In this article, we report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope’s depth-of-focus beyond the physical limitations of its optics. As a demonstration, we built a microscope prototype with a resolution of 0.78 μm, a field-of-view of ~120 mm2, and a resolution-invariant depth-of-focus of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify FPM’s successful operation. The reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

In the field of biomedical optics, optical scattering has traditionally limited the range of imaging within tissue to a depth of one millimetre. A recently developed class of wavefront-shaping techniques now aims to overcome this limit and achieve diffraction-limited control of light beyond one centimetre. By manipulating the spatial profile of an optical field before it enters a scattering medium, it is possible to create a micrometre-scale focal spot deep within tissue. To successfully operate in vivo, these wavefront-shaping techniques typically require feedback from within the biological sample. This Review summarizes recently developed ‘guidestar’ mechanisms that provide feedback for intra-tissue focusing. Potential applications of guidestar-assisted focusing include optogenetic control over neurons, targeted photodynamic therapy and deep tissue imaging.

Focusing of light in the diffusive regime inside scattering media has long been considered impossible. Recently, this limitation has been overcome with time reversal of ultrasound-encoded light (TRUE), but the resolution of this approach is fundamentally limited by the large number of optical modes within the ultrasound focus. Here, we introduce a new approach, time reversal of variance-encoded light (TROVE), which demixes these spatial modes by variance-encoding to break the resolution barrier imposed by the ultrasound. By encoding individual spatial modes inside the scattering sample with unique variances, we effectively uncouple the system resolution from the size of the ultrasound focus. This enables us to demonstrate optical focusing and imaging with diffuse light at unprecedented, speckle-scale lateral resolution of ~ 5 μm.

The optical memory effect is a well-known type of wave correlation that is observed in coherent fields that scatter through thin and diffusive materials, like biological tissue. It is a fundamental physical property of scattering media that can be harnessed for deep-tissue microscopy or 'throughthe-wall' imaging applications. Here we show that the optical memory effect is a special case of a far more general class of wave correlation. Our new theoretical framework explains how waves remain correlated over both space and angle when they are jointly shifted and tilted inside scattering media of arbitrary geometry. We experimentally demonstrate the existence of such coupled correlations and describe how they can be used to optimize the scanning range in adaptive optics microscopes.