Automatic tube lens design from stock optics for microscope remote-refocusing systems

The remote-refocusing approach of Botcherby et al. [Opt. Lett. 32, 2007 (2007) [CrossRef] ] has been applied widely to 2D and 3D fluorescence microscopes to enable rapid refocusing of the optical system without mechanically perturbing the sample. In order for this approach to operate correctly, it requires that the overall magnification of the first two microscope systems matches the ratio of the refractive indices in sample and intermedia image spaces. However, commercially available tube lenses are not always suitable to produce the desired overall magnification. Therefore, a practical approach to produce tube lenses with low expense and diffraction-limited performance is required. Tube lenses can be formed using a pair of stock achromatic doublets, however, selecting appropriate pairs of achromatic doublets from stock optics is a time-consuming process, as many combinations can be considered. In this paper, we present two software packages (Catalogue Generator and Doublet Selector) developed in MATLAB that use the application programming interface (ZOS-API) to the Zemax OpticStudio optical design software to realise an automatic search of stock achromatic doublets to produce microscope tube lenses with a specified focal length, entrance pupil diameter and maximum design field angle. An algorithm to optimise principal plane positions in versions of OpticStudio before 20.2 was also introduced to enable the use of older software versions. To evaluate the performance of Catalogue Generator and Doublet Selector, we used them to generate ten tube lens designs. All of the software-produced tube lenses have a better optical performance than those using manually selected pairs of stock doublets lenses

Cosmic Electromagnetic Fields due to Perturbations in the Gravitational Field

We use non-linear gauge-invariant perturbation theory to study the interaction of an inflation produced seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We compare the effects of this coupling under the assumptions of poor conductivity, infinite conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the rotation of the electric field dominates the power spectrum on small scales, in agreement with previous arguments.Comment: 16 pages, 3 figures, published in PR

Photon deflection and precession of the periastron in terms of spatial gravitational fields

We show that a Maxwell-like system of equations for spatial gravitational fields $\bf g$ and $\bf B$ (latter being the analogy of a magnetic field), modified to include an extra term for the $\bf B$ field in the expression for force, leads to the correct values for the photon deflection angle and for the precession of the periastron

Adaptive light-sheet fluorescence microscopy with a deformable mirror for video-rate volumetric imaging

Light-sheet fluorescence microscopy (LSFM) achieves optically sectioned imaging with the relatively low photobleaching and phototoxic effect. To achieve high-speed volumetric LSFM imaging without perturbing the sample, it is necessary to use some form of remote refocusing in the detection beam path. Previous work used electrically tunable lenses, tunable acoustic gradient index of refraction lenses, or the remote-refocusing approach of Botcherby et al. [Opt. Lett. 32(14), 2007 (2007)] to achieve remote refocusing. However, these approaches generally only provide low-order defocus correction, which is not compatible with higher-NA objectives that require higher order defocus corrections or reduce the optical throughput. In order to simultaneously achieve high-speed remote refocusing and correct system aberrations, we employ a deformable mirror in the detection path that is capable of providing higher orders of defocus and aberration correction in an optical system with an NA of 0.72–0.75. We demonstrate high-speed volumetric imaging at 26.3 volumes per second and 35 frames per volume for a defocus range of −50 to 50 μm

A fully covariant description of CMB anisotropies

Starting from the exact non-linear description of matter and radiation, a fully covariant and gauge-invariant formula for the observed temperature anisotropy of the cosmic microwave background (CBR) radiation, expressed in terms of the electric ($E_{ab}$) and magnetic ($H_{ab}$) parts of the Weyl tensor, is obtained by integrating photon geodesics from last scattering to the point of observation today. This improves and extends earlier work by Russ et al where a similar formula was obtained by taking first order variations of the redshift. In the case of scalar (density) perturbations, $E_{ab}$ is related to the harmonic components of the gravitational potential $\Phi_k$ and the usual dominant Sachs-Wolfe contribution $\delta T_R/\bar{T}_R\sim\Phi_k$ to the temperature anisotropy is recovered, together with contributions due to the time variation of the potential (Rees-Sciama effect), entropy and velocity perturbations at last scattering and a pressure suppression term important in low density universes. We also explicitly demonstrate the validity of assuming that the perturbations are adiabatic at decoupling and show that if the surface of last scattering is correctly placed and the background universe model is taken to be a flat dust dominated Friedmann-Robertson-Walker model (FRW), then the large scale temperature anisotropy can be interpreted as being due to the motion of the matter relative to the surface of constant temperature which defines the surface of last scattering on those scales.Comment: 18 pages LaTeX, 1 figure. Submitted to Classical and Quantum Gravity. Also available at http://shiva.mth.uct.ac.za/preprints/9705.htm

Cosmological perturbation theory and conserved quantities in the large-scale limit

The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on hypersurfaces of constant expansion, constant curvature or constant energy density. The existence of conserved perturbation quantities on scales larger than the Hubble scale is discussed. The quantity which is conserved on large scales in a flat background universe may be expressed in terms of the fractional, spatial gradient of the energy density on constant expansion hypersurfaces or, alternatively, with the help of expansion or curvature perturbation variables on hypersurfaces of constant energy density. For nonvanishing background curvature the perturbation dynamics is most suitably described in terms of energy density perturbations on hypersurfaces of constant curvature.Comment: 12 pages, Revtex, to appear in Class.Quantum Gra

SUMOylation inhibits FOXM1 activity and delays mitotic transition

The forkhead box transcription factor FOXM1 is an essential effector of G2/M-phase transition, mitosis and the DNA damage response. As such, it is frequently deregulated during tumorigenesis. Here we report that FOXM1 is dynamically modified by SUMO1 but not by SUMO2/3 at multiple sites. We show that FOXM1 SUMOylation is enhanced in MCF-7 breast cancer cells in response to treatment with epirubicin and mitotic inhibitors. Mutation of five consensus conjugation motifs yielded a SUMOylation-deficient mutant FOXM1. Conversely, fusion of the E2 ligase Ubc9 to FOXM1 generated an auto-SUMOylating mutant (FOXM1-Ubc9). Analysis of wild-type FOXM1 and mutants revealed that SUMOylation inhibits FOXM1 activity, promotes translocation to the cytoplasm and enhances APC/Cdh1-mediated ubiquitination and degradation. Further, expression of the SUMOylation-deficient mutant enhanced cell proliferation compared with wild-type FOXM1, whereas the FOXM1-Ubc9 fusion protein resulted in persistent cyclin B1 expression and slowed the time from mitotic entry to exit. In summary, our findings suggest that SUMOylation attenuates FOXM1 activity and causes mitotic delay in cytotoxic drug response

More examples of structure formation in the Lemaitre-Tolman model

In continuing our earlier research, we find the formulae needed to determine the arbitrary functions in the Lemaitre-Tolman model when the evolution proceeds from a given initial velocity distribution to a final state that is determined either by a density distribution or by a velocity distribution. In each case the initial and final distributions uniquely determine the L-T model that evolves between them, and the sign of the energy-function is determined by a simple inequality. We also show how the final density profile can be more accurately fitted to observational data than was done in our previous paper. We work out new numerical examples of the evolution: the creation of a galaxy cluster out of different velocity distributions, reflecting the current data on temperature anisotropies of CMB, the creation of the same out of different density distributions, and the creation of a void. The void in its present state is surrounded by a nonsingular wall of high density.Comment: LaTeX 2e with eps figures. 30 pages, 11 figures, 30 figure files. Revision matches published versio

Perturbations of a Universe Filled with Dust and Radiation

A first-order perturbation approach to $k=0$ Friedmann cosmologies filled with dust and radiation is developed. Adopting the coordinate gauge comoving with the perturbed matter, and neglecting the vorticity of the radiation, a pair of coupled equations is obtained for the trace $h$ of the metric perturbations and for the velocity potential $v$. A power series solution with upwards cutoff exists such that the leading terms for large values of the dimensionless time $\xi$ agree with the relatively growing terms of the dust solution of Sachs and Wolfe.Comment: 9 pp, typeset in late