A beam expander is a small telescope used backwards: it widens a laser beam and, in exchange, reduces its divergence. Expanded beams can be focused to smaller spots and travel farther without spreading.
How to use the Laser Beam Expander Calculator
- Design
- Input (image) lens focal length |f_I|
- Output (objective) lens focal length f_O
- Input beam diameter
- Input divergence (mrad)
- Distance from the expander
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the design. Keplerian expanders use two positive lenses (with an internal focus); Galilean ones use a negative input lens and are shorter. Enter the input beam and the distance to evaluate.
Inputs explained
| Field | What to enter |
|---|---|
| Design | Choose one: Keplerian, Galilean |
| Input (image) lens focal length |f_I| | Units: mm, cm, m, in, µm |
| Output (objective) lens focal length f_O | Units: mm, cm, m, in, µm |
| Input beam diameter | Units: mm, cm, m, in, µm |
| Input divergence (mrad) | A number |
| Distance from the expander | Units: m, cm, mm, km, in, ft … |
What each result means
- Magnification = [Output (objective) lens focal length f_O]÷[Input (image) lens focal length |f_I|]
- Output diameter = [Magnification]×[Input beam diameter]
- Output divergence = [Input divergence (mrad)]÷[Magnification]
- Diameter at distance L = [Magnification]×[Input beam diameter] + [Distance from the expander]×[Input divergence (mrad)]÷[Magnification]÷1000
Example values
How the main result changes when Input changes and everything else stays at the example values above:
| Input (image) lens focal length |f_I| (mm) | Magnification (×) |
|---|---|
| 12.5 | 8 |
| 18.75 | 5.3333 |
| 25 | 4 |
| 31.25 | 3.2 |
| 37.5 | 2.6667 |
| 50 | 2 |
Formula
M = |f_O / f_I|, D_O = M·D_I, Θ_O = Θ_I / M, D_L = D_O + L·Θ_O
Worked example
Inputs — Design: Keplerian; Input (image) lens focal length |f_I|: 25 mm; Output (objective) lens focal length f_O: 100 mm; Input beam diameter: 1 mm; Input divergence (mrad): 1; Distance from the expander: 10 m.
Results — Magnification = 4 ×; Output diameter = 4 mm; Output divergence = 0.25 mrad; Diameter at distance L = 6.5 mm; Lens separation = 125 mm.
Key terms
- Beam expander
- An afocal telescope that enlarges a beam.
Frequently asked questions
Why expand a laser beam?
To reduce divergence and allow a smaller focused spot.
Keplerian or Galilean?
Galilean is shorter and has no internal focus (better for high power).
Does the expander change the laser power?
No, apart from small lens losses.
What is the lens spacing?
The sum (Keplerian) or difference (Galilean) of the focal lengths.