Introduction to Microscopy

It is up to the microscopist to choose the most appropriate instrument and then to maximize the most important characteristics for his specimen to produce a good image. For example Ansel Adams has long been regarded as one of the foremost photographers in the world. The equipment he was using would be considered primitive by today's standards, yet it is rare for anyone to produces pictures of higher quality. Ansel Adams was able to produce such high quality pictures because he understood and manipulated the attributes of his optical system. He new what the resolution of the medium he was using (Film). From that he back calculated the maximum resolution of the film to determine what f-stop/focal length to use. Since, he was photographing landscapes, time (brightness) was not a factor. So he could trade off brightness for contrast without sacrificing any resolution. Manipulation of these attributes is the key to producing a good image. A similar analogy is in a biology lab which uses microscopes. Even though all the instruments are exactly alike, each student's specimen looks different. Some have an excellent image while others can't even see it. This is because the students did not optimize there instrument to the specimen they are viewing.

Historically, most college biology classes do not teach the principles of how to obtain a good image. One reason is that the demands on the microscope were not very critical to the subject being taught. Students were only asked to observe some specimen of which they were the only one to see the quality of the image. Their grade in the class was certainly not dependent on their visual experience. In the courses taught at this school, the quality of the image will have a direct impact of the interpretation of the results of an experiment and ultimately your grade. Microscopes are enigmatic instruments, for two reasons. First, most of the controls have such an obvious effect that leads the operator to think that that's what the control is there for. For example most people believe that the iris diaphragm is used to control the amount of light. This is a rational assumption since when it is adjusted the images does get brighter or darker. However, its operation has nothing to do with brightness or regulating the amount of light. Second, the operation of the microscope has evolved over a couple of centuries and as every improvement was made, there was a change in the operation. Now, even the most basic student microscope will not perform unless particular sets of procedures are done.

Of the four characteristics, resolution is generally regarded as the most coveted by the microscopist. Though it is by far not the only thing that makes a good image. Resolution is the ability to see fine detail. Most people confuse this with magnification. They think by simply magnifying something you will see more detail. But every optical instrument has a finite resolution. If you magnify past the resolution you will get empty magnification. This is when the image starts to appear fuzzy as you increase magnification. There is essentially no more information in the image. Keep in mind that magnification is not regarded as a necessary characteristic. It is the resolution that determined quality of an instrument. Here is a case in point, most hobby shops sell small microscopes that can magnify 1500 times for about fifty dollars yet a good college student microscope that only magnifies 1000 times costs about a thousand dollars. What the hobby shop microscope doesn't tell you is the resolution of the microscope, plus the quality of the other characteristics. In fact it cost no more to manufacture a microscope to magnify a thousand times as it does to magnify a few times. When buying a high quality microscope a reputable manufacturer will state what the resolution is. For example, a good student microscope will have a resolving power of 0.25 micrometer (roughly half the diameter of a small bacteria). What this means is if there are two particles that are closer together than 0.25 micrometer they will appear as one. Anything larger than this dimension will be visible. Viruses, which are much smaller than 0.25 micrometer, are invisible. If you use a standard electron microscope, which has a typical resolution of about 0.0002 micrometer, the viruses are easily seen. So when the value for resolution gets smaller it means that you are able to see more detail and you have a better instrument.

So why do some microscopes have better resolution than others. There are three factors that determine what a microscope can theoretically resolve. They are the wavelength of the light, the angle of acceptance of the lens and the optical index of the media. The shorter the wavelength, the better the resolution. This is why electron microscopes have far superior resolution, the wavelength of an electron is about 0.005nm and the wavelength of visible light is around 500nm. That is a hundred thousand times shorter. The same can be said of visible light. Blue light has a wavelength around 400 nm and red light around 700 nm. So a microscope designed to work with just blue light would theoretically have better resolution. The angle of acceptance is determined by two factors, the size of the lens and it's focal length. The larger the lens the better the theoretical resolution will be. You can think of a larger lens as being able to gather more information, which extrapolates to better resolution. The shorter the focal length, the better the resolution. This is just what happens when you want to see something clearer (better resolution) you bring it closer to your eyes. There by reducing the focal length. The figure below shows the effect the size of the lens and the focal length has on the angle of acceptance and ultimately the resolution. The third factor is the index of refraction of the media between the lens and the specimen. This concept will be used extensively at this school. Many of the lenses you will be using will be "oil" lenses and in conjunction with your specimen will require special handling. Normal lenses are design to work in air, which has an index of refraction of 1.0. The immersion oil that is generally used has an index of refraction around 1.5. The higher the index of refraction the better the resolution will be.

All of these factors are used to determine the theoretical resolution of any optical instrument by Abbe's equation. Here the theoretical resolving power is determined by the wavelength of light times a constant (0.61) divided by the numerical aperture of the lens. The numerical aperture takes into account the angle of acceptance and the index of refraction. It is the most important value used to describe the quality of a lens. It is usually the bold face number under the magnification on the microscopes objective lens. A good rule of thumb is the maximum magnification of any microscope is 1000 times the NA. So a microscope that has a NA of 0.65 should be able to magnify 650 times. Likewise using Abbe's equation it should have a theoretical resolution of 0.5 micrometers, which means it should be able to just barely "see" bacteria.

Keep in mind that we have been discussing what resolution is theoretically possible from a lens. If a lens is cracked or broken it certainly will not perform to the quality of the numerical aperture value printed on its side. There is a practical resolution that every lens system has that is always less than what is theoretically possible. The cholera epidemic of the early 1800's in Europe spurred the study of optics to produce a lens that would have the resolving power as predicted by Abbe's equation. As the opticians made their lenses larger and larger to get more resolution what they got was poorer resolution. This is because optical aberrations will increase exponentially as a lens diameter increases. Joseph Lister in 1829 developed what is now probably the most significant advancement in the field of microscopy and optics, the achromat objective.

There were several types of aberration that were contributing to the poor image quality. The most significant being spherical aberration. This occurs when the outer portions of a lens are optically stronger than the central portion. The rays of light from the rim of the lens bend producing a shorter focal length than the rest. In the illustration, light coming from the left is from a point light at an infinite distance. The rays will be essential parallel. When the rays of light meet a surface of a different refractive index they will be bent. The higher the refractive index or the higher the entry angle the more they will bend (Snell's Law). Ideally, a lens should reproduce an image of a point at its focal length. However, as the illustration shows, none of the rays of light intersect at the same point. So the focus length is essentially smeared over the distance (l). The outer rays are in focus at A while the others focus at B and C. In order to have a sharp image all the rays must come together at the same point. One could grind the lens aspheriaclly to minimize the effect but the result would lead to an even worst problem, chromatic aberration.

Every piece of glass will separate white light into a spectrum given the appropriate angle. This is called dispersion. Some types of glasses such as flint glasses have a high level of dispersion and are great for making prisms. Crown glass produces less dispersion for light entering the same angle as flint, and is much more suited for lenses. Chromatic aberration occurs when the shorter wavelength light (blue) is bent more than the longer wavelength (red). So a lens that suffers from chromatic aberration will have a different focal length for each color. A classic example of this commonly occurs in a beginning microbiology class. Students will be asked to identify bacteria as being either gram positive (blue) or negative (red). Since most student don't correct their microscope for chromatic aberration, the colors of light will focus at different levels. The effect is as you pass through focus the specimen turns from gram positive to negative. The student then reports the specimen as being gram variable. In the illustration above, a simple uncorrected lens has split the white light into red, green and blue. If you were to use the green focal point (A), the image would have a blue and red halo around each point.

To make an achromat, two lenses are put together to work as a group called a doublet. A positive (convex) lens made of high quality crown glass is combined with a weaker negative (concave) lens that is made of flint glass. The result is that the positive lens controls the focal length of the doublet, while the negative lens is the aberration control. The negative lens is of much weaker strength than the positive, but has higher dispersion. This brings the blue and the red light back together (B). However, the green light remains uncorrected (A), producing a secondary spectrum consisting of the green and blue-red rays. The distance between the green focal point and the blue-red focal point indicates the quality of the achromat. Typically, most achromats yield about 70 to 80 %of their numerical aperture with practical resolution.

In addition, to the correction for the chromatic aberration the achromat is corrected for spherical aberration, but just for green light. The Illustration shows how the green light is corrected to a single focal length (A), while the blue-red (purple) is still uncorrected with respect to spherical aberration. This illustrates the fact that spherical aberration has to be corrected for each color, called spherochromatism. The effect of the blue and red spherochromatism failure is minimized by the fact that human perception of the blue and red color is very weak with respect to green, especially in dim light. So the color halos will be hardly noticeable. However, in photo microscopy, the film is much more sensitive to blue light, which would produce a fuzzy image. So achromats that are used for photography will have a green filter placed in the optical path. Naturally, this means if you want the best resolution your images will be green.

As the optician's understanding of optical aberrations improved they were able to engineer achromats with shorter and shorter secondary spectrums. They were able to do this by using special types of glass call fluorite. If the two spectra are brought very close together the lens is said to be a semi-apochromat or fluor. However, to finally get the two spectra to merge, a third optical element is needed. The resulting triplet is called an apochromat. These lenses are at the pinnacle of the optical family, and their quality and price reflect that. The apochromat lenses are corrected for chromatic aberration in all three colors of light and corrected for spherical aberration in red and blue. Unlike the achromat, the green light has the least amount of correction, though it is still very good. The beauty of the apochromat is that virtually the entire numerical aperture is corrected, resulting in a resolution that achieves what is theoretically possible as predicted by Abbe equation.

In just 10 years after the Listers invention of the achromat lens all the major components of the cell were described. This led to the cellular revolution in biology, the cell as the fundamental unit of life. As a side note, optics did not make any substantial contribution to the halting the cholera epidemic. For that you can thank the field of statistics.

The graph below shows the relationship between numerical aperture, resolution and aberration for typical achromat. Keep in mind that as the values for the resolution gets larger the quality of the images is getting worst. The black line is the theoretical resolution from Abbe equation. The red line is just some arbitrary uncorrected lens. It really could be any exponential curve. The orange line is for the achromat lens illustrated. It has a numerical aperture of 1.30. The point at which the achromat line crosses the theoretical line is the practical resolution. On this graph it works out to about a numerical aperture of 0.95 or about 75% of the NA.

The illustration above is a close up of the focal point of a lens that suffers from aberrations. The red horizontal line is the optical axis and the other lines are the rays of light that are not quite converging onto a single point. You can see how it is difficult to determine where the actual focal point is. The aberrations smear the point along the optical axis. It takes a little calculus to exactly determine the true focal point where most of the light rays converge with the least distance from the optical axis (A). At this point the distance off the optical axis in the y direction, as shown by the red vertical line is an indication of how sharp this lens can focus. The smaller the red line the sharper the image and the better the acceptable focus.

The top illustration shows a lens with a full numerical aperture, the red vertical line is the range of acceptable focus at the focal point. The pink rectangle defines the limits of the acceptable focus and the angle of acceptance. The length of the pink rectangle is the depth of field as indicated by the blue line. Obviously from the illustration, depth of field is dependant on the numerical aperture.

The two photos above were taken of a histological section that is only 40 micrometers thick. The objective lens that was used has a numerical aperture of 0.65. Assuming the average wavelength of white light is 0.5 micrometers (actually green light) and since it is an achromat lens we will only use 75% of the NA. The math works out to a depth of field of only 2 micrometers. The arrows point to the exact same nucleus but are at different focus levels. Notice how the nucleus of one of the cells completely disappears out of the plane of focus while others appear. This seems even more amazing when you take into account how thin the slice of tissue is. If you wanted to see more thickness of the section in view at the same time you would use a lower NA lens. The table shows the depths of fields typical for the type of microscope you will be using.

Objective magnification	Numerical Aperture	Depth of Field @ 75% NA
4X	0.10	89 um
10X	0.25	14 um
40X	0.65	2 um
100X	1.30	0.5 um

Contrast is number of shades found in an image. A high contrast picture will have only two shades, black and white. The more shades you have, the less contrast, but it should be understood that you also have more information. This is called dynamic range. Color is also considered a form of contrast. As an example, the more colors or shades a computer picture has the more memory it will take. Optically speaking, contrast is necessary since it is possible to generate an image of high resolution but it is the contrast that lets you see it.

There are four types of mechanism of contrast formation generally used in light microscopy. They are absorption, diffraction, interference and fluorescence. Absorption (simple) contrast is the contrast that is involved in normal human vision and bright field microscopy. The light is literally absorbed by pigments in the specimen. The result is less light is transmitted to the eye so the specimen appears dark. If the pigments absorb only a specific wavelength of light the specimen will appear the complimentary color. The important thing to remember about absorption contrast is inversely proportional to the numerical aperture of a lens. As the numerical aperture goes up the contrast goes down.

Diffraction contrast is when light hitting the edge of the specimen bends and will diffracted out of the optical path. This is the mechanism used for dark field and stop contrast microscopy. Interference contrast uses constructive and destructive wave interference. It requires the splitting of light waves to create a reference and analytic waves. The analytic wave passes through the specimen and will be retarded relative to the density of the specimen. The two waves will then be brought together where they can interfere with each other producing contrast.

This is the basis of phase contrast and differential interference contrast microscopy. Which are highly desirable for biologist since they do not erode resolution and do not require staining of the specimen. Fluorescence microscopy, which will be used extensively in this course, is beyond the scope of this introduction and will be dealt with in a special appendix.

Brightness is the forth attribute desired in a microscope. It too is dependent on the numerical aperture. Obviously the large the NA the brighter the image will appear. But all modern microscopes do not use the numerical aperture to control the brightness they simply use a brighter light source as needed.

As should be apparent by now all the attributes that a microscope should have are directly associated with the numerical aperture of the lens. In addition, the aberrations that detract from an image are also associated with the numerical aperture. Since, all these attributes are under one control they are optically antagonistic to each other. For example, you can't have high resolution and high absorption contrast simultaneously. Also, you can't high a large depth of field and high resolution either. These are the optical trade offs that are dependent on the numerical aperture.

The microscopist has to determine how to trade off each of these attributes to enhance the image of a particular specimen. There is no one procedure that will work for every type of specimen. As an example of how to logically trade off the attributes for optimizing an image of a specimen might be something like this. You are given a prepared specimen of kidney that has been section at 20 micrometers and stained. You are asked to see the glomerulus, which is fairly large, so you decide to use the 10x objective. You notice from the table above, that the depth of field is less than the thickness of the section. You make the decision that you would rather see the whole section in focus than be able to see the finest detail, since you are not interested in any of the small structures. You estimate a good NA would be around 0.15, which would give you a resolution of 2 micrometers and a depth of field of 22 micrometers. This is more than enough to see your specimen. When you look at it however, you see that it had not been well stained. So you decide to reduce your numerical aperture even further while you are scanning the specimen to comfortably look for the glomerulus.

Microscope Parts

Updated 5/26/98