CALCULATORS / OPTICS, IMAGING AND ILLUMINATION

Diffraction-limited spot screening calculator

Circular-aperture first-zero angular radius, scalar far-field diffraction.

optics-diffraction.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	anglerad	spotRadiusum
	0.0000671	67.1
	0.00005368	53.68

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

spot radius budget67.10 um✓ passes

BASELINE INPUTS

wavelength550 nmdiameter10 mmdistance1 m

CALCULATED

angle0.0000671 rad

spotRadius67.1 um

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Diffraction-limited spot screening
# Scope: Circular-aperture first-zero angular radius, scalar far-field diffraction.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

wavelength = 550 nm
diameter = 10 mm
distance = 1 m

angle := 1.22*wavelength/diameter [rad]
spotRadius := distance*angle [um]

check spot radius budget: spotRadius <= 100 um

scenario alternative: wavelength = 440 nm

Calculated from your source · not saved

Baseline · Baseline

spot radius budget67.10 um ✓ passes

alternative · alternative

spot radius budget53.68 um ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

angle: angle = 1.22*wavelength/diameter [rad]
spot radius: spotRadius = distance*angle [um]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

wavelength: 550 nm
diameter: 10 mm
distance: 1 m

Calculated

angle: 0.0000671 rad
spot radius: 67.1 um

Assumptions and limits

Circular-aperture first-zero angular radius, scalar far-field diffraction.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Diffraction-limited spot screening. Inputs: wavelength; aperture; focal length. Outputs: Airy size; nominal resolution. Model scope: Paraxial geometry or calibrated radiometric/photometric models. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: wavelength, aperture, focal length
Outputs: Airy size, nominal resolution
Modes: calculate, compare, sweep
Drawing: Ray diagram and camera view

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS