introduce undesired effects.
Inspired by the recent progress in structured illumination microscopy [13, 16–19], here we present an easy-to-implement method termed as structured illumination differential interference contrast (SI-DIC) microscopy to break the diffraction resolution limit of the DIC microscopy. The idea is to apply the concept of structured illumination to the conventional DIC microscopy to expand the bandwidth of coherent transfer function (CTF) of DIC imaging system, and thus reconstruct DIC image with resolution significantly better than the diffraction limit.
2. Experimental setup and theory
2.1 Experimental setup
The general layout of the SI-DIC microscopy is shown in Fig. 1 . It is built around an upright microscope (BX51WI, Olympus) equipped with a water objective (LUMPlanFLN 40 × /0.8, Olympus), a 0.8-NA dry condenser lens and a regular de Sénarmont compensator  DIC configuration. The de Sénarmont compensator DIC configuration consists of two prisms, a polarizer, an analyzer and a quarter wave plate. And the DIC bias setting was adjusted by rotating the polarizer.
The microscope was modified in the illumination optical path to implement structured illumination. A high power blue LED (λ = 462 ± 27 nm) was used as light source. The beam from LED was collected and expanded to illuminate an SLM (LC-R 1080, Holoeye) at an incident angle <10°, and diffracted mainly into zero and ± 1 order beams. The unwanted zero-order beam was blocked by a mask. The desired ± 1 order beams were focused with three lenses (L3, L4 and L5) onto the back focal plane of the condenser. And the structured illumination pattern was formed on the sample plane by the interference of the two beams. The period of the structured illumination was set near the diffraction limit to realize the maximum improvement of resolution. And then the transmitted light was directed through the objective prism, analyzer, tube lens and detected by a 8-bit CCD camera (DMK 41BU02, 4.65 × 4.65 μm, Imaging Source). Six DIC images were acquired with 0°and 90° orthogonal illumination patterns at three phases (0, 2π/3, 4π/3) for each pattern displayed on the SLM (see Fig. 1 inset) to reconstruct a super-resolution DIC image. For the purpose of comparison, the conventional DIC image was also recorded by imaging only with the zero-order beam uniform illumination.
A detailed theoretical analysis of coherent structured illumination was given in reference . Here we applied the coherent structured illumination analysis to DIC imaging to show the working principle for SI-DIC microscopy to achieve super-resolution.
The illumination light is sinusoidal (or cosine) pattern modulated by the SLM, and the field distribution of the illumination can be expressed as, with spatial frequency and phase shift of the illumination pattern.
The illumination field and object distribution will multiply to produce the effective transmitted field, given by , where, is the transmittance of the object. And the field distribution on the imaging plane can be given by 22]
From the expression of the structured illumination field distribution and Eq. (1), we readily obtain
The Fourier transform of the above transmitted field can be written as
The coherent image is given as And the spectrum is obtained by Fourier transform of the coherent image, And using Eq. (4), the spectrum is written as
In order to understand the super-resolution, we analyze a coherent image taken using uniform illumination from a larger CTF
Using the above-mentioned coherent imaging theory, and utilizing the shift theorem for Fourier transform, the Fourier transform of the image taken from the larger CTF can be expressed as
Changing the phase of the illumination pattern in Eq. (5), and capturing three images at different phases, we can obtain the following three terms,, , and , by solving 3 × 3 system of linear equations. And then they are combined together to obtain Eq. (7). Therefore, we can obtain a spectrum with enlarged CTF by structured illumination, which means that higher spatial frequency information can be achieved. We can reconstruct the DIC image with improved resolution by inverse Fourier transform of Eq. (7). Figure 2 shows the principle of resolution improvement of the SI-DIC based on the expansion of the bandwidth of CTF. The above-mentioned three terms (shown in Figs. 2(a)-(c)) are obtained by solving the linear equations. Then the two terms (shown in Figs. 2(a) and 2(c)) are shifted back + and -, respectively, and then be added to the remaining term (shown in Fig. 2(b)) to form the final spectrum (shown in Fig. 2(d)). Because the final spectrum extends the CTF in the structured illumination direction, therefore, the spatial resolution is enhanced in the same direction. The image reconstruction process is similar to that of the incoherent fluorescence structured illumination, for more detail please refer to the literature .
It is noted that the incoming illumination light beam is also limited by diffraction. Therefore, the limit on spatial frequency of structured illumination is thus defined by the maximum observable region within CTF. And so the maximum value of is equal to. Therefore, the maximum observable region of the reconstructed image is , and thus the improvement of spatial resolution is a factor of two, at best.
To verify the correctness of the theory of SI-DIC, we firstly developed a simulation program. In the simulation, the optical parameters of the simulated system were chosen to match those of the practical setup as closely as possible, using a 40 × , 0.8-NA objective and 4.65 μm square pixel size in the image plane (equal to 4.65/40 μm in the object space). And the wavelength was set 462 nm. The simulated regular DIC image was obtained based on the coherent paraxial model  with several randomly distributed 116.25 nm beads specimen, since one pixel size in the object space corresponds to 116.25 nm. The simulated SI-DIC image was reconstructed based on the theory presented in Part 2 of this paper. The important parameters of DIC, the shear and bias, were set 340 nm and π/2, and the direction of the shear is indicated with the double-headed arrow in Fig. 3(e) . The simulated reconstructed SI-DIC image and regular DIC image are shown in Figs. 3(b) and 3(e); the corresponding spectra are shown in Figs. 3(a) and 3(d). Figures 3(c) and 3(f) show the intensity distributions along the dotted line in Figs. 3(b) and 3(e). Obviously, SI-DIC does extend the CTF (see the parts of the circle in Figs. 3(a) and 3(d)), thus the spectrum is expanded. Consequently, the spatial resolution is improved, since the two beads close to each other, which cannot be separated in conventional DIC image, can be resolved clearly in reconstructed SI-DIC image (indicated by the arrow in Figs. 3(b) and 3(e)). And the quantitative resolution comparison is shown in Figs. 3(c) and 3(f) with Gaussian fit. The average FWHM of reconstructed SI-DIC image is 212 ± 14 nm, while the average FWHM is 426 ± 18 nm from the conventional DIC image. The simulation results show that the spatial resolution of the SI-DIC is improved by a factor of about two, than that of regular DIC. For our DIC microscopy, Rayleigh diffraction limit  is , calculated with NAo = 0.8, NAc = 0.8 and λ = 462 nm. Here the spatial resolution of simulated conventional DIC is a little poorer than the diffraction limit, which may be caused by not good enough contrast.
Experimentally, to test the resolution enhancement in SI-DIC, a comparison of conventional DIC and SI-DIC images of the same field of 53 nm polystyrene beads is shown in Fig. 4 . The conventional DIC image is captured by using zero order light as the uniform illumination light source. Clearly, the CTF is expanded by SI-DIC (see the parts of the circle in Figs. 4(a) and 4(d)), therefore the spectrum is also extended. Accordingly, the SI-DIC image reveals superior resolution. It is difficult to resolve two beads close to each other of the conventional DIC image, while in the SI-DIC image, they can be clearly resolved as two individual beads (see the arrow place in Figs. 4(b) and 4(e)). To quantify the resolution improvement, a comparison of intensity profiles of individual bead in conventional DIC and SI-DIC images along the dotted line (perpendicular the shear direction of DIC) is shown in Figs. 4(c) and 4(f); the solid lines represent Gaussian-fits. The reason why we choose the profile data direction perpendicular the shear direction of DIC is that DIC suffers from the directional shadow artifact parallel the shear direction, while the intensity distribution is approximately Gaussian distribution perpendicular the shear direction. We obtain the average FWHM of 190 ± 18 nm from SI-DIC image and of 380 ± 17 nm from conventional DIC image, respectively. The spatial resolution is thus improved by a factor of two.
To demonstrate the biological application, we also observed the filaments of human umbilical vein endothelial cells with SI-DIC microscopy. The cells were cultured in Dulbecco modified Eagle medium (DMEM) supplemented with 10% fetal bovine serum (FBS) and antibiotics (100 U/mL penicillin and 100 lg/L streptomycin) at the 37°C incubator with a humidified atmosphere of 5% CO2. For DIC imaging, the cells were seeded in a 35 mm glass bottom dish. After incubation for 48 hours, the cells were washed with phosphate buffered saline (PBS) solution and then fixed with paraformaldehyde (4%) for about 20 minutes. And the cells were washed again with PBS solution before immersion in water for imaging. The cells images obtained with SI-DIC and conventional DIC are shown in Figs. 5(a) and 5(b) for comparison. Figures 5(c) and 5(d) are magnified views of the boxed regions in Figs. 5(a) and 5(b), respectively. And the intensity distributions along the dotted lines are shown in Fig. 5(e). It is observed, SI-DIC image shows finer structures than conventional one; two fine fibers with a separation of about 378 nm read from Fig. 5(e), below the practical resolution (380 nm) of conventional DIC can be resolved clearly in SI-DIC image (see Fig. 5(c) indicated with the arrow), but not resolvable in the conventional DIC image (see Fig. 5(d) indicated with the arrow). Since Fig. 5 only shows the filaments (parts) of a cell, here we observe the whole cell. Figures 6(a) and 6(b) show a comparison between SI-DIC and conventional DIC images of human umbilical vein endothelial cells. And Figs. 6(c) and 6(d) are enlargements of the boxed regions in Figs. 6(a) and 6(b), respectively. And again, SI-DIC microscopy increases the image clarity; SI-DIC image provides more details than traditional DIC image, as the region indicated with the arrow in Fig. 6(c) reveals more fine structures than that of in Fig. 6(d). Therefore, SI-DIC, with the capability of super-resolution, can exhibit more details than the conventional DIC.
It should be noted that, with pattern illumination, the residual fringe artefacts can appear in the reconstructed image (see the region indicated by the arrow in Fig. 5(a)). And there are several sources could cause fringe artefacts. Errors in the estimation of the pattern illumination phase and fluctuations in the illumination can lead to artefacts. Besides, the movement of the specimen during capturing six images needed for reconstructing one high resolution DIC image and anisotropic resolution improvement with just two orthogonal illumination pattern directions could also bring in artefacts. These two are the major sources of artefacts in our imaging system, which can be overcome by making the specimen still or shorter duration of exposure and using more illumination pattern directions.
In summary, we have developed an SI-DIC microscopy to surpass the diffraction resolution limit, achieving lateral resolution enhancement twice that of conventional DIC microscopy. Biological observations of unstained cells are demonstrated, providing finer structure with improved spatial resolution. The configuration of the system is straightforward. Traditional commercial DIC microscopy can be readily modified as an SI-DIC system by changing the illumination parts. And SI-DIC can also switch back to traditional DIC mode by switching between the ± 1 order beams and the zero-order beam illumination by a mask. In contrast to AVEC-DIC  microscopy, SI-DIC microscopy only needs SLM to generate structured illumination patterns and simple calculation, and thus comparatively simple to implement.
It should be pointed out that we use 0° and 90° orthogonal pattern orientations for the reason of simplicity of pattern design and light path arrangement, which may cause anisotropic lateral resolution improvement. Further efforts will be made on three pattern orientations to obtain near isotropic resolution enhancement in the lateral direction. Biological applications of SI-DIC have been demonstrated on fixed cells with improved resolution. Potential applications in living cells can be achieved with reduced exposure duration by using more sensitive CCD or higher power LED light source. Further developments in SI-DIC microscopy are expected to provide quantitative SI-DIC microscopy, just like the quantitative DIC microscopy [9, 26, 27] and more biological sample application [28, 29]. It must be mentioned that the new emerged ‘super-resolution’ field [12–15] now can achieve about 20 nm lateral resolution, which are both based on fluorescence imaging. However, here we provide a non-invasive and label-free method that can improve the spatial resolution of traditional DIC by a factor of two.
This work is supported by the National Nature Science Foundation of China (Grant Nos. 30925013, 30900331), Science Fund for Creative Research Group of China (Grant No. 61121004) and 863 project 2012AA020404).
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