A. Resolution

What does a microscope do besides take up space on the counter? The standard answer is that a microscope magnifies small objects.Like so many standard answers this one is wrong. A microscope reduces the angle of view of the observers eye thus improving the resolution of the observer. So there! Resolution is a much abused and misunderstood word so lets take a long look at it.

Resolution is the ability to distinguish two points as two points. For instance if you look at a red brick wall from a distance you will see a reddish object and think "A hah a brick wall". However you don't know for sure that it is a brick wall until you get close enough to see the mortar lines and the bricks. At this point you have resolved the bricks and mortar.

In a microscope a lot of resolving power in the system would let you see bands on chromosomes, small bacteria or granularity in a blood cell. Since these are very small features from experience we know they can only be seen with a high power objective. Doesn't this mean that magnification is resolution? No, magnification is not resolution.If you increase the magnification of the microscope with out increasing the resolution you get a big fuzzy image not one with more detail. We will learn more about this later.

The word resolution has been used in microscopy as a synonym for good when what it is a quantifiable factor. The sole and only determinate of resolution in a microscope is the numerical aperture of the objective. Numerical aperture is printed on each objective and is found in the manufactures literature.

Lets take a look at this bold assertion of the relationship between numerical aperture (here after called N.A.) and resolution. To understand this we need to know a few things about light. Light is mysterious and wonderful stuff. It appears to act in two ways as a wave effect (like sound waves) and as a physical or quantum effect (like electrons). When we think of light as a wave effect it is much easier to see how lens systems work. However light as quantum bundles makes photo-electric effects such as photo meters understandable.

People interact with light in several ways. We can see changes in light intensity and most of us can see color.Color is the way our eyes show us the difference in light wave length. A wave length of light is the distance from one end of a light wave to the other. The average human can see from around 400 nanometersto around 700 nm. The nanometer (nm) is the usual measure of the length of a light wave, light waves are very small.The eye see 400nm light as very deep blue and 700nm light as bright red. Because the wave length at 400nm is shorter than at 700nm and the velocity of all light is the same 400nm light has more energy. This will be important in fluoresence.

When light strikes an object several things happen. If the object is transparent then the light will be transmitted through it but will be reduced in amount by absorption. Colored transparent objects allow only the wave length (color) that it contains. This produces the intensity changes and color changes in a specimen. If we look at the light passing through a specimen we see that if the light passes through a homogeneous substance, like a mounting medium all the light in that area will travel the same distance.

Well what has distance to do with it? Since light slows down in different substances based on the refractive index of the material two waves going through closely spaced points of different refractive indexes will appear to have travelled different distances. One wave will be at a different part of its cycle than the other one.

This difference in light travel time can also take place if the light has to go through thicker or thinner materials. This is how a lens works. The lens bends light based on the thickness or the lens. A lens thick in the center will bend light toward the center and away from the thin edges. Lenses that are thick at the edges will bend light towards the edges. The amount of bending is based on the curvature of the lens and the material it is made of. Refractive index is the measure of how much the light will bend when passing from one material to another. Air has a refractive index of one (1) while immersion oil has a refractive index of 1.512. This is why oil is used, its high refractive index can bend the light towards the lens better than air.

This is commonly seen in fluorescence instruments when the fluorescence cube is removed. The image goes very slightly out of focus. This is because the light now has less distance to travel based on the refractive index of the filters. The tube length of the microscope is now less than before so it must be refocused. Many manufactures have non-fluorescence cubes, called zero cubes, to correct for this.

Light does something strange when it hits a thin object, it diffracts or bends around the object. Lets use this as an example, we take a slide and coat it with a material that leaves a lot of very, very tiny holes in the coating. Then we look at it with our microscope. What do we see? Well a lot of little tiny holes and faintly around the holes we see rings of light!These rings are the diffracted light that has angled itself away from the main column of light passing through the hole. The very thin edges of the hole have caused the light to diffract. Lets count the number of rings that we see and then change objectives to one with a higher N.A.. What happens? We can see more rings around the holes!

Rather than keep calling these things rings and light columns and such lets refer to the rings as diffracted orders of light and the center undiffracted light as the zero order. We can then number the diffracted orders 1 through n.

Why is diffraction so important? Well in a microscope diffraction is the mechanism that creates most of the image. The more diffracted orders the microscope can take in the more resolution. Because of this a microscope is referred to as a diffraction limited optical system since the availibilty of diffracted light limits resolution. The angle that the lens can accept diffracted orders is the angle or acceptance.Numerical aperture is defined as sin (1/2 (A)) were A is the angle of acceptance of the lens. Numerical aperture we can see the amount of diffraction that the lens can take in and process. This is true for a lens with air between it and the specimen. If the lens is designed to use oil you need to multiply that times the refractive index of the oil.An immersion objective is designed from the ground up, you can't improve a dry objective by immersing it.

Ernst Abbe the famous optical physicist and the first scientist at the Carl Zeiss Works took all this information and formulated a single formula for the resolution of a microscope.

R = L/na(cond)+na(obj).

Were R is the resolution in microns (spacing between resolvable objects), L is the wave length of light, na(cond) is the numerical aperture of the condenser and na(obj) is the numerical aperture of the objective. It is assumed that the na(cond) is always less than the na(obj).

From this equation we can see that there are very few ways to control the resolution of a microscope. We can lower the wave length of the light used but quite soon we will go into the invisible Ultra-violet range and we won't be able to see. The only practical way to increase the resolution of a microscope is to increase the N.A. of the objective since the N.A. of condensers is quite high.

But.... we all know that 100X objectives have more resolution than 4X's so what gives. What is going on is that the equations used to produce objectives show that it is easier to produce high magnification, high N.A. objectives. However high N.A. low magnification objectives are made, they are just very expensive.

But what is this about the condenser in the equation? Well if the light source can't produce the diffraction that the objective accepts then there will be less resolution. Think of the condenser as an objective and you will be real close to what it is. So the N.A. of the condenser and the centration of the condenser matters.

The equation shows that half the resolution potential of the microscope is generated by the condenser. By using Kohler's system of illumination we place the condenser at the optical center of the system and at the correct planar relationship to the specimen and objective.

B. Contrast

However resolution is not the only thing that is necessary to generate an image we can use. We need contrast. Contrast is the difference between the brightest point in the image and the darkest point in the image.A human on a very bright, sunny day can see a difference of 500 or more to one. If there is to much contrast in a scene you will have trouble seeing into the bright areas (called highlights) or in the dark areas (called shadows, no surprises here!). Contrast is rated by its range; ie. 1 to 100 gives a 100 times light to dark range.

Contrast is particularly important to microscopists because biological specimens are very low contrast. A well stained specimen my have no more than 12 to one, an unstained specimen may have 1 to 3 or less. Without contrast our brains can't use the resolution information, the image appears "flat" at best and invisible at worst.

To control contrast we use the condenser diaghragm. This diaphragm reduces the N.A. of the condenser and increases the contrast. This is a trade off, if you have some other way to increase contrast, electronic imaging or optical staining for instance, you can use the condenser wide open and get the best possible resolution. If not trading some resolution for some contrast is a good idea.

Contrast can also be viewed as the relative intensity of the zero order versus the diffracted orders. This reduction along with phase angle shifting of the light is the basis for optical staining techniques (also called contrast enhancement) such as phase contrast and Nomarski.

To understand phase angle shift lets look at a wave of light and see what happens when we add another wave to it. If they are at the same phase angle, in phase, they add up and the light becomes more intense. This is constructive interference. If they are 180 degrees out of phase they cancel each other out and the intensity is zero. This is destructive interference. At a quarter wave length out of phase there is constructive and destructive interference.

When the zero order light is shifted by a quarter wave length then when it encounters the diffracted orders it will set up a constructive and destructive interference with them.This effect and the reduction in the intensity of the zero order light is what produces the contrast enhancement in the phase system.

C. Depth of Focus

As we lower the total N.A. of the system another thing changes, more of the images depth is in focus. Try this; get a really poorly prepared histologically prepared specimen since your work is not bad enough for this experiment go borrow one from the turkey down the hall. Examine it with a 10X objective and then with a 40X objective. At 10X you didn't have to refocus when you saw all those folds but at 40X only a very small part of the folds were in focus.

The part of the folds (call it depth of Z axis) that is in focus is the depth of field. There is more of it with a low N.A. 10X objective than with a 40X objective. Now while using the 40X open up the condenser diaphragm all the way. Now slowly close the condenser diaphragm.See, the depth of field increases as you close the condenser diaphragm.

Depth of field can be approximated by the equation : DF = 1/N.A. of the objective. Were DF is depth of field and n.a. is the numerical aperture of the objective. This equation has some caveats however. If the N.A. of the condenser is reduced the depth of focus increases and if the working distance of the objective is increased the depth of focus increases.

D. Working Distance

Working distance is the distance from the front of the objective to the specimen plane. Usually the higher the N.A. of the objective the less working distance. However Olympus in the mid-70's increased both working distance and N.A. with its S Plan series of objectives. There are, however, limits to how much working distance can be had with how much N.A..

Working distance is important in a microscope to keep objectives away from the specimen or what is around the specimen, like oil. Since we all know that "high, dry" is neither why aren't all objectives made with as much working distance as possible?

The limits are objective N.A. and cost. It is possible to increase working distance but the cost is complexity. Some objectives for industrial purposes have enormous working distances but their cost is very high. The manufacturers publish the working distance of their objectives in their literature.

E. Immersion

This still doesn't explain oil objectives. Do we really have to use oil? Why do we have to use oil? Is this a conspiracy to keep oil makers in business?

If the objective is designed to use oil you must use oil to get an acceptable image or an image at all. What oil does is provide an improved channel for the image to travel between the specimen and objective. The characteristic we look for in an oil to do this is the index of refraction.

The index of refraction is the ability of material to bend light. Mineral oil has a higher index of refraction than water for instance. Air has an index of refraction of one while standard immersion oil is 1.55. This means that immersion oil will funnel more of the diffractive orders from the specimen to the objective.

Practically this means that the highest N.A. that can be achieved with air between the objective and specimen is 1. In practice the highest commercially available N.A. in air is .95. The highest commercially available N.A. with oil is 1.4. This is a 32% improvement!

Oil has another advantage, simplicity of use. Yes I know about the mess oil makes. I repair microscopes, believe me I know! The problem is with high N.A. 40X-60X objectives. If N.A. exceeds .8 then the cover slip thickness becomes very critical. To adjust for this the manufacturers build a cover slip compensating collar on to the objective. This must be set correctly or the image will be poor.

This is the trade of with high performance mid-range objective, oil or compensating collars. Look at it this way mess or time. Of course cost raises its ugly head. Oil objectives are easier to build than high performance dry objectives.

F. Magnification

Now that we understand resolution we can discuss the less important area of magnification. The total magnification of a microscope is the magnification of the objective times the magnification of the eyepiece times the magnification of any intermediate modules (if any). For example using a 10X objective and a 10X eyepiece and no intermediate modules will yield a total magnification of 100X.

So why not use 100X eyepieces and get 1000X total power? It could be done. In fact magnification is cheap to produce, resolution is expensive.

Well what you would get is a big fuzzy image. Eyepieces don't improve resolution. As we have seen only N.A. improves resolution. A good rule of thumb for visual observation is that the total magnification of a microscope should not exceed 1000 times the N.A. of the objective in use.

If we are using a 100X oil with a N.A. of 1.25 with 10X eyepieces we have a total magnification of 1000. Since this is significantly less that 1000 times the N.A. of 1.25 (1250) we should expect to have a very pleasant image. If we are using a dry 100X objective (these are made!) with an N.A. of .95 (950) we would expect the image to look fuzzy.

G. Parfocality

A modern microscope must have the ability to change objectives easily.In the very early days of microscopy the user unscrewed the objective and screwed in another. With the advent of the revolving nosepiece parcentricity and parfocality became important.

Parfocality means that the specimen stays in focus when the objective is changed. To judge this correctly the microscope is properly set up and then focused at high power. Then switch objectives to a low power and see how much focusing is necessary. Because depth of field is greater at lower powers parfocality is always judged from high power to low. A good microscope will require very little focus knob movement.

If you are using achromats or other curved field objectives remember to judge parfocality only in the center of the field. Parfocality is very influenced by the set up of the instrument. If the eyepieces, in particular, are not set up correctly parfocality will suffer.

Parfocality can be adjusted on most microscopes by the user or, at worst, a service person. Usually all that is required is to properly set up the eyepieces. Some times adjustments must be made to the eyetube mechanism. Leave that to a qualified service person. If parfocality can't be corrected the odds are that a bad objective is to blame.

Sometimes parfocality is corrected by a service person installing thin brass rings called shims between the objective seat and the nosepiece. This is to adjust the tube length of the microscope by extending the objective a very small amount. You can only shim an objective down (extend the tube length) not up. Shimming should be viewed as a desperate last gasp, a band aid solution not a true fix. When an objective is shimmed it no longer sits quite flat on the nosepiece.This can cause a loss of of parcentration. Brass shims are used because brass adapts to the objective seat and nosepiece the best of any material.

A service person who shims all objectives, uses other than brass shims, excessively shims or tries to adjust parfocality by screwing the objective on very tight just doesn't know what they are doing. At most one less than the total of objectives will have to be shimmed. If a lot of shims are required (more than 3 or 4 thick ones) then it is proof that the objective of microscope has sever problems that requires attention not a band aid.

H. Parcentricity

Parcentricity means that an object in the center of the field will stay in the center of the field no matter which objective is being used. To test this set the microscope up properly and find an identifiable object at high power. Switch to each objective in turn and see if it is in the center.

If you have performed Kohler illumination correctly you can close the field diaphragm and observe the image of the field diaphragm's position in the field of view. It should stay in the center of the field. Any deviation is a loss of parcentricity.

There will be some variation in the field center objective to objective. To be acceptably parcentric the center of the field should not vary more than one third of the field of view; ie. if the object is at the center with one objective it will not go out side the inner one third of the field of view with any objective.

Sometimes parcentration can be corrected by a skilled service person but usually parcentration problems are caused by a bad nosepiece or is inherent in the construction of the instrument. Parcentricity is based on the design and manufacture of the nosepiece, mainly, and is a good indication of the general quality of the instrument.

VI. Conjugate focal planes. Were is it anyway?

How often have you seen a dirty smudge through the eyepieces and had a hard time finding it to clean it? Probably a lot. Because a microscope is a convergent-divergent instrument with conjugate focal planes tracking dirt can be a problem. Of course so can the those long words we just used.

A microscope is a convergent-divergent instrument as opposed to a parallel or infinity instrument. In an infinity instrument all light rays are parallel to each other and the optical center line of the instrument. In a microscope light rays are moving towards the center line (converging) or away (diverging) from the center line at all times. Even "infinity corrected" objectives do this.

This sets up a series of locations in the microscope were things will be in focus. At the top end of the microscope the image is in focus at our eye's retina. However if we looked at our own eye's lens (don't ask me I don't know how) we would see an image of the lamp! These are the conjugate focal planes, the retina and lens planes.

If an image is in focus when another image is in focus then it is conjugate to it. For instance if a microscope is set up correctly using Kohler illumination then when we close the field diaphragm it will be in focus along with the specimen; the field diaphragm and the specimen are said to be conjugate to each other or in the same conjugate plane. That conjugate plane is also occupied by the diaphragm of the eyepiece. This is were we put measuring reticules so they will be in focus along with specimen.

So what does the lens conjugate plane do? Well it generates the information the retinal plane sees. If we remove an eyepiece we will see the lens planes components, light source, condenser diaphragm and objective back plane.

In some microscopes you will see the filament of the lamp in the field. Most microscopes use a diffusing filter to diffuse (fuzz) the filament image so that low power objectives can be used. Even if you can't see it the filament of the lamp it is the first lens conjugate plane.

The next plane is the condenser diaphragm. To observe the condenser diaphragm remove an eyepiece and open the condenser diaphragm all the way. Now close it slowly. You will see it reduce the illuminated area in the objective back plane.

When you have reduced the maximum size of the illuminated area by a third to a half replace the eyepiece and observe the specimen. The contrast will have increased from when the condenser diaphragm was fully open. This is a very good way to set the contrast of the microscope for an objective.

While we are seeing the condenser diaphragm change we are actually seeing the back focal plane of the objective. The size of the fully illuminated area will vary by the N.A. of the objective. This means that a one third to one half reduction is individual to that N.A.. This method of setting contrast is great for photography and all forms of documentation.

There are other uses for the lens back plane. Geologists observe cross polarized specimens at the back focal plane using a Bertand lens. This is called conoscopic observation. While biologists haven't used this to any extent you never know what will be used next.

What Kohler did by defining these planes (this is the why of Kohler illumination) was to place the image of the lamp were it would do the most good. The lamp is brightest were it is in focus, so focusing it just before it goes through the condenser makes it the brightest.

Why don't we see these all at once? Well we do but we see the lens conjugate plane as an effect and the retinal plane as the image. Like dirt on our glasses we can't see the lens conjugate plane but it affects us.

This also makes dirt hunting easier. If we can see the dirt we know that it has to be conjugate to the plane we are see. For instance if we can see a blob of dirt we know that it can't be on the back of the objective since that is not conjugate to the specimen. We also know that it can't be on the front of the objective since that is not conjugate to anything.

A lot of dirt that we see in a microscope is on the lens covering the field diaphragm. This is near enough to a conjugate of the specimen that the depth of focus of the condenser will bring it in focus. Clean this area with air or with methanol and Q-tips.
What this means to you
Conjugate planes are parts of the microscope that are optically the same. Knowing what is conjugate to what helps us to find dirt and properly set up the microscope.