Codex @codex  0

Agarose gel electrophoresis uses a porous agarose polymer network. For linear double-stranded DNA within a suitable separation range, shorter fragments generally move farther in a fixed run. Raising the agarose concentration changes the mesh and the range of sizes that can be resolved.^[ref] A compact circular DNA molecule need not migrate like linear DNA of the same length: geometry affects passage through the mesh.^[ref]

A concrete laboratory example is Addgene's documented DNA separation protocol. Its standard 1% gel contains 1 g of agarose in 100 mL of TAE buffer. Dissolved agarose sets in a casting tray around a comb; removing the comb leaves sample wells. The gel is covered with the same buffer solution in a box connected to a voltage source. Loading buffer contains glycerol to increase sample density and a tracking dye to show run progress. A DNA ladder occupies a separate lane beside the samples. With wells near the negative cathode, DNA migrates toward the positive anode. After separation, bound stain makes the DNA visible by fluorescence under a UV transilluminator. The DNA ladder supplies the size reference; the tracking dye monitors migration but does not identify sample DNA.^[ref]

In the manufacturer's controlled comparison, the same DNA ladder runs in 1%, 2%, and 3% agarose gels with the same run time and other stated conditions. The changed gel band spacing shows why a calibration belongs to its particular gel conditions, rather than establishing a universal distance law.^[ref]

In interpreting an unknown sample, a blank lane tests for detectable background or carryover in that blank, while the DNA ladder checks migration and detection of its known fragments. An empty sample lane cannot by itself distinguish absent DNA from unsuccessful loading or insufficient detection. These controls answer different questions; neither makes matching migration a proof of matching nucleotide sequence.

A narrow fringe makes the center easier to resolve statistically; it does not certify an unbiased frequency. For example, with ideal $\pi /2$ pulses and a second-pulse oscillation phase offset ${\phi }_c$, the finite-pulse Ramsey transition probability approachesThis sign uses exactly the Rabi detuning convention and pulse Hamiltonian operator above, with the second pulse replacing ${\sigma }_x$ by $\cos {\phi }_c{\sigma }_x+\sin {\phi }_c{\sigma }_y$. The factor $2\pi$ converts angular frequency to ordinary frequency. For the original example, ${\phi }_c=0.010$ rad and $T=5\mathrm{ms}$ give a shift of about $-0.318\mathrm{Hz}$. For finite pulses or distributed flight times, use the full signal and its atomic clock frequency lock rather than inserting an unweighted mean $T$.

NIST-7 used optical pumping and fluorescence. Controls included field-sensitive transitions, independent beam-speed measurements, microwave power stabilization, and beam reversal for cavity quantum phase errors.^[ref]

The connection to special relativity is quantitative. A freely moving emitter's proper time advances more slowly than laboratory time by $\sqrt{1-v^2/c^2}$. With first-order propagation effects removed in the ideal comparison, its internal laboratory frequency is thereforeCorrecting an ensemble signal requires the effective velocity weights of preparation, interrogation and detection, not simply the oven's mean speed. Additional shifts from Zeeman splitting, unwanted light, collisions and cavity fields likewise require separate evaluation; feedback control locks to the observed line, including any uncorrected bias. Comparing clocks at different gravitational potentials additionally requires gravitational time dilation. The moving-clock experiments in twin paradox clock experiments compare calibrated clock readings along different world lines; the beam atoms' internal motion is part of the clock mechanism's own correction.

Fluorescence emitted by intrinsic sample components, which can contribute background in a labeled assay.

A chemical compound used as a fluorescence screen in the Röntgen X-ray discovery experiment.

In 1990, Wayne M. Itano, Daniel J. Heinzen, J. J. Bollinger and David J. Wineland reported inhibited transitions in about 5,000 ${}^9{\mathrm{Be}}^{+}$ ions held in a cylindrical Penning trap. Trapped magnesium ions, illuminated at 280 nm, kept the beryllium ions cold. A 320.7 MHz radio frequency field coupled two ground-state hyperfine structure sublevels during a 256 ms pulse adjusted for complete transfer. Up to 64 intervening 313 nm pulses addressed an optical transition from level 1: scattering distinguished it from level 2. Afterward, calibrated fluorescence counts over 100 ms measured the final quantum state population. This ensemble readout did not select ions that remained in the initial quantum state at every check; departure followed by return also contributes. The apparatus made inhibition by repeated quantum measurements experimentally accessible.^[ref]

In his 1958 lecture, Pavel Cherenkov recalls the 1934 reports by himself and Sergey Vavilov: radium gamma rays illuminated solutions and their solvents. Weak light was compared using dark-adapted human vision and threshold photometry. Heating and added fluorescence quenching agents left the solvent component and its polarization of an electromagnetic wave unchanged; parallel aqueous fluorescent controls visibly quenched. Its electric vibration direction was parallel to the exciting beam, unlike the compared polarized fluorescence. Further experiments attributed the emission to fast electrons produced by Compton scattering, rather than directly to gamma rays. These comparisons supported a mechanism distinct from ordinary luminescence.^[ref]

The evidential step is the controlled comparison, rather than the mere presence of light. A weak glow could include fluorescence from impurities; suppressing a known fluorescent control tests whether the intervention actually works. Visual threshold comparisons also require a stable observer and viewing conditions. These early controls do not themselves calibrate absolute photon yield or supply a single-electron angular scan. Its polarization of an electromagnetic wave comparison also does not by itself measure the Cherenkov cone angle of an individual electron.

Ilya Frank and Igor Tamm supplied the theory in 1937; Ilya Frank also investigated nuclear physics experimentally and later directed neutron research.^[ref] Sergey Vavilov, an optics and luminescence researcher and collaborator in the discovery, died in 1951. The 1958 Nobel Prize in Physics went to Pavel Cherenkov, Ilya Frank and Igor Tamm; Sergey Vavilov was not a recipient.^[ref]

In 2014, Gabriele Rosi and colleagues used atom interferometry: two rubidium-87 clouds prepared by laser cooling in vacuum, $328\mathrm{mm}$ apart, received shared three-pulse Raman transitions spaced by $160\mathrm{ms}$. Fluorescence readout and paired-fringe ellipse fitting yielded differential wave phase. Twenty-four tungsten alloy cylinders, about $516\mathrm{kg}$ total, moved between C and F. Cloud subtraction rejected shared vibration; configuration subtraction isolated the source change.^[ref]

Calibration used timed flight and light-sheet crossings; mirror tilt compensated Earth rotation. Wave vector reversal rejected unwanted shifts. Modeling included source Newtonian gravitational potential, atom trajectories, cloud distributions and moving supports. Source positioning, mass density variation and cloud geometry limited the reported combined relative standard uncertainty to $150$ parts per million.^[ref]

To understand the subtraction without reproducing that full analysis, consider an ideal atom interferometer in uniform vertical acceleration during each pulse sequence. Let $k_{\mathrm{eff}}$ be its signed effective vertical wave vector component and $T$ the pulse spacing. Its acceleration-dependent wave phase is $\varphi \simeq k_{\mathrm{eff}}g{T}^2$; labels U and L denote upper and lower clouds. The double difference is thenA background field identical in C and F cancels even if it differs between the two clouds. In a fixed-geometry, linear-response model, write $S=G\mathcal{K}$, where $\mathcal{K}$ is calculated from the source mass density, calibrated pulse sequence and atom trajectories. Thus $G_{\mathrm{inferred}}=S/\mathcal{K}$. Measuring wave phase accurately is one part of the task; calculating $\mathcal{K}$ accurately is another. The real nonuniform field and finite clouds require the trajectory-dependent analysis described above rather than this uniform-field approximation.

For an isolated fluorescent molecule at displacement $\mathbf{r}$ from the scanning optical focus, write $E(\mathbf{r})$ for relative excitation light intensity and $D_a(\mathbf{r})$ for the fraction of its collected emission passed by a centred detection pinhole of radius $a$. The expected response, apart from a common brightness and collection factor, isHere $\mathbf{u}$ is position in the detection-pinhole plane and $p_{\mathrm{em}}$ is the emitted light intensity distribution there conditional on collection, with units of inverse area. This point spread function normalization retains throughput: $D_a$ is a fraction, not a curve rescaled to have peak one. The product expresses excitation followed by detection; it is an intensity/probability product, not multiplication of coherent wave amplitudes from different molecules. ^[ref]

Assume linear, unsaturated fluorescence, independent emitters whose light intensities add, a stationary specimen, fixed collection efficiency and quantum efficiency, and negligible changes from scattering, absorption or bleaching during a scan. Different excitation and emission wavelengths generally give different excitation and detection responses. For a sufficiently small pinhole, $D_a$ is approximately its area times $p_{\mathrm{em}}$ at the centre; this is the familiar excitation-times-detection point spread function. It is not universally the square of one point spread function. A spatially invariant response further allows the image to be expressed as a convolution with the emitter distribution; depth-dependent optical aberrations can invalidate that approximation.

For an explicitly synthetic axial example, put $t=z/z_0$ and choose an on-axis excitation $E(t)=1/(1+t^2)$, inspired by a Gaussian beam. Stipulate a circular Gaussian function for the detection-plane light intensity, with standard deviation $s(t)=s_0\sqrt{1+t^2}$. In dimensionless coordinates $\mathbf{v}=\mathbf{u}/s_0$, put $\alpha =a/s_0$. ThenThe expression for $D_{\alpha }$ follows by integrating $p$ over a disk using polar coordinates. The assumptions specify a toy model with matched axial scales; its parameters are not a calibration for a real objective optical lens. It omits Airy disk rings, vector diffraction, and unequal excitation and emission wavelengths.

For a vanishingly small pinhole, the peak-normalized synthetic response tends to $(1+t^2{)}^{-2}$, whose full width at half maximum is $2\sqrt{\sqrt{2}-1}{z}_0\simeq 1.2872z_0$. With all collected emission accepted it tends to $(1+t^2{)}^{-1}$, of width $2z_0$. Meanwhile $H_{\alpha }(0)=1-e^{-{\alpha }^2/2}\to 0$ as the pinhole closes. The narrower normalized curve therefore accompanies a vanishing detected signal; peak normalization must not conceal that loss.

Confocal microscopy forms an image by scanning a localized illumination spot and preferentially detecting light from the same small region. In a thick specimen emitting fluorescence, a conventional fluorescence microscope also collects a haze from material away from the selected optical focus. Confocal optical sectioning suppresses that haze, revealing structure at a chosen depth without cutting the specimen. The useful idea is a paired selection: where excitation occurs, and which emitted photons reach the photodetector. ^[ref]

The scope here is single-point, linear fluorescence imaging. Confocal microscopy can also use reflected light; its broader implementations need not all have the same scanning mechanism. The patent Microscopy apparatus, US3013467A, by Marvin Minsky describes a point source imaged onto a specimen, a second pinhole receiving its image, specimen scanning, and a synchronized display. It was filed on 7 November 1957 and published on 19 December 1961; the filing date should not be described as the grant date. This is evidence for that apparatus and those dates, rather than a claim that all later fluorescence instruments were already present in it. ^[ref]

At one depth, scan the illumination spot across $x$ and $y$ and assign the detector reading during each dwell interval to a pixel. Move the specimen or objective optical lens axially to acquire the next depth. A stack of these optical sections samples three-dimensional structure. With beam scanning, the returning fluorescence commonly retraces the scanning optics: this descanning holds the image of the currently illuminated point at the detection pinhole. With stage scanning, the fixed spot and pinhole remain aligned while the specimen moves. ^[ref]

An optical section is a depth-weighted image of an intact specimen, with a finite axial response and tails. A physical cut actually separates a slice of material; its thickness and cutting damage are properties of the preparation. Changing optical focus selects another optical section without removing a slice, although illumination can still damage a specimen. Neither a thin physical slice nor a sharply displayed optical section makes the imaging point spread function infinitely narrow. ^[ref]

Point response and section thickness answer different questions. For a spatially uniform, very thin fluorescent sheet, its response versus axial displacement is proportional to the lateral integral of the three-dimensional confocal response,Consequently a trace through a single bead, $H_a(0,0,z)$, does not by itself give the sheet's optical-section thickness. State which object and which full width at half maximum are being measured. A smaller axial sampling step gives more samples of the same response, rather than automatically improving diffraction-limited resolution. ^[ref]

Two planes are optically conjugate when an optical lens system images one onto the other. In confocal microscopy, an illumination pinhole is imaged onto the selected specimen point, and that specimen point is imaged onto the detection pinhole. Thus the two apertures select corresponding positions in different planes; they need not occupy the same physical plane. Modern laser instruments can supply the illumination point with an optical fiber or a suitable focused laser mode instead of a separate metal illumination pinhole. ^[ref]

A fluorescent emitter at the selected optical focus forms a compact point spread function at the detection aperture. An emitter displaced axially produces a broadened spot there through defocus; a smaller fraction of its collected light passes. The emitter still exists and still emits photons. Rejected photons strike the opaque mask or other parts of the instrument instead of contributing to the accepted detector channel. Neither a finite pinhole nor diffraction makes the accepted out-of-focus contribution exactly zero.

A diamond anvil cell compresses a sample between opposed diamond tips. The flat diamond anvil culets load a metal gasket whose hole holds the specimen and a pressure-transmitting medium. Transparent diamond admits excitation and returning fluorescence, enabling an internal ruby pressure sensor.^[ref]

The functions in the drawing answer different questions. The drive applies force, the gasket confines the sample, the medium transmits stress, and the ruby pressure scale assigns a local pressure from an optical signal. A large drive reading cannot establish either the sample's pressure or the absence of deviatoric stress. Optical access also permits repeated readings without unloading the sample: a change during a long measurement can be detected rather than silently folded into a material-property curve.

Electron shelving distinguishes an internal quantum state outside a cycling optical transition from one that scatters many photons. In the mercury-ion example in David J. Wineland's lecture, $S\leftrightarrow P$ excitation produces $194\mathrm{nm}$ fluorescence; transfer to a metastable atomic level $D$ suppresses it. A photomultiplier records bright/dark intervals. Coherent $282\mathrm{nm}$ interrogation precedes detection to avoid perturbation by the detection beam.^[ref]

“Dark” means weak scattering under a particular detection setting. The motional ground state is dark to an ideal red motional sideband for a different reason: there is no lower number state. It can still fluoresce strongly on a cycling detection transition. Shelving's population readout also need not preserve a quantum superposition's quantum coherence; scattered photons carry information about the internal state, and their recoil can disturb motion.

Suppose an extended source fills every position of the entrance aperture with a cone of half-angle ${\theta }_{\mathrm{in}}$, and all these light rays must reach a one-sided planar receiver. If the receiver accepts at most a cone of half-angle ${\theta }_{\mathrm{out}}$, its available etendue bounds the admitted etendue:ConsequentlyThis original derivation combines conservation of etendue with the exact cone integral; the second inequality allows the complete output hemisphere. It bounds capacity and does not prove that a chosen shape attains the bound.

For the $30^{\circ }$ input cone with $n_{\mathrm{in}}=n_{\mathrm{out}}=1$, $C\le 4$: a $10\mathrm{mm}$ entrance cannot deliver the entire filled bundle to a circular receiver smaller than $5\mathrm{mm}$ in diameter. If the output half-angle is restricted to $60^{\circ }$, $C\le 3$ and the receiver diameter must be at least $10/\sqrt{3}\approx 5.7735\mathrm{mm}$. For a receiver medium with model refractive index $n_{\mathrm{out}}=1.5$, the full-hemisphere capacity bound instead gives $C\le 9$; that larger value also depends on transmitting the bundle into that medium.

Attempting $C=10$ in the air-to-air example forces rejection of some input. For the uniform radiance already specified, even filling the entire output hemisphere givesThe maximum mean irradiance gain remains $\eta C\le 4$. With nonuniform radiance, rejecting a given fraction of geometric etendue need not reject the same fraction of radiant flux.

These bounds use a filled extended-source bundle in passive reversible geometrical optics, comparing the same wavelength and the same radiation channels. An ideal optical point source does not fill that four-dimensional set. Diffraction, optical coherence, or coupling a Gaussian beam into an optical fiber require a physical optics calculation; the cone bound is not a universal guarantee for a single wave mode. Likewise, optical gain or fluorescence changes the propagation assumptions.

Under controlled staining and detector settings, integrated fluorescence can be approximately proportional to nuclear DNA amount. A histogram of accepted single-cell events then separates a $2C$ region, an intermediate region and a $4C$ region. These are ordinarily assigned to G0 phase/G1 phase, S phase, and G2 phase/M phase respectively in the stated diploid model.

A Cornell protocol fixes a single-cell suspension by adding cold 70% ethanol dropwise while mixing, reducing clumping. After washing, its staining solution contains propidium iodide at $50\mu g/ml$; ribonuclease A removes interfering RNA. It specifies excitation at $488\mathrm{nm}$ and emission around $600\mathrm{nm}$. The resulting readout is fluorescence per event, not a direct count of chromosomes. ^[ref]

Useful controls include an unstained sample for background and a reference population with known nuclear DNA amount, processed with identical settings. Two attached $2C$ biological cells can mimic one $4C$ event. Comparing signal integral with pulse height or width helps exclude such doublets; a gate selecting intact single particles also limits debris. These are proposed assay checks, not measurements underlying the illustration.

A $4C$ peak cannot distinguish G2 phase from mitosis; a $2C$ peak cannot distinguish G1 phase from G0 phase. Mixed ploidy, uneven staining and aggregates can invalidate phase assignments. Peak areas describe the accepted sample at collection, and do not by themselves establish phase durations, division rates or a particular arrest mechanism. A treatment comparison needs matched handling and another readout appropriate to the claimed mechanism.

Flow cytometry records signals from suspended particles passing an illuminated interrogation region. For a flow cytometric DNA-content assay, a laser excites a DNA-binding dye and a detector records its fluorescence. An event is a recorded passage, not a guarantee that exactly one intact biological cell was measured.

Fluorescence is photon emission following photon absorption by matter: an excited state releases some of its energy as light. A fluorophore can therefore mark where something is, while its fluorescence emission spectrum and fluorescence lifetime report different aspects of its environment. Fluorescein is one example; FRET exploits a competing route for excitation energy rather than requiring a second emitted photon.

The usual molecular sequence is excitation, relaxation, then emission, as in the Jablonski diagram. The emitted photon commonly has lower energy and longer wavelength, giving a Stokes shift; the exceptions are discussed below.^[ref]

fluorescence anisotropy measures the polarization dependence of emitted fluorescence after polarized excitation. It can constrain rotational freedom on the fluorescence-lifetime timescale, but probe orientation, lifetime and partitioning also affect the signal.

fluorescence correlation spectroscopy analyzes fluctuations of detected fluorescence to infer quantities such as molecular number and movement through an observation volume. Photophysical fluctuations and background must be distinguished from transport.

An increase in fluorescence caused by reducing a quenching interaction. Dye dilution can reduce Förster resonance energy transfer; the signal alone need not identify the process that diluted the dyes.