# psfmodels
[](https://pypi.org/project/psfmodels)
[](https://python.org)
[](https://github.com/tlambert03/psfmodels/actions/workflows/ci.yml)
[](https://codecov.io/gh/tlambert03/psfmodels)
Python bindings for scalar and vectorial models of the point spread function.
Original C++ code and MATLAB MEX bindings Copyright © 2006-2013, [Francois
Aguet](http://www.francoisaguet.net/software.html), distributed under GPL-3.0
license. Python bindings by Talley Lambert
This package contains three models:
1. The vectorial model is described in Auget et al 2009<sup>1</sup>. For more
information and implementation details, see Francois' Thesis<sup>2</sup>.
2. A scalar model, based on Gibson & Lanni<sup>3</sup>.
3. A gaussian approximation (both paraxial and non-paraxial), using paramters from Zhang et al (2007)<sup>4</sup>.
<small>
<sup>1</sup> [F. Aguet et al., (2009) Opt. Express 17(8), pp.
6829-6848](https://doi.org/10.1364/OE.17.006829)
<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)
<sup>3</sup> [F. Gibson and F. Lanni (1992) J. Opt. Soc. Am. A, vol. 9, no. 1, pp. 154-166](https://opg.optica.org/josaa/abstract.cfm?uri=josaa-9-1-154)
<sup>4</sup> [Zhang et al (2007). Appl Opt
. 2007 Apr 1;46(10):1819-29.](https://doi.org/10.1364/AO.46.001819)
</small>
### see also:
For a different (faster) scalar-based Gibson–Lanni 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)
## Install
```sh
pip install psfmodels
```
### from source
```sh
git clone https://github.com/tlambert03/PSFmodels.git
cd PSFmodels
pip install -e ".[dev]" # will compile c code via pybind11
```
## Usage
There 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
_Note, all output dimensions (`nx` and `nz`) should be odd._
```python
import psfmodels as psfm
import matplotlib.pyplot as plt
from matplotlib.colors import PowerNorm
# generate centered psf with a point source at `pz` microns from coverslip
# shape will be (127, 127, 127)
psf = psfm.make_psf(127, 127, dxy=0.05, dz=0.05, pz=0)
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.imshow(psf[nz//2], norm=PowerNorm(gamma=0.4))
ax2.imshow(psf[:, nx//2], norm=PowerNorm(gamma=0.4))
plt.show()
```
```python
# instead of nz and dz, you can directly specify a vector of z positions
import numpy as np
# generate 31 evenly spaced Z positions from -3 to 3 microns
psf = psfm.make_psf(np.linspace(-3, 3, 31), nx=127)
psf.shape # (31, 127, 127)
```
**all** PSF functions accept the following parameters. Units should be provided
in microns unless otherwise stated. Python API may change slightly in the
future. See function docstrings as well.
```
nx (int): XY size of output PSF in pixels, must be odd.
dxy (float): pixel size in sample space (microns) [default: 0.05]
pz (float): depth of point source relative to coverslip (in microns) [default: 0]
ti0 (float): working distance of the objective (microns) [default: 150.0]
ni0 (float): immersion medium refractive index, design value [default: 1.515]
ni (float): immersion medium refractive index, experimental value [default: 1.515]
tg0 (float): coverslip thickness, design value (microns) [default: 170.0]
tg (float): coverslip thickness, experimental value (microns) [default: 170.0]
ng0 (float): coverslip refractive index, design value [default: 1.515]
ng (float): coverslip refractive index, experimental value [default: 1.515]
ns (float): sample refractive index [default: 1.47]
wvl (float): emission wavelength (microns) [default: 0.6]
NA (float): numerical aperture [default: 1.4]
```
## Comparison with other models
While 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.
For an interactive comparison, see the [examples.ipynb](notebooks/examples.ipynb) Jupyter
notebook.
## Lightsheet PSF utility function
The `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](notebooks/lightsheet.ipynb) Jupyter notebook for
examples.
Raw data
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Express 17(8), pp.\n6829-6848](https://doi.org/10.1364/OE.17.006829)\n\n<sup>2</sup> [F. Aguet. (2009) Super-Resolution Fluorescence Microscopy Based on\nPhysical Models. Swiss Federal Institute of Technology Lausanne, EPFL Thesis no.\n4418](http://bigwww.epfl.ch/publications/aguet0903.html)\n\n<sup>3</sup> [F. Gibson and F. Lanni (1992) J. Opt. Soc. Am. A, vol. 9, no. 1, pp. 154-166](https://opg.optica.org/josaa/abstract.cfm?uri=josaa-9-1-154)\n\n<sup>4</sup> [Zhang et al (2007). Appl Opt\n. 2007 Apr 1;46(10):1819-29.](https://doi.org/10.1364/AO.46.001819)\n\n</small>\n\n### see also:\n\nFor a different (faster) scalar-based Gibson\u2013Lanni PSF model, see the\n[MicroscPSF](https://github.com/MicroscPSF) project, based on [Li et al\n(2017)](https://doi.org/10.1364/JOSAA.34.001029) which has been implemented in\n[Python](https://github.com/MicroscPSF/MicroscPSF-Py),\n[MATLAB](https://github.com/MicroscPSF/MicroscPSF-Matlab), and\n[ImageJ/Java](https://github.com/MicroscPSF/MicroscPSF-ImageJ)\n\n## Install\n\n```sh\npip install psfmodels\n```\n\n### from source\n\n```sh\ngit clone https://github.com/tlambert03/PSFmodels.git\ncd PSFmodels\npip install -e \".[dev]\" # will compile c code via pybind11\n```\n\n## Usage\n\nThere are two main functions in `psfmodels`: `vectorial_psf` and `scalar_psf`.\nAdditionally, each version has a helper function called `vectorial_psf_centered`\nand `scalar_psf_centered` respectively. 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