IMG-26

Modulation-transfer frequency

f50 = √(ln2 / (2 π² σ²)). Spatial frequency where Gaussian MTF = 0.5.

Reading speed

Image qualityMTF50

Governing equation

f_{50}=\sqrt{\ln 2/(2\pi^{2}\sigma^{2})}

where

\sigma: PSF σ (mm)
f_{50}: MTF50 frequency (1/mm)

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-26 — Modulation-transfer frequency) is the form associated with MTF50. Working symbols: $\sigma$ $\rightarrow$ $f_{50}$ . MTF50 (or MTF10) is a handy spatial-resolution figure. Limiting resolution is often MTF10.

Purpose

Purpose: compute

f_{50}

from

\sigma

in Medical imaging via

f_{50}=\sqrt{\ln 2/(2\pi^{2}\sigma^{2})}

f50 = √(ln2 / (2 π² σ²)). Spatial frequency where Gaussian MTF = 0.5. 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

\sigma = 0.350\,\mathrm{mm}

, the governing relation

f_{50}=\sqrt{\ln 2/(2\pi^{2}\sigma^{2})}

yields

f_{50} = 0.535\,\mathrm{1/mm}

. An MTF curve crossing one half. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

PSF σ \sigma0.35 mm

Outputs

MTF50 frequency f_{50}0.535 1/mm

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

An MTF curve crossing one half.

MTF50 (or MTF10) is a handy spatial-resolution figure. Limiting resolution is often MTF10.

Reading speed

Watch on YouTube