Spacetime Paths as a Whole

The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a whole. It is well known that Feynman’s original derivation of the path integral formulation of non-relativistic quantum mechanics uses time-slicing to calculate amplitudes as sums over all possible paths through space, but along a definite curve through time. Here, a 3+1D spacetime wave distribution and its 4-momentum dual are formally developed which have no external time parameter and therefore cannot change or evolve in the usual sense. Time is thus seen “from the outside”. A given 3+1D momentum representation of a system encodes complete dynamical information, describing the system’s spacetime behavior as a whole. A comparison is made to the mathematics of holograms, and properties of motion for simple systems are derived.

Focusing of Light Pulses by Different Types of Wavy Parabolic Mirrors

The propagation of an ultra-short light pulse is studied in the framework of scalar diffraction theory. Light pulses are focused by different types of wavy parabolic surfaces. The temporal-spatial behavior of the two-dimensional wave field is computed in the vicinity of the focal plane. It is shown that the slightly perturbation from the perfect parabolic shape leads a space-time dispersion of the pulse in the neighborhood of the focus.

Multidither coherent optical adaptive technique for deep tissue two-photon microscopy

Two-photon microscopy normally suffers from the scattering of the tissue in biological imaging. Multidither coherent optical adaptive technique (COAT) can correct the scattered wavefront in parallel. However, the determination of the corrective phases may not be completely accurate using conventional method, which undermines the performance of this technique. In this paper, we theoretically demonstrate a method that can obtain more accurate corrective phases by determining the phase values from the square root of the fluorescence signal. A numerical simulation model is established to study the performance of adaptive optics in two-photon microscopy by combining scalar diffraction theory with vector diffraction theory. The results show that the distortion of the wavefront can be corrected more thoroughly with our method in two-photon imaging. In our simulation, with the scattering from a 450-[Formula: see text]m-thick mouse brain tissue, excitation focal spots with higher peak-to-background ratio (PBR) and images with higher contrast can be obtained. Hence, further enhancement of the multidither COAT correction performance in two-photon imaging can be expected.