The vector Slepian multipole fields are recently published basis functions that are naturally suitable for approximating
the focal electric field of a high numerical aperture lens, because their plane-wave amplitude spectrum
shows an angular energy distribution that is highly confined to the spherical cap corresponding to the numerical
aperture of the lens. Thus when solving inverse problems, no additional constraints are needed to ensure
the directionality of the focused field, and the number of degrees of freedom can be reduced, as opposed to a
representation using conventional multipole fields.
In this paper we demonstrate the applicability of this new basis to an inverse problem of focusing where the
three-dimensional intensity distribution is prescribed in some reasonably chosen volume around the focus. Using
numerical optimization, an approximation of the focused electric field in terms of the vector Slepian multipole
fields is obtained and the illuminating field is calculated in a straightforward way. Three examples from recent
literature have been chosen to illustrate the method.
KEYWORDS: Luminescence, Contrast transfer function, Super resolution microscopy, Super resolution, Point spread functions, Fluorescence spectroscopy, Spectroscopy, Diffraction, Spatial resolution, Rhodamine
We quantitatively investigated image properties in super-resolution microscopy using two-color fluorescence dip
spectroscopy. To evaluate the properties, the point spread function (PSF) and contrast transfer function (CTF) were
measured using a fluorescent scale together with a fluorescent bead. From the CTF, it has been found that visible light
can resolve a 100 nm line-and-space pattern by microcopy, and provide a contrast of 10%. The CTF corresponds to a
PSF with a FWHM of 130 nm. The value is two times finer than the diffraction limit size. An evaluation using a 100 nm
Φ fluorescent bead consistently supports the result given by the CTF for super-resolution microscopy. The measured
CTF shows that super-resolution microscopy can indeed improve the optical properties of fluorescent images and enable
us to observe a structure with a spatial resolution overcoming the diffraction limit.
A new type of optical instrument, the curved hologram, is introduced that allows us the unique opportunity to independently control its spatial phase function and its shape. We show how proper design of the hologram shape (using a simple analytic procedure) yields perfect uniform collimation, and also collimation and concentration of diffuse (monochromatic) light at the thermodynamic limit of brightness conservation.
A computer program package for numerical simulation of speckle phenomena has been developed. It is suitable for simulating both objective and subjective speckle effects in various optical setups. Several simulation results are presented in this paper. The simulations was made in UNIX and Windows NT environment.
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