The construction of wavefront phase plays a critical role in focusing light through turbid media. We introduce the curve fitting algorithm (CFA) into the feedback control procedure for wavefront optimization. Unlike the existing continuous sequential algorithm (CSA), the CFA locates the optimal phase by fitting a curve to the measured signals. Simulation results show that, similar to the genetic algorithm (GA), the proposed CFA technique is far less susceptible to the experimental noise than the CSA. Furthermore, only three measurements of feedback signals are enough for CFA to fit the optimal phase while obtaining a higher focal intensity than the CSA and the GA, dramatically shortening the optimization time by a factor of 3 compared with the CSA and the GA. The proposed CFA approach can be applied to enhance the focus intensity and boost the focusing speed in the fields of biological imaging, particle trapping, laser therapy, and so on, and might help to focus light through dynamic turbid media.
With the transmission matrix (TM) of the whole optical system measured, the image of the object behind a turbid medium can be recovered from its speckle field by means of an image reconstruction algorithm. Instead of Tikhonov regularization algorithm (TRA), the total variation minimization by augmented Lagrangian and alternating direction algorithms (TVAL3) is introduced to recover object images. As a total variation (TV)-based approach, TVAL3 allows to effectively damp more noise and preserve more edges compared with TRA, thus providing more outstanding image quality. Different levels of detector noise and TM-measurement noise are successively added to analyze the antinoise performance of these two algorithms. Simulation results show that TVAL3 is able to recover more details and suppress more noise than TRA under different noise levels, thus providing much more excellent image quality. Furthermore, whether it be detector noise or TM-measurement noise, the reconstruction images obtained by TVAL3 at SNR=15 dB are far superior to those by TRA at SNR=50 dB.
High-efficiency imaging through highly scattering media is urgently desired for various applications. Imaging speed and imaging quality, which determine the imaging efficiency, are two inevitable indices for any optical imaging area. Based on random walk analysis in statistical optics, the elements in a transmission matrix (TM) actually obey Gaussian distribution. Instead of dealing with large amounts of data contained in TM and speckle pattern, imaging can be achieved with only a small number of the data via sparse representation. We make a detailed mathematical analysis of the elements-distribution of the TM of a scattering imaging system and study the imaging method of sparse image reconstruction (SIR). More specifically, we focus on analyzing the optimum sampling rates for the imaging of different structures of targets, which significantly influences both imaging speed and imaging quality. Results show that the optimum sampling rate exists in any noise-level environment if a target can be sparsely represented, and by searching for the optimum sampling rate, it can effectively balance the imaging quality and the imaging speed, which can maximize the imaging efficiency. This work is helpful for practical applications of imaging through highly scattering media with the SIR method.
A method to recover the image of an object behind a highly scattering medium with higher accuracy is presented. Instead of the Pearson correlation coefficient (PCC) used in the existing methods, structural similarity (SSIM), which is known as an excellent evaluation indicator of image quality, is employed as the cost function for the wavefront optimization. Compared to PCC, better imaging quality can be acquired with SSIM, because the latter comprehensively analyzes the luminance, the contrast, and the structure of imaging results. By comparing the performances of the three commonly used global optimization algorithms, including a genetic algorithm (GA), particle swarm optimization and differential evolution algorithm, we verify that GA has the best reliability and stability to solve this multidimensional wavefront modulation problem among these global optimization algorithms, including in strong noise environments. This work can improve the quality of imaging through a highly scattering medium with a wavefront optimization technique and can be applied to the fields of optical detection or biomedical imaging.
Due to the multiple scattering of light in turbid media such as biological tissues, the image of target becomes highly deteriorated and even disappears entirely. Only speckle patterns, which result from multiple scattering and interference in turbid media and contain disordered objects-information, can be acquired. Two typical methods to recover the image of target behind a turbid medium are described and simulated in this paper. The first approach is based on image correlation and wavefront shaping technique, in which the Pearson correlation coefficient is applied as a cost function for the optimization and genetic algorithm (GA) is employed to control a spatial light modulator to generate the optimal wavefront to maximize the cost function. For the second approach, the target images can be reconstructed from the speckle patterns with total variation minimization by augmented Lagrangian and alternating direction algorithms (TVAL3). Circular Gaussian distribution model and Fresnel diffraction theory are exploited in our simulations to describe turbid media and light propagation between optical devices, respectively. The anti-noise capabilities of the two methods are analyzed to demonstrate their stabilities applied in low signal-to-noise environment. This work will be beneficial to the fields of microscopic imaging and biomedical imaging in micro/nano scale.
We present a simulation method for studying turbid media in the optical field based on circular Gaussian distribution (CGD) model, by which the transmission matrix, representing the modulation of a turbid medium on the amplitude and the phase of incident light, can be generated directly and efficiently. As an application example, light refocusing through a turbid medium is realized employing the CGD model approach, combining with wavefront–phase modulation technique and Fresnel diffraction theory, which is applied to describe the light propagation between optical elements of the entire system. Simulation results based on this approach agree well with theoretical analysis for light refocusing, which can validate the feasibility of CGD model. This work can be used for exploring the potential applications of turbid media in the optical field further, especially for developing new microscopic imaging technologies beyond the diffraction limit.
Multiple scattering of light in highly disordered medium can break the diffraction limit of conventional optical system combined with image reconstruction method. Once the transmission matrix of the imaging system is obtained, the target image can be reconstructed from its speckle pattern by image reconstruction algorithm. Nevertheless, the restored image attained by common image reconstruction algorithms such as Tikhonov regularization has a relatively low signal-tonoise ratio (SNR) due to the experimental noise and reconstruction noise, greatly reducing the quality of the result image. In this paper, the speckle pattern of the test image is simulated by the combination of light propagation theories and statistical optics theories. Subsequently, an adaptive total variation (ATV) algorithm—the TV minimization by augmented Lagrangian and alternating direction algorithms (TVAL3), which is based on augmented Lagrangian and alternating direction algorithm, is utilized to reconstruct the target image. Numerical simulation experimental results show that, the TVAL3 algorithm can effectively suppress the noise of the restored image and preserve more image details, thus greatly boosts the SNR of the restored image. It also indicates that, compared with the image directly formed by ‘clean’ system, the reconstructed results can overcoming the diffraction limit of the ‘clean’ system, therefore being conductive to the observation of cells and protein molecules in biological tissues and other structures in micro/nano scale.
Due to the multiple scattering of light in turbid media such as biological tissues, the image of target becomes highly deteriorated even disappears entirely. The adaptive total variation (ATV) image reconstruction algorithm, which is based on majorization-minimization approach together with Bayesian framework, is utilized to recover the object from its speckle pattern. Numerical simulation results indicates that, compared with Tikhonov regularization method, the ATV approach can effectively suppress the noise of the restored image and preserve more image details as well, consequently greatly boosts the SNR and the sharpness of the result image. Furthermore, the recovered results by ATV algorithm have overcome the diffraction-limit of the conventional optical system. Consequently, the combination of ATV algorithm with multiple scattering of turbid media will be beneficial to the observation of cells and protein molecules in biological tissues and other structures in micro/nano scale.