Wrap-safe transfer functions

waveorder/models/isotropic_fluorescent_thick_3d.py

@@ -1,9 +1,10 @@
 from typing import Literal
 
+import numpy as np
 import torch
 from torch import Tensor
 
-from waveorder import optics, util
+from waveorder import optics, sampling, util
 
 
 def generate_test_phantom(
@@ -28,6 +29,49 @@ def calculate_transfer_function(
     index_of_refraction_media,
     numerical_aperture_detection,
 ):
+
+    transverse_nyquist = sampling.transverse_nyquist(
+        wavelength_emission,
+        numerical_aperture_detection,  # ill = det for fluorescence
+        numerical_aperture_detection,
+    )
+    axial_nyquist = sampling.axial_nyquist(
+        wavelength_emission,
+        numerical_aperture_detection,
+        index_of_refraction_media,
+    )
+
+    yx_factor = int(np.ceil(yx_pixel_size / transverse_nyquist))
+    z_factor = int(np.ceil(z_pixel_size / axial_nyquist))
+
+    optical_transfer_function = _calculate_wrap_unsafe_transfer_function(
+        (
+            zyx_shape[0] * z_factor,
+            zyx_shape[1] * yx_factor,
+            zyx_shape[2] * yx_factor,
+        ),
+        yx_pixel_size / yx_factor,
+        z_pixel_size / z_factor,
+        wavelength_emission,
+        z_padding,
+        index_of_refraction_media,
+        numerical_aperture_detection,
+    )
+    zyx_out_shape = (zyx_shape[0] + 2 * z_padding,) + zyx_shape[1:]
+    return sampling.nd_fourier_central_cuboid(
+        optical_transfer_function, zyx_out_shape
+    )
+
+
+def _calculate_wrap_unsafe_transfer_function(
+    zyx_shape,
+    yx_pixel_size,
+    z_pixel_size,
+    wavelength_emission,
+    z_padding,
+    index_of_refraction_media,
+    numerical_aperture_detection,
+):
     radial_frequencies = util.generate_radial_frequencies(
         zyx_shape[1:], yx_pixel_size
     )
@@ -97,7 +141,7 @@ def apply_transfer_function(
     Returns
     -------
     Simulated data : torch.Tensor
-        
+
     """
     if (
         zyx_object.shape[0] + 2 * z_padding

waveorder/models/isotropic_thin_3d.py

@@ -1,9 +1,10 @@
 from typing import Literal, Tuple
 
+import numpy as np
 import torch
 from torch import Tensor
 
-from waveorder import optics, util
+from waveorder import optics, sampling, util
 
 
 def generate_test_phantom(
@@ -42,6 +43,64 @@ def calculate_transfer_function(
     numerical_aperture_illumination,
     numerical_aperture_detection,
     invert_phase_contrast=False,
+):
+    transverse_nyquist = sampling.transverse_nyquist(
+        wavelength_illumination,
+        numerical_aperture_illumination,
+        numerical_aperture_detection,
+    )
+    yx_factor = int(np.ceil(yx_pixel_size / transverse_nyquist))
+
+    absorption_2d_to_3d_transfer_function, phase_2d_to_3d_transfer_function = (
+        _calculate_wrap_unsafe_transfer_function(
+            (
+                yx_shape[0] * yx_factor,
+                yx_shape[1] * yx_factor,
+            ),
+            yx_pixel_size / yx_factor,
+            z_position_list,
+            wavelength_illumination,
+            index_of_refraction_media,
+            numerical_aperture_illumination,
+            numerical_aperture_detection,
+            invert_phase_contrast=invert_phase_contrast,
+        )
+    )
+
+    absorption_2d_to_3d_transfer_function_out = torch.zeros(
+        (len(z_position_list),) + tuple(yx_shape), dtype=torch.complex64
+    )
+    phase_2d_to_3d_transfer_function_out = torch.zeros(
+        (len(z_position_list),) + tuple(yx_shape), dtype=torch.complex64
+    )
+
+    for z in range(len(z_position_list)):
+        absorption_2d_to_3d_transfer_function_out[z] = (
+            sampling.nd_fourier_central_cuboid(
+                absorption_2d_to_3d_transfer_function[z], yx_shape
+            )
+        )
+        phase_2d_to_3d_transfer_function_out[z] = (
+            sampling.nd_fourier_central_cuboid(
+                phase_2d_to_3d_transfer_function[z], yx_shape
+            )
+        )
+
+    return (
+        absorption_2d_to_3d_transfer_function_out,
+        phase_2d_to_3d_transfer_function_out,
+    )
+
+
+def _calculate_wrap_unsafe_transfer_function(
+    yx_shape,
+    yx_pixel_size,
+    z_position_list,
+    wavelength_illumination,
+    index_of_refraction_media,
+    numerical_aperture_illumination,
+    numerical_aperture_detection,
+    invert_phase_contrast=False,
 ):
     if invert_phase_contrast:
         z_position_list = torch.flip(torch.tensor(z_position_list), dims=(0,))

waveorder/models/phase_thick_3d.py

@@ -4,7 +4,7 @@
 import torch
 from torch import Tensor
 
-from waveorder import optics, util
+from waveorder import optics, sampling, util
 from waveorder.models import isotropic_fluorescent_thick_3d
 
 
@@ -40,6 +40,60 @@ def calculate_transfer_function(
     numerical_aperture_illumination,
     numerical_aperture_detection,
     invert_phase_contrast=False,
+):
+    transverse_nyquist = sampling.transverse_nyquist(
+        wavelength_illumination,
+        numerical_aperture_illumination,
+        numerical_aperture_detection,
+    )
+    axial_nyquist = sampling.axial_nyquist(
+        wavelength_illumination,
+        numerical_aperture_detection,
+        index_of_refraction_media,
+    )
+
+    yx_factor = int(np.ceil(yx_pixel_size / transverse_nyquist))
+    z_factor = int(np.ceil(z_pixel_size / axial_nyquist))
+
+    real_potential_transfer_function, imag_potential_transfer_function = (
+        _calculate_wrap_unsafe_transfer_function(
+            (
+                zyx_shape[0] * z_factor,
+                zyx_shape[1] * yx_factor,
+                zyx_shape[2] * yx_factor,
+            ),
+            yx_pixel_size / yx_factor,
+            z_pixel_size / z_factor,
+            wavelength_illumination,
+            z_padding,
+            index_of_refraction_media,
+            numerical_aperture_illumination,
+            numerical_aperture_detection,
+            invert_phase_contrast=invert_phase_contrast,
+        )
+    )
+
+    zyx_out_shape = (zyx_shape[0] + 2 * z_padding,) + zyx_shape[1:]
+    return (
+        sampling.nd_fourier_central_cuboid(
+            real_potential_transfer_function, zyx_out_shape
+        ),
+        sampling.nd_fourier_central_cuboid(
+            imag_potential_transfer_function, zyx_out_shape
+        ),
+    )
+
+
+def _calculate_wrap_unsafe_transfer_function(
+    zyx_shape,
+    yx_pixel_size,
+    z_pixel_size,
+    wavelength_illumination,
+    z_padding,
+    index_of_refraction_media,
+    numerical_aperture_illumination,
+    numerical_aperture_detection,
+    invert_phase_contrast=False,
 ):
     radial_frequencies = util.generate_radial_frequencies(
         zyx_shape[1:], yx_pixel_size

waveorder/sampling.py

@@ -0,0 +1,94 @@
+import numpy as np
+import torch
+
+
+def transverse_nyquist(
+    wavelength_emission,
+    numerical_aperture_illumination,
+    numerical_aperture_detection,
+):
+    """Transverse Nyquist sample spacing in `wavelength_emission` units.
+
+    For widefield label-free imaging, the transverse Nyquist sample spacing is
+    lambda / (2 * (NA_ill + NA_det)).
+
+    Perhaps surprisingly, the transverse Nyquist sample spacing for widefield
+    fluorescence is lambda / (4 * NA), which is equivalent to the above formula
+    when NA_ill = NA_det.
+
+    Parameters
+    ----------
+    wavelength_emission : float
+        Output units match these units
+    numerical_aperture_illumination : float
+        For widefield fluorescence, set to numerical_aperture_detection
+    numerical_aperture_detection : float
+
+    Returns
+    -------
+    float
+        Transverse Nyquist sample spacing
+
+    """
+    return wavelength_emission / (
+        2 * (numerical_aperture_detection + numerical_aperture_illumination)
+    )
+
+
+def axial_nyquist(
+    wavelength_emission,
+    numerical_aperture_detection,
+    index_of_refraction_media,
+):
+    """Axial Nyquist sample spacing in `wavelength_emission` units.
+
+    For widefield microscopes, the axial Nyquist cutoff frequency is:
+
+    (n/lambda) - sqrt( (n/lambda)^2 - (NA_det/lambda)^2 ),
+
+    and the axial Nyquist sample spacing is 1 / (2 * cutoff_frequency).
+
+    Perhaps surprisingly, the axial Nyquist sample spacing is independent of
+    the illumination numerical aperture.
+
+    Parameters
+    ----------
+    wavelength_emission : float
+        Output units match these units
+    numerical_aperture_detection : float
+    index_of_refraction_media: float
+
+    Returns
+    -------
+    float
+        Axial Nyquist sample spacing
+
+    """
+    n_on_lambda = index_of_refraction_media / wavelength_emission
+    cutoff_frequency = n_on_lambda - np.sqrt(
+        n_on_lambda**2
+        - (numerical_aperture_detection / wavelength_emission) ** 2
+    )
+    return 1 / (2 * cutoff_frequency)
+
+
+def nd_fourier_central_cuboid(source, target_shape):
+    """Central cuboid of an N-D Fourier transform.
+
+    Parameters
+    ----------
+    source : torch.Tensor
+        Source tensor
+    target_shape : tuple of int
+
+    Returns
+    -------
+    torch.Tensor
+        Center cuboid in Fourier space
+
+    """
+    center_slices = tuple(
+        slice((s - o) // 2, (s - o) // 2 + o)
+        for s, o in zip(source.shape, target_shape)
+    )
+    return torch.fft.ifftshift(torch.fft.fftshift(source)[center_slices])