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Super resolution microscopy has become a staple in optical microscopy with applications ranging from imaging sub-cellular features to monitoring the stages of chemical reactions. In this chapter we present a brief background on the origin of the diffraction limit, a summary of the key techniques and their individual strengths and weaknesses.

For almost a century, the resolution of optical microscopy was thought to be limited by Abbe's law describing the diffraction limit of light. At the turn of the millennium, aided by new technologies and fluorophores, the field of optical microscopy finally surpassed the diffraction barrier: a milestone achievement that has been recognized by the 2014 Nobel Prize in Chemistry. Many super-resolution methods rely on the unique photophysical properties of the fluorophores to improve resolution, posing significant limitations on biological imaging, such as multicoloured staining, live-cell imaging and imaging thick specimens. Structured Illumination Microscopy (SIM) is one branch of super-resolution microscopy that requires no such special properties of the applied fluorophores, making it more versatile than other techniques. Since its introduction in biological imaging, SIM has proven to be a popular tool in the biologist's arsenal for following biological interaction and probing structures of nanometre scale. SIM continues to see much advancement in design and implementation, including the development of Image Scanning Microscopy (ISM), which uses patterned excitation via either predefined arrays or raster-scanned single point-spread functions (PSF). This review aims to give a brief overview of the SIM and ISM processes and subsequent developments in the image reconstruction process. Drawing from this, and incorporating more recent achievements in light shaping (i.e. pattern scanning and super-resolution beam shaping), this study also intends to suggest potential future directions for this ever-expanding field.

This paper describes the design and testing of a multispot structured illumination microscopy system using computer-generated holograms to create the required excitation patterns. Furthermore, it demonstrates the use of an adapted direct search algorithm for calculating the holograms that allows for imaging across an extended field of view. The system was tested on fixed targets and live cells yielding a two times resolution increase over conventional diffraction-limited imaging. LAY DESCRIPTION: We present the design and testing of a multispot structured illumination microscopy system using computer-generated holograms to create the required excitation patterns. It demonstrates the use of an adapted direct search algorithm for calculating the holograms that allows for imaging across an extended field of view. The system was tested on fixed targets and live cells yielding a two times resolution increase over conventional diffraction-limited imaging. The results here demonstrate that holography provides an efficient means of pattern projection for MSIM imaging. It provides a significant improvement in the efficiency of pattern projection and more importantly it allows for the testing of more diverse excitation patterns than possible with amplitude-only projection. For example, PSF engineering using phase modulation can be easily incorporated into the calculated holograms, potentially generating subdiffraction structures in the excitation pattern. The ability to incorporate PSF engineering into SIM opens up holographic MSIM as a potential method for further increasing resolution with little or no change to the imaging system.

The problem of intercepting a ballistic missile optimally at moderate range is discussed. The problems of minimum time and minimum fuel consumption are specifically reported. A procedure is given for determining the trajectory on a digital computer, and some necessary and sufficient conditions are given for the corresponding optima. The computational procedure is a method of successive approximations. The simpler cases were checked out on the digital computer and further programming is under way. In the examples run, each iteration takes somewhat less than one second computing time on the CDC 1604. From three to six iterations are usually required to determine a trajectory, so that the trajectory is determined in five seconds or so. The variational equations, used to determine the trajectory, can also be used to determine the corrective thrust should the actual trajectory deviate slightly from the planned trajectory.