From Transmission Percentage to F-Stops: Speaking the Same Language Across Your Vision System

The Tower of Babel Problem in Optical Specifications

Here's a situation that happens all the time in machine vision: your filter datasheet says "25% transmission," your camera operator thinks in "stops," and your lighting engineer talks about "4× power multipliers." Everyone is describing the same physical reality—light attenuation—but using completely different vocabularies.

This isn't just an inconvenience. When your filter manufacturer, camera documentation, and lighting specifications all use different units, mistakes happen. You might under-light a scene, saturate your sensor, or waste hours troubleshooting a "mysterious" exposure problem that's really just a unit conversion error.

The good news? These different vocabularies are all describing the same underlying physics, and the translation between them is surprisingly elegant.

Understanding the Three Languages

Language 1: Transmission (T)

Transmission is the most direct physical measurement: what fraction of incident light makes it through the filter? A filter with T = 0.50 (or 50% transmission) passes half the light and blocks half. A filter with T = 0.25 (25%) passes one-quarter and blocks three-quarters.

This is how filter manufacturers typically spec their products because it directly describes what the filter does optically.

Language 2: Filter Factor (F)

Filter factor answers a practical question: how much more exposure (or light) do I need to compensate for adding this filter? If a filter has a factor of 4, you need 4× the exposure—whether that means quadrupling your exposure time, quadrupling your light intensity, or some combination.

The relationship to transmission is beautifully simple: Filter Factor = 1 / Transmission

A 50% transmission filter has factor 2 (you need 2× more light). A 25% transmission filter has factor 4 (you need 4× more light). A 12.5% transmission filter has factor 8 (you need 8× more light).

Language 3: Stops

Photographers and cinematographers think in stops because each stop represents a clean doubling or halving of light. One stop darker means half the light. Two stops darker means one-quarter the light. Three stops means one-eighth.

The math: Stops = log₂(Filter Factor) = –log₂(Transmission)

This logarithmic relationship is why stops are so intuitive for exposure work—they turn multiplication into addition.

Language 4: Optical Density (OD or D)

Scientists and engineers often prefer optical density because it adds linearly when you stack filters (more on this later). OD uses base-10 logarithms: OD = log₁₀(1/T)

The relationship to stops: Stops ≈ OD / 0.301 (because log₁₀(2) ≈ 0.301)

The Master Translation Guide

Once you internalize these relationships, you can convert instantly between any specification format:

50% transmission equals filter factor 2, equals OD 0.3, equals 1 stop of light loss.

25% transmission equals filter factor 4, equals OD 0.6, equals 2 stops of light loss.

12.5% transmission equals filter factor 8, equals OD 0.9, equals 3 stops of light loss.

6.25% transmission equals filter factor 16, equals OD 1.2, equals 4 stops of light loss.

~0.1% transmission equals filter factor ~1000, equals OD 3.0, equals 10 stops of light loss.

The pattern is elegant: every doubling of the filter factor (or halving of transmission) adds exactly one stop and approximately 0.3 to the optical density.

Practical Application: Exposure Planning

Let's work through a real scenario. You've added a bandpass filter with 25% transmission to isolate your target wavelength. Your image is now too dark. What are your compensation options?

Since 25% transmission equals 2 stops, you need to recover 2 stops of light somehow. Here are your three pathways:

Option A: Open the aperture by 2 stops. If you're currently at f/8, open to f/4. This quadruples the light reaching your sensor. The trade-off? You've reduced your depth of focus.

Option B: Increase exposure time by 4×. If you're at 1ms, go to 4ms. This quadruples the total light collected. The trade-off? More potential for motion blur.

Option C: Increase lighting power by 4×. Crank up your LED drivers or move lights closer. This quadruples the illumination on your subject. The trade-off? Possible heat issues, higher power consumption, or hitting your lighting system's limits.

In machine vision, these trade-offs matter enormously. Motion blur tolerance, depth of focus requirements, and lighting constraints are often non-negotiable specs. By understanding the stop-based math, you can immediately see which compensation strategies are viable for your application.

The Power of Thinking in Stops

The real magic of stop-based thinking is that it makes exposure planning predictable and systematic.

Every single stop change—whether from a filter, aperture, exposure time, or lighting—represents exactly a factor-of-two change in light. When you need to compensate for a filter that removes 3 stops, you know you need to add 3 stops back somewhere. The math becomes addition and subtraction rather than multiplication.

This is why experienced vision engineers can quickly evaluate whether a filter is practical for their application. They see "OD 1.5" on a spec sheet and immediately think "5 stops of loss—that's 32× the light needed. Can our lighting system deliver that? Can we afford to open the aperture that far?"

With this translation fluency, you stop being surprised by filter effects and start designing with confident predictability.

This is part of KUPO's educational series on optical filters for machine vision. Mastering the vocabulary of light attenuation helps you communicate clearly across disciplines and avoid costly specification errors.