Linearisation in industrial inkjet: why every head needs its own curve

By Piotr Jędrzejczyk, AssembleX Industrial Services

Two printheads fed with the same digital value never put down exactly the same amount of ink. Linearisation is the measurement-based correction that makes them behave alike, and it is the foundation of every stable, repeatable print.

The problem: identical settings, different results

Every printhead is slightly different. Drop volume, jet velocity and the response to a given drive signal vary from head to head, and even between nozzle groups of the same head. They also drift with temperature, ink batch and wear. Send the same grey level to two heads and one of them lays down a little more ink than the other.

On a single-pass line, where the heads sit side by side across the full width, this shows up as visible bands or stripes at the boundaries between heads (Figure 1). On large-format slabs with soft marble or natural-stone graphics, even a small, regular difference is easy to see.

Figure 1. Four heads printing the same smooth gradient. Top: uncorrected, each head has a slightly different response, so steps appear at the head boundaries. Bottom: after linearisation the response matches and the gradient is continuous.

What linearisation does

Linearisation measures how each printhead and colour channel responds across the whole tonal range, and then applies a correction curve so that the measured result follows a defined target. The target is usually a straight line: a 50% input produces half of the maximum density, on every head.

The same procedure gives two results. Within one colour it balances the intensity between heads, so the bands disappear. Across the tonal range it gives the colour channel a predictable behaviour, which is the starting point for any colour profile.

Figure 2. Measured output against digital input. Dashed curves: three heads before correction. Solid line: the target. After correction, all heads follow the target.

The procedure

Make the machine ready. Check the mechanical alignment and stitching, run a nozzle check, and stabilise the ink temperature and circulation. Linearising a head that does not jet properly only bakes the fault into the curve.
Print a test chart. A wedge of grey levels for every colour and every head, at the real production settings: resolution, drop size, speed and substrate.
Process it like production. On ceramics, fire the tiles; on UV lines, cure them. The final colour appears only after the process, so that is what has to be measured.
Measure. Read the patches with a spectrophotometer, in a fixed geometry and under constant conditions.
Calculate the correction. For every head and colour, compute the curve that brings the measured response onto the target.
Load and verify. Apply the curves in the machine or the RIP, print again, and check that the result is uniform across the full width. Repeat if needed.

When to repeat it

After a printhead is replaced or repaired.
After an ink change or a new ink batch.
When bands or colour drift reappear.
After mechanical work that changes head position or stitching.
When the substrate, glaze or primer changes.

Common mistakes

Linearising before the mechanical setup and jetting are stable.
Measuring unfired or uncured samples.
Mixing measurement conditions between sessions, which makes the curves incomparable.
Correcting a banding problem that is really caused by stitching, a failed nozzle or ink starvation. Always find the cause first.

Linearisation is the base on which colour management is built. Once the curves are stable, the next step is a colour profile.