FresnelPropagation#

class deepinv.physics.FresnelPropagation(img_size, wavelength, distance, pixel_size, dtype=torch.cfloat, device='cpu', **kwargs)[source]#

Bases: 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 and a transmission function. To model propagation-based phase-contrast CT, additionally compose with deepinv.physics.Tomography or 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[int, ...]) – Shape of an unbatched input. The final two entries are (height, width).

  • wavelength (float) – Wavelength in the same length unit as distance and pixel_size.

  • distance (float) – Propagation distance.

  • pixel_size (float, tuple[float, float]) – Sampling pitch dy, dx. If float, then dy, dy, default 1.

  • dtype (torch.dtype) – Complex dtype of the transfer function. Default: torch.cfloat.

  • device (torch.device, str) – Device on which the operator is created.

Examples:

Using FresnelPropagation for phase retrieval

>>> 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:

>>> 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:#

Multi-distance Fresnel phase retrieval

Multi-distance Fresnel phase retrieval