Nyquist Limit
Definition
The sampling theorem's constraint: to faithfully record a feature, the sensor must sample it at least twice per cycle. A feature smaller than two pixels is aliased or lost entirely. There is no software recovery for sub-Nyquist detail.
- Basis
- Sampling theorem
- Rule
- Sample a feature at least twice per cycle to record it faithfully
- Consequence of undersampling
- Aliasing or total loss of the feature
- Recoverability
- No software can recover sub-Nyquist detail
Common questions
What does it mean in practice for a forensic image of a small item, like a fingerprint ridge, to be below the Nyquist limit?+
If the sensor's pixel pitch is too coarse relative to the ridge spacing, adjacent ridges can blend into a single blurred band or produce a false moire pattern instead of distinct lines. No sharpening or upscaling algorithm can restore ridge detail that was never captured, since the information was lost at capture, not merely obscured.
Why do image enhancement tools sometimes appear to add detail below the Nyquist limit?+
Interpolation and AI upscaling algorithms generate plausible-looking pixels based on patterns learned elsewhere, not from the actual scene. This can produce a sharper-looking image that is misleading rather than accurate, which is why enhancement claims below the sampling limit require careful validation before use as evidence.
How does an examiner determine whether a piece of evidence was adequately sampled?+
The examiner compares the known physical size of the smallest feature of interest against the sensor's effective resolution at the capture distance, calculating pixels per unit length, and checks that this meets or exceeds twice the feature's spatial frequency before relying on the image for fine-detail comparison.
Related terms
- CLAHE
- Contrast Limited Adaptive Histogram Equalisation. Divides the image into local tiles, equalises each tile's contrast separately, and blends results. Recovers shadow detail...
- Deconvolution
- A computational technique that estimates the PSF and inverts its effect to recover a sharper image. The quality depends entirely on how...
- Point Spread Function (PSF)
- A mathematical description of how the imaging system spreads the light from a single point source across neighbouring pixels. Defocus, diffraction, and...
- Spatial Resolution
- The finest detail a camera system can record, determined by pixel size and lens quality, measured in line pairs per millimetre or...
- Super-Resolution
- Methods that attempt to produce an image with higher pixel density than the source. Interpolation-based SR fills in values by estimation; learning-based...