graph22  ·  film scanning pipeline

H&D curve electron well · zone limits

How scene log exposure maps to film density, and how that density translates into electrons in a 14-bit sensor well — showing the fraction of the well that film actually uses, and where the linear zone of the characteristic curve lands within that fraction.

log H probe
density D  ·  log exposure H (log lux·s)
H&D characteristic curve.
toe linear shoulder
electrons in well  ·  0 → 16 383 (14-bit)
Electron well fill curve with zone bands.
log H
density D
transmittance
electrons
zone
linear band
film DR
well used

~8 stops
Dynamic range of a color negative (Dmin 0.05 → Dmax 2.26). A 14-bit sensor can capture 12+ stops — leaving ~4 stops of well capacity unused.
1:316
Transmittance ratio across the negative. At Dmax ≈ 2.26, only 0.5% of scanning light passes through — those photons must compete with sensor read noise.
<40%
Fraction of the electron well that the linear zone of a color negative occupies. Exposing to use the full well maximises SNR before inversion.
wasted headroom — above Dmin
Even clear film base blocks some light. Color negative has a base-plus-fog density of roughly 0.05, plus the orange mask adds further absorption. This means the scanning illuminant can never fill the sensor well to 16 383 — the top red band on the right chart is permanently unreachable. The practical consequence: if you expose the scanner for the sensor's midpoint, you are throwing away dynamic range. Optimal scanning exposure pushes Dmin as close to the sensor ceiling as possible without clipping, maximising the electron count in the usable band.
wasted floor — below Dmax
At maximum density (deep shadows in the scene, which become the thinnest part of the negative after development), transmittance T = 10−Dmax ≈ 0.5%. The sensor receives almost no photons from these areas. Electron counts near zero are indistinguishable from read noise. This is why shadow detail in a scanned negative is noisy even with a good scanner — the signal is genuinely tiny, not a software failing. Scanning at a higher ISO equivalent or using a brighter illuminant raises the absolute photon count but cannot change the transmittance ratio.
the linear band — where tonal relationships are preserved
The green band on the right chart shows which electron counts correspond to the linear portion of the H&D curve. In this region, equal steps in log exposure produce equal steps in density — and therefore a predictable, invertible relationship between scene luminance and sensor signal. Shadow and highlight detail that falls outside this band (into toe or shoulder) is compressed and cannot be fully recovered by inversion alone. Notice that for color negative the linear band occupies only a fraction of the already-narrow usable well range — the film's toe and shoulder consume significant stops at both ends.
slide / reversal — more of the well, steeper gamma
Switch to slide/reversal film. Dmax rises to ~3.0, which means the usable well range widens — more of the 16 383 electrons are put to work. But the curve is inverted (more exposure = less density) and the gamma is steeper (~1.8 vs ~0.65 for negative). Equal steps in log H produce larger steps in density, so the toe and shoulder compress more aggressively at both ends. A one-stop scanning error on a reversal film destroys far more tonal information than the same error on a negative — which is why slide scanning has less exposure latitude.
practical implication — expose to the right, then invert
Because the electron curve is exponential (T = 10−D), the relationship between density and electron count is not linear. Equal density steps in the linear zone of the H&D curve produce unequal electron steps — larger at low density (highlights in the negative, shadows in the scene), smaller at high density (shadows in the negative, highlights in the scene). Scanning software should expose so that Dmin — the film base — lands just below the sensor ceiling. This packs the maximum number of electrons into the usable band before any inversion or colour correction is applied, giving the highest possible signal-to-noise ratio in the final image.