Efficient Fourier single-pixel imaging based on weighted sorting.

Fourier single-pixel imaging (FSI) has attracted increased attention in recent years with the advantages of a wide spectrum range and low cost. FSI reconstructs a scene by directly measuring the Fourier coefficients with a single-pixel detector. However, the existing sampling method is difficult to balance the noise suppression and image details within a limited number of measurements. Here we propose a new sampling strategy for FSI to solve this problem. Both the generality of the spectral distribution of natural images in the Fourier domain and the uniqueness of the spectral distribution of the target images in the Fourier domain are considered in the proposed method. These two distributions are summed with certain weights to determine the importance of the Fourier coefficients. Then these coefficients are sampled in order of decreasing importance. Both the simulations and experiments demonstrate that the proposed method can capture more key Fourier coefficients and retain more details with lower noise. The proposed method provides an efficient way for Fourier coefficient acquisition.

High-order spatial phase shift method realizes modulation analysis through a single-frame image.

For the modulation-based structured illumination microscopy system, how to obtain modulation distribution with an image has been a research hotspot. However, the existing frequency-domain single-frame algorithms (mainly including the Fourier transform method, wavelet method, etc.) suffer from different degrees of analytical error due to the loss of high-frequency information. Recently, a modulation-based spatial area phase-shifting method was proposed; it can obtain higher precision by retaining high-frequency information effectively. But for discontinuous (such as step) topography, it would be somewhat smooth. To solve the problem, we propose a high-order spatial phase shift algorithm that realizes robust modulation analysis of a discontinuous surface with a single-frame image. At the same time, this technique proposes a residual optimization strategy, so that it can be applied to the measurement of complex topography, especially discontinuous topography. Simulation and experimental results demonstrate that the proposed method can provide higher-precision measurement.

Single-exposure height-recovery structured illumination microscopy based on deep learning.

Modulation-based structured illumination microscopy (SIM) is performed to reconstruct three-dimensional (3D) surface topography. Generally speaking, modulation decoding algorithms mainly include a phase-shift (PS) method and frequency analysis technique. The PS method requires at least three images with fixed PSs, which leads to low efficiency. Frequency methods could decode modulation from a single image, but the loss of high-frequency information is inevitable. In addition, these methods all need to calculate the mapping relationship between modulation and height to recover the 3D shape. In this paper, we propose a deep learning enabled single-exposure surface measurement method. With only one fringe image, this method can directly restore the height information of the object. Processes such as denoising, modulation calculation, and height mapping are all included in the neural network. Compared with traditional Fourier methods, our method has higher accuracy and efficiency. Experimental results demonstrate that the proposed method can provide accurate and fast surface measurement for different structures.

Fast structured illumination microscopy with a large dynamic measurement range.

Fast structured illumination microscopy plays an important role in micro-nano detection due to the features of high accuracy, high efficiency, and excellent adaptability. The existing method utilizes the linear region of the axial modulation response curve (AMR), and by building the relationship between the modulation and the real height, achieves topography recovery. However, the traditional method is limited to narrow dynamic measurement range due to the linear region of the AMR being very short. In this paper, a double-differential fast structured illumination microscopy (DDFSIM) is proposed. By introducing two additional detectable branches for building the double-differential axial modulation response curve (DDAMR), the proposed method can obtain a large dynamic measurement range. In the measurement, three charge-coupled devices are respectively placed in and behind and before the focal plane to generate three axial modulation response curves. Three AMRs are used to set up the DDAMR, which has a large dynamic measurement range. Through simulation and experimental verification, the measurement range of DDFSIM is twice that of the conventional method under the same system parameters.