Is it possible to identify this microscopic particle?

Is it possible to identify this microscopic particle?

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So I was playing amateur scientist with my 11 year old.

This photograph is from rainwater in a bird-feeding bowl in south England, at 300x.

It looks biological, but I have no idea what this is. Is it possible to know, beyond speculation, what this item is?

This is an plain old ice crystal. Welcome to the microscopic world! When water evaporates, high-energy molecules escape, leaving low-energy molecules of water. The droplets cool this way, and they freeze - the dirt or debris in the crystallizing droplets make curious patterns. Here are some in my samples I made last week, for comparison:

How about a close-up?

Here's one I made by accident, this time featuring a fluorescent dye.

Notice how cooling droplets never freeze the same way twice. You'll never find two identical crystallized droplets!

If you want to avoid these, prevent evaporation by putting nail polish or glycerol around and between your coverslip and slide, so that water cannot escape.

OFFTOPIC: You should also encourage your kid to try make some of his/her own crystals. You can use food dyes to make beautifully patterned art. Good moment to teach your kid about nucleation; why water doesn't freeze at 0° C, but rather at temperatures that tend to decrease as the volume of the water decreases and as the water impurity increases. And maybe sneak in a funfact about how the freezing of small water droplets into ice is an important process in cloud formation.

Is it possible to identify this microscopic particle? - Biology

The absorption and subsequent re-radiation of light by organic and inorganic specimens is typically the result of well-established physical phenomena described as being either fluorescence or phosphorescence. The emission of light through the fluorescence process is nearly simultaneous with the absorption of the excitation light due to a relatively short time delay between photon absorption and emission, ranging usually less than a microsecond in duration. When emission persists longer after the excitation light has been extinguished, the phenomenon is referred to as phosphorescence.

Figure 1 - Epi-Fluorescence Microscope

British scientist Sir George G. Stokes first described fluorescence in 1852 and was responsible for coining the term when he observed that the mineral fluorspar emitted red light when it was illuminated by ultraviolet excitation. Stokes noted that fluorescence emission always occurred at a longer wavelength than that of the excitation light. Early investigations in the 19th century showed that many specimens (including minerals, crystals, resins, crude drugs, butter, chlorophyll, vitamins, and inorganic compounds) fluoresce when irradiated with ultraviolet light. However, it was not until the 1930s that the use of fluorochromes was initiated in biological investigations to stain tissue components, bacteria, and other pathogens. Several of these stains were highly specific and stimulated the development of the fluorescence microscope.

The technique of fluorescence microscopy has become an essential tool in biology and the biomedical sciences, as well as in materials science due to attributes that are not readily available in other contrast modes with traditional optical microscopy. The application of an array of fluorochromes has made it possible to identify cells and sub-microscopic cellular components with a high degree of specificity amid non-fluorescing material. In fact, the fluorescence microscope is capable of revealing the presence of a single molecule. Through the use of multiple fluorescence labeling, different probes can simultaneously identify several target molecules simultaneously. Although the fluorescence microscope cannot provide spatial resolution below the diffraction limit of specific specimen features, the detection of fluorescing molecules below such limits is readily achieved.

A variety of specimens exhibit autofluorescence (without the application of fluorochromes) when they are irradiated, a phenomenon that has been thoroughly exploited in the fields of botany, petrology, and the semiconductor industry. In contrast, the study of animal tissues and pathogens is often complicated with either extremely faint or bright, nonspecific autofluorescence. Of far greater value for the latter studies are added fluorochromes (also termed fluorophores), which are excited by specific wavelengths of irradiating light and emit light of defined and useful intensity. Fluorochromes are stains that attach themselves to visible or sub-visible structures, are often highly specific in their attachment targeting, and have a significant quantum yield (the ratio of photon absorption to emission). The widespread growth in the utilization of fluorescence microscopy is closely linked to the development of new synthetic and naturally occurring fluorophores with known intensity profiles of excitation and emission, along with well-understood biological targets.

Fundamentals of Excitation and Emission

The basic function of a fluorescence microscope is to irradiate the specimen with a desired and specific band of wavelengths, and then to separate the much weaker emitted fluorescence from the excitation light. In a properly configured microscope, only the emission light should reach the eye or detector so that the resulting fluorescent structures are superimposed with high contrast against a very dark (or black) background. The limits of detection are generally governed by the darkness of the background, and the excitation light is typically several hundred thousand to a million times brighter than the emitted fluorescence.

Illustrated in Figure 1 is a cutaway diagram of a modern epi-fluorescence microscope equipped for both transmitted and reflected fluorescence microscopy. The vertical illuminator in the center of the diagram has the light source positioned at one end (labeled the episcopic lamphouse) and the filter cube turret at the other. The design consists of a basic reflected light microscope in which the wavelength of the reflected light is longer than that of the excitation. Johan S. Ploem is credited with the development of the vertical illuminator for reflected light fluorescence microscopy. In a fluorescence vertical illuminator, light of a specific wavelength (or defined band of wavelengths), often in the ultraviolet, blue or green regions of the visible spectrum, is produced by passing multispectral light from an arc-discharge lamp or other source through a wavelength selective excitation filter. Wavelengths passed by the excitation filter reflect from the surface of a dichromatic (also termed a dichroic) mirror or beamsplitter, through the microscope objective to bath the specimen with intense light. If the specimen fluoresces, the emission light gathered by the objective passes back through the dichromatic mirror and is subsequently filtered by a barrier (or emission) filter, which blocks the unwanted excitation wavelengths. It is important to note that fluorescence is the only mode in optical microscopy where the specimen, subsequent to excitation, produces its own light. The emitted light re-radiates spherically in all directions, regardless of the excitation light source direction.

Epi-fluorescence illumination is the overwhelming choice of techniques in modern microscopy, and the reflected light vertical illuminator is interposed between the observation viewing tubes and the nosepiece housing the objectives. The illuminator is designed to direct light onto the specimen by first passing the excitation light through the microscope objective (which in this configuration, acts as a condenser) on the way toward the specimen, and then using that same objective to capture the emitted fluorescence. This type of illuminator has several advantages. The fluorescence microscope objective serves first as a well-corrected condenser and secondly as the image-forming light gatherer. Being a single component, the objective/condenser is always in perfect alignment. A majority of the excitation light reaching the specimen passes through without interaction and travels away from the objective, and the illuminated area is restricted to that which is observed through the eyepieces (in most cases). Unlike the situation in some contrast enhancing techniques, the full numerical aperture of the objective is available when the microscope is properly configured for Köhler illumination. Finally, it is possible to combine with or alternate between reflected light fluorescence and transmitted light observation and the capture of digital images.

Figure 2 - Fluorescence Filters

As presented in Figure 1, the reflected light vertical illuminator comprises an arc-discharge lamphouse at the rear end (usually a mercury or xenon burner). Excitation light travels along the illuminator perpendicular to the optical axis of the microscope, passes through collector lenses and a variable, centerable aperture diaphragm, and then through a variable, centerable field diaphragm (see Figure 1). The light then impinges upon the excitation filter where selection of the desired band and blockage of unwanted wavelength occurs. The selected wavelengths, after passing through the excitation filter, reach the dichromatic beamsplitting mirror, which is a specialized interference filter that efficiently reflects shorter wavelength light and efficiently passes longer wavelength light. The dichromatic beamsplitter is tilted at a 45-degree angle with respect to the incoming excitation light and reflects this illumination at a 90-degree angle directly through the objective optical system and onto the specimen. Fluorescence emission produced by the illuminated specimen is gathered by the objective, now serving in its usual image-forming function. Because the emitted light consists of longer wavelengths than the excitation illumination, it is able to pass through the dichromatic mirror and upward to the observation tubes or electronic detector.

Most of the scattered excitation light reaching the dichromatic mirror is reflected back toward the light source, although a minute quantity often passes through and is absorbed by the internal coating of the mirror block. Before the emitted fluorescence can reach the eyepiece or detector, it must first pass through the barrier or suppression filter. This filter blocks (suppresses) any residual excitation light and passes the desired longer emission wavelengths. In most reflected light illuminators, the excitation filter, dichromatic mirror, and barrier filter are incorporated into an optical block (often referred to as a cube), as illustrated in Figure 2. Modern fluorescence microscopes are capable of accommodating between four and six fluorescence cubes (usually on a revolving turret or through a slider mechanism see Figure 1) and permit the user to easily attach replacement aftermarket excitation and barrier filters, as well as dichromatic mirrors.

The vertical illuminator design should enable the user to adjust the microscope for Köhler illumination, providing a bright and even illumination aperture across the entire field of view. The corrected condensing lenses of the optical system should ensure that the image of the centerable aperture diaphragm is conjugate with the rear aperture of the focused objective. In modern illuminators, the image of the pre-focused, centerable field diaphragm is conjugate to the focused specimen and the plane of the fixed eyepiece diaphragm.

The illuminator lamphouse usually incorporates an infrared light suppression filter. The lamphouse itself should not leak harmful ultraviolet wavelengths and, preferably, should incorporate a switch to automatically shut down the lamp if the housing is inadvertently opened during operation. The lamphouse should be sturdy enough to withstand a possible burner (arc-discharge lamp) explosion during operation. In modern lamphouses, the lamp socket is equipped with adjustment knobs to permit centering the arc lamp image within the rear aperture of the objective (in Köhler illumination, these planes are conjugate). Somewhere in the light path, usually closer to the lamphouse and preceding the excitation filter, it is desirable to have a shutter in order to completely block excitation light when the specimen is not being viewed or imaged with the detector. In addition, provisions for neutral density filters should be made available (either on a wheel, turret, or slider) in order to enable the user to reduce the intensity of excitation illumination.

Stokes’ Shift

Vibrational energy is lost when electrons relax from the excited state back to the ground state. As a result of the energy loss, the emission spectrum of an excited fluorophore is usually shifted to longer wavelengths when compared to the absorption or excitation spectrum (note that wavelength varies inversely to radiation energy). This well-documented phenomenon is known as Stokes’ Law or Stokes' shift. As Stokes' shift values increase, it becomes easier to separate excitation from emission light through the use of fluorescence filter combinations.

The fluorophore emission (or absorption) intensity peak is usually lower in wavelength and magnitude than that exhibited by the excitation peak, and the emission spectral profile (curve) is often a mirror image (or nearly so) of the excitation curve, but shifted to longer wavelengths, as illustrated in Figure 3 for Alexa Fluor 555, a useful probe that absorbs light in the yellow-green region and produces yellow-orange emission. In order to achieve maximum fluorescence intensity, a fluorophore (often termed a dye) is usually excited at wavelengths near or at the peak of the excitation curve, and the widest possible range of emission wavelengths that include the emission peak are selected for detection. The selection of excitation and emission wavelengths is typically based on interference filters (Figure 2). In addition, the spectral response of a microscope optical system will also depend on such factors as glass transmission efficiency (due to anti-reflection coatings), the number of lens and mirror elements, and the responsivity of the detector system.

Figure 3 - Fluorophore Absorption and Emission Profiles

The effective separation and detection of excitation and emission wavelengths is achieved in fluorescence microscopy through the proper selection of filters to block or pass specific wavelength bands in the ultraviolet, visible, and near-infrared spectral regions. Fluorescence vertical illuminators are designed with the purpose of controlling the excitation light through the application of readily interchangeable filter (neutral density and interference excitation balancers) insertions into the light path on the way toward the specimen, and again in the path between the specimen and the observation tubes or camera detector system. Perhaps the most important criteria, in view of relatively low fluorescence emission intensities (see discussion above), is that the light source utilized for excitation be of sufficient brightness so that the weak emission light can be maximized, and that the fluorochromes possess adequate absorption properties and emission quantum yields.

The efficiency with which a particular fluorophore absorbs a photon of the excitation light is a function of the molecular cross-section, and the likelihood of absorption is known as the extinction coefficient. Larger extinction coefficients indicate that the absorption of a photon (or quantum) in a given wavelength region is more likely. The quantum yield denotes the ratio of the number of quanta emitted compared to those absorbed (and is usually a value between 0.1 and 1.0). Quantum yield values below 1 are the result of the loss of energy through nonradiative pathways, such as heat or a photochemical reaction, rather than the re-radiative pathway of fluorescence. Extinction coefficient, quantum yield, mean luminous intensity of the light source, and fluorescence lifetime are all important factors that contribute to the intensity and utility of fluorescence emission.

Fading, Quenching, and Photobleaching

A wide spectrum of conditions often come into play that ultimately affect the re-radiation of fluorescence emission and thus reduce the intensity. The general term for a reduction of fluorescence emission intensity is fading, a catch-all category that is usually further subdivided into quenching and photobleaching phenomena for more precise descriptions. Photobleaching is the irreversible decomposition of the fluorescent molecules in the excited state because of their interaction with molecular oxygen before emission. The occurrence of photobleaching is exploited in a technique known as fluorescence recovery after photobleaching (FRAP), a very useful mechanism for investigating the diffusion and motion of biological macromolecules. The method is based upon photobleaching a sharply defined region of the specimen by an intense burst of laser light, accompanied by the subsequent observation of the rates and pattern of fluorescence recovery in the photobleached area. A related technique, known as fluorescence loss in photobleaching (FLIP), is employed to monitor the decrease of fluorescence in a defined region lying adjacent to a photobleached area. Similar to FRAP, the latter technique is useful in the investigation of molecular mobility and dynamics in living cells.

Figure 4 - Photobleaching Rates in Multiply Stained Specimens

Presented in Figure 4 is a typical example of photobleaching (fading) observed in a series of digital images captured at different time points for a multiply-stained culture of Indian Muntjac deer epidermis fibroblast cells. The nuclei were stained with a bis-benzimidazole derivative (Hoechst 33258 blue fluorescence), while the mitochondria and actin cytoskeleton were stained with MitoTracker Red CMXRos (red fluorescence) and a phalloidin derivative conjugated to Alexa Fluor 488 (green fluorescence), respectively. Time points were taken in two-minute intervals using a fluorescence filter combination with bandwidths tuned to excite the three fluorophores simultaneously while also recording the combined emission signals. Note that all three fluorophores have a relatively high intensity in Figure 4(a), but the Hoechst fluorophore (blue) intensity starts to drop rapidly at two minutes and is almost completely gone at 6-8 minutes. The mitochondrial and actin stains are more resistant to photobleaching, but the intensity of both drops significantly over the course of the timed sequence (10 minutes).

The excited state relaxation process of quenching results in reduced fluorescence intensity through a variety of mechanisms involving non-radiative energy loss and frequently occurs as a result of oxidizing agents or the presence of salts or heavy metals or halogen compounds. In some cases, quenching results from the transfer of energy to another molecule (termed the acceptor), which resides physically close to the excited fluorophore (the donor), a phenomenon known as fluorescence resonance energy transfer (FRET). This particular mechanism has become the basis for a useful technique involving the study of molecular interactions and associations at distances far below the lateral resolution of the optical microscope.

Fluorescence Light Sources

An unfortunate consequence of low emission levels in most fluorescence microscopy applications is that the number of photons that reach the eye or camera detector is also very low. In most cases, the collection efficiency of optical microscopes is less than 30 percent and the concentration of many fluorophores in the optical path ranges in the micromolar or nanomolar regions. In order to generate sufficient excitation light intensity to produce detectable emission, powerful compact light sources, such as high-energy short arc-discharge lamps, are necessary. The most common lamps are mercury burners, ranging in wattage from 50 to 200 Watts, and the xenon burners that range from 75 to 150 Watts (see Figure 5). These light sources are usually powered by an external direct current supply, furnishing enough start-up power to ignite the burner through ionization of the gaseous vapor and to keep it burning with a minimum of flicker.

The microscope arc-discharge lamp external power supply is usually equipped with a timer to track the number of hours the burner has been in operation. Arc lamps lose efficiency and are more likely to shatter if used beyond their rated lifetime (200-300 hours). The mercury burners do not provide even intensity across the spectrum from ultraviolet to infrared, and much of the intensity of the lamp is expended in the near ultraviolet. Prominent peaks of intensity occur at 313, 334, 365, 406, 435, 546, and 578 nanometers. At other wavelengths in the visible light region, the intensity is steady although not nearly so bright (but still useable in most applications). In considering illumination efficiency, mere lamp wattage is not the prime consideration. Instead, the critical parameter is the mean luminance must be considered, taking into account the source brightness, arc geometry, and the angular spread of emission.

Figure 5 - Arc-Discharge Fluorescence Lamps

In the past few years, optical microscopy has experienced an increase in the application of laser light sources, particularly the argon-ion and argon-krypton (ion) lasers. These lasers have the virtues of small source size, low divergence, near-monochromicity, and high mean luminance. They have become essential in scanning confocal microscopy, a technique that has proven to be a powerful tool in rendering very sharp fluorescence images through rejection of non-focused light removed from the specimen focal plane. Confocal microscopes accomplish this task through point or line scanning with coincident imaging through a conjugate aperture. Optical sections of the specimens can be stored in a host computer and reconstructed into the final image, which is then displayed on the monitor.

Filter Terminology

The common terminology applied to fluorescence microscopy filter combinations has become confusing as a result of the various initials and codes utilized by different manufacturers to identify their filters. Basically, there are three major categories of filters: excitation (often referred to as exciters), barrier (emission), and dichromatic beamsplitters (or dichroic mirrors). Fluorescence filters were formerly almost exclusively constructed from dyed glass or gelatin sandwiched between two glass plates. However, the current trend is to manufacture high-resolution filters with interference optics for excitation filters to pass or reject wavelengths of light with a great specificity and high transmission. Dichromatic beamsplitters are specialized interference filters designed to reflect or pass light of specific wavelengths when placed into the light path at a 45-degree angle (see Figures 1 and 2). Barrier filters are fabricated with both colored glass or interference coatings (or a combination of the two).

Abbreviations employed by manufacturers to identify the properties of their excitation filters include: UG (ultraviolet glass) and BG (blue glass). Shortpass filters often are denoted as KP(K is an abbreviation for kurz, which means "short" in German) or simply as SP. Several manufacturers now label their interference filters with the designation IF. Narrow band excitation interference filters are especially helpful if the Stokes' shift is small.

Acronyms or abbreviations for barrier filters include: LP or L for longpass filters, Y or GG for yellow or gelb (German) glass, R or RG for red glass, OG or O for orange glass, K for kante, a German term for edge (filter), and BA for barrier filter. When the filter type is also associated with a number, such as BA515, that designation refers to the wavelength (in nanometers) at 50-percent of its maximum transmission.

Dichromatic beamsplitters also are described by numerous abbreviations including CBS for a chromatic beam splitter, DM for dichroic mirror, TK for "teiler kante", German for edge splitter, FT for "farb teiler" (German for color splitter), and RKP for reflection short pass. All of these terms should be considered interchangeable, and modern dichromatic beamsplitters are always manufactured with interference coatings on optical glass (as opposed to organic or metallic dyes). The interference thin films are designed to produce high reflectivity for shorter wavelengths and high transmission for longer wavelengths. Dichromatic beamsplitters are oriented at a 45-degree angle to the path of the excitation light entering the optical block through the reflected light fluorescence illuminator. Their primary function is to re-direct the selected excitation (shorter) wavelengths through the objective and onto the specimen. These specialized filters also have the additional functions of passing longer wavelength fluorescence emission to the barrier filter, and reflecting any scattered excitation light back in the direction of the lamphouse.

Figure 6 - Nikon B-2E (Medium Band Blue Excitation)

Presented in Figure 6 are the transmission profiles for a typical fluorescence filter combination used in modern microscopes. The excitation filter spectrum (red curve) exhibits a high level of transmission (approximately 75 percent) between 450 and 490 nanometers with a center wavelength (CWL) of 470 nanometers. The dichromatic mirror (yellow curve) reflects wavelengths in the region of the excitation spectrum, while passing higher and lower wavelengths with relatively high efficiency. Note that zero percent transmission on the dichromatic mirror curve corresponds to 100 percent reflection. The pronounced dip in the transmission profile between 450 and 500 nanometers, which represents a peak in reflectance, serves to reflect the band of wavelengths passing from the excitation filter at a 90-degree angle and onto the specimen. The final component in the optical train, an emission or barrier filter (white curve), transmits wavelengths in the green visible light region, in the range between 520 and 560 nanometers. Boundaries between transmitted and reflected wavelength bands of the various superimposed spectra are designed to be as steep as possible to assure nearly complete separation of the reflected and transmitted wavelengths. A pattern of sinusoidally rising and falling spikes appearing in the dichromatic mirror spectrum is a common effect of the thin-film deposition process known as ringing. The performance of this filter combination is remarkable and is a clear demonstration of the rapid advances being achieved in thin film interference filter technology.

The filter nomenclature employed by Nikon derives from a mixture of terms dating back to the early 1990s. At that time, all of the Nikon complementary filter combinations were produced using the hard coat sputter technique, but many of the currently available filters take advantage of newer softer coating methods. Although soft coats are more susceptible to humidity and heat degradation, and must be handled more carefully than hard coat filters, they exhibit higher blocking value optical densities and provide greater ease of fine-tuning specific wavelength bands. Understanding the Nikon filter combination code nomenclature provides a mechanism to quickly determine whether a particular set will perform adequately for a specific fluorophore.

The first letter in the Nikon proprietary alphanumeric filter designation code indicates the wavelength excitation spectral region (for example, UV, V, B, and G, which are simple abbreviations for ultraviolet, violet, blue, and green, respectively). The number following the excitation code relates to the excitation filter passband width: 1 for narrow band excitation, 2for medium and wide band excitation, and 3 for very wide band excitation. Finally, one or more letters following the excitation bandpass size number identifies the barrier filter characteristics. The code letter A indicates a standard longpass barrier filter with the lowest cut-on wavelength, while B designates a higher cut-on wavelength value for a longpass emission filter. Bandpass emission filters are identified with the letter E (referring to the term "enhanced") to indicate their superior performance with regard to eliminating crossover. The E/C filters are soft coat interference combinations designed for best performance with specific probes, such as DAPI, FITC, TRITC, and Texas Red.

The Fluorescence Light Budget

An estimation of the light fluxes in a typical fluorescence microscope is useful to outline constraints that will be encountered in producing digital images or during the visual observation of specimens. The excitation source is assumed, for this exercise, to be a standard 75-Watt xenon arc-discharge lamp having a mean luminous flux density of approximately 400 candelas per square millimeter (for other sources, see Table 1). When the lamp output is collected and directed through a 490-nanometer interference filter (having a 10-nanometer bandwidth and 75 percent transmission), about 2 milliWatts of light will pass through. After reflection by a 90-percent efficient dichromatic mirror, a light flux of 1.8 milliWatts enters the rear aperture of the microscope objective as the excitation beam.

With a 100x objective having a numerical aperture of 1.4, the area of the specimen illuminated will be 12 x 10 × E(-6) square centimeters, assuming a circular field of view about 40 micrometers in diameter. The light flux on the specimen is then about 150 Watts per square centimeter, which corresponds to a flux density of 3.6 x 10 × E(20) photons per square centimeter. Thus, the specimen illumination intensity is about 1000 times higher than that incident on the Earth's surface on a sunny day.

The fluorescence emission that results from the light flux discussed above depends on the absorption and emission characteristics of the fluorophore, its concentration in the specimen, and the optical path length of the specimen. In mathematical terms, the fluorescence produced (F) is given by the equation:

Formula 1 - Fluorescence Produced

where σ is the molecular absorption cross-section, Q is the quantum yield, and I is the incident light flux (as calculated above). Assuming that fluorescein is the fluorophore, the absorption cross-section (σ) is 3 x 10 × E(-16) square centimeters per molecule, Q equals 0.99, resulting in a value for F of 100,000 photons per second per molecule. If the dye concentration is 1 micromole per liter and is uniformly distributed in a 40-micrometer diameter disk with a thickness of 10 micrometers (volume equal to 12 picoliters), there are approximately 1.2 x 10 × E(-17) moles of dye or 7.2 million molecules in the optical path. If all of the molecules were excited simultaneously, the fluorescence emission rate would be 7.2 x 10 × E(11) photons per second (given the product of F and the number of dye molecules). The question of interest is how many of the emitted photons would be detected and for how long could this emission rate continue?

Table 1 - Luminous Density of Selected Light Sources

Luminous Flux
Mean Luminous
Density (cd/mm2)
Arc Size
(H x W)
Mercury Arc
(100 Watt)
5220017000.25 x 0.25
Xenon Arc
(75 Watt)
5.48504000.25 x 0.50
Xenon Arc
(500 Watt)
30900035000.30 x 0.30
82800454.2 x 2.3

The efficiency of detection is a function of the optical collection efficiency and the detector quantum efficiency. A 1.4-numerical aperture objective with 100-percent transmission (an unrealistic condition) has a maximum collection efficiency, limited by the acceptance angle of about 30 percent. The transmission efficiency of the dichromatic mirror is 85 percent and that of the barrier filter is 80 percent. The overall collection efficiency is then about 20 percent or 140 billion photons per second. If the detector is a conventional charge-coupled device (CCD), the quantum efficiency is about 50 percent for the green fluorescein emission (at 525 nanometers), so the detected signal would be 70 billion photons per second or about 10 percent of the emitted fluorescence. Even with a perfect detector (100 percent quantum efficiency), only about 20 percent of the fluorescence emission photons can be detected.

The duration of fluorescence emission depends upon the rate of fluorophore destruction as a result of photobleaching. For fluorescein in an oxygenated saline solution, measurements indicate that each molecule can only emit about 36,000 photons before being destroyed. In a deoxygenated environment, the rate of photodestruction diminishes about tenfold, so 360,000 photons are produced per fluorescein molecule. The entire dye pool, in this example (7.2 million molecules), would then be capable of producing a minimum of 2.6 x 10 × E(11) and a maximum of 2.6 x 10 × E(12) photons. Assuming the emission rate of 100,000 photons per second per molecule calculated above, fluorescence could continue for only 0.3 to 3 seconds before photodestruction. In the case where 10 percent of the photon flux is detected, a signal of 7.2 x 10 × E(10) electrons per second would be obtained.

Following the argument of this example, if the detector is a 1000 x 1000 pixel CCD camera, this signal would be distributed over a million sensors, with approximately 72,000 electrons per sensor. For a scientific-grade CCD with 9-micrometer square sensors, the full well storage capacity is about 80,000 electrons and the read-out noise is less than 10 electrons. The signal-to-noise ratio would then be largely determined by photon statistical noise equal to the square root of the signal, approximately 268. In almost all cases, this high signal level could only continue for a very brief period of time before photodestruction occurs. The compromise utilized by most microscopists to prolong the observation period is a reduction in the incident light flux intensity so that only a fraction of the fluorophore molecules in the dye pool are excited and subjected to photodestruction. Thus, the signal-to-noise ratio rarely equals the theoretical maximum and typically ranges between 10 and 20 in fluorescence microscopy.

Detecting Single Molecules

Under ideal conditions, it is often possible to detect the fluorescence emission from a single molecule, provided that the optical background and detector noise are sufficiently low. As discussed above, a single fluorescein molecule could emit as many as 300,000 photons before it is destroyed by photobleaching. Assuming a 20-percent collection and detection efficiency, about 60,000 photons would be detected. Using avalanche photodiode or electron multiplying CCD detectors for these experiments, investigators have been able to monitor the behavior of single molecules for many seconds and even minutes. The major problem is adequate suppression of the optical background noise. Because many of the materials utilized in construction of microscope lenses and filters display some level of autofluorescence, efforts were initially directed toward the manufacture of very low fluorescence components. However, it soon became evident that fluorescence microscopy techniques utilizing total internal reflection (TIR) provided the desired combination of low background and high excitation light flux.

Total internal reflection fluorescence microscopy (TIRFM) takes advantage of the evanescent wave that is developed when light is totally internally reflected at the interface between two media having dissimilar refractive indices. The principle employing an external light source is illustrated in Figure 7(a). In this technique, a beam of light (usually an expanded laser beam) is directed through a prism of high refractive index, such as glass or sapphire, which abuts a lower refractive index medium of glass or aqueous solution. If the light is directed into the prism at higher than the critical angle, the beam will be totally internally reflected at the interface. The reflection phenomenon develops an evanescent wave at the interface by the generation of an electromagnetic field that permeates about 200 nanometers or less into the lower refractive index space. The light intensity in the evanescent wave is sufficiently high to excite the fluorophores within it, but because of its shallow depth, the volume excited is very small. The result is an extremely low-level background because so little of the specimen is exposed to the excitation light (only that portion within a 200-nanometer distance of the interface).

Figure 7 - Inverted Microscope TIRFM Configurations

Total internal reflection fluorescence microscopy can also be conducted through a modification of the epi-illumination approached utilized in widefield techniques (as illustrated in Figure 7(b)). This method requires a very high numerical aperture objective (at least 1.4, but preferably 1.45 to 1.6) and partial illumination of the microscope field from one side by a small sport or more uniform illumination by a thin annulus. Nikon offers 60x and 100x TIRF objectives with numerical aperture 1.49. High refractive index lens immersion medium and microscope cover glass are required to achieve the illumination angle resulting in total internal reflection. As presented in Figure 7(b), light rays exiting the objective front lens element at an angle less than the critical angle (denoted as A(1)) in figure 7(b)) are transmitted away from the microscope. When the angle is increased to or beyond the critical angle (indicated a angle A(2) in Figure 7(b)), total internal reflection results.

Other popular advanced fluorescence techniques, such as fluorescence resonance energy transfer (FRET) and fluorescence recovery after photobleaching (FRAP), as well as spectroscopy, are often combined with total internal reflection to achieve additional information, as is possible with the Nikon Ti2-LAPP modular illumination system. The result is a very powerful tool for the study of individual fluorophores and fluorescently labeled molecules. The advantages resulting from the study of the properties of single molecules are only beginning to be appreciated. Thus, the current range of optical microscopy now extends from the single molecule to the entire animal.


The modern fluorescence microscope combines the power of high performance optical components with computerized control of the instrument and digital image acquisition to achieve a level of sophistication that far exceeds that of simple observation by the human eye. Microscopy now depends heavily on electronic imaging to rapidly acquire information at low light levels or at visually undetectable wavelengths. These technical improvements are not mere window dressing, but are essential components of the light microscope as a system.

The era when optical microscopy was purely a descriptive instrument or an intellectual toy is past. At present, optical image formation is only the first step toward data analysis. The microscope accomplishes this first step in conjunction with electronic detectors, image processors, and display devices that can be viewed as extensions of the imaging system. Computerized control of focus, stage position, optical components, shutters, filters, and detectors is in widespread use and enables experimental manipulations that were not humanly possible with mechanical microscopes. The increasing application of electro-optics in fluorescence microscopy has led to the development of optical tweezers capable of manipulating sub-cellular structures or particles, the imaging of single molecules, and a wide range of sophisticated spectroscopic applications.

Contributing Authors

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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As soon as the genome sequence of the virus was reported by Professor Zhang Yongzhen from the Institutes of Biomedical Sciences, Fudan University, China, and colleagues, the McLellan Lab set to preparing a purified sample of its spike protein. This was key as previous studies had shown that coronaviruses invade cells by making these spiky appendages that then penetrate a host cell.

Then, with the purified sample in hand, the researchers swiftly reconstructed the atomic-scale 3D structural map of the spike protein using single particle cryo-electron microscopy. It took just twelve days.

PhD candidate, Daniel Wrapp, right, working with Professor Jason McLellan in the McLellan Lab [Vivian Abagiu/Univ. of Texas at Austin]

With the atomic structure resolved and swiftly published in Science, the researchers quickly joined forces with the US National Institute of Allergy and Infectious Diseases (NIAID) and biotechnology company, Moderna, to design a COVID-19 vaccine. By mid-March, the trial vaccine had been injected into the first human, as part of the first phase of clinical trials.

The road to the vaccine
While a final vaccine is some way off yet, the pace of scientific progress, so far, has been blisteringly fast. According to NIAID Director, Dr Anthony S Fauci, the Phase 1 study launched in 'record speed', and of course, the rapid determination of the virus spike structure has helped.

All viruses have antigens, which are usually proteins. Any vaccine works by triggering the immune system to recognise and fight against a virus' antigen. However, to design that vaccine, researchers need to have a clear picture of how the virus attacks human cells, which makes atomic-resolution structures so very important. And from word go, the McLellan group knew the clock was ticking.

According to Daniel Wrapp, PhD candidate in the McLellan Lab, as soon as Yongzhen and colleagues had released the genome sequence of the novel coronavirus, his colleague, postdoctoral researcher, Dr Nianshuang Wang, sourced gene fragments from a biopharmaceutical company. These fragments offer a quick route to gene reconstruction for virus and antibody research.

As Wrapp highlights: “Rather than trying to clone the whole spike gene at once, he broke this down into six fragments and then stitched these all together.”

“Synthesizing an entire gene would have taken a couple of weeks but he did this in just a few days - it was a huge advantage.”

With gene reconstruction complete, the researchers set to making a purified sample of the coronavirus, then called 2019-nCoV but since officially named SARS-CoV-2. Thanks to past coronavirus research, the researchers already knew how what to do: stabilize this virus' all-important spike protein.

This illustration, created at the Centers for Disease Control and Prevention (CDC), reveals ultrastructural morphology exhibited by coronaviruses. Note the spikes that adorn the outer surface of the virus, which impart the look of a corona surrounding the virion, when viewed electron microscopically. [CDC/ Alissa Eckert, MS Dan Higgins, MAMS]

During transmission, the spike protein recognizes a human cell's receptor. A portion of that spike then binds to that receptor. In a next step, other portions of the spike then fuse the viral and human cell membranes together so the virus can enter the human cell and infect it.

As part of this process, receptor binding triggers the spike protein to massively change its structure from its metastable pre-fusion conformation, prior to infection, to a stable post-fusion conformation, during infection. Understanding the mechanism for this all-important switch is critical to vaccine design, and with their past experiences, Wrapp and colleagues could quickly lock the protein in its pre-fusion structure, prior to human cell binding and infection, ready for cryo-EM analysis.

“Back in 2016, we published the structure of a coronavirus spike protein called HKU1,” says Wrapp. “Most people haven't heard of this as its only a really mild respiratory disease but it heavily circulates through the human population.”

“From this, we learned a lot about these coronavirus spike proteins and the way they go about this transition from pre-fusion to post-fusion,” he adds. “So by looking at that HKU1 protein spike, we were able to quickly design a couple of pretty subtle mutations into the [SARS-CoV-2] spike protein that make it thermodynamically unfavourable to undergo a transition and help it maintain its pre-fusion conformation.”

Dr Nianshuang Wang (right) and Daniel Wrapp review cryo-EM images in the The Sauer Structural Biology Laboratory just before the structure of the spike protein was published [Vivian Abagiu/Univ. of Texas at Austin]

Crucially, with purified protein in hand, the researchers were also able to quickly prepare the sample for cryo-EM analysis, again thanks to the coronavirus proteins they had worked with in the past.

“During cryo-electron microscopy you are worried about vitrifying your sample and you have to play with the buffer conditions, blotting conditions or your protein conditions,” explains Wrapp. “But because we already knew what had been successful with SARS and MERS coronavirus samples, we had a good ballpark range to get started.”

“I'd been working on the testing, freezing and blotting conditions needed for the SARS spike protein, so even before we'd purified this novel coronavirus spike, I had assumed the conditions would be translatable,” he adds.

And with sample preparation complete, the researchers were able to get the cryo-EM data they needed in only 24 hours. According to Wrapp, they set up automated data collection the evening they purified the protein, and by the next evening, a mighty 3207 micrograph movies had been collected. “Given we were working with a homologous sample, we could really get the ideal conditions for data collection,” he says.

The researchers were working with a Thermo Fisher Scientific Titan Krios equipped with a Gatan K3 detector while movies were collected using Leginon, a system developed in 2000 to automatically acquire micrographs from vitreous ice specimens.

Loading a sample in the Thermo Fisher Scientific Krio G4.

As the data were collected, the researchers used Warp software to evaluate, correct and process the data, in real-time. They then turned to cryoSPARC to obtain 3D structural information from the extracted single particles, and used UCSF Chimera and other packages to visualise and build the protein spike model.

“Both Warp and cryoSPARC were truly instrumental here,” highlights Wrapp. “We could run Warp whilst collecting data, so as soon as the first movies came off the microscope we were already processing those with this software.”

“At the same time - as soon as the movies were processed by Warp, we could import them in cryoSPARC and start looking at 2D and 3D class averages in real-time,” he adds.

Rapid progress
But without a doubt, the Krios and its K3 direct detection camera were truly instrumental to the swift determination of the pre-fusion structure of SARS-CoV-2 to an impressive 3.5-angstrom-resolution. The McLellan lab used standard cryo-EM protocols, and as Wrapp puts it: “Five years ago, our quick results would have been pretty unimaginable.”

“There's been so many advances since then that now we see this kind of thing happening all the time, unbelievably,” he adds.

Electron micrograph of SARS-CoV-2 virions with visible coronae. Virus particles are shown emerging from the surface of cells cultured in the lab. [NIAID Rocky Mountain Laboratories (RML), U.S. NIH]

The PhD researcher points to how the Krios allows precise control and is also very stable, so he didn't have to worry about vibrations or stage motion contributing to noise in images. “We'd also upgraded our K2 detector to a K3 detector six months ago so for an average user like me, the key advantage here was the speed with which I could collect the movies,” he says. “I think we probably doubled the number of movies that we could collect in a single day by moving from the K2 to K3.”

“Also, just the physical parameters of the detector itself are larger – so if you're trying to get a greater number of particles, this means you can collect fewer movies,” he adds.

Eric Chen, Director of Market Development APAC with Thermo Fisher Scientific, echoes Wrapp's sentiments. As he points out: “A couple of years ago, even just the cryo-EM imaging of part [of McLellan's research] could have taken weeks, even months.”

“We have better and more stable system workflows - everything has gotten better from both the hardware side including the microscope and detectors and software making it easier to find those virus particles and produce high quality reconstructions,” he says.

Eric Chen, Director of Market Development APAC with Thermo Fisher Scientific.

Chen is also keen to highlight the rapid speed of scientific development elsewhere in recent weeks, driven by cryo-EM. Following the McLellan Lab's results, he points to how researchers from the Westlake Institute for Advanced Study in Hangzhou, China, swiftly published results on the SARS-CoV-2 spike protein bound to a human cell's surface receptor, the angiotensin-converting enzyme 2. These results are helping researchers to develop antibodies to block this critical binding interaction.

And he also highlights how Professor David Veesler's group at the University of Washington School of Medicine published their structure of the SARS-CoV-2 spike protein, just five days after the McLellan Lab. “Within just one month we have all these results - it's just unprecedented and would have taken months, even years, using other diffraction methods,” he says.

Structure of the SARS-CoV-2 spike protein from Professor David Veesler and colleagues [Alexandra C. Walls, Young-Jun Park & David Veesler]

“Diffraction techniques are very good but can be erratic in terms of 'can I grow these crystals' or 'do I have enough sample' - cryo-EM only requires a couple of hundred microlitres of a sample and makes it possible to extrapolate a protein, in this case virus from human patients and derive more knowledge of disease related proteins in native conditions,” he adds. “So cryo-EM, has had a huge impact on virology and immune response, and this is something that requires a lot of basic science investment.”

Chen also reckons that cryo-EM's solid workflow has been instrumental to the recent, rapid progress. Single particle analysis allows researchers to swiftly identify a virus and also test new antibodies as targets for inhibitors and vaccine development, driving therapeutics forward.

“This is an ongoing battle and viruses mutate,” he says. “But the advent of the direct electron detector has revolutionised what we can do with cryo-electron microscopes, and this along with the stability in the software, has really changed the game. to go from a sequence to the structure within a month is just remarkable and shows how the community is coming together and sharing every data point.”

Virus surprise
On publishing their results in Science, the McLellan Lab researchers also provided the first glimpse into how SARS-CoV-2 infects humans so very quickly and efficiently. For example, while results confirmed that the SARS-CoV-2 spike protein was similar to that of its predecessor, the SARS-CoV virus, it appears to bind human cells more tightly. The researchers reckon this could go some way to explain why this latest SARS-CoV-2 appears to spread more easily from person to person.

The researchers also tested several published SARS-CoV antibodies on the SARS-CoV-2 virus, which could have been used to develop a treatment for people exposed to this latest version of SARS, including healthcare workers. But results were not as hoped.

“We knew that there was a decent amount of sequence variation on the surface of the SARS-CoV-2 virus' receptor binding domain, [compared to other coronaviruses] so we were expecting to lose some binding with antibodies,” says Wrapp. “But to observe no appreciable binding of these antibodies to SARS-CoV-2 was a surprise.”

Still, McLellan and colleagues are currently using the spike protein - stabilised in its pre-fusion state - as a probe to isolate naturally produced antibodies from people who have recovered from COVID-19. These will serve as the basis for a new treatment. And of course, vaccine development worldwide continues apace.

“Using cryo-EM has allowed us to capture, for example, the discrete movement of this virus as it binds to the human cell receptor and we just couldn't have captured this with X-ray crystallography,” says Wrapp.

“Having this really precise atomic level information allows labs such as ourselves and around the world to design and screen small molecules with fusion-inhibiting potential that further stabilize the spike,” he adds. “And this will support precision vaccine design and the discovery of antiviral therapeutics.”

What Is the Smallest Thing in the Universe?

The answer to the enduring question of the smallest thing in the universe has evolved along with humanity. People once thought grains of sand were the building blocks of what we see around us. Then the atom was discovered, and it was thought indivisible, until it was split to reveal protons, neutrons and electrons inside. These too, seemed like fundamental particles, before scientists discovered that protons and neutrons are made of three quarks each.

"This time we haven't been able to see any evidence at all that there's anything inside quarks," said physicist Andy Parker. "Have we reached the most fundamental layer of matter?"

And even if quarks and electrons are indivisible, Parker said, scientists don't know if they are the smallest bits of matter in existence, or if the universe contains objects that are even more minute. [Graphic: Nature's Tiniest Particles]

Parker, a professor of high-energy physics at England's Cambridge University, recently hosted a television special on the U.K.'s BBC Two channel called "Horizon: How Small is the Universe?"

Strings or points?

In experiments, teensy, tiny particles like quarks and electrons seem to act like single points of matter with no spatial distribution. But point-like objects complicate the laws of physics. Because you can get infinitely close to a point, the forces acting on it can become infinitely large, and scientists hate infinities.

An idea called superstring theory could solve this issue. The theory posits that all particles, instead of being point-like, are actually little loops of string. Nothing can get infinitely close to a loop of string, because it will always be slightly closer to one part than another. That "loophole" appears to solve some of these problems of infinities, making the idea appealing to physicists. Yet scientists still have no experimental evidence that string theory is correct.

Another way of solving the point problem is to say that space itself isn't continuous and smooth, but is actually made of discrete pixels, or grains, sometimes referred to as space-time foam. In that case, two particles wouldn't be able to come infinitely close to each other because they would always have to be separated by the minimum size of a grain of space.

A singularity

Another contender for the title of smallest thing in the universe is the singularity at the center of a black hole. Black holes are formed when matter is condensed in a small enough space that gravity takes over, causing the matter to pull inward and inward, ultimately condensing into a single point of infinite density. At least, according to the current laws of physics.

But most experts don't think black holes are really infinitely dense. They think this infinity is the product of an inherent conflict between two reigning theories &mdash general relativity and quantum mechanics &mdash and that when a theory of quantum gravity can be formulated, the true nature of black holes will be revealed.

"My guess is that [black hole singularities] are quite a lot smaller than a quark, but I don't believe they're of infinite density," Parker told LiveScience. "Most likely they are maybe a million million times or even more than that smaller than the distances we've seen so far."

That would make singularities roughly the size of superstrings, if they exist.

The Planck length

Superstrings, singularities, and even grains of the universe could all turn out to be about the size of the "Planck length." [Tiny Grandeur: Stunning Photos of the Very Small]

A Planck length is 1.6 x 10^-35 meters (the number 16 preceded by 34 zeroes and a decimal point) &mdash an incomprehensibly small scale that is implicated in various aspects of physics.

The Planck length is far and away too small for any instrument to measure, but beyond that, it is thought to represent the theoretical limit of the shortest measureable length. According to the uncertainty principle, no instrument should ever be able to measure anything smaller, because at that range, the universe is probabilistic and indeterminate.

This scale is also thought to be the demarcating line between general relativity and quantum mechanics.

"It corresponds to the distance where the gravitational field is so strong that it can start to do things like make black holes out of the energy of the field," Parker said. "At the Planck length we expect quantum gravity takes over."

Perhaps all of the universe's smallest things are roughly the size of the Planck length.

In order to get a better view of the structure of a virus, researchers have been using a number of techniques including electron tomography, immunoelectron microscopy and cryo-electron microscopy.

These have also been shown to be important techniques for showing how viruses attach to cells, how they assimilate during replication as well as their their association with various cellular mechanisms during replication.

In cryo-electron microscopy, the sample is frozen using liquid nitrogen and observed under a transmission electron microscope that is equipped with a cryo-stage. However, the images may be reconstructed in order to obtain a three dimension of the virus.

Evolution of Viruses

The evolution of viruses is speculative as they do not fossilize biochemical and genetic information is used to create virus histories.

Learning Objectives

Describe the difficulties in determining the origin of viruses

Key Takeaways

Key Points

  • Scientists agree that viruses don’t have a single common ancestor, but have yet to agree on a single hypothesis about virus origins.
  • The devolution or the regressive hypothesis suggests that viruses evolved from free-living cells.
  • The escapist or the progressive hypothesis suggests that viruses originated from RNA and DNA molecules that escaped from a host cell.
  • The self-replicating hypothesis posits a system of self-replication that most probably involves evolution alongside the host cells.

Key Terms

  • self-replicating: able to generate a copy of itself
  • devolution: degeneration (as opposed to evolution)

Evolution of Viruses

Although biologists have accumulated a significant amount of knowledge about how present-day viruses evolve, much less is known about how viruses originated in the first place. When exploring the evolutionary history of most organisms, scientists can look at fossil records and similar historic evidence. However, viruses do not fossilize, so researchers must conjecture by investigating how today’s viruses evolve and by using biochemical and genetic information to create speculative virus histories.

While most findings agree that viruses don’t have a single common ancestor, scholars have yet to find one hypothesis about virus origins that is fully accepted in the field. One possible hypothesis, called devolution or the regressive hypothesis, proposes to explain the origin of viruses by suggesting that viruses evolved from free-living cells. However, many components of how this process might have occurred are a mystery. A second hypothesis (called escapist or the progressive hypothesis) accounts for viruses having either an RNA or a DNA genome and suggests that viruses originated from RNA and DNA molecules that escaped from a host cell. A third hypothesis posits a system of self-replication similar to that of other self-replicating molecules, probably evolving alongside the cells they rely on as hosts studies of some plant pathogens support this hypothesis.

Common ancestor tree of life: This phylogenetic tree of the three domains of life (Bacteria, Archaea, and Eukarya) attempts to identify when various species diverged from a common ancestor. Finding a common ancestor for viruses has proven to be far more difficult, especially since they do not fossilize.

As technology advances, scientists may develop and refine further hypotheses to explain the origin of viruses. The emerging field called virus molecular systematics attempts to do just that through comparisons of sequenced genetic material. These researchers hope to one day better understand the origin of viruses, a discovery that could lead to advances in the treatments for the ailments they produce.

Is it possible to identify this microscopic particle? - Biology

Systems biology has existed loosely under many definitions for a couple of decades. It’s the notion of describing living systems using first-principle physics and mathematics to capture life in equations that are both descriptive and predictive – and let’s add productive by which we mean being able to deliver therapies (drugs et. al) to enhance health and fight disease.

Doing that has proven difficult at best and disappointing at worst as even a cursory glance at the state of healthcare reveals that’s notwithstanding many marvelous breakthroughs such as sequencing the human genome and the steady chipping away at functional genomics (and other ‘omics) to understand better how DNA informs what we become.

With apologies to ISC organizers I’ve stolen the name of the opening keynote by Ivo Sbalzarini – The Algorithms of Life – Scientific Computing for Systems Biology – for the headline of this article in an attempt to capture his expansive presentation. Thanks also to Sbalzarini for providing a few of his slides.

Given all we know today and the steady gush of experimental data from modern instruments, what we are missing, said Sbalzarini, are the algorithms to make sense of it all. Having poked away at this problem for nearly as long as it has been around, Sbalzarini presented a sweeping approach to digging out those algorithms by capitalizing on recent advances in imaging technology, immersive virtual/augmented reality, a sophisticated analysis approach that leverages particle-mesh mathematics and which has been built into a software platform (OpenFPM), and lastly, no surprise, the steadily growing power of HPC.

As in many important life sciences advances the ‘lowly’ fruit fly took center stage. In this instance the analysis was to investigate a dysregulation in embryogenesis – specifically the failure of tissue to fold properly. In the end, the researchers identified the DNA influence, the chemical environment influence, and the mechanical environment influence, and delivered a predictive understanding of the embryo’s tissue response. Lest you think this is old work, it was presented last week at the New York Scientific Data Summit.

Getting from Sbalzarini’s early nascent research 15 years ago to the impressive results (and tool suite) presented is a long journey. We’ll summarize as practical but the ISC is likely to archive its keynote for biologists it is well worth watching.

Advanced imaging, such as light sheet microscopy, now makes it possible to observe life science phenomena in 3D and great detail at the cellular and intracellular level.

“We can image an embryo from the time it is a fertilized to the time it moves out of the microscope field by itself and continues its life. When we image the fruit fly embryo over the 72 hours of development, we gather 180 TB of image data. If you would like to visualize that in real-time. That means a rendering performance or a rendering throughput in real-time of about 1.8 Gigapixels per second,” said Sbalzarini [i]. A key advantage here is the animal stays alive unlike older approaches requiring stains and fixing.

Hardly just pretty pictures, the extensive image data captured (and visualizations possible) are the raw input for building hypotheses and predictive models. The other primary driver is Sbalzarini clever adaption of particle-mesh technology to convert the data into actionable, in silico simulation. Underlying HPC infrastructure, of course, is the engine without which the whole process would grind to a halt.

“The numerical methods are particle methods or hybrid particle mesh methods. They comprise an interesting class of numerical methods. They discretize the system by particles, so if you have a complex geometry, you don’t need to generate the mesh for the simulation, but you simply fill the geometry with particles that store the variables there can be a mesh in addition in order to do far field equations in order to compute for example forces for far field equations, for example,” he said.

“This is a classic framework of particle-mesh methods to solve partial differential equations, but particle methods as an algorithm are much more general than that. I would define everything as a particle method that is composed of dots of zero dimension elements that are characterized by a position in some space and some properties that they carry. Such an algorithm can be used to solve partial differential equations where the particles are the colocation points of your various discretization and they store the values of the field at that position.”

He adds quickly, “There is nothing that limits us to having particles interacting in a deterministic fashion and this then also allows us to solve stochastic different equations, numerically or to perform agent based simulation or agent based modeling.”

Building the computational tools to deliver these models has been a challenging and lengthy task for which Sbalzarini is well-qualified. He is the chair of scientific computing for systems biology on the faculty of computer science of TU Dresden, as well as the faculty of mathematics, and director of the TUD-Department in the Center for Systems Biology Dresden. He also is a permanent Senior Research Group Leader with the Max Planck Institute of Molecular Cell Biology and Genetics in Dresden.

Leaving out many details and with regrets for over-simplification, Sbalzarini and colleagues imaged the fruit fly embryo used machine learning to identify ‘algorithms’, converted the data and algorithms into models based on particle-mesh approaches using their home-developed platform ran computational experiments to test their hypotheses and used immersive visualization technology as a step to allow researchers to see the real process and simulations unfold. “It is possible to walk around inside the simulation,” he said. Informed by what they saw and their knowledge, researchers tweaked parameters and hypotheses, iteratively converging on a solution.

“To me it is a very nice example of how HPC and these numerically intricate simulations that we can do with these machines allow us to bridge really from the molecular scale to the tissue scaler in order to explain how things work and in order to propose remedies,” said Sbalzarini.

Sbalzarini reminded the audience living systems are computing machines themselves, “[A fruit fly embryo] is a massively parallel and fully self-organized system in which we can view every single cell as a processing element that executes programs. [It’s a] highly interconnected computer and able to solve NP hard problems with billions or hundreds of billions of processing elements. We know a lot about the hardware of this computer – the proteins, the molecules, the lipids, the fats out of which this computer is made – and thanks to sequencing technology, [we’re] able to read the source code of this computer, which is the genomic sequence. However we have no idea what algorithms this source code implements on his hardware.”

Now, advanced imaging and machine learning capabilities are catalyzing researchers’ ability to identify ‘mechanistic’ guidelines and incorporate traditional formulations (ODEs/PDEs) of physics laws and mathematics into the life sciences tool box. Chemical diffusion. Fluid dynamics. EMI influences. Activation energy thresholds. These are the kinds of attributes that can be captured in particle-mesh models.

When Sbalzarini began his studies in earnest, he used an NEC SX-5 with 512 processors housed at CSCS (Swiss Supercomputer Center). In 2005 that became a Cray XT-3 with 1664 processors. A lot has changed since. The first iteration of the system biology software platform his team developed was Parallel Particle Mesh Library (PPM) written in Fortran 90 many years ago. It served as layer between MPI and Client Applications for simulations of physical systems using Particle-Mesh methods. The PPM library runs on single and multi-processor architectures, and handles 2D and 3D problems.

“The PPM library had two parts, what we call the PPM core, which is implemented in all the communication primitives, the load balancing, the file IO, [and] the distributed data structures. And the PPM numerics using frequently used numerical solvers it does this in part by using the abstractions from the core and in part by renting third party libraries such as PETSc or FFTW. On top of PPM there is a domain specific programming language called PPM Language which provides a reasonably simple way of coding PPM but you could also directly interface with the Fortran API,”

PPML used overloading and generic interfaces and provided for the limitations of the important routines for different hardware platforms such as vector processors, like the NEC system, shared memory, distributed memory, even single processor systems, said Sbalzarini.

It was a beast to maintain. “Because of overloading the amount of source code in the PPM library was huge, several millions of lines of code that needed to be maintained here and ported. What we liked about PPML was the abstraction on which it is based. It’s a set of abstract data types and abstract operators for computing that are in our opinion the most coarse-grained abstractions possible that still cleanly separate computation from communication. So in PPM an abstraction would either only compute but not incur any communication overhead or it would only communicate but not do any computation,” he said.

Five years ago the platform was upgraded, “We decided to keep the abstractions, to keep the definitions of the data types and the operators, but now implement a C++ library which is called OpenFPM (Open Framework for Particle Method Library) and make use of template metaprogrammingin C++ for compiled time code generation. OpenFPM can do much more than PPM, for example it can do simulations in arbitrary dimensional spaces where PPM is limited to 2D and 3D. OpenFPM allowed particle properties to be objects of any C++ that the user can define and all the communication and file IO will work for it,” he said.

Adopting template metaprogramming reduced the amount of code needed to “about a factor of ten less complexity than the PPM.”

Sbalzarini presented many more details in his rich talk. It will be interesting to watch how widely OpenFPM is used and if it gains tractions in other domains. Ease of use is a key question for many biomedical researchers and clinicians. Sbalzarini said, “This hopefully makes HPC so easy to use that every science-based application in biology, in computational biology, and also in other fields can benefit.”

That said computer expertise, particularly HPC expertise, has historically been lacking in life science although that is changing and fairly quickly.

The main motivation is to understand biology and to understand how cells form tissues, and eventually to be able to provide novel explanations for disease phenotypes and maybe therapies for disease, said Sbalzarini. Nevertheless, “For us as computer scientists it’s also just a lot of fun because what we do combines several technologies that we think are fun to work with, technologies like virtual reality, HPC, massively scalable software systems, building microscopes and playing with optics, or using and developing artificial intelligence and learning algorithms to interface with the living things in the microscope.”

Is it possible to identify this microscopic particle? - Biology

Birefringence is formally defined as the double refraction of light in a transparent, molecularly ordered material, which is manifested by the existence of orientation-dependent differences in refractive index. Many transparent solids are optically isotropic, meaning that the index of refraction is equal in all directions throughout the crystalline lattice. Examples of isotropic solids are glass, table salt (sodium chloride, illustrated in Figure 1(a)), many polymers, and a wide variety of both organic and inorganic compounds.

Figure 1 - Crystalline Structure of Isotropic and Anisotropic Materials

The simplest crystalline lattice structure is cubic, as illustrated by the molecular model of sodium chloride in Figure 1(a), an arrangement where all of the sodium and chloride ions are ordered with uniform spacing along three mutually perpendicular axes. Each chloride ion is surrounded by (and electrostatically bonded to) six individual sodium ions and vice versa for the sodium ions. The lattice structure illustrated in Figure 1(b) represents the mineral calcite (calcium carbonate), which consists of a rather complex, but highly ordered three-dimensional array of calcium and carbonate ions. Calcite has an anisotropic crystalline lattice structure that interacts with light in a totally different manner than isotropic crystals. The polymer illustrated in Figure 1(c) is amorphous and devoid of any recognizable periodic crystalline structure. Polymers often possess some degree of crystalline order and may or may not be optically transparent.

Crystals are classified as being either isotropic or anisotropic depending upon their optical behavior and whether or not their crystallographic axes are equivalent. All isotropic crystals have equivalent axes that interact with light in a similar manner, regardless of the crystal orientation with respect to incident light waves. Light entering an isotropic crystal is refracted at a constant angle and passes through the crystal at a single velocity without being polarized by interaction with the electronic components of the crystalline lattice.

The term anisotropy refers to a non-uniform spatial distribution of properties, which results in different values being obtained when specimens are probed from several directions within the same material. Observed properties are often dependent on the particular probe being employed and often vary depending upon the whether the observed phenomena are based on optical, acoustical, thermal, magnetic, or electrical events. On the other hand, as mentioned above, isotropic properties remain symmetrical, regardless of the direction of measurement, with each type of probe reporting identical results.

Anisotropic crystals, such as quartz, calcite, and tourmaline, have crystallographically distinct axes and interact with light by a mechanism that is dependent upon the orientation of the crystalline lattice with respect to the incident light angle. When light enters the optical axis of anisotropic crystals, it behaves in a manner similar to the interaction with isotropic crystals, and passes through at a single velocity. However, when light enters a non-equivalent axis, it is refracted into two rays, each polarized with the vibration directions oriented at right angles (mutually perpendicular) to one another and traveling at different velocities. This phenomenon is termed double refraction or birefringence and is exhibited to a greater or lesser degree in all anisotropic crystals.

Electromagnetic radiation propagates through space with oscillating electric and magnetic field vectors alternating in sinusoidal patterns that are perpendicular to one another and to the direction of wave propagation. Because visible light is composed of both electrical and magnetic components, the velocity of light through a substance is partially dependent upon the electrical conductivity of the material. Light waves passing through a transparent crystal must interact with localized electrical fields during their journey. The relative speed at which electrical signals travel through a material varies with the type of signal and its interaction with the electronic structure, and is determined by a property referred to as the dielectric constant of the material. The vectorial relationship defining the interaction between a light wave and a crystal through which it passes is governed by the inherent orientation of lattice electrical vectors and the direction of the wave's electric vector component. Therefore, a careful consideration of the electrical properties of an anisotropic material is fundamental to the understanding of how a light wave interacts with the material as it propagates through.

Figure 2 - Light Path Through a Calcite Crystal

The phenomenon of double refraction is based on the laws of electromagnetism, first proposed by British mathematician James Clerk Maxwell in the 1860s. His elaborate series of equations demonstrate that the velocity of light through a material equals the speed of light in a vacuum (c) divided by the product of the square root of the material's dielectric constant (e) multiplied by the magnetic permeability (m) of the medium. In general, biological and related materials have a magnetic permeability very near 1.0, as do many conducting and non-conducting specimens of interest to the microscopist. The dielectric constant of a material is therefore related to the refractive index through a simple equation:

where e is a variable representing the dielectric constant, and n is the material's measured refractive index. This equation was derived for specific frequencies of light and ignores dispersion of polychromatic light as it passes through the material. Anisotropic crystals are composed of complex molecular and atomic lattice orientations that have varying electrical properties depending upon the direction from which they are being probed. As a result, the refractive index also varies with direction when light passes through an anisotropic crystal, giving rise to direction-specific trajectories and velocities.

Perhaps one of the most dramatic demonstrations of double refraction occurs with calcium carbonate (calcite) crystals, as illustrated in Figure 2. The rhombohedral cleavage block of calcite produces two images when it is placed over an object, and then viewed with reflected light passing through the crystal. One of the images appears as would normally be expected when observing an object through clear glass or an isotropic crystal, while the other image appears slightly displaced, due to the nature of doubly-refracted light. When anisotropic crystals refract light, they split the incoming rays into two components that take different paths during their journey through the crystal and emerge as separate light rays. This unusual behavior, as discussed above, is attributed to the arrangement of atoms in the crystalline lattice. Because the precise geometrical ordering of the atoms is not symmetrical with respect to the crystalline axes, light rays passing through the crystal can experience different refractive indices, depending upon the direction of propagation.

One of the rays passing through an anisotropic crystal obeys the laws of normal refraction, and travels with the same velocity in every direction through the crystal. This light ray is termed the ordinary ray. The other ray travels with a velocity that is dependent upon the propagation direction within the crystal, and is termed the extraordinary ray. Therefore, each light ray entering the crystal is split into an ordinary and an extraordinary ray that emerge from the distant end of the crystal as linearly polarized rays having their electric field vectors vibrating in planes that are mutually perpendicular.

Figure 3 - Birefringent Calcite Crystal Electric Vector Orientations

These phenomena are illustrated in Figures 2 through 4. The calcite crystal presented in Figure 3(b) is positioned over the capital letter A on a white sheet of paper demonstrating a double image observed through the crystal. If the crystal were to be slowly rotated around the letter, one of the images of the letter will remain stationary, while the other precesses in a 360-degree circular orbit around the first. The orientation of the electric vector vibration planes for both the ordinary (O) and extraordinary (E) rays are indicated by lines with doubled arrows in Figure 3(b). Note that these axes are perpendicular to each other. The crystal optical axis, which makes an equal angle (103 degrees) with all three crystal faces joined at the corner, is also indicated at the lower portion of the crystal. The degree of birefringence in calcite is so pronounced that the images of the letter A formed by the ordinary and extraordinary rays are completely separated. This high level of birefringence is not observed in all anisotropic crystals.

Transparent dichroic polarizers can be utilized to determine the electric vector directions for the extraordinary and ordinary rays in a calcite crystal, as presented in Figures 3(a) and Figure 3(c). When the polarizer is oriented so that all light waves having electric vectors oriented in the horizontal direction are transmitted (Figure 3(a)), waves having similar vectors in the vertical direction are absorbed, and vice versa (Figure 3(c)). In the calcite crystal presented in Figure 3, the extraordinary ray has a vertical electric vector vibration angle, which is absorbed when the polarizer is oriented in a horizontal direction (Figure 3(a)). In this case, only light from the ordinary ray is passed through the polarizer and its corresponding image of the letter A is the only one observed. In contrast, when the polarizer is turned so that the vibration transmission direction is oriented vertically (Figure 3(c)), the ordinary ray is blocked and the image of the letter A produced by the extraordinary ray is the only one visible.

In Figure 3, the incident light rays giving rise to the ordinary and extraordinary rays enter the crystal in a direction that is oblique with respect to the optical axis, and are responsible for the observed birefringent character. The behavior of an anisotropic crystal is different, however, if the incident light enters the crystal in a direction that is either parallel or perpendicular to the optical axis, as presented in Figure 4. When an incident ray enters the crystal perpendicular to the optical axis, it is separated into ordinary and extraordinary rays, as described above, but instead of taking different pathways, the trajectories of these rays are coincident. Even though the ordinary and extraordinary rays emerge from the crystal at the same location, they exhibit different optical path lengths and are subsequently shifted in phase relative to one another (Figure 4(b)). The two cases just described are illustrated in Figure 4(a), for the oblique case (see Figures 2 and 3), and Figure 4(b) for the situation where incident light is perpendicular to the optical axis of a birefringent crystal.

In the case where incident light rays impact the crystal in a direction that is parallel to the optical axis (Figure 4(c)), they behave as ordinary light rays and are not separated into individual components by an anisotropic birefringent crystal. Calcite and other anisotropic crystals act as if they were isotropic materials (such as glass) under these circumstances. The optical path lengths of the light rays emerging from the crystal are identical, and there is no relative phase shift.

Figure 4 - Separation of Light Waves by a Birefringent Crystal

Although it is common to interchangeably use the terms double refraction and birefringence to indicate the ability of an anisotropic crystal to separate incident light into ordinary and extraordinary rays, these phenomena actually refer to different manifestations of the same process. The actual division of a light ray into two visible species, each refracting at a different angle, is the process of double refraction. In contrast, birefringence refers to the physical origin of the separation, which is the existence of a variation in refractive index that is sensitive to direction in a geometrically ordered material. The difference in refractive index, or birefringence, between the extraordinary and ordinary rays traveling through an anisotropic crystal is a measurable quantity, and can be expressed as an absolute value by the equation:

where n(e) and n(o) are the refractive indices experienced by the extraordinary and ordinary rays, respectively. This expression holds true for any part or fragment of an anisotropic crystal with the exception of light waves propagated along the optical axis of the crystal. Because the refractive index values for each component can vary, the absolute value of this difference can determine the total amount of birefringence, but the sign of birefringence will be either a negative or positive value. A determination of the birefringence sign by analytical methods is utilized to segregate anisotropic specimens into categories, which are termed either positively or negatively birefringent. The birefringence of a specimen is not a fixed value, but will vary with the orientation of the crystal relative to the incident angle of the illumination.

The optical path difference is a classical optical concept related to birefringence, and both are defined by the relative phase shift between the ordinary and extraordinary rays as they emerge from an anisotropic material. In general, the optical path difference is computed by multiplying the specimen thickness by the refractive index, but only when the medium is homogeneous and does not contain significant refractive index deviations or gradients. This quantity, as well as the value of birefringence, is usually expressed in nanometers and grows larger with increasing specimen thickness. For a system with two refractive index values (n(1) and n(2)), the optical path difference (D) is determined from the equation:

Optical Path Difference D = (n1 - n2) • t (Thickness)

In order to consider the phase relationship and velocity difference between the ordinary and extraordinary rays after they pass through a birefringent crystal, a quantity referred to as the relative retardation is often determined. As mentioned above, the two light rays are oriented so that they are vibrating at right angles to each other. Each ray will encounter a slightly different electrical environment (refractive index) as it enters the crystal and this will affect the velocity at which the ray passes through the crystal. Because of the difference in refractive indices, one ray will pass through the crystal at a slower rate than the other ray. In other words, the velocity of the slower ray will be retarded with respect to the faster ray. This retardation value (the relative retardation) can be quantitatively determined using the following equation:

Retardation (Γ) = Thickness (t) x Birefringence (B)

Where G is the quantitative retardation of the material, t is the thickness of the birefringent crystal (or material) and B is the measured birefringence, as defined above. Factors contributing to the value of retardation are the magnitude of the difference in refractive indices for the environments seen by the ordinary and extraordinary rays, and also the specimen thickness. Obviously, the greater the thickness or difference in refractive indices, the greater the degree of retardation between waves. Early observations made on the mineral calcite indicated that thicker calcite crystals caused greater differences in splitting of the images seen through the crystals, such as those illustrated in Figure 3. This observation agrees with the equation above, which indicates retardation will increase with crystal (or sample) thickness.

The behavior of an ordinary light ray in a birefringent crystal can be described in terms of a spherical wavefront based on the Huygens' principle of wavelets emanating from a point source of light in a homogeneous medium (as illustrated in Figure 5). The propagation of these waves through an isotropic crystal occurs at constant velocity because the refractive index experienced by the waves is uniform in all directions (Figure 5(a)). In contrast, the expanding wavefront of extraordinary waves, which encounter refractive index variations as a function of direction (see Figure 5(b)), can be described by the surface of an ellipsoid of revolution.

Figure 5 - Wavefront Propagation in Anisotropic Crystals

The upper and lower limits of extraordinary wave velocities are defined by the long and short axes of the ellipsoid (Figure 5(c)). The wavefront reaches its highest velocity when propagating in the direction parallel to the long axis of the ellipsoid, which is referred to as the fast axis. On the other hand, the slowest wavefronts occur when the wave travels along the short axis of the ellipsoid. This axis is termed the slow axis. Between these two extremes, wavefronts traveling in other directions experience a gradient of refractive index, which is dependent upon orientation, and propagate with velocities of intermediate values.

Transparent crystalline materials are generally classified into two categories defined by the number of optical axes present in the molecular lattices. Uniaxial crystals have a single optical axis and comprise the largest family of common birefringent specimens, including calcite, quartz, and ordered synthetic or biological structures. The other major class is biaxial crystals, which are birefringent materials that feature two independent optical axes. The ordinary and extraordinary wavefronts in uniaxial crystals coincide at either the slow or the fast axis of the ellipsoid, depending upon the distribution of refractive indices within the crystal (illustrated in Figure 6). The optical path difference or relative retardation between these rays is determined by the lag of one wave behind the other in surface wavefronts along the propagation direction.

In cases where the ordinary and extraordinary wavefronts coincide at the long or major axis of the ellipsoid, then the refractive index experienced by the extraordinary wave is greater than that of the ordinary wave (Figure 6(b)). This situation is referred to as positive birefringence. However, if the ordinary and extraordinary wavefronts overlap at the minor axis of the ellipsoid (Figure 6(a)), then the opposite is true. In effect, the refractive index through which the ordinary wave passes exceeds that of the extraordinary wave, and the material is termed negatively birefringent. A diagrammatic ellipsoid relating the orientation and relative magnitude of refractive index in a crystal is termed the refractive index ellipsoid, and is illustrated in Figures 5 and 6.

Figure 6 - Refractive Index Ellipsoids

Returning to the calcite crystal presented in Figure 2, the crystal is illustrated having the optical axis positioned at the top left-hand corner. Upon entering the crystal, the ordinary light wave is refracted without deviation from the normal incidence angle as if it were traveling through an isotropic medium. Alternatively, the extraordinary wave deviates to the left and travels with the electric vector perpendicular to that of the ordinary wave. Because calcite is a negatively birefringent crystal, the ordinary wave is the slow wave and the extraordinary wave is the fast wave.

Birefringent Crystals in a Polarizing Optical Microscope

As mentioned above, light that is doubly refracted through anisotropic crystals is polarized with the electric vector vibration directions of the ordinary and extraordinary light waves being oriented perpendicular to each other. The behavior of anisotropic crystals under crossed polarized illumination in an optical microscope can now be examined. Figure 7 illustrates a birefringent (anisotropic) crystal placed between two polarizers whose vibration directions are oriented perpendicular to each other (and lying in directions indicated by the arrows next to the polarizer and analyzer labels).

Non-polarized white light from the illuminator enters the polarizer on the left and is linearly polarized with an orientation in the direction indicated by the arrow (adjacent to the polarizer label), and is arbitrarily represented by a red sinusoidal light wave. Next, the polarized light enters the anisotropic crystal (mounted on the microscope stage) where it is refracted and divided into two separate components vibrating parallel to the crystallographic axes and perpendicular to each other (the red open and filled light waves). The polarized light waves then travel through the analyzer (whose polarization position is indicated by the arrow next to the analyzer label), which allows only those components of the light waves that are parallel to the analyzer transmission azimuth to pass. The relative retardation of one ray with respect to another is indicated by an equation (thickness multiplied by refractive index difference) that relates the variation in speed between the ordinary and extraordinary rays refracted by the anisotropic crystal.

Figure 7 - Birefringent Crystals Between Crossed Polarizers

In order to examine more closely how birefringent, anisotropic crystals interact with polarized light in an optical microscope, the properties of an individual crystal will be considered. The specimen material is a hypothetical tetragonal, birefringent crystal having an optical axis oriented in a direction that is parallel to the long axis of the crystal. Light entering the crystal from the polarizer will be traveling perpendicular to the optical (long) axis of the crystal. The illustrations in Figure 8 present the crystal as it will appear in the eyepieces of a microscope under crossed-polarized illumination as it is rotated around the microscope optical axis. In each frame of Figure 8, the axis of the microscope polarizer is indicated by the capital letter P and is oriented in an East-West (horizontal) direction. The axis of the microscope analyzer is indicated by the letter A and is oriented in a North-South (vertical) direction. These axes are perpendicular to each other and result in a totally dark field when observed through the eyepieces with no specimen on the microscope stage.

Figure 8(a) illustrates the anisotropic tetragonal, birefringent crystal in an orientation where the long (optical) axis of the crystal lies parallel to the transmission azimuth of the polarizer. In this case, light passing through the polarizer, and subsequently through the crystal, is vibrating in a plane that is parallel to the direction of the polarizer. Because none of the light incident on the crystal is refracted into divergent ordinary and extraordinary waves, the isotropic light waves passing through the crystal fail to produce electric vector vibrations in the correct orientation to traverse through the analyzer and yield interference effects (see the horizontal arrow in Figure 8(a), and the discussion below). As a result the crystal is very dark, being almost invisible against the black background. For the purposes of illustration, the crystal depicted in Figure 8(a) is not totally extinct (as it would be between crossed polarizers) but passes a small portion of red light, to enable the reader to note the position of the crystal.

Microscopists classically refer to this orientation as being a position of extinction for the crystal, which is important as a reference point for determining the refractive indices of anisotropic materials with a polarizing microscope. By removing the analyzer in a crossed polarizing microscope, the single permitted direction of light vibration passing through the polarizer interacts with only one electrical component in the birefringent crystal. The technique allows segregation of a single refractive index for measurement. Subsequently, the remaining refractive index of a birefringent material can then be measured by rotation of the polarizer by 90 degrees.

Figure 8 - Birefringent Crystal Orientation in Polarized Light

The situation is very different in Figure 8(b), where the long (optical) axis of the crystal is now positioned at an oblique angle (a) with respect to the polarizer transmission azimuth, a situation brought about through rotation of the microscope stage. In this case, a portion of the light incident upon the crystal from the polarizer is passed on to the analyzer. To obtain a quantitative estimate of the amount of light passing through the analyzer, simple vector analysis can be applied to solve the problem. The first step is to determine the contributions from the polarizer to o and e (see Figure 8(b) the letters refer to the ordinary (o) ray and extraordinary (e) ray, which are discussed above). Projections of the vectors are dropped onto the axis of the polarizer, and assume an arbitrary value of 1 for both o and e, which are proportional to the actual intensities of the ordinary and extraordinary ray. The contributions from the polarizer for o and e are illustrated with black arrows designated by x and y on the polarizer axis (P) in Figure 8(b). These lengths are then measured on the vectors o and e(illustrated as red arrows designating the vectors), which are then added together to produce the resultant vector, r'. A projection from the resultant onto the analyzer axis (A) produces the absolute value, R. The value of R on the analyzer axis is proportional to the amount of light passing through the analyzer. The results indicate that a portion of light from the polarizer passes through the analyzer and the birefringent crystal displays some degree of brightness.

The maximum brightness for the birefringent material is observed when the long (optical) axis of the crystal is oriented at a 45 degree angle with respect to both the polarizer and analyzer, as illustrated in Figure 8(c). Dropping the projections of the vectors o and e onto the polarizer axis (P) determines the contributions from the polarizer to these vectors. When these projections are then measured on the vectors, the resultant can be determined by completing a rectangle to the analyzer axis (A). The technique just described will work for the orientation of any crystal with respect to the polarizer and analyzer axis because o and e are always at right angles to each other, with the only difference being the orientation of o and ewith respect to the crystal axes.

When the ordinary and extraordinary rays emerge from the birefringent crystal, they are still vibrating at right angles with respect to one another. However, the components of these waves that pass through the analyzer are vibrating in the same plane (as illustrated in Figure 8). Because one wave is retarded with respect to the other, interference (either constructive or destructive) occurs between the waves as they pass through the analyzer. The net result is that some birefringent samples acquire a spectrum of color when observed in white light through crossed polarizers.

Figure 9 - Michel-Levy Birefringence Chart

Quantitative analysis of the interference colors observed in birefringent samples is usually accomplished by consulting a Michel-Levy chart similar to the one illustrated in Figure 9. As is evident from this graph, the polarization colors visualized in the microscope and recorded onto film or captured digitally can be correlated with the actual retardation, thickness, and birefringence of the specimen. The chart is relatively easy to use with birefringent samples if two of the three required variables are known. When the specimen is placed between crossed polarizers in the microscope and rotated to a position of maximum brightness with any one of a variety of retardation plates, the color visualized in the eyepieces can be traced on the retardation axis to find the wavelength difference between the ordinary and extraordinary waves passing through the specimen. Alternatively, by measuring the refractive indices of an anisotropic specimen and calculating their difference (the birefringence), the interference color(s) can be determined from the birefringence values along the top of the chart. By extrapolating the angled lines back to the ordinate, the thickness of the specimen can also be estimated.

The lower section of the Michel-Levy chart (x-axis) marks the orders of retardation in multiples of approximately 550 nanometers. The area between zero and 550 nanometers is known as the first order of polarization colors, and the magenta color that occurs in the 550 nanometer region is often termed first-order red. Colors between 550 and 1100 nanometers are termed second-order colors, and so on up the chart. The black color at the beginning of the chart is known as zero-order black. Many of the Michel-Levy charts printed in textbooks plot higher-order colors up to the fifth or sixth order.

The most sensitive area of the chart is first-order red (550 nanometers), because even a slight change in retardation causes the color to shift dramatically either up in wavelength to cyan or down to yellow. Many microscope manufacturers take advantage of this sensitivity by providing a full-wave retardation plate or first-order red compensator with their polarizing microscopes to assist scientists in determining the properties of birefringent materials.

Categories of Birefringence

Although birefringence is an inherent property of many anisotropic crystals, such as calcite and quartz, it can also arise from other factors, such as structural ordering, physical stress, deformation, flow through a restricted conduit, and strain. Intrinsic birefringence is the term utilized to describe naturally occurring materials that have asymmetry in refractive index that is direction-dependent. These materials include many anisotropic natural and synthetic crystals, minerals, and chemicals.

Structural birefringence is a term that applies to a wide spectrum of anisotropic formations, including biological macromolecular assemblies such as chromosomes, muscle fibers, microtubules, liquid crystalline DNA, and fibrous protein structures such as hair. Unlike many other forms of birefringence, structural birefringence is often sensitive to refractive index fluctuations or gradients in the surrounding medium. In addition, many synthetic materials also exhibit structural birefringence, including fibers, long-chain polymers, resins, and composites.

Stress and strain birefringence occur due to external forces and/or deformation acting on materials that are not naturally birefringent. Examples are stretched films and fibers, deformed glass and plastic lenses, and stressed polymer castings. Finally, flow birefringence can occur due to induced alignment of materials such as asymmetric polymers that become ordered in the presence of fluid flow. Rod-shaped and plate-like molecules and macromolecular assemblies, such as high molecular weight DNA and detergents, are often utilized as candidates in flow birefringence studies.

In conclusion, birefringence is a phenomenon manifested by an asymmetry of properties that may be optical, electrical, mechanical, acoustical, or magnetic in nature. A wide spectrum of materials display varying degrees of birefringence, but the ones of specific interest to the optical microscopist are those specimens that are transparent and readily observed in polarized light.

Contributing Authors

Douglas B. Murphy - Department of Cell Biology and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205.

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Thomas J. Fellers and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.


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