Rayleigh Criterion
Definition
The condition that two point sources are just resolved when the central maximum of one Airy disc coincides with the first minimum of the other, giving a minimum resolvable distance r = 0.61 lambda / NA.
- Formula
- r = 0.61 lambda / NA
- Defines
- Minimum resolvable distance between two points
- Condition
- First Airy minimum meets adjacent central maximum
- Depends on
- Wavelength and numerical aperture
Common questions
How does the Rayleigh criterion affect the choice of microscope objective in trace evidence work?+
Because resolution improves with higher numerical aperture and shorter wavelength, an examiner needing to distinguish fine structural detail in a fibre or particle selects a higher-NA objective or shorter-wavelength illumination to push the minimum resolvable distance smaller.
What happens to two point sources closer together than the Rayleigh limit?+
Their diffraction patterns overlap enough that they blur into what appears to be a single feature, so detail below that limit cannot be resolved as two separate points regardless of magnification.
Related terms
- Abbe Diffraction Limit
- The minimum period of a periodic grating structure that can be resolved: d = lambda / (2 NA). Sets the hard optical...
- ASTM E766
- The ASTM International standard practice for image-scale calibration in microscopy, extended by OSAC to govern optical microscope calibration in US forensic trace-evidence...
- Depth of Field
- Axial thickness of the specimen that appears acceptably in focus at one time. High in stereoscopic microscopes, very low in oil-immersion compound...
- Empty Magnification
- Magnification beyond approximately 1000 times the objective NA; enlarges the image without adding resolvable structural information, producing blurred detail that can be...
- Infinity-Corrected Optics
- An objective design in which the back focal plane produces a collimated (afocal) beam rather than a converging beam, allowing optical elements...
- ISO 8576
- The ISO standard governing the accuracy of stage micrometers and reticle eyepieces, specifying Class I and Class II tolerance levels traceable to...
- Koehler Illumination
- The standard illumination method for research microscopy in which the light source is focused at the condenser back focal plane, producing uniform...
- Numerical Aperture (NA)
- The product of the refractive index of the medium between objective and specimen and the sine of the half-angle of the maximum...
- Parfocality
- The property of an objective nosepiece turret such that switching objectives keeps the specimen approximately in focus without re-focusing; defined by ISO...
- Plan Objective
- An objective corrected for field curvature so that the entire image field is simultaneously in focus; required for photomicrographic evidence documentation to...
- Stage Micrometer
- A calibrated glass slide with a ruled scale of known spacing (typically 0.01 mm divisions), used to establish the pixels-per-micrometre calibration factor...