GaussianApodization

class deeptrack.aberrations.GaussianApodization(sigma: float | Callable[[...], float] = 1, offset: tuple[int, int] | Callable[[...], tuple[int, int]] = (0, 0), **kwargs: dict[str, Any])

Bases: Aberration

Introduces pupil apodization.

This class modifies the amplitude of the pupil function to decrease progressively at higher spatial frequencies, following a Gaussian distribution. The apodization helps simulate the effects of optical attenuation at the edges of the pupil.

Parameters

sigma: float, optional

The standard deviation of the Gaussian apodization. Defines how quickly the amplitude decreases towards the pupil edges. A smaller value leads to a more rapid decay. The default is 1.

offset: tuple of float, optional

Specifies the (x, y) offset of the Gaussian center relative to the pupil’s geometric center. The default is (0, 0).

Methods

get(pupil: np.ndarray, offset: tuple[float, float], sigma: float, rho: np.ndarray, **kwargs: dict[str, Any]) -> np.ndarray

Applies Gaussian apodization to the input pupil function.

Examples

Apply Gaussian apodization to a simulated fluorescence image:

>>> import deeptrack as dt

>>> particle = dt.PointParticle(z = 2 * dt.units.micrometer)
>>> aberrated_optics = dt.Fluorescence(
>>>     pupil = dt.GaussianApodization(sigma=0.5),
>>> )
>>> aberrated_particle = aberrated_optics(particle)
>>> aberrated_particle.plot(cmap="gray")

Methods Summary

get(pupil, offset, sigma, rho, **kwargs)

Applies Gaussian apodization to the input pupil function.

Methods Documentation

get(pupil: ndarray, offset: tuple[float, float], sigma: float, rho: ndarray, **kwargs: dict[str, Any]) → ndarray

Applies Gaussian apodization to the input pupil function.

This method attenuates the amplitude of the pupil function based on a Gaussian distribution, where the amplitude decreases as the distance from the Gaussian center increases.

Parameters

pupil: np.ndarray

A 2D array representing the input pupil function.

offset: tuple of float

Specifies the (x, y) offset of the Gaussian center relative to the pupil’s center.

sigma: float

The standard deviation of the Gaussian apodization.

rho: np.ndarray

A 2D array of radial coordinates normalized to the pupil aperture.

**kwargs: dict, optional

Additional parameters for compatibility with other features or inherited methods. These are typically passed by the parent class and may include: - z (float): The depth or axial position of the image,

used in certain contexts.

Returns

np.ndarray

The modified pupil function after applying Gaussian apodization.

Examples

>>> import deeptrack as dt
>>> import numpy as np
>>> import matplotlib.pyplot as plt

>>> pupil = np.ones((128, 128))
>>> rho = np.linspace(0, 1, 128).reshape(-1, 1) @ np.ones((1, 128))
>>> x = np.linspace(-1, 1, 128)
>>> y = np.linspace(-1, 1, 128)
>>> X, Y = np.meshgrid(x, y)
>>> rho = np.sqrt(X**2 + Y**2) 
>>> pupil[rho > 1] = 0
>>> apodizer = dt.GaussianApodization(sigma=0.5, offset=(25, -3))
>>> modified_pupil = apodizer.get(
>>>     pupil, 
>>>     offset=(5, -3), 
>>>     sigma=0.5, 
>>>     rho=rho
>>> )
>>> fig, axes = plt.subplots(1, 2, figsize=(12, 6))
>>> axes[0].imshow(np.abs(modified_pupil), cmap="gray")
>>> axes[0].set_title("Modified Pupil Magnitude")
>>> axes[1].imshow(np.angle(modified_pupil), cmap="hsv")
>>> axes[1].set_title("Modified Pupil Phase")
>>> plt.show()
>>> modified_pupil.shape
(128, 128)