Diffraction-limited spot size
Know the smallest spot your optics can focus: the Airy disk measures 2.44 × wavelength × f-number, so light of 5.5 × 10⁻⁷ m at f/2 gives a core 0.000002684 m across and 0.000001342 m in radius. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Wavelength
- 0.00000055
- F number
- 2
- Spot diameter
- 0.000002684
- Spot radius
- 0.000001342
- Airy factor
- 2.44
When a circular lens or objective focuses monochromatic light, wave diffraction sets a hard lower bound on how small the central bright core can be. That core is the Airy disk: a bright central lobe surrounded by faint rings. The diameter of the central disk, measured from the first dark ring on one side to the first dark ring on the other, is given by the classic relation d equals 2.44 times wavelength times the working f-number. This diffraction-limited spot size calculator takes wavelength and f-number, returns that diameter and the matching first-null radius, and runs as pure deterministic arithmetic with no network and no model tokens.
How the Airy disk sets the diffraction-limited spot diameter
A circular aperture of diameter D focusing light of wavelength lambda produces a far-field intensity pattern whose first zero of the circular diffraction integral lies at an angular radius of about 1.22 lambda over D from the optical axis. In the focal plane of a system whose working f-number is N equals f over D, that angular radius maps to a linear radius r equals 1.22 lambda N, so the full first-null diameter is d equals 2.44 lambda N.
The factor 2.44 is twice the classic 1.22 Airy radius coefficient for a uniformly illuminated circular pupil in air; it is the textbook value used for quick diffraction-limited spot estimates in photography, microscopy, laser focusing, and telescope design. Longer wavelengths or slower (larger) f-numbers enlarge the spot; shorter wavelengths or faster optics shrink it. This capability evaluates only that closed-form Airy diameter and radius from wavelength and f-number.
It does not integrate the full Bessel intensity envelope, does not treat rectangular slits or single-slit minima, does not convert f-number to numerical aperture, and does not include aberration, beam quality factor M-squared, or sensor pixel sampling. Both inputs must be finite and strictly positive; wavelength carries the length unit of the returned spot sizes while f-number is dimensionless.
Where diffraction-limited spot size calculators show up in real work
Laser process engineers estimate the smallest focused core they can claim before specifying beam expanders, focusing optics, and pulse energy, and the Airy diameter from wavelength and f-number is the first-order diffraction floor for a circular pupil. Camera, microscope, and telescope designers compare that diameter to pixel pitch or sensor sampling to see whether the system is diffraction limited or sampling limited at a design wavelength.
University optics courses assign endless problems that ask for the Airy disk diameter or the Rayleigh-related first-null radius from lambda and f-stop; a single trusted oracle that returns both lengths speeds grading and demo setup. If you later need f-number from focal length and aperture diameter, numerical aperture conversions, single-slit diffraction minima, or thin-lens image distance, treat those as separate search intents and landings rather than overloading this diffraction-limited spot size page.
What you can do with it
Laser focus and micromachining estimates
Compute the Airy first-null spot diameter from laser wavelength and focusing f-number before sizing optics and claiming a diffraction-limited process floor.
Homework and lab answer keys
Return deterministic Airy diameter and radius from textbook wavelength and f-stop so teachers and auto-graders share one ground truth.
FAQ
What formula does this diffraction-limited spot size calculator use?
Spot lengths use the same unit as λ.
Is this the same as the Rayleigh criterion?
Related but not identical. Rayleigh angular resolution is about 1.22 λ/D between two points. This tool reports the Airy disk diameter 2.44 λ N (first dark ring to first dark ring) and the matching radius for a single focused spot.
What does it cost?
The browser tool is free and runs locally.
Which unit should I use for the wavelength?
Any length unit you like. The spot diameter and radius come back in that same unit, while the f-number has no unit. Enter metres and you get metres; enter nanometres and you get nanometres.
Does the spot size include lens aberrations or pixel size?
No. It is the pure diffraction floor for a circular aperture. Aberrations, beam quality and sensor pixels are not included, but you can compare the diameter with your pixel pitch to see which one limits sharpness.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/optics/diffraction-limited-spot-size \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"wavelength":5.5e-7,"f_number":2}'const res = await fetch("https://api.kit.forhosting.com/optics/diffraction-limited-spot-size", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"wavelength": 5.5e-7,
"f_number": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/diffraction-limited-spot-size",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"wavelength": 5.5e-7,
"f_number": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/diffraction-limited-spot-size", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"wavelength":5.5e-7,"f_number":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"wavelength":5.5e-7,"f_number":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/diffraction-limited-spot-size", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"wavelength": 5.5e-7,
"f_number": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.diffraction_limited_spot_size",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How the Airy disk sets the diffraction-limited spot diameter
The pipeline is pure floating-point arithmetic with no network, no random seeds, and no wall-clock timestamps, so identical lambda and N always produce identical JSON.
What you send and what you get back
Both fields are required. Wire the free browser form for homework and lab demos, then call the identical contract from scripts when you need bulk design tables. Send two numbers under the fields wavelength and f_number. wavelength is lambda in any length unit you prefer for the answer, and f_number is the working relative aperture N equals f over D. Aliases such as lambda, wave_length, or wl for the wavelength, and fnumber, f_stop, fstop, N, fn, f_num, or aperture_number for the f-number are accepted so scripts written against common textbook notation do not need a rename layer. Missing fields, non-numeric strings, NaN, Infinity, zero or negative wavelength, and zero or negative f-number fail with invalid_input and are not charged. On success the response echoes cleaned wavelength and f_number, returns spot_diameter equal to 2.44 times lambda times N, returns spot_radius equal to 1.22 times lambda times N, includes airy_factor 2.44, adds a short formula string d equals 2.44 lambda N, and a unit_note reminding you that spot lengths match the wavelength unit. Classic checks include five hundred fifty nanometres written as five point five times ten to the minus seven metres at f-number two, giving a micrometre-scale spot diameter; a helium-neon wavelength six hundred thirty two point eight nanometres at f-number eight for a slower optic; and a zero or negative f-number as the mandatory invalid_input path. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where diffraction-limited spot size calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Camera and telescope resolution sketches
Compare d = 2.44·λ·N to pixel pitch or sampling criteria to see whether a design is diffraction limited at a chosen wavelength.
Technical questions
What units should I use for wavelength?
Any consistent length unit (metres, nanometres, micrometres). The returned spot_diameter and spot_radius are in that same unit. Example: λ = 5.5e-7 m and N = 2 yields d in metres.
What happens if f-number or wavelength is zero or negative?
The request fails with invalid_input. Both wavelength and f_number must be finite and strictly positive; validation failures are not charged.