Total internal reflection microscopy is a specialized optical imaging technique for object tracking and detection utilizing the light scattered from an evanescent field in the vicinity of a dielectric interface. Its advantages are a high signal-to-noise ratio and a high spatial resolution in the vertical dimension.
Total internal reflection of light occurs at the interface between materials of differing indices of refraction at incident angles greater than the critical angle, , where
and is the index of the incident medium and the index of the transmission medium and is measured from the normal to the interface.
Under conditions of total internal reflection, the electromagnetic field in the transmission medium takes on the form of an evanescent wave, whose intensity decays exponentially with distance from the interface such that,
with . For practical purposes, the transmission medium is often chosen to be a fluid—usually water—in which a microscopic object can be immersed. The object, when brought close to the interface, is expected to scatter light proportional to the intensity of the field at its height, . [1] Since the penetration depth of the evanescent field is on the order of hundreds of nanometers, this technique is among the most sensitive for tracking displacements in the direction perpendicular to a surface. [2]
The thin excitation region of an evanescent field allows for wide-field imaging of a select sample area with high signal-to-noise ratio. Rather than relying on optical scattering, however, often fluorophores are introduced into the sample for more selective visualization in biological applications. This popular imaging technique is known as a Total internal reflection fluorescence microscopy.
Using a calibrated evanescent wave, [1] the position of a colloidal particle or microscopic probe may be tracked with nanometer precision by monitoring the intensity of light scattered via frustrated total internal reflection. Detailed dynamics of the probe or particle can then be obtained, either in thermal equilibrium or non-equilibrium conditions.
For instance, by collecting the time-independent position probability distribution of a probe particle in thermal equilibrium, and inverting the Maxwell–Boltzmann distribution,
where is the partition function, and the Boltzmann constant, one can obtain the potential energy profile of interactions between the particle and a surface. [3] In this manner, sub-picoNewton forces may be detected. [4]
On the other hand, diffusive dynamics of a cell or a colloid can be deduced from its position time-series obtained via TIRM or another particle-tracking method. Hydrodynamic coupling effects resulting in a particle's reduced diffusion in the vicinity of a solid interface have been studied in this way. [5]
In physics, the cross section is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Diffraction is the same physical effect as interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed.
The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.
In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig. 1).
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.
In particle physics, bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.
In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source. Even when there is a propagating electromagnetic wave produced, one can still identify as an evanescent field the component of the electric or magnetic field that cannot be attributed to the propagating wave observed at a distance of many wavelengths.
In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.
A total internal reflection fluorescence microscope (TIRFM) is a type of microscope with which a thin region of a specimen, usually less than 200 nanometers can be observed.
In physical chemistry, the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory explains the aggregation and kinetic stability of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium. It combines the effects of the van der Waals attraction and the electrostatic repulsion due to the so-called double layer of counterions. The electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential energy of an elementary charge on the surface is much smaller than the thermal energy scale, . For two spheres of radius each having a charge separated by a center-to-center distance in a fluid of dielectric constant containing a concentration of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa potential,
The contact angle is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the surface tangent on the liquid–vapor interface and the tangent on the solid–liquid interface at their intersection. It quantifies the wettability of a solid surface by a liquid via the Young equation.
Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative transfer describes these interactions mathematically. Equations of radiative transfer have application in a wide variety of subjects including optics, astrophysics, atmospheric science, and remote sensing. Analytic solutions to the radiative transfer equation (RTE) exist for simple cases but for more realistic media, with complex multiple scattering effects, numerical methods are required. The present article is largely focused on the condition of radiative equilibrium.
Second-harmonic generation (SHG), also known as frequency doubling, is the lowest-order wave-wave nonlinear interaction that occurs in various systems, including optical, radio, atmospheric, and magnetohydrodynamic systems. As a prototype behavior of waves, SHG is widely used, for example, in doubling laser frequencies. SHG was initially discovered as a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of the initial photons, that conserves the coherence of the excitation. It is a special case of sum-frequency generation (2 photons), and more generally of harmonic generation.
The Goos–Hänchen effect (named after Hermann Fritz Gustav Goos and Hilda Hänchen is an optical phenomenon in which linearly polarized light undergoes a small lateral shift when totally internally reflected. The shift is perpendicular to the direction of propagation in the plane containing the incident and reflected beams. This effect is the linear-polarization analog of the Imbert–Fedorov effect.
Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A2, can be calculated.
Surface second harmonic generation is a method for probing interfaces in atomic and molecular systems. In second harmonic generation (SHG), the light frequency is doubled, essentially converting two photons of the original beam of energy E into a single photon of energy 2E as it interacts with noncentrosymmetric media. Surface second harmonic generation is a special case of SHG where the second beam is generated because of a break of symmetry caused by an interface. Since centrosymmetric symmetry in centrosymmetric media is only disrupted in the first atomic or molecular layer of a system, properties of the second harmonic signal then provide information about the surface atomic or molecular layers only. Surface SHG is possible even for materials which do not exhibit SHG in the bulk. Although in many situations the dominant second harmonic signal arises from the broken symmetry at the surface, the signal in fact always has contributions from both the surface and bulk. Thus, the most sensitive experiments typically involve modification of a surface and study of the subsequent modification of the harmonic generation properties.
Electrophoretic light scattering is based on dynamic light scattering. The frequency shift or phase shift of an incident laser beam depends on the dispersed particles mobility. With dynamic light scattering, Brownian motion causes particle motion. With electrophoretic light scattering, oscillating electric field performs this function.
Diffusiophoresis is the spontaneous motion of colloidal particles or molecules in a fluid, induced by a concentration gradient of a different substance. In other words, it is motion of one species, A, in response to a concentration gradient in another species, B. Typically, A is colloidal particles which are in aqueous solution in which B is a dissolved salt such as sodium chloride, and so the particles of A are much larger than the ions of B. But both A and B could be polymer molecules, and B could be a small molecule. For example, concentration gradients in ethanol solutions in water move 1 μm diameter colloidal particles with diffusiophoretic velocities of order 0.1 to 1 μm/s, the movement is towards regions of the solution with lower ethanol concentration. Both species A and B will typically be diffusing but diffusiophoresis is distinct from simple diffusion: in simple diffusion a species A moves down a gradient in its own concentration.
Surface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal and electromagnetic waves in the air or dielectric ("polariton").
