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Updating optics and scatterers for Tutorial Review. (#210)
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* first_commit_review

* Fixing documentation for parameters and defining new parameters.

- Íscat is defined by setting the input/output polarization to circular and adding a phase_shift_correction term.
- Documentation for all variables

* Update optics.py
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@SkariZ
SkariZ authored Aug 26, 2024
1 parent 4b5e023 commit 35891bd
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Showing 3 changed files with 196 additions and 23 deletions.
2 changes: 1 addition & 1 deletion deeptrack/holography.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -27,7 +27,7 @@ def get_propagation_matrix(shape, to_z, pixel_size, wavelength, dx=0, dy=0):


class Rescale(Feature):
"""Rescales an optical field by subtracting the real part of the field beofre multiplication.
"""Rescales an optical field by subtracting the real part of the field before multiplication.
Parameters
----------
Expand Down
152 changes: 146 additions & 6 deletions deeptrack/optics.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -353,12 +353,13 @@ def _pupil(

defocus = np.reshape(defocus, (-1, 1, 1))
z_shift = defocus * np.expand_dims(z_shift, axis=0)

#print(self.pupil)
if include_aberration:
pupil = self.pupil
if isinstance(pupil, Feature):

pupil_function = pupil(pupil_function)

elif isinstance(pupil, np.ndarray):
pupil_function *= pupil

Expand Down Expand Up @@ -669,6 +670,12 @@ def get(self, illuminated_volume, limits, fields, **kwargs):
include_aberration=True,
**kwargs,
)[0],
self._pupil(
volume.shape[:2],
defocus=[0],
include_aberration=True,
**kwargs,
)[0]
]

pupil_step = np.fft.fftshift(pupils[0])
Expand All @@ -677,7 +684,7 @@ def get(self, illuminated_volume, limits, fields, **kwargs):
light_in = self.illumination.resolve(light_in)
light_in = np.fft.fft2(light_in)

K = 2 * np.pi / kwargs["wavelength"]
K = 2 * np.pi / kwargs["wavelength"]*kwargs["refractive_index_medium"]

z = z_limits[1]
for i, z in zip(index_iterator, z_iterator):
Expand All @@ -690,14 +697,17 @@ def get(self, illuminated_volume, limits, fields, **kwargs):
light = np.fft.ifft2(light_in)
light_out = light * np.exp(1j * ri_slice * voxel_size[-1] * K)
light_in = np.fft.fft2(light_out)

shifted_pupil = np.fft.fftshift(pupils[-1])
shifted_pupil = np.fft.fftshift(pupils[1])
light_in_focus = light_in * shifted_pupil

#import matplotlib.pyplot as plt
#plt.imshow(light_in_focus.imag)
#plt.show()
if len(fields) > 0:
field = np.sum(fields, axis=0)
light_in_focus += field[..., 0]

shifted_pupil = np.fft.fftshift(pupils[-1])
light_in_focus = light_in_focus * shifted_pupil
# Mask to remove light outside the pupil.
mask = np.abs(shifted_pupil) > 0
light_in_focus = light_in_focus * mask
Expand All @@ -724,6 +734,136 @@ def get(self, illuminated_volume, limits, fields, **kwargs):
Holography = Brightfield


class ISCAT(Brightfield):
"""Images coherently illuminated samples using ISCAT.
Images samples by creating a discretized volume, where each pixel
represents the effective refractive index of that pixel. Light is
propagated through the sample iteratively by first propagating the
light in the fourier space, followed by a refractive index correction
in the real space.
Parameters
----------
illumination : Feature
Feature-set resolving the complex field entering the sample. Default
is a field with all values 1.
NA : float
The NA of the limiting aperature.
wavelength : float
The wavelength of the scattered light in meters.
magnification : float
The magnification of the optical system.
resolution : array_like[float (, float, float)]
The distance between pixels in the camera. A third value can be
included to define the resolution in the z-direction.
refractive_index_medium : float
The refractive index of the medium.
padding : array_like[int, int, int, int]
Pads the sample volume with zeros to avoid edge effects.
output_region : array_like[int, int, int, int]
The region of the image to output (x,y,width,height). Default
None returns entire image.
pupil : Feature
A feature-set resolving the pupil function at focus. The feature-set
receive an unaberrated pupil as input.
illumination_angle : float
The angle relative to the optical axis. Default is π radians in ISCAT.
amp_factor : float
The amplitude factor of the field. Default is 1.
The relative amplitude off the illuminating field and the reference field.
"""

def __init__(
self,
illumination_angle = np.pi,
amp_factor = 1,
**kwargs
):

super().__init__(
illumination_angle=illumination_angle,
amp_factor=amp_factor,
input_polarization="circular",
output_polarization="circular",
phase_shift_correction=True,
**kwargs
)

class Darkfield(Brightfield):
"""Images coherently illuminated samples using Darkfield.
Images samples by creating a discretized volume, where each pixel
represents the effective refractive index of that pixel. Light is
propagated through the sample iteratively by first propagating the
light in the fourier space, followed by a refractive index correction
in the real space.
Parameters
----------
illumination : Feature
Feature-set resolving the complex field entering the sample. Default
is a field with all values 1.
NA : float
The NA of the limiting aperature.
wavelength : float
The wavelength of the scattered light in meters.
magnification : float
The magnification of the optical system.
resolution : array_like[float (, float, float)]
The distance between pixels in the camera. A third value can be
included to define the resolution in the z-direction.
refractive_index_medium : float
The refractive index of the medium.
padding : array_like[int, int, int, int]
Pads the sample volume with zeros to avoid edge effects.
output_region : array_like[int, int, int, int]
The region of the image to output (x,y,width,height). Default
None returns entire image.
pupil : Feature
A feature-set resolving the pupil function at focus. The feature-set
receive an unaberrated pupil as input.
illumination_angle : float
The angle relative to the optical axis. Default is π/2 radians.
"""

def __init__(
self,
illumination_angle = np.pi/2,
**kwargs
):
super().__init__(
illumination_angle=illumination_angle,
**kwargs)

#Retrieve get as super
def get(self, illuminated_volume, limits, fields, **kwargs):
"""Retrieve the darkfield image of the illuminated volume.
Parameters
----------
illuminated_volume : array_like
The volume of the sample being illuminated.
limits : array_like
The spatial limits of the volume.
fields : array_like
The fields interacting with the sample.
**kwargs : dict
Additional parameters passed to the super class's get method.
Returns
-------
numpy.ndarray
The darkfield image obtained by calculating the squared absolute
difference from 1.
"""

field = super().get(illuminated_volume, limits, fields, return_field=True, **kwargs)
return np.square(np.abs(field-1))


class IlluminationGradient(Feature):
"""Adds a gradient in the illumination
Expand Down
65 changes: 49 additions & 16 deletions deeptrack/scatterers.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -489,10 +489,12 @@ class MieScatterer(Scatterer):
input_polarization: float or Quantity
Defines the polarization angle of the input. For simulating circularly
polarized light we recommend a coherent sum of two simulated fields. For
unpolarized light we recommend a incoherent sum of two simulated fields.
unpolarized light we recommend a incoherent sum of two simulated fields.
If defined as "circular", the coefficients are set to 1/2.
output_polarization: float or Quantity or None
If None, the output light is not polarized. Otherwise defines the angle of the
polarization filter after the sample. For off-axis, keep the same as input_polarization.
If defined as "circular", the coefficients are multiplied by 1. I.e. no change.
L : int or str
The number of terms used to evaluate the mie theory. If `"auto"`,
it determines the number of terms automatically.
Expand All @@ -507,8 +509,16 @@ class MieScatterer(Scatterer):
If True, the feature returns the fft of the field, rather than the
field itself.
coherence_length : float
The temporal coherence length of a partially coherent light given in meters. If None, the illumination is
assumed to be coherent.
The temporal coherence length of a partially coherent light given in meters.
If None, the illumination is assumed to be coherent.
amp_factor : float
A factor that scales the amplification of the field.
This is useful for scaling the field to the correct intensity. Default is 1.
phase_shift_correction : bool
If True, the feature applies a phase shift correction to the output field.
This is necessary for ISCAT simulations.
The correction depends on the k-vector and z according to the formula:
arr*=np.exp(1j * k * z + 1j * np.pi / 2)
"""

__gpu_compatible__ = True
Expand Down Expand Up @@ -540,6 +550,9 @@ def __init__(
position_objective=(0, 0),
return_fft=False,
coherence_length=None,
illumination_angle=0,
amp_factor=1,
phase_shift_correction=False,
**kwargs,
):
if polarization_angle is not None:
Expand Down Expand Up @@ -569,6 +582,9 @@ def __init__(
position_objective=position_objective,
return_fft=return_fft,
coherence_length=coherence_length,
illumination_angle=illumination_angle,
amp_factor=amp_factor,
phase_shift_correction=phase_shift_correction,
**kwargs,
)

Expand Down Expand Up @@ -617,7 +633,7 @@ def get_XY(self, shape, voxel_size):
def get_detector_mask(self, X, Y, radius):
return np.sqrt(X**2 + Y**2) < radius

def get_plane_in_polar_coords(self, shape, voxel_size, plane_position):
def get_plane_in_polar_coords(self, shape, voxel_size, plane_position, illumination_angle):

X, Y = self.get_XY(shape, voxel_size)
X = image.maybe_cupy(X)
Expand All @@ -633,9 +649,10 @@ def get_plane_in_polar_coords(self, shape, voxel_size, plane_position):

# get the angles
cos_theta = Z / R3
illumination_cos_theta=np.cos(np.arccos(cos_theta)+illumination_angle)
phi = np.arctan2(Y, X)

return R3, cos_theta, phi
return R3, cos_theta, illumination_cos_theta, phi

def get(
self,
Expand All @@ -657,9 +674,11 @@ def get(
return_fft,
coherence_length,
output_region,
illumination_angle,
amp_factor,
phase_shift_correction,
**kwargs,
):

# Get size of the output
xSize, ySize = self.get_xy_size(output_region, padding)
voxel_size = get_active_voxel_size()
Expand All @@ -683,9 +702,10 @@ def get(
)

# get field evaluation plane at offset_z
R3_field, cos_theta_field, phi_field = self.get_plane_in_polar_coords(
arr.shape, voxel_size, relative_position * ratio
R3_field, cos_theta_field, illumination_angle_field, phi_field = self.get_plane_in_polar_coords(
arr.shape, voxel_size, relative_position * ratio, illumination_angle
)

cos_phi_field, sin_phi_field = np.cos(phi_field), np.sin(phi_field)
# x and y position of a beam passing through field evaluation plane on the objective
x_farfield = (
Expand All @@ -706,43 +726,55 @@ def get(
cos_theta_field = cos_theta_field[pupil_mask]
phi_field = phi_field[pupil_mask]

if isinstance(input_polarization, (float, int, Quantity)):

illumination_angle_field=illumination_angle_field[pupil_mask]

if isinstance(input_polarization, (float, int, str, Quantity)):
if isinstance(input_polarization, Quantity):
input_polarization = input_polarization.to("rad")
input_polarization = input_polarization.magnitude

S1_coef = np.sin(phi_field + input_polarization)
S2_coef = np.cos(phi_field + input_polarization)
if isinstance(input_polarization, (float, int)):
S1_coef = np.sin(phi_field + input_polarization)
S2_coef = np.cos(phi_field + input_polarization)

# If the input polarization is circular set the coefficients to 1/2.
elif isinstance(input_polarization, (str)):
if input_polarization == "circular":
S1_coef = 1/2
S2_coef = 1/2

if isinstance(output_polarization, (float, int, Quantity)):
if isinstance(input_polarization, Quantity):
output_polarization = output_polarization.to("rad")
output_polarization = output_polarization.magnitude

S1_coef *= np.sin(phi_field + output_polarization)
S2_coef *= np.cos(phi_field + output_polarization)
S2_coef *= np.cos(phi_field + output_polarization) * illumination_angle_field

# Wave vector
k = 2 * np.pi / wavelength * refractive_index_medium

# Harmonics
A, B = coefficients(L)
PI, TAU = D.mie_harmonics(cos_theta_field, L)
PI, TAU = D.mie_harmonics(illumination_angle_field, L)

# Normalization factor
E = [(2 * i + 1) / (i * (i + 1)) for i in range(1, L + 1)]

# Scattering terms
S1 = sum([E[i] * A[i] * PI[i] + E[i] * B[i] * TAU[i] for i in range(0, L)])
S2 = sum([E[i] * B[i] * PI[i] + E[i] * A[i] * TAU[i] for i in range(0, L)])

arr[pupil_mask] = (
-1j
/ (k * R3_field)
* np.exp(1j * k * R3_field)
* (S2 * S2_coef + S1 * S1_coef)
)
) / amp_factor

# For phase shift correction (a multiplication of the field by exp(1j * k * z)).
if phase_shift_correction:
arr *= np.exp(1j * k * z + 1j * np.pi / 2)

# For partially coherent illumination
if coherence_length:
Expand Down Expand Up @@ -778,6 +810,7 @@ def get(
),
)
fourier_field = fourier_field * propagation_matrix * np.exp(-1j * k * offset_z)

if return_fft:
return fourier_field[..., np.newaxis]
else:
Expand Down

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