Caustic patterns combined with second and third order astigmatism in high resolution scanning electron microscopes

Tracking nanoparticles in an optical microscope using caustics

“…The images with aperture closed are a subset of those used to generate the x-z and z-y sections (right). defocused as shown in figures 2, 3 and 7 and found by Kanaka et al [8]. This behavior was explored using a z-stack of images created by moving the objective in equal increments along the light path (z-direction).…”

Optical Signatures of Small Nanoparticles in a Conventional Microscope

“…These signatures have been shown to consist of a 3D envelope of bright light and a shadow zone, which is characteristic of caustics formed by the refraction of light by larger particles and spheres 3, 4. In scanning electron microscopy(SEM) caustics can also appear but are treated as inconvenient obstructions to viewing nanoparticles 5. Gold particles as small as 5 nm were observed using light scattering more than a century ago by Zsigmondy6 and more recently, Berciaud et al7 have recorded absorption spectra for such particles.…”

“…[3,4] In scanning electron microscopy(SEM) caustics can also appear but are treated as inconvenient obstructions to viewing nanoparticles. [5] Gold particles as small as 5 nm were observed using light scattering more than a century ago by Zsigmondy [6] and more recently, Berciaud et al [7] have recorded absorption spectra for such particles. In direct far-field observation, diffraction at a small aperture is known to produce a bright spot known as an Airy disc surrounded by fainter bright rings whilst, conversely, an opaque circular disc generates essentially the negative of this, with the exception of very small, bright circular spot at the center of the pattern, known as Poisson's spot.…”

Optical catastrophes of the swallowtail and butterfly beams

“…Numerical calculations of equation (1) are in very good agreement with the experimental realizations. Beneath the transverse intensity distributions in figure 4(1-6), the corresponding calculated or measured spatial phases are shown in figure 4 (7)(8)(9)(10)(11)(12). Again, the experimentally obtained Fourier spectra are represented by polynomials and expressions with rational exponents, as predicted in the SM.…”

“…Caustics are ubiquitous in nature and our daily life, motivating scientists to investigate and utilize this general phenomenon in versatile fields, reaching from astrophysics [1][2][3] to models in social sciences [4][5][6], and oceanography [7][8][9]. Also, they are present in imaging of any kind of imperfect lens as well as in microscopic imaging [10][11][12][13][14]. For example, caustics play an important role in astrophysics, as the probability density function of particles (light, matter) distributed in a caustic network bears similarities to mass distribution in galaxies [1,3] and may be related to predictions of the millennium simulation.…”