AbstractConicSag#

class optika.sags.AbstractConicSag(*, transformation=None, parameters_slope_error=None, parameters_roughness=None, parameters_microroughness=None)[source]#

Bases: AbstractSag

An interface describing a general conic surface of revolution.

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__`(*[, transformation, ...])
`intercept`(rays)	Compute the intercept of the given rays with this conic surface of revolution.
`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:

transformation (None | AbstractTransformation)
parameters_slope_error (None | SlopeErrorParameters)
parameters_roughness (None | RoughnessParameters)
parameters_microroughness (None | RoughnessParameters)

intercept(rays)[source]#

Compute the intercept of the given rays with this conic surface of revolution.

The intersection is found in closed form by solving the ray-quadric intersection, which avoids the spurious root that an iterative solver can converge to on the steep flank of a grazing-incidence conic.

Parameters:: rays (AbstractRayVectorArray) – The rays to intercept with this surface.
Return type:: RayVectorArray

Notes

A conic of revolution about the \(z\) axis, with its vertex at the origin, satisfies the implicit equation

\[c (x^2 + y^2) + (1 + k) c z^2 - 2 z = 0,\]

where \(c = 1 / R\) is the vertex curvature and \(k\) is the conic constant. Substituting the parametric ray \(\mathbf{x} = \mathbf{o} + t \mathbf{u}\) gives a quadratic \(A t^2 + B t + C = 0\) in the path length \(t\), with

\[\begin{split}A &= c \left[ u_x^2 + u_y^2 + (1 + k) u_z^2 \right] \\ B &= 2 \left[ c (o_x u_x + o_y u_y + (1 + k) o_z u_z) - u_z \right] \\ C &= c \left[ o_x^2 + o_y^2 + (1 + k) o_z^2 \right] - 2 o_z.\end{split}\]

Of the (up to two) real roots, the intercept is the one on the same sheet of the conic as the vertex (identified by \(z \, (c (x^2 + y^2) - z) \geq 0\)) that is nearest the ray’s starting point. An iterative solver, by contrast, can converge to the far or wrong-sheet root on the steep flank of a grazing conic.

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

abstract property conic: float | AbstractScalar#: 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.

abstract property radius: Quantity | AbstractScalar#: The effective radius of this conic section.

abstract 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.