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Confocal laser scanning microscopy (CLSM) is a powerful imaging tool providing high resolution and optical sectioning. In its standard optical configuration, a pair of confocal pinholes is used to reject out-of-focus light. The diffraction limited resolution can be broken by reducing the confocal pinhole size. But this comes at the cost of extremely low signal-to-noise ratio (SNR). The limited SNR problem can be solved by image scanning microscopy (ISM), in which the single-point detector of a regular point-scanning confocal microscopy is substituted with an array detector such as CCD or CMOS, thus the two-fold super-resolution imaging can be achieved by pixel reassignment and deconvolution. However, the practical application of ISM is challenging due to its limited image acquisition speed. Here, we present a hybrid microscopy technique, named multifocal refocusing after scanning using helical phase engineering microscopy (MRESCH), which combines the double-helix point spread function (DH-PSF) engineering with multifocal structured illumination to dramatically improve the image acquisition speed. In the illumination path, sparse multifocal illumination patterns are generated by a digital micromirror device for parallel imaging information acquisition. In the detection path, a phase mask is introduced to modulate the conventional PSF to the DH-PSF, which provides volumetric information, and meanwhile, we also present a digital refocusing strategy for processing the collected raw data to recover the wild-filed image from different sample layers. To demonstrate imaging capabilities of MRESCH, we acquire the images of mitochondria in live HeLa cells and make a detailed comparison with those from the wide-field microscopy. In contrast to the conventional wide-field approach, the MRESCH can expand the imaging depth in a range from –1 μm to 1 μm. Next, we sample the F-actin of bovine pulmonary artery endothelial cells to characterize the lateral resolution of the MRESCH. The results show that the MRESCH has a better resolution capability than the conventional wide-field illumination microscopy. Finally, the proposed image scanning microscopy can record three-dimensional specimen information from a single multi-spot two-dimensional scan, which ensures faster data acquisition and larger field of view than ISM.

The development of nanoscale single-molecule localization and tracking technology for multiple bio-molecules in intact cells has important significance for studying the dynamic process in life process. Since most of cells are several microns in depth, but the focal depth of traditional optical microscopes are less than one micron, the limited depth of field is the main drawback of conventional single molecular localization microscopy that prevents observation and tracking of multiple molecules in intact cells. In this paper, based on the wavefront coding technique, a new type of holographic phase plate with high efficiency is proposed and designed to extend the depth of field of single molecular localization microscopy, which combines the distorted multi-value pure-phase grating (DMVPPG) with the double-helix point spread function (DH-PSF). The DMVPPG can be used to realize multiplane imaging of several tens of layers of a sample in a single detection plane. And the DH-PSF is an engineered point spread function which encodes the lateral and axial position with high precision of a molecule in the center of its two lobes and the angle between them respectively. Using the combined holographic phase plate, the molecules in dozens layers of a whole cell can be simultaneously imaged on the same detection plane with DH-PSF. Not only can the axial resolving power be improved, but the imaging depth can also be extended without scanning. Adding such a holographic phase plate to the imaging path, the limited imaging depth problem in single-molecule-localization microscopy can be solved without sacrificing the localization accuracy. The proposed new type of holographic phase plate can also be implemented with a spatial light modulator. In the following numerical simulation experiments, the designed holographic phase plate is composed of 600×600 pixels with a pixel size of 10 μm. The distance between two adjacent focal planes is designed to be 0.5 μm. Such a holographic phase plate is placed on the Fourier transform plane of the detection light path. When an emitter is located on the focal plane, it can be imaged as two lobes without rotation in a center area of the field of view. If an emitter is -6 μm away from the focal plane, the DH-PSF appears in the upper-left area of the field of view. Simulation results demonstrate that a total of 25 sample layers can be simultaneously imaged on the single detection plane and the 12 μm detection range can be achieved, thus proving the feasibility of this method.

Two-photon excitation fluorescence (2PEF) and coherent anti-Stokes Raman scattering (CARS) are both third-order nonlinear optical processes, but for a long time, the true relationship and differences between them are not clearly understood. For decades, the second harmonic generation has been studied in conjunction with two-photon excitation fluorescence, so it was thought that the latter was a second-order nonlinear optical process. In order to make the two nonlinear interaction processes clear enough, the two nonlinear interaction processes are worthy to study at the same time. In this paper, firstly, we give the relationships between the 2PEF, CARS signal and their third-order nonlinear susceptibility, respectively; secondly, we use our own near infrared super-continuum CARS microscopy system to study both processes. In doing so, we describe the relationship between their third-order nonlinear susceptibility and the signal. The reconstructed images derived from CARS and those derived from 2PEF differ significantly when imaging the same 1.01 $\muup$m fluorescence polystyrene beads. If the lateral spatial resolution of the CARS imaging system is larger than the fluorescence polystyrene beads, the measured size cannot be used to calculate the real spatial resolution of the CARS system. However, the resolution of the 2PEF microscopy system can be obtained through the de-convolution of the 2PEF image, which is approximately equivalent to the current resolution of the CARS imaging system, which is measured using 280 nm polystyrene beads. The images of 280 nm polystyrene beads and 190 nm fluorescent polystyrene beads also exhibit differences between the two samples and the environment around them, respectively. This means that although CARS and 2PEF are both third-order nonlinear optical processes, they have their own properties. In particular, CARS is a third-order nonlinear optical oscillation process which is caused by the phasing match condition, but 2PEF is not influenced by the phasing match condition. The phase matching condition is responsible for the differences around the sample in the images of the 280 nm pure polystyrene beads, but not for the 190 nm fluorescent polystyrene beads. The de-convolution results for the 1.01 $\muup$m fluorescence polystyrene beads and the 280 nm pure polystyrene beads are very similar, so we can use the de-convolution results for 2PEF by the 1.01 $\muup$m fluorescence polystyrene beads to approximate the current measure condition and the resolution of the CARS imaging system. If we want to gain a more accurate resolution from the CARS imaging system, the spherical sample should be smaller than the lateral spatial resolution of this system.

In this paper, we analyze the process of coherent anti-Stokes Raman scattering (CARS) based on quantum theory and set up a traditional point-scanning CARS microscope. With this microscope, high-contrast images of polystyrene microspheres are obtained. By scanning polystyrene beads with 110 nm diameter, we reconstruct the point spread faction (PSF) of the system. And the full width at half maximum (FWHM) of the PSF shows a lateral resolution about 600 nm, which is larger than the theoretical value (～ 300 nm). Therefore, we propose several resolution-improvement approaches, which lay a strong foundation for the realization of nano-CARS microscopy.

An approach to breaking through the diffraction limitation in infrared microscopies is put forward in this paper. In this method, instead of Gaussian pump beam, an intensive vortex beam is first focused on the sample, leading to the saturation absorption of peripheral molecules in the point spread function (PSF). The vortex beam is followed by a Gaussian probe beam with the same wavelength. Because of the previous saturation absorption, the probe beam can only be absorbed by the molecules near the center, resulting in a shrunk PSF which means super-resolution. Furthermore, the PSF of a system based on this approach is numerically simulated. With a 100 nJ pulse energy vortex beam and a 0.1 nJ pulse energy probe beam, the theoretical resolution FWHM (full width at half maximum) is measured to be about 236 nm which is 14 times better than that of the traditional infrared microscopy.

The super-resolution optical fluctuation imaging (SOFI) technique enhances image spatial resolution by evaluating the independent stochastic intensity fluctuations of emitters. In principle, it eliminates any noise uncorrelated temporally, and provides unlimited spatial resolution since the calculation of the nth-order cumulant followed by a deconvolution results in an image with n-fold resolution improvement in three dimensions. But in practice, due to limited data length, the statistical uncertainty of cumulants will affect the continuity and homogeneity of SOFI image, which results in the fact that the high order SOFI (typically over 3rd order) cannot improve spatial resolution significantly. Since the variance characterizes the statistical uncertainty of cumulant, we deduce its theoretical expression based on a single dataset. In traditional SOFI techniques, due to lack of statistical analysis of cumulant, there is no noise constraint condition of cumulant in the Lucy-Richardson deconvolution to prevent the algorithm from causing noise amplification. In this paper, based on the cumulant variance formula, we calculate the cumulant standard deviation in each pixel of SOFI image and introduce the results into the Lucy-Richardson algorithm as a DAMPAR to suppress the noise generation in such pixels. The simulation and experimental results show that under the same data length, the deconvolution optimization based on cumulant standard deviation significantly improves the uniformity and continuity of SOFI image. On the other hand, under the premise of identical image quality, this optimization technique can also greatly shorten the image frames to less than half the original, thus promoting the development of super-resolution imaging of living cells.

Coherent anti-Stokes Raman scattering (CARS) microscopy can break through the optical diffraction limit by applying the additional probe beam induced phonon depletion (APIPD). Using this method, we can obtain a spatial resolution beyond the optical diffraction limit by introducing a doughnut additional probe beam to deplete phonons at the periphery of the focal spot. To achieve higher spatial resolution and better phase matching conditions, it is necessary to use high numerical aperture objectives, whereas scalar diffraction theory is no longer valid. According to the full vector diffraction theory, we calculate the intensity distributions at the focal plane when the linearly and circularly polarized lights pass through a spiral phase plate and an objective with high numerical aperture successively. The result shows that the circular polarization can generate the perfectly doughnut-shaped focal spot, which is more suitable for the additional beam than the linear polarization induced beam. Furthermore, we analyze the APIPD induced CARS process with the full quantum theory. Simulations indicate that a spatial resolution as high as 45 nm could be realized when the ratio between the intensities of additional probe and probe is 80. And the spatial resolution turns higher with increasing the power of additional probe.

In a fluorescent nano-resolution microscope based on single molecular localization, drift of focal plane will bring an additional deviation to the accuracy of single molecular localization. Consequently, this will reduce the final resolution of the reconstructed image and cause image degradation. Therefore, it is vital to control the system drift to a minimum level as much as possible. In recent years, the anti-drift ways emerged in endlessly. In this paper we made a systematic study aiming at the method in which optical measurement and negative feedback control are used. The basic principle and its implementation of the system are analyzed, and possible error is also evaluated. Finally, the precision of the system is tested experimentally. With this device, axial drift can be detected and corrected automatically in time, and the axial anti-drift accuracy as high as 9.93 nm can be achieved, which is one order higher than that of the existing commercial microscopies.

Profile of a dark hollow beam in sub-diffraction -limit imaging is of crucial importance for its spatial resolution when using the coherent anti-Stokes Raman scattering microscopy, as far as the imaging quality is concerned. Therefore, the generation of dark hollow beams through a vortex phase plate will be theoretically analyzed based on the Fresnel diffraction theory. Influences of different incidence conditions on the intensity distribution of the generated dark hollow beams are also investigated. And it is shown that a perfect dark hollow beam could be produced when a Gaussian beam is vertically incident upon a first-order vortex phase plate, with the incident light wavelength equal to that of the phase plate. However, both the circular symmetry of the incident beam's intensity distribution and the alignment between the centers of Gaussian beam and phase plate may affect the intensity distribution of the dark hollow beam, which will almost be in circular symmetry though it may shift some distance from the image center when at a small incident angle. Furthermore, the dark hollow beam's intensity distribution will scarcely change when the central wavelength deviation is very small from the incidence light and the phase plate. These results may be of great value in generation of perfect dark hollow beams in sub-diffraction –limit imaging by coherent anti-Stokes Raman scattering microscopy.

We provide an approach to breaking the diffraction limit in coherent anti-Stokes Raman scattering (CARS) microscopy and report a theoretical analysis of detection limit (DL) forit. The additional probe beam, whose profile is doughnut shaped and wavelength is different from the size of Gaussian probe beam, interacts with the coherent phonons at the rim of the diffraction-limited spot to increase theresolution by re-engineering the point spreadfunction of the system. The signal strength reduces with the size of focal volume decreasing, besides, when CARS is used in biology, the molecules of interest are usually in low concentration, which makes the signal detection more difficult. Accordingly, a remaining crucial problem is whether the reduced signal generated in the suppressed focal volume can be detected from the noise background and the analysis of DL, so it is an important precise in implementation of CARS nanoscopy. We describe T-CARS process with full quantum theory and estimate the extreme power density levels of the pump and Stokes beams determined by saturation behavior of coherent phonons. When the pump and Stokes intensities reach such extreme values and total intensity of the excitation beams arrives at a maximum tolerable by most biological samples in acertain suppressed focal volume, the DL of T-CARS nanoscopy correspondingly varies with the exposure time. For an attainable spatial resolution of ～40 nm in three dimension and areasonable exposure time of 20 ms, the DL in the suppressed focal volume is approximately ～103. The signal can be well detected from the noise fluctuation only if the number of molecules of interest exceeds this limit.

Evolutions of ultrashort pulse in time and frequency domain are modeled based on the nonlinear schrödinger equation by predictor-corrector split-step flourier method when the pulse travels in an all normal dispersion photonic crystal fiber. And the influences of the pulse duration and energy on generated continuum are also investigated. It is shown that a single pulse is maintained in the time domain and that a larger spectrum broadening is achieved with higher peak power. When the fiber is pumped by an unchirped Gaussian pulse centred at 1060 nm with duration about 50 fs and energy 1.5 nJ, good continuum is available after only 12 cm traveling distance with fine continuity and coherence. And a perfect continuum is achieved with duration about 15 fs and spectrum about 700 nm after pulse compression by a pair of prisms.

Double helix point spread function possesses continuously rotating invariant features with defocus, and it can be used for performing nano-resolution image of thick samples and for studying singleparticle tracking by combining the single-molecule localization method. However, the inadequacy of the original double helix point spread function is that the transfer function efficiency is very low, so it is difficult to achieve photon limited applications for the bio-imaging. The double-helix point spread function is optimized by introducing an iterative algorithm so that the constraints of the point spread function can be optimized best in three different domains: the Laguerre-Gauss modal plane, the spatial domain, and the Fourier domain. The simulation results show that the peak intensity of high efficiency double helix point spread function is 30 times higher than the original one. The design and fabrication of the phase plate are also proposed. The experimental results are in good agreement with the theoretical predictions, thus proving the feasibility of this method.

The development of real-time single-molecule detection and tracking technology in time and space for multiple bio-molecules in intact cells has important significance for the study on molecular behaviors in life processes. However, limited depth of field is the main drawback of conventional microscopy that prevents observation and tracking of multiple molecules in intact cells. Based on the principle of wavefront coding, the design and fabrication of a novel diffractive optical element (DOE) which combines a distorted diffraction grating with a double-helix point spread function (PSF) phase plate so that it can simultaneously perform multi-plane imaging with double-helix PSF and realize an extended depth of field is presented. Experiments have been carried out on a self-built microscopic system based on the novel DOE, showing that a depth of field can be up to 12 μm. Experimental results are in good agreement with the theoretical predictions, thus proving the feasibility of this method.

The combination of switch effect and single molecule positioning can realize the sample super diffraction resolution imaging, and double helix point spread function will be a single molecular orientation nanometer resolution extending from two dimensions to three dimensions. In this paper, three-dimensional (3D) positioning accuracy of the double helix point spread function is discussed. First, the theoretical localization accuracy for an unbiased estimator of the double-helix point spread function is compared with that for 3D localization using Fisher information and the influences of localization accuracy including photon number, varying levels of background and pixel size are analyzed. Second, based on the localization algorithm of gaussian fitting, which is usually adopted in data analysis of single molecular orientation in the experimental process, the axial localization accuracy of double helix point spread function is obtained by the error transfer function law. Computer simulation results show that under the condition of more than 1000 photons in number, the positioning accuracy of gaussian fitting localization algorithm and theory localization accuracy of Fisher information are in good agreement. The discussion of the paper provides not only the theoretical basis for 3D positioning accuracy of double helix point spread function, but also the theoretical guidance for the experiment at the same time.

Nano-resolution imaging based on single molecule localization is simulated with Matlab. A sample consisted of several lines of molecules are simulated imaged. The results demonstrate that two lines of molecules separated by 20 nm can be resolved. Effect of pixel size on the localization accuracy is also discussed here. Nano-resolution imaging is realized on an IX71 inverted fluorescent microscope with the resolution (FWHM) of 48 nm. Nano-resolution images of filopodias are reconstructed, in which filopodias with diameter of 75 nm are resolved.