Filter Diagrams on Log Scales: How to See What Your Filter Really Blocks

Beyond Single Numbers

For neutral density filters, life is simple: one transmission number tells you most of what you need to know. But most filters in machine vision aren't neutral—they're designed to pass some wavelengths while blocking others. Bandpass filters, longpass filters, shortpass filters, notch filters: all of these have transmission that varies dramatically across the spectrum.

When transmission depends on wavelength, you stop living in a single number and start living in a curve. Understanding how to read that curve—the filter diagram—is essential for selecting the right filter and predicting how it will perform in your system.

Why Log Scales Matter

If you look at filter diagrams from different vendors, you'll notice that many plot transmission on a logarithmic scale rather than a linear one. This isn't arbitrary—it reflects something important about how filters actually perform.

Consider a filter designed to pass visible light (400-700nm) while blocking infrared. On a linear scale, you might see that transmission drops from 90% to "essentially zero" beyond 700nm. But "essentially zero" could mean 1%, or 0.1%, or 0.001%—and those differences matter enormously.

If your camera sensor is IR-sensitive and your lighting has significant IR content, the difference between 0.1% IR leakage and 0.001% IR leakage can mean the difference between clean images and mysterious artifacts.

Logarithmic scales reveal these details. On a log plot, you can clearly distinguish between OD 2 (1% transmission), OD 3 (0.1% transmission), and OD 4 (0.01% transmission) blocking performance. This matters for understanding whether your filter actually suppresses unwanted light sufficiently for your application.

Key Vocabulary for Reading Filter Curves

Cut-On and Cut-Off Wavelengths

These terms describe where a filter transitions between blocking and passing light. Different sources define the exact threshold differently, but a common convention uses 5% transmission as the dividing line.

For a longpass filter, the cut-on wavelength is where transmission rises above 5% as you move toward longer wavelengths. Everything below this wavelength is blocked; everything above is passed.

For a shortpass filter, the cut-off wavelength is where transmission drops below 5% as you move toward longer wavelengths. The filter passes shorter wavelengths and blocks longer ones.

Half-Power Points (HPP)

The half-power points are wavelengths where transmission reaches exactly 50% of the filter's peak transmission. For a bandpass filter with 90% peak transmission, the half-power points occur at 45% transmission.

These points are particularly useful for defining bandwidth. The distance between the two half-power points tells you how wide your passband is.

Center Wavelength

For bandpass filters, the center wavelength defines the "middle" of the passband. When the half-power points are λ₁ and λ₂, the center wavelength is calculated as: Center = 2λ₁λ₂ / (λ₁ + λ₂)

Notice this isn't a simple arithmetic average—it's a harmonic-style calculation that accounts for the fact that wavelength and frequency have an inverse relationship.

Bandwidth

Bandwidth is typically specified at the half-power points (sometimes called FWHM for "full width at half maximum"). A "10nm bandpass filter centered at 550nm" means the passband runs approximately from 545nm to 555nm, with the half-power points roughly 10nm apart.

Connecting Transmission to Optical Density

When reading filter diagrams, remember that transmission and optical density are just two ways of expressing the same thing. If a curve shows transmission of 10⁻³ (or 0.1%) at some wavelength, that's OD 3 at that wavelength—meaning the filter blocks 99.9% of light at that wavelength.

This connection matters because OD directly tells you blocking effectiveness. OD 2 means 99% blocked (1% leaks through). OD 3 means 99.9% blocked. OD 4 means 99.99% blocked.

For most machine vision applications, OD 2-3 is adequate blocking. But when you're trying to isolate a narrow emission line against strong background, or when you're working with very sensitive sensors, OD 4 or higher may be necessary.

Context Is Everything

Here's the critical insight: a filter diagram is only meaningful relative to your complete system.

That curve showing transmission versus wavelength tells you what the filter does in isolation. But what actually matters is the product of multiple spectral curves working together:

Your illumination spectrum determines what wavelengths are actually hitting your subject. If you're using a 450nm LED with a tight spectral output, you don't particularly care what your filter does at 600nm—there's no 600nm light in your system to begin with.

Your target's reflectance or emission spectrum determines which wavelengths bounce back (or are emitted) toward your camera. A bandpass filter perfectly matched to your illumination is useless if your target doesn't reflect that wavelength.

Your lens transmission may have its own wavelength dependence, particularly at UV and IR extremes where optical coatings often have reduced performance.

Your sensor's spectral sensitivity weights everything by how efficiently it converts photons to signal at each wavelength. Standard silicon sensors are very IR-sensitive but may have poor UV response; this changes how much various filter "leaks" actually affect your final image.

Angle Effects: The Hidden Variable

One detail that filter diagrams often don't adequately convey: the spectral behavior of interference filters depends on the angle of incidence. Light hitting a filter perpendicular to the surface behaves differently than light hitting at an angle.

In real optical systems, even with well-collimated light, the cone of light accepted by your lens has some angular spread. The effect is usually a shift of the passband toward shorter wavelengths at increasing angles.

For narrow bandpass filters (10nm or less), this angle sensitivity can be significant. If your filter is spec'd at 550nm center wavelength for normal incidence, the effective center wavelength might shift to 545nm for light arriving at 15° off-axis. In telecentric systems or with high-NA lenses, this effect deserves attention during design.

Practical Reading Tips

When evaluating a filter diagram for your application, ask these questions:

What does transmission look like at my target wavelength(s)? Is it high enough to give adequate signal? Is there unwanted absorption that will hurt your light budget?

How strong is the blocking in regions I want to suppress? Look at the OD (or transmission on a log scale) at ambient light wavelengths, at unwanted illumination wavelengths, or at whatever else you're trying to reject.

How sharp are the transitions? Steep cut-on/cut-off edges mean better separation between passed and blocked regions. Gradual transitions might allow unwanted light to leak through.

What happens at wavelengths beyond the diagram? Many filters have unexpected transmission windows in the far-IR or UV that aren't shown on standard diagrams. If your sensor is sensitive in those regions, investigate.

The filter diagram is your window into predicting real-world filter performance. Learning to read it fluently—especially on log scales—is an essential skill for machine vision optical design.

This is part of KUPO's educational series on optical filters for machine vision. Understanding how to interpret filter specifications helps you select the right filter for your application and avoid costly surprises during integration.