Why CircleSFR measures circles, not slanted edges

Rex Lee·July 25, 2026
An engineer examining a test chart of circles with a loupe, camera lens and lens cross-section nearby
The idea arrived in a talk. The conviction came from checking the sampling math.

Every camera lab measures sharpness the same way: print a slanted edge, capture it, run the ISO 12233 SFR math. CircleSFR measures circles instead. That was not contrarianism. It goes back to something my technical lead was saying twenty years ago, and to my own eventual realization that he had been right the whole time.

Early in my career I worked at Aptina, the imaging company that began as the Imaging Division of Micron Technology. My technical lead was Richard Baer. Rick had published the original circular-edge SFR paper at the Electronic Imaging conference in 2004, back when he was at Agilent Labs, and by around 2005 he was presenting the idea to imaging teams as a serious alternative to the slanted edge: run the same SFR math, just along the edge of a circle. Most of the room filed it under interesting. It stuck with me, because the slanted edge always felt like a workaround. You tilt a straight line a few degrees so the pixel grid samples it at slightly different phases, and then you hope the angle you picked cooperates with your sensor.

Years later I dug into it properly, and the sampling argument fell straight out of the geometry. A slanted edge crosses the pixel grid at one shallow angle, so the sub-pixel phases you need for super-resolution accumulate slowly along the edge. A circle presents every edge orientation at once, and the phases sweep the pixel grid far more uniformly. That efficiency is worth real oversampling: our circular-edge pipeline runs at a super-sampling rate of 6, where slanted-edge implementations typically settle for 4. Same chart area, same capture, a finer reconstruction of the edge profile.

A circle crosses the pixel grid at every angle at once, which is exactly what you want when the whole game is seeing between the pixels.

The sampling efficiency is what convinced me. The clean separation is what made it a product. Fit an ellipse to each ring, take the radial direction from the optical center, and every circle hands you the sagittal and tangential MTF at that point in the field, cleanly split. That matters because sagittal and tangential curves versus field position are exactly what numerical optical simulation produces when a lens is designed. A slanted-edge chart gives you horizontal and vertical edges, which mix the two components everywhere except dead center. With circles, the measurement finally speaks the same language as the lens model, and you can lay the measured field map directly over the simulation and see where the as-built lens departs from the design.

Cameras were not the only field to notice. Medical imaging physicists validated circular-edge MTF measurement for CT scanners (Takenaga et al., Radiological Physics and Technology, 2015; Rolstadaas et al., Biomedical Physics & Engineering Express, 2018), where a disk phantom plays the role our rings play. And on the camera side the method became the basis of US patent 11,546,515: measure a chart of circles, store each camera's tangential and sagittal blur data, and use it to correct that camera's images.

CircleSFR is where that thread ends up: 83 rings on one printed target, a dense sagittal and tangential field map from a single capture, and a pip-installable package that runs the analysis. The idea took the long way here, from a 2004 paper and a talk that most of the room forgot, through CT phantoms and a patent filing, to a chart you can order in a tube. Rick was right. The circle was the right primitive all along.

Measure your camera the way your lens was designed.

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