Fixed Pattern Noise

Fixed pattern noise is the specific error correlated double sampling was built to fight — a spatial, repeatable deviation from ideal response across an array of nominally identical elements, caused by device mismatch rather than randomness. The name describes the defining property directly: the pattern is fixed, meaning it reappears identically frame after frame, measurement after measurement, which is exactly what separates it from thermal or flicker noise and exactly what makes it correctable by techniques that temporal noise defeats.

The word "fixed" is doing the real work here, and it is why averaging more frames or taking more samples never helps. Random, temporal noise sources — thermal noise, 1/f noise, shot noise — average down as more independent measurements are combined, because each new measurement draws a fresh, uncorrelated noise sample. Fixed pattern noise does the opposite: it comes from a physical mismatch baked into the silicon itself, device-to-device threshold voltage variation, dark current differences, gain-element mismatch across an array, and that mismatch does not change from frame to frame. Averaging a thousand frames of a fixed pattern leaves the identical pattern behind, unchanged, because there was never any randomness to average away in the first place.

Fixed pattern noise actually splits into two physically distinct categories, and conflating them is a common source of confusion about what any given correction technique actually fixes. Offset FPN is additive — a per-element error present even with zero input, visible as dark-current nonuniformity in an image sensor's black frame or a converter channel's own zero-input reading, and it shows up identically regardless of signal level. Gain FPN is multiplicative instead — a per-element response-slope mismatch, commonly called photoresponse nonuniformity in imaging, that produces no visible error at zero input but grows in direct proportion to how large the actual signal is, since the error is a percentage of signal rather than a fixed quantity added on top.

This distinction is exactly why correlated double sampling's real scope is narrower than a casual description of it suggests. CDS subtracts a reset-level sample from a signal-level sample, which removes additive offset FPN completely and exactly, since that offset is present identically in both samples and cancels in the subtraction. It does nothing for gain FPN, because a multiplicative error does not cancel through subtraction — a 2% gain error on a bright pixel and the same 2% gain error on a dark pixel produce different absolute error magnitudes, and no amount of subtracting a reset level changes a multiplicative relationship. CDS is, specifically and only, an offset-FPN correction technique; describing it more broadly as removing fixed pattern noise overstates what the mechanism actually touches.

Gain FPN instead requires calibration-based correction, a fundamentally different kind of fix than anything this series' real-time sampling techniques provide. Flat-field correction, the standard answer in imaging, works by capturing a reference frame under known, uniform illumination, measuring each element's actual gain relative to the ideal response, and storing a per-element gain correction map that gets divided back out of every subsequent frame. This is calibration performed once — or periodically, to track drift — rather than a technique applied continuously during normal operation the way autozeroing, chopper stabilization, and correlated double sampling all are; it requires storage for the correction map and a controlled calibration step neither of the real-time techniques needs.

This same device-mismatch root cause is what common-centroid layout addresses at the circuit level, just applied here across a much larger population of elements than a single matched pair. A differential pair relies on common-centroid placement to make two devices see the same process gradient and match closely; an imaging array or a multi-channel converter has thousands or millions of elements, far too many to match through layout geometry alone, which is exactly why array-scale fixed pattern noise needs its own correction techniques — layout discipline reduces the magnitude of the mismatch, but at this scale it cannot eliminate it, and something has to correct whatever mismatch remains after the best layout a process allows.

Fixed pattern noise is the spatial counterpart to every temporal noise mechanism this series has already covered, and the distinction matters precisely because the fix has to match which kind of error is actually present. Correlated double sampling earns its place as a real-time, calibration-free technique by solving exactly one half of this problem — the additive half — while the multiplicative half waits for a completely different kind of correction, measured once and divided back out rather than sampled and subtracted on every cycle.