IMG-20

SPECT system resolution

R = √(R_int² + R_coll²). Intrinsic plus collimator in quadrature.

Reading speed

SPECTSPECT resolution

Governing equation

R=\sqrt{R_{\mathrm{int}}^{2}+R_{\mathrm{coll}}^{2}}

$R_{coll} \in \left[3, 20\right]$

where

R_{int}: Intrinsic FWHM (mm)
R_{coll}: Collimator FWHM (mm)
R: System FWHM (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

R=\sqrt{R_{\mathrm{int}}^{2}+R_{\mathrm{coll}}^{2}}

$R_{coll} \in \left[3, 20\right]$

$R_{coll} = 3$ $R = 5$

Along the curve

②

Domain of the variable — blue

R_{coll}_{\min} = 3,\quad R_{coll}_{\max} = 20

$R_{coll} \in \left[3, 20\right]$

$R_{coll} = 3$ $R_{coll} = 3$

Along the curve

③

Response curve — green

R=\sqrt{R_{\mathrm{int}}^{2}+R_{\mathrm{coll}}^{2}}

$R_{coll} \in \left[3, 20\right]$

$R_{coll} = 3$ $R = 5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R}{\mathrm{d}R_{coll}}

$R_{coll} \in \left[3, 20\right]$

$R_{coll} = 3.107$ $R^{\prime} = 0.613$

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-20 — SPECT system resolution) is the form associated with SPECT resolution. Working symbols: $R_{int}$ , $R_{coll}$ $\rightarrow$ $R$ . Collimator resolution dominates at depth. A LEHR collimator is ~7–12 mm at 10 cm.

Purpose

Purpose: compute

R

from

R_{int}

R_{coll}

in Medical imaging via

R=\sqrt{R_{\mathrm{int}}^{2}+R_{\mathrm{coll}}^{2}}

R = √(R_int² + R_coll²). Intrinsic plus collimator in quadrature. 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

R_{int} = 4.000\,\mathrm{mm}

R_{coll} = 8.000\,\mathrm{mm}

, the governing relation

R=\sqrt{R_{\mathrm{int}}^{2}+R_{\mathrm{coll}}^{2}}

yields

R = 8.94\,\mathrm{mm}

. A camera, a collimator, a blurred point. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Intrinsic FWHM R_{int}4 mmCollimator FWHM R_{coll}8 mm

Outputs

System FWHM R8.94 mm

Reading speed

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Narration of this film

A camera, a collimator, a blurred point.

Collimator resolution dominates at depth. A LEHR collimator is ~7–12 mm at 10 cm.

Reading speed

Watch on YouTube