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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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 АВ /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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
anastigmate.
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. Distortion 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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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. Distortion 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 orthoscopic.
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. Optical system of human eye. Accommodation and refractive power of human eye.
Optical aberrations of the eye and their correction
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,
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
formation of
Fig. 6. 3. 3. Reduced eye and the
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Myopi
a
Hyper
opia
Astig
matism
Presby
opia
Commo
n term
Near
sight
Far sight
Old age
sight
Physical cause
Elongated eyeball or
over curved cornea
Flattened eyeball or
under curved cornea
Unequally curved
cornea
Lack of accommodation
Physical correction
Diverging eye glass
Converging eye
glass
Cylindrical lens
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 nonaccommodated 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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 retinoscop 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 ophthalmometer (keratometer).
The tonometer 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
electroretinography 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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 flux , 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,
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
compared to the distance R, it can be regarded as a point source of light. The luminous intensity, I, of a
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 luminous power,
this is the luminous flux emitted per
Source of light
Irradiance
Illuminance
unit area of the surface. It is measured
(in W.m-2)
(in lux)
in lumens per square meter (lm/m2).
Sun light
1000
100 000
The brightness of this light source is
Sky light
100
10 000
defined as the intensity of light emitted
Overcast day light
10
1000
from a unit area of surface in a given
Moon light
0.001
0.1
direction. It is measured in candelas
Star light
0.0001
0.01
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.
Tabl. 6.4.1. Relation between irradiance and illuminance at
different light sources.
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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,
Tab. 6. 4. 2. Color areas in the
photopic vision) involves only the cones which are about 30
spectrum of visible light
times less numerous than the rods. In addition, the pupil
decreases its area around 16 times. All this helps, along with
From 380 to 450 nm - violet
From 450 to 480 nm - blue
neuro-physiological suppression of excitement, the human eye
From 480 to 510 nm - blue-green
to perceive light which differs in its intensity about 1012 times.
From 510 to 530 mn - Green
While adaptation to low light intensity is aimed at
From 530 to 575 nm - a yellow-green
achieving high acuity of vision, the adaptation to bright light
From 575 to 585 nm - yellow
allows the eye to see the colors of observed objects. How is
From 585 to 620 nm - orange
this achieved? The spectral sensitivity of the eye, adapted to
From 620 to 760 nm - red
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
process involves the cones, i.e., at the photopic vision when the objects are illuminated with bright light.
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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
(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-
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
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
Table. Approximated dimentions of some
with
additional
appendages, polarizer and analyzer,
biological and physical objects
for monitoring the object in plane polarized light is
used. The polarizer is located between the
Object
Approximal
condenser and the sample, while the analyzer is
dimention
placed between the objective lens and the eyepiece.
Atoms
0.1 nm
The ordinary light, passing through the polarizer, is
Molecules
1 nm
converted into plane polarized light. In turn, the
Macromolecules
10 nm
analyzer, which can be rotated about its axis, allows
Viruses
100 nm (0.1 μm)
only light beams, polarized in a particular plane, to
Bacteria
1000 nm (1 μm)
come out of it. Thus, the polarization microscope
Cells
10 000 nm (10 μm)
could determine the plane of polarization of the
Protozoa
100 000 (100 μm)
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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 (linearly) 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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 leftward (Fig. 6.7.2 - A) and rightward
(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,
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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
opticallyactive
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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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, Iθ = 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
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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 V2 i.e.,
6
with D ! 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.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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.
ektacytometer.
8.
2.
Schematic
diagram
of
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
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.