Calculator Inputs
Plotly Graph
This graph shows how Airy disk diameter changes as wavelength changes while your numerical aperture stays fixed.
Formula Used
Airy disk radius: r = 0.61λ / NA
Airy disk diameter: d = 1.22λ / NA
Rayleigh diameter using aperture and focal length: d = 1.22λf / D
Gaussian beam waist approximation: w₀ ≈ (2M²λf#) / π
Depth of focus: DOF = 2nλ / NA²
Here, λ is wavelength, NA is numerical aperture, f is focal length, D is aperture diameter, n is refractive index, and M² is beam quality. These equations help estimate the smallest achievable focused spot under diffraction-limited or near-diffraction-limited conditions.
How to Use This Calculator
- Enter the wavelength and choose its unit.
- Provide the numerical aperture of the optical system.
- Enter aperture diameter and focal length for cross-check calculations.
- Set refractive index and beam quality if needed.
- Press the calculate button to display results above the form.
- Review the graph, then export the results as CSV or PDF.
Example Data Table
| Case | Wavelength | NA | Focal Length | Aperture | Estimated Airy Diameter |
|---|---|---|---|---|---|
| Green laser objective | 532 nm | 0.25 | 50 mm | 8 mm | 2.596 µm |
| Red diode system | 650 nm | 0.40 | 35 mm | 6 mm | 1.983 µm |
| Blue microscope path | 450 nm | 0.80 | 20 mm | 5 mm | 0.686 µm |
Frequently Asked Questions
1. What is diffraction limited spot size?
It is the smallest optical focus size set by wave physics, not lens perfection alone. Even ideal lenses cannot focus light into a point smaller than the diffraction limit.
2. Why does numerical aperture matter so much?
A larger numerical aperture captures and focuses light at steeper angles. That reduces the Airy disk size and improves spatial resolution in imaging and laser focusing systems.
3. Does shorter wavelength always reduce spot size?
Yes, if other factors stay constant. Shorter wavelengths lower the diffraction limit, so blue light generally reaches a smaller focused spot than red light under the same NA.
4. What is the difference between Airy diameter and Gaussian waist?
Airy diameter comes from circular aperture diffraction theory. Gaussian waist describes beam focusing in Gaussian beam optics. They are related but describe different beam models and measurement conventions.
5. Why include focal length and aperture diameter?
They allow a Rayleigh-style estimate through f-number and aperture geometry. This gives a practical cross-check when NA is derived from the lens layout instead of directly specified.
6. What does beam quality M² change?
M² shows how closely a real beam matches an ideal Gaussian beam. Values above one indicate poorer beam quality, which increases the achievable focused waist.
7. Can this calculator help in microscopy and laser systems?
Yes. It is useful for microscopy, fiber coupling, photonics labs, laser machining, and imaging design where spot size, depth of focus, and wavelength tradeoffs matter.
8. Are these values exact experimental results?
No. They are theoretical or near-theoretical estimates. Real performance also depends on aberrations, alignment, truncation, coatings, beam shape, and measurement method.