Cut-off Wavelength λc

|Team Syronoptics
The Cut-off Wavelength is the specific spectral wavelength at which the transmission of an optical filter decreases to 50% of its peak value.

It serves as the primary reference point for defining the transition between the filter's Passband (the range where light is transmitted) and its Stopband (the range where light is blocked).

Technical Specifications

  • Symbol: Commonly denoted as λc or λcutoff.
  • Standard Definition: Unless otherwise specified by the manufacturer, λc is strictly defined at the 50% transmission point (T(50%)).
    • Note: While 50% is the industry standard, some custom applications may define the cut-off at the 10% or 5% transmission points for stricter blocking requirements.
  • Role in Shortpass Filters: For a shortpass filter, the Cut-off Wavelength marks the upper limit of the passband.
    • Wavelengths < λc are transmitted.
    • Wavelengths > λc are blocked.

Practical Example: The "650 nm Shortpass" Filter

To understand how this specification works in practice, consider a standard shortpass filter labeled with a Cut-off Wavelength of 650 nm.
Here is how the filter behaves across the spectrum:
  1. In the Passband (e.g., 550 nm Green Light): This wavelength is well below the cut-off. The filter transmits this light efficiently (typically 90–95%transmission).
  2. At the Cut-off (650 nm Red Light): This is the defined transition point. The filter transmits exactly 50% of the light at this specific wavelength.
  3. In the Stopband (e.g., 750 nm Infrared Light): This wavelength is well above the cut-off. The filter blocks this light, resulting in near 0% transmission (often <0.01% or OD4).

Transition Width

Real-world filters do not switch instantly from 100% to 0%. There is a "slope" or transition width. For a 650 nm cut-off filter, the transmission might start dropping at 640 nm (90%) and hit the bottom at 660 nm (near 0%). The 650 nm mark is simply the halfway point of this slope.

Importance in System Design

  • Component Identification: The Cut-off Wavelength is the "name" of the filter. If you order a filter, you order it by this number (e.g., "I need a 500 nm Shortpass").
  • Manufacturing Tolerance: Precision optics always list a tolerance for λc (e.g., λ(c) = 650 nm). This means the actual 50% point could physically land anywhere between 645 nm and 655 nm. Engineers must account for this margin when designing systems that require precise spectral separation, such as laser fluorescence setups.