Stacking Filters Without Guesswork: Filter Factor vs. Optical Density

Filter specs can feel like three different languages arguing at a bar: transmission, filter factor, and optical density. But here's the key insight—they're not competing ideas. They're interchangeable ways to describe how much light you lose.

The Three Languages, Translated

Transmission (T) is the most direct: it's the ratio of light passing through versus light entering. A 50% transmission filter lets half your photons through.

Filter factor is a practical exposure concept: how much must exposure be "prolonged" to get the same brightness? A filter factor of 2 means you need twice the exposure (or twice the light) to compensate.

Optical density (D) is the compact math form: D = log(1/T). Engineers love it because densities add together cleanly when you stack filters.

How These Numbers Map Together

Let's walk through the relationships with real examples.

A filter with 50% transmission has a filter factor of 2 and an optical density of 0.3. In camera terms, that's about one f-stop of compensation—open your lens by one stop to maintain the same exposure.

Drop to 25% transmission, and you're at filter factor 4, optical density 0.6, requiring about two stops of compensation. At 12.5% transmission, it's factor 8, density 0.9, and roughly three stops.

This matters enormously in machine vision because you often can't freely adjust every parameter. Exposure time might be limited by motion blur requirements. F-stop might be constrained by depth-of-focus needs. Knowing exactly how much light you're losing—and being able to calculate it precisely—lets you plan around these constraints.

The Golden Rule for Stacking

When combining multiple filters, you have two equivalent approaches: multiply filter factors together, or add optical densities.

Say you stack a 50% transmission filter with a 25% transmission filter. The combined filter factor is 2 × 4 = 8. Or if you prefer, combined optical density is 0.3 + 0.6 = 0.9. Either way, you land at 12.5% transmission overall.

That single calculation prevents a classic integration failure: adding "just one more filter" and then wondering why the image got noisy or why exposure time blew out your takt time.

The Takeaway

Calculate your total light budget before finalizing your filter stack, not after. The math is simple, and the headaches it prevents are significant.

This is part of KUPO's technical resource series on optical filters for machine vision. For custom filter solutions, contact KUPO CO. LTD.