How scene log exposure maps through the film's characteristic curve to density — and how that density translates into a count of electrons trapped in a 14-bit sensor photosite. Equal steps in log exposure produce equal steps in density, but very unequal steps in electron count.
T = 10^−D
Transmittance is an exponential function of density. Each unit increase in D reduces transmitted light by 10×. This is why equal D steps produce unequal electron steps.
3 zones
Toe, linear, and shoulder. Only in the linear zone does a given change in log H produce a proportional change in density — and a predictable electron count.
14-bit
A 14-bit sensor well holds 16,383 electrons. The probe dot on the right chart shows exactly how many fall into the well at each point on the H&D curve.
what the H&D curve shows
The Hurter & Driffield characteristic curve plots density D (vertical) against log exposure H (horizontal). Density is a measure of how opaque the developed film is at any point — higher density means more silver or dye, less light passes through. Log exposure is used because the eye and film both respond logarithmically to light: each step on the horizontal axis represents a doubling (or halving) of exposure, i.e. one stop. The slope of the curve at any point is the local contrast of the film — steep = contrasty, shallow = compressed.
toe, linear, shoulder — why they matter for scanning
The toe is the underexposed end: shadows in the scene that didn't receive enough light to develop fully. The curve here is shallow — a large change in exposure produces a small change in density, so shadow detail is compressed. The linear region in the middle is where the curve is straight: tonal relationships are preserved faithfully and inversion is mathematically clean. The shoulder is the overexposed end: highlights that have driven the film to maximum density. Any detail that falls in the toe or shoulder of the original exposure cannot be fully recovered during scanning inversion — the compression happened in the chemistry, before the scanner sees the film.
why the electron count curve is exponential
Transmittance is defined as T = 10^(−D). The sensor photosite fills with electrons in proportion to T — it is a photon counter, not a density meter. So while the H&D curve is plotted with density on a linear vertical axis, the electron count is an exponential function of that density. Drag the probe from the toe into the linear zone and watch the electron count on the right chart jump disproportionately — a small move in D near the low end produces a large change in electrons, while the same D step near Dmax produces almost nothing. This asymmetry is why shadow detail in a scanned negative always has lower signal-to-noise ratio than highlight detail.
reversal film — same curve, opposite direction
Switch to slide/reversal. The curve flips: more exposure produces lower density, because reversal film is a positive — the bright parts of the scene become the thin, transparent parts of the slide. The slope is steeper (gamma ≈ 1.8 vs ≈ 0.65 for negative), meaning contrast is higher and the toe and shoulder compress more aggressively. A one-stop error when scanning a slide destroys more tonal information than the same error on a negative — which is why reversal film has a reputation for demanding precise exposure, both at the camera stage and at the scanner stage.
practical implication — what to aim for when scanning
The goal when setting scanner exposure is to land the brightest part of the film — the base-plus-fog area, the thinnest part of the negative — as close to the sensor ceiling as possible without clipping. This maximises the electron count in the usable density range, which maximises signal-to-noise ratio before any inversion or colour correction is applied. Scanning "to the right" in raw histogram terms is not overexposure — it is deliberate use of the sensor's full dynamic range. The orange mask in color negative film means the base density is never truly clear, so the ceiling is never quite reached, but the principle still holds: more electrons in the raw scan means more information to work with downstream.