Microscope heads come in three types, monocular, binocular and trinocular. Monocular microscopes were the standard as late as the 1950's but now monocular microscopes are only made for the low end student market. Monocular head modules are becoming commercially extinct. The modern microscope has at least a binocular.
Binocular and trinocular heads come in three optical types, focusing eyetube, compensating and Siedontoff . These designs all address the same problem, how to compensate for the distance between different peoples eyes. If this distance were the same for everyone then there would be no need for adjustment at all, however it does vary and the correct adjustment of the head is neccesary to fuse vision.
A binocular head works by taking one light beam and splitting it into two parts that then go to the eyes. The prism that does this is called the splitter prism. Once the light leaves the splitter prism the problems begin. There must be some mechanism in the binocular to allow the user to adjust the distance between the eyepieces to match the distance between their eyes. As this distance changes the tube length of the microscope changes. If this is not corrected the microscope will not be parfocal.
One way to correct for the change in tube length is to make both eyepieces focus. This way the user can adjust the parfocality of the microscope by either using an indicator or setting the microscope empirically. To set the head using an indicator you look at the reading on a dial or scale indicating the distance between the eyepieces. Then you set each eyepiece to the same number. As long as everything is in sync this works however it is better to set the parfocality of the microscope empirically.
A binocular head with two focusing eyepieces is set by focusing the specimen on high power(40X or more) and switching to low power (10X or less). Then focus each eyepiece by closing one eye and turning the other eyepiece counter clockwise until the image is out of focus. Now rapidly focus by turning clockwise. When it is in focus stop. Repeat this for the other eye.
A compensating head has a mechanism in it to move the eyepiece tubes as the distance between the eyepieces is changed. If everything works correctly a compensating head works very well. The only adjustment the user has is the left eye tube. This is focused at low power (10X or less) to compensate for differences in vision. Focus the specimen using you right eye only then close your right eye. Now turn the left eye tube counter clockwise until the image blurs. Focus the image by turning the eye tube clockwise rapidly. When the image is in focus stop.
The Siedontoff binocular head solves the problem by swiveling the eyetubes around the splitter prism. This allow the distance to change without changing the tube length. This type of head must have two focusing eyepieces or tubes for best results. When equipped this way the microscope should be perfectly parfocal. A Seidontoff head is set up the same way a dual focusing eyepiece is set up.
Most Nikon heads and some Zeiss heads are Siedontoff. Olympus and Leitz mostly use compensating heads. Twin eyepiece heads are more and more things of the past. The problem with twin eyepiece heads and Siedontoff heads are that people don't use them correctly. Compensating heads work very well as long as they are made correctly, if not they are very difficult to fix.
Trinoculars are a binocular with a moving prism assembly that directs light either to the binocular assembly or towards the camera. Some trinoculars are either 100% of the light to the camera or 100% of the light to the eyepieces. The best modern trinoculars have at least three positions. These trinoculars allow either 100% to the binocular, 80% camera and 20% binocular (app) or 100% to the camera.
The advantage of at least a three position trinocular is its versatility. For most brightfield photographic purposes a 20% visual-80% photo system will work quite well. There should be enough light with a modern microscope that the camera will have a very short exposure time and the user will be able to see the specimen at the same time. This make photography a lot easier.
If you are photographing fluorescence you will need all the light you can get. First you search for the right area of the specimen with the trinocular set for 100% to the binocular. When you want to take a picture, set the trinocular for 100% to the camera to get the shortest possible exposure time.
Two position trinoculars are available from most manufacturers for less money than a three position. I feel that if a three position is available that the three position is the best buy. Manufacturers are making multi-position heads that are basically three position trinoculars with the ability to accept two or more cameras. These can be quite useful if you need them. They can make the microscope look quite top heavy however. Sometimes a support stand for one of the cameras will be needed.
Some heads take the reversed image that all biology people know and correct it. This means that when the stage is moved left the image moves left. This is how all heads should be. These heads are found in industry were their higher cost is justified by their ease of use.
Industry also pioneered the Ergo head. Invented by Leitz the Ergo head lets the user adjust the angle of the head to suit there needs. This is usually combined with the image reversing feature to produce a truly usable binocular or trinocular head. Most manufacturers produce a head like this. Once you have tried one you won't want to let it go.
Why aren't these heads seen in biology? Well the excuse is cost and I do mean excuse. Since a microscope lasts 25 years at least a small difference in price is easy to make up in a large increase in productivity. If you use a microscope a lot and have never seen a head like this then get your representative to bring one.
There are heads designed especially for polarization. These correct for problems that happen when polarized light goes through a prism. If polarization is the most important thing that you are doing then you need a polarizing head. They also have positions for reticule equipped eyepieces so the reticules will be at the correct angles.
What this means to you
The type of head you have will determine how you set the microscope up.