Spatial resolution

Spatial resolution describes how well an imaging system can distinguish small structures that are close together.

It determines the level of fine detail visible in an image.

Spatial resolution is limited by both system design (e.g. pixel size, focal spot geometry) and patient- or motion-related factors.

Definition

Spatial resolution is the minimum distance by which two separate objects can be distinguished as distinct.

It is usually expressed in line pairs per millimetre (lp/mm), with one line pair consisting of a dark and a light line.

Higher spatial resolution = finer detail.

Ways to Measure Resolution

Method	Description	Example use
Line-pair test pattern	Alternating black and white bars; the highest frequency distinguishable defines limiting resolution.	3–5 lp/mm (typical DR)
Edge spread or slit response function	Measures blurring of a sharp edge; used to calculate the Line Spread Function (LSF) and the Modulation Transfer Function (MTF).	Quantitative system assessment
Point spread function (PSF)	Response of system to a single point source; smallest theoretical spot imaged.	Used in theoretical modelling

What does “line pairs per millimetre” actually mean?

• A line pair consists of one dark line and one adjacent light line — essentially one cycle of alternating contrast.
• Line pairs per millimetre (lp/mm) expresses how many of these line pairs fit into one millimetre on the image.
• It is a direct measure of spatial frequency — higher lp/mm values correspond to finer details.

Measuring lp/mm experimentally

The most straightforward way to measure spatial resolution is by using a line-pair test pattern (resolution phantom).

Typical phantoms include a Bar pattern or line-pair phantom: alternating lead and radiolucent bars with precisely known spacing.

How it’s used

1. The test object is placed at the image receptor (usually in contact).
2. An exposure is made with standard technique.
3. The resulting image shows sets of black and white line pairs of varying spatial frequency (e.g., 0.5, 1, 2, 3, 4, 5 lp/mm).
4. The highest frequency pattern where lines can still be distinguished as separate is recorded as the limiting resolution.

How does this differ to the edge spread function (ESF)?

The edge spread function (ESF) is is a technique used in imaging systems to measure an image’s quality and spatial resolution. The ESF describes how image intensity (signal) changes across a sharp edge. It is essentially a plot of pixel value versus distance across that edge. It works by analysing the sharpness of an edge in an image. From this the line spread function (LSF) can be calculated. The LSF represents the rate of change of signal across that edge which is essentially, how sharply the edge transitions. The modulation transfer function (MTF) describes how well contrast is preserved at each spatial frequency. It is obtained by taking the Fourier transform of the LSF.

Therefore, the derivative of the ESF gives the LSF, and the Fourier transform of the LSF yields the MTF.

Let look at the very basic of MTF.

Modulation Transfer Function (MTF)

MTF describes how well the system preserves contrast at different spatial frequencies.

MTF(f) = Output contrast at frequency (f) / Input contrast at frequency (f)

• MTF = 1 → perfect reproduction (no blurring).
• MTF = 0 → no ability to reproduce detail at that frequency.
• The cut-off frequency (where MTF ≈ 0) defines the limiting spatial resolution.

A higher MTF curve indicates a sharper imaging system.

This is a very basic explanation of ESF, LSF and MTF. I’ll leave a more detailed explanation at the end of this section, for those who want more detail (which I don’t think is needed for exams)* – see end of section.

Factors Affecting Spatial Resolution

A. Detector Pixel Size (Sampling Interval)

• Each pixel represents one sample of the X-ray signal.
• Smaller pixels = higher sampling frequency = higher potential spatial resolution.
• Nyquist frequency = ½ × sampling frequency → defines the maximum resolvable detail.
• In DR, pixel size typically 100–200 µm → limiting resolution ≈ 2.5–5 lp/mm.
• In mammography, pixel size ~50–100 µm → 5–10 lp/mm.

B. Focal Spot Size and Geometric Unsharpness

Because the X-ray focal spot has finite size, each point in the object projects as a small blur rather than a perfect point.

U_g = F × OID/SOD

where:
U_g​ = geometric unsharpness,
F = focal spot size,
OID = object-to-image distance,
SOD = source-to-object distance.

To reduce unsharpness:

• Use a smaller focal spot.
• Reduce OID (bring patient closer to detector).
• Increase SOD (move tube further from patient).

C. Motion Unsharpness

• Movement of the patient, table, or tube during exposure blurs the image.
• More pronounced with long exposure times or large focal spot sizes.
• Minimise with:
  • Short exposure times (higher mA).
  • Immobilisation aids.
  • Suspended respiration for chest radiographs.
  • Coaching patient.

D. Detector System Unsharpness

• In indirect DR (CsI, Gd₂O₂S), light spread within the scintillator causes slight blurring.
• Direct DR (a-Se) eliminates light spread → better resolution.
• In CR, laser beam diameter and phosphor thickness limit sharpness.

E. Sampling Frequency and Nyquist Limit

• For digital detectors, spatial resolution cannot exceed half the sampling frequency (Nyquist limit).
• Undersampling produces aliasing artefacts, where fine patterns appear as false coarse structures.
• Anti-aliasing filters or matched sampling intervals aim to prevent this.

Trade-offs and Interactions

• Increasing spatial resolution generally reduces SNR, because smaller pixels collect fewer photons.
• Increasing mAs to restore SNR increases dose.
• Image quality optimisation therefore balances resolution, noise, and dose.

Key Takeaways and Exam Tips:

• Spatial resolution = ability to depict fine detail (measured in lp/mm).
• Limited by pixel size, focal spot geometry, motion, and detector design.
• Geometric unsharpness can be reduced by small focal spot, small OID, large SOD.
• Higher resolution = lower SNR → balance required.
• Common exam question: “Describe the factors affecting spatial resolution in digital radiography.”

Up Next

Next, we’ll move on to Contrast Resolution, explaining how systems differentiate small differences in tissue attenuation, including the roles of bit depth, kVp, detector performance, and noise.

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* For those wanting more detail on ESF, LSF and MTF. See the below. Please don’t get caught up in the detail here. It requires knowledge of calculus and Fourier transformation. For those mathematically inclined. I hope this section helps further your understanding of MTF.

Edge Spread Function (ESF), Line Spread Function (LSF), and Modulation Transfer Function (MTF)

The concept

Every imaging system blurs a sharp boundary to some extent. Instead of recording a perfectly sharp step (black → white), the system records a gradual transition. Analysing the shape of that transition tells us how the system transfers detail, i.e. its spatial resolution performance.

Edge Spread Function (ESF)

Definition

The ESF describes how image intensity (signal) changes across a sharp edge.
It is essentially a plot of pixel value versus distance across that edge.

ESF(x) = Recorded signal intensity as a function of position across a sharp edge.

How it’s measured

1. Image a high-contrast, straight edge (e.g. a lead or tungsten plate) placed at a slight angle (~2–5°) to the pixel grid.
2. Acquire a digital image under normal exposure conditions.
3. Extract a profile across the edge, averaging many rows perpendicular to the edge (to reduce noise).
4. Plot signal intensity vs distance → this is the ESF.

The ESF typically looks like an S-shaped curve:

• Flat region (low signal, before edge)
• Smooth transition (the blurred edge)
• Plateau (high signal, after edge)

From ESF to Line Spread Function (LSF)

The LSF represents the rate of change of signal across that edge — essentially, how sharply the edge transitions.

Mathematically, it is the derivative of the ESF:

LSF(x) = d(ESF)/dx

• The LSF peaks at the point where the signal changes most rapidly.
• The width of the LSF indicates the amount of system blur, a narrower LSF = sharper system.
• The area under the LSF equals 1 (normalised).

Visually:

• ESF = S-curve
• LSF = bell-shaped curve centred on the edge

From LSF to Modulation Transfer Function (MTF)

The MTF describes how well contrast is preserved at each spatial frequency.
It is obtained by taking the Fourier transform of the LSF:

MTF(f) = ∣ Ӻ{LSF(x)} ∣

where Ӻ denotes the Fourier transform and f is spatial frequency (line pairs per mm).

• The Fourier transform converts the LSF (a function in space) into its frequency components.
• The resulting MTF curve shows how contrast (modulation) decreases with increasing spatial frequency.

Interpretation:

• MTF = 1 → perfect transfer (no blur).
• MTF = 0.1 → contrast reduced to 10% of original at that frequency.
• The cut-off frequency (where MTF ≈ 0) = limiting spatial resolution (lp/mm).

Why this method is used

The edge method (ESF → LSF → MTF) is preferred in modern digital imaging because:

• It requires only a simple edge phantom (easy to make).
• It’s robust to noise and alignment errors.
• It allows high-precision measurement of system resolution without needing ideal “point sources.”

Practical steps in digital systems

1. Acquire image of sharp metal edge.
2. Rotate slightly to oversample pixels (sub-pixel precision).
3. Extract and average profile perpendicular to edge → ESF.
4. Differentiate numerically → LSF.
5. Apply Fourier transform → MTF(f).
6. Normalise MTF so that MTF(0) = 1 (zero frequency = 100% contrast).