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Open toolRayleigh Criterion Calculator
Find the ideal circular-aperture Rayleigh angular resolution. Provide Wavelength (m), Circular aperture diameter (m) to compute results directly in your browser. Theta=1.22*wavelength/diameter in radians using small-angle far-field diffraction. Arcseconds also shown; no atmospheric seeing, sensor sampling or real-equipment performance guarantee. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
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Enter the inputs, then select Calculate.
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How the Rayleigh Criterion Calculator Works & Core Formula
The Rayleigh Criterion Calculator evaluates Wavelength (m), Circular aperture diameter (m) in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Find the ideal circular-aperture Rayleigh angular resolution.
Theta=1.22*wavelength/diameter in radians using small-angle far-field diffraction. Arcseconds also shown; no atmospheric seeing, sensor sampling or real-equipment performance guarantee. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
Rayleigh Criterion Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Rayleigh Criterion Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Wavelength (m) | 5e-07 | Range: 1e-30 to 1000000000.0 | Required workspace parameter |
| Input: Circular aperture diameter (m) | 0.1 | Range: 1e-09 to 1000000000.0 | Required workspace parameter |
| Worked Case 1: Baseline run (Wavelength (m) = 5e-07) | Preloaded / test values | Find the ideal circular-aperture Rayleigh angular resolution | Wavelength (m) = 5e-07; Circular aperture diameter (m) = 0.1. The displayed output is Radians: 0.0000061 Arcseconds: 1.25821531811. |
| Worked Case 2: Comparison scenario (rayleigh criterion formula) | Preloaded / test values | Find the ideal circular-aperture Rayleigh angular resolution | Wavelength (m) = 6e-7; Circular aperture diameter (m) = 0.2. The displayed output is Radians: 0.00000366 Arcseconds: 0.754929190864. |
Step-by-Step Guide to Using the Rayleigh Criterion Calculator
Follow these three steps to configure Wavelength (m), Circular aperture diameter (m), verify unit and boundary rules, and export your Rayleigh Criterion Calculator output.
Input and settings
Complete the other inputs
Set circular aperture diameter (m). Use wavelength and circular-aperture diameter under the stated small-angle diffraction approximation.
Tool result
Calculate and read the output
Select Calculate to see the ideal resolution angle in radians and arcseconds. Copy result copies this text; Download saves it as a TXT file.
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Practical Worked Examples for Rayleigh Criterion Calculator
These concrete scenarios illustrate how the Rayleigh Criterion Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Wavelength (m) = 5e-07)
Wavelength (m) = 5e-07; Circular aperture diameter (m) = 0.1. The displayed output is Radians: 0.0000061 Arcseconds: 1.25821531811.
Comparison scenario (rayleigh criterion formula)
Wavelength (m) = 6e-7; Circular aperture diameter (m) = 0.2. The displayed output is Radians: 0.00000366 Arcseconds: 0.754929190864.
Boundary & unit check (Rayleigh Criterion Calculator)
When solving for 'rayleigh criterion calculator', verify that Wavelength (m), Circular aperture diameter (m) use consistent units and stay within the documented scope: Theta=1.22*wavelength/diameter in radians using small-angle far-field diffraction. Arcseconds also shown; no atmospheric seeing, sensor sampling or real-equipment performance guarantee. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
How to Read and Verify the Rayleigh Criterion Calculator Output
The output panel reports the exact result derived from Wavelength (m), Circular aperture diameter (m) alongside any unit or formatting notes.
The result is the ideal resolution angle in radians and arcseconds. Estimate a circular aperture's Rayleigh diffraction angle.
This ideal diffraction limit does not include seeing, sensor sampling or a real instrument's measured performance.
Numerical output shows up to 12 significant digits. Floating-point arithmetic and display rounding can affect the last digits.
- Example input
- Wavelength (m) = 5e-07; Circular aperture diameter (m) = 0.1
- Example output
- Radians: 0.0000061 Arcseconds: 1.25821531811
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Rayleigh Criterion Calculator output.
Operational scope: Theta=1.22*wavelength/diameter in radians using small-angle far-field diffraction. Arcseconds also shown; no atmospheric seeing, sensor sampling or real-equipment performance guarantee. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Rayleigh Criterion Calculator
Answers about using Rayleigh Criterion Calculator and understanding its results.
What formula or rule does the Rayleigh Criterion Calculator use?
The Rayleigh Criterion Calculator applies the rule: Find the ideal circular-aperture Rayleigh angular resolution. Enter Wavelength (m), Circular aperture diameter (m) into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Rayleigh Criterion Calculator?
Yes. Provide Wavelength (m), Circular aperture diameter (m) using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Rayleigh Criterion Calculator?
Theta=1.22*wavelength/diameter in radians using small-angle far-field diffraction. Arcseconds also shown; no atmospheric seeing, sensor sampling or real-equipment performance guarantee. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Rayleigh Criterion Calculator free and does it keep my inputs private?
Yes. All calculations for the Rayleigh Criterion Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
Get the ideal resolution angle in radians and arcseconds
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