geometries.odd_asphere

Odd Asphere Geometry

The Odd Asphere geometry represents a surface defined by an odd asphere polynomial superimposed on a base conic surface. The surface is defined as:

z = r^2 / (R * (1 + sqrt(1 - (1 + k) * r^2 / R^2))) + sum(Ci * r^i)

where - r^2 = x^2 + y^2 - R is the radius of curvature - k is the conic constant - Ci are the aspheric coefficients

Kramer Harrison, 2025

Classes

OddAsphere(coordinate_system, radius[, ...])

Represents an odd asphere geometry defined as:

class OddAsphere(coordinate_system, radius, conic=0.0, tol=1e-10, max_iter=100, coefficients=None)[source]

Represents an odd asphere geometry defined as:

z = r^2 / (R * (1 + sqrt(1 - (1 + k) * r^2 / R^2))) + sum(Ci * r^i)

where - r^2 = x^2 + y^2 - R is the radius of curvature - k is the conic constant - Ci are the aspheric coefficients - i is an integer from 1 to n

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.

  • coefficients (list[float], optional) – A list of odd aspheric coefficients C_i, where the term is C_i * r^i. The list index corresponds to i-1 (e.g., coefficients[0] is C_1 for r^1). Defaults to an empty list (no aspheric contribution).

c

List of aspheric coefficients.

Type:

list[float]

distance(rays)

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()

Flip the geometry.

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

classmethod from_dict(data)

Creates an asphere from a dictionary representation.

Parameters:

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

Returns:

An instance of EvenAsphere.

Return type:

EvenAsphere

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.

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

Calculates the sag of the asphere at the given coordinates.

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 sag value(s) at the given coordinates.

Return type:

be.ndarray or float

scale(scale_factor: float)[source]

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)

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()

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.