geometries.newton_raphson

Newton Raphson Geometry

The Newton Raphson geometry represents a surface utilizing the Newton-Raphson method for ray tracing. This is an abstract base class that should be inherited by any geometry that uses the Newton-Raphson method for ray tracing.

Kramer Harrison, 2024

Classes

NewtonRaphsonGeometry(coordinate_system, radius)

Represents a geometry that uses the Newton-Raphson method for ray tracing.

class NewtonRaphsonGeometry(coordinate_system, radius, conic=0.0, tol=1e-10, max_iter=100)[source]

Represents a geometry that uses the Newton-Raphson method for ray tracing.

Parameters:
  • coordinate_system (CoordinateSystem) – The coordinate system of the geometry.

  • radius (float) – The radius of curvature of the base sphere.

  • conic (float, optional) – The conic constant of the base sphere. Defaults to 0.0.

  • tol (float, optional) – Tolerance for Newton-Raphson iteration. Defaults to 1e-10.

  • max_iter (int, optional) – Maximum iterations for Newton-Raphson. Defaults to 100.

distance(rays)[source]

Calculates the distance from the ray origin to the surface intersection using a robust Newton-Raphson method. This version uses the base conic intersection as a strong initial guess.

Parameters:

rays (RealRays) – The rays used for calculating distance.

Returns:

An array of propagation distances ‘t’ from each ray’s current position to its intersection point with the geometry.

Return type:

be.ndarray

flip()[source]

Flip the geometry.

Changes the sign of the radius of curvature. The conic constant remains unchanged.

classmethod from_dict(data)[source]

Creates a geometry from a dictionary representation.

Parameters:

data (dict) – The dictionary representation of the geometry.

Returns:

An instance of a subclass of NewtonRaphsonGeometry, created from the dictionary data.

Return type:

NewtonRaphsonGeometry

globalize(rays)

Convert rays from the local coordinate system to the global coordinate system.

Parameters:

rays (RealRays) – The rays to convert.

localize(rays)

Convert rays from the global coordinate system to the local coordinate system.

Parameters:

rays (RealRays) – The rays to convert.

abstract sag(x=0, y=0)[source]

Calculate the surface sag of the geometry.

Parameters:
  • x (float or be.ndarray, optional) – The x-coordinate(s). Defaults to 0.

  • y (float or be.ndarray, optional) – The y-coordinate(s). Defaults to 0.

Returns:

The surface sag of the geometry at the given coordinates.

Return type:

float or be.ndarray

scale(scale_factor: float)

Scale the geometry parameters.

Parameters:

scale_factor (float) – The factor by which to scale the geometry.

set_radius(value: float) None

Set the radius of curvature.

Parameters:

value (float) – The new radius of curvature.

surface_normal(rays)[source]

Calculates the surface normal of the geometry at the given rays.

Parameters:

rays (RealRays) – The rays, positioned at the surface, for which to calculate the surface normal.

Returns:

The surface normal components (nx, ny, nz).

Return type:

tuple[be.ndarray, be.ndarray, be.ndarray]

to_dict()[source]

Converts the geometry to a dictionary.

Returns:

The dictionary representation of the geometry.

Return type:

dict

update_normalization(semi_aperture: float) None

Update the normalization attributes of the geometry based on its defined normalization_mode (‘auto’ or ‘manual’). Base geometry generally does not maintain a normalization radius.

Parameters:

semi_aperture (float) – The current semi-aperture of the surface.