SimpleDistortionModel#

class optika.distortion.SimpleDistortionModel(plate_scale, dispersion, angle, reference)[source]#

Bases: AbstractLinearDistortionModel

A simple analytic distortion model consisting of a rotation of the field, an isotropic plate scale, and a linear spectral dispersion along the rotated \(x\) axis.

This captures the distortion of an idealized spectrograph: the field center at the reference wavelength maps to the reference position on the sensor, and other wavelengths are displaced along the dispersion direction.

Examples

Distort a grid of scene coordinates and plot the result on the sensor, colored by wavelength.

import matplotlib.pyplot as plt
import astropy.units as u
import named_arrays as na
import optika

model = optika.distortion.SimpleDistortionModel(
    plate_scale=1 * u.arcsec / u.pix,
    dispersion=2 * u.nm / u.pix,
    angle=15 * u.deg,
    reference=na.SpectralPositionalVectorArray(
        wavelength=550 * u.nm,
        position=na.Cartesian2dVectorArray(0, 0) * u.pix,
    ),
)

scene = na.SpectralPositionalVectorArray(
    wavelength=na.linspace(500, 600, axis="wavelength", num=3) * u.nm,
    position=na.Cartesian2dVectorLinearSpace(
        start=-10 * u.arcsec,
        stop=+10 * u.arcsec,
        axis=na.Cartesian2dVectorArray("field_x", "field_y"),
        num=5,
    ),
)

sensor = model.distort(scene)

fig, ax = plt.subplots(constrained_layout=True)
ax.set_aspect("equal")
for wavelength in scene.wavelength.ndarray:
    na.plt.scatter(
        sensor.position.x,
        sensor.position.y,
        where=scene.wavelength == wavelength,
        label=f"{wavelength}",
        ax=ax,
    )
ax.set_xlabel(f"detector $x$ ({na.unit(sensor.position.x):latex_inline})")
ax.set_ylabel(f"detector $y$ ({na.unit(sensor.position.y):latex_inline})")
ax.legend();

../_images/optika.distortion.SimpleDistortionModel_0_0.png

Attributes

`angle`	The angle of the dispersion direction with respect to the scene.
`center`	The reference point subtracted from the coordinates before applying `matrix`.
`dispersion`	The magnitude of the spectral dispersion, in units such as \(\text{nm} / \text{pix}\).
`intercept`	The constant offset added after applying `matrix`.
`matrix`	The linear part of the affine transformation.
`plate_scale`	The spatial plate scale, in units such as \(\text{arcsec} / \text{pix}\).
`reference`	The reference wavelength and the sensor position that the field center maps to at that wavelength.

Methods

`__init__`(plate_scale, dispersion, angle, ...)
`distort`(coordinates)	Convert scene coordinates to sensor coordinates.
`to_string`([prefix])	Public-facing version of the `__repr__` method that allows for defining a prefix string, which can be used to calculate how much whitespace to add to the beginning of each line of the result.
`undistort`(coordinates)	Convert sensor coordinates to scene coordinates.

Inheritance Diagram

Parameters:

plate_scale (Quantity | AbstractScalar)
dispersion (Quantity | AbstractScalar)
angle (Quantity | AbstractScalar)
reference (AbstractSpectralPositionalVectorArray)

distort(coordinates)#

Convert scene coordinates to sensor coordinates.

Parameters:: coordinates (AbstractSpectralPositionalVectorArray) – The wavelength and position of each point in the scene.
Return type:: SpectralPositionalVectorArray

to_string(prefix=None)#

Public-facing version of the __repr__ method that allows for defining a prefix string, which can be used to calculate how much whitespace to add to the beginning of each line of the result.

Parameters:: prefix (None | str) – an optional string, the length of which is used to calculate how much whitespace to add to the result.
Return type:: str

undistort(coordinates)#

Convert sensor coordinates to scene coordinates.

Parameters:: coordinates (AbstractSpectralPositionalVectorArray) – The wavelength and sensor position of each point.
Return type:: SpectralPositionalVectorArray

angle: Quantity | AbstractScalar = <dataclasses._MISSING_TYPE object>#: The angle of the dispersion direction with respect to the scene.

property center: SpectralPositionalVectorArray#: The reference point subtracted from the coordinates before applying matrix.

dispersion: Quantity | AbstractScalar = <dataclasses._MISSING_TYPE object>#: The magnitude of the spectral dispersion, in units such as \(\text{nm} / \text{pix}\).

property intercept: AbstractSpectralPositionalVectorArray#: The constant offset added after applying matrix.

property matrix: SpectralPositionalMatrixArray#: The linear part of the affine transformation.

plate_scale: Quantity | AbstractScalar = <dataclasses._MISSING_TYPE object>#: The spatial plate scale, in units such as \(\text{arcsec} / \text{pix}\).

reference: AbstractSpectralPositionalVectorArray = <dataclasses._MISSING_TYPE object>#: The reference wavelength and the sensor position that the field center maps to at that wavelength.