Scalar and vectorial models of the microscope point spread function (PSF).

# PSFmodels-py

Python bindings for scalar and vectorial models of the point spread function.

The model is described in Auget et al 20091. For more information and implementation details, see Francois' Thesis2.

For a different (faster) scalar-based Gibsonâ€“Lanni PSF model, see the MicroscPSF project, based on Li et al (2017) which has been implemented in Python, MATLAB, and ImageJ/Java

## Install

Prebuilt binaries available on pypi for OS X and Windows, sdist available for linux

``````pip install psfmodels
``````

### from source

(requires cmake and a c++ compiler)

``````git clone https://github.com/tlambert03/PSFmodels-py.git
cd PSFmodels-py
python setup.py install
``````

## 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.

```import psfmodels as psfm
import matplotlib.pyplot as plt
from matplotlib.colors import PowerNorm

# generate centered psf with a point source at `pz` from coverslip
nx = 127
nz = nx
dxy = 0.05
psf = psfm.vectorial_psf_centered(nz=nz, nx=nx, dxy=dxy, dz=dxy, 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()
```

```# 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
zv = np.linspace(-3, 3, 31)
psf = psfm.vectorial_psf(zv, nx=127)
psf.shape  # (31, 127, 127)
```

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.

``````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: 1.515]
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]
tg (float):     coverslip thickness, experimental value (microns) [default: 170]
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]
sf (int):       oversampling factor to approximate pixel integration [default: 3]
mode (int):     if 0, returns oversampled PSF [default: 1]
``````

## Comparison with other models

While these models are definitely slower than the one implemented in Li et al (2017) and 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 Jupyter notebook.