Surfaces in pyOpTools¶

The basic object to create optical components in pyOpTools are the surfaces. They are used to define the border that separates 2 materials (for example air-glass) in an optical component.

Below are some of the Surface Objects supported by pyOpTools.

[1]:

from pyoptools.all import *
from numpy import pi

Plane Surface¶

The Plane surface is the most simple surface class in the library. It is defined as an ideal infininite $XY$ plane, located at $Z=0$ . To define the Plane limits, its constructor receives as an argument a sub-class of Shape. This sub-classes (Circular, Rectangular, Triangular, etc ) define the limits of the Surface (plane in this case).

Some Plane examples¶

Below are some examples of Plane surfaces limited by different shapes.

[2]:

P1 = Plane(shape=Circular(radius=(25)))
Plot3D(P1, center=(0, 0, 0), size=(60, 60), rot=[(0, 0, 0)], scale=6)

[2]:

[3]:

P2 = Plane(shape=Rectangular(size=(50, 50)))
Plot3D(P2, center=(0, 0, 0), size=(60, 60), rot=[(0, 0, 0)], scale=6)

[3]:

[4]:

P3 = Plane(shape=Triangular(coord=((0, 25), (25, -25), (-25, -25))))
Plot3D(P3, center=(0, 0, 0), size=(60, 60), scale=6)

[4]:

Spherical Surface¶

The Spherical surface is another very useful Class to define optical components. It is used to define an spherical cap that has its vertex located at the origin ( $(0,0,0)$ ). The normal to the spherical cap at $X=0$ and $Y=0$ is the vector $(0,0,1)$ . As it was the case with the Plane surface, it is used with a Shape subclass to define its edges.

Spherical surface limited by a circular shape example¶

[5]:

S = Spherical(curvature=1 / 200.0, shape=Circular(radius=145.0), reflectivity=0)
Plot3D(S, center=(0, 0, 0), size=(400, 400), scale=1)

[5]:

Cylindrical Surface¶

pyOpTools has 2 different types of cylindrical surfaces. The first one is the Cylinder , as its name implies defines a closed cylinder. It is mainly used to define the border of a lens. For example a plano-convex lens can be defined as one circular-limited plane, one circular limited spherical surface, and one cylindrical surface.

Below is an example of a cylindrical surface. Please note that this surface does not receive a Shape subclass.

[6]:

S3 = Cylinder(radius=36, length=100, reflectivity=1)
Plot3D(S3, center=(0, 0, 0), size=(100, 100), rot=[(0, pi / 32, 0)], scale=4)

[6]:

The second class is the Cylindrical.

[7]:

S1 = Cylindrical(shape=Rectangular(size=(50, 100)), curvature=1 / 20.0)
Plot3D(S1, center=(0, 0, 0), size=(150, 150), rot=[(pi / 4, 0, 0)], scale=2)

/home/docs/checkouts/readthedocs.org/user_builds/pyoptools/envs/latest/lib/python3.12/site-packages/jupyter_client/session.py:721: UserWarning: Message serialization failed with:
Out of range float values are not JSON compliant: nan
Supporting this message is deprecated in jupyter-client 7, please make sure your message is JSON-compliant
  content = self.pack(content)

[7]:

[8]:

S2 = Cylindrical(shape=Circular(radius=(50)), curvature=1 / 100.0)
Plot3D(S2, center=(0, 0, 0), size=(150, 150), rot=[(-pi / 4, 0, 0)], scale=2)

[8]:

Aspherical Surface¶

[9]:

%%latex
$$Z=\frac{(Ax*x^2+Ay*y^2)}{(1+\sqrt{(1-(1+Kx)*Ax^2*x^2-(1+Ky)*Ay^2*y^2))}}+ Poly2D()$$

$Z=\frac{(Ax*x^2+Ay*y^2)}{(1+\sqrt{(1-(1+Kx)*Ax^2*x^2-(1+Ky)*Ay^2*y^2))}}+ Poly2D()$

[10]:

sa = Aspherical(
    shape=Rectangular(size=(5, 5)),
    Ax=0.2,
    Ay=0.2,
    Kx=0.1,
    Ky=0.15,
    poly=Poly2D((0, 0, 0, 0.5, 0, 0.5)),
)
Plot3D(sa, center=(0, 0, 5), size=(10, 10), rot=[(-3 * pi / 10, pi / 4, 0)], scale=40)

[10]:

[11]:

sa = Aspherical(
    shape=Circular(radius=2.5),
    Ax=0.2,
    Ay=0.2,
    Kx=0.1,
    Ky=0.15,
    poly=Poly2D((0, 0, 0, 0.5, 0, 0.5)),
)
Plot3D(sa, center=(0, 0, 5), size=(10, 10), rot=[(-3 * pi / 10, pi / 4, 0)], scale=40)

[11]:

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