Глава 6 - СТРАНИЦА ЗА ПРАБЪЛГАРИТЕ - ЕЗИК ... of Medical Physics... · Web viewCHAPTER 6. OPTICS 6.1. Fundamentals of geometric optics. Refraction and

$Page 1: Глава 6 - СТРАНИЦА ЗА ПРАБЪЛГАРИТЕ - ЕЗИК ... of Medical Physics... · Web viewCHAPTER 6. OPTICS 6.1. Fundamentals of geometric optics. Refraction and$
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016

CHAPTER 6. OPTICS

6.1. Fundamentals of geometric optics. Refraction and reflection of light. Fiber optics. Endoscopes

Electromagnetic radiation with from 1 nm to 1 mm is usually termed as optical radiation or light. Propagation of light in different media is studied in the geometric optics, a physical discipline that is based on four main principles:

1. In a homogeneous optical medium, light propagates in straight lines, in the form of light rays.

Fig. 6. 1. 1. Refraction and reflection of the light beam

at the boundary between two transparent optical media.

2. When two beams of low intensity cross at some point they preserve their initial parameters (frequency, intensity, phase angle) after their separation. This is the principle of independence of the light rays. For example, when the fundus (eye botom) is observed with reflected light (fundus reflex), the incident and reflected light do not interfere. This principle is, however, violated with the laser rays which have high intensity (nonlinear optics).

3 and 4. At the boundary between two different transparent media the light beam is reflected (the third principle) and refracted (the fourth principle).

Fig. 6. 1. 2. Dispersion of a white beam of light into multitude of colored rays during refraction through a glass prism.

Consider two different optical media in which light propagates at different speeds, C1, in the first medium and, C2, in the second one,

respectively. Assume a monochromatic light beam falling on the interface of the two media. As shown in the figure (Fig. 6.1.1), the incident light beam is partially reflected and refracted. The law of reflection states that the incident, reflected and refracted rays all lie in a common plane and the angle of incidence, , is equal to the angle of reflection, . The law of refraction (Snellius law) states that the angle of incidence, , and the angle of refraction, , are related: sin /sin = C1/C2 = n21. The n21 is dimensionless number called a relative refractive index of the second medium compared to that of the first one. If the first medium is a vacuum (C1 = Co), then n21 = n20 = Co/C2 = n2 is called a refractive index of the second medium. The refractive index is equal to 1 for air, approximately 1.33 for water, 1.5 for flint glass and could reach about 5 for optically dense media, such as the crown or heavy glass. For many optical media, n depends on , hence the angle of refraction is different for different wavelengths. In this case, a beam of white light, upon refraction, decomposes into a multitude of weaker beams with different colors; this is called dispersion of the light (Fig. 6.1.2).

The ability of a transparent media to decompose white light into its components of colored rays is expressed by their coefficient of dispersion, V, called the number of Abbe:

where nD is the refractive index for the yellow line with = 589.3 nm, nF for the blue line with = 486.1 nm and nC for the red line with = 656.3 nm. The greater

is the Abbe number the stronger is the ability of a medium to decompose the light and


the more pronounced is the chromatic aberration of the medium.The laws of reflection and refraction remain valid if the beam is passed in the opposite direction -

the principle of reversibility.

Fig. 6. 1. 3. Ray 1: refraction and reflection of a light beam at the boundary between glass (n = 1.5) and air (n = 1.0). The ray 2 defines the critical angle of incidence whereat total reflection takes place (rays 2 and 3).

The mirrors reflect virtually all light fallen on them. In most optical devices, however, the reflected light must be sufficiently low because it is an undesirable loss of energy. Upon reflection from the interface between two dielectric media the reflected light and, hence, the energy losses are smaller in case the speeds of light in both media are close to each other (as it is for the different layers of eye). Based on this

rule, lenses with special multy-layers coating, which reduce the loss of reflected light are used in optics (anti-reflective glass, optics).

. Fig. 6. 1.

4. Usage of the total internal reflection for the determination of unknown concentration (left) and for the transmitting of light beam through optical fiber (right).

When a light beam passes from an optically dense to optically less dense medium (n1 > n2), the angle of refraction, , is greater than the angle of incidence, , (fig. 6.1.3, ray 1). At a specific angle of incidence, called critical angle, cr, the angle of refraction is = 90° (fig. 6.1.3, ray 2). At greater angles of incidence there is no refraction and the entire beam is reflected remaining in the optically dense medium (fig. 6.1.3, ray 3). This phenomenon is called total internal reflection. Obviously, sin cr = n2/n1. The concentration of drugs, amino acids, sugars, etc., can be determined by measuring the cr of their solution with respect to a medium of optically dense glass (Fig. 6.1.4). This is the method of refractometry, whereby the second medium is a heavy glass (n around 5) and the first medium is the tested solution whose refractive index and, hence, critical angle depends on the unknown concentration. Similar devices (refractometers) are used in ophthalmology to determine the optical parameters of the eye. Prisms with total internal reflection are used in operational microscopes at surgery, where the path of light rays can be changed depending on the observed internal organ.

The total internal reflection is used for passing the light beam through transparent flexible filament with a diameter of 5-6 m (optical fiber) - fig. 6.1.4. The optical fiber consists of two concentric cylindrical glass layers, whereat the inner layer is optically denser towards the outside one. This condition provides the light beam to remain in the optical fiber. Bundle of flexible optical fibers forms an optical


cable, which is used to carry light beams and transmit an image at a distance (Fig. 6.1.5). Such an optical cable (flexible periscope) is used for observing and photographing the inner walls of tubes and the internal organs of human (blood vessels, stomach, heart), and for the observation of small objects in various anatomical cavities (ear, eye, nose) with needle-microscope (biomicroscope). Some modern spectrophotometers use an optical caples, which allow the configuration of the optical scheme and the function of the apparatus to be changed.

Фиг. 6.1.5. Make up of an optic cable.

Endoscopes (fig. 6.1.6) are thin, flexible and sterile tubes, which use optical cables for invasive monitoring of internal organs. Usually they contain four channels. An optical cabel equipped with light guide for illumination of the tested area with a "cold" light is inserted into the first channel. The second channel contains a second optical cabel for monitoring the illuminated spot. The third channel

is used for biopsy. If necessary, a fourth channel is used for the insertion of a therapeutic laser beam, electrocoagulator, rinsing solution, compressed air, and others. The “cold” light is a visible light, devoid of any infrared components by filtration in order to prevent overheating of the illuminated spot.

Fig. 6. 1. 6. Schematic structure of an endoscope.

In general, endoscopes are necessary tool in the so called non-invasive

or minimally invasive surgery (laparoscopy, laparotomy). In this type of surgery smallest possible incisions and interventions are made in order to strongly reduce the recovery period after surgery. Modern medicine uses different types of endoscopes: fibrogastroscopes, colonoscopes, rectoscopes.

In some modern endoscopes light emitting diods (LEDs) and miniature television (TV) cameras are mounted at the forehead of a flexible optical cable. The cable is inserted into the endoscope allowing the LED to illuminate the observed cavity or object. At the same time the television camera creates wide angle image that is transmitted and displayed on a screen at the other end of the endoscope.

6.2. Optical lenses and their optical aberrations

The optical lens is a transparent body enclosed by two curved surfaces. The main function of lenses is to deflect and focus the light beams through refraction. Most often, the surfaces are spherical because the lenses with such surfaces are most easily produced. Lenses with spherical surfaces, however, have special optical flaws - spherical aberration and distorted focal plane. Lenses made with parabolic surfaces do not have these disadvantages, but they are ground and polished with more difficulty.


Fig. 6. 2. 1. Course of the light rays at a positive or converging (A) and negative or diverging (B) optical lenses.

In general, the lenses are positive (converging) and negative (diverging). If a sheaf of parallel light rays passes through an optical lens, each ray is refracted at the lens surfaces. The converging lens refracts each ray in such a way that all the output beams collect at a single point, F, called real focal point or focus (fig. 6.2.1 - A). At the diverging lens the incident rays are deflected in such a way that their backward projections meet at a point called imaginary focus, F (fig. 6.2.1 - B). The type of the lens, convergent or divergent, depends on whether its surfaces are convex (bulging outwards from the lens, positive curvature and radius) or concave (negative curvature and radius) or planar (flat).

Fig. 6. 2. 2. Kinds of spherical lenses. Under each lens the sign of the curvature of the front and rear surfaces is shown.

The main (cardinal) elements of an optical lens are: 1. Main optical axis - this is the common normal to both surfaces of the lens; 2. Main plane - the plane in which each incident and refracted rays cross themself; 3. Optical center - the intersection point of the main optical axis with the main plane; 4. Focal plane - a plane parallel to the main plane and passing through the focal point.

The focal length, f, is the distance between focal point and optical center. For thin lenses it depends on the radii, R1, and, R2, of curvature of the spherical surfaces according to the equation:

1/ f = (n - no). (1 / R1 1 / R2) = F

In this formula F is called optical power (refractive ability) of the lens and is measured in diopters, where f is in meters. Fig. 6.2.2 shows the types of spherical lenses and the sing "+" or "-" of the radius of their front (R1) and a rear surface (R2). The double convex lens is often called a monocle while the double concave one – a meniscus. The index of refraction, n, of the lens must have a larger value than that of the environment medium, no, in order to obtain a greater optical power. For air, nо = 1. The ocular lens has greater optical power due to the protein crystalline, dissolved in it. The curvature of surfaces of ocular lens, i.e., the radii R1 and R2 and, correspondingly, the optical power of ocular lens can change to


allow the eye to accommodate for near and distant vision.Each optical system (eye, a microscope, etc.) represent a suitable combination of optical elements;

lenses, prisms, mirrors, light filters, diaphragms, optical stops and so on used to obtain the image of an object. Its radiant diagram, i.e., the optical course of the light beams, is obtained on the basis of the principles of linear optics, including the laws of reflection and refraction. Typically, optical systems are centered, this means that the focuses of all lenses and their principal optical axes coincide with a common straight line. Each optical element is made using suitable material transparent for the light in the respective optical region. For example, if visible light should be processed, the lenses and prisms are made of usual glass while quartz glass is used for the light from the ultraviolet and near infrared region. On the other hand, lens of alkali metal salts are used for the light from the far infrared region.

Fig. 6. 2. 3.

Radiant diagrams showing how the image of the object is formed using a convergent lens. (A) - the object is between the lens and its front focal point, (B) - the object is far away in front of the front

focal point.

Consider the point A of a given object emitting light rays which refract through a lens to gather at the point A', called an image of the point A. Fig. 6.2.3 shows how, using two beams, we can find the image of an object obtained by a convergent lens. In case B, the object is placed far away from the frontal focus and its image is real, inverted, and atenuated. The image is real when it can be projected on a screen and becomes visible. If a photographic plate is put on the screen, the image will be preserved. In this way an image of a distant subject is obtained in the photographic camera and on the retina of the eye. However, if the object is placed closely to the frontal focus of the lens, the image is again real and inverted, however, it becomes magnified. In this way the first lens, objective, of each light microscope works creating an enlarged image of the observed microobject. In case A (fig. 6.2.3), the object is placed between the focus and the lens and the obtained image is magnified, upright and virtual. It can be seen by a human eye, located closely behind the lens, observing the backward projections of the beams where they intersect. In this case, the lens is called a magnifying glass. The ratio of the segments АВ /АВ is called magnification of the magnifying glass (typically 3 to 10 times). The second lens, eyepiece, of each microscope works as a magnifying glass additionally increasing the image, formed by the first lens.

Consider a lens having focal length, f, and diameter, D. The ratio N = f/D ratio is called focal ratio (relative aperture or f-ratio, f-stop, f-number). It is expressed as a fraction with a numerator equal to f and denominator equal to the f/D ratio.

The D/f ratio, raised in square power, (D/f)2, is called light power. The larger is the light power, the brighter and well illuminated will be the image produced by the lens.

Lenses with small relative aperture (large light power) produce small sized but brighter images. Lenses with larger relative aperture (small light power) create faded images that have large sizes. Such lenses have higher space resolution, because they allow the object to be seen in details if sufficiently illuminated. The lens of human eye is adapted for daylight vision and it has a large relative aperture. Conversely, the ocular lenses of the night waking animals have small relative apertures.

If the lens is perfect, each point of the observed object will correspond to a single point in his


image. In this case, the obtained image will be without optical flaws. This is not true for the real lenses which demonstrate the following optical shortcomings (aberrations): spherical aberration, chromatic aberration, coma, astigmatism, curvature of the image field and distortion.

1. Spherical aberration (fig. 6.2.4 and fig. 6.2.6). The light rays passing through a spherical lens at different distances from its optical center are not collected in a single focus. In the converging as well as in diverging lenses the peripheral rays are stronger refracted than the central ones, resulting in a shift in the focus of the peripheral beams in respect to that of central beams. Fig. 6.2.4 indicates that the focus of a converging lens for the peripheral rays will be displaced in opposite direction in respect to the same focus in diverging lens. In other words, the sign of the spherical aberration of converging lenses is opposite to that of diverging lenses.

Fig. 6. 2. 4. Spherical aberration of converging and diverging lens.

2. Chromatic aberration (Fig. 6.2.5). The light rays of different colors are not collected at a single focus. This is due to the dispersion of light - the dependence of the refractive index, n, of the lens on the wavelength, , whereat the blue rays are stronger refracted than the red ones. As a consequence, the focus of blue rays is displaced from the focus of red rays. As for spherical aberration, the focus of converging lenses for the blue light is displaced in the opposite direction compared to that of the diverging lenses. Thus, chromatic aberration has opposite signs in converging lenses in respect to that in diverging lenses.

Fig. 6.2.5. Chromatic aberration in converging and diverging lenses.

Each spherical lens has both spherical and chromatic aberrations. Instead of single lenses, the optical devices (light microscopes, projectors and the like) use double or even triple complexes of lenses. Each such double lens (dublex) consists of one converging and another one diverging lens, adjacent to each other. In general, such a dublex is entirely devoid of spherical aberration and, partially of chromatic aberration. Its color shortcomings could be removed for two or three different colors. Removal of these optical drawbacks is due to the fact that each of them has an opposite signs in converging and diverging lenses. In addition, the two components of each duplex are made from glasses with different refractive indexes (flint glass and crown glass) or glasses, containing fluoride or lanthanum. The dublex is achromate if its chromatic aberration is corrected for two different wavelengths of light (two colors), however, it may have residual chromatic aberration for other colors. Optical system of two or more lenses in which the chromaticism is zero for three colors is called apohromate. The lens of the human eye is achromatic for the red and chromatic for the blue light.

3. Coma. This is a special case of spherical aberration and occurs when the incident beams are inclined to the optical axis (Fig. 6.2.6). The peripheral beams of the light bundle falls obliquely to the optical axis, hence, they are refracted more than the central rays due to the non-uniform refraction of the


different zones of the lens. The rays passing through different zones of the lens focus at different focal points. The peripheral rays falling at large angles (50-70°) to the optical axis form an image of a point that represents a stain with a tail like a comet. Similar to the spherical aberration the coma is removed using dublex of lenses with different refractive indexes, n, and different radii of their spherical surfaces. In addition, any optical instrument contains optical stops (rings, diaphragms, lens rims) that admit the passage only of the central rays falling at small angles to the optical axis. In the eye, the pupil plays the role of such aperture. Lenses with corrected coma and spherical aberration are called aplanats.

Fig. 6. 2. 6. Spherical aberration (on the left) and coma (to the right) for a converging lens.

4. Astigmatism (from the Greek word “stigma” = point, speck and the suffix “a” = no). It is due to the unequal refractive power of the lens in its various longitudinal cross sections. Astigmatism occurs in two cases. The first, main reason for astigmatism is the unequality of the curvatures of the two mutually perpendicular planes of the lens, causing different focal lengths in these planes. This mechanism underlies the astigmatism of eye lenses, which is corrected by cylindric lenses. If a lens is stretched horizontally in its main plane a cylindrical lens will be produced. Thereby, the curvature and refraction power of the lens in the extended direction will decrease. For a given object such lens will produce defected image consisting of large number of images horizontally shifted and overlapping each other. The astigmatism of ocular lenses can be corrected using a cylindrical lens which is deformed in the perpendicular direction compared to that of the ocular lens. Lens or combination of lenses devoid of astigmatism is called anastigmat e .

Fig. 6.2.7. Astigmatism of oblique rays.

In the second case, astigmatism occurs when the incident sheaf of beams is inclined to the optical axis (fig. 6.2.7). The beams of the two mutually perpendicular longitudinal sections of the sheaf, such as in the vertical and horizontal planes, do not focus in a single

point. Hence, the image of a point is not a point but a spot with the shape of a circle, ellipse or segment.5. D istortion of the image field . In spherical lenses this shortcoming is due to the fact that the

multitude of focal points of beams falling at different angles to the optical axis of the lens is not a plane but a part of the sphere whose edges are closer to the lens. In other words, the focal plane of these lenses is a portion of a spherical surface. Since the screens and the photographic plates are flat, the image can be sharp at the center and blurred at the edges or sharp at the edges and blurred at the center . In human eye,


the retina lies on the rear spherical surface of the vitreous body and, thus, the ocular lens lacks this optical shortcoming.

6. D istortion is due to the fact that the linear magnification of the lens is not constant and depends on the height of the monitored object. This shortcoming causes a square figure to be displayed as spherically convexed or concaved quadrangle (tetragon) (fig. 6.2.7). Distortion is positive (cushion like) and negative (barrel like). It is positive when the linear magnification of the lens increases with the slope of the light beam, and vice versa. Distortion is most frequently corrected using a diaphragm (aperture). If the aperture is placed between the lens and the object the distortion becomes negative; if the aperture is placed between the lens and the image – it is positive. There is no distortion when the diaphragm is placed in the middle of the optical system, for example if the system contains two lenses (like the human eye) the diaphragm must be placed between them. Such an image, devoid of distortion, is called ort h os c opic .

Fig. 6. 2. 8. Distortion of the image. A) shape of the observed object; b) shape of the image with positive distortion, c) shape of the image with negative distortion.

Each optical system should have minimal, i.e., balanced optical aberrations. This is achieved by using suitable combinations of lenses (converging and diverging), suitable types of glasses for the manufacture of the individual lenses, and sometimes by the use of non-spherical lenses with parabolic surfaces. Diaphragms, restricting the peripheral rays are also used.

6.3. O ptical system of human eye . Accommodation and refractive power of human eye. Optical aberrations of the eye and their correct ion

Human eye is a complex optical and physiological system for converting the energy of visible

optical radiation into nerve impulses. Through the optical nerve the impulses reach the visual center of the brain and provide information on the shape, size and color of objects and their location in space. Humans obtain over 80 % of the information for outside world through the vision.

The most important point in the vision is the absorption of light by the photosensitve protein, the visual pigment. Prior to this end point, the light entering the eye is directed towards the visual pigment through refraction at several interfaces. The outermost surface of eye is covered by an opaque coating, sclera, which at its front part is salient and transparent, cornea (Fig. 6.3.1). Inside the volume enclosed by the sclera a possitive presure (intraocular presure) is created that supports the sclera in a stretched condition. There is a second layer under the sclera which in its front part is colored and contains an opening, pupil. Pupil acts as a variable diaphragm, restricting the flow of light rays through the lens of the eye and reduces optical aberrations. Eye lens is composed of tightly stacked transparent cells (fiber cells) whose cytosol contains the soluble protein crystallin. The concentration of this protein (about 30%) provides high refractive index to the eye lens. Eye lens can change the radiuses of its front and rear surfaces due to the lateral ciliary muscles and the ciliary bodies. The contraction of lateral muscle allows the shrinkage of eye lens and increase in its refractive power. The anterior chamber, filled with an aqueous solution, is situated in front of the eye lens while a spherical body, filled with vitreous substance (vitreous body, back chamber), is placed behind the eye lens.

The rear surface of the vitreous body is coated with a retina - a layer of visual cells (photoreceptors). The visual cells contain a photosensitive (visual) pigment, which is a protein substance.

Light rays passing through the pupil of the eye are focused by the eye lens onto the retina, respectively, on the layer of visual cells. Thus, the image of the observed objects is always placed on the


retina. Photons of light falling on a given visual cell are absorbed by the molecules of visual pigment which change their conformation. This triggers a photobiological process in the visual cell leading to the generation of photoreceptor potential, which reaches the nearby layer of nerve cells. In turn, the nerve cells transform the photoreceptor potential into nerve-electric impulses that have the ability to travel over a long distance down the optic nerve reaching the visual center of the brain. Brain is connected with the retina through the optic nerve, which enters the rear side of eye and reaches the retina in the area called blind spot. Of course, there is no visual cells in the blind spot and objects whose image falls in its place are not visible.

Fig. 6.3.1. Cross-section of a human eye.

Visual cells in the retina are of two types, designated according to their shapes as rods and cones. In fact, they also differ by their light-sensitive pigments. The rods are more numerous than cones and contain only one type of pigment capable to absorb the light primarily from the short-wave end of the visible spectrum. Rods have a uniform distribution in the retina and are responsible for the night and peripheral vision as well as for viewing the low intensity light and various shades of grey. According to their visual pigments the cones are divided into three subtypes, which are sensitive to the blue, green and red light, respectively. The cones are responsible for the color vision in bright light. They are concentrated in one place, the yellow spot (fovea, macula). Objects whose images fall in the macula are seen in color and with greatest clarity. Therefore, the visual axis of the eye passes through the macular and does not coincide with the optical axis (fig. 6.3.1).

Fig. 6.3.2. A simplified optical diagram of Fig. 6. 3. 3. Reduced eye and the formation of

human eye. image on the retina.


An important feature of human vision is that when the image formed on the retina is stationary (static), it does not cause visual sensation. This is probably due to the mechanism transforming the photoreceptional potential into nerve impulses in the adjacent layer of neural cells. To have a visual perception, the image must either be moved from one place to another on the retina, or the light intensity must vary. Such conditions exist when the observed object is moving. To maintain the visual perception of an immobile object, the eye itself performs continuous and rapid movements (tremor) which directs the visual axis in different directions and makes the image of the object to move on the retina.

The optical system of the eye consists of two lenses - cornea (positive meniscus, converging lens) and eye lens (biconvex, converging lens) (fig. 6.3.2). This combination of two lenses (dublex) removes the chromatic aberration for red, but not for blue light. The spherical aberration is completely removed as the eye lens is non-homogenous; compared to peripheral cells, the cells located in the center of the lens contain more crystalline, which increases the refractive index of the central rays. The distorted field aberration is also removed due to the spherical form of the retina.

Fig. 6.3.4. Correction of hyperopia (far sight) with a converging lens (A) and myopia (near sight) with diverging lens (B).

The eye is usually engaged in the observation of objects, situated far away from the frontal focus of its optical system. Hence, the eye forms real, attenuated and reversed images on its retina. This type of image formation can be explained replacing the optical system of eye by a single and virtual lens called reduced eye (fig. 6.3.3). Indeed, in the first weeks after birth, children see the objects reversed, but soon after the images are corrected due to the neuro-physiological processing of the visual perception.

Table 1. Optical defects of the eye

Vision defect

Common term

Physical cause Physical correction

Myopia Near sight

Elongated eyeball or over curved cornea

Diverging eye glass

Hyperopia Far sight Flattened eyeball or under curved cornea

Converging eye glass

Astigmatism - Unequally curved cornea

Cylindrical lens

Presbyopia Old age sight

Lack of accommodation

Converging lens (reading glasses)

The reduced eye consists of a single converging lens whose optical center is positioned closer to the cornea than the retina. As a result, the eye has small relative aperture and reduced ability to collect light energy. However, the image size on the retina is large and ocupies an area containing large number of visual cells. Hence, the optical resolution of eye, i.e., its ability to distinguish two closely spaced points


on the observed object is very high. This is typical for a viewing suitable for daylight conditions. In animals adapted to night vision (mice, cats), the relative aperture of their eyes is large (wide lens, small focal length), and their eyes have a strong ability to gather light, but they have lower optical resolution.

Similar to the binaural hearing effect, the viewing with two eyes allows for the determination of distance to observed objects and in depth location of objects. This is the so called stereoscopic effect or three-dimensional vision (volumetric vision, vision with perspective). In humans and many animals (hunters, predators) the main optical planes of both ocular lenses coincide with the face plane. This reduces the angle of vision, but enables stereoscopic observation and, at the same time, both eyes form a single image of the observed field. For other animals and birds (particularly victims of predators) the eyes

are located laterally of the head in two different planes. This greatly increases the angle of view, furthermore, each eye forms its own image of the observed field.

Fig. 6.3.5. Astigmatism of human eye and its correction with a combination of cylindrical and spherical lenses.

The eye is an auto fucusing optical system. This is due to the ciliary muscle, positioned like a ring around the ocular lens and linked to the eye rim (Fig. 6.3.1). When the muscle is relaxed, the radius of

the ring is the largest and the links pull the lens along its equator stretching it radially. At this state the lens has the longest focal length and is adapted to long range vision. Contraction of the ciliary muscle reduces its radius allowing the ocular lens to shrink elastically. At this state the eye lens has the minimal focal length and is adapted to short range vision. The maximal contraction of ciliary muscle is accompanied by increase in the curvature of ocular lens, reduction of focal length and increase in the optical power of the eye by about 20 %. The relaxation and contraction of ciliary muscle allows the images of objects which differ in their distance to the eye to be formed at the same place (accommodation). For the normal eye this place is the retina (emmetropia). However, for the eye whose lens has optical defects this place does not coincides with the retina (ammetropia).

Fig. 6. 3. 6. Monitoring the eye fundus with the usage of ophthalmoscope.

When we look at an object distant away from us at more than 8-10 meters (distant point of clear vision), the ciliary muscles are relaxed and at rest. This condition is called n on- accommodated eye. While looking at closer

objects the ciliary muscle is contracted and the eye lens shrinks. This condition is refered to as accommodated eye. At maximum contraction of the ciliary muscle, the rear focal length of the eye lens is reduced by about 20 %, whereby the image of a point located approximately 92 mm from the top of the


cornea (the proximal point of clear vision) is projected on the retina. The distance between the proximal and distal points of clear vision, expressed in diopters, is the power (volume) of accommodation - usually about 11 diopters. For normal eye the distance of 25 cm between the object and the eye is called distance of the clearest vision as it is the distance for most comfortable reading and working with small objects.

The most common optical defects of the eye are enlisted in Table 1. The ammetropia takes place when looking at infinity (accommodation at long range vision) and the rear focus does not lie on the retina. In short sight (myopia), this focus is in front of the retina (increased refractive power) while at far sight (hyperopia) the focus is behind the retina (reduced refractive power). In the first case, only nearby objects are seen clearly as their images are focused on the retina. To achiev clear vision for distant objects, a diverging lens is placed in front of the eye reducing the refractive power of the eye (Fig. 6.3.4 right). In hyperopia, all objects appear blurred, especially those placed close to the eye. The reduced refractive power of the ocular lens is corrected by a suitable converging lens (Fig. 6.3.4 left).

In some cases, the refractive powers of the eye, measured in two meridional planes, horizontal and vertical ones, are different - astigmatism. The defect is compensated using a cylindrical lens with refractive power in such a meridional plane where the eye has reduced refractive power (Fig. 6.3.5). Usually, this defect is combined with myopia, which is corrected with a diverging lens. Both lenses, for the correction of astigmatism and myopia, are combined into a single lens with suitably tailored surfaces.

Ophthalmoscope and ofthalmometer are invented by the French physicist Helmholtz (1851). Ophthalmoscope (Fig. 6.3.6) allows the light reflected from the fundus to be focused in a clear image, in which the retina and the adjacent layer of nerve cells and blood vessels are well differentiated. Using this valuable tool the disorders of blood vessels, caused by high blood pressure, are easily established. There is newer method for this purpose, the fluorescein angiography, whereby the fluorescent substance fluorescein is injected into the circulatory blood system of the patient and prompt monitoring of the fluorescence of fundus is accomplished with ophthalmomicroscope. Fluorescein penetration into the blood makes the tissues of fundus visible, allowing the study of passability of vascular system and permeability of tissue of the eye. The detachment of retina is established by the usage of ultrasonography A or B of the eye. The detached retina is fixed with the help of a laser beam that thermally denatures proteins in a certain point of the retina and glues them to the base. In cataracts, the crystalline of ocular lens and vitreous body is changed becoming insoluble. The formed aggregates of crystallin strongly scatter light and the lens becomes opaque. In this case, the eye can be examined with an ultrasonic echography A and B.

Optical power of the eye is measured by r etinoscop which allows measurement of the accommodation ability of the eye in prescribing appropriate glasses. In prescribing the anti - astigmatism glasses the shape and curvature of the cornea is controlled with the help of o ph t h almomet e r (keratometer). The t onometer represents a gauge for indirect measurement of intraocular positive pressure, used in prevention of the optic nerve damage at glaucoma, a disorder causing partial or complete blindness. In ele c troretinogra phy the temporary course of the electric potential of the retina is measured and recorded over time.

6.4. Photometric quantities and units. Spectral sensitivity of human eye. Mechanism of color vision

Photometry is a branch of optics which studies the transfer of light energy from one medium to another. In a narrower sense, photometry studies the effects of light, induced in human eye. In this regard, the main photometric quantities (luminous flux, illuminance, luminous intensity, etc.) that characterize the visible optical radiation are studied and used in medicine as important hygienic standards.

Optical radiation is emitted from light sources and arriving at a given surface illuminates it. The radiant (radiometric) flux, Ф, (watt, W) equals the ratio of radiant energy (the energy of light radiation) flowing through a given surface per unit time interval t, much greater than the period of oscillation of the light wave. The radiant energy is actually the number of photons multiplied by the average energy of the photons, it is an objective value, independent of the way it is measured. The radiant flux, Ф, is always


transfered through a given area, S, and the ratio Ф/S is referred to as radiant flux density or irradiance (W/m2). In general, the irradiance, E = Ф/S, where Ф is the radiant flux arriving at the infinitesimal area, S. For uniform radiant flux flowing across a finite surface area, S, the irradiance, E = Ф/S.

Monochromatic (single color) light means a stream of light beams having the same wavelength (), i.e., of the same color. Human eye perceives the light rays, having higher radiant flux density, as being brighter. When the eye receives monochromatic light, the visual perception (sense of brightness) depends not only on the radiant flux density, but also on . In other words, at the same radiant flux density, the sense of brightness depends on the color of light rays.

Therefore, to express quantitatively the light perception, the radiant flux, Ф, is replaced by another similar quantity, called luminous fl ux , Фlum, which gives the exact visual assessment of the magnitude of the radiant flux: Фlum = V. Ф. The multiplier, V, is called spectral sensitivity of human eye. The V

strongly depends on the wavelength, , and has a bell shaped plot as shown in fig. 6.4.1. For an eye, adapted to bright light (photopic vision), the bell-shaped dependence of V has a maximum at 555 nm. In this condition the human eye is most sensitive to radiation at 555 nm, while it is less sensitive to the rays of blue and red ends of the visible range. However, for an eye, adapted to dark light (scotopic vision), the bell-shaped dependence of V is displaced to shorter wavelengths and has a maximum at 507 nm (fig. 6.4.1).

Fig. 6. 4. 1. Curves of spectral sensitivity of human eye for the scotopic (dark - adapted) and photopic (light - adapted) vision.

Luminous flux is a photometric equivalent of the radiant flux according to the response of the eye of a “standard observer”. Its unit of measurement is lumen (lm). Luminous flux density (illuminance) is photometric equivalent of the radiant flux density

(irradiance). It is measured in lux (lx) or lumens per square meter (lm.m-2). Based on above, the photometry could be defined as a science for measuring visible light in units

that are weighted according to the sensitivity of the human eye, adapted to seeing at either day light or night light.

Thus, photometry convertes the radiant (physically measured) values into luminous (visually perceived) values using two internationally accepted photometric curves for the spectral sensitivity of human eye, obtained at photopic (day light) and scotopic (night light) conditions. In photopic curve, yellow-green light (max = 555 nm) receives the greatest weight because it stimulates the eye more than the light with other colors of equal radiant flux. In scotopic curve the blue-green light (max = 507 nm) receves the greatest weight because it stimulates the eye more than the light with other colors of equal radiant flux.

Looking at a given area, S, from a distant point we say, that the area is seen under the solid angle = S / R2, where R is the distance from the area to the point of observation. Consider a light source is placed at the point of observation, illuminating the area, S. If the size of the light source is negligible, compared to the distance R, it can be regarded as a point sourc e of light . The luminous intensity , I, of a

Tabl. 6.4.1. Relation between irradiance and illuminance at different light sources.

Source of light Irradiance(in W.m-2)

Illuminance(in lux)

Sun light 1000 100 000Sky light 100 10 000Overcast day light 10 1000Moon light 0.001 0.1Star light 0.0001 0.01


point sourse is the luminous flux, Фlum, emitted by the point sourse per unit solid angle, , into a given direction, i.e., I = Фlum / . The luminous intensity is measured in candela (cd) and is photometric equivalence of the radiance (or rediance intensity), which is measured in watts per steradian (W/sr). The unit of candela (cd) is reproduced with platinum body, heated to the temperature of solidification of platinum (1773.4°C), which emits light with intensity of 60 candelas per 1 cm2 area.

The light sources which have the form of large radiant surface (radiant screen, a large lamp, etc.), are characterized by their l uminous power , this is the luminous flux emitted per unit area of the surface. It is measured in lumens per square meter (lm/m2). The brightness of this light source is defined as the intensity of light emitted from a unit area of surface in a given direction. It is measured in candelas per square meter (cd/m2). For far, very remote light sources, visible as point sources, it is more correct to use the

term luminance instead of brightness.The illuminance, E, (lm/m2 or lux, lx) of a surface with area, S, means the luminous flux, Фlum,

falling perpendicularly on unit area, i.e., Е = Фlum/S (Kepler's law). Consider a point source of light with luminous intensity, I, is placed at a distance, R, from the illuminated surface and the light beams fall at an angle to the normal of the surface. Then the illuminance will be E = I.cos()/ R2 - Lambert' cosine law. Illuminance is the photometric equivalent of irradiance (table 6.4.1). What we perceive in our visual perception is the illuminance.

The above quantities and laws are basic in determining the hygiene standards for illumination of the working and recreation premises. Violation of these standards is an important cause for eye disease.

Fig. 6.4.2.(A) - Spectral curves for light sensitivity of eye in dark and bright light vision. (B) - Differential spectral curves of light sensitivity of the three types of visual cones.

The photometric quantities are measured with photometers which rely on

the photoelectric effect. This effect is explained by the quantum conceptions of light, considering the light energy as concentrated in microscopic corpusculs called photons. Thus, each photon carries energy E = h.. Photoelectric effect consists in absorbing a photon by an atom followed by knocking out of valent electron. In order to release such electron, the photon must have energy higher than the binding energy of the valent electron. The released electron increases conductivity or generates electromotive force. Each photometer converts the energy of light into electric current or voltage whose magnitude is proportional to the irradiance of the light flow.

Similar to human eye, the photometers have different sensitivity to different light rays depending on their color. Using monochromatic light with various and the same irradiance, the indications of the photometer will depend on , i.e., they will give different values at the same irradiance. Fortunately, the


spectral sensitivity of most photometers is similar to that of the human eye and is described by the same curve as that shown in fig. 6.4.1. Therefore, not the radiant but luminant quanitities (flux, intensity of the light source, illuminance) are used in the practice as they are actually measured by photometers and are important for the perception of light by human eye.

The weakest light, perceived by the eye, defines the so called absolute threshold of vision. Photosensitivity of the eye (the visual acuity) is reciprocal to the absolute threshold of vision, and both variables are dependent on the wavelength of light. The human eye is capable of perceiving light rays largely differing by its irradiance. This is achieved thanks to the visual adaptation which is based on the following mechanisms. Only photoreceptor cells of the type rods participate during the viewing in dark light (night, scotopic vision). Due to the large number of these cells, the sensitivity and visual acuity at scotopic vision are very high. In addition, they are further enhanced by the synthesis of additional visual

pigment in the rods. During the viewing at twilight a part of the cones is also included. The viewing at bright light (day, photopic vision) involves only the cones which are about 30 times less numerous than the rods. In addition, the pupil decreases its area around 16 times. All this helps, along with neuro-physiological suppression of excitement, the human eye to perceive light which differs in its intensity about 1012 times.

While adaptation to low light intensity is aimed at achieving high acuity of vision, the adaptation to bright light allows the eye to see the colors of observed objects. How is this achieved? The spectral sensitivity of the eye, adapted to low light intensity, depends only on the sensitivity of rods. The rods contain only one type of visual pigment, hence, this

sensitivity has only one peak, located in the blue end of the spectrum at 507 nm (fig. 6.4.2 (A), curve 1). This explains the fact that objects, observed in low light intensity, have no colors, indeed, they have dim, weak bluish hue. The visual pigment of rods is the protein yodopsin. In isolated state yodopsin has spectral curve of absorption matching the spectral curve of the photosensitivity of rods. This coincidence is explained by the fact that the photobiological process in rods begins with the absorption of light by their visual pigment.

Fig. 6.4.3. New colors obtained by mixing the three basic spectral colors; red, green and blue.

The visual pigment of cones is the protein rhodopsin. The rhodopsin is of three variants, whereat each variant is found in a separate group of cones. Thus, there are three types of cones all involved in the bright light vision. Each type of rhodopsin and, respectively, cones has its own spectral absorption curve, as shown in fig. 6.4.2 (B). One type of cones has a maximum

absorption at 562 nm, the second at 500 nm, and the third at 449 nm. According to their pigment, the different types of cones are sensitive to red, green or blue-violet light. This allows objects to be seen in a different colors depending on the spectral composition of light coming from them. Depending on their wavelength, the individual rays are absorbed by the respective type of cones which generate respective flow of nerve impulses to the visual center of brain. Thus, depending on which type of rays dominates, the respective perception of color will result. Accordingly, color vision is only possible when the viewing process involves the cones, i.e., at the photopic vision when the objects are illuminated with bright light.

Tab. 6. 4. 2. Color areas in the spectrum of visible light

From 380 to 450 nm - violetFrom 450 to 480 nm - blueFrom 480 to 510 nm - blue-greenFrom 510 to 530 mn - GreenFrom 530 to 575 nm - a yellow-greenFrom 575 to 585 nm - yellowFrom 585 to 620 nm - orangeFrom 620 to 760 nm - red


In the adaptation to intense light, the spectral sensitivity of the eye reflects the total, integrated (averaged on individual cells) sensitivity of cones (Fig. 6.4.2 (a), curve 2). Due to the smaller number of these cells, it is much weaker than the sensitivity of eye adapted to scotopic vision.

Within the range of visible light from 380 to 760 nm, the human eye differentiates 8 color areas shown in Table 6.4.2. The discovery of three types of pigments in the cones and thus three types of cones in humans confirmed the three-component theory of color vision. It was created by the physicists Young and Helmholtz far before the discovery of visual cells and is based on the following physical facts. Upon the decomposition of white light by dispersion prism a large number of color rays are obtained, each one with a certain . Six of these colors are considered to be pure spectral colors: red, orange, yellow, green, blue and violet. When mixing light rays with two different spectral pure colors with various intensity the light with new, intermediate colors are obtained. For example, by combining beams of green and red, a new color light having yellow color is obtained (Fig. 6.4.3). However, mixing the light beams of only two spectral pure colors we can not produce all possible colors. For example, the blue color can not by obtained by mixing red and green lights. The theory of Jung and Helmholtz postulates that all known colors can be obtained by mixing lights of three specially selected spectrally pure colors, called basic colors and changing their intensity. The red, green and blue-violet colors have been selected as basic colors, taking into account the observation that upon reducing the illumination of the objects, these colors disappear after all others.

Fig. 6.4.4. Circle of colors whereat each color is represented by a vector.

The main results of this theory are illustrated with the so called circle of colors (fig. 6.4.4). Each color is represented by a vector starting from the center of the circle and having a certain direction (phase angle). The magnitude of the vector corresponds to the light intensity and the phase angle

– to its color. Each two opposite vectors represent the so called additional (complementary) colors. According to the rule of complementarity, mixing two opposite colors results in white light, if they are of equal intensity. Such pairs of complementary colors are purple and yellow, red and green, orange and blue. Thus, the white color is represented by a small circle in the center of the color wheel. By contrast, all types of complementary colors can be obtained by the decomposition of white light. If the complementary rays have unequal intensity their mixing results in a whitish color. The less whitish is the color, the more intense it is, and more pronounced is its color tone.

Modern color monitors and television sets all operate based on the three-component theory of color vision. All colors on their screens are obtained by mixing the three basic colors: red, green (yellow in Japanese) and violet-blue. Some people, instead of three color pigments, have only two visual pigments. In this condition (dichromatism) only two basic colors and their combinations are observable. Rarely, some people possess only one visual pigment - monochromatism. In some species, the visual pigment and consequently eyesighting has other characteristics that affect their behavior. In cats, the visual cells are just from the type rods and the color vision is impossible, but scotopic (night) vision has high acuity. Conversely, the birds lack rods, but they have four types of cones, each with its owne visual pigment. Three of the pigments are identical to those in humans, and the fourth is sensitive to the ultraviolet light from the nearby UV-region. This deteriorates the night vision, but determines a very rich color vision in the day light, helping to find food. Most insects only see part of the ultraviolet rays up to 300 nm, for which the human eye is insensitive.


6.5. Light microscope - magnification and resolution. Limit of resolution of the light microscope

Usage of magnifying glasses (magnifying lenses) for the observation of small objects is dated back to XI c in Italy. Alone, each magnifying lens, however, produces low magnification. For the first time a combination of two magnifying lenses (light microscope) was used by the Dutch discoveres Hans Jansen and Hans Lipershi in the late 16th century. First, detailed description of this device was given by Robert Hooke in 1665.

Optical (light) microscope allowed the discovery of the cell, the basic unit of living matter. Thus, it becomes the first physical instrument, which played a crucial role in biology. In modern medicine microscope is used as an important tool in bacteriology, cytology, histology and hematology for research and identification of different cells. The optical microscope is used in microsurgery, where the surgeon monitors the operated microstructure (eye, inner ear, vascular vessel, brain, nerves), and performs the operation by micromanipulation tools.

The optical microscope is comprised of two parts, mechanical and optical one. The mechanical part contains a tripod column with support arm, tube, revolver with interchangeable objective lenses, stage (object table), holder of the condenser system, knobs for coarse and fine adjustment of the distance between the object and the objective lens. The optical system is the core of the microscope. It contains a light source, a condenser lens, objective lens and eyepiece.

Fig. 6.5.1. A view of the optical microscope.

The light source emits a sheaf of light rays passing through or reflected from the observed object to form the image of the object. The light source represents a lamp, placed in front of converging lens with mounted sectoral (field) aperture. Low-voltage incandescent lamps with helical filament are most commonly used as light source in optical microscopy. The halogen lamps are also widely used for this purpose. They are distinguished by high durability and intensity of the emitted light. For specific aims other sources of light are also applied as mercury lamps (UV radiation), xenon arc (when projecting the image on a screen) and others.

The optical part of light microscope containes two converging lenses called objective lens and eyepiece (fig. 6.5.1). The observed object is usually partially transparent and is placed on a thin glass slide secured to the object table (stage), which can be moved horizontally. A separate system of lenses


(condenser) located below the object, collects the light from the light source on the subject, in order to make the magnified image of the object sufficiently illuminated.

There are different types of condensers: widefield condenser with a single lens (for the weakest objectives), usual double lens condenser of Abbe, pancriatic condenser (with continuously variable aperture), special type condensers (dark field, phase-contrast e.t.c.). According to the method of Koehler, the object is illuminated by a sheaf of parallel beams formed by the condenser.

Light microscopes are characterized by three main parameters: magnification, resolution and contrast.

The observed object is located just in front of the front focus of objective lens. In this situation, the objective lens forms magnified, real and inverted image of the object (Fig. 6.5.2). The magnification of this lens is L'/L = /fob, as evidenced by the equivalent triangles in Fig. 6.5.2. Here is the length of the microscope tube and fob is the focal length of the objective lens.

The image produved by the objective lens is located just behind the front focus of the eyepiece, whose focal length is further denoted by foc. In this situation the eyepiece acts as a magnifying glass through which the human eye observes this image. The eye accommodates so that the image formed by the eyepiece to be located about 25 cm from its retina - the distance of the clearest vision. Thus, the magnification of the eyepiece is L''/L' = 25/foc, which also follows from the corresponding equivalent triangles in Fig. 6.5.2. The total magnification of the microscope is W:

W = L''/L = (L''/L') . (L'/L) = Wob .W2 = 25. / (fob.f2),

Thus, the total magnification of the microscope is equal to the magnification of the eyepiece Woc, multiplied by the magnification of the objective lens, Wob. The magnifications of objective lens, Wob, and eyepiece, Woc, are marked on them. An additional increase (about 1.5x) in the total magnification could be obtained by the use of a binocular tube appendage, and, in the microphotography, through the projection distance between the eyepiece and the photograph plate (projection magnification).

Fig. 6. 5. 2. Formation of magnified image with an optical microscope. The optical center of the eyepiece coincides with the focus of the eye lens.

The smallest distance, , between two

points of the object, which may be seen as distinct ones by a naked eye determines the resolution power of the eye. The resolution power of the microscope is defined similarly. The eye can see two distinct light emitting points as resolved, provided either of their images falls on separate photoreceptor cells of the retina. Therefore, the resolving power of the naked eye is limited by the smallest distance between two adjacent photoreceptor cells, which is about 10 m. Hence, the naked eye can not distinguish a pair of points unless they are set at a distance at least 0.2 mm, i.e., 200 m.

The resolution of the microscope is as much greater than that of naked eye as much the microscope magnifies. This means that progressively increasing the magnification of the microscope, we can see smaller and smaller details with increasingly greater resolution. However, this way of increasing


the resolution has its upper limit. The limit is reached in microscopes with a magnification of about 1000-1200 x. Further increase in the magnification does not result in more resolution power. The reason is in the wave-like nature of light. Consider we use a microscope to observe two points, emitting monochromatic light beams. Let the distance, , between both points be progressively decreased. When becomes too small and comparable to the wavelength of light, , the light beams start to interfere with each other. In this case, instead of two separate images we will obtain two fused images in the form of a stretched stain. This extremely short distance, respectively the maximum resolution of the optical microscope, is approximately equal to min = /2n.sin. In this expression, is the wavelength of light, n is the refractive index of the medium between the object and the objective lens, and is the half angle of the cone with a base equal to the diameter of the lens and with peak coinciding with the lens focus. The expresion n.sin is called numerical aperture of the objective lens, it is a dimensionless number between 0.1 and 1.35. The larger this number is, the higher the resolution of the lens. Under the best conditions, the maximum resolution of light microscope can reach the limit of 0.2 m, which is about 1000 times higher than that of naked eye.

Considering the above formule, the maximal resolution of light microscopes can be improved increasing the n or reducing . Replacing the air space (n = 1.0) between the object and objective lens by oil (n = 1.3) the index of refraction, n, is significantly increased. This method is known as observation under oil immersion. To reduce we use blue light or even ultraviolet light. Microscopes that use ultraviolet light achieve even better resolution to about 0.1 m. The ultraviolet microscopes require luminescent screen to produce visual image and quartz glass lenses as the ordinary glass absorbs the ultraviolet light. In some ultraviolet microscopes mirrors, instead of glass lenses, are used (reflective microscopes).

A third important characteristic of the light microscopes is the contrast of their image . The contrast of the image is assessed by the formule (Iim - Io). 100 / Io, where Iim and Io are the light intensity of the image and background, respectively. The lower is the background, the higher will be the contrast, and accordingly, the image quality will be high. The ordinary light microscope has no good contrast because a large amount of reflected and scattered light is present in the resulting image. Very good contrast and high quality image are obtained using the modern scanning confocal microscope.

Fig. 6.5.3. Types of objective lenses.

Microscopic objective lenses (Fig. 6.5.3). The objective lens forms a real and inverted image of the observed object. With increasing its magnification (3x, 25x, 40x, 100x), its focal length decreases. The working distance, i.e., the distance between the object and the frontal lens of the objective also becomes shorter. The so called depth of observation, i.e., the thickness of the observed layer is also reduced. When using objectives of medium magnification (25x and 40x), the working distance is increased adding one more lens with convex-concave shape (meniscus), placed between the object and the objective. It should be aplanat - free of spherical aberration and coma. Most powerful objectives (100 x) work with immersion, when an oil drop is placed between the object and the frontal lens of the objective. As the refractive index of oil is close to that of glass, the oil increases the numerical aperture of the objective and, hence, the resolution of the microscope allowing the usage of the maximum possible magnification of about 1200x. The immersion objective usually consists of a frontal hemispherical lens, one aplanat and several dublexes of converging-diverging lenses.


Simple objective lenses. These contain only one lens (fig. 6.5.3). The monocle (double convex lens) has all possible aberrations and is avoided. The meniscus (convex-concave lens) has slightly better qualities. Using a diaphragm somewhat corrects the spherical aberration and coma. Of the simple objective lenses used today are only the achromatic dublex, representing a combination of converging and diverging lens made of glasses with different optical properties.

Complex objective lenses. The so called periscopic objective lens includes two lenses with a diaphragm between them. This eliminates the distortion as the two lenses, symmetrically arranged relative to the diaphragm, musually compensate their shortcomings. Its angular range is about 30°. The aplanate is composed of two achromatic pairs of lenses, arranged symmetrically on the both sides of a diaphragm as in the periscopic objective. At this objective lens the optical shortcomings are minimized. Its angular range is 45°. The anastigmate is a modern objective lens with all aberrations removed. Its angular range is from 30 to 140°. It provides uniform and sharp image. The triplets are asymmetric anastigmates. They are composed of three lenses at a distance from one another, the middle lens is diverging and the other two - converging. The optical scheme of triplets has been subsequently complicated adding a compound lens to the final third lens, thereby increasing the relative aperture and the angular range of the lens (complex triplet).

Microscope eyepieces. The eyepiece acts as a magnifier glass, which monitors the real image created by the objective lens at a distance of 25 cm from the eye (distance of the clearest vision). The magnification of the eyepiece rarely exceeds 16 x (typically 10 x). Therefore, the optical design of the eyepiece is much simpler. To make a snapshot of the observed object the eyepiece has to be replaced by a photographic camera so that the real image created by the objective lens must overlay the photoplate or the photomicrography film. There is another, better way to do this using a special projection eyepiece that enlarges and projects the image on the photoplate. The eyepiece can be replaced by television camera which converts the real image of the objective lens into a video signals. The video signals can be directly observed on screen (television microscopy) or submited to a computer that allows the processing of the image.

Some operation microscopes for microsurgery are equipped with such television camera so that the operation may be observed on creen. This technique makes it possible to remove tumors of the brain and spinal cord, to connect nerves, blood vessels, tendons and muscles.

Mechanical system of the light microscope. The objective lens and eyepiece of each microscope are mounted at the both ends of a tube, called a tubus (fig. 6.5.1), which have a standard length of 160 mm () in biological microscopes. This allows the usage of objective lenses and eyepieces with different magnifications while preserving the same image quality (i.e., a minimal aberrations). To focus the microscope on different objects the three main parts; objective lens, the eyepiece, and tube have to be moved simultaneously by micrometer as a single unit. The observed object is placed on a stage that can be moved in three perpendicular directions. When high-magnification lenses are used the accuracy at which the microscope tube and the stage should be moved strongly increases reaching tens of micrometers.

6. 6. Methods for observation using a light microscope. Using ordinary light microscope some of the structures and details of biological objects can not be

seen or can not be distinguished from other structures. This occurs when the investigated structures are colorless or transparent or have a color that is identical to that of the surrounding background. Usually this problem is solved applying appropriate dye which specifically binds and stains the structure under interest. In other cases, a specific method for observation is applied, which makes visible the investigated structures. In the first case, prior to any observation under a microscope, the sample is subjected to a variety of treatments - fixation, dyeing, drying, heating and the like. This pretreatment can result in loss or distortion of some components of the sample and produces the so called artifact. Therefore, even in this case, several methods for observation of the sample are used and if always the same image is obtained, it probably represents a real structure, rather than an artifact. In some cases, another problem arise, the contrast of the image is not sufficient and should be increased. All these problems substantiate the necessity of using a number of methods for observation under microscope, as described below.

1. Observation of objects in transient light (bright field observation). Condenser, the observed object and the light microscope all are arranged in one line and the luminous flux of the condenser

Table. Approximated dimentions of some biological and physical objects

Object Approximal dimention

Atoms 0.1 nmMolecules 1 nm

Macromolecules 10 nmViruses 100 nm (0.1 μm)Bacteria 1000 nm (1 μm)

Cells 10 000 nm (10 μm)Protozoa 100 000 (100 μm)


penetrates the object. Those structures of the object which have color, absorb more light and their images in the eyepiece field appear as a dark elements against the ambient bright field. To increase the contrast, different structures of the object can be pre-stained with specific dyes, but this sometimes introduces artifacts.

This type of microscopes can be only used for observation of such objects which have colors or are pre-stained. In general, the color of a body depends on which part of the visible spectrum it absorbs or reflects. Bodies with gray to black color absorb equally all rays of white light. Certain bodies, however, absorb only part of the light beams according to their wavelength. These bodies have own color depending on the color of the lost or reflected light. For example, hemoglobin of red blood cells strongly absorbs blue light and, accordingly, the blood color is red.

Many biological samples contain structures that hardly absorb light; hence, they have no color and can not be seen in the eyepiece field of ordinary light microscope. In such case, the following methods for observation are used.

2. Observation of transparent objects in transient polarized light (polarization microscope). This method is used when the sample contains structures which exhibit birefringence and optical activity. In biological objects, those structures are optically active whose molecules have asymmetric carbon atoms. For example, such are certain membranes, collagen fibers, liquid crystals of the fatty acids and so

on.In this method, a light microscope equipped

with additional appendages, polarizer and analyzer, for monitoring the object in plane polarized light is used. The polarizer is located between the condenser and the sample, while the analyzer is placed between the objective lens and the eyepiece. The ordinary light, passing through the polarizer, is converted into plane polarized light. In turn, the analyzer, which can be rotated about its axis, allows only light beams, polarized in a particular plane, to come out of it. Thus, the polarization microscope could determine the plane of polarization of the light coming out from the sample.

Although it does not absorb light, the object or some of its internal structures have birefringence and are optically active (rotate the plane of polarization of the light passing through them). When the analyzer and polarizer are crossed the visual field of eyepiece will be dark due to the mismatch between the planes of polarization and transmission. Rotating the analyzer, at a certain angle it will begin to transmit the light beams having a particular plane of polarization, i.e., those light beams that have come out of the optically active structures of sample. Thus, the image of those optically active structures will become bright against the surrounding dark field of microscope. The analyzer finds out those structures of the sample which are optically active and measures their optical activity. In addition, it can establish the presence of internal mechanical stress and the like.

Using additional appendage, compensator, differences in the polarization of various parts of the sample are converted into color differences. Some polarization microscopes are equipped with a polarizing retarder, which shifts the phase angle of light between the selected polarization directions, in order to measure the degree of elliptical polarization caused by the object.

Some polarization microscopes use circularly polarized light, which makes it possible to see the micro objects (crystals, minerals, fatty droplets) having birefringence. Such objects are invisible by ordinary light.

3. Observation of transparent objects in transmited light with altered phase (phase-contrast microscope). Phase-contrast microscopy is widely used to monitor live, colorless and unstained cell objects, which is of particular interest to cytology. In this type of observation, the object must contain


structures with different refractive indexes, n. The observed object is illuminated with a sheaf of coherent beams having the same frequency and phase angle, i.e., the electric field oscillations must occur simultaneously in all beams. When two such beams pass through media with different refractive indexes each of them travel different optical paths, nL. Consequently, the beams coming out from the object have different phase angles, i.e., their oscillations take place at different time intervals. The changed phase angles of oscillation in different light rays are used to construct the image of the object. This is done using a special appendage, converting the phase difference in light intensity. Based on the appendage, these types of microscopes are termed interference and phase contrast microscopes.

A phase plate with round shape is placed in the eyepiece of the phase-contrast microscope. The refractive index of this plate must have different values at the periphery (edge) and in the central zone of the plate. If the edge of the phase plate is less refractive than the central zone, the samples with higher refractive index look darker than the background – this is the so-called positive phase contrast. In other case, when the edge is more refractive than the center, the objects look brighter on the dark background - negative phase contrast. Introduction of additional absorption of the light in the edge reduces the halo around the image of objects. This is characteristic of the so-called anoptral contrast (according to the Finnish histolog A. Vilska). The negative and anoptral contrasts are preferred to the positive one in the observation of small objects.

Using the interference microscope the phase difference introduced by the object can be measured. This is done comparing the light sheaf, passing through the observed object, with another one passing apart to the object. The interference microscope of Lebedev (1930) is most commonly used. The phase difference depends on the refractive index and, in turn, this index depends on the concentration of substances dissolved in the object. Hence, measuring the phase difference we can calculate the volume, dry weight and protein content of the object. Conducting two successive measurements it is possible to determine the mass of the solute, or the number of receptors that bind substances of known molecular weights in the individual cells.

4. Observation of objects through the scattered light (dark field observation, ultramicroscope, dark field microscope). This type of microscope is used for observation of colloidal particles suspended in an aqueous medium, which are too small to be seen in an ordinary light microscope. Each ordinary microscope can become dark field ultra microscope by replacing its ordinary condenser with the so called dark field condenser. The central part of the sheaf of beams, emitted by the light source, is shadowed in the frontal focal plane of the dark field condenser while the peripheral part of the beams is directed obliquely to the object. As the condenser illuminates the sample obliquely, only scattered light rays fall into the objective lens of the microscope. The individual particles are visible as dots, glowing with reflected light against the dark surrounding field. This method allows observation of only the movement and concentration of the particles, while their structure can not be seen. It is especially valuable when investigating the motility of bacteria and sperm cells using relatively long exposure in order to register the trajectory of the moving particles.

Sometimes instead of a lens condenser a spherical mirror (cardioid) condenser is used.5. Observation with fluorescent light (fluorescence microscope). The light source is a mercury

lamp of high pressure, emitting light highly rich with ultraviolet or blue rays. This type of short-wave radiation is capable of causing photo-luminescence (fluorescence). Fluorescence is a property of certain substances (luminophors) to emit light with a longer wavelength under the influence of shortwave radiation. When illuminated the electrons of the luminophor go to higher orbits and, after a short delay, return back releasing photons.

The condenser illuminates obliquely the sample which plays the role of luminophor. A shortwave light falling across the sample excites photoluminescence, which can be intrisic (own, due to the molecules of sample) or extrinsic (due to preliminary introduced fluorescent dyes - fluorophores, fluorescent markers or probes). Light emitted by the fluorescent structures of the sample is collected by the objective lens and forms magnified image. The luminescent microscope contains lenses made of quartz glass as the ordinary glass absorbs the ultraviolet light.


This method of observation provides good contrast of the image, since the exciting and emitted light are filtered through narrow band, monochromatic filters. The fluorescence microscope could be used for fluorescence analysis which can determine the concentration of a fluorescent substance as low as about 50 molecules of fluorochrome per square micrometer. Prior to the observation, appropriate antibodies, conjugated with fluorescent markers, could be bound to specific sites of the sample (for example, to a bacteria strain). Upon the excitation, these sites become visible in the fluorescence microscope.

6. Stereoscopic microscope. It contains two identical optical microscope tubes, whose optical axes form a small, acute angle with each other so as to allow observation of an object with both eyes. In this case the natural stereoscopic effect characteristic of human vision is restored. With this microscope, the individual parts of the object can be distinguished according to their height and position in depth. Magnification is usually between 5 and 50 times. Stereoscopic microscope is used in cases where it is necessary to correctly adjust the microinstruments and details in three-dimensional space: in dissection of tissues, when micromanipulations with different cells are needed, in microsurgery, during mounting the microelectronic circuits, precision mechanics, in archeology and more.

7. Confocal scanning microscope. Ordinary light microscope has a sight field with intence background and low contrast. Each point of the image receives both light coming from the corresponding point of the object and an additional light reflected from other sections of the observed object. This increases the background level and deteriorates the contrast of the image. Moreover, it is difficult to produce a lens that can simultaneously see all points of the object and has a low aberration. With the scanning confocal microscope all these drawbacks are overcomed. This microscope uses a laser beam to illuminates the observed object point by point. When a point is illuminated it starts to fluoresce. The emitted fluorescent light is used to create enlarged image of the point, which is projected onto a small orifice in a screen. The light beams scattered from other parts of the object are projected aside off the orifice and do not pass behind the screen. The light passing through the orifice forms an image of the illuminated point which is stored in the computer. Then the laser beam is directed towards another point and its image behind the screen is again stored. Thus, the whole object is scanned point by point within a small portion of a second. Finally, the computer program combinds all collected images to form the entire three dimentional image of the object.

6.7. Polarization of light. Optical methods for the study of biopolymers and drugs - polarimetry, circular dichroism and birefringence.

Light is a transverse electromagnetic wave composed of rapidly changing electric and magnetic fields. Vectors of the electric field, E, and the magnetic field, H, vibrate perpendicularly to the axis of beam propagation and, at the same time, they remain perpendicular to one another. Because light is a transverse wave, it can be polarized, i.e. only the oscillations in a specific direction or plane could be allowed. Typically, each sheaf of light contains a great number of individual beams each one having its own plane of vibration. In the ordinary unpolarized light the individual planes of vibration have random angular distribution (fig. 6.7.1 - A). The individual planes of vibration are close to each other in the partially polarized light (B), and completely coincide in the plane (linear ly ) polarized light (C). The plane where the electric field vector vibrates is called plane of vibration while its perpendicular plane, where the vibrations of E are blocked, is the plane of polarization.

Fig. 6. 7. 1. Direction of oscillation of the electric field vector E of the individual rays. (A) ordinary light, (B) partially polarized light, and (C) completely polarized light.


Another type of polarization occurs when the E rotates in a certain direction about the axis of propagation of light with a frequency equal to the frequency of the light wave. In case the E does not change its amplitude during its rotation the light is circularly polarized (Fig. 6.7.2 - A and B) and if the amplitude of E changes slightly we have elliptically polarized light (Fig. 6.7.2 - C). In such cases, the tip of the E describes a full circle or ellipse during the time interval equal to one period of oscillation. Depending on the direction of rotation of the E we differentiate left ward (Fig. 6.7.2 - A) and right ward (Fig. 6.7.2 - B) rotating circularly polarized light.

Generally, the plane polarized light can be represented as a sum of two circularly polarized components, whose vectors E have the same magnitude but rotate in opposite directions, i.e. as a sum of one levorotatory and another one dextrorotatory ingredients.

Most light sources (lamps, flame, Sun) emit unpolarized light. In general, the light, especially plane polarized light, has a healing effect on skin diseases, open wounds and the like. The plane polarized light is produced in the following cases:

a) Reflection and refraction of ordinary light at the boundary between two transparent dielectric media, such as water and air (Fig. 6.7.3). Therefore, many insects, living near the water surfaces, are adapted to see only plane polarized light. The degree of polarization of the reflected light depends on the angle of incidence and at a certain angle of incidence, B (Brewster angle), it becomes 100 % (Fig. 6.7.3). The plane of vibration of reflected light is parallel, while that of refracted light is perpendicular, to the boundary surface.

Fig. 6. 7. 2. Direction of rotation of the electric field vector, E, in the circular polarized light (A, B) and the elliptically polarized light (B).

b) Refraction of ordinary, unpolarized light by special, birefringent crystals (calcite, tourmaline, gerapatit). In the 17th century the Danish physician Erasmus Bartolini found that the crystal of calcite (calcium carbonate) is birefringent, i.e., it produces not a single but a pair of refracted beams. Hence, this crystal has two indices of refraction of light (Fig. 6.7.4). At the time of refraction, the incident beam splits into two beams, ordinary (o), which obeys to the law of Snellius and extraordinary (e), which is not subject to this law. Both beams are plane polarized but have different velocities of propagation (this is called birefringence) and are absorbed differently by the crystal (dichroism).

Fig. 6. 7. 3. Polarization of light upon its reflection and refraction at the boundary between two dielectric media.

The polarizers represent special optical elements, designed to produce plane polarized light through birefringence. The birefringent crystal produces two plane polarized beams, one of which is removed and the other, usually the extraordinary one, is used. In the prism of


Nicole, made of calcite, the ordinary beam is removed due to his stronger refraction. In the so called polaroid (plastic plate, covered with uniformly oriented crystals of tourmaline or gerapatit), the ordinary beam is removed due to its stronger absorption by the crystal.

Each polarizer has a plane of transmition and plane of polarization, which are perpendicular to each other. The plane of transmission coincides with the plane of vibration of the electric vector, E, of the light coming out from the polarizer. The polarizer will block all the vibrations of E in its plane of polarization. The name “plane of transmission” is given because a sheaf of polarized light can pass through a particular polarizer, only if its plane of vibration coincides with the plane of transmission.

Let us have two polarizers P and P', whose planes of transmission differ by the angle, (Fig. 6.7.5). Consider a sheaf of ordinary light beams enters into the first polarizer and coming out of the first polarizer it goes into the second polarizer. The first polarizer will convert the ordinary light into polarized one with intensity, Io. The second polarizer will transmit only a part of the polarazied light due to the mismatch of both transmission planes. The intensity, I, of the light beam coming out from the second polarizer is given by the law of Maluse: I = Io.cos2. In this case, the polarizer P' functions as an analyzer, which could be used to determine the plane of polarization of a linearly polarized light.

Fig. 6. 7. 4. Polarization of light by a birefringent crystal.

Birefringence and dichroism are also observed when a sheaf of plane polarized light rays passes through a solution of organic compounds with asymmetric organic molecules (sugars, amino acids, proteins, some drugs). These molecules contain a central carbon atom with four asymmetric links. Let us have a cuvette with the length, L, containing a solution of such substance with

the concentration, C. Consider a sheaf of plane polarized light rays enters this cuvette (Fig. 6.7.6). The incident, plane polarized light can be represented as a sum of two circulary polarized components, one levorotatory and the next dextrorotatory, which both have the same amplitudes. Because the dissolved molecules are asymmetric, they absorb unequally the levorotatory and dextrorotatory components (dichroism) and transmit them with different speeds (birefringence). At the outlet of the cuvette, the two components will have different amplitudes (as they are differently attenuated) and different phases (because they have been propagating at different speeds). The outgoing light is obtained by the summation of these two ingredients. As the two components have different amplitudes, their summation results in elliptically polarized light. On the other hand, the phase difference between the two components causes the polarization plane of outgoing light to be shifted by angle, i.e., rotated, in respect to that of incoming light, at an angle = []. L.C.

Fig. 6. 7. 5. Passing of light beam through a sequence of two polarizers whose planes of transmission differ by an angle to each other.

Substances which rotate the plane of polarization are called optically active, and the obtained angle of rotation, , is denoted optical activity. By measuring the optical activity () we determine the


concentration, C, of the optically active substances - polarimetry. Often these optical devices are used to measure the concentration of the sugar solution - saccharimeters.

The dependence of on the wavelength of light, , is called dispersion of optical activity, and the dependence of the ellipticity on - dispersion of the circular dichroism. We can obtain the spectra of optical activity and circular dichroism of tested biopolymer using special optical devices, spectropolarimeters. These two dispersions represent valuable information about the structure of tested macromolecules (degree of spiralization, polymerization) and about the change of this structure (denaturation) under the impact of various denaturing factors.

Optical activity of the substances is often used to detect differences in the structure of their molecules. The molecules of an optically active substance contain asymmetric carbon atom, called a center of isomerism. The four links of this atom are oriented differently in space and may be associated with other atoms or atomic groups. This gives rise to the existence of several mirror-asymmetric molecules of the same substance (chirality). Although they contain the same atoms and interatomic bonds the mirror-asymetric molecules rotate the plane of polarization of incident plane polarized light in opposite directions. This phenomenon is called an optical isomery, and the mirror-symmetric molecules - optical isomers.

Fig. 6. 6. 7. Passing of plane polarized light through a solution of an optically-active substance.

In purified form some substances represent natural mixtures of two types of molecules, identical in their atomic content, however, the one is levorotatory isomer and the other - dextrorotatory isomer. Such chirality is demonstrated by many biologically important substances - sugars, amino acids and drugs, as they contain molecules which are optical isomers. Usually, only the levorotatory isomer has useful biological activity, while the dextrorotatory isomer is either neutral or has another, sometimes harmful effect. This can be of crucial importance for the medicinal substances and hence, their optical activity is frequently studied. In recent years, pharmacologists have proposed only the purified levorotatory isomers of drug substances to be used.

Locating the lines of internal mechanical stress. Glass and polymer bodies are not crystalline and do not have the ability to polarize light. However, their deformation, for example, by mechanical pressure or heat treatment, gives rise to internal mechanical tension resulting in the required ability to polarize the incident light. The lines of internal mechanical stress can be seen when a plane polarized light is passed thought the deformed plate of polymer material. This effect is used to detect mechanically weak units and points in some mechanical constructions which, when placed under mechanical presure, develop overcritical internal stress. For this purpose, a miniature model of the tested construction is firstly made of plastics and after the model is subjected to mechanical deformation a plane polarized light is passed through it.

Light switches. Many transparent materials begin to polarize light when placed in an electric or magnetic field, for example when they are between the plates of a capacitor or in an electromagnet. That phenomenon is used to make very fast light switches.

Liquid crystal displays. A liquid crystal layer becomes optically active when placed in an electric field. Consider a sheaf of plane polarized light transmitted through a sequence of liquid crystal layer and a polaroid plate. When an electric voltage is imposed on a particular figure on the liquid crystal layer, the layer becomes optically active, and rotates the plane of polarization which prevents the light to pass


through the polaroid plate. The figure will become dark on the ambient bright field. This effect is used in many electronic devices with digital display, flat screen TV sets and more.

Polarization microscopes. A great number of minerals, crystals, chemicals and, to a lesser extent, biological structures exhibits birefringence. These micro objects can be observed under a polarization microscope eventhough they are invisible with ordinary light. The polarization microscope respresents ordinary microscope equipped with a pair of crossed polarizing plates called polarizer and analyzer. This type of microscope is fitted for observation of birefringent microobjects using both plain and circular polarized light.

Sunglasses. In some cases (in summer, in winter snow, at mountains), the ambient light is very strong. Falling in human eye the light can cause burning of cornea and whitening of retina. This can be avoided using spectacles whose lenses are tinted and equipped with polaroid coating. Most of the light beams entering the eye has been previously reflected and polarized by some surfaces. The light reflected from different dielectric surfaces (water, snow and ice, glass plates) becomes plane polarized. Polaroid coating of the sunglasses acts as an analyzer for the reflected polarized light and blocks it. In addition, the tinted lenses of these spectacles absorb the light from the near ultraviolet region completely and by half the light from the visible spectrum. These effects greatly reduce the intensity of light and protect the eyes.

6.8. Light scattering from polydisperse systems. Turbidimetric determination of the form and concentration of cells

The scattering of light (optical radiation) is any deviation of the light rays from their straight line propagation due to the inhomogeinity of the medium or nonuniformity of the interface between variuos transparent media. Polydisperse systems (cell suspensions, emulsions, sols and the like) scatter light because they are optically inhomogeneous and contain particles having a refractive index different from that of the medium. Even in a homogeneous medium (air atmosphere, a water pool), the thermal chaotic motions of the molecules of the medium cause random fluctuations in the density, which also scatter light - molecular scattering .

When a sheaf of light beams reaches an interface, which is highly uneven, the light becomes scattered - diffuse reflection. A special case of surfaces producing perfect diffuse reflection is the Lambertian surface. The light scattered by this surface obeys to the Lamberet’s cosine law. Any element of the Lambertian surface scatters light in all directions. Let us indicate by Iθ the luminous intensity of the light scattered in the direction, displaced by the angle, θ, to the normal of the surface. Then, I θ = In cosθ, where In is the intensity of the light scattered perpendicularly to the surface.

Prior to fall in our eyes the light is reflected by some object allowing us to see this object. Only a portion of the incident light energy is reflected, depending on the wavelength (frequency) of light. Hence, each body reflects predominantly the light with particular spectrum, which determines the color of the body.

If the wavelength, λ, of the scattered light is preserved the same as that of the incident light, the scattering is elastic, otherwise it is nonelastic scattering. Light scattered by moving particles changes its frequency, this constitutes the so called Doppler effect. The mere change in frequency, the Doppler shift, can be measured and used to determine the velocity of the scattering particles.

When the scattered light is measured within a time frame of few ms, its intensity is found varying due to the Brownian motion of scattering particles. In this case we have a dynamic light scattering. Most often, the scattered light is measured and averaged over a period of several seconds (s), it is the so called static light scattering. Only the static light scattering will be discussed below.

There are several mechanisms of light scattering depending on the ratio of the average diameter, D, of the scattering particles to the wavelength of light, .

1) Light scattering by tiny particles with small diameter (D/ < 0.1), such as biomacromoleculs, liposomes, viruses, bacteria, and some others. This is a type of elastic scattering called Rayleigh scattering following the name of its discoverer, Rayleigh. The shape of the particles, which scatter the light, is of no importance and could be assumed spherical. The Rayleigh scattering is explained by the phenomenon of


dielectric polarization, therefore it is also termed as diffractive scattering. The alternating electric field of the light, falling on the scattering particle, induces alternating electric dipole (spatially separated charges) in the particle. The induced electric dipole of the particle oscillates in time with the vector, E, of incident electric field, emiting light in all directions. Therefoe, this is a wide-angle scattering. The scattered light has nearly uniform angular distribution (Fig. 6.8.1 - A) and is plane polarized. The intensity of light, scattered by such small particles, including the molecular scattering, is described by the formula of Rayleigh:

I = Io . к. N. V2 / 4,

where I and Io are the intensities of the scattered and incident light, and k is a parameter that depends only on the angle of scattering. This formula allows the determination of the concentration, N, of the scattering particles and their mean volume, V, by measuring the intensity of perpendicularly scattered light (nephelometry) or intensity of residual light, transmitted through the scattering medium in the same direction (turbidimetry).

As it can be seen from the formula of Rayleigh, the intensity of scattered light increases by V 2 i.e., with D6! Conversely, the intensity of scattered light decreases with λ4, and therefore if a beam of white light is scattered, the shortwave (violet, blue) beams will be scattered stronger compared to the longwave (red, green) beams. As a consequence, if the incident light is white, the scattered light will be enriched in blue rays, while the transmitted light will be rich in red beams. This renders a bluish color of the scattered light as in case of the light scattered by liquid biological media containing proteins, colorless cells, liposomes, etc. (Tyndall effect). As the transmitted light is depleted of its blue rays it will have a reddish color. This explains the blue color of the sky and of (pure) sea water and the red color of the sun at sunrise and sunset. Because red rays are poorly scattered and reach greater distances, the red color has been chosen for the light signals emitted by railway semaphores, traffic lights, lighthouses, etc. Based on the same reason, the observation and photographing of objects that are covered by clouds or mist, are preferentially conducted using red light.

The Rayleigh scattering is the main reason for the loss of light energy in optical fibers.2) Light scattering by particles with size, close to that of the wavelength (D/ ≈1). Such particles

are the human erythrocytes and some bacteria. In this case, the scattering depends inversely on the volume, V, of particles. For example, the shrinkage of human erythrocytes increases their ability to scatter light and vice versa, swelling of erythrocytes reduces this ability. This result is used to measure the volume changes of the suspended erythrocytes, liposomes and the like.

Fig. 6. 8. 1. Mechanisms of light scattering: diffractive scattering by small particles (A) and small angle scattering by large particles (B).

3) Scattering of light by larger particles

(D/ >> 10), for example, animal and plant cells, dust, and the like. The light rays are both reflected and refracted by these particles and the scattered light is predominantly oriented forward (Fig. 6.8.1 - B). This is called small angle scattering (0.1-10°). In this case, a broad angle scattering (e.g., scattering at 90°) will occur if the scattering particles (cells) contain small intrinsic (intracellular) discontinuities, e.g., organelles. This is used in microbiology to measure the size of organelles and cells.

There are several particular mechanisms explaining the scattering of light by such large particles. If the scattering particles have spherical shape this mechanism is referred to as mechanism of Mie,


according to its discoverer. In this case, the intensity of the scattered light does not depend on λ, but depends on the diameter, D, of the scattering particles as D2. Scattering from larger particles which do not have spherical shape is referred to as Tyndall scattering. Such type of scattering takes place in colloidal mixtures and cell suspensions.

4) Light scattering in gaseous and liquid medium, when a mechanical wave (sound) is propagating within the medium - Brillouin scattering. The propagation of a mechanical wave in such a media is accompanied by the formation of zones of compression and rarefaction of constituent particles. The zones of compression are called acoustic phonons and just they represent the scattering centers that divert the light rays. This scattering is not elastic, because the energy of the scattered light photons is different from that of the incident one with a value equal to the energy of phonons, the elastic oscillation of the medium.

5) Another type of non-elastic light scattering is the so called combinational or Raman scattering. In this case the beams of monochromatic light with the frequency, νo, are scattered by molecules which vibrate around their center of mass and rotate about their axis. The vibrational and /or rotational energy of the molecule, pertaining to these intramolecular motions, is called an optical phonon. Compared to the photons of incident light, the photons of scattered light will have greater or lower energy, respectively, greater or lower frequency, depending on whether they are scattered by a non-excited or excited molecules. In the first case the incident photons excite optical phonons in molecules losing a part of their energy. Hence, the scattered light has lower frequency than that of incident light. In the second case, the incident photons take the energy of the optical phonons of excited molecules and the scattered light has a higher frequency. As a consequence, the spectrum of the scattered radiation containes the lines of incident light and the lines of scattered light. The scattered light contains new frequencies representing the sum and the difference between the frequency, νо, of the incident radiation and the frequency of vibration (νvibr) and frequency of rotation (νrot) of molecules, i.e., νo ± νvibr and νo ± νrot. Especially valuable are the spectra of combinational scattering of molecules with high asymmetry in their construction.

The light scattering has important application in biological sciences and medicine. In the turbidimetric study of a cell suspension, which does not absorb light, we usually measure

the quantity, D = lg (Io/I), generally called optical density, or sometimes density of light scattering. Here Io

and I represent the intensity of the incident and the transmitted light through the suspension, respectively. When the light scattering is strong, the transmitted light is much weaker than the incident light and the optical density is great. For very dilute suspensions the optical density linearly depends on the concentration of scattering cells. Thus, measuring the optical density at about 600-700 nm, we could determine the concentration of cells, establish the phase of bacterial growth, measure the degree of erythrocyte hemolysis, and the like. By measuring the optical density of erythrocyte suspensions we could determine the resistance of erythrocytes against various hemolytic factors and assess the osmotic fragility of erythrocytes, which is increased in certain hemolytic anemias.

The lens and the vitreous body of the eye are transparent to visible light, because they contain the soluble protein, crystalline. Under certain conditions (cataract, irradiation of eye by UV-light and ionizing radiation) the crystalline changes becoming insoluble and aggregated. The crystalline aggregates, which are formed in the eye lens, scatter light rays, so the eye lens becomes opaque and obstructs vision.

Fig. 6. 8. 2. Schematic diagram of ektacytometer.

Light scattering of cell suspensions is used in the modern method of ektacytometry for determining the deformability of erythrocytes (Fig. 6.8.2). When a


volume of erythrocyte suspension flows through a narrow cuvette at a given speed, all cells arrange uniformly and deform longitudinally as much as greater is their deformability. At the same time the cuvette is illuminated obliquely by a beam of laser light which is scattered by the cells. The angular distribution of scattered light depends on the shape of cells, respectively, on the degree of cell deformation. The scattered light forms a spot on a screen, and a television camera is used to digitize the spot shape, respectively, the angular distribution pattern of scattered light. Thus, the shape of erythrocytes and their ability to deform is determined fully automatically and assessed quantitatively. In some diseases, such as diabetes, the deformability of erythrocytes is reduced.

When the particles (cells) are freely suspended in an appropriate medium they occupy random orientation in all directions. In this case, the pattern of light scattering does not substantially depend on the shape of the particles. However, under the impact of an external electric field, the particles can be oriented in a single direction. This takes place when the particles have their own dipole moment or such a dipole moment is induced by the external electric field. In case the particles have uniform, unidirectionally orientation, the light scattering strongly depends on their shape and has a characteristic angular distribution. Measuring the angular distribution of scattered light one can study the shape, structure and the dielectric properties of various particles; cells, viruses, biopolymers and colloids. This method is called electroorientational light scattering.

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Глава 6 - СТРАНИЦА ЗА ПРАБЪЛГАРИТЕ - ЕЗИК ... of Medical Physics... · Web viewCHAPTER 6. OPTICS 6.1. Fundamentals of geometric optics. Refraction and