# FresnelPropagation
### *class* deepinv.physics.FresnelPropagation(img_size, wavelength, distance, pixel_size, dtype=torch.cfloat, device='cpu', \*\*kwargs)
Bases: [`AngularSpectrumPropagation`](https://deepinv.org/api/stubs/deepinv.physics.AngularSpectrumPropagation.html.md#deepinv.physics.AngularSpectrumPropagation)
Fresnel (paraxial angular-spectrum) propagation of a complex wave field.
For wavelength $\lambda$, propagation distance $z$, and spatial
frequencies $(f_x, f_y)$, this class uses
$$
H(f_x, f_y) = \exp\left[-\mathrm{i}\pi\lambda z
(f_x^2 + f_y^2)\right].
$$
This transfer function assumes a coherent plane wave illumination and paraxial approximation.
It is used in the near-field case where the propagation distance $z \ll a^2/\lambda$,
with $a$ being the feature size of the object (or pixel size).
#### NOTE
To model in-line holography, compose this physics with [`deepinv.physics.PhaseRetrieval`](https://deepinv.org/api/stubs/deepinv.physics.PhaseRetrieval.html.md#deepinv.physics.PhaseRetrieval) and a transmission function.
To model propagation-based phase-contrast CT, additionally compose with [`deepinv.physics.Tomography`](https://deepinv.org/api/stubs/deepinv.physics.Tomography.html.md#deepinv.physics.Tomography) or [`deepinv.physics.TomographyWithAstra`](https://deepinv.org/api/stubs/deepinv.physics.TomographyWithAstra.html.md#deepinv.physics.TomographyWithAstra).
#### HINT
Holography geometries are often described in terms of the Fresnel number.
The Fresnel number is defined from the physical parameter as
$$
a_F = \frac{a^2}{\lambda z},
$$
with $a$ being the characteristic size of the object, typically the pixel size, $\lambda$ the wavelength, and $z$ the propagation distance.
* **Parameters:**
* **img_size** ([*tuple*](https://docs.python.org/3.12/library/stdtypes.html#tuple) *[*[*int*](https://docs.python.org/3.12/library/functions.html#int) *,* *...* *]*) – Shape of an unbatched input. The final two
entries are `(height, width)`.
* **wavelength** ([*float*](https://docs.python.org/3.12/library/functions.html#float)) – Wavelength in the same length unit as `distance`
and `pixel_size`.
* **distance** ([*float*](https://docs.python.org/3.12/library/functions.html#float)) – Propagation distance.
* **pixel_size** ([*float*](https://docs.python.org/3.12/library/functions.html#float) *,* [*tuple*](https://docs.python.org/3.12/library/stdtypes.html#tuple) *[*[*float*](https://docs.python.org/3.12/library/functions.html#float) *,* [*float*](https://docs.python.org/3.12/library/functions.html#float) *]*) – Sampling pitch `dy, dx`. If `float`, then `dy, dy`, default 1.
* **dtype** ([*torch.dtype*](https://docs.pytorch.org/docs/stable/tensor_attributes.html#torch.dtype)) – Complex dtype of the transfer function. Default:
`torch.cfloat`.
* **device** ([*torch.device*](https://docs.pytorch.org/docs/stable/tensor_attributes.html#torch.device) *,* [*str*](https://docs.python.org/3.12/library/stdtypes.html#str)) – Device on which the operator is created.
* **Examples:**
Using FresnelPropagation for phase retrieval
```pycon
>>> import torch
>>> from deepinv.physics import FresnelPropagation, PhaseRetrieval
>>> B = FresnelPropagation(
... img_size=(1, 64, 64),
... wavelength=500e-9,
... distance=0.1,
... pixel_size=5e-6,
... )
>>> physics = PhaseRetrieval(B=B)
>>> transmission = torch.randn(2, 1, 64, 64, dtype=torch.cfloat)
>>> physics(transmission).dtype
torch.float32
>>> physics(transmission).size()
torch.Size([2, 1, 64, 64])
```
If a transmission function should be added, proceed like:
```pycon
>>> from deepinv.physics import Physics, compose
>>> k = 2 * torch.pi / 500e-9
>>> transmission_model = Physics(
... A=lambda x: torch.exp(-1j * k * x[:, 0:1] - k * x[:, 1:2])
... )
>>> physics = compose(transmission_model, physics)
```
## Examples using `FresnelPropagation`: