Angular Resolution Calculator

Calculate the angular resolution of optical instruments using the Rayleigh criterion

Calculate Angular Resolution

Light wavelength (Green)

Lens or mirror diameter

Quick Wavelength Presets:

Calculation Results

27.681
Angular Resolution (arcsec)
7.689e-3
Angular Resolution (deg)
0.461
arcmin
0.134
mrad
134.2
μrad
1.342e-4
rad

Rayleigh Criterion: θ = 1.22 × λ / d

• θ = 1.22 × 5.50e-7 / 5.00e-3 = 1.342e-4 rad

Linear Resolution at Distance

At 1 meter: 0.134 mm
At 1 kilometer: 0.134 m

Example Calculation

Human Eye vs Hubble Telescope

Human Eye: d = 2 mm, λ = 550 nm (green light)

Hubble Telescope: d = 2.4 m, λ = 550 nm

Solution

Human Eye: θ = 1.22 × 550×10⁻⁹ / 0.002 = 3.355×10⁻⁴ rad ≈ 69 arcsec

Hubble: θ = 1.22 × 550×10⁻⁹ / 2.4 = 2.796×10⁻⁷ rad ≈ 0.058 arcsec

Improvement: Hubble is ~1200 times better than human eye!

Angular Resolution Concepts

Rayleigh Criterion:
Two sources are just resolved when the central maximum of one coincides with the first minimum of the other
Diffraction Limit:
Fundamental physical limit due to wave nature of light
Aperture Size:
Larger apertures provide better resolution
Wavelength Effect:
Shorter wavelengths give better resolution

Typical Angular Resolutions

👁️
Human Eye
~1 arcmin (60 arcsec)
🔭
Amateur Telescope (8")
~0.6 arcsec
🛰️
Hubble Space Telescope
~0.05 arcsec
🔬
Optical Microscope
~0.2 μm linear
📷
Camera Lens
Limited by pixel size

Understanding Angular Resolution

What is Angular Resolution?

Angular resolution is the ability of an optical instrument to distinguish small details or separate two objects that appear close together. It represents the smallest angle between two point sources that can be resolved as separate objects.

Rayleigh Criterion

  • θ = 1.22λ/d - Basic Rayleigh formula
  • Based on diffraction through circular aperture
  • First minimum coincides with central maximum
  • Fundamental limit due to wave nature of light

Applications

θ = 1.22λ/d

  • θ: Angular resolution (radians)
  • λ: Wavelength of light (meters)
  • d: Aperture diameter (meters)
  • 1.22: Constant for circular aperture

Key Insight: Larger apertures and shorter wavelengths provide better (smaller) angular resolution.

Practical Notes:
• 1 arcsec = 1/3600 degree
• Atmospheric seeing limits ground telescopes to ~1 arcsec
• Space telescopes achieve diffraction-limited performance