Explain X-ray contrast, attenuation and CT imaging
Connect X-ray absorption differences to image contrast and describe how CT combines projections into a three-dimensional image.
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. Topic 24 was checked against Cambridge’s 2028–2030 syllabus; the other remaining syllabus-year changes are still being reconciled. Online study supports the theory but cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use exponential functions, wave speed, energy conservation and SI units; convert between joules and electronvolts when required.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What produces contrast in a transmitted X-ray image?
What you will learn
- Explain contrast in an X-ray image
- Use the exponential attenuation model for X-rays
- Describe how CT combines views to form a 3D image
Different tissues attenuate X-rays by different amounts
As X-rays pass through matter, some photons are absorbed or scattered, so transmitted intensity can be modelled by I = I₀e⁻μˣ. The coefficient μ depends on the material and the X-ray conditions.
Image contrast is the difference in detector signal from different parts of the body. Tissues with different attenuation leave different transmitted intensities; bone commonly attenuates more strongly than soft tissue, making their outlines visible.
CT builds a volume from many directions
A CT scanner takes X-ray images through the same section from multiple angles. A computer combines those projections to reconstruct a two-dimensional image of that section.
The scanner repeats the process at positions along an axis. Combining the resulting 2D sections produces a 3D representation of the internal structure. A single projection does not by itself contain the same depth information as the reconstructed CT volume.
Pause and explain
How does CT form a 3D image?
Worked example
An X-ray beam enters tissue with intensity I₀. The attenuation coefficient is 0.30 cm⁻¹ and thickness is 2.0 cm. Find the transmitted fraction.
Show the worked solution
- Calculate μx = 0.30 × 2.0 = 0.60.
- Use I/I₀ = e⁻⁰·⁶⁰.
- I/I₀ ≈ 0.549, so about 54.9% is transmitted in this model.
Answer I/I₀ ≈ 0.549.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An X-ray beam passes through 3.0 cm of tissue with μ = 0.20 cm⁻¹. Calculate I/I₀.
Give me a hint
Find μx, then evaluate the exponential.
Compare my reasoning
- μx = 0.20 × 3.0 = 0.60.
- I/I₀ = e⁻⁰·⁶⁰.
- I/I₀ ≈ 0.549.
About 0.549, or 54.9% transmitted.
Look for these in your work
- Uses matching length units
- Applies the negative exponent
- Interprets the transmitted fraction
Two equal-thickness regions have μ values 0.10 cm⁻¹ and 0.40 cm⁻¹. Which region gives the lower detector intensity? Explain.
Give me a hint
Compare the exponentials for the same x.
Compare my reasoning
- For a fixed thickness x, I/I₀ = e⁻μˣ.
- The larger μ makes the negative exponent more negative.
- Therefore the 0.40 cm⁻¹ region transmits less intensity.
The region with μ = 0.40 cm⁻¹ gives the lower intensity because it attenuates the beam more strongly.
Look for these in your work
- Uses the same-thickness condition
- Compares attenuation coefficients
- Links higher μ to a lower transmitted fraction
Describe the image-building steps a CT scanner uses after collecting X-ray views at several angles through one slice.
Give me a hint
Separate reconstruction of a slice from the later stacking of slices.
Compare my reasoning
- Combine the projections from different angles to reconstruct a 2D image of that section.
- Repeat the collection and reconstruction at positions along an axis.
- Combine the 2D sections to represent the internal structure in 3D.
CT reconstructs a 2D section from many-angle projections, repeats along an axis and combines the sections into a 3D image.
Look for these in your work
- Mentions multiple angles for one section
- Describes repeating along an axis
- Ends with a 3D representation
Common mistakes
- Assuming image contrast comes from the detector alone
- Treating attenuation as a fixed intensity loss per centimetre
- Describing CT as a single X-ray photograph rather than a reconstruction from projections
What can you explain now?
What produces contrast in a transmitted X-ray image?
Compare with the explanation
Different parts transmit different intensities because they attenuate X-rays differently
Different attenuation gives different detector signals.
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Make it stick
Why can a CT image show structure that a single X-ray projection superimposes?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.