Structured illumination microscopy and its new developments

Optical microscopy allows us to observe the biological structures and processes within living cells. However, the spatial resolution of the optical microscopy is limited to about half of the wavelength by the light di®raction. Structured illumination microscopy (SIM), a type of new emerging super-resolution microscopy, doubles the spatial resolution by illuminating the specimen with a patterned light, and the sample and light source requirements of SIM are not as strict as the other super-resolution microscopy. In addition, SIM is easier to combine with the other imaging techniques to improve their imaging resolution, leading to the developments of diverse types of SIM. SIM has great potential to meet the various requirements of living cells imaging. Here, we review the recent developments of SIM and its combination with other imaging techniques.


Introduction
Recently, the optical microscopy has become an indispensable tool in biological and medical re-search¯eld. Optical microscopy provides a powerful method for researchers to observe the microscopic biological world. However, the imaging resolution of the optical microscopy is limited by the light di®raction, which is called Abbe di®raction limit 1 (d ¼ 0:61 NA , is the wavelength of light, NA stands for the numerical aperture of the microscope objective lens). That is to say, the structure of the sample, which is smaller than the di®raction limit, is unresolvable under the optical microscope observation.
In the past two decades, many attempts to break the di®raction limit to obtain super-resolution have achieved great progress in the°uorescence imaginḡ eld. Researchers have developed several super-resolution°uorescence microscopy, such as, stimulated emission depletion (STED) microscopy, 2 structured illumination microscopy (SIM), 3 stochastic optical reconstruction microscopy (STORM) 4 and photo-activated localization microscopy (PALM). 5 Although the resolution improvement of SIM is less than that of the other super-resolution techniques, the sample requirements of SIM are not as strict as the other superresolution methods. Unlike PALM/STORM that require specialized photo-switchable labeling, SIM can use common°uorophores with no special properties, and another advantage of SIM is that low illumination intensity (1-100 W/cm 2 ) can be used, which is important for imaging living cell. With low illumination intensity, the°uorophores experience less photo-bleaching. Besides, structured illumination is easier to combine with the other imaging techniques to improve their imaging resolution. Therefore, many researchers devoted to the SIM technique development and its application research. Although several researchers have published reviews on the advancements of super-resolution°u orescence microscopy, 6-8 including SIM, 9 this paper will focus on the development of SIM and its combination with other imaging techniques.

The Understanding of SIM 2.1. Two-dimensional linear SIM
The use of structured illumination to obtain superresolution information can be explained in the context of the \spatial frequency" of an image. The optical microscopy can be regarded as a low-pass lter in reciprocal (frequency) space. The schematic diagram of frequency spectrum expansion by structured illumination is shown in Fig. 1. The pentagon stands for the spectrum information of the sample. Figure 1(a) represents the optical transfer function (OTF) of common wide-¯eld°uorescence microscopy, and the high frequency information, Fig. 1. Schematic of frequency spectrum expansion by structured illumination. (a) The OTF of common°uorescence microscopy, (b) is superposition of three frequency spectra components by structured illumination, (c)-(e) are three components of frequency spectra, multiplying the OTF, separating from each other, moving to the corresponding place, respectively, (f) addition of the three components of frequency spectra, having been moved to the corresponding place.
which is higher than the cuto® frequency k 0 of the microscopy, is lost after light passes through the optical microscope. Three superimposed frequency spectrum components can be produced by structured illumination, shown in Fig. 1(b). According to optical imaging theory, the three mixed components are multiplied by the OTF, and then we separate them from each other and move them to the correct position through image processing, as shown in Figs. 1(c)-1(e). To separate the three components, a set of three images with illumination phases shifted by steps of 2/3 is required. Figure 1(c) is the separated zeroth-order frequencies components, and Figs. 1(d) and 1(e) are the AE¯rst-order components. The three frequency spectrum components are superposed to extend the region of the frequency space, shown in Fig. 1(f). Accordingly, when using structured light to illuminate the sample, we can obtain the sample structure information from three superimposed frequency information. The observable frequency region contains not only the usual information (region 1 in Fig. 1(f)), but also information that originates in two o®set regions (regions 2 and 3 in Fig. 1(f)), which is not available in a conventional microscope. That is to say, with structured illumination, the high frequency information of the sample is encoded into the low frequency region to make it pass through the optical microscope, and then we decoded the mixed frequency information to recover the high frequency information, therefore extending the observable frequency region of optical microscope. High resolution objects in real space carry high spatial frequencies in reciprocal region, while low-resolution objects have low spatial frequencies. Expansion of the frequency region means the resolution improvement.
The above schematic diagram only shows one single direction spectrum expansion with structured illumination. Taking inverse Fourier transform of this extended spectrum, we can only obtain the image with one-direction resolution improvement. In order to obtain isotropic resolution improvement, we usually need to obtain two-or three-direction structured illumination images, shown in Fig. 2. The frequency spectrum expansion of two orthogonal directions structured illumination pattern is shown in Fig. 2(a), while three patterns direction with /3 interval is shown in Fig. 2(b). The resolution improvement of SIM is linearly proportional to the frequency of the sinusoidal pattern (Ák in Fig. 1(b)). Since the maximum spatial frequency of the sinusoidal pattern is also limited by the di®raction limit of the imaging system, the maximum frequency spectrum expansion of structured illumination is only twice that of the traditional°u orescence microscope. Thus, the maximum improvement of resolution by structured illumination is a factor of two.

Two-dimensional nonlinear SIM
As the maximum resolution enhancement with linear structured illumination is a factor of two. The researchers proposed nonlinear SIM in order to further improve the resolution, and the nonlinear SIM was¯rst achieved by°uorescent saturation. In the process of°uorescence excitation, the°uorescence intensity is proportional to the excitation light intensity. When the intensity of the excitation is a sinusoidal function, the°uorescence intensity is also a sinusoidal function. With the increase of the excitation light intensity, the¯rst excited state of the°uorescent molecule is saturated, and the°uorescence intensity distribution is no longer a sinusoidal function, as shown in Fig. 3(a). Therefore, the saturated°uorescence intensity distribution generates a series of nonlinear terms in the frequency domain, as shown in Fig. 3(b), and the spatial frequency of these nonlinear terms are the second harmonic, three harmonic or higher order harmonic frequency of the spatial frequency of linear structured illumination, which depends on the excitation light intensity (saturated degree of°uorescent molecules in the¯rst excited state). Accordingly, these nonlinear higher order spatial frequency terms further extend the OTF, making the more information of the higher spatial frequency shifting into the observable OTF, as shown in Fig. 4. It is noted that°uorescent saturation is the only way to achieve nonlinear e®ect, and reversible photo-activation of molecules can also be used to perform nonlinear SIM for higher resolution.

Three-dimensional linear SIM
For a conventional optical microscope, the threedimensional OTF is a torus-like region, as shown in Figs. 5(a) and 5(b), and the \hole" of the torus is the \missing cone" of information near the k z -axis, and to extend the resolution is equivalent to¯nding a method to detect information that is outside of this observable region. The principle of three-dimensional SIM is similar to the two-dimensional SIM. In the three-dimensional SIM, the specimen is illuminated with three mutually coherent beams, as shown in Fig. 5(c). The interference between the three illumination beams generates a three-dimensional excitation pattern that includes seven Fourier components at each di®erence vector between the three illumination wave vectors, as shown in Fig. 5(d). The observable region that becomes accessible with this illumination pattern is the convolution of the sevendot illumination structure of  procedure can be repeated with the illumination pattern rotated to other orientations. Figure 5(f) exhibits the observable region using three illumination pattern directions. This region¯lls in the missing cone while maintaining the full factor of two of lateral resolution enhancement, and doubles the axial resolution as well.  14 and they showed the imaging results with $ 115 nm spatial resolution, which is twice the di®raction limited resolution. The linear structured illumination can only achieve two times resolution enhancement. In 2002, the Heintzmann et al. 10¯r st proposed the saturated patterned excitation microscopy (SPEM). They used saturated°uorescence excitation to achieve nonlinear°uorescence excitation so as to obtain higher spatial frequency information, therefore further improving the spatial resolution. In the following year, Heintzmann reported a two-dimensional excitated saturation excitation microscopy. 15 By using of two-dimensional grating to produce two-directions structured illumination, simulation result with 57 nm resolution were obtained through computer simulation. In 2005, Gustafsson experimentally con¯rmed that saturated structured illumination can further improve the spatial resolution. They obtained experimental results with $ 50 nm spatial resolution, and termed the method as the saturated structured illumination microscopy (SSIM). 11 The saturated°uorescence excitation needs very high excitation intensity, and high excitation light intensity could cause severe sample photo-bleaching, thus, hindering the application of this technique in the study of biological samples. In order to reduce the nonlinear excitation power, using the photo-switchable°uorescent protein to replace the°uorescent saturation method to realize the nonlinear structured illumination was¯rst reported by Heintzmann group. 16 It is a pity that they did not present good biological experimental results. In 2012, Gustafsson team used the same method to generate nonlinear structured illumination and showed the experimental results of biological samples with $ 50 nm spatial resolution. 17 The required excitation light power decreased six-orders of magnitude than that of saturated°u orescence excitation. In 2015, Li et al. 18 proposed patterned activation nonlinear SIM to improve the imaging speed of nonlinear SIM.

The Development of the SIM
In 2008, Gustafsson team¯rst achieved threedimensional structured illumination super-resolu-tion°uorescence microscopy, doubling both the lateral and axial resolution. 12 In the same year, the research team also combined structured illumination with the I 5 M technique 19 and proposed the concept of I 5 S. They demonstrated the results with all the three-dimensional resolution at 100 nm. 20 However, a physical grating was initially used to generate structured illumination, and mechanical translational or rotational of the grating were needed to generate stripe patterns with various phases and directions. Therefore, the method had low temporal resolution, and was limited to¯xed samples imaging. In 2009, the two groups have both used a spatial light modulator (SLM) to replace the initial physical grating to generate structured illumination, achieved two-dimensional superresolution imaging of living cells. 21,22 Without any mechanical movement of the optical element, they greatly enhanced the switching time between the di®erent illumination styles, enabling live cell superresolution imaging. In 2011, Gustafsson et al. 23 have also realized the super-resolution imaging of threedimensional living cells. In 2012, the same team introduced two-color imaging method into the three-dimensional structured illumination live cell imaging technique, and they demonstrated the results with two-color three-dimensional superresolution imaging of living cells. 24

The enhancement of SIM by other researchers
The above two groups have made pioneering work in the SIM super-resolution imaging¯eld, and they continued to develop this method, and achieved main improvement of the SIM super-resolution imaging technique, meeting the various needs of biological research. Besides the two teams, many other researchers were also engaged in the improvements and developments of SIM super-resolution technique. Chung et al. 25¯r st combined structured illumination with the total internal re-°e ction°uorescence (TIRF) microscope and put forward standing wave-TIRF (SW-TIRF) (SW: standing wave represents structured illumination) method. Fiolka et al. 26 further developed the TIRFbased SIM technology, they used an SLM to generate structured illumination, so that the phase and direction of the structured illumination can be easily switched. Gliko et al. 27,28 used four acousto-optic de°ectors, (AOD) to achieve the SW-TIRF, and the strips can be changed in milliseconds because of the rapid scanning capabilities of AOD. In 2009, Zhang et al. 29 used an SLM to generate four-direction structured illumination. Compared with the commonly used two or three illumination directions, it achieved better isotropic resolution enhancement. In 2011, Wang et al. 30 combined structured illumination with aplanatic solid immersion lenses-based°u orescence microscopy. As the solid immersion lens itself has very high NA, the combination can generate a wide-¯eld high-resolution imaging system with bandwidth corresponding to an NA of three. In 2013, Dan et al. 31 used LED as the light source and digital micromirror device (DMD) to produce structured illumination. They showed the super-resolution capability and sectioning ability with structured illumination, respectively. Their experimental setup has several advantages, such as, low cost, easy switching of multiple wavelength and free of speckle noise. In 2012, York et al. 32 presented multifocal SIM (MSIM). MSIM used a DMD to generate sparse 2D excitation patterns and digital processing after acquisition to obtain optically-sectioned images with $ 145 nm lateral and $ 400 nm axial resolution at 1-Hz frame rate. Mudry et al. 33 reported a blind-SIM that super-resolution information can be made available by illuminating with several uncontrolled speckle patterns.  37 tried to combine structured illumination with coherent anti-Stokes Raman scattering (CARS) microscopy, however, they only reported the computer simulation super-resolution results without experiment results, and super-resolution imaging with structured illumination has been extended to the scattered light imaging systems. In 2011, Zhang et al. 38 used SLM to achieve three-dimensional structured illumination scattered light super-resolution imaging, assisted by gold nanoparticles. In 2012, Chowdhury et al. 39 proposed a structured oblique illumination microscope for non°uorescent coherent scattering samples superresolution imaging. In 2013, Chen et al. 40,41 reported a structured illumination di®erential interference contrast (SI-DIC) microscopy, achieving lateral resolution enhancement twice that of conventional DIC microscopy.

Conclusions
In the last two decades, the SIM technique has been greatly developed. The improvement of main technical parameters of SIM, have been achieved by two research teams, Heintzmann and Gustafsson groups. They improved the spatial and temporal resolution of SIM, and developed three-dimensional super-resolution imaging and multicolor imaging.
The other researchers contributed to the SIM development were mainly by exploiting di®erent methods to realize structured illumination or combining structured illumination with the other imaging techniques. These techniques includes TIRF, confocal°uorescence microscopy and the other non°uorescence imaging methods, such as CARS, DIC and scattered light imaging. The combination of SIM with the other imaging techniques to improve their imaging resolution is also one direction of further development of SIM, and the other direction is to apply current-developed SIM superresolution imaging to biological and medical research to obtain new information that are not available before.