Densitometer: drifting zero

Lifted from photodiodes, ADCs and measuring light and the calibration tests on the densitometer optical head. The register assigns the densitometer fault signatures to Part XV, and the pages that establish them are written.

What you see

Readings that creep. The same step, undisturbed, read ten minutes apart, gives two different numbers. Over a session the whole scale walks in one direction, usually upward at the dense end and hardly at all at the clear end.

The shape is what names the fault. Part XV sets out four instrument faults and four different-shaped errors, and this is the one that shifts the scale without bending it: stray light compresses only the top, an amplifier running out of range compresses the bottom, a wrong logarithm bends the whole thing, and a drifting zero moves it.

Likely causes

1. Amplifier output offset moving with temperature. The commonest cause, and the least obvious.
2. Warm-up. Lamp, detector, or both, still settling.
3. A dark reading taken once. An offset subtracted at switch-on is an offset that was right at switch-on.
4. A lamp falling through the session with no monitor channel to divide it out.

What is happening: the chemistry and physics

Part XV works the arithmetic and the surprise in it is worth repeating. Dark current is not the problem. The OPT101’s photodiode passes 2.5 pA at effectively short-circuit, which through the internal 1 MΩ feedback resistor is 2.5 µV at the output — negligible even after two doublings.

The output offset is the problem. The datasheet gives 5 to 10 mV, typically 7.5 mV, with a temperature coefficient of ±10 µV/°C. Set the air reading at 2.0 V and the signal at 3.0 D is a thousandth of that: 2.0 mV, smaller than the offset sitting under it. Subtract the offset once and walk away, and a 10 °C change in room temperature moves it by 100 µV — five per cent of a 2.0 mV signal, which is log₁₀(1.05) = 0.021 D of error at the top of the range and essentially none at the bottom.

That is a bigger number than the whole error budget of a good commercial instrument. A professional bench densitometer concedes the same physics in its own units: zero stability of ±0.02 D per eight hours, after a two-minute warm-up.

!The confirming test: T1, twice

Take the dark reading with the lamp off, head closed, room dark — 64 readings, mean and spread. Then repeat it after half an hour with the lamp running.

• The dark reading has moved: the head is warming, and you have just measured your own warm-up requirement rather than guessed it.
• The dark reading is stable but the sample reading still creeps: the lamp is changing, and the monitor channel is the fix.
• Neither moves and the readings still creep: the drift is mechanical, and T4’s replaced-versus-undisturbed pair separates the mechanics from the electronics in twenty readings.

The distinguishing feature against every other instrument fault is that a drifting zero does not change the shape of the scale. Read a wedge of equal steps: if the steps are still equal and the whole set has moved, this is your fault.

Diagnostic questions

• Is there a written warm-up rule, and was it followed? An instrument without one has a different specification every morning.
• Does the firmware take a dark reading with every measurement, or once? This is the single design decision that removes most of the fault.
• What has the room temperature done since the zero was set? A radiator, a lamp housing, or a window in the sun are all ±10 °C events over a session.
• Is there a monitor channel? A second detector watching the lamp lets you report a ratio, and a ratio is immune to a lamp that dims uniformly. Part XV’s own question 7 sets out what it will not protect against.
• Is the drift larger at the dense end? It should be, on this mechanism. If it is uniform across the scale, suspect the lamp instead.

Corrective action

Re-zero, and then keep re-zeroing. Take the dark and air readings immediately before each measurement session, and prefer firmware that retakes the dark reading with every measurement.

Write and obey a warm-up rule derived from your own T1 repeat rather than from any published figure. Two minutes is a professional instrument in a metal case; a home-built head in a plywood box is probably longer.

Discard readings taken during the drift. Densities read while an instrument was settling are not correctable after the fact, because you do not know where the zero was at each moment.

Prevention

Record the instrument’s own numbers on a certificate — the dark reading and its spread, the stray-light floor, the repeatability with and without replacement, and the warm-up time — and re-run them on a schedule. Part XV calls that the build record, and the calibration records worksheet is where it goes.

Keep the instrument at a stable temperature, which mostly means keeping it away from the enlarger lamp and the radiator.

Add the monitor channel. It is one more detector and it turns a class of lamp faults into arithmetic.