CONTENTS A Few Photomicrographs  Introduction  Background  Aberration  Parts of the Scope  Resolving Power  Kinds of Scopes  Care  Eyestrain  Aperture  Filters  Condensers  Light Sources  Stages  Types of Illumination  Color  Microtechnique  Photomicrography  Measuring  Image Enhancement  Crystals  Aquaria  Other Specimens  Appendix 1 Project  Appendix 2 Suppliers  References  Glossary

This site would be much more fun for you in a web standards browser. The links lead to download sites of free web standards browsers. Mozilla Opera The form searches the entire domain of many subsites for one or more keywords. Use your browser's search function to search this web page. domain map The Microscope on a Budget A Complete Guide to the Low Cost Light Microscope for the Laboratory, Photographers, and Hobbyists copyright © M. Brian Stevens, 1993, all rights reserved No part of this book, including text and illustrations, may be reproduced; nor may they be hosted anywhere except at the author's domain -- http://www.mbstevens.com/ ISBN 0-9638839-1-7 Library of Congress Catalog Number 93-93667 You can resize the text in most browsers under the View menu. WARNING: Some projects in this book are potentially dangerous. Follow any instructions in this book absolutely at your own risk; M.B.Stevens will assume no responsibility whatever for damage, death, or injury. No one under 18 years of age should follow any instruction herein without competent adult supervision and permission. M.B.Stevens is a hobby microscopist (although he uses it as a tool for an occasional commercial photograph), and does not represent or warrant that every instruction in this book is correct.

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Introduction

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This book is an introduction to microscopy for any laboratory or hobbyist on a tight budget. The microscopes featured for discussion are the standard models, costing between one hundred and two thousand dollars. These are usually brightfield microscopes, the kind used in biology classrooms, although a few specialized instruments have become affordable in this price range. Because many more of these instruments are in use than are expensive research microscopes, a specialized treatment is long overdue.

Surprising improvements in the performance of these microscopes can be quickly and easily made. We will stress experimentation with optics, and present some very easy construction projects. These projects will help anyone get a better view of the microscopic world with one of these instruments. None of the projects (except the final advanced project in the Appendix) will take more than an hour to complete, and only simple tools are required. Experimenting with optics should also help you to form opinions about the kind of microscope to acquire if you should decide to trade up to an expensive model.

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A common task in microscopy is the preparation of specimens on glass slides. A well prepared slide, made at little cost and viewed with a standard microscope, may afford a better visualization of a specimen than thousands of dollars worth of fancy optics. Slide preparation requires fixatives, stains, and other chemicals. The hobby microscopist no longer has access to many of these materials; biology suppliers (in the U.S.A.) now only furnish chemicals to educational, medical, and research institutions.

I will suggest everyday substitutes for unobtainable supplies, presenting a bit of practical chemistry at the same time; alternative sources of supply are also suggested. Because individual microscopists are likely to vary widely in age, many health and safety warnings are included.

Why Microscopy?

Microscopy is closely allied with many other sciences, and owning a microscope is a good way to gain familiarity with them. Anyone interested in biology, microbiology or botany should own a microscope; it will also help with crystallography, forensics, criminology, textile science, and chemistry.

Your body, home, and yard harbor living things so small that they can be seen only with a microscope. You may find an uncataloged organism in local pond water. Many small aquaria, each as interesting as any full sized one, can be easily kept in jars on a shelf. The jars will be populated by microscopic creatures with surprisingly complex behaviors. A chapter is devoted to introducing you to the denizens of pond water and aquaria.

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Tissues from any animal are worth examining microscopically, and we will discuss methods of preparing these tissues for examination. Allergy causing pollens and molds are also easy to see under magnification.

Children benefit from access to a microscope. Learning to search out and prepare microscopic objects imparts an immediacy of experience no book or instructor can rival. Using the microscope is a markedly rewarding activity for those with failing vision, being an active method of adapting to the impairment most of us suffer after the age of forty. There is an entirely new world waiting all around us. Microscopy is more than a science; it is a great joy and an art.

Reading Diagrams

In later chapters there are some diagrams with arrows representing rays of light traveling through optical elements. These diagrams will always be read from left to right or bottom to top. There is actually no such thing as a single light ray. We use the term here as a convenient shorthand for the direction that the light is traveling. If we think of light as particles, then the arrows represent the direction of travel of those particles. If we think of light as waves, then the arrows represent the direction of travel of the wavefront as it moves away from the light source.

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Background

Simple Lenses

Before the function of a compound microscope can be explained, we must understand a bit of basic optical theory, beginning with the way a simple lens works. If rays of light diverging from a small object strike a lens with convex surfaces (a double convex lens), the light will be bent (refracted) so that it is not so divergent. The lens is being used, in this case, as a magnifier. When the lens is being used as a magnifier, the object appears to be larger than it really is. The human eye is comfortable with objects between a distance of about ten inches and infinity. Light from any point on an object located within this distance will have parallel or slightly divergent rays when it reaches the eye.

Two convex lenses can give the eye the kind of ray angles it needs when looking at small objects that are closer than ten inches to the eye. At the same time, the objects appear larger. This is because the rays are bent, and a virtual image forms. This allows the eye to look at small objects much more comfortably. In the figure the solid arrows show rays diverging from a small object, passing through a lens, and into the eye of the viewer. Notice that the rays are approximately parallel by the time they reach the eye. The virtual image is depicted to the left of the dotted lines. Notice also that the dotted lines are simply a continuation of the angle of the rays that have passed through the lens. Because the rays are almost parallel, the virtual image would actually be located much further away than shown in the drawing. The image would appear to be at an infinite distance. If the rays were diverging slightly when they reached the eye, the image would appear closer. Also note that, because the rays from the object are spread over a large area, the virtual image appears dimmer than the object appears to the naked eye.

We can think about and define magnification using any of the following ratios:
(1) image size / object size;
(2) image distance from viewer / object distance from viewer;
(3) angle from viewer to point on image / angle from viewer to corresponding point on object.

The same double convex lens that we used for magnification can be used in a completely different way. If light traveling in parallel rays (collimated light) strikes such a lens, the light is refracted so that it converges. In this case, the lens is being used to condense the light. When light is condensed, the plane onto which it shines becomes not only smaller, but brighter. This is because light from a large plane is being focused on a very small plane. Microscopes use condensers to get concentrated light on the specimen being investigated.

To summarize, the same lens type can be used both as a magnifier to create a large, dim image and as a condenser to create a small, bright spot at the focal plane of the lens. Microscopes use lenses in both of these ways -- to make objects appear larger and to light tiny objects more brightly.

In practice, several lens shapes will work in this way. The only requirement is that the center of the lens be thicker than the periphery. Such a lens is called positive. Lenses that are thinner in the center than at the periphery disperse light and make objects appear brighter and smaller. These are called negative lenses. A negative lens is illustrated in the figure.

Transmitted light is another concept that we need to understand. Normally, when we look at an object, light bounces off of its surface and then into our eye. This kind of light is called incident or reflected light. Many microscopic specimens are nearly transparent. These objects are difficult to see in reflected light. To get the best view, it is better to place the objects between the light source and the eye, allowing the light to pass through them. This is known as brightfield illumination. The specimen will act as a tiny irregular lens, refracting some of the light that passes through it. At points where the light is refracted away from the optical path leading to the eye, the specimen will appear darker. Parts of the specimen may also absorb the light, not allowing it to pass through at all. This results in much better contrast between light and dark areas than would be possible with reflected light.

Anthony von Leeuwenhoek, a seventeenth century Dutchman, was the first microscopist to combine magnification with transmitted light. With this combination he discovered bacteria and larger single-celled creatures that we now call protozoans or protists. He was also the first microscopist to carefully measure or quantify his observations. His microscopes were really quite simple. He placed a single lens between two metal plates. Then he set a needle on an adjustable screw in front of the lens. To use transmitted light, all he needed to do was hold the microscope up to the light with the specimen mounted on the tip of the needle between the light source and the lens. The figure shows how he would have positioned one of his microscopes.

A simple lens like Leeuwenhoek's can be quite powerful, but it forms an imperfect image. It is difficult to get specimens into proper position for viewing. The more magnifying power the lens has, the closer the specimen must be to the lens, and the closer the lens must be to the eye. Only the center of the specimen can be brought into perfect focus. These problems were so difficult that Leeuwenhoek would often build a new microscope for a particular specimen. He made hundreds of instruments during his long lifetime.

There are other problems with simple lenses. Different colors in white light do not focus at the same point. This is the problem of chromatic aberration. In order to explain chromatic aberration, we must first introduce another concept. Every transparent material has a refractive index:
I -refractive index of the material;
c -velocity of light through a vacuum;
m -velocity of light through the material;
I = c/m.
Here are some common refractive indices:
vacuum 1.00
air 1.00
water 1.33
glycerin 1.46
immersion oil 1.52
crown glass 1.52
Canada balsam 1.53
gelatin 1.53
medium flint glass 1.62
diamond 2.42

These values are approximate; the refractive index of a given material changes with the wavelength (color) of light passing through it.

Chromatic aberration is a problem. White light is made up of different colors, and these color components travel through the lens at different speeds. Traveling at different speeds causes the different colors to refract at different angles.

Another problem with simple lenses is spherical aberration. Rays of light passing through the center of the lens tend to focus on a different plane than those entering near the periphery. If the curvature of the lens is not perfect, some other aberrations also occur. These include barreling (in which the center of an object appears too large and its periphery too small), pincushioning (in which the center of an object appears too small and its periphery too large), astigmatism (in which rays striking the lens along right angled meridians focus in different planes), and coma (in which rays striking the lens at an angle do not intersect correctly on the other side of the lens). The only way that these problems can be overcome is by using a series of lenses, each lens carefully designed to counteract the aberrations of the other lenses.

Early Compound Microscopes

Compound microscopes have been around since the late sixteenth century. In England Robert Hooke, a contemporary of Leeuwenhoek, was using a compound microscope; he is remembered for his book, Micrographia, which contained many observations and fine prints of tiny specimens. First published in 1665, the book popularized microscopes and microscopy with scientists and the educated public. Indeed, during the next century microscopy was more popular as a hobby than it is today.

By today's standards, Hooke's microscopes were primitive. They were arrangements of three lenses: an objective near the specimen, and an eyepiece comprised of a field lens facing the objective and an eyelens near the eye. Hooke's compound microscopes actually magnified less than most of Leeuwenhoek's simple microscopes, and there were several kinds of aberrations that were not corrected. However, the microscopes did make observation easier because the specimen did not have to be positioned near the eye.

These early instruments worked on the same principles as modern microscopes. A rudimentary compound microscope made with only two lenses is illustrated by the figure. The solid arrows show light from the object entering the objective lens. When the light passes through this lens, it is refracted so sharply that it crosses before reaching the eyelens. After passing through the eyelens, the rays become parallel or slightly divergent before entering the eye. Because the rays cross before reaching the eyelens, the image is inverted -- it appears to the viewer as flipped top to bottom, left to right. This can be disconcerting to the novice microscopist. When the specimen is moved it appears to be going in the opposite direction of the hand that moves it. It takes a few minutes of concentrated effort to learn how to 'drive,' but soon everything becomes automatic.

Modern Microscopes

Microscopes with more lenses obey the same principles. The extra lenses serve not only to correct aberrations, but also to widen the field of view and to allow smaller diameter lenses to be used. The modern microscope uses multiple lenses for both the objective and the eyepiece, and does a good job of correcting aberrations in the lens system. Most of these instruments can provide magnifications of 40 to more than 1000 times the size of the specimen.

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The Parts of the Modern Microscope

The figure illustrates the parts of the modern microscope. Light from the lamp below the stage passes through a condenser lens, a glass slide, and a specimen on the stage, into an objective, up through the body tube, into the eyepiece, and into the observer's eye. While most modern light microscopes work this way, your microscope may differ in some details.

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Correction of Aberration

The lens closest to the specimen is the objective. Informally, the part that we call the objective on a modern microscope consists of a metal tube that screws into the nosepiece and has a compound lens inside. A compound lens consists of two or more lenses glued together or mounted mechanically in close proximity to one another. Similarly, the eyepiece has multiple lenses. The eyepiece lens closest to the eye is called the eyelens, and the eyepiece lens closest to the objective is called the field lens.

Lens systems become more expensive as they correct for more types of aberration and distortion. With more correction, more lenses are needed, and the quality of the individual lenses must be higher.

Achromatic optical systems are standard. They usually correct spherical aberrations of yellow-green light and chromatic aberrations of red and blue light. The color sensitivity of the human eye determines this choice of colors, although special purpose achromats may correct for different ones. Figure 1.9 illustrates an achromatic doublet. The lens to the left of the illustration is made of crown glass, the one on the right is flint glass. Each lens shape tends to compensate for the other's chromatic aberrations. The two types of glass are carefully formulated to have different color dispersion capabilities. Flint glass is more color dispersive than crown glass, but the flint glass lens is less negative than the crown glass lens is positive. This makes it possible for the two lenses, taken together as a compound lens, to be positive and have no blue-red chromatic aberration.

Improved optical systems include some fluorite elements which work with the glass elements to provide chromatic correction over more of the visual spectrum. Apochromatic lens systems correct almost perfectly throughout the entire visual spectrum; they correct for three chromatic wavelengths and two spherical wavelengths. Apochromats are extremely expensive, and appear only on the finest research microscopes.

Reading objectives

Every microscopist should know how to read an objective's engraving. The engraving contains important information about the microscope. The amount and ordering of information on the engraving is not completely standardized; the illustration reproduces the most common ordering.

In the illustration, the type, given on the top line, is "oil," which means that this is an oil immersion objective. When using any objective, the specimen is normally sandwiched to a glass slide under a thin glass cover slip. A clear liquid or resin is placed under the cover slip surrounding the specimen, so the specimen must be kept very thin. When an oil immersion objective is being used, a drop of oil is placed on top of the cover slip, and the nose of the objective is carefully lowered into the oil. If the objective does not specify oil, do not use oil; the objective could be damaged. You may run across an objective that specifies water or glycerine. Use only the specified liquid.

If the objective is a fluorite or apochromat, that will also be indicated on this line. The objective will also indicate polarization or fluorescence objectives. (These topics will be discussed later.) If the microscope has a selection of substage light condensers, the objective may also indicate which of these should be used.

The top line on the objective will also indicate whether the objective is a plan or flat field objective. This indicates that, when imaging a flat object, parts of the object at the edge of the visual field are almost as well focused as those in the center. Straight lines on the specimen appear straight throughout the visual field, without any pincushioning or barreling effects. Such microscopes are especially good for photomicrography -- photography through a microscope. A plan microscope is less important if publication quality photographs are not needed. The edge blurring of non-plan objectives is slight and easily corrected by a tweak of the fine focus knob as one looks toward the edge of the field.

The center line of the objective's engraving gives the magnification and the numerical aperture (NA). The NA is an expression of the light gathering capability of a lens. For the objective, the NA can be expressed as follows:
NA -numerical aperture;
n -refractive index of immersion medium --
n = 1.00 for air;
n = 1.33 for water;
n = 1.46 for glycerin;
n = 1.52 for oil;
a -angular aperture --
the angle between the most divergent rays that
can enter the objective lens and participate in
image formation;
u -angle between the optical axis ( the most central
ray passing through the optical system would pass
along the optical axis) and the most
marginal ray that can enter the objective and
participate in image formation;
NA = n sin ½a;
NA = n sin u.

Depth of field decreases as numerical aperture increases. Because more powerful objectives tend to have higher numerical aperture, depth of field also decreases as magnifying power of the objective increases.

Here is an example. When looking at a bacterium with a 40X objective, the entire organism will appear sharply focused. When looking at the same bacterium with the 100X objective, only part of the organism will be in focus. Do not confuse flatness of field with improved depth of field.

Shallow depth of field can cause problems in photomicrography, but is generally useful. Small objects that are not in the focal plane disappear and do not interfere with the view of objects that are in the plane. One can see thin optical sections of transparent objects by focusing in and out.

The relationship of depth of field to NA can be elaborated with the following equation:
D -depth of field;
λ -wavelength (which determines the color) of the light
being used;
r -highest refractive index of any optical component below the objective;
u -same as in numerical aperture equation;
D = λ / (4 * r * sin² * (u/2)).

On the bottom line of the objective's engraving we find the mechanical tube length and the cover slip thickness for which the objective was designed.

The mechanical tube length is the length of the tube into which the objective and eyepiece inserts. Different standards have been instituted that require specific mechanical tube lengths.

The optical tube length, which does not appear on the objective, is figured differently. One of the focal planes of the objective is in the direction of the eyepiece, and one of the focal planes of the eyepiece is in the direction of the objective. The distance between these adjacent focal planes is the optical tube length. Standards do not specify an optical tube length, even though it is of more importance in the design of the microscope.

Objectives on some research microscopes use the infinity symbol, "∞," as the tube length. Light leaving such an objective moves up the body tube as a bundle of parallel rays which would theoretically focus at an infinite distance. Lenses in the eyepiece focus this bundle of rays so that they converge before reaching the eyelens. Because the ray bundle leaving the objective is parallel, the tube length is not critical. Microscopes with such objectives can use sliding or rotating modules to change between many specialized illumination setups, each of which would otherwise require a specialized microscope.

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Resolving Power

The resolving power of a microscope is its ability to produce a detailed image. A bigger image is not necessarily more detailed, and if the eyepiece is too powerful for the objective, resolution will decrease. Some cheap microscopes provide tremendous magnification with little resolving power. Resolving power increases as aberration of the lens system decreases. The theoretical limit of resolving power depends on the wavelength of the light being used and the NA of the optical system -- magnification does not even enter into the equation:
R -theoretical limit of resolution;
λ -wavelength of the light being used;
o -numerical aperture of the objective;
c -numerical aperture of the condenser --
controlled by the aperture diaphragm;
ω -working numerical aperture,
ω = ½(o + c);
R = (1.2λ) / (o + c)
R = (1.2λ) / (2ω).

(The constant factor 1.2 comes from Fraunhofer diffraction theory. Light is bent, or diffracted, when it passes close to obstructions. The aperture and specimen provide such obstructions. The diffracted light present in the image influences resolving power.)

We can infer from the equation that an objective's depth of field and resolving power can be adjusted by closing the aperture diaphragm, which reduces the condenser's numerical aperture. If the objective's numerical aperture is larger than the condenser's, the objective's working numerical aperture will be reduced. Some expensive objectives also have an internal aperture that can be adjusted by a collar on the outside of the objective.

The best objectives tend to have a large numerical aperture for their power and therefore high resolution and a shallow depth of field. Anyone considering the purchase of a microscope should compare the NA of its objectives to those of the competition.

All real optical systems have some aberration, so the theoretical limit of the equation is never reached in practice. Most microscopes have several objectives and may have more than one eyepiece. Each combination of eyepiece with objective lens will provide a different combination of resolving power and magnification. Multiplying the magnification of the eyepiece by the magnification of the objective will give the total magnification of the lens system. The total magnification will be used to select the correct eyepiece. For an achromatic lens system, the maximum magnification can be about 1000 times the working NA before resolution suffers. Apochromats can use about 2000 times working NA, and lens systems with some fluorite elements will fall between these extremes.

If an eyepiece of too low a power is used, the resolving power of the human eye limits making full use of an objective's resolving power. A person with extremely good eyesight can resolve about one degree of arc, or .075mm at the eye's near point of 10 inches. A more conservative estimate for average eyesight is .15mm. Minimum necessary magnification can be given as:
M -minimum necessary magnification for the eye to make use of the microscope's magnification
e -resolving power of the eye
m -resolving power of microscope
M = e / m.

For example, assume that we have a 10X achromatic .25 NA objective and a condenser with an NA of .25. (Such a small condenser NA can be achieved by partially closing the aperture diaphragm.) We are using a violet filter that only transmits light of .00042mm wavelength. First, we use the maximum resolution equation to find the resolving power:
(1.2 * .00042) / (.25 + .25) = .001008mm.
Now we can compute the minimum necessary magnification:
.15 / .001008 = 148X.

In this example, if the microscopist has only a 10X eyepiece and does not own a more powerful objective, purchase of a higher power eyepiece should be considered. The eye cannot resolve as much detail as the objective can below 148X and only 100X is available. There is no real harm in using an objective a bit below its minimum necessary magnification. A wider view of the specimen may be more important to the microscopist than a completely detailed view. Using more than the maximum magnification, however, is definitely a mistake.

Now assume the same setup as before, but with a 100X achromatic 1.25 NA objective and a 1.25 NA condenser with the aperture diaphragm wide open:
(1.2 * .00042) / (1.25 + 1.25) = .0002016 resolving power, and
.15 / .0002016 = 744X minimum necessary magnification.
In this case a 10X eyepiece works, but a 15X would create empty magnification because:
1.25 * 1000 = 1025 maximum magnification for an achromat, and
100 * 15 = 1500 magnification.

The technical term for the range of magnifications between the minimum necessary magnification and the maximum necessary magnification is called usable magnification, and any objective-eyepiece combination that magnifies within this range will give a highly resolved view of the specimen.

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