Sampling Frequency is the number of pixels (typically measured in ppi, or pixels per inch) used to represent the physical object. This measurement does not represent how much meaningful detail is present; it is unaffected by inherent sharpness or additional sharpening added in post processing.
Imagine that a professor asks his students to write a 20-page essay, and every student in the class turns in an essay that fills 20 pieces of paper. In the strict sense, all students have fulfilled the requirements of the assignment. However, some students use double spacing, others add padding between the letters, and many use filler words and phrases that add no actual detail to their arguments, and only a few actually fill 20-pages with precise and meaningful content.
This example is very similar to the way that many, perhaps even most, digitization systems claim to scan objects at a particular PPI; at closer inspection the amount of precise and meaningful image content is well below that PPI. Worse, over time such marketing misrepresentation of the actual detail level has become better hidden.
For many years, Cultural Heritage Institutions have known to look for “optical resolution” in scanning systems, as scanner manufacturers would often provide non-optical interpolated resolutions in their marketing material and only show their optical resolution deep in technical specification lists. This is the equivalent of double-spacing an essay, and is quite obvious and well-known. Here are more subtle forms of marketing inflation:
- Theory vs. Measured: Stating only the resolution of the sensor, which provides a theoretical maximum resolution, rather than the as-measured resolution of the entire system. A 36 megapixel sensor used with a mediocre lens does not record files with anywhere near 36 megapixels of actual subject detail.
- Center vs. Edge: Stating the resolution measured in the center of the image, rather than the resolution in the corners or edges. Most general purpose photographic lenses, including even expensive, high-end lenses, are not as sharp in the corners as in the center.
- One Axis vs. Both Axis: Stating the resolution measured in one axis, rather than both. Scanning systems (planetary, flatbed, or rotary fed) that move during the capture of the image often have measurably better detail along the axis of the scanning array than along the axis of their motion. In other words, the image is subtly blurry in the direction of the motion.
- Sharpened vs. Native: Many systems have excessive sharpening applied automatically or in the background, hiding the native sharpness (or lack thereof) from the user. The resulting image appears visually sharp in the same way an auto-tuned singer sounds on-pitch.
As manufacturers exaggerate resolution in increasingly sophisticated ways, it has become clear that the community needs a foolproof, objective way of measuring resolution. The members of the FADGI Still Image Working Group assessed many proposed measurements for the level of actual subject detail recorded in an image, and settled on Spatial Frequency Response (SFR).
SFR is a fairly complicated mathematical modeling of how well detail is recorded at various feature sizes. It has many features, including the ability to reveal when an image has been over-sharpened, and allows a more holistic analysis of detail than any metric based on a single number. Simplicity, however, is not among its advantages. The formula used to generate a graph, which is then analyzed to provide the final relevant rating number, is available on the Wikipedia article on Optical Resolution. It is unlikely that any institution would undertake manual calculation of SFR. Instead, SFR is almost always calculated by one of the several image-analysis software packages discussed in Numerically Evaluating Image Quality.
The bottom line is summarized well at Archives.gov:
“Do not rely on manufacturers’ claims regarding the resolution of scanners/digital cameras, even optical resolution specifications are not a guarantee the appropriate level of image detail will be captured. Most claims are over-rated in regards to resolution, and resolution is not the best measure of spatial frequency response (modulation transfer function is the best measurement).”
– (page 33, www.archives.gov/preservation/technical/guidelines.pdf)