"""
Implements class CTF and CTFReconstruced.
Copyright (c) 2024 European Molecular Biology Laboratory
Author: Valentin Maurer <valentin.maurer@embl-hamburg.de>
"""
import re
import warnings
from typing import Tuple, Dict
from dataclasses import dataclass
import numpy as np
from ..types import NDArray
from ..backends import backend as be
from .compose import ComposableFilter
from ..parser import StarParser, XMLParser
from ._utils import (
frequency_grid_at_angle,
compute_tilt_shape,
crop_real_fourier,
fftfreqn,
shift_fourier,
)
__all__ = ["CTF", "CTFReconstructed", "create_ctf"]
[docs]
@dataclass
class CTF(ComposableFilter):
"""
Generate a per-tilt contrast transfer function mask.
"""
#: The shape of the to-be reconstructed volume.
shape: Tuple[int] = None
#: The defocus value in x direction.
defocus_x: float = None
#: The tilt angles.
angles: Tuple[float] = None
#: The microscope projection axis, defaults to None.
opening_axis: int = 2
#: The axis along which the tilt is applied, defaults to 2 (z).
tilt_axis: int = 0
#: Whether to correct defocus gradient, defaults to 0 (x).
correct_defocus_gradient: bool = False
#: The sampling rate, defaults to 1 Angstrom / Voxel.
sampling_rate: Tuple[float] = 1
#: The acceleration voltage in Volts, defaults to 300e3.
acceleration_voltage: float = 300e3
#: The spherical aberration coefficient, defaults to 2.7e7.
spherical_aberration: float = 2.7e7
#: The amplitude contrast, defaults to 0.07.
amplitude_contrast: float = 0.07
#: The phase shift in degrees, defaults to 0.
phase_shift: float = 0
#: The defocus angle in degrees, defaults to 0.
defocus_angle: float = 0
#: The defocus value in y direction, defaults to None.
defocus_y: float = None
#: Whether the returned CTF should be phase-flipped.
flip_phase: bool = True
#: Whether to return a format compliant with rfft. Only relevant for single angles.
return_real_fourier: bool = False
[docs]
@classmethod
def from_file(cls, filename: str) -> "CTF":
"""
Initialize :py:class:`CTF` from file.
Parameters
----------
filename : str
The path to a file with ctf parameters. Supports extensions are:
+-------+---------------------------------------------------------+
| .star | GCTF file |
+-------+---------------------------------------------------------+
| .xml | WARP/M XML file |
+-------+---------------------------------------------------------+
| .* | CTFFIND4 file |
+-------+---------------------------------------------------------+
"""
func = _from_ctffind
if filename.lower().endswith("star"):
func = _from_gctf
elif filename.lower().endswith("xml"):
func = _from_xml
data = func(filename=filename)
# Pixel size needs to be overwritten by pixel size the ctf is generated for
return cls(
shape=None,
angles=data.get("angles", None),
defocus_x=data["defocus_1"],
sampling_rate=data["pixel_size"],
acceleration_voltage=data["acceleration_voltage"],
spherical_aberration=data["spherical_aberration"],
amplitude_contrast=data["amplitude_contrast"],
phase_shift=data["additional_phase_shift"],
defocus_angle=data["azimuth_astigmatism"],
defocus_y=data["defocus_2"],
)
def __post_init__(self):
self.defocus_angle = np.radians(self.defocus_angle)
self.phase_shift = np.radians(self.phase_shift)
[docs]
def __call__(self, **kwargs) -> NDArray:
func_args = vars(self).copy()
func_args.update(kwargs)
ret = self.weight(**func_args)
ret = be.astype(be.to_backend_array(ret), be._float_dtype)
return {
"data": ret,
"shape": func_args["shape"],
"return_real_fourier": func_args.get("return_real_fourier"),
"is_multiplicative_filter": True,
}
@staticmethod
def _pad_to_length(arr, length: int):
ret = np.atleast_1d(arr)
return np.repeat(ret, length // ret.size)
[docs]
def weight(
self,
shape: Tuple[int],
defocus_x: Tuple[float],
angles: Tuple[float],
opening_axis: int = 2,
tilt_axis: int = 0,
amplitude_contrast: float = 0.07,
phase_shift: Tuple[float] = 0,
defocus_angle: Tuple[float] = 0,
defocus_y: Tuple[float] = None,
correct_defocus_gradient: bool = False,
sampling_rate: Tuple[float] = 1,
acceleration_voltage: float = 300e3,
spherical_aberration: float = 2.7e3,
flip_phase: bool = True,
return_real_fourier: bool = False,
cutoff_frequency: float = 0.5,
**kwargs: Dict,
) -> NDArray:
"""
Compute the CTF weight tilt stack.
Parameters
----------
shape : tuple of int
The shape of the CTF.
defocus_x : tuple of float
The defocus value in x direction.
angles : tuple of float
The tilt angles.
opening_axis : int, optional
The axis around which the wedge is opened, defaults to 2.
tilt_axis : int, optional
The axis along which the tilt is applied, defaults to 0.
amplitude_contrast : float, optional
The amplitude contrast, defaults to 0.07.
phase_shift : tuple of float, optional
The phase shift in radians, defaults to 0.
defocus_angle : tuple of float, optional
The defocus angle in radians, defaults to 0.
defocus_y : tuple of float, optional
The defocus value in y direction, defaults to None.
correct_defocus_gradient : bool, optional
Whether to correct defocus gradient, defaults to False.
sampling_rate : tuple of float, optional
The sampling rate, defaults to 1.
acceleration_voltage : float, optional
The acceleration voltage in electron microscopy, defaults to 300e3.
spherical_aberration : float, optional
The spherical aberration coefficient, defaults to 2.7e3.
flip_phase : bool, optional
Whether the returned CTF should be phase-flipped.
**kwargs : Dict
Additional keyword arguments.
Returns
-------
NDArray
A stack containing the CTF weight.
"""
angles = np.atleast_1d(angles)
defoci_x = self._pad_to_length(defocus_x, angles.size)
defoci_y = self._pad_to_length(defocus_y, angles.size)
phase_shift = self._pad_to_length(phase_shift, angles.size)
defocus_angle = self._pad_to_length(defocus_angle, angles.size)
spherical_aberration = self._pad_to_length(spherical_aberration, angles.size)
amplitude_contrast = self._pad_to_length(amplitude_contrast, angles.size)
sampling_rate = np.max(sampling_rate)
ctf_shape = compute_tilt_shape(
shape=shape, opening_axis=opening_axis, reduce_dim=True
)
stack = np.zeros((len(angles), *ctf_shape))
# Shift tilt axis forward
corrected_tilt_axis = tilt_axis
if opening_axis and tilt_axis is not None:
if opening_axis < tilt_axis:
corrected_tilt_axis -= 1
for index, angle in enumerate(angles):
defocus_x, defocus_y = defoci_x[index], defoci_y[index]
correction = correct_defocus_gradient and angle is not None
chi = create_ctf(
angle=angle,
shape=ctf_shape,
defocus_x=defocus_x,
defocus_y=defocus_y,
sampling_rate=sampling_rate,
acceleration_voltage=self.acceleration_voltage,
correct_defocus_gradient=correction,
spherical_aberration=spherical_aberration[index],
cutoff_frequency=cutoff_frequency,
phase_shift=phase_shift[index],
defocus_angle=defocus_angle[index],
amplitude_contrast=amplitude_contrast[index],
tilt_axis=corrected_tilt_axis,
opening_axis=opening_axis,
full_shape=shape,
)
stack[index] = chi
# Avoid contrast inversion
np.negative(stack, out=stack)
if flip_phase:
np.abs(stack, out=stack)
stack = be.to_backend_array(np.squeeze(stack))
return stack
[docs]
class CTFReconstructed(CTF):
"""
Create a simple contrast transfer function mask without the ability to specify
per-tilt parameters like in :py:class:`CTF`.
"""
[docs]
def weight(
self,
shape: Tuple[int],
defocus_x: Tuple[float],
amplitude_contrast: float = 0.07,
phase_shift: Tuple[float] = 0,
defocus_angle: Tuple[float] = 0,
defocus_y: Tuple[float] = None,
sampling_rate: Tuple[float] = 1,
acceleration_voltage: float = 300e3,
spherical_aberration: float = 2.7e3,
flip_phase: bool = True,
return_real_fourier: bool = False,
cutoff_frequency: float = 0.5,
**kwargs: Dict,
) -> NDArray:
"""
Compute the CTF weight tilt stack.
Parameters
----------
shape : tuple of int
The shape of the CTF.
defocus_x : tuple of float
The defocus value in x direction.
opening_axis : int, optional
The axis around which the wedge is opened, defaults to 2.
amplitude_contrast : float, optional
The amplitude contrast, defaults to 0.07.
phase_shift : tuple of float, optional
The phase shift in radians, defaults to 0.
defocus_angle : tuple of float, optional
The defocus angle in radians, defaults to 0.
defocus_y : tuple of float, optional
The defocus value in y direction, defaults to None.
sampling_rate : tuple of float, optional
The sampling rate, defaults to 1.
acceleration_voltage : float, optional
The acceleration voltage in electron microscopy, defaults to 300e3.
spherical_aberration : float, optional
The spherical aberration coefficient, defaults to 2.7e3.
flip_phase : bool, optional
Whether the returned CTF should be phase-flipped.
**kwargs : Dict
Additional keyword arguments.
Returns
-------
NDArray
A stack containing the CTF weight.
"""
stack = create_ctf(
shape=shape,
defocus_x=defocus_x,
defocus_y=defocus_y,
sampling_rate=np.max(sampling_rate),
acceleration_voltage=self.acceleration_voltage,
correct_defocus_gradient=False,
spherical_aberration=spherical_aberration,
cutoff_frequency=cutoff_frequency,
phase_shift=phase_shift,
defocus_angle=defocus_angle,
amplitude_contrast=amplitude_contrast,
)
stack = shift_fourier(data=stack, shape_is_real_fourier=False)
# Avoid contrast inversion
np.negative(stack, out=stack)
if flip_phase:
np.abs(stack, out=stack)
stack = be.to_backend_array(np.squeeze(stack))
if return_real_fourier:
stack = crop_real_fourier(stack)
return stack
def _from_xml(filename: str):
data = XMLParser(filename)
params = {
"PhaseShift": None,
"Amplitude": None,
"Defocus": None,
"Voltage": None,
"Cs": None,
"DefocusAngle": None,
"PixelSize": None,
"Angles": data["Angles"],
}
ctf_options = data["CTF"]["Param"]
for option in ctf_options:
option = option["@attributes"]
name = option["Name"]
if name in params:
params[name] = option["Value"]
if "GridCTF" in data:
ctf = data["GridCTF"]["Node"]
params["Defocus"] = [ctf[i]["@attributes"]["Value"] for i in range(len(ctf))]
ctf_phase = data["GridCTFPhase"]["Node"]
params["PhaseShift"] = [
ctf_phase[i]["@attributes"]["Value"] for i in range(len(ctf_phase))
]
ctf_ast = data["GridCTFDefocusAngle"]["Node"]
params["DefocusAngle"] = [
ctf_ast[i]["@attributes"]["Value"] for i in range(len(ctf_ast))
]
missing = [k for k, v in params.items() if v is None]
if len(missing):
raise ValueError(f"Could not find {missing} in {filename}.")
params = {
k: np.array(v) if hasattr(v, "__len__") else float(v) for k, v in params.items()
}
# Convert units to sampling rate (we assume it is Angstrom)
params["Cs"] = float(params["Cs"] * 1e7)
params["Defocus"] = params["Defocus"] * 1e4
mapping = {
"angles": "Angles",
"defocus_1": "Defocus",
"defocus_2": "Defocus",
"azimuth_astigmatism": "DefocusAngle",
"additional_phase_shift": "PhaseShift",
"acceleration_voltage": "Voltage",
"spherical_aberration": "Cs",
"amplitude_contrast": "Amplitude",
"pixel_size": "PixelSize",
}
return {k: params[v] for k, v in mapping.items()}
def _from_ctffind(filename: str):
parameter_regex = {
"pixel_size": r"Pixel size: ([0-9.]+) Angstroms",
"acceleration_voltage": r"acceleration voltage: ([0-9.]+) keV",
"spherical_aberration": r"spherical aberration: ([0-9.]+) mm",
"amplitude_contrast": r"amplitude contrast: ([0-9.]+)",
}
with open(filename, mode="r", encoding="utf-8") as infile:
lines = [x.strip() for x in infile.read().split("\n")]
lines = [x for x in lines if len(x)]
def _screen_params(line, params, output):
for parameter, regex_pattern in parameter_regex.items():
match = re.search(regex_pattern, line)
if match:
output[parameter] = float(match.group(1))
columns = {
"micrograph_number": 0,
"defocus_1": 1,
"defocus_2": 2,
"azimuth_astigmatism": 3,
"additional_phase_shift": 4,
"cross_correlation": 5,
"spacing": 6,
}
output = {k: [] for k in columns.keys()}
for line in lines:
if line.startswith("#"):
_screen_params(line, params=parameter_regex, output=output)
continue
values = line.split()
for key, value in columns.items():
output[key].append(float(values[value]))
for key in columns:
output[key] = np.array(output[key])
output["additional_phase_shift"] = np.degrees(output["additional_phase_shift"])
return output
def _from_gctf(filename: str):
parser = StarParser(filename)
ctf_data = parser["data_"]
mapping = {
"defocus_1": ("_rlnDefocusU", float),
"defocus_2": ("_rlnDefocusV", float),
"pixel_size": ("_rlnDetectorPixelSize", float),
"acceleration_voltage": ("_rlnVoltage", float),
"spherical_aberration": ("_rlnSphericalAberration", float),
"amplitude_contrast": ("_rlnAmplitudeContrast", float),
"additional_phase_shift": (None, float),
"azimuth_astigmatism": ("_rlnDefocusAngle", float),
}
output = {}
for out_key, (key, key_dtype) in mapping.items():
if key not in ctf_data and key is not None:
warnings.warn(f"ctf_data is missing key {key}.")
key_value = ctf_data.get(key, [0])
output[out_key] = [key_dtype(x) for x in key_value]
longest_key = max(map(len, output.values()))
output = {k: v * longest_key if len(v) == 1 else v for k, v in output.items()}
return output
def _compute_electron_wavelength(acceleration_voltage: int = None):
"""Computes the wavelength of an electron in angstrom."""
# Physical constants expressed in SI units
planck_constant = 6.62606896e-34
electron_charge = 1.60217646e-19
electron_mass = 9.10938215e-31
light_velocity = 299792458
energy = electron_charge * acceleration_voltage
denominator = energy**2
denominator += 2 * energy * electron_mass * light_velocity**2
electron_wavelength = np.divide(
planck_constant * light_velocity, np.sqrt(denominator)
)
# Convert to Ångstrom
electron_wavelength *= 1e10
return electron_wavelength
def create_ctf(
shape: Tuple[int],
defocus_x: float,
acceleration_voltage: float = 300,
defocus_angle: float = 0,
phase_shift: float = 0,
defocus_y: float = None,
sampling_rate: float = 1,
spherical_aberration: float = 2.7e7,
amplitude_contrast: float = 0.07,
correct_defocus_gradient: bool = False,
cutoff_frequency: float = 0.5,
angle: float = None,
tilt_axis: int = 0,
opening_axis: int = None,
full_shape: Tuple[int] = None,
) -> NDArray:
"""
Create CTF representation using the definition from [1]_.
Parameters
----------
shape : Tuple[int]
Shape of the returned CTF mask.
defocus_x : float
Defocus in x in units of sampling rate, e.g. 30000 Angstrom.
acceleration_voltage : float, optional
Acceleration voltage in keV, defaults to 300.
defocus_angle : float, optional
Astigmatism in radians, defaults to 0.
phase_shift : float, optional
Phase shift from phase plate in radians, defaults to 0.
defocus_y : float, optional
Defocus in y in units of sampling rate.
tilt_axis : int, optional
Axes the specimen was tilted over, defaults to 0 (x-axis).
sampling_rate : float or tuple of floats
Sampling rate throughout shape, e.g., 4 Angstrom per voxel.
amplitude_contrast : float, optional
Amplitude contrast of microscope, defaults to 0.07.
spherical_aberration : float, optional
Spherical aberration of microscope in Angstrom.
angle : float, optional
Assume the created CTF is a projection over opening_axis observed at angle.
opening_axis : int, optional
Projection axis, only relevant if angle is given.
full_shape : tuple of ints
Shape of the entire volume we are observing a projection of. This is required
to compute aspect ratios for correct scaling. For instance, the 2D CTF slice
could be (50,50), while the final 3D CTF volume is (50,50,25) with the
opening_axis being 2, i.e., the z-axis.
Returns
-------
NDArray
CTF mask.
References
----------
.. [1] CTFFIND4: Fast and accurate defocus estimation from electron micrographs.
Alexis Rohou and Nikolaus Grigorieff. Journal of Structural Biology 2015.
"""
electron_wavelength = _compute_electron_wavelength(acceleration_voltage)
electron_wavelength /= sampling_rate
aberration = (spherical_aberration / sampling_rate) * electron_wavelength**2
if correct_defocus_gradient or defocus_y is not None:
if len(shape) < 2:
raise ValueError(f"Length of shape needs to be at least 2, got {shape}")
sampling = tuple(float(x) for x in np.divide(sampling_rate, shape))
grid = fftfreqn(
shape=shape,
sampling_rate=sampling,
return_sparse_grid=True,
)
# This should be done after defocus_x computation
if correct_defocus_gradient:
if angle is None:
raise ValueError("Cannot correct for defocus gradient without angle.")
angle_rad = np.radians(angle)
defocus_gradient = np.multiply(grid[tilt_axis], np.sin(angle_rad))
if tilt_axis == 0:
defocus_x = np.add(defocus_x, defocus_gradient)
elif tilt_axis == 1 and defocus_y is not None:
defocus_y = np.add(defocus_y, defocus_gradient)
# 0.5 * (dx + dy) + cos(2 * (azimuth - astigmatism) * (dx - dy))
if defocus_y is not None:
defocus_sum = np.add(defocus_x, defocus_y)
defocus_difference = np.subtract(defocus_x, defocus_y)
angular_grid = np.arctan2(grid[1], grid[0])
defocus_difference = np.multiply(
defocus_difference,
np.cos(2 * (angular_grid - defocus_angle)),
)
defocus_x = np.add(defocus_sum, defocus_difference)
defocus_x *= 0.5
frequency_grid = fftfreqn(shape, sampling_rate=True, compute_euclidean_norm=True)
if angle is not None and opening_axis is not None and full_shape is not None:
frequency_grid = frequency_grid_at_angle(
shape=full_shape,
tilt_axis=tilt_axis,
opening_axis=opening_axis,
angle=angle,
sampling_rate=1,
)
frequency_mask = frequency_grid < cutoff_frequency
# k^2*π*λ(dx - 0.5 * sph_abb * λ^2 * k^2) + phase_shift + ampl_contrast_term)
np.square(frequency_grid, out=frequency_grid)
chi = defocus_x - 0.5 * aberration * frequency_grid
np.multiply(chi, np.pi * electron_wavelength, out=chi)
np.multiply(chi, frequency_grid, out=chi)
chi += phase_shift
chi += np.arctan(
np.divide(
amplitude_contrast,
np.sqrt(1 - np.square(amplitude_contrast)),
)
)
np.sin(-chi, out=chi)
np.multiply(chi, frequency_mask, out=chi)
return chi