Optical sectioning selects signal from a thin depth range of a specimen without physically cutting it. Repeating the measurement at successive focal depths gives a stack of sections from which three-dimensional organization can be reconstructed.

In a scanning confocal microscope, illumination is focused into the specimen and a detection pinhole rejects much of the fluorescence originating away from focus. A thick fluorescent specimen imaged with a wide-open and then a reduced pinhole demonstrates the rejected background; reducing the pinhole also discards useful photons, so section thickness and signal-to-noise ratio must be considered together.^[ref]

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.

Super-resolution microscopy recovers spatial detail beyond the conventional diffraction limit by acquiring information beyond a single ordinary image. Stimulated emission depletion microscopy confines detectable fluorescence with a depletion beam; photoactivated localization microscopy separates emitters in time and estimates each emitter's position before combining the estimates.

The distinction between finding one isolated emitter and resolving many adjacent emitters matters. An isolated point spread function can be localized more precisely than its width if enough photons are collected, but overlapping unknown emitters cannot simply be treated as isolated ones. Label density, photon shot noise and specimen motion therefore constrain the final optical resolution, even when the reconstructed image uses very small pixels.

The spatial height and shape of a surface. In atomic force microscopy, apparent lateral shape also depends on AFM tip convolution and the controller response.

A conducting scanning-probe tip acts as a movable electrostatic gate. Mapping conductance changes as the tip perturbs a quantum point contact or surrounding electron gas probes quantum transport. The image is a response to the tip, not automatically a noninvasive map of the unperturbed local current density.

Imaging with X-rays, combining suitable focusing or image-forming optics with contrast from absorption, phase or emitted signals. Photon-energy selection can make core-edge chemical contrast accessible, while achievable resolution depends on the optics, detector and measurement geometry.

Electrical detection of particles passing through a conducting-liquid aperture. A particle changes the effective pore conductance transiently; pulse amplitude and duration depend on geometry, transport and interfacial charge, so calibration is essential.

Conjugate addition involving a nitroalkene electrophile or a nitronate nucleophile. Identifying which partner supplies the carbon nucleophile is essential for following a tandem reaction.

A sequence in which one conjugate addition generates or exposes a nucleophile for another conjugate addition. Atom mapping distinguishes successive bond-forming steps from a concerted cycloaddition.

Conjugate addition of a thiol-derived sulfur nucleophile to an activated alkene. The sulfur substituent is installed at the beta carbon of an enone, not at its carbonyl carbon.

A conjugate addition followed by intramolecular enolate acylation that closes a ring.

In a sharp-core spherical micelle of aggregation number $n$, incompressible tail volume $v$ per molecule and effective head-group area $a_0$ give $nv=4\pi R^3/3$ and $n{a}_0=4\pi R^2$. Division gives the displayed radius and aggregation number. If the maximum tail extension is $l_c$, the model requires $R\le l_c$, equivalently the amphiphile packing parameter $v/(a_0{l}_c)\le 1/3$. Input dimensions violating that inequality cannot describe an exact spherical filled core without modifying the molecular geometry assumptions.