basic microscope optics

The ability of the microscope to both magnify and resolve (or allow small structures to be seen) firstly depends on the refraction or bending of light. Refraction occurs when light goes from a medium of one density or refractive index to one of another. In the example to the left, parallel light rays from an infinitely distant source enter a glass lens from air and are bent and made to converge at the point F1. The distance from the centre of the lens to this focal point is the Focal Length (f) of the lens.

The amount of refraction that occurs depends on the difference in Refractive Index of the two media or materials and is described by Snell's law: η1 sin θ1 = η2 sin θ2

The refractive index (η) equals the speed of light in vacuum divided by its speed in the material in question. Some examples of refractive indices are:	Air =	1.0003
	Water =	1.33
	Glycerol =	1.47
	Immersion Oil =	1.515
	Crown Glass =	1.52
	Diamond =	2.42

The exact refractive index for a given material varies with the colour or wavelength of light. This explains dispersion, or the ability of a prism to separate out the deferent colours of light:

Material	Blue (486nm)	Yellow (589nm)	Red (656nm)
Crown Glass	1.524	1.517	1.515
Flint Glass	1.639	1.627	1.622
Water	1.337	1.333	1.331
Cargille Oil	1.530	1.520	1.516
Zeiss Oil	1.525	1.515	1.512

Unfortunately, an image made by a single lens suffers from a number of optical defects. These can include:

chromatic aberration, resulting in different wavelengths or colours of light being focused at different distances;
coma, resulting in the images of structures out from the center being smeared outwards;
spherical aberration, resulting in light passing through the lens center being focused at a different distance to light passing through the outer portion of the lens;
astigmatism, resulting in light in the X plane being focused differently to light in the Y plane, and
curvature of field, resulting in a flat subject plane being imaged as the surface of a sphere rather than a flat plane.

In order to combat these defects and produce sharp images, microscope objectives and eyepieces are far more complex and are comprised of multiple lenses made of glass with differing refractive indices. Microscope objectives come in several grades of correction. The illustration below shows three 40X lenses. The left lens is an achromat and is corrected for two colours of light, red and blue, but it still suffers from chromatic aberration in the green region. The apochromat in the middle is corrected for three colours, red, green and blue. On the right the plan achromat is not fully corrected for colour but is corrected for spherical aberration and it has a flat field which is particularly important for photography. When photographing in gray scale, rather than colour, using a green filter will eliminate the effects of chromatic aberration while often enhancing the contract of biological stains.

While the power of a lens indicates the magnification it gives, the numerical aperture gives a relative indication of its resolving power, which is more important than magnification. Bigger is not always better, especially when it comes to magnification, unless it is accompanied by increased resolution of fine detail. The final magnification will be the product of the objective magnification, the eyepice magnification and perhaps other factors such as the tube factor, the nose piece factor and the camera factor. An old rule of thumb says that the final image magnification should not be more than 1000 times the numerical aperture of the lens used. Magnification greater that that will include "empty magnification". The image will be bigger, but since there is no more information or detail, the image will not appear satisfyingly sharp.

The numerical aperture, or N.A., of an objective results from the sine of half of the entrance angle of the light cone (shown as u' in the figure below) multiplied by n, the refractive index of the medium between the cover slip and the objective. When a lens is designed to be used dry n = 0 but when a lens is intended to be joined to the prep with immersion oil (oel) the refractive index is 1.515. Numerical aperture generally increases with magnification and/or degree of optical correction.

N.A. = n*sin u'

		numerical aperture
		achromat	plan	fluorite	planapo
	4x	---	---	---	0.16
	6.3x	0.16	0.16	0.2	---
	25x	0.45	0.45	0.6	0.65
	40x	0.65	0.65	0.75	0.95 (oil)
	100x	1.25 (oil)	1.25 (oil)	1.25 (oil)	1.3 (oil)

The table shows some typical magnifications and numerical apertures of Zeiss lenses. Microscope objectives are labeled so as to give a number of pieces of information such as seen below.

Ph 2 Plan 40/0.65 160/0.17

Neofluar 10/0.30 160/-

The left example is for a planachromat, or flat field lens, which is capable of phase contrast. To be used for phase contrast enhancement it must be used with a number 2 phase ring in the condenser in a Zeiss microscope. This lens gives a magnification of 40X, cannot be immersed (since it doesn't say oil or oel) and has a numerical aperture of 0.65. The bottom row numbers tell us that this lens is designed to be used with an instrument with a 160 mm tube length which is the distance between objective and eyepiece nodal points. Many recently made microscopes are infinity corrected and have no stated tube length. This lens requires the use of a standard cover slip, which is 0.17 mm in thickness. A significant decrease in resolution will occur if a cover slip is not used.

The right example is of a lens made of fluorite rather than crown glass. It is better corrected than an achromat, it has a magnification of 10x, has a N.A. of 0.3, is intended for an instrument with a 160 mm tube length. The little dash means it doesn't matter whether or not a coverslip is used. Many modern lenses are infinity corrected and the tube length doesn't matter.

 

The basic light path of the microscope can be clearly seen at the left. Light from the bulb in the base is focused by the collector lenses in the base and sent upward, via a mirror or prism, as an illuminating cone of light which fills the substage condenser with light. The condenser then focuses the light and the image of the fields diaphragm on the specimen. If the aperture diaphragm is set properly the emerging light will fill the objective and give maximum resolution. The preliminary image produced by the objective is deflected by the prism into the eyetubes and then it is further magnified by the eyepieces which project the image into the eye, or if fitted into the camera. The adjustment of the condenser and the field and aperture diaphragms can be found under the discussion on Köhler illumination.

The illustration above shows a schematic of the optics and light paths of the microscope. The condenser focuses the image of the field diaphragm into the specimen plane and the plane of the eyepiece field stop. It also focuses the filament of the lamp into the plane of the aperture diaphragm and the objective exit pupil. The objective produces a primary or intermediate image of the specimen which is further magnified by the eyepiece and projected into the eye or camera. The condenser plays a critical role in image formation. Highly corrected condensers are complex and are made of a number of lenses as seen below. Like a microscope objective, a condenser has a numerical aperture and it should equal or better that of the highest magnification objective being used. The wavelength of light used (which can be selected by a filter), the objective numerical aperture and the condenser numerical aperture all affect the resolution of the instrument according to the formulae below.

If NAobj is the objective's numerical aperture, NAcdn is the condenser's numerical aperture and λ (lambda) is the wavelength of light used in microns, then the least resolvable space between two points (in microns) can be determined by the formula below. Resolution is proportional to the Numerical Aperture of the lens and the Numerical Aperture of the condenser. The higher the NA, the more orders of diffracted light will enter the objective and the higher the resolution will be:

Resolution = 1.22 λ/(NAobj + NAcdn)

If the lens has a NA of 1.4 and the condenser has a NA of 1.25 and green light at 500 nm is used, the resolution will be 230 nm, which is to say that the system should be able to resolve two structures that are 230 nm apart.

At the end of the day, resolution is limited by diffraction, which results in secondary, weak wavefronts being generated which interfere with the primary wavefront when light passes through a small aperture. As a result a small spot is imaged, not as a small spot, but as a spot surrounded by a series of concentric circles (called Airy disks after their discoverer). If two of these Airy disks are separated at least by their radius, the meet the Rayleigh criterion and are resolable as two spots. As you might assume from the formula above, resolution can be improved somewhat by imaging with shorter wavelength light.

Some of our higher magnification objectives are designed to be joined to the cover slip of the preparation with an immersion oil that has a refractive index of 1.515. Ideally the mounting medium will also have a refractive index of 1.515 as will the coverslip. These lenses will be labeled oil or oel. The figure below shows light emerging from the specimen and being gathered by the objective. The light first travels through the coverslip and then, on the right side of the figure, it travels through air until it reaches the front glass of the objective. On the left side of the figure the void between the coverslip and the objective is filled with immersion oil. This results in more rays of light, which otherwise would have been lost, being gathered since more light is refracted toward the objective and none is lost in reflection from the coverslip upper surface. More information is gathered as a result and a higher resolution image is obtained.

Other specialized lenses are made for water or glycerol immersion. The table below shows the refractive indices of some other common media. If there is a difference between the medium and the lens's requirement, some aberrations will be increased.

	medium	refractive index
	air =	1.00
	water =	1.33
	glycerol + water =	1.4
	glycerol =	1.456
	paraffin oil =	1.482
	m-xylene =	1.497
	immersion oil =	1.515
	monobromonaphthalene =	1.655
	methyl iodide =	1.76