Imaging through multimode fiber (MMF) provides high-resolution imaging through a fiber with cross section down to tens of micrometers. It requires interferometry to measure the full transmission matrix (TM), leading to the drawbacks of complicated experimental setup and phase instability. Reference-less TM retrieval is a promising robust solution that avoids interferometry, since it recovers the TM from intensity-only measurements. However, the long computational time and failure of 3D focusing still limit its application in MMF imaging. We propose an efficient reference-less TM retrieval method by developing a nonlinear optimization algorithm based on fast Fourier transform (FFT). Furthermore, we develop an algorithm to correct the phase offset error of retrieved TM using defocused intensity images and hence achieve 3D focusing. The proposed method is validated by both simulations and experiments. The FFT-based TM retrieval algorithm achieves orders of magnitude of speedup in computational time and recovers 2286 × 8192 TM of a 0.22 NA and 50 μm diameter MMF with 112.9 s by a computer of 32 CPU cores. With the advantages of efficiency and correction of phase offset, our method paves the way for the application of reference-less TM retrieval in not only MMF imaging but also broader applications requiring TM calibration.

Two-dimensional (2D) bismuth, bismuthene, is an emerging pnictogen family member that has received increasing research attention in the past few years, which could yield exotic electrical, thermal, and optical properties due to unique band structure. This review provides a holistic view of recent research advances on 2D bismuth material synthesis and device applications in complementary metal oxide semiconductor (CMOS) technology. Firstly, the atomic and band structure of bismuthene is reviewed as the fundamental understanding of its physical properties. Then, it highlights material synthesis of 2D bismuth atomic sheets with emphasis on physical vapor deposition method with accurate layer controllability and process compatibility with CMOS technology. Moreover, it will survey latest applications of 2D bismuth in terms of electronic, optic, thermoelectric, spintronic and magnetic nanodevices. 2D bismuth derivatives (Bi–X, X = Sb, Te, Se) will also be mentioned as a promising strategy to further improve device performance. At last, it concludes with a brief summary on the current challenges and future prospects in 2D bismuth and its derivatives for innovative electronics, sensors and other devices compatible with CMOS techniques.