| Name | ZernikePy JSON |
| Version |
0.0.2
JSON |
| download |
| home_page | |
| Summary | A minimalistic Python package to generate individual or a series of Zernike polynomials of arbitrary orders with visualization. |
| upload_time | 2024-02-27 13:47:48 |
| maintainer | |
| docs_url | None |
| author | |
| requires_python | >=3.8 |
| license | |
| keywords |
zernike
psf
optics
polynomials
basis
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
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No coveralls.
|
_ZernikePy_ is a minimalistic Python library to compute and visualize Zernike polynomials of any given orders.
A typical usage is to generate basis functions for phase modulation in optics.
# Installation
```
pip install ZernikePy
```
# Requirements
```
numpy
scipy
matplotlib
```
# How to use
After installation, first import the main function from the library
```
from zernikepy import zernike_polynomials
```
## Examples
Generate a (256, 256)-sized Zernike polynomial of order 4 (defocusing):
```python
p = zernike_polymonials(mode=4, size=256)
```
or
```python
p = zernike_polymonials(mode='defocusing', size=256)
```
Generate the first 55 modes and display them:
```python
ps = zernike_polymonials(mode=55, select='all', show=True)
```
Generate the following selected modes defocusing, vertical coma, oblique astigmatism and
display them:
```python
ps = zernike_polynomials(mode=10, select=[4, 'vertical coma', 'oblique astigmatism'], show=True)
```
Note that regardless of the order of the elements in the list `select`, the output stores the polynomials in ascending
order in the last dimension. Hence, in the output `ps[:, :, 0]` is oblique astigmatism, `ps[:, :, 1]` is defocusing and
`ps[:, :, 2]` is vertical coma.
## Detailed explanation
The main function `zernike_polynomials(mode, size, select, show)`
takes four variables:
- `mode`: which (or up to which) order of the polynomial. It follows the [OSA standard indexing](https://en.wikipedia.org/wiki/Zernike_polynomials#OSA/ANSI_standard_indices) convention
and should be a nonnegative integer. It is also possible to pass a string of the corresponding name for the first 15 modes. Default is `'defocus'`.
- `size`: numerical size of the square Cartesian mesh. It should be a postive integer. Default is `128`.
- `select`: in the case of passing more than one polynomial, i.e. some selected modes up to the given `mode`,
give a list of integers or strings or a mixture of both. A special case is `select='all'` where all the polynomials up to
the given `mode` is passed. Default is `None` in which case only a single polynomial of the given `mode` is passed.
- `show`: boolen variable to determine whether to display the polynomials. Default is `False`.
The output is a Numpy array, either 2D for a single mode, or 3D for multiple modes.
### Name of the first 15 modes
| Mode / OSA index | Name |
|------------------|:------------------------------:|
| 0 | piston |
| 1 | vertical tilt |
| 2 | horizontal tilt |
| 3 | oblique astigmatism |
| 4 | defocus |
| 5 | vertical astigmatism |
| 6 | vertical trefoil |
| 7 | vertical coma |
| 8 | horizontal coma |
| 9 | oblique trefoil |
| 10 | oblique quadrafoil |
| 11 | oblique secondary astigmatism |
| 12 | primary spherical |
| 13 | vertical secondary astigmatism |
| 14 | vertical quadrafoil |
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