Transmission matrix (TM) allows light control through complex media, such as multimode fibers (MMFs), gaining great attention in areas, such as biophotonics, over the past decade. Efforts have been taken to retrieve a complex-valued TM directly from intensity measurements with several representative phase-retrieval algorithms, which still see limitations of slow or suboptimum recovery, especially under noisy environments. Here, we propose a modified nonconvex optimization approach. Through numerical evaluations, it shows that the optimum focusing efficiency is approached with less running time or sampling ratio. The comparative tests under different signal-to-noise levels further indicate its improved robustness. Experimentally, the superior focusing performance of our algorithm is collectively validated by single- and multispot focusing; especially with a sampling ratio of 8, it achieves a 93.6% efficiency of the gold-standard holography method. Based on the recovered TM, image transmission through an MMF is realized with high fidelity. Due to parallel operation and GPU acceleration, our nonconvex approach retrieves a 8685 × 1024 TM (sampling ratio is 8) with 42.3 s on average on a regular computer. The proposed method provides optimum efficiency and fast execution for TM retrieval that avoids the need for an external reference beam, which will facilitate applications of deep-tissue optical imaging, manipulation, and treatment.
SignificanceDouble-helix point spread function (DH-PSF) microscopy has been developed for three-dimensional (3D) localization and imaging at super-resolution but usually in environments with no or weak scattering. To date, super-resolution imaging through turbid media has not been reported.AimWe aim to explore the potential of DH-PSF microscopy in the imaging and localization of targets in scattering environments for improved 3D localization accuracy and imaging quality.ApproachThe conventional DH-PSF method was modified to accommodate the scanning strategy combined with a deconvolution algorithm. The localization of a fluorescent microsphere is determined by the center of the corresponding double spot, and the image is reconstructed from the scanned data by deconvoluting the DH-PSF.ResultsThe resolution, i.e., the localization accuracy, was calibrated to 13 nm in the transverse plane and 51 nm in the axial direction. Penetration thickness could reach an optical thickness (OT) of 5. Proof-of-concept imaging and the 3D localization of fluorescent microspheres through an eggshell membrane and an inner epidermal membrane of an onion are presented to demonstrate the super-resolution and optical sectioning capabilities.ConclusionsModified DH-PSF microscopy can image and localize targets buried in scattering media using super-resolution. Combining fluorescent dyes, nanoparticles, and quantum dots, among other fluorescent probes, the proposed method may provide a simple solution for visualizing deeper and clearer in/through scattering media, making in situ super-resolution microscopy possible for various demanding applications.
Double-helix point spread function (DH-PSF), which can convert the axial position of an object into double-spot rotation, is widely used in single-molecule localization microscopy due to its excellent axial localization ability. However, the current single-molecule localization microscopy techniques based on the DH-PSF are mostly applied in non-scattering or weak scattering environments, and are only applicable to sparse objects. In this paper, we study the three-dimensional positioning and imaging through scattering media based on the DH-PSF. The image of the object can be reconstructed from the recorded speckle pattern via speckle autocorrelation and phase retrieval techniques, and the three-dimensional coordinate information of the object can be obtained by the rotation angle and the center of the double spots modulated by the DH-PSF. The positioning accuracy in axial direction for non-sparse objects in simulation is better than 10μm, which is greatly improved compared with our previous work (Journal of Optics, 2021, 23(2):025602 (5pp)). This method has many potential applications in acquiring dynamical information of the micro-object motion.
Speckle autocorrelation based on optical memory effect is an interesting and important method to realize scattering imaging. However, the effective detection range is limited by the radiation phenomenon of the speckle field when there is a wide spectral illumination. In this paper, by utilizing the response of point spread function (PSF) to image distance (the distance between the detector plane and the scattering medium), we propose a method to improve the imaging quality under wide spectral illumination. PSF is sensitive to the image distance, as the distance between the detection plane and reference plane increases, the correlation coefficient between their PSFs will decreases. Superposing the autocorrelations of speckle patterns under different image distances can suppress the statistical noise, and thus improve the reconstruction quality. This method reduces the dependence on light source power and effective detection range, having certain prospect in seeing through natural turbid media.
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