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Analysis

PSF and MTF Calculation

Convert wavefront data into Point Spread Functions and MTF curves.

AdvancedAberrationsNumPy backend12 min read

Introduction

This tutorial shows how to calculate the point spread function (PSF) and modulation transfer function (MTF) of a lens.

Core concepts used

psf.FFTPSF(lens)
Uses the Fast Fourier Transform of the pupil function to compute the complex field at the image plane. Fastest method for PSF.
psf.HuygensPSF(lens)
Calculates the PSF by direct integration of spherical wavelets. Slower but more robust for extreme aberrations.
mtf.FFTMTF(lens)
Computes the MTF by taking the autocorrelation of the pupil function. Shows the contrast for every spatial frequency.
psf_result.strehl_ratio()
The ratio of the peak intensity of the actual PSF to the peak intensity of a perfect unaberrated Airy disk.

Step-by-step build

1

Import PSF and MTF modules

python
from optiland import mtf, psf
from optiland.samples.objectives import CookeTriplet
2

Instantiate and draw the Cooke Triplet

python
lens = CookeTriplet()
lens.draw()
Step
3

Compute and view the on-axis FFT PSF in 3D

We first compute the PSF using the FFT-based approach. We demonstrate various ways to generate and plot the PSF.

python
lens_psf = psf.FFTPSF(lens, field=(0, 0), wavelength=0.55)
lens_psf.view(projection="3d", num_points=256)
Step
4

Calculate the Strehl ratio

python
print(f"Strehl Ratio: {lens_psf.strehl_ratio():.3f}")
5

View the FFT PSF at 0.7 field height

python
lens_psf = psf.FFTPSF(lens, field=(0, 0.7), wavelength=0.55)
lens_psf.view(num_points=512)
Step
6

View the FFT PSF at full field in 2D

python
lens_psf = psf.FFTPSF(lens, field=(0, 1.0), wavelength=0.55)
lens_psf.view(projection="2d", num_points=256)
Step
7

Compute the Huygens PSF at full field

We can also generate the PSF using direct Huygens-Fresnel integration. This is referred to as the "Huygens PSF".

python
lens_huygens_psf = psf.HuygensPSF(lens, field=(0, 1.0), wavelength=0.55)
lens_huygens_psf.view(projection="2d", num_points=256)
Step
8

Plot the geometric MTF

Now, we generate the geometric MTF, which uses only ray intersection locations on the image plane and ignores diffraction. The geometric MTF is a reasonable approximation when the lens is far from the diffraction limit.

As is standard, the geometric MTF is scaled based on the diffraction-limited MTF curve. This assures that the geometric MTF cannot show performance better than the diffraction limit.

python
geo_mtf = mtf.GeometricMTF(lens)
geo_mtf.view()
Step
9

Plot the diffraction-based FFT MTF

Finally, we show the standard FFT-based MTF.

python
lens_mtf = mtf.FFTMTF(lens)
lens_mtf.view()
Step
Show full code listing
python
from optiland import mtf, psf
from optiland.samples.objectives import CookeTriplet

lens = CookeTriplet()
lens.draw()

lens_psf = psf.FFTPSF(lens, field=(0, 0), wavelength=0.55)
lens_psf.view(projection="3d", num_points=256)

print(f"Strehl Ratio: {lens_psf.strehl_ratio():.3f}")

lens_psf = psf.FFTPSF(lens, field=(0, 0.7), wavelength=0.55)
lens_psf.view(num_points=512)

lens_psf = psf.FFTPSF(lens, field=(0, 1.0), wavelength=0.55)
lens_psf.view(projection="2d", num_points=256)

lens_huygens_psf = psf.HuygensPSF(lens, field=(0, 1.0), wavelength=0.55)
lens_huygens_psf.view(projection="2d", num_points=256)

geo_mtf = mtf.GeometricMTF(lens)
geo_mtf.view()

lens_mtf = mtf.FFTMTF(lens)
lens_mtf.view()

Conclusions

  • The FFT PSF (psf.FFTPSF) efficiently converts the pupil function into an irradiance distribution at the image plane and supports both 2D and 3D projection modes for visual inspection at any field position.
  • The Strehl ratio — retrieved via strehl_ratio() — provides a single, normalized metric that captures overall wavefront quality relative to a perfect diffraction-limited system.
  • The Huygens PSF (psf.HuygensPSF) offers an alternative integration-based calculation that can be more robust for highly aberrated systems where the FFT approximation breaks down.
  • The geometric MTF (mtf.GeometricMTF) gives a fast, ray-based estimate of spatial-frequency contrast that is automatically capped by the diffraction-limited envelope, making it useful as a rapid design-stage check.
  • The diffraction-based FFT MTF (mtf.FFTMTF) yields the most physically accurate modulation transfer function by propagating the full complex pupil, enabling rigorous performance evaluation across all field positions.

Next tutorials

NextZernike DecompositionDecompose complex wavefronts into orthogonal polynomial modes.RelatedOPD CalculationsThe underlying phase data used to generate these diffraction-based results.

Original notebook: Tutorial_4b_PSF_%26_MTF_Calculation.ipynb on GitHub · ReadTheDocs