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Analysis

OPD Calculations

Understand the phase of the light as it propagates through your lens.

IntermediateAberrationsNumPy backend8 min read

Introduction

This tutorial demonstrates how to compute the optical path difference in the exit pupil and the various ways to plot it.

Core concepts used

wavefront.OPDFan(lens)
Plots the OPD across the pupil for various fields and wavelengths. Like ray fans, but for phase.
wavefront.OPD(lens, field)
Creates a high-resolution grid of wavefront data for a specific field point.
opd.view(projection='3d')
Renders the wavefront error as a topological surface, clearly showing coma and astigmatism "ridges".
opd.rms()
Returns the Root Mean Square of the wavefront error, often used to determine if a system is "diffraction-limited".

Step-by-step build

1

Import libraries and load the Erfle eyepiece

Import the wavefront module and instantiate the built-in Erfle eyepiece, then draw the system layout for reference.

python
from optiland import wavefront
from optiland.samples.eyepieces import EyepieceErfle

lens = EyepieceErfle()
lens.draw()
Erfle eyepiece optical layout
2

Compute and view the OPD fan across all fields

Compute the OPD fans for each field point and wavelength. The OPD fan shows the wavefront error across the pupil — analogous to a ray fan, but for phase.

python
opd_fan = wavefront.OPDFan(lens)
opd_fan.view()
OPD fan across all fields
3

View the on-axis wavefront error map in 2D

Compute a high-resolution wavefront map for the on-axis field and render it as a 2D color map to inspect the aberration structure.

python
opd = wavefront.OPD(lens, field=(0, 0), wavelength=0.5876)
opd.view(projection="2d", num_points=512)
On-axis OPD map (2D)
4

View the 70% field wavefront error map in 2D

Repeat the same 2D wavefront map at 70% field height to see how off-axis aberrations begin to dominate.

python
opd = wavefront.OPD(lens, field=(0, 0.7), wavelength=0.5876)
opd.view(projection="2d", num_points=512)
0.7 field OPD map (2D)
5

Render the full-field wavefront error as a 3D surface

Switch to the "3d" projection at full field to visualize the wavefront topography — coma ridges and astigmatism saddles become immediately apparent.

python
opd = wavefront.OPD(lens, field=(0, 1.0), wavelength=0.5876)
opd.view(projection="3d", num_points=512)
Full-field OPD map (3D surface)
Show full code listing
python
from optiland import wavefront
from optiland.samples.eyepieces import EyepieceErfle

lens = EyepieceErfle()
lens.draw()

opd_fan = wavefront.OPDFan(lens)
opd_fan.view()

opd = wavefront.OPD(lens, field=(0, 0), wavelength=0.5876)
opd.view(projection="2d", num_points=512)

opd = wavefront.OPD(lens, field=(0, 0.7), wavelength=0.5876)
opd.view(projection="2d", num_points=512)

opd = wavefront.OPD(lens, field=(0, 1.0), wavelength=0.5876)
opd.view(projection="3d", num_points=512)

Conclusions

This tutorial covered the two main OPD tools in Optiland:

  • OPDFan gives a compact, multi-field view of the wavefront error across the pupil — useful for quickly spotting which aberrations dominate at each field point.
  • OPD computes a full high-resolution wavefront map for a single field and wavelength, with a choice of 2D color map or 3D surface projections.
  • Comparing on-axis (pure spherical) with 70% and full-field maps clearly reveals how coma and astigmatism grow with field angle.
  • The rms() method can convert any OPD map to a single merit-function number for use in optimization or tolerance budgets.

Next tutorials

NextPSF and MTF CalculationConvert wavefront data into Point Spread Functions and MTF curves.RelatedChromatic AberrationsSee how color shifts impact the phase of the wavefront.

Original notebook: Tutorial_4a_Optical_Path_Difference_Calculation.ipynb on GitHub · ReadTheDocs