Densitometer: high-density compression

Lifted from photodiodes, ADCs and measuring light, whose stray-light section is where the course derives the ceiling, and from test T2 on the densitometer optical head.

What you see

A scale that agrees for two decades and then bends over. Step 1 to step 12 of a 21-step wedge read as they should; from about step 15 the reported differences shrink; by step 21 the instrument has nearly stopped responding, and a completely opaque blank reads about the same as the densest step.

Part XV names this shape as the diagnosis: stray light compresses only the top of the scale. Compare it with the three faults it is confused with — an amplifier running out of range compresses the bottom, a wrong logarithm bends the whole thing, and a drifting zero shifts the scale without bending it at all.

Likely causes

1. Light from your own lamp reaching the detector without going through the sample. Around the aperture plate, through a box seam, off the arm underside, past the shroud.
2. An interior that is not black, or not baffled. Matt black paint is a calibration operation on this instrument, not a finish.
3. An aperture plate too thick or too wide, which widens the acceptance cone and lets the detector see places the sample is not.
4. Infrared leakage. Silicon peaks near 920 nm, so an indicator LED inside the case, or an LED switched off through a resistor rather than a hard low, arrives where the detector is up to three times more sensitive than at the measuring wavelength — and where you cannot see it to find it.

What is happening: the chemistry and physics

Every other error in this instrument is proportional. Stray light is not: it adds a fixed quantity of light to every reading, whatever the film is doing, because it never went through the film.

Let f be the stray light as a fraction of the clear-film signal, with the instrument zeroed on air with the stray light present, as it inevitably will be:

D_measured = −log₁₀ ( (10^−D + f) ÷ (1 + f) )

What a stray-light floor does to a reading

Let the true density run to infinity — put a coin over the aperture — and the reported density does not. It approaches a ceiling:

D_max ≈ −log₁₀ f

The ceiling

A floor of 0.1 per cent caps the instrument at 3.0 D. One per cent caps it at 2.0. One hundredth of a per cent caps it at 4.0. That one line sets the specification of a home-built densitometer more than any component on the parts list.

!The confirming test: T2, and it takes a coin

Put an opaque blank over the aperture, close the head, lamp on, room dark. Subtract the dark reading. What is left is your own lamp arriving by the wrong route.

Then compute f = (blank − dark) ÷ (air − dark), and D_max ≈ −log₁₀ f. Part XV calls this the single most important number the optical-head page produces, and it belongs on the instrument’s certificate.

The test that separates this from ambient leakage is T3: run T2 twice, once with the room lights on and once off. A difference between them is room light through the shroud, which is a different fault with a different cure — the foam seal and the box seams, not the blackening.

The test that separates it from a scale error is a wedge of equal steps. Stray light leaves the low steps correct and shrinks the high ones; a scale error shrinks them all by a similar fraction.

Diagnostic questions

• What is f, and when was it last measured? An instrument without that number cannot state a range.
• Does step 21 read the same as an opaque blank? Then nothing is broken: you have hit D_max and the instrument is reporting its own floor. State the range honestly and exclude those steps.
• Have you torch-tested from the inside? A lamp inside the closed head, viewed in a dark room, shows every seam that leaks.
• Is anything else inside the case emitting? Power indicators are the classic offender, and they are usually invisible against the instrument’s own lamp.
• How thick is the aperture plate, and how wide is the bore? Both set the acceptance half-angle, and both change what quantity the instrument is measuring rather than merely how well.

Corrective action

Reduce the floor, or state the range. Those are the only two honest options, and the second is not a failure — an instrument certified to 2.5 D is a perfectly good instrument for paper work.

Flock the arm underside, re-tape the seams, and blacken the interior, in that order; Part XV’s own table maps a measured f to the action worth taking.

Do not recalibrate around it. Rescaling against a wedge makes the low end agree again and leaves the ceiling exactly where it was, which converts a visible fault into an invisible one.

Prevention

Measure f at commissioning and put it on the certificate. A range that has been stated cannot be silently exceeded.

Design the baffling before the electronics. Part XV devotes a whole build stage to blackening for this reason.

Keep infrared out. Switch LEDs hard off rather than through a resistor, and keep indicators outside the optical enclosure.