HTI5203 Chap.6 Distance, Exposure and the Inverse Square Law
Distance, Exposure and the Inverse Square Law
The distance practical turns inverse-square theory into controlled measurement. Students vary source-to-image distance, hold technique and phantom conditions stable, use a consistent receptor region and compare measured response with the reciprocal-square predictor.
This chapter separates theoretical values from observations, practises distance compensation with mAs and shows how a useful report diagnoses outliers without deleting inconvenient data or hiding receptor conventions. Before calculation, predict that intensity falls as distance increases, then form the squared ratio and check that the result follows that direction.
In the practical, name independent, dependent and controlled variables and preserve every observed value. Plotting intensity against reciprocal distance squared offers a direct test of the model, while departures should be linked to alignment, distance reference, scatter, background or technique consistency.
A conclusion compares observation with prediction and states the point-source assumptions rather than forcing data to agree.
What this chapter covers
- 01
Inverse-square intensity
- 02
Distance compensation with mAs
- 03
Controlled practical variables
- 04
Region-of-interest consistency
- 05
Theoretical prediction against measurement
- 06
Outlier checks and error analysis
- 07
Reciprocal-square graphs and controlled practical comparisons
Worked example · free
Predict intensity at a greater distance
- 2Write the old-to-new distance ratio.
- 3Square the ratio and calculate intensity.
- 3Check the direction and state the assumption.
Key terms
- Inverse Square Law
- Intensity varies inversely with the square of distance from a point-like source.
- Source-Image Distance
- The distance from the X-ray source to the image receptor.
- Region Of Interest
- A defined receptor area used for consistent measurement.
- Controlled Variable
- A factor held constant so the effect of the selected independent variable can be examined.
Distance, Exposure and the Inverse Square Law FAQ
Why does doubling distance reduce intensity to one-quarter?
The same output spreads across an area that grows with the square of distance. Doubling distance produces four times the area, so ideal intensity per unit area becomes one-quarter rather than one-half.
Why plot response against one over distance squared?
The theoretical predictor is proportional to the reciprocal square of distance. Plotting the measured response against that predictor makes the expected relationship easier to inspect, while still requiring the receptor's pixel-value direction to be established.
What should I do with a practical outlier?
Check recorded distance, technique, detector, phantom position, collimation, region of interest and copied response. Repeat or exclude only with a documented reason. Preserve measured data rather than replacing a point with the theoretical value.
Exam move
Calculate normalized intensity at several distances and sketch the nonlinear curve. Then write a practical method that distinguishes independent, dependent and controlled variables. Finish by explaining one specific error pathway and the check that would reveal it. Start by predicting the direction before using the inverse-square equation.
If distance increases, intensity must decrease; if distance doubles, the ideal intensity becomes one-quarter. Write I-one d-one squared equals I-two d-two squared and form the ratio so the known and unknown positions remain visible. Work three examples with increasing distance and two with decreasing distance. After each calculation, ask whether the magnitude agrees with geometric spreading.
A result that rises when the detector moved farther away is a ratio error, not evidence that the law has changed. Turn the calculation into a graph. Set one reference distance to normalized intensity one, calculate several points and plot intensity against distance. Then plot intensity against reciprocal distance squared.
The first relation should curve and the transformed relation should approach a straight line under the ideal assumptions. Explain what each graph reveals rather than treating linearisation as decoration. The curved plot shows how rapidly intensity changes close to the source; the transformed plot gives a direct way to evaluate whether measured data follow the proposed inverse-square relationship.
Label axes and units before interpreting slope or departure. For practical preparation, write a method with an independent variable, dependent measurement and controlled conditions. Change distance systematically; hold technique, alignment, field, detector setup and measurement procedure constant; take repeat readings if instructed; and record values before calculating transformed quantities.
Identify how an error would appear. Misread distance can shift the horizontal coordinate, poor alignment can alter measured intensity, background or scatter can prevent a clean reciprocal-square relation, and an inconsistent exposure setting can imitate distance effects. Link every limitation to a specific check instead of listing generic sources of error. Finish by separating prediction from observation.
The model predicts a relation under point-source and uncomplicated geometry assumptions; the experiment supplies measurements that may depart for identifiable reasons. In a report-style response, state the trend, show the calculation or graph, compare it with the prediction and discuss one plausible mechanism supported by the pattern. Do not alter inconvenient readings to fit the law.
For timed revision, alternate one arithmetic problem with one method question and one graph interpretation. Log errors under ratio direction, squaring, distance reference, variable control or unsupported explanation, then design the next problem to isolate that error.
