advanced imaging laboratory
basic microscope optics
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:
Unfortunately, an image made by a single lens suffers from a number of optical defects. These can include:
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'
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.
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.
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.
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