What is the MTF cutoff frequency?

The diffraction cutoff frequency is 1 / (λ × f#), where λ is the wavelength in mm and f# is the f-number. Beyond this frequency, the diffraction-limited system produces zero contrast. For example, at 550 nm and f/4, the cutoff is about 455 lp/mm.

What does a normalized frequency of 1 mean?

Normalized frequency 1 corresponds to the diffraction cutoff. Most real sensors sample well below this limit. The chart uses normalized units so the shape is independent of specific wavelength or aperture choices.

How does defocus affect the MTF?

Defocus introduces a sinc-like envelope that causes the MTF to drop faster than the diffraction limit and can even go negative (phase reversal) at certain frequencies. The Rayleigh quarter-wave criterion corresponds to roughly 80% peak MTF.

What Gaussian blur radius should I enter?

Enter the 1-sigma (standard deviation) blur radius in the same units as your pixel size or image plane dimension. A Gaussian envelope MTF = exp(−2π²σ²f²), so a 1-micron sigma significantly attenuates frequencies above ~160 lp/mm.

Can I combine all three effects?

Yes. The system MTF is the product of the diffraction MTF, the defocus OTF, and the Gaussian MTF. The tool multiplies them together and displays the combined curve in red on the plot.

Modulation Transfer Function Helper

Name: Modulation Transfer Function Helper
Availability: InStock
Author: Nham Vu

Compute and plot the MTF of an optical system from diffraction limit, defocus, or Gaussian blur parameters.

System Parameters

Wavelength (nm)

Visible range: 400–700 nm. Default 550 nm (green).

Lens f-number

e.g. f/4 → enter 4. Larger f# = lower cutoff.

Defocus W₀₂₀ (waves)

Peak wavefront error in waves. 0.25 = Rayleigh limit.

Gaussian blur σ (normalized)

As fraction of cutoff period. 0 = no blur.

MTF vs. Spatial Frequency

Contrast (%)

Diffraction limit Defocus Gaussian blur System (combined)

MTF Table

Norm. Freq.	Diffraction (%)	Defocus (%)	Gauss (%)	System (%)
Press "Compute MTF" to populate

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Summary

Compute and plot the MTF of an optical system from diffraction limit, defocus, or Gaussian blur parameters.

How it works

Enter the lens f-number, light wavelength, optional defocus (mm), and optional Gaussian blur radius (pixels or microns).
The tool computes the diffraction cutoff frequency from f-number and wavelength.
The diffraction-limited MTF curve is derived from the classical optical transfer function integral.
If defocus is non-zero, a focus-error OTF is multiplied in; if blur is non-zero, a Gaussian envelope is applied.
The combined MTF is plotted as contrast (0–100%) versus normalized spatial frequency (0–1 × cutoff).
Read the MTF value at any frequency of interest directly from the chart or the data table.

Use cases

Evaluate the resolving power of a camera lens at a given aperture and wavelength.
Estimate image blur caused by defocus or motion and how it reduces contrast.
Compare diffraction-limited performance to real-world measured MTF data.
Select aperture settings that balance diffraction with depth-of-field.
Assess sensor resolution relative to the optical cutoff frequency.
Verify optical design simulations against analytical MTF approximations.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu