Apertia · Library
How can magnification expose a mistaken close-focus distance?
Check a close-focus distance with magnification: 100 mm at 500 mm from the sensor gives m = 0.381966 and a 94.2 mm frame, not the 144 mm of a lens-plane error.
Magnification from the two distances
Apertia measures focus distance from the sensor plane and splits it into u and v with u = (d + √(d² − 4df)) ÷ 2 and v = u × f ÷ (u − f). Magnification is v ÷ u, and the width of a flat subject that fills the frame is the sensor width divided by that ratio. A ruler or a printed scale photographed at a known distance lets you compare the predicted width with what the camera actually records.
If d is mistakenly used as the lens-side distance, the magnification becomes f ÷ (d − f). At portrait distances the difference is small; close up it becomes large enough to make a ruler test reveal the error immediately.
Worked example
The model gives about 0.026334 image-to-subject magnification at this sensor-plane distance. A flat width of approximately 1367.052 mm then maps to the 36 mm sensor width.
- Model image-to-subject scale
- 0.026334
- Flat-subject width filling the 36 mm frame (mm)
- 1367.051975
Run a ruler test
- Tape a ruler flat at the subject position and measure its distance from the sensor-plane mark.
- Enter the focal length and that distance; compute u, v and m = v ÷ u.
- Divide the sensor width (36 mm for full frame) by m to get the predicted frame width.
- Photograph the ruler and read how many millimetres span the frame.
- If the two widths disagree, recheck the distance reference and the recording area first.
Worked example: two distances
50 mm at 2000 mm: u = 1948.683 mm, v = 51.317 mm, m = 0.026334, frame width 1367.1 mm. Treating 2000 mm as u gives m = 0.025641 and 1404 mm — about 37 mm wider.
100 mm at 500 mm: u = 361.803 mm, v = 138.197 mm, m = 0.381966, frame width 94.2 mm. Treating 500 mm as u gives m = 0.25 and a 144 mm frame, half as large again as the thin-lens prediction.
- 100 mm · d = 500 mm · m
- 0.381966
- Predicted frame width
- 94.2 mm
- Width if d is used as u
- 144 mm
Common mistakes
- Measuring to the front element and entering that as the sensor-plane distance.
- Using a video crop or a digital teleconverter mode without changing the sensor width in the calculation.
- Taking a matching ruler test with one lens as proof that another lens will behave the same.
Limits of a scale check
The magnification is a thin-lens estimate. Internally focusing lenses can have a shorter effective focal length up close, so a mismatch is not necessarily a measuring error. The DOFMaster equations linked below use the same lens-side distances.