Ray Tracing

Tilting & De-centering Components

Complex ray tracing through misaligned or deliberately folded optics.

BeginnerRay TracingNumPy backend8 min read

Introduction

This tutorial shows how to tilt and de-center surfaces in a lens. We will use a spot diagram to show how ray intersection on the image plane are impacted by tilt/decentering.

Core concepts used

rx=np.radians(theta)

Rotates the surface (or group) around the X-axis. Rotations are always in radians.

dy=value

Translates (de-centers) the surface vertex along the Y-axis relative to the optical axis.

analysis.SpotDiagram(lens)

Calculates the geometric distribution of rays on the image plane.

Step-by-step build

Set up and examine the baseline aligned lens

Import the required libraries, build a simple singlet with all surfaces perfectly aligned, draw the layout, and view the baseline spot diagram.

python

import numpy as np

from optiland import analysis, optic

lens = optic.Optic()

# add surfaces
lens.add_surface(index=0, radius=np.inf, thickness=np.inf)
lens.add_surface(index=1, thickness=7, radius=19.93, is_stop=True, material="N-SF11")
lens.add_surface(index=2, thickness=21.48)
lens.add_surface(index=3)

# add aperture
lens.set_aperture(aperture_type="EPD", value=25.4)

# add field
lens.set_field_type(field_type="angle")
lens.add_field(y=0)

# add wavelength
lens.add_wavelength(value=0.587, is_primary=True)

lens.draw(num_rays=10)

spot = analysis.SpotDiagram(lens)
spot.view()

Tilt the first surface by 5° and observe spot degradation

Now, let's tilt the first surface by 5 degrees and redraw the lens.

python

lens = optic.Optic()

# add surfaces
lens.add_surface(index=0, radius=np.inf, thickness=np.inf)

# == WE ADD THE TILT TO THIS SURFACE ===============
lens.add_surface(
 index=1,
 thickness=7,
 radius=19.93,
 is_stop=True,
 material="N-SF11",
 rx=np.radians(5.0),
)
# ==================================================

lens.add_surface(index=2, thickness=21.48)
lens.add_surface(index=3)

# add aperture
lens.set_aperture(aperture_type="EPD", value=25.4)

# add field
lens.set_field_type(field_type="angle")
lens.add_field(y=0)

# add wavelength
lens.add_wavelength(value=0.587, is_primary=True)

lens.draw(num_rays=10)

spot = analysis.SpotDiagram(lens)
spot.view()

Decenter the first surface by 1 mm and compare

Let's decenter the first surface of the lens.

python

lens = optic.Optic()

# add surfaces
lens.add_surface(index=0, radius=np.inf, thickness=np.inf)

# == WE DECENTER THIS SURFACE =====================
lens.add_surface(
 index=1,
 thickness=7,
 radius=19.93,
 is_stop=True,
 material="N-SF11",
 dy=1.0,  # 1 mm decenter
)
# ==================================================

lens.add_surface(index=2, thickness=21.48)

lens.add_surface(index=3)

# add aperture
lens.set_aperture(aperture_type="EPD", value=25.4)

# add field
lens.set_field_type(field_type="angle")
lens.add_field(y=0)

# add wavelength
lens.add_wavelength(value=0.587, is_primary=True)

lens.draw(num_rays=10)

spot = analysis.SpotDiagram(lens)
spot.view()

Show full code listing

python

import numpy as np

from optiland import analysis, optic

lens = optic.Optic()

# add surfaces
lens.add_surface(index=0, radius=np.inf, thickness=np.inf)
lens.add_surface(index=1, thickness=7, radius=19.93, is_stop=True, material="N-SF11")
lens.add_surface(index=2, thickness=21.48)
lens.add_surface(index=3)

# add aperture
lens.set_aperture(aperture_type="EPD", value=25.4)

# add field
lens.set_field_type(field_type="angle")
lens.add_field(y=0)

# add wavelength
lens.add_wavelength(value=0.587, is_primary=True)

lens.draw(num_rays=10)

spot = analysis.SpotDiagram(lens)
spot.view()

lens = optic.Optic()

# add surfaces
lens.add_surface(index=0, radius=np.inf, thickness=np.inf)

# == WE ADD THE TILT TO THIS SURFACE ===============
lens.add_surface(
  index=1,
  thickness=7,
  radius=19.93,
  is_stop=True,
  material="N-SF11",
  rx=np.radians(5.0),
)
# ==================================================

lens.add_surface(index=2, thickness=21.48)
lens.add_surface(index=3)

# add aperture
lens.set_aperture(aperture_type="EPD", value=25.4)

# add field
lens.set_field_type(field_type="angle")
lens.add_field(y=0)

# add wavelength
lens.add_wavelength(value=0.587, is_primary=True)

lens.draw(num_rays=10)

spot = analysis.SpotDiagram(lens)
spot.view()

lens = optic.Optic()

# add surfaces
lens.add_surface(index=0, radius=np.inf, thickness=np.inf)

# == WE DECENTER THIS SURFACE =====================
lens.add_surface(
  index=1,
  thickness=7,
  radius=19.93,
  is_stop=True,
  material="N-SF11",
  dy=1.0,  # 1 mm decenter
)
# ==================================================

lens.add_surface(index=2, thickness=21.48)

lens.add_surface(index=3)

# add aperture
lens.set_aperture(aperture_type="EPD", value=25.4)

# add field
lens.set_field_type(field_type="angle")
lens.add_field(y=0)

# add wavelength
lens.add_wavelength(value=0.587, is_primary=True)

lens.draw(num_rays=10)

spot = analysis.SpotDiagram(lens)
spot.view()

Conclusions

Tilting and de-centering surfaces is a powerful way to model both manufacturing errors and intentional folded-optic designs. In this tutorial you:

Built a baseline singlet with all surfaces perfectly aligned and established a reference spot diagram.
Applied a 5° rotation (rx=np.radians(5.0)) to a single surface and observed how the degradation of the on-axis spot.
Applied a 1 mm decenter (dy=1.0) to the same surface and compared the resulting off-axis asymmetry with the tilt case.
Used SpotDiagram consistently to quantify image-quality changes after each perturbation.

These same techniques apply to tolerance analysis, fold-mirror systems, and any design where component misalignment must be simulated explicitly.

Next tutorials

NextMonte Carlo Ray TracingStochastic methods for stray light and complex geometry analysis.RelatedTracing and Analyzing RaysExplore the fundamental real ray tracing engine used here.

Original notebook: Tutorial_2b_Tilting_%26_Decentering_Components.ipynb on GitHub · ReadTheDocs