Optical resolution

Optical resolution is the ability of an imaging system to distinguish spatially separated features under specified observation conditions. A finite numerical aperture spreads a point object into a point spread function; neighboring point images overlap. A criterion such as the Rayleigh criterion assigns a separation to this overlap rather than marking a sharp universal boundary between visible and invisible detail.^[ref]

A practical test images two small sources at known separations, keeping exposure and display image contrast fixed. Decreasing their separation until the chosen criterion fails measures lateral resolution; moving them along the imaging axis tests axial resolution. Magnification alone cannot narrow the specimen-space point spread function.

For incoherent imaging with an unobstructed circular aperture of diameter $D$, the intensity-image spatial-frequency cutoff is $D/(\lambda f)$ in the focal plane. The Nyquist–Shannon sampling theorem therefore gives the displayed pitch limit. The Rayleigh criterion instead gives a point-image separation $1.22\lambda f/D$. Consequently two samples per Rayleigh separation and sampling the full optical bandwidth differ by the factor $1.22$. Neither sampling estimate guarantees useful contrast at arbitrarily low signal-to-noise ratio.

The resolution scale imposed by a finite-aperture wave-imaging system under a stated criterion. For conventional optical microscopy, a common lateral scale is $\lambda /(2\mathrm{NA})$. Changing the illumination, measured signal or reconstruction assumptions can change the applicable criterion.

Axial resolution describes the ability to distinguish features separated along an imaging system's axis. In optical microscopy, the three-dimensional point spread function is usually longer along that axis than across it, so two layers can overlap even when comparable sideways separations are distinguishable.

A small fluorescent bead moved through focus provides an experimental response curve: record the detected intensity at successive axial positions and measure a stated width, such as its full width at half maximum. The result depends on numerical aperture, wavelength, specimen refractive index and the detection method. Confocal microscopy can reject much of the signal from outside the focal plane, improving optical sectioning.

Lateral resolution describes distinguishable separation in a plane perpendicular to an imaging system's axis. For incoherent point objects imaged through a circular aperture, the Rayleigh criterion gives the specimen-space scale $d\simeq 0.61\lambda /\mathrm{NA}$, where $\lambda$ is the vacuum wavelength and $\mathrm{NA}$ the numerical aperture.^[ref]

For example, $\lambda =550\mathrm{nm}$ and $\mathrm{NA}=1.0$ give $d\simeq 336\mathrm{nm}$ under that criterion. Sampling the image with more pixels can represent this blur more accurately, but cannot by itself distinguish closer features. Comparisons between instruments must specify both the object and the criterion.