IMG-08

Pixel size FOV/N

Δx = FOV / N. The reconstructed pixel.

Reading speed

GeometryPixel size

Governing equation

\Delta x=\mathrm{FOV}/N

$N \in \left[64, 1024\right]$

where

FOV: Field of view (mm)
N: Matrix size (—)
\Delta x: Pixel size (mm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta x=\mathrm{FOV}/N

$N \in \left[64, 1024\right]$

$N = 64$ $\Delta x = 3.75$

Along the curve

②

Domain of the variable — blue

N_{\min} = 64,\quad N_{\max} = 1024

$N \in \left[64, 1024\right]$

$N = 64$ $N = 64$

Along the curve

③

Response curve — green

\Delta x=\mathrm{FOV}/N

$N \in \left[64, 1024\right]$

$N = 64$ $\Delta x = 3.75$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta x}{\mathrm{d}N}

$N \in \left[64, 1024\right]$

$N = 70.04$ $\Delta x^{\prime} = -0.049$

Along the curve

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-08 — Pixel size FOV/N) is the form associated with Pixel size. Working symbols: $FOV$ , $N$ $\rightarrow$ $\Delta x$ . In MRI, Δx = 1/(N Δk) with Δk = 1/FOV. Smaller pixels cost SNR and time.

Purpose

Purpose: compute

\Delta x

from

FOV

N

in Medical imaging via

\Delta x=\mathrm{FOV}/N

Δx = FOV / N. The reconstructed pixel. 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

FOV = 240.000\,\mathrm{mm}

N = 256.000\,\mathrm{—}

, the governing relation

\Delta x=\mathrm{FOV}/N

yields

\Delta x = 0.938\,\mathrm{mm}

. A FOV box divided into N bins. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Field of view FOV240 mmMatrix size N256 —

Outputs

Pixel size \Delta x0.938 mm

Reading speed

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Narration of this film

A FOV box divided into N bins.

In MRI, Δx = 1/(N Δk) with Δk = 1/FOV. Smaller pixels cost SNR and time.

Reading speed

Watch on YouTube