Exercise set

Diagnostic Image Quality, Resolution, Contrast, and QA Exercises

Solved diagnostic image-quality exercises for CNR, pixel size, resolution, quantization, SNR, saturation, latency, registration and phantom QA.

Branch: Biomedical Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises focus on diagnostic image quality and QA evidence. They cover contrast-to-noise ratio, pixel sampling, spatial resolution, detector quantization, optical SNR, saturation headroom, latency, registration error, motion error, slice coverage and phantom drift.

The goal is to decide whether the imaging chain preserves task-relevant information. Dose and exposure safety calculations are handled in the companion medical imaging dose exercise set.

Release Evidence Notes

Image-quality evidence should identify the full acquisition and processing chain: modality, scanner, detector, phantom, reconstruction, filtering, display, software version, measurement method and acceptance criterion. A CNR, resolution or registration value is meaningful only inside that chain.

QA evidence should compare current measurements with release baseline and control limits. When a result is close to a limit, the package should include uncertainty, repeatability, phantom positioning and reviewer disposition.

Engineering Boundary Notes

These are screening exercises. They do not replace clinical reader studies, formal acceptance testing, regulatory submission evidence, medical-physics commissioning or manufacturer service procedures. They are intended to make image-quality and QA margins explicit before release.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Contrast and sampling	1, 2, 3, 4, 13, 14	CNR, pixel size, Nyquist sampling, line pairs and low-contrast detectability	Decide whether the target can be resolved and distinguished.
Detector and optical chain	5, 6, 7, 15	Quantization, SNR, saturation and display luminance	Decide whether electronics and display preserve image information.
Timing and geometry	8, 9, 10, 11	Latency, registration, motion and slice coverage	Decide whether guidance and spatial interpretation are accurate.
QA release	12, 16, 17, 18	Phantom drift, repeatability, uncertainty and all-of release	Decide whether the installed imaging chain can be released.

Exercise 1: Contrast-to-Noise Ratio

A phantom image has target mean $1320$ , background mean $1180$ and background noise standard deviation $35$ . Compute CNR.

Solution

CNR=\dfrac{|\mu_t-\mu_b|}{\sigma_b}

CNR=\dfrac{|1320-1180|}{35}=\dfrac{140}{35}=4.0

Engineering Comment

CNR is task-dependent. A value of four may be adequate for one lesion-size task and weak for another.

Plausibility Check

The contrast difference is four times the background noise, so CNR of four is exact.

Exercise 2: Pixel Size and Target Sampling

A detector field of view is $320\ \text{mm}$ with a $1024$ pixel matrix. A target is $1.2\ \text{mm}$ wide. Find pixel size and pixels across the target.

Solution

p=\dfrac{320}{1024}=0.3125\ \text{mm/pixel}

Pixels across target:

N=\dfrac{1.2}{0.3125}=3.84

Engineering Comment

Nearly four pixels across the target is a screening pass for visibility, but resolution also depends on blur, reconstruction and contrast.

Plausibility Check

One millimeter contains about three pixels at this pixel size, so a $1.2\ \text{mm}$ target near four pixels is plausible.

Exercise 3: Nyquist Sampling for Spatial Detail

A feature has spatial period $0.80\ \text{mm}$ . What maximum pixel pitch satisfies two samples per period?

Solution

Nyquist sampling requires:

p\le\dfrac{0.80}{2}=0.40\ \text{mm}

Engineering Comment

Meeting Nyquist pitch does not guarantee diagnostic resolution if focal spot, motion or reconstruction blur dominate.

Plausibility Check

Two pixels per cycle means each pixel must be at most half the feature period.

Exercise 4: Ultrasound Axial Resolution

An ultrasound pulse has spatial pulse length $0.90\ \text{mm}$ . Estimate axial resolution using half the pulse length.

Solution

R_a=\dfrac{SPL}{2}=\dfrac{0.90}{2}=0.45\ \text{mm}

Engineering Comment

Axial resolution improves with shorter pulses and bandwidth, but real performance also depends on focusing, tissue attenuation and processing.

Plausibility Check

Half of just under one millimeter is just under half a millimeter.

Exercise 5: Detector ADC Quantization Step

A detector maps $0$ to $2.5\ \text{V}$ into a 12-bit ADC. Find the voltage per count.

Solution

q=\dfrac{2.5}{2^{12}}=\dfrac{2.5}{4096}=0.000610\ \text{V}

So:

q=0.610\ \text{mV/count}

Engineering Comment

Quantization is acceptable only if it is small relative to detector noise and clinical contrast.

Plausibility Check

Twelve bits gives about four thousand levels, so a few volts span gives sub-millivolt counts.

Exercise 6: Optical Signal-to-Noise Ratio

An optical channel has signal current $48\ \text{nA}$ and RMS noise $6\ \text{nA}$ . Compute SNR and decibel SNR.

Solution

SNR=\dfrac{48}{6}=8

SNR_{dB}=20\log_{10}(8)=18.1\ \text{dB}

Engineering Comment

This is an amplitude SNR. The release package should state bandwidth, integration time and whether ambient light was present.

Plausibility Check

An eight-to-one amplitude ratio corresponds to just over eighteen decibels.

Exercise 7: Detector Saturation Headroom

A detector saturates at $3000$ counts. A bright phantom region measures $2460$ counts. Compute headroom percentage relative to saturation.

Solution

Remaining counts:

H_c=3000-2460=540

Headroom:

H=\dfrac{540}{3000}=0.18=18\%

Engineering Comment

Eighteen percent headroom may be adequate for a phantom but weak if clinical exposure or gain can vary.

Plausibility Check

The signal is a bit over four-fifths of saturation, leaving a bit under one-fifth headroom.

Exercise 8: Imaging Latency for Guidance

An image-guided system has acquisition latency $35\ \text{ms}$ , reconstruction latency $70\ \text{ms}$ , network latency $18\ \text{ms}$ and display latency $27\ \text{ms}$ . Compute total latency.

Solution

L=35+70+18+27=150\ \text{ms}

Engineering Comment

Latency is an image-quality issue when the displayed anatomy or tool position is used for guidance.

Plausibility Check

The reconstruction term dominates, and all terms sum to one hundred fifty milliseconds.

Exercise 9: Registration Error Budget

A guidance workflow has calibration error $0.7\ \text{mm}$ , tracking error $0.9\ \text{mm}$ and image segmentation error $0.6\ \text{mm}$ . Estimate RSS registration error.

Solution

e=\sqrt{0.7^2+0.9^2+0.6^2}

e=\sqrt{0.49+0.81+0.36}=\sqrt{1.66}=1.29\ \text{mm}

Engineering Comment

RSS is appropriate only when errors are reasonably independent. Systematic bias should be added directly or corrected.

Plausibility Check

The combined error is larger than any one term but less than their arithmetic sum.

Exercise 10: Motion Error from Latency

A target moves at $18\ \text{mm/s}$ . Imaging latency is $150\ \text{ms}$ . Estimate motion error.

Solution

e=vt=18(0.150)=2.7\ \text{mm}

Engineering Comment

Motion error can dominate geometric QA. The solution may require gating, tracking, faster reconstruction or warning limits.

Plausibility Check

At about twenty millimeters per second, a small fraction of a second gives a few millimeters error.

Exercise 11: Slice Coverage and Voxel Count

A volume scan covers $120\ \text{mm}$ with slice thickness $1.25\ \text{mm}$ . Each slice has a $512\times512$ matrix. Find slice count and total voxel count.

Solution

Slice count:

N_s=\dfrac{120}{1.25}=96

Voxels:

N_v=96(512)(512)=25165824

Engineering Comment

Voxel count affects storage, transfer, reconstruction and review workflow. It is not only an image-detail number.

Plausibility Check

About one hundred slices times about a quarter million pixels per slice gives about twenty-five million voxels.

Exercise 12: Phantom QA CNR Drift

Baseline phantom CNR is $5.2$ . Current CNR is $4.7$ . The action threshold is a drop greater than $8\%$ . Check status.

Solution

Drop fraction:

d=\dfrac{5.2-4.7}{5.2}=0.096=9.6\%

Since:

9.6\%>8\%

the action threshold is exceeded.

Engineering Comment

The QA result should trigger review of calibration, reconstruction version, detector state and phantom placement.

Plausibility Check

A half-point drop from a baseline just above five is close to ten percent.

Exercise 13: Line-Pair Resolution Screen

A phantom pattern has $2.5\ \text{line pairs/mm}$ . What line-pair period must the system distinguish?

Solution

The period per line pair is:

T=\dfrac{1}{2.5}=0.40\ \text{mm}

Engineering Comment

Resolving the pattern requires the whole imaging chain to preserve contrast at this spatial frequency, not just pixel pitch.

Plausibility Check

More line pairs per millimeter means smaller periods; $2.5$ gives less than half a millimeter.

Exercise 14: Low-Contrast Detectability Margin

A low-contrast target requires CNR at least $3.5$ . The measured CNR is $3.9$ , and uncertainty guard is $0.3$ . Decide status.

Solution

Guarded CNR:

CNR_g=3.9-0.3=3.6

Since:

3.6>3.5

the target passes with margin $0.1$ .

Engineering Comment

The pass is narrow. Reader variability or phantom placement could consume the remaining margin.

Plausibility Check

The nominal value is only $0.4$ above the limit, and the guard removes most of that margin.

Exercise 15: Display Luminance Ratio

A display QA test measures white luminance $420\ \text{cd/m}^2$ and black luminance $0.9\ \text{cd/m}^2$ . Compute luminance ratio.

Solution

LR=\dfrac{420}{0.9}=466.7

Engineering Comment

Display performance is part of the diagnostic chain. Poor luminance or ambient conditions can erase image-quality gains upstream.

Plausibility Check

A black level below one and white level above four hundred gives a ratio of several hundred.

Exercise 16: QA Repeatability

Three repeated phantom measurements of slice thickness are $1.02$ , $1.00$ and $1.04\ \text{mm}$ . The nominal is $1.00\ \text{mm}$ and allowed deviation is $0.08\ \text{mm}$ . Check maximum deviation.

Solution

Largest deviation from nominal is:

\Delta_{max}=|1.04-1.00|=0.04\ \text{mm}

Since:

0.04<0.08

the repeatability screen passes.

Engineering Comment

The screen passes, but the measurement method should be consistent before trending small drifts.

Plausibility Check

All readings are within four hundredths of a millimeter of nominal.

Exercise 17: Image-Quality Uncertainty Guard

A measured resolution limit is $0.62\ \text{mm}$ , where lower is better. The acceptance limit is $0.70\ \text{mm}$ and uncertainty is $0.05\ \text{mm}$ . Use a conservative guard.

Solution

Guarded value:

R_g=0.62+0.05=0.67\ \text{mm}

Since:

0.67<0.70

the result passes.

Engineering Comment

For metrics where lower is better, uncertainty is added before comparing with the maximum allowed value.

Plausibility Check

The nominal margin is $0.08\ \text{mm}$ and the guard is $0.05\ \text{mm}$ , so a small pass remains.

Exercise 18: Diagnostic Image-Quality Release Gate

A release gate requires CNR pass, resolution pass, registration pass, latency pass and phantom drift pass. Results are pass, pass, pass, fail and pass. Decide status.

Solution

The gate is all-of:

G=R_{CNR}\land R_{res}\land R_{reg}\land R_{lat}\land R_{QA}

The latency result fails, so release is blocked.

Engineering Comment

A system can have good static image quality and still be unsafe for guidance if latency creates spatial error.

Plausibility Check

One failed required condition blocks an all-of release gate.

Common Release Mistakes

Quoting CNR, resolution or SNR without acquisition and reconstruction context.
Treating pixel size as the same thing as spatial resolution.
Ignoring display, latency or registration when images guide action.
Averaging QA drift across metrics instead of acting on the failed control.
Applying uncertainty in the wrong direction for pass/fail metrics.
Comparing phantom results from different software versions or reconstruction kernels.

Validation Package Checklist

Modality, scanner, software, acquisition protocol and reconstruction settings.
Phantom method, placement, baseline and control limits.
CNR, resolution, pixel sampling, quantization and SNR evidence.
Registration, latency, motion and slice-coverage calculations where applicable.
Display QA and viewing-condition evidence when diagnostic interpretation depends on display.
Uncertainty guard, repeatability records and reviewer disposition.
Release gate with every required metric explicitly passed or blocked.

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