Optical techniques, which have been widely used in various fields including bio-medicine, remote sensing, astronomy, and industrial production, play an important role in modern life. Optical focusing and imaging, which correspond to the basic methods of utilizing light, are key to the implementation of optical techniques. In free space or a nearly transparent medium, optical imaging and focusing can be easily realized by using conventional optical elements, such as lenses and mirrors, due to the ballistic propagation of light in these media. However, in scattering media like biological tissue and fog, refractive index inhomogeneities cause diffusive propagation of light that increases with depth, which restricts the use of optical methods in thick, scattering media. Generally speaking, scattering media poses three challenges to optical focusing and imaging: wavefront aberrations, glare, and decorrelation. Wavefront aberrations can randomize light traveling through a scattering medium, disrupt the formation of focus, and break the conjugate relation in imaging. Glare caused by backscattering will largely impair the visibility of imaging, and decorrelation in dynamic media requires systems that counter the effect of scattering to operate faster than the decorrelation time. In this thesis, we explored solutions to the problem of scattering from different aspects. We presented Time Reversal by Analysis of Changing wavefronts from Kinetic targets (TRACK) technique to realize noninvasive optical focusing through a scattering medium. We showed that by taking the difference between time-varying scattering fields caused by a moving object and applying optical phase conjugation, light can be focused back to the location previously occupied by the object. To tackle the decorrelation of living tissue, we built up a fast digital optical phase conjugation (DOPC) system based on FPGA and DMD, which has a response time of 5.3 ms and was the fastest DOPC system in the world before 2017. We demonstrated that the system is fast enough to focus light through 2.3mm-thick living mouse skin. As for glare, inspired by noise canceling headphones, we invented an optical analogue termed coherence gated negation (CGN) technique. CGN can optically cancel out the glare in an active illumination imaging scenario to realize imaging through scattering media, like fog. In the experiment, we suppressed the glare by an order of magnitude and allowed improved imaging of a weak target. Finally, we demonstrated a method to image a moving target through scattering media noninvasively. Its principle roots are in the speckle-correlation-based imaging (SCI) invented by Ori Katz. We improved the technique and extended its application to bright field imaging of a moving target.</p
