![]() ![]() Fast, background-free, 3D super-resolution optical fluctuation imaging (SOFI). Imaging live-cell dynamics and structure at the single-molecule level. Far-Field Optical Nanoscopy (Springer, 2015). Diffraction-unlimited imaging: from pretty pictures to hard numbers. Vandenberg, W., Leutenegger, M., Lasser, T., Hofkens, J. Imaging intracellular fluorescent proteins at nanometer resolution. Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). The 4D microscope platform unifies the sensitivity and high temporal resolution of phase imaging with the specificity and high spatial resolution of fluorescence microscopy. This allowed us to not only image live cells in 3D at up to 200 Hz, but also to integrate fluorescence super-resolution optical fluctuation imaging within the same optical instrument. We realized multi-plane imaging using a customized prism for the simultaneous acquisition of eight planes. The non-iterative phase retrieval relies on the acquisition of single images at each z-location and thus enables straightforward 3D phase imaging using a classical microscope. We propose the combination of a novel label-free white light quantitative phase imaging with fluorescence to provide high-speed imaging and spatial super-resolution. However, going ‘beyond the diffraction barrier’ comes at a price, since most far-field super-resolution imaging techniques trade temporal for spatial super-resolution. The math is way over my head.Super-resolution fluorescence microscopy provides unprecedented insight into cellular and subcellular structures. This will probably involve either runtime mesh modification, or translation, rotation, and scaling of a cube-shaped mesh. Hopefully whatever code you have already can help you with calculating where the vertices should be! Basically what you need to calculate is the 3-dimensional projection of the shape is in a 3D world. Now what about a 4d "box" shape? That projection would probably look like a box sometimes? but that's probably where your piece of code comes into play. ![]() I think that's about all that can happen for a sphere, since rotating it does nothing. When you move it on the "w" axis the scale of the sphere may change and it may even disappear. Based on my intuition, and what happened for 3d -> 2d I'd guess a 4d sphere projected in a 3d world would look like. Now let's think about 4d objects in a 3d world. I think that projection would always be a quadrilateral, but thee shape can be strange and can change a lot as you move it on the z axis, or worse, rotate it on some arbitrary axis. Now imagine you rotate the cube on a weird angle and project it into 2d again. do absolutely nothing in the 2d world until you reach of edge of the square, at which point it will disappear. If you move it around on z, the square will. If you move it around on x or y, the square will move. On a 2d plane it will just look like a square. But if you move the sphere on the z axis, the 2d circle will appear to grow or shrink or even completely disappear, depending on which part of the axis is currently intersecting the plane. but if you imagine a 3d sphere projected in a 2d plane, it just looks like a circle, right? Then if you move that sphere on the x or y axis, the circle can just move around on the 2d plane as normal. ![]()
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