Transmission matrix (TM) has applications ranging from imaging through scattering, communication, to multimode fiber imaging. TM retrieval for binary amplitude modulation recovers the TM from the intensity outputs of probing binary incident fields. However, the computational complexity limits the application for retrieval of large TM. We propose an efficient algorithm for TM retrieval with binary amplitude modulation. Our method designs the probing binary fields with convolution matrix and develops efficient retrieval algorithm based on fast Fourier transform (FFT). It improves the computational complexity by orders of magnitude. We verify the proposed algorithm with simulated data.
KEYWORDS: In vivo imaging, Super resolution, Nanoimaging, Image resolution, Microspheres, Evanescence, Spatial frequencies, Multimode fibers, Modulation, Imaging systems
Existing super-resolution imaging technology relies on rigid and bulky systems, which limits its application in narrow space. Endoscopy based on multimode fibers (MMF) has emerged as a significant solution for in vivo imaging. There is a high requirement to observe samples inside the lumen of the body simultaneously break through the diffraction limit. We propose the frequency-shift mechanism for universal super-resolution imaging with light-field encoded modulation. In this paper, we demonstrate our method for a single MMF in vivo imaging at subcellular resolution through light-field encoded, which can also ensure stable imaging under various operating conditions.
Image projection through a multimode fiber (MMF) or scattering media has applications ranging from optogenetics to near eye-displays. It requires developing computer-generated holography algorithm to obtain phase pattern of spatial light modulator. In order to accurately project light, conventional methods measured the transmission matrix (TM) of the imaging system by interference. However, it is sensitive to phase instability, easily caused by thermal drift and mechanical vibration. In this work, we proposed to use the TM retrieved from intensity-only measurements and develop a nonlinear optimization algorithm to obtain the displayed phase patterns. Our method formulates the forward model with the retrieved TM, derives the analytical derivative and adopts a second-order optimization method. We validate the improved quality of the projected intensity image by an experiment setup with a MMF.
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.
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