Optical clearing is a versatile approach to improve imaging quality and depth of optical microscopy by reducing scattered light. However, conventional optical clearing methods are restricted in the efficiency-first applications due to unsatisfied time consumption, irreversible tissue deformation, and fluorescence quenching. Here, we developed an ultrafast optical clearing method (FOCM) with simple protocols and common reagents to overcome these limitations. The results show that FOCM can rapidly clarify 300-μmthick brain slices within 2 min. Besides, the tissue linear expansion can be well controlled by only a 2.12% increase, meanwhile the fluorescence signals of GFP can be preserved up to 86% even after 11 d. By using FOCM, we successfully built the detailed 3D nerve cells model and showed the connection between neuron, astrocyte, and blood vessel. When applied to 3D imaging analysis, we found that the foot shock and morphine stimulation induced distinct c-fos pattern in the paraventricular nucleus of the hypothalamus (PVH). Therefore, FOCM has the potential to be a widely used sample mounting media for biological optical imaging. optical clearing | tissue clearing | deep tissue imaging

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Non-invasive, real-time imaging and deep focus into tissue are in high demand in biomedical research. However, the aberration that is introduced by the refractive index inhomogeneity of biological tissue hinders the way forward. A rapid focusing with sensorless aberration corrections, based on machine learning, is demonstrated in this paper. The proposed method applies the Convolutional Neural Network (CNN), which can rapidly calculate the low-order aberrations from the point spread function images with Zernike modes after training. The results show that approximately 90 percent correction accuracy can be achieved. The average mean square error of each Zernike coefficient in 200 repetitions is 0.06. Furthermore, the aberration induced by 1-mm-thick phantom samples and 300-µm-thick mouse brain slices can be efficiently compensated through loading a compensation phase on an adaptive element placed at the back-pupil plane. The phase reconstruction requires less than 0.2 s. Therefore, this method offers great potential for in vivo real-time imaging in biological science.

SUMMARYThe boundary knot method is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the solution of partial differential equations. In this paper, the method is applied to the solution of some inverse problems for the Helmholtz equation, including the highly ill-posed Cauchy problem. Since the resulting matrix equation is badly ill-conditioned, a regularized solution is obtained by employing truncated singular value decomposition, while the regularization parameter for the regularization method is provided by the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometry. The stability of the method with respect to the noise in the data is investigated by using simulated noisy data. The results show that the method is highly accurate, computationally efficient and stable, and can be a competitive alternative to existing methods for the numerical solution of the problems.

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