ConicSag#

class optika.sags.ConicSag(radius=<Quantity inf mm>, conic=<Quantity 0.>, *, transformation=None, parameters_slope_error=None, parameters_roughness=None, parameters_microroughness=None)[source]#

Bases: AbstractConicSag

Surface of revolution of a conic section

The sag (\(z\) coordinate) of a conic sag function is calculated using the expression

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

where \(c\) is the curvature, \(x,y\), are the 2D components of the evaluation point. and \(k\) is the conic constant. See the table below for the meaning of the conic constant.

conic constant	conic section type
\(k < -1\)	hyperbola
\(k = -1\)	parabola
\(-1 < k < 0\)	ellipse
\(k = 0\)	sphere
\(k > 0\)	oblate ellipsoid

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.ConicSag(
    radius=100 * u.mm,
    conic=na.ScalarArray(
        ndarray=[-1.5, -1, -0.5, 0, 0.5] * u.dimensionless_unscaled,
        axes="conic",
    )
)

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.conic)
    plt.legend(title="conic constant")

Attributes

`conic`	The conic constant of this conic section.
`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 effective radius of this conic section.
`shape`	The array shape of this object.
`transformation`	The transformation between the surface coordinate system and the sag coordinate system.

Methods

`__init__`([radius, conic, 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)
conic (float | AbstractScalar)
transformation (None | AbstractTransformation)
parameters_slope_error (None | SlopeErrorParameters)
parameters_roughness (None | RoughnessParameters)
parameters_microroughness (None | RoughnessParameters)

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.

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

normal(position)#

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

conic: float | AbstractScalar = <Quantity 0.>#: The conic constant of this conic section.

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 effective radius of this conic section.

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.