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        "author": "Talley Lambert",
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        "description": "# PSFmodels-py\n\nPython bindings for scalar and vectorial models of the point spread function.\n\nOriginal C++ code and MATLAB MEX bindings Copyright &copy; 2006-2013, [Francois Aguet](http://www.francoisaguet.net/software.html), distributed under GPL-3.0 license.\nPython bindings by Talley Lambert\n\nThe model is described in Auget et al 2009<sup>1</sup>. For more information and implementation details, see Francois' Thesis<sup>2</sup>.\n\n<sup>1</sup> [F. Aguet et al., (2009) Opt. Express 17(8), pp. 6829-6848](https://doi.org/10.1364/OE.17.006829)\n\n<sup>2</sup> [F. Aguet. (2009) Super-Resolution Fluorescence Microscopy Based on Physical Models. Swiss Federal Institute of Technology Lausanne, EPFL Thesis no. 4418](http://bigwww.epfl.ch/publications/aguet0903.html)\n\n### see also:\n\nFor a different (faster) scalar-based Gibson\u2013Lanni PSF model, see the [MicroscPSF](https://github.com/MicroscPSF) project, based on [Li et al (2017)](https://doi.org/10.1364/JOSAA.34.001029) which has been implemented in [Python](https://github.com/MicroscPSF/MicroscPSF-Py), [MATLAB](https://github.com/MicroscPSF/MicroscPSF-Matlab), and [ImageJ/Java](https://github.com/MicroscPSF/MicroscPSF-ImageJ)\n\n## Install\n\nPrebuilt binaries available on pypi for OS X and Windows, sdist available for linux\n\n```\npip install psfmodels\n```\n\n### from source\n\n(requires cmake and a c++ compiler)\n\n```\ngit clone --recurse-submodules https://github.com/tlambert03/PSFmodels-py.git\ncd PSFmodels-py\npython setup.py install\n# or python setup.py build to just build but not install\n```\n\n## Usage\n\nThere are two main functions in `psfmodels`: `vectorial_psf` and `scalar_psf`. Additionally, each version has a helper function called `vectorial_psf_centered` and `scalar_psf_centered` respectively. The main difference is that the `_psf` functions accept a vector of Z positions `zv` (relative to coverslip) at which PSF is calculated. As such, the point source may or may not actually be in the center of the rendered volume. The `_psf_centered` variants, by contrast, do _not_ accecpt `zv`, but rather accept `nz` (the number of z planes) and `dz` (the z step size in microns), and always generates an output volume in which the point source is positioned in the middle of the Z range, with planes equidistant from each other. All functions accept an argument `pz`, specifying the position of the point source relative to the coverslip. See additional keyword arguments below\n\n_Note, all output dimensions (`nx` and `nz`) should be odd._\n\n```python\nimport psfmodels as psfm\nimport matplotlib.pyplot as plt\nfrom matplotlib.colors import PowerNorm\n\n# generate centered psf with a point source at `pz` from coverslip\nnx = 127\nnz = nx\ndxy = 0.05\npsf = psfm.vectorial_psf_centered(nz=nz, nx=nx, dxy=dxy, dz=dxy, pz=0)\nfig, (ax1, ax2) = plt.subplots(1, 2)\nax1.imshow(psf[nz//2], norm=PowerNorm(gamma=0.4))\nax2.imshow(psf[:, nx//2], norm=PowerNorm(gamma=0.4))\nplt.show()\n```\n\n![Image of PSF](fig.png)\n\n```python\n# instead of nz and dz, you can directly specify a vector of z positions\nimport numpy as np\n\n# generate 31 evenly spaced Z positions from -3 to 3 microns\nzv = np.linspace(-3, 3, 31)\npsf = psfm.vectorial_psf(zv, nx=127)\npsf.shape  # (31, 127, 127)\n```\n\n**all** PSF functions accept the following parameters. In general, units should be provided in microns. Python API may change slightly in the future.  See function docstrings as well.\n\n```\nnx (int):       XY size of output PSF in pixels, must be odd.\ndxy (float):    pixel size in sample space (microns) [default: 0.05]\npz (float):     depth of point source relative to coverslip (in microns) [default: 0]\nti0 (float):    working distance of the objective (microns) [default: 1.515]\nni0 (float):    immersion medium refractive index, design value [default: 1.515]\nni (float):     immersion medium refractive index, experimental value [default: 1.515]\ntg0 (float):    coverslip thickness, design value (microns) [default: 170]\ntg (float):     coverslip thickness, experimental value (microns) [default: 170]\nng0 (float):    coverslip refractive index, design value [default: 1.515]\nng (float):     coverslip refractive index, experimental value [default: 1.515]\nns (float):     sample refractive index [default: 1.47]\nwvl (float):    emission wavelength (microns) [default: 0.6]\nNA (float):     numerical aperture [default: 1.4]\nsf (int):       oversampling factor to approximate pixel integration [default: 3]\nmode (int):     if 0, returns oversampled PSF [default: 1]\n```\n\n## Comparison with other models\n\nWhile these models are definitely slower than the one implemented in [Li et al (2017)](https://doi.org/10.1364/JOSAA.34.001029) and [MicroscPSF](https://github.com/MicroscPSF), there are some interesting differences between the scalar and vectorial approximations, particularly with higher NA lenses, non-ideal sample refractive index, and increasing spherical aberration with depth from the coverslip.\n\nFor an interactive comparison, see the [examples.ipynb](examples.ipynb) Jupyter notebook.\n\n## Lightsheet PSF utility function\n\nThe `psfmodels.tot_psf()` function provides a quick way to simulate the total system PSF (excitation x detection) as might be observed on a light sheet microscope (currently, only strictly orthogonal illumination and detection are supported).  See the [lightsheet.ipynb](lightsheet.ipynb) Jupyter notebook for examples.",
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