Correlative microscopy: providing new understanding in the biomedical and plant sciences

Correlative microscopy is the application of two or more distinct microscopy techniques to the same region of a sample, generating complementary morphological, structural and chemical information that exceeds what is possible with any single technique. As a variety of complementary microscopy approaches rather than a specific type of instrument, correlative microscopy has blossomed in recent years as researchers have recognised that it is particularly suited to address the intricate questions of the modern biological sciences. Specialised technical developments in sample preparation, imaging methods, visualisation and data analysis have also accelerated the uptake of correlative approaches. In light of these advances, this critical review takes the reader on a journey through recent developments in, and applications of, correlative microscopy, examining its impact in biomedical research and in the field of plant science. This twin emphasis gives a unique perspective into use of correlative microscopy in fields that often advance independently, and highlights the lessons that can be learned from both fields for the future of this important area of research.     

Vector Slepian basis functions with optimal energy concentration in high numerical aperture focusing

A series expansion method is proposed for high numerical aperture focusing problems. The angular spectrum of the focused field is expressed using orthogonal vector basis functions that are obtained by solving Slepian's concentration problem for a spherical cap and expressed in terms of the vector spherical harmonics. This newly obtained Slepian-type basis automatically satisfies the transversality condition and a subset exhibits excellent energy concentration inside the solid angle of illumination. This property makes the Slepian-type basis very useful in inverse focusing problems. The corresponding vector basis for focused fields is constructed as well. Examples are presented for linearly and radially polarized illumination, revealing the fact that, compared to an expansion using the vector spherical harmonics themselves, a lower number of terms is sufficient to achieve the same accuracy, suggesting that the Slepian-type basis is preferable even in direct focusing problems.     

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