Interactions between biomolecules are characterized by where they occur and how they are organized, e.g., the alignment of lipid molecules to form a membrane. However, spatial and angular information are mixed within the image of a fluorescent molecule–the microscope’s dipole-spread function (DSF). We demonstrate the pixOL algorithm to simultaneously optimize all pixels within a phase mask to produce an engineered Green’s tensor–the dipole extension of point-spread function engineering. The pixOL DSF achieves optimal precision to simultaneously measure the 3D orientation and 3D location of a single molecule, i.e., 4.1° orientation, 0.44 sr wobble angle, 23.2 nm lateral localization, and 19.5 nm axial localization precisions in simulations over a 700 nm depth range using 2500 detected photons. The pixOL microscope accurately and precisely resolves the 3D positions and 3D orientations of Nile red within a spherical supported lipid bilayer, resolving both membrane defects and differences in cholesterol concentration in six dimensions.

中文翻译：

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用于同时测量荧光分子的 3D 方向和 3D 位置的偶极子扩展函数工程

生物分子之间的相互作用的特征在于它们发生的位置和它们的组织方式，例如，脂质分子排列形成膜。然而，空间和角度信息混合在荧光分子的图像中——显微镜的偶极子扩展函数 (DSF)。我们演示了 pixOL 算法，以同时优化相位掩模中的所有像素，以产生工程格林张量——点扩展函数工程的偶极子扩展。pixOL DSF 在 700 nm 深度范围内的模拟中实现了最佳精度，可同时测量单个分子的 3D 方向和 3D 位置，即 4.1° 方向、0.44 sr 摆动角、23.2 nm 横向定位和 19.5 nm 轴向定位精度使用 2500 个检测到的光子。