Choose a model, enter values with units, then calculate. For best accuracy, keep optical parameters consistent with your setup.
Airy disk (aperture) gives the radius to the first minimum: r = 1.22 · λ · f / D. Here, λ is wavelength, f focal length, and D aperture diameter.
Airy disk (NA) expresses the same limit using numerical aperture: r = 0.61 · λ / NA and d = 1.22 · λ / NA.
Gaussian focus (1/e² radius) estimates: w₀ = (M² · λ · f) / (π · wL), where wL is the beam radius at the lens.
- Select a model that matches your known optical parameters.
- Enter the wavelength and choose its unit.
- Fill in the required fields for your selected model.
- Pick an output unit to match your reporting needs.
- Press Calculate to view results above the form.
- Use the export buttons to save your latest calculation.
| Scenario | Inputs | Model | Typical Output (Diameter) |
|---|---|---|---|
| Green laser, modest lens | λ=532 nm, f=50 mm, D=10 mm | Airy (aperture) | ≈ 6.49 µm |
| Microscope objective | λ=550 nm, NA=0.65 | Airy (NA) | ≈ 1.03 µm |
| Beam-limited focusing | λ=1064 nm, f=100 mm, beam=5 mm, M²=1.2 | Gaussian | ≈ 16.26 µm |
Example outputs are illustrative and depend on real alignment and aberrations.
1) Diffraction-Limited Spot Size in Context
When a beam is focused, diffraction sets a lower bound on how tightly energy can be concentrated. For a circular pupil, the focal pattern is an Airy distribution with a bright core and rings. This calculator estimates spot size using wavelength, aperture geometry, numerical aperture, or Gaussian beam parameters.
2) Why the Limit Matters in Real Systems
Spot size affects intensity, resolution, and coupling efficiency. In laser micromachining, a smaller diameter increases peak fluence and can lower ablation thresholds. In microscopy, lateral resolution scales with wavelength and NA, so raising NA usually improves detail more effectively than increasing magnification.
3) Inputs That Control the Result
The most influential inputs are wavelength and effective focusing strength. Shorter wavelengths shrink the spot linearly. For lens-based focusing, increasing clear aperture or reducing focal length reduces the Airy radius. For objective lenses, NA summarizes acceptance angle and refractive effects and is the preferred parameter.
4) Airy Disk Using Aperture Geometry
With focal length f and aperture diameter D, the first-minimum radius is r = 1.22·λ·f/D. As a benchmark, λ=532 nm, f=50 mm, D=10 mm yields a diameter near 6.49 µm. This is a diffraction-only estimate; aberrations, clipping, and misfocus can enlarge it.
5) NA-Based Airy Estimate
For imaging optics, r = 0.61·λ/NA is commonly used. Using λ=550 nm and NA=0.65 gives a diameter around 1.03 µm. High-NA oil immersion objectives can exceed NA≈1.3, while many fiber collimators and small lenses sit near NA≈0.1–0.3.
6) Gaussian Beam Focusing and M²
Many lasers are closer to Gaussian beams than hard-aperture pupils. For a beam of radius wL at the lens, the focused 1/e² radius is w₀ = (M²·λ·f)/(π·wL). An M² of 1.5 increases the waist by 50% versus an ideal beam, so measuring beam diameter and quality is critical for power density predictions.
7) Practical Benchmarks and Reporting
Visible wavelengths (450–650 nm) generally support smaller spots than infrared (1064 nm or 1550 nm) at the same NA. Reporting a spot diameter alone can be ambiguous, so this tool also shows radius and an approximate spot area. Use the export buttons to capture parameters and results for lab notebooks and test reports.
8) Common Pitfalls and How to Avoid Them
Diffraction-limited does not mean system-limited. Spherical aberration, imperfect focus, beam clipping, and dirty optics often dominate. Ensure the input diameter corresponds to the effective illuminated aperture, confirm wavelength in the medium of interest, and keep unit selections consistent to prevent scaling errors.
1) What does “spot radius to first minimum” mean?
It is the Airy-core radius from the center to the first dark ring for a circular aperture. It is a common diffraction metric and differs from Gaussian 1/e² radius or FWHM definitions.
2) Should I use the aperture method or NA method?
Use aperture inputs when you know focal length and clear diameter. Use NA when your optic is specified by NA (objectives, condensers) or when the system geometry is not easily reduced to f and D.
3) Why do Airy and Gaussian results differ?
Airy assumes a uniformly filled circular pupil. Gaussian focusing assumes a Gaussian field profile at the lens. Real systems can fall between these limits, especially when the beam under-fills or over-fills the aperture.
4) What is M² and why does it matter?
M² measures how close a beam is to an ideal Gaussian. Values greater than 1 indicate higher divergence and larger achievable waists. In the Gaussian model, spot size scales directly with M².
5) Can I treat the computed value as the real focused spot?
Treat it as the best-case diffraction estimate. Aberrations, alignment, thermal lensing, and surface contamination often enlarge the spot. Verify with a beam profiler, knife-edge scan, or imaging method when possible.
6) What wavelength should I enter for materials or immersion optics?
Use the wavelength relevant to your focusing medium and application. If refractive index changes are significant, base calculations on the wavelength in the medium or use NA values specified for that immersion condition.
7) Which spot definition is best for intensity calculations?
For Gaussian beams, 1/e² radius is standard for peak intensity and area estimates. For Airy patterns, specify the definition used (first minimum or FWHM) so comparisons remain consistent across reports.