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## Microscopes

### Contents

Optical Microscopes
Electron Microscopes
Other Microscopes
Ptychography

### Optical Microscopes

The first powerful magnifier was probably made by Anthony Leeuwenhoek (1632-1723) while working with magnifying glasses in a dry goods store. He used the magnifying glass to count threads in woven cloth. He became so interested that he learned how to make lenses. By grinding and polishing, he was able to make small lenses with great curvatures. These rounder lenses produced greater magnification, and his microscopes were able to magnify up to 270X. Because it had only one lens, Leeuwenhoek's microscope is now referred to as a single-lens microscope. Its convex glass lens was attached to a metal holder and was focused using screws. With such microscope, he discovered microorganisms - bacteria, yeast, blood cells and many tiny animals swimming about in a drop of water - thereby founding the science of microbiology and providing the basis for the development of the germ theory of disease. From his great contributions, many discoveries and research papers, Anthony Leeuwenhoek has since been called the "Father of Microscopy".

#### Figure 1 Anthony van Leeuwenhoek[view large image]

Microscope is an instrument for producing a magnified image of a small object. There are many types of microscopes, ranging from simple, single-lens instruments (magnifying glasses) to compound microscopes and high-powered electron microscopes:

• Magnifying Glasses -- The simple magnifier achieves angular magnification by permitting the placement of the object closer to the eye than the eye could normally focus. If the standard close focus distance1 is taken as 25 cm (see Figure 2a), then the angular magnification can be written as: = (h/f)/(h/25) -------------------- (1).
• This formula is applicable when the virtual image h' is at infinity by placing the object at the focal point. Thus the object distance is the focal length f. The formula shows that lens with shorter focal length (greater curvature) yields more magnifying power. You can get a bit more magnification from the magnifier by focusing it so that the virtual image is at 25 cm rather than infinity, but it is not a good idea because it puts the eye of the viewer under strain to accommodate the image in that close distance. The relaxed eye is focused at infinity, so if you are going to use a microscope all day, you had better focus it at infinity.

#### Figure 2a Magnifier

• Compound Microscopes -- Compound microscopes are two lens systems. The object lens is positioned close to the object to be viewed. It forms an upside-down and magnified image called a real image because the light rays actually pass through the place where the image lies. The ocular lens, or eyepiece, acts as a magnifying glass for this real image. The eyepiece makes
the light rays spread more, so that they appear to come from a large inverted image beyond the object lens. Because light rays do not actually pass through this location, the image is called a virtual image. The linear magnification or transverse magnification is the ratio of the image size to the object size. If the image and object are in the same medium it is just the negative of the image distance L + fo divided by the object distance fo (by basic trigonometry, see Figure 2b). The commonly stated expressions for microscope magnification are

#### Figure 2b Compound Microscope [view large image]

based on the assumption that the length of the tube L is large compared to either fo or fe so that the following relationships hold (the negative sign denotes inverted or virtual image) :
Mo - L / fo ---------- (2).
The total magnification M is the product of Eqs. (1) and (2), i.e., M = Mo x = - (L/fo)(25/fe) ---------- (3).

Resolution of the microscope is given by the formula :

d = (0.612 x ) / (n x sinA) --------------------- (4),

where is the wavelength of the energy source, n is the index of refraction of the lens, and A is the aperture angle2.

According to Eq.(4) improvement of the resolution can be achieved by increasing the size of the aperture. However, until recently (in 2013) the design was limited by diffraction - light spreads out when passing through a small aperture (Figure 3a). That makes any details smaller than 2x10-5 cm (including many basic structures of the living cells) look fuzzy. But new strategies, hardware, and software have shattered that limit.
A technology called structured illuminartion microscopy (SIM) can improve the resolution to about 10-5 cm with the cells tagged with fluorescent dyes. An image of microtubules in an epithelial cell from SIM is shown in Figure 3b (microtubules in red, DNA in blue, and the anchoring protein structures in green). The next challenge is to obtain unlimited resolution in living biological material.

### Electron Microscopes

• Electron Microscopes -- Electron Microscopes were developed due to the limitations of Light Microscopes which are limited by the physics of light to 500x or 1000x magnification and a resolution of 0.2 micrometers (with = 0.4 micrometers - yellow light, n = 1.3, and sinA = 0.8 in Eq.(4)). In the early 1930's this theoretical limit had been reached and there was a scientific desire to see the fine details of the interior structures of organic cells (nucleus, mitochondria...etc.). This required 10,000x plus magnification which was just not possible using Light Microscopes.
• The Transmission Electron Microscope (TEM) was the first type of Electron Microscope to be developed and is patterned exactly on the Light Transmission Microscope except that a focused beam of electrons is used instead of light to examine the specimen. It was developed by Max Knoll and Ernst Ruska in Germany in 1931. The first Scanning Electron Microscope (SEM) debuted in 1942 with the first commercial instruments around 1965. Its late development was due to the electronics involved in "scanning" the beam of electrons across the sample (see Figure 4).

#### [view large image]

The basic steps involved in all EMs regardless of type:

1. A stream of electrons is formed (by the Electron Source) and accelerated toward the specimen using a positive electrical potential.
2. This stream is confined and focused using metal apertures and magnetic lenses (condenser) into a thin, focused, monochromatic beam.
3. This beam is focused onto the sample using a magnetic lens.
4. Interactions occur inside the irradiated sample, affecting the electron beam.
5. These interactions and effects are detected and transformed into an image, which contains information such as structure and composition.

The conventional electron microscopy is nowadays called TEM (transmission electron microscopy). The ray of electrons is produced by a pin-shaped cathode heated up by current. The electrons are collected by the anode. The acceleration voltage is between 50 and 150 kV. The higher it is, the shorter are the electron waves and the higher is the power of resolution. But this factor is hardly ever limiting. The power of resolution of electron microscopy is usually restrained by the quality of the lens-systems and especially by the technique with which the preparation has been achieved. Modern gadgets have powers of resolution that range from 0.5 - 10 nm. The useful magnification is therefore more than 1,000,000X.

#### Figure 5 TEM [view large image]

The accelerated ray of electrons passes a drill-hole at the bottom of the anode. Its path is analogous to that of a ray of light in a light microscope. The lens-systems consist of electronic coils, which generate the magnetic fields. The ray is first focused by a condenser. It then passes through the object, where it is partially deflected. The degree of deflection depends on the electron density of the object. The greater the mass of the atoms, the greater is the degree of deflection. Biological objects have only weak contrasts since they consist mainly of atoms with low atomic numbers (C, H, N, O). Consequently it is necessary to treat the preparations with special contrast enhancing chemicals (heavy metals) to get at least some contrast. Additionally they are not to be thicker than 100 nm, because the temperature increases due to electron absorption. This again can lead to destruction of the preparation. After passing the object the scattered electrons are collected by an objective. Thereby an image is formed, that is subsequently enlarged by an additional lens-system (called projective with electron microscopes). The thus formed image is made visible on a fluorescent screen or it is documented on photographic material. Photos taken with electron microscopes are always black and white. The degree of darkness corresponds to the electron density (= differences in atom masses) of the preparation.

The path of the electron beam within the scanning electron microscope (SEM) differs from that of the TEM. The technology used is based on
television techniques. The method is suitable for the depiction of preparations with conductive surfaces. Biological objects have thus to be made conductive by coating with a thin layer of heavy metal (usually gold is taken). The power of resolution is normally smaller than in transmission electron microscopes, but the depth of focus is several orders of magnitude greater. The surface of the object is scanned with the electron beam point by point whereby secondary electrons are set free. The intensity of this secondary radiation is dependent on the angle of inclination of the object's surface. The secondary electrons are collected by a detector that sits at an angle at the side above the object. The signal is then enhanced electronically. The magnification can be chosen smoothly and the image appears a little later on a viewing screen.

#### Figure 6 SEM [view large image]

The table below compares the different types of microscope:

Characteristic Compound Microscope Transmission E. Microscope Scanning E. Microscope
Resolution (Average) 500 nm 10 nm 2 nm
Resolution (Special) 100 nm 0.5 nm 0.2 nm
Magnifying Power up to 1,500X up to 5,000,000X ~ 100,000X
Depth of Field poor moderate high
Type of Objects living or non-living non-living non-living
Preparation Technique usually simple skilled easy
Preparation Thickness rather thick very thin variable
Specimen Mounting glass slides thin films on copper grids aluminum stubs
Field of View large enough limited large
Source of Radiation visible light electrons electrons
Medium air vacuum vacuum
Nature of Lenses glass 1 electrostatic + a few em. lenses 1 electrostatic + a few em. lenses
Focusing mechanical current in the objective lens coil current in the objective lens coil
Magnification Adjustments changing objectives current in the projector lens coil current in the projector lens coil
Specimen Contrast by light absorption by electron scattering by electron scattering

### Other Microscopes

• Other Microscopes -- Phase-contrast and interference3 microscopes are types of light microscopes with modified illumination and optical systems that make it possible for unstained transparent specimens to be clearly seen. These microscopes are particularly useful for examining living cells and tissues.

• A scanning tunneling microscope (STM) measures the small current produced by electrons moving, or tunneling, between a stylus and a
conducting sample (see Figure 7). A STM can resolve images at the atomic level. As the stylus moves across the sample, the current produced is monitored and kept constant to a value set by a gauge (depicted by the arrow in Figure 7). To keep the current constant, the height of the stylus changes as it scans the sample. The display shows the height of the stylus as changes in brightness or color (to represent the third dimension) as the tip is scanned across the display. Figure 8 shows the scanning tunnelling micrograph of gold atoms on a graphite substrate. It displays

#### Figure 8 Gold Atoms [view large image]

electron clouds surrounding the atomic nuclei, which have high concentration of positive charges.
The scanning tunneling microscope is the tool to conduct research in nanotechnology -- the manipulation of atoms as raw materials. Inside the microscope, experiments are done at a temperature about 3 oK. The atoms are guarded from vibration, electricity, magnetic waves and radio waves. There's an ultra-high vacuum inside, so stray oxygen and nitrogen molecules will not interfere with the atomic manipulation. The device is made primarily from the element molybdenum, which can withstand dramatic temperature fluctuations.

The AFM (Atomic Force Microscope, Figure 9) is a slight variation of the STM. Here's a summary of its design:
1. There is a moving cantilever to execute the plotting in the horizontal x-y plane.
2. Force between the tip and the sample lead to a deflection of the cantilever.
3. The deflection is measured by reflection of a laser spot on the top surface of the cantilever into an array of photodiodes.
4. A feedback mechanism is employed to maintain a constant force between the tip-to-sample. The rise and fall of the tip plots the topography of the sample.

#### Figure 10 AFM Imaging

This kind of microscope has been in used since 1986. Recently in 2009, an improvement has been made by placing a carbon monoxide molecule on the tip. Choosing
the right molecule for the tip enabled repulsion due to the quantum exclusion principle to dominate over the blurring caused by attractive Van Der Waals and electrostatic forces. The bottom picture in Figure 10 shows the remarkable clarity of a five-ringed hydrocarbon molecule thanks to such modification.
An AFM imaging in 2010 shows another organic molecule called cephalandole A taken from deep sea bacteria. The image was captured by placing it on the surface of a salt crystal. Figure 11 shows the chemical formula (as deduced from the imaging), the atomic locations (in middle), and electron density (on the right). Researchers are still debating what these AFM images are really showing. They are also worrying that the structure of

#### Figure 11 Molecular Images [view large image]

the molecule might be altered when it is deposited on the crystal surface. The technique is not going to replace crystallography any time soon.

### Ptychography

• Ptychography --

#### Figure 13 Diffraction [view large image]

Normal photography relies on the contrast of luminosity (modulus) over the image to show the details. However, for nano-sized or faraway objects subtend very small solid angle, ptychograpy can render details otherwise not shown.

The diffraction pattern produced by an object is shown in Figure 13, while Figure 14 sketches the experiment to capture the diffraction pattern produced by the scattered radiation (size of the object x = a in Figure 13). Figures 15a,b show the luminosity (modulus) and phase at the edge of a zone plate which is a device for collecting diffraction data from light or electron beam. A brief explanation of the panels :

• (a) Luminosity (modulus) data at the edge with normalized scale from 0 to 1.
• (b) Phase data at the edge from - to +.
• (c) Main probe image with both modulus and phase data.
• (d,e) Orthogonal probe images with both modulus and phase data.
• (f) Main probe modulus data, 65% of the total in unit of photons/pixel.
• (g,h) Orthogonal probes' modulus data 19% and 7% of the total in photons/pixel.

#### Figure 15 Modulus and Phase [view large image]

• (i,j,k) Enlarged 2015 improved phase data of three selected regions in (b).
• (l,m,n) Enlarged 2008 phase data of three selected regions in (b) for comparison.

• The ptychographic image is compared with the one taken by the compound microscope in Figure 16. While the ptychography shows clearly the hexagonal pattern of the MoS2 crystal down to a sulfur vacancy (indicated by the red arrow), the bright field photograph could display only a blurring image for

#### Figure 16 Ptychographic Image [view large image]

each hexagon. See "Electron Ptychography of 2D Materials to Deep Sub-angstrom Resolution" for the latest development in 2018.

1Close focus distance is also referred to as "minimum focus distance" or "near focus distance". It is the closest distance to which a lens or human eye can approach a subject and still achieve focus.
2The aperture angle is defined as the angle formed between a line from the sample through the center of the lens and a line from the sample through the edge of the aperture opening. The problem with optical microscopy is that a high power objective lens has a short focal length, increasing the aperture angle and decreasing the depth of field - a large aperture has a shallow depth of field, anything behind or in front of the main focus point will appear blurred.
3The inference microscope is a special form of microscope used with perfectly transparent objects that are invisible under an ordinary microscope. The object is placed in one beam of a tiny interferometer so that variations in optical thickness appear as variations in the brightness of the image.