IMG-07

Modulation transfer function

MTF(f) = exp(−2 π² σ² f²). Gaussian-PSF contrast transfer.

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Image qualityMTF

Governing equation

\mathrm{MTF}(f)=e^{-2\pi^{2}\sigma^{2}f^{2}}

where

f: Spatial frequency (1/mm)
\sigma: PSF σ (mm)
MTF: MTF (—)

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-07 — Modulation transfer function) is the form associated with MTF. Working symbols: $f$ , $\sigma$ $\rightarrow$ $MTF$ . MTF is the modulus of the OTF, the Fourier transform of the PSF. Pixel aperture contributes a sinc.

Purpose

Purpose: compute

MTF

from

f

\sigma

in Medical imaging via

\mathrm{MTF}(f)=e^{-2\pi^{2}\sigma^{2}f^{2}}

MTF(f) = exp(−2 π² σ² f²). Gaussian-PSF contrast transfer. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f = 1.000\,\mathrm{1/mm}

\sigma = 0.350\,\mathrm{mm}

, the governing relation

\mathrm{MTF}(f)=e^{-2\pi^{2}\sigma^{2}f^{2}}

yields

MTF = 0.0891\,\mathrm{—}

. A bar pattern fading with spatial frequency. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Spatial frequency f1 1/mmPSF σ \sigma0.35 mm

Outputs

MTF MTF0.0891 —

Reading speed

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Narration of this film

A bar pattern fading with spatial frequency.

MTF is the modulus of the OTF, the Fourier transform of the PSF. Pixel aperture contributes a sinc.

Reading speed

Watch on YouTube