CylindricalSag#

class optika.sags.CylindricalSag(radius=<Quantity inf mm>, *, transformation=None, parameters_slope_error=None, parameters_roughness=None, parameters_microroughness=None)[source]#

Bases: AbstractSag

A cylindrical sag function, where the local \(y\) axis is the axis of symmetry for the cylinder.

The sag (\(z\) coordinate) of a spherical surface is calculated using the expression

\[z(x, y) = \frac{c x^2}{1 + \sqrt{1 - c^2 x^2}}\]

where \(c\) is the curvature, and \(x\) is the horizontal component of the evaluation point.

Examples

Plot a slice through the sag surface

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

sag = optika.sags.SphericalSag(
    radius=na.linspace(100, 300, axis="radius", num=3) * u.mm,
)

position = na.Cartesian3dVectorArray(
    x=na.linspace(-90, 90, axis="x", num=101) * u.mm,
    y=0 * u.mm,
    z=0 * u.mm
)

z = sag(position)

with astropy.visualization.quantity_support():
    plt.figure()
    plt.gca().set_aspect("equal")
    na.plt.plot(position.x, z, axis="x", label=sag.radius)
    plt.legend(title="radius")

../_images/optika.sags.CylindricalSag_0_0.png

Attributes

`parameters_microroughness`	The microroughness parameters for this sag profile.
`parameters_roughness`	The roughness parameters for this sag profile.
`parameters_slope_error`	The slope error parameters for this sag profile.
`radius`	The radius of this cylinder.
`shape`	The array shape of this object.
`transformation`	The transformation between the surface coordinate system and the sag coordinate system.

Methods

`__init__`([radius, transformation, ...])
`intercept`(rays)	A set of new rays with the same direction as the input rays, but with the `optika.rays.RayVectorArray.position` updated to their interception point with this sag function.
`normal`(position)	The vector perpendicular to the surface at the given position.
`propagate_rays`(rays)	For the given input rays, calculate new rays based off of their interation with this object.
`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.

Inheritance Diagram

Parameters:

radius (Quantity | AbstractScalar)
transformation (None | AbstractTransformation)
parameters_slope_error (None | SlopeErrorParameters)
parameters_roughness (None | RoughnessParameters)
parameters_microroughness (None | RoughnessParameters)

intercept(rays)[source]#

A set of new rays with the same direction as the input rays, but with the optika.rays.RayVectorArray.position updated to their interception point with this sag function.

Parameters:: rays (AbstractRayVectorArray) – input rays that will intercept this sag function
Return type:: AbstractRayVectorArray

normal(position)[source]#

The vector perpendicular to the surface at the given position.

Parameters:: position (AbstractCartesian3dVectorArray) – The location on the surface to evaluate the normal vector
Return type:: AbstractCartesian3dVectorArray

propagate_rays(rays)#

For the given input rays, calculate new rays based off of their interation with this object.

Parameters:: rays (AbstractRayVectorArray) – a set of input rays that will interact with this object
Return type:: AbstractRayVectorArray

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

parameters_microroughness: None | RoughnessParameters = None#: The microroughness parameters for this sag profile.

parameters_roughness: None | RoughnessParameters = None#: The roughness parameters for this sag profile.

parameters_slope_error: None | SlopeErrorParameters = None#: The slope error parameters for this sag profile.

radius: Quantity | AbstractScalar = <Quantity inf mm>#: The radius of this cylinder.

property shape: dict[str, int]#: The array shape of this object.

transformation: None | AbstractTransformation = None#: The transformation between the surface coordinate system and the sag coordinate system.