Light Optical Microscopy Techniques

Vũ Trung Kiên - 20071634

Materials Science & Engineering, Center for Training Excellent Students,

Hanoi University of Science and Technology, Dai Co Viet Street No.1, Hai Ba Trung, Ha Noi, Viet Nam

Abstract: Light optical microscope is known as a type of microscope which uses the seeing-light and a system of lenses to magnify images of small samples. Nowadays, inventors over the world be in success with many kind of useful microscope, such as, Scanning Electron Microscope, Transmission Electron Microscope, Scanning Tunneling Microscope … but these are very, very expensive and only used by scientists, and rarely used by students. In Vietnam, not only students cannot be user but also Vietnamese scientists, whom be hardly allowed to use them because of many troubles. It’s too for using light optical microscope. In this situation, Vietnamese young students should think about how to solve this problems. This document will tell you all about light optical microscopy techniques, in details, and then readers should have the ideas and skills to make a simple light optical microscope - own microscope.

Keywords: Light optical microscopy techniques, LOM, own microscope.

I. Introduction

Credit for the first microscope is usually given to Zacharias Jansen, in Middleburg, Holland, around the year 1595. Since Zacharias was very young at that time, it's possible that his father Hans made the first one, but young Zach took over the production. Another favorite for the title of 'inventor of the microscope' was Galileo Galilei. He developed an occhiolino or compound microscope with a convex and a concave lens in 1609 and the first such device to be given the name "microscope" in 1625 by fellow Lincean Giovanni Faber. Over the past decades the number of applications of optical microscopy has grown enormously, and is now found in almost any field of science and industry, such as microelectronics, nanophysics, biotechnology, pharmaceutic industry and microbiology. These microscopes use visible light (or UV light in the case of fluorescence microscopy) to make an image. Optical microscopes can be further subdivided into several categories: Compound Microscope - These microscopes are composed of two lens systems, an objective and an ocular (eye piece). The maximum useful magnification of a compound microscope is about 1000x. Stereo Microscope (dissecting microscope) - These microscopes magnify up to about maximum 100x and supply a 3-dimensional view of the specimen. They are useful for observing opaque objects. Confocal Laser scanning microscope - Unlike compound and stereo microscopes, these devices are reserved for research organizations. They are able to scan a sample also in depth. A computer is then able to assemble

the data to make a 3D image. Following this document, we concentrate in very simple light optical microscope that all readers may build up.

The paper is structured in the following fashion. Section II describes the theory and basic principles. It’s very important for optical microscope engineering, with a discussion of Abbe’s theory, resolution limit, magnification, and some used techniques in light optical microscope. In Sec. III, the four main systems of light optical microscope be cracked in details. Finally, Sec. IV gives the way to solve regular problems when building a microscope. Tricks and helpful hints for light optical microscopy are also putted in that section.

II. Theoretical formalism and basic principles1. Theory and basic principles

+ Refraction

The lens of an optical magnifying glass forms an image of an object because the refractive index of glass is much greater than that of the atmosphere, and reduces the wavelength of the light passing through the glass. A parallel beam of light incident at an angle on a polished block of glass is deflected, and the ratio of the angle of incidence on the surface to the angle of transmission through the glass is determined by the refractive index of the glass (Figure 3.3).

In the case of a convex glass lens (a lens having positive curvature), the spherical curvature of the front and back surfaces of the lens results in the angle of deflection of a parallel beam of light varying with the distance of the beam from the axis of the lens, and bringing the parallel light beam to a point focus at a distance f that, for a given wavelength, is a characteristic of the lens, and is termed its focal length

If the lens curvature is negative, then the lens is concave and a parallel beam incident on the lens will be made to diverge. The beam of light will now appear to originate at a point in front of the lens: an imaginary focus corresponding to a negative focal length -f.

For symmetric focal length f, an object at -u gives an image at v which is magnified by a factor M, where:

Note: asymmetric lenses can have multiple focal lengths.

There is no reason why the front and back surfaces of the lens should have the same curvature, nor even why one surface should not have a curvature of opposite sign to the other. It is the net curvature of the two surfaces taken together which determine whether the lens is convex or concave. Similarly, there is no reason why the refractive index should be the same for all the lenses in an optical system, and different grades of optical glass possess different refractive indices. The “lenses” used in the optical microscope are always assemblies of convex and concave lens components with refractive indices selected to optimize the performance of the lens assembly. Depending on their position in the microscope, these lens assemblies are referred to as the objective lens, the intermediate or tube lens and the eyepiece. It is also quite common for the medium between the sample and the near side of an objective lens to be a liquid, rather than air. An immersion lens is one that is designed to be used with such an inert, high refractive index liquid between the sample and the objective lens.

+ Abbe’s theory of image formation

The image of a light absorbing specimen is formed due to diffraction. The specimen is seen by the light as a complex superposition of gratings with varying grating constants and holes. Some of the light will pass through the specimen undeviated and will only give rise to a uniformly bright image. The deviated (diffracted) light carries the information about the structures in the specimen. To simplify things, consider the grating specimen schematically shown in Figure 1. Parallel light (i.e. a plane wave) which enters from below along the optical axis, will be diffracted and the different diffraction orders will emerge at different angles. The smaller the distance between the grids, i.e. the smaller the periodicity, the bigger the angles will be.

In the rear focal plane of the objective we find the diffraction pattern, which is the Fourier transform of the image. The grid will appear as bright spots on a line. The central spot is the zeroth order. All light that go through the sample undeviated will pass this spot in the back aperture of the objective. The spots next to the zeroth order are the first diffraction orders and so on. As illustrated in Figure 2, blocking all spots but the zeroth order will result in an evenly intense image in the image plane. Blocking all light but the first order spots will result in an image with an intensity variation having the same frequency as the grid. The second and third diffraction order alone gives a false period. However, by adding the four orders (zeroth to third) we get a reasonable image of the specimen. Ernst Abbe, a German microscopist of the 19th hundred century, stated that an image will be formed only if at least two of the diffraction orders are captured by the objective. The more diffraction orders that can be captured by the objective the finer details can be resolved.

+ The resolution limit

Knowing that at least the first diffraction order is needed to obtain an image we can calculate the resolution limit. Consider a grating with the grating constant d. The grating equation gives:

where θ is the angle to the optical axis, m is the diffraction order and λ is the wavelength of light. According to this equation the smaller the distance d, the higher the angle θ for the

same diffraction order. Hence, the smaller the spatial distances in the specimen, the more the light will bend off . Resolution is therefore dependent on how many of the diffraction orders we can capture with the objective.

For the first order m=1, the grating equation gives:

This would be the smallest distance which can be resolved with the microscope. This limit could be decreased by using an oil or water immersion objective.

If only air is in between the cover slide and the objective the light will bend off in a higher angle due to refraction. See Figure 3. Oil and water have a higher refractive index than air (approximately 1.5 and 1.3 compared to 1). By using oil or water in between the cover slide the light will travel to the objective at a lower angle Hence, the resolution limit will decrease.

According to Snell’s law of refraction:

where n is the refraction index. If n2 =1, as for air, we get:

The resolution limit could now be written:

where NA is the numerical aperture. The NA is given on all objectives and therefore we could calculate the resolution limit of the microscope. However, this expression is not true

unless the light is emerging from one point. Also the NA of the condenser has to be taken into account. Consider the following figure:

Parallel light from the condenser travels from refractive index n1 and into the specimen, which has a lower refractive index of n2. Assume NAcondenser = n1sinα. According to refractive and diffraction laws

From the equations we can calculate the smallest distance d to be resolved. As we only need the zeroth and first diffraction orders to be captured by the objective we put m=1. The wavelength of light λ=λ0/n2 and we find that:

If we would use a higher NA of the condenser than the NA of the objective the zeroth order would not be captured by the objective. The maximal resolution limit can therefore be written as:

The resolution limit with incoherent light gives another equation of resolution. Also in this case the resolution limit is determined by Fraunhofer diffraction phenomenon and a point object is imaged as an Airy disk which is shown in Figure 5.

However, in the case of incoherent light the, there will be no interference between two Airy disks overlapping. The resolution can therefore be determined by the Rayleigh criteria: two points are just resolved when the centre of one Airy disk falls on the first minimum of the other Airy pattern. That will give us: (Raleigh criteria)

This expression is similar to the equation for coherent light. As a rule of thumb the resolution limit is said to be approximately λ/2. It means that from Raleigh criteria equation, the absolute value of NAcondenser is so much more than NAobjective then we obtain the Engineer’s “ultimate resolution” by putting NAcondenser = NAobjective :

This resolution chart shows that influence of objective numerical aperture and light wavelength on the resolution of the light microscope. This illustrates this relationship for k=0.61 and 4 light wavelengths

Essentially, NA provides a measure of the ability of the objective to gather and resolve light from the object plane. high NA means more efficient light gathering, better resolution, and better image – BUT, shorter working distance too

For example,

+ Magnification

The overall magnification is given as the product of the lenses and the distance over which the image is projected:

Where D – projection (tube) length (usually = 250mm);

M1, M2 – magnification of objective and ocular.

(250mm – minimum distance of distinct vision for 20/20 eyes)

+ Depth of field

Depth of field is the distance along the optical axis over which image details are observed with acceptable clarity. those factors that influence resolution also affect depth of field, but in the opposite direction. therefore, a compromise must be reached between these two parameters, which is more difficult as magnification increases. this is one reason light etching is preferred for high magnification examination. the depth of field d can be estimated from:

where n is the refractive index of the medium between the specimen and the objective (n ~ 1.0 for air), λ is the wavelength of light, and NA is the numerical aperture. this equation shows that depth of field increases as the NA decreases and when longer wavelength light is used, as shown in Figure.

For simplification, depth of field can be showed as the following method:

+ Depth of focus

The resolution available for an object whose image is in focus in the image plane is finite and limited by the NA of the objective lens, so it follows that the object need not be at the exact object distance from the lens u, but may be displaced from this plane without sacrificing resolution. Since the resolution is finite, the object need not be in the exact object plane in order to remain in focus: there is an allowed depth of field d. Similarly, the image may be observed without loss of resolution if the image plane is slightly displaced: there is an allowed depth of focus D.

where M is the magnification. Both these expressions are approximate and assume that the objective can be treated as a “thin lens”, which is not the case in commercial microscopes. Since the resolution is given by , it follows that the depth of field decreases as the NA increases. For the highest image resolution, the specimen should be positioned to an accuracy of better than 0.5 mm, and this is an essential requirement when specifying the mechanical stability of the specimen stage. The depth of focus is considerably less critical. Bearing in mind that a magnification greater than x100 may be necessary if all the resolved detail visible in the optical microscope is to be recorded, then displacements in the image plane of the order of a millimeter are acceptable.

NA ↑ (i.e. the lens gets better) ~ Depth of field and Depth of focus ↓.

2. Some techniques

+ Köhler illumination

The equipment needed to build an optical microscope is basically a light source to illuminate the specimen and a good lens for magnification. However, depending on the design of the microscope, the illumination and resolution of the microscope can be improved significantly. In 1893 August Köhler of the Carl Zeiss corporation introduced the design of a microscope which is used in all modern microscopes today. The principle is shown in Figure.

The two illumination pathways of Köhler illumination. Note that the conjugate planes for the two pathways are completely opposite. Hence, in the image planes the lamp filament is totally out of focus. Further, using Köhler illumination the field of view and the NA of the condenser can easily be changed.

In Köhler illumination there are two light pathways, the illumination pathway and the image-forming pathway. The illumination pathway originates from the parallel light from the whole lamp, where as the light in the image forming pathway originates from each point in the lamp. By placing the lenses at specific distances from each other the light in the illumination pathway is totally out of focus when the light in the image forming pathway is in focus, and the other way around. By putting the sample in the plane when the light from each point in the lamp is totally out of focus the sample will be perfectly evenly illuminated. This is not the only beauty with Köhler illumination. By putting diaphragms in the all conjugate planes where the light is in focus one can also correct for illumination area, using the illumination field diaphragm, and the angle of illumination with the illuminating aperture diaphragm.

+Phase contrast

We have discussed how an image is formed due to diffract ion. A biological specimen is almost uniformly transparent, and therefore the intensity variation in the image will be poor. However, the light does not go through the specimen unaffected. The light going through the specimen will be shifted in phase. Our eyes cannot detect this phase shift. However, using phase contrast microscopy, developed by Frits Zernike in the early 1930s, we can produce an intensity image based on the phase shift. To illustrate what happens, consider a cubic cell with a thickness d and refractive index n2 in a media with refractive index of n1, as shown in Figure 7.

The two light rays wil l experience an optical pathway length difference of (n1 – n2) d which gives the phase shift of:

For a cell this phase shift is approximately π/2. Frits Zernike understood that if the undeviated light would be speeded up with π/2, the phase difference would be π and an intensity image could be formed, due to constructive and destructive interference. To speed up the light a phase shifter is placed in the rear focal plane of the objective. The phase shifter is optically thinner in areas where the undeviated light will pass. To know there the phase shifter has to be optically thinner the illuminating light goes through a annulus ring, placed directly in front if the condenser and conjugate to the phase shifter. This is shown in Figure 8.

The light going through the specimen undeviated will continue in the same optical path and, with the correct phase shifter, through the optically thinner part of the phase shifter. The deviated light is spread over the entire rear back aperture and most of the light will therefore go through the optically thicker area of the phase shifter. In this way a phase shift of π, and an intensity image can be formed.

+Dark field

Objects witch significantly scatter light can be studied with dark field microscopy. As the name implies the image of the specimen will be bright against a dark background. The concept of dark field microscopy is to let the illuminating light hit the specimen with an angle so high that undeviated light will not be captured by the objective. In other words, the zeroth order is removed. This can be achieved using special dark field condensers or by blocking the central part of the illuminating light, as is shown in Figure 10. Dark field can be used to study submicron particles.

+ Bright field

In bright field illumination, the surface of the specimen is normal to the optical axis of the microscope, and white light is used. A ray diagram for bright-field illumination is illustrated in Figure 42. light that passes through the objective and strikes a region of the specimen surface that is perpendicular to the beam will be reflected back up the objective through the eyepieces to the eyes where it will appear to be bright or white. light that strikes grain boundaries , phase boundaries , and other features not perpendicular to the optical axis will be scattered at an angle and

will not be collected by the objective. these regions will appear to be dark or black in the image. Bright field is the most common mode of illumination used by metallographers.

+ Oblique illumination

The surface relief of a metallographic specimen can be revealed using oblique illumination. this involves offsetting the condenser lens system or, as is more usually done, moving the condenser aperture to a position slightly off the optical axis. Although it should be possible to continually increase the contrast achieved by oblique illumination by moving the condenser farther and farther from the optical axis, the numerical aperture of a lens is reduced when this happens because only a portion of the lens is used. For this reason, there is a practical limit to the amount of contrast that can be achieved. Illumination also becomes uneven as the degree of “obliqueness” increases. Since differential interference contrast systems have been available, oblique illumination is rarely offered as an option on new microscopes.

+ Polarized light

Because many metals and metallic and nonmetallic phases are optically anisotropic, polarized light is particularly useful in metallography. Polarized light is obtained by placing a polarizer (usually a

Polaroid filter) in front of the condenser lens of the microscope and placing an analyzer (another Polaroid filter) before the eyepiece, as illustrated in Figure 44. the polarizer produces plane polarized light that strikes the surface and is reflected through the analyzer to the eyepieces. If an anisotropic metal is examined with the analyzer set 90° to the polarizer, the grain structure will be visible. however, viewing of an isotropic metal (cubic metals) under such conditions will produce a dark, “extinguished” condition (complete darkness is not possible using Polaroid filters). Polarized light is particularly useful in metallography for revealing grain structure and twinning in anisotropic metals and alloys (see the appendix for crystal structure information) and for identifying anisotropic phases and inclusions.

III. Construction of microscope

A simplified design for a reflection optical microscope is shown in Figure 3.13.

The microscope is an assembly of three separate systems. The illuminating system which provides the source of light illuminating the sample, the specimen stage that holds the sample in position and controls the x, y and z coordinates of the area under observation, and the imaging system, which transfers a magnified and undistorted image to the plane of observation and to the recording medium. We will discuss each of these in turn.

1. Light sources and Condenser systems

There are two conflicting requirements for the light source. On the one hand, the area of the specimen being examined beneath the objective lens needs to be uniformly flooded with light in order to ensure that all the microstructural features experience the same illuminating conditions, but on the other hand the incident light needs to be focused onto the specimen to ensure that the reflected intensity is always sufficient for comfortable viewing and recording.

The source of light should be as bright as possible. Fifty years ago this was achieved by striking a carbon arc, which gave an excellent, though somewhat unstable, source of white light. Alternatively, a mercury arc lamp generated an intense monochromatic emission line in the green (λ=0.546 µm), which corresponded well to the peak sensitivity of the human eye. Today, while some small instruments still use a conventional light bulb, high performance optical microscopes are now equipped with a tungsten-halide discharge tube that provides a stable and intense source of white light corresponding to a temperature of about 3200K(compare the temperature of the sun, about 5500K). Filters can then be used to select a narrow band of wavelengths, usually in the green, for monochromatic viewing, or to simulate sunlight more closely (“daylight” filters).

In addition to the source itself, there are other important components in the illuminating system (Figure 3.13). The condenser lens assembly focuses an image of the source close to the back focal plane of the objective lens so that the surface of the specimen is uniformly illuminated by a near-parallel beam of light. The condenser aperture limits the amount of light from the source which is admitted into the microscope by reducing the effective source size. Contrast in the image can often be improved by using a small condenser aperture, although at the cost of reducing the image intensity and, if the aperture is too small, introducing image artifacts which are associated with the Abbe diffraction pattern of a “point” source. A second aperture, the objective or virtual image aperture, is placed in the virtual image plane of the sample (Figure 3.13), so that only light illuminating the area under observation is admitted to the microscope. This ensures that light is not internally reflected within the microscope, leading to unwanted background intensity. The size of the virtual image aperture should be adjusted to the field of view of the microscope at the magnification used. Both the condenser and the virtual image apertures are continuously variable irises which can be adjusted to the required size.

Many reflection microscopes also permit the illuminating system to be repositioned so that optically transparent specimens can be viewed in transmission. This is important not only for the thin tissue samples of biology and medicine, but also for mineralogical samples, partially crystalline polymers and thin-film semiconductor materials. It is also extremely useful when monitoring the quality of thin-film samples prepared for transmission electron microscopy.

Alternatively, the virtual image aperture may be provided with a central stop that allows an annulus of light to illuminate the area under observation from the periphery of a special objective lens assembly. Such dark-field illumination (see below) may greatly enhance the contrast.

2. The specimen stage

The primary requirement for the specimen stage is mechanical stability and, given the expected ~0.3 µm resolution for a good optical microscope, it is clearly essential that the positioning of the specimen be accurate to better than this limit. The accurate positioning of the specimen in

the x–y plane is only one aspect of the stability required. The image is brought into focus by adjusting the vertical location of the specimen and the accuracy of this z-adjustment must be within the depth of field for the largest NA objective lens, typically also ~0.3 µm.

The necessary mechanical precision is commonly achieved by coarse and fine micrometre screws for all three (x, y and z) coordinates, and both the time-dependent drift of the stage and the mechanical “slack” in the system need to be minimized. (The “slack” is the difference in the micrometre reading when the same feature is brought into position from opposite directions.)

In general, it is the z-adjustment that presents the most problems, since the necessary stage rigidity implies a fairly massive and hence heavy construction. Two possibilities exist, depending on whether the specimen is to be placed beneath or above the objective lens. In the former and more usual case (Figure 3.13), the plane of the prepared sample surface must be positioned accurately normal to the microscope axis. This is commonly achieved by supporting the specimen from below on soft plasticine and applying light pressure with a suitable jig (Figure 3.14)

3. Selection of Objective lenses

A very wide range of objective lenses are available, depending on the nature of the specimen and the desired imaging mode. The performance of the objective lens is primarily dependent on its NA, and this is almost universally to be found inscribed on the side of the objective lens assembly, together with the magnifying power for that lens. Most objective lenses are achromatic, that is they are not limited to monochromatic light, but are nevertheless recommended for viewing high resolution monochromatic images in the green. While

achromatic lenses are corrected for both spherical aberration in the green and chromatic aberration at two wavelengths (red and blue), they only yield a focused image in the central region of the field of view. Plan achromat objectives ensure that the periphery of the field of view is also in focus and they are therefore more suitable for image recording. Apochromatic objectives are free of chromatic aberration for three wavelengths (red, green and blue), and, correspondingly, plan apochromats are designed for recording image detail in full colour.

Histological examination of soft tissues, which accounts for the major proportion of the work of the optical microscope in the life sciences, requires that the specimen be protected from the environment by mounting a thin tissue slice on a glass slide and then protecting it with a thin cover slip. Similar techniques are used for many polymer specimens, particularly those that are partially crystalline. These materials can be cast onto the slide and the specimen thickness controlled by spinning or by applying uniform pressure to a cover slip. Objective lenses designed for use with such specimens are corrected for the refractive index and thickness (often 0.1mm) of the optically flat cover slip.

Not only the resolution, but also the brightness (the intensity per unit area of the image) depends on the NA of the objective lens. For any given conditions of specimen illumination, the brightness of the image decreases as the square of the magnification. However, larger NA lenses increase the cone acceptance angle for the lens, so that more light is collected. The NA may vary by an order of magnitude in going from a low-power (low magnification) lens to a high-power (high magnification) immersion objective. A similar order of magnitude increase in the magnification will then be required in order to observe all the image detail. It follows that there is still an overall reduction in brightness by a factor of 102/10=10.

The working distance of the objective lens from the specimen surface also decreases dramatically as the NA of the objective lens assembly is increased, down to of the order of 0.1mm for the highest-powered lenses. It is only too easy to damage a lens by driving the specimen through focus and into the glass lens, and good lenses are expensive to replace.

Special long working distance lenses are available that allow high magnification observation without having the sample in close proximity to the objective lens. One inexpensive design creates an intermediate image at unit magnification by reflection (Figure 3.15) and permits a specimen to be imaged while in a hostile environment, for example in a corrosive medium or at an elevated or cryogenic temperature. Despite the attraction of in situ experiments, little optical microscopy has been done under such dynamic conditions. There are difficulties: the dimensional stability of the specimen and its support structure is one problem; another is to ensure that the optical path between the specimen and the objective lens assembly is not obscured by a condensate or by chemical attack.

Cryomicroscopy is subject to the formation of ice crystals, while a high temperature stage may form opaque deposits that derive from the heating elements, the specimen or the supporting structure. To be successful, an in situ stage must combine a rapid response time with experimental stability. In the case of a heating stage, a compromise is required between the large heat capacity needed to ensure thermal stability, and the small heat capacity necessary to allow a rapid experimental response.

Many other specialized objective lens and stage assemblies are available. One of the most useful, for both reflection and transmission work, is the dark-field objective which illuminates the specimen with a cone of light surrounding the lens aperture. The light scattered by the specimen into the lens aperture is then used to form a dark-field image in which the intensity is the inverse of that observed in normal illumination (Figure 3.16).

4. Image Observation and Recording

The image magnification provided by the objective lens assembly is limited, and insufficient if the image is to be fully resolvable by the human eye. There are three options available. The first is to insert an eyepiece and an additional intermediate or tube lens, in order to view the image directly at a working magnification that is comfortable for the observer. Most microscopes now available are designed with a tube lens that allows the sample to be placed in the focal plane of the objective, so that the light returning to the microscope through the objective is essentially

parallel, and only brought to an intermediate focus by the tube lens. This allows for a wide range of optical accessories to be inserted between the objective and the tube lens. The second option is to use the additional lenses to focus the image onto a light-sensitive, photographic emulsion or charge-coupled device (CCD), usually for subsequent enlargement. For the third option it is possible to scan the image in a television raster and display it on a monitor. For the recording of dynamic events in the microscope this may in fact be the preferred technology. In recent years the improved availability of high quality, CCD cameras has made it possible to record a digital image from an objective lens without any additional lenses. The consumer market for digital cameras has allowed high quality CCD technology to all but replace photographic recording, while conventional television camera technology is now seldom used, even for teaching purposes. Nevertheless, professional photographers still make use of photo- graphic emulsions, since they usually require the highest performance CCD systems, which are still extremely expensive. More recently, there have been significant advances in a new technology, complementary metal oxide semiconductor (CMOS), which essentially places the camera on a single chip. For colour recording in both CCD and CMOS devices individual pixels (picture elements) can be filtered by red, green and blue dyed photodiodes, but while both CCD and CMOS cameras offer pixel sizes of 6 µm or even less, the CMOS cameras are limited to of the order of a million pixels per frame, an order of magnitude less than the CCD cameras. To make the most of high resolution digital colour recording it may be necessary to invest in planapochromatic objective lenses

+Monocular and Binocular Viewing

Visual observation is most commonly performed with a monocular eyepiece, which enlarges the primary image by a factor of x3to x15. A typical 0.95NA (non-immersion) objective may have a primary magnification of x40 and a resolution of 0.4 µm, so that, to ensure that all resolved features are readily visible to the eye (0.2mm), some further magnification is required, simply calculated as: (0.2 x 103)/(0.4 x 40)= x12.5.

Most good microscopes have an additional intermediate or tube lens (x4, for example), so that a x3or x5 eyepiece should then be sufficient to resolve all image detail. Even without an intermediate lens there is no real reason to use a x15 eyepiece, since superfluous additional magnification reduces the field of view, enlarging the resolved features to the point where they appear blurred to the eye of the observer.

Some microscopes are equipped with a beam splitter and a binocular viewer. For those who have difficulty viewing comfortably through one eye this is undoubtedly a convenience, but the microscopist should be aware that there are some disadvantages. In particular, it is unusual for the focal plane of both eyes to be identical, so that one eyepiece of the pair needs to be independently focused. The user first focuses a feature of interest in the plane of the specimen, using just one eye and a fixed-focus eyepiece. He then adjusts the variable focus of the second eyepiece (without touching the specimen stage controls) until the images seen by both eyes

merge into a single, simultaneously focused, image. This procedure of adjusting the binocular settings is completed by adjusting the separation of the two eyepieces to match the separation of the observer’s eyes. It is important to note that a binocular eyepiece does not provide stereoscopic (three-dimensional) viewing of the sample, which would require two independent objective lenses focused on the same field of view. Stereo binoculars (or stereomicroscopes), with twin objectives, are available, but with magnifications limited to about x50. This limit is dictated by the geometrical problems associated with the positioning of the twin objective lenses close to the specimen surface. Stereo binoculars are important tools for inspection in the electronics industry.

+ Photographic Recording

A photographic emulsion and the human eye react very differently to light. The emulsions have their maximum sensitivity in the ultraviolet (about 0.35 µm) and both black and white, and colour films rely on dyes to extend the photosensitivity of silver halide emulsions beyond the green (Figure 3.17).

Orthochromatic emulsions are not sensitive to red light, which is a convenience in dark-room processing, and are a common choice for photographic recording of monochromatic microscope images in green light. Panchromatic film is a common choice for black and white photographic recording in daylight, but here too the sensitivity falls steadily with increasing wavelength in the visible range. In classical black and white photography the recording medium always yields a negative in which the clear areas, corresponding to zero excitation (no silver precipitation) and the opaque (black) areas correspond to maximum light excitation. This does not have to be the case, and Polaroid cameras commonly produce a positive grey scale image. Colour recording films may also be negative, and are then used for colour printing, or positive, for use as slides or

transparencies. The convention is to use the suffix chrome for positive transparencies (Kodachrome, Ektachrome, etc.), but to use the suffix colour for negative film (Fujicolor, Agfacolor, etc.).

The speed of an emulsion is its response to a fixed radiation dose at a standard wavelength and depends on three factors: the exposure time, the “grain” of the emulsion and the development process. A photosensitive silver halide grain will react to subsequent development only if it can absorb a pair of photons. The time interval between the arrival of the two photons is important, since the grain may decay from its initial excited state in the interim. As the incident intensity decreases, the interval between photon excitations of the same grain increases, and the response of the emulsion is reduced, a phenomenon termed reciprocity failure. Larger halide grain sizes increase the photon collision cross-section and improve the photosensitivity (the speed of the emulsion). The price paid is a “grainier” image with poorer inherent resolution. It follows that some compromise is usually required between fine-grained, slow-speed emulsions and coarse-grained, high-speed emulsions.

During development, the grain of silver, which is nucleated at an activated halide crystal, grows into a cluster of silver grains which encompasses a much larger volume than that associated with the original halide crystal, so that the resolution in the final recorded image is affected by the growth of the silver grains during the development process. An emulsion designed for photomicroscopy, and developed according to the recommendations of the manufacturer, should have a resolution of the order of 10–20 µm and be capable of enlargement by a factor of x10. It should therefore be possible to photograph a high resolution image without any loss of information at an appreciably lower magnification than that required to view the fully resolved microstructure. It follows that a low magnification, high resolution recorded image contains far more information than is available in the field of view required for observation at full resolution.

The contrast attainable in a given emulsion is defined in terms of the dose dependence of the blackening in the developed emulsion. The dose is the amount of light per unit area E multiplied by the time of exposure t, while the blackening D is the logarithm of the ratio of the intensity incident on the emulsion I0 to the intensity of light transmitted through the exposed and developed emulsion I:

The contrast γ is defined as the maximum slope of the curve of D plotted against log Et. Emulsions with a high γ lose image detail because they tend to register as black or white with few intermediate grey levels, while low γ emulsions lack contrast because the grey levels are too close together. A major disadvantage of photographic recording is the nonlinearity of the response of the emulsion and the difficulty of controlling the many parameters involved in exposing, developing, enlarging and printing the emulsion. It is very difficult to make

quantitative measurements of image intensity or contrast based on photographic recording and digital recording, using a CCD camera, is therefore preferable.

The range of information which can be recorded, either by a photographic emulsion or by a CCD camera, is never unlimited. This is illustrated in Figure 3.18.

At very low values of the dose Et background noise will start to become a problem, while at very high doses the response of the recording media will saturate. High resolution, negative, black and white film is quite capable of responding to four orders of magnitude of the dose, but positive prints are limited to about two orders of magnitude. CCD cameras usually come somewhere in between (see below), but have the distinct advantage that there response is linear over this range. The response of photographic emulsions to high energy electrons is also linear in dose, since the halide grains are excited by a single electron impact (compare the excitation process for visible light, which requires two photons to strike a halide grain within a critical time interval). Similar considerations apply to CMOS cameras.

5. Specimen Preparation

For many students, good specimen preparation is a major obstacle to successful optical microscopy. It is unfortunate that every material presents its own individual and unique problems of specimen preparation. For example, the elastic modulus and the hardness of the material usually determine the response of the sample to sectioning, grinding and polishing, while the chemical activity determines the response to electrolytic attack and chemical etching. In what follows we will generalize as far as possible, while recognizing that each metal alloy, every ceramic material and all plastic compositions are almost certain to respond differently.

IV. The complete assisted section1. Common Optical Defects & Solutions

Microscopes and other optical instruments are commonly plagued by lens errors that distort the image by a variety of mechanisms associated with defects (commonly referred to as aberrations) resulting from the spherical geometry of lens surfaces. There are three primary sources of non-ideal lens action (errors) that are observed in the microscope.

Of the three major classes of lens errors, two are associated with the orientation of wavefronts and focal planes with respect to the microscope optical axis. These include on-axis lens errors such as chromatic and spherical aberration, and the major off-axis errors manifested as coma, astigmatism, and field curvature. A third class of aberrations, commonly seen in stereo microscopes that have zoom lens systems, is geometrical distortion, which includes both barrel distortion and pincushion distortion.

In general, the ultimate effect of optical aberrations in the microscope is to induce faults in the tiny features and specimen detail of an image that is being observed or digitally recorded. Lens artifacts in the microscope were first addressed in the Eighteenth Century when the London instrument maker John Dollond discovered that chromatic aberrations could be reduced or eliminated by using a combination of two different types of glass in the fabrication of lenses. Several decades later, during the Nineteenth Century, achromatic (free of chromatic aberration) objectives with a high numerical aperture were developed, although there were still geometrical distortion problems with the lenses. Modern glass formulations and antireflective coatings, coupled to advanced grinding and manufacturing techniques, have all but eliminated a majority of the aberrations from today's microscope objectives. However, careful attention must still be paid to these artifacts, especially when conducting high-magnification digital microscopy or when working with stereo microscopes that have zoom lens systems.

Chromatic Aberration - One of the most common faults observed in spherical lenses, chromatic aberration occurs because the lens refracts the various colors present in white light at a different angle according to the wavelength (see Figure 1). Red light is not refracted at the same

angle as green or blue light so the focal point on the optical axis of the lens is farther away from the lens for red light. Likewise, green light is focused closer to the lens than red light, and blue light is focused in a plane that is closest to the lens. This phenomenon is commonly referred to as dispersion and occurs to a certain degree in all spherically shaped lens elements. The inability of the lens to bring all of the colors into a common focal plane results in a slightly different image size and focal point for each of the three predominant wavelength groups. The result is a colored fringe or halo surrounding the image, with the halo color changing as the focal point of the objective is varied.

Explore how the component wavelengths of white light are split according to frequency when they pass through a simple lens system to produce the common optical artifact known as chromatic aberration.

Chromatic aberration artifacts are compounded by the difference in image magnification that occurs as a result of the varying focal planes for each color group, an effect termed chromatic difference of magnification. Aberrations of this type can be significantly reduced, or eliminated, by making compound lenses that are composed of individual elements having different color-dispersing properties. A wide variety of optical glasses are now available to lens designers. For example, crown glass has dispersive properties that enable it to be paired in a lens doublet with a flint glass element to produce an achromatic doublet lens system that focuses blue and red wavelengths in the same image plane. Additional refinement of an optical system with even more sophisticated glass formulas and shapes can reduce chromatic aberration even further.

Spherical Aberration - A potentially serious artifact that can have serious consequences on images produced by the microscope, spherical aberration is the result of using lenses having spherical surfaces, which is currently the only practical approach to lens design. Spherical aberration occurs when light waves passing through the periphery of a lens are not brought into exact focus with those passing through the center (see Figure 2 for an example using monochromatic red light). The result is that a well-defined image plane does not exist, and the specimen cannot be correctly focused. As an example, a point source of light appears as a spot

surrounded by a bright halo or series of diffraction rings when the microscope is brought into its "best" focus. Complex specimens that have a significant thickness are often so blurred as to be unrecognizable, especially at the periphery of the view field.

Correction of an optical system (such as a microscope) for spherical aberration is often accomplished by utilizing a combination of positive and negative lens elements with different thickness, which are cemented together to form a compound lens group. Spherical aberrations are very important in terms of the resolution of a lens because they affect the coincident imaging of points along the optical axis and degrade the performance of the lens, which will seriously affect specimen sharpness and clarity. These lens defects can frequently be reduced by limiting the outer edges of the lens from exposure to light using diaphragms, and also by utilizing a spherical lens surfaces within the optical system.

The highest-quality modern microscope objectives address spherical aberrations in a number of ways including special lens-grinding techniques, improved glass formulations, and better control of optical pathways. Objectives that are highly corrected for spherical aberration are often designed for specific conditions, such as strict cover glass thickness restrictions, oil immersion, and a narrow refractive index tolerance. Adjustable correction collars are available on some high-dry oil-free objectives to account for cover glass thickness variations. Microscope operators should carefully study the basic requirements of specialized objectives to make certain spherical aberration is not introduced due to utilization of the objective under conditions for which it was not designed.

Coma - Similar to spherical aberration in many respects, coma is generally encountered with off-axis light rays and is most severe when the microscope is out of proper alignment. The aberration is named for its strong resemblance to the shape of a comet tail, and is manifested by a streak of

light that appears to emanate from a focused spot at the periphery of the viewfield. Coma is often considered the most problematic aberration due to the asymmetry it produces in images. It is also one of the easiest aberrations to demonstrate. For example, on a bright, sunny day, when a magnifying glass is used to focus an image of the sun on the sidewalk, coma aberration can be seen in the image when the magnifying glass is tilted with respect to the principal rays from the sun. The sun's image, when projected onto the concrete, will elongate into a comet-like shape that is characteristic of coma aberration.

Discover how the off-axis coma aberration affects digital images captured in the microscope. The tutorial explores progressive degrees of coma and demonstrates the detrimental effect on resulting images.

The distinct shape displayed by images suffering from coma aberration is the result of refraction differences by light rays passing through the various lens zones as the incident angle becomes more oblique (off-axis). The severity of comatic aberration is a function of thin lens shape. In the extreme, coma results in meridional rays passing through the periphery of the lens to arrive at the image plane closer to the axis than do light rays passing through the central portion of the lens (and closer to the principal ray, as illustrated in Figure 3). In this case, the peripheral rays produce the smallest image and the coma aberration is said to be negative. In contrast, when the peripheral rays are focused farther down the axis to produce a much larger image, the aberration is termed positive. The "comet" shape may have its "tail" pointing toward the center of the view field or away, depending upon whether the aberration has a positive or negative value. The degree of coma aberration is greater for lenses with wider apertures, and can be corrected (in part) by reducing aperture size. Microscope designers usually attempt to correct coma aberration to accommodate the diameter of the object field for a given objective and eyepiece combination.

Astigmatism - Astigmatism aberration is similar to coma; however, this artifact is not as sensitive to aperture size and depends more strongly on the oblique angle of the light beam. The aberration is manifested by the off-axis image of a specimen point appearing as a line or ellipse instead of a discrete point. Depending on the angle of the off-axis light rays entering the lens, the line image may be oriented in either of two different directions (see Figure 4), tangentially (meridionally) or sagitally (equatorially). The intensity ratio of the unit image will diminish, with definition, detail, and contrast being lost as the distance from the center is increased.

In less expensive microscopes, astigmatism is often the result of asymmetric lens curvature due to mistakes in manufacture or improper mounting of a lens in its frame or orientation within the objective barrel. Astigmatism lens errors are usually corrected by designing microscope objectives to provide precise spacing of individual lens elements as well as appropriate lens shapes and refractive indices. Careful alignment and adjustment of the individual lens elements is accomplished with spacers and shims to reduce or eliminate the effects of astigmatism.

Field Curvature - Also commonly referred to as curvature of field, this aberration, which is the natural result of employing lenses that have curved surfaces, is very familiar to many experienced microscopists. When light is focused through a curved lens, the image plane produced by that lens will be curved, as illustrated in Figure 5. The image can be focused over the range between points A and B to produce a sharp focus either on the edges or in the center. Categorized as an off-axis aberration, field curvature produces an image plane having the shape of a concave spherical surface (resembling a convex lens surface), as seen from the objective. Although successive zones can be brought into focus by translating the objective, the entire image cannot be simultaneously focused onto a flat surface such as a film plane or the surface of a CCD or CMOS image sensor.

Examine how distortion aberrations are manifested in changes to image shape rather than a reduction in sharpness or alterations to color balance.

Optical designers deal with field curvature by adding corrective lens elements to the objective in specially designed flat-field objectives. Although the optical correction for field curvature requires the addition of several new lenses to the design, these objectives (termed plan or plano) are the most common type of objective in use today. Field curvature is seldom totally eliminated, but it is often difficult to detect edge curvature with most plan-corrected objectives. As a result, very limited degrees of field curvature often do not degrade photomicrographs or digital images. The artifact is more severe at low magnifications and can be a serious problem with stereo microscopes.

Geometrical Distortion - Image distortion is an aberration commonly observed in stereo microscopy, and is manifested by changes in the shape of an image rather than the sharpness or color spectrum. The two most prevalent types of geometrical distortion, positive and negative (often termed pincushion and barrel, respectively), can often be present in very sharp images that are otherwise well-corrected for spherical and chromatic aberrations, as well as coma and astigmatism. When images suffer from distortion, the true geometry of a specimen is no longer maintained in the image. Figure 6 illustrates examples of rather significant pincushion and barrel distortion in the image of a computer microprocessor integrated circuit.

Geometric distortion can be difficult to detect, especially when the aberration is relatively slight and the specimen lacks periodic structures. This type of artifact is most severe in specimens that have straight lines, such as periodic grids, squares, rectangles or other regular polygonal features that readily show the curvature present from distortion. Distortion is often found in optical designs utilizing compound lens systems (telephoto, fisheye, and zoom) containing meniscus, concave, hemispherical, and thick convex lenses. Complex lens systems, such as the zoom design, can have rather pronounced distortion, which may vary with focal length, producing pincushion distortion at long focal lengths and barrel distortion at short focal lengths. For this reason, stereoscopic zoom microscopes classically have a significant amount of distortion present and microscope manufacturers have expended considerable effort in alleviating this aberration.

Flare - Flare is non-image forming light. Reduces contrast and color saturation. Flare is caused by very bright subject areas and produces internal reflections in the lens. Stacking of filters can increase flare. Lens coatings by the Mfg. keeps flare to a minimum. The use of a suitable hood (not the stock hood) can also aid in reducing flare.

Ghost Images - Not a true defect but is seen quit often and sometimes confused as one. Distinct images, usually in the shape of the diaphragm or a very bright light source included in the scene. Caused by high intensity light producing rays which bounce around in the lens and form an image. Often multiple images appear in a row across the scene, starting at or near the source. Ghost images can be reduced by the use of a suitable lens hood.

2. Tricks & Helpful Hints

Objective-related factors

Correction of lens errors: In contrast to achromatic objectives, apochromatic objectives focus more colors of the spectrum to one point. This results in a sharper image.

The numerical aperture of the objective: This value is printed on the objective. The higher the value, the higher the resolution. The numerical aperture is a dimension less value which represents the cone of light that can be caught by the objective.

Lighting system

General color of light: The shorter the wavelength, the higher the resolution. If your microscope uses halogen or tungsten lamps (instead of LEDs), then the color of the light will shift towards the red end of the spectrum with increasing age. This will reduce the resolution. The color of the light also changes with its intensity. If you turn up the light to maximum intensity, then the color of the light will be more towards the blue end of the spectrum (shorter wavelength and higher resolution). LEDs do not change their color with age or brightness.

Light spectrum (color range): The color range may also impact on resolution. In the case of monochromatic light, chromatic aberration does not play a role and the light can be focused on one point.

Specimen-related factors

The correct thickness of the cover glass: The correct cover glass thickness is extremely important for high numerical-aperture objectives. For other objectives, the effect may not be noticeable.

The correct refractive index of the cover glass: This is something that you do not have to worry about, this is the task of the cover glass manufacturer.

The correct refractive index of the mounting medium: This one should be as close to the refractive index of glass as possible.

Thickness of the mounting medium: the thinner the better.

The presence of immersion oil: Objectives that carry the label “OIL” need the correct immersion oil for best resolution.

Adjustments of the microscope

The correct condenser diaphragm setting: This setting must match the numerical aperture of the microscope in use.

The correct setting of the correction collar: Some objectives have a correction collar (a turnable ring) to adjust to the cover glass thickness. Most objectives do not have one, however.

Maintenance-related factors

The cleanness of the optical parts: Dust and dirt generally decrease image quality and are a big annoyance, especially if one uses dark-field microscopy.

Stability of the photomicrographic system

Moving objects: Moving cells naturally cause a blurring when long exposure times are used. This decreases resolution of the moving object.

Stability: A shaky photographic system generally decreases resolution of the image.

The checlkist: how to obtain the best image quality

Use new light bulbs and turn up the light. This will reduce the wavelength of the light. Alternatively, use a blue filter.

Use cover glasses of the correct thickness and make sure that the mounting medium has a refractive index which is close to the refractive index of glass.

Adjust the condenser aperture diaphragm to the numerical aperture of the objective

If you use oil immersion, make sure that the oil has the correct refractive index

Use fresh light bulbs (low in red light, high in blue light)

Keep the microscope free of dust

Make sure that the objectives, eye pieces are clean

Helpful hints

It can be difficult to determine which object you are using with an inverted microscope due to limited view, as the magnification value may not be easily observed. However, each objective has a color-coded ring on it that is usually visible. The colors and corresponding magnification are: red-x5; yellow-x10; green-x20; blue-x50; and white-x100.

V. Conclusions

The optical microscope is the tool of preference for the microstructural characterization of engineering materials, both because of the wealth of information available in the magnified image and the ready availability of high quality microscopes, specimen preparation facilities and inexpensive methods of image recording and data processing. The visual impact of the magnified image is immediate, and its interpretation is in terms of spatial relationships which are already familiar to the casual observer of the macroscopic world.

Geometrical optics determines the relationship between the object placed on the microscope stage and its magnified image. The ability to resolve detail in the image is limited primarily by the wavelength of the light used to form the image, together with the angle subtended by a point in the object plane at the objective aperture. The aperture of the eye and the range of wavelengths associated with visible light limit the resolution of the eye to approximately 0.2mm. That is, the unaided eye can distinguish between two features at a comfortable reading distance (30 cm) if they are separated by 0.2mm.

The numerical aperture (NA) of an objective lens is the product µsinα, where µ is the refractive index of the medium between the lens and the object and α is the half-angle subtended at the objective (the angular aperture of the lens). Values of NA vary from of the order of 0.15 for a low magnification objective used in air to about 1.3 for a high-power, oil- immersion objective, leading to a limiting (best possible) resolution of the order of half the wavelength of visible light, about 0.3 µm.

A sharply focused image will only be obtained if the features to be imaged are all in the plane of focus, and high NA lenses require accurate focusing. It follows that specimens to be imaged at the best resolution must be accurately planar. This limited depth of field is the primary reason why samples of opaque materials must be polished optically flat, while those of transparent materials must be prepared as thin, parallel-sided sections.

The components of the optical microscope include the light source and condenser system, the specimen stage, the imaging optics and the image recording system. Each of these components has its own engineering requirements: the intensity and uniformity of the light source; the mechanical stability and positional accuracy of the specimen stage; the optical precision and alignment of the imaging system, and the sensitivity and reproducibility of the image data-recording system. While in the past photographic recording was the primary option, the rapid development of charge-coupled device (CCD) and complementary metal oxide semiconductor (CMOS) digital image data systems has led to the development of a new range of microscopes in which digital recording and computer- aided image enhancement have, to a large extent, made the photographic darkroom obsolete.

A major consideration in the application of the optical microscope is the selection and preparation of a suitable sample. In the first place, the sample must be representative of the features which are to be observed. That is, the sampling procedure must take account of both in homogeneity (spatial variations in the features and their distribution) and morphological anisotropy (orientational variations, as in fibrous or lamellar structures). Secondly, preparation of the sample surface must reveal the intersection of bulk features with the plane of the section without introducing artifacts (such as scratches or stains). In most cases, surface preparation is a two-stage process. The first step is to prepare a flat, polished, mirror- like surface, while the second is to develop contrast by the use of suitable chemical etchants, solvents or differential staining agents.

Image contrast is a sensitive function of the mode of operation of the microscope, but most engineering materials are examined by reflection microscopy. The contrast then reveals local differences in the absorption and scattering of the incident light. Chemical etchants commonly develop topographic features which scatter the incident beam outside the objective aperture, but they may also differentially stain the surface, so that some features absorb more light than others. In many cases, the different phases and impurities present (“inclusions”) will also give contrast

that is associated with differences in the reflectivity of the different phases for the incident light, quite independent of the action of an etchant.

The optical imaging conditions can also be controlled in order to enhance the image contrast. A “dark-field” image is formed by collecting the scattered light from the object, rather than the specularly reflected light used to form a “bright-field” image. If the specimen is illuminated with plane-polarized light, then the changes in polarization that accompany the interaction of the light with the specimen can be analyzed using “crossed polars” that convert any rotation of the plane of polarization into variations in image intensity. An optical wedge or sensitive tint plate can be used to introduce a controlled phase shift and further enhance the image contrast in polarized light, often yielding quantitative information on the optical properties of the sample and its constituents.

In phase contrast reflection microscopy small (>20 nm) topological differences at the sample surface can be converted into variations in image intensity, while in transmission- microscopy differences in refractive index can be similarly imaged. By combining the light reflected from the sample surface with that reflected from an optically flat reference surface it is possible to obtain two-beam optical interference, in which the interference fringes again reflect the topology of the sample surface. Multiple beam interference allows very small differences in the height of surface features to be detected with a sensitivity of a few nanometre, and this vertical “resolution” is several orders of magnitude better than the lateral image resolution, which is limited by the NA of the objective lens.

The quality of digital and analogue recorded images depends on three independent factors: the preparation of the sample, the optical imaging in the microscope; and the system used to record and process the final image data. The observed image in the microscope, the image recorded on a transparency, the digitized image viewed on a computer screen and the printed image reproduced in a published text will all differ in quality, reflecting the different technologies being used. The eye is the best judge of that combination of resolution and contrast which yields the most information, but digital image data processing software now provides the microscopist with some excellent tools for making that judgement and ensuring that results will be recorded and presented with minimal loss of image quality.

VI. References

1. http://en.wikipedia.org/wiki/Optical_microscope#References

2. http://www.microbehunter.com

3. Microstructural Characterization of Materials, 2nd Edition - David Brandon and Wayne d. Kaplan

4. Metals Handbook, Volume 7: Atlas of Microstructures of Industrial Alloys, American Society for Metals, Metals Park, OH, 1972.

5. J.L.McCall and P.M. French (eds), Metallography in Failure Analysis, Plenum Press, London, 1978.

6. J.B. Wachtman, Characterization of Materials, Butterworth-Heinemann, London, 1993.

7. J. Russ, The Image ProcessingHandbook, 4th edn, CRC Press, Boca Raton, FL, 2002.

8. O1 Optical Microscopy By Katarina Logg. Chalmers Dept. Applied Physics. 2006-01-20

9. D. Courjon and J. Bulabois (1979). "Real Time Holographic Microscopy Using a Peculiar Holographic Illuminating System and a Rotary Shearing Interferometer". +Journal of Optic 10

10. "Demonstration of a Low-Cost, Single-Molecule Capable, Multimode Optical Microscope“ Retrieved February 25, 2009.

11. Documents of Asst. Prof Philip D.Rack – Dept. of materials Science and Engineering – University of Tennessee

12. Documents of Dr. Nguyen Hoang Viet - Dept. Iron and Steelmaking – Hanoi University of Science and Technology