Introduction
Optical microscopy uses visible light, and its performance is inherently limited by the wavelength of light. This ranges from 400nm (violet) to 650nm (red). There are two different ways of calculating resolution, according to whether the specimen is illuminated externally (Abbe calculation) or is effectively self luminous as in fluorescence microscopy (Rayleigh calculation). Both give similar results, the difference lies in how to set up the microscope for best performance. With an ideal lens, diffraction limits the resolution to about half the wavelength of light, and our best objectives come within 95% of this.
What makes an objective good?
The most important quality of a lens is not its magnification, essential though that is, but its numerical aperture. This is defined as the sine of the maximum angle (from the vertical) at which light can enter. It is ‘numerical’ because it is a ratio – the actual size of the lens makes no difference. It could be – and usually is – a small lens very close to the slide, but where a large working distance is required it can be larger and further away (and probably more expensive).
The largest acceptance angle we can get, in practice, is about 72°, which gives us a numerical aperture (NA) of 0.95. Considering that even if we put the lens flat on the specimen the NA would only be 1, it’s clear there is little room for improvement. NA 0.75 would be the highest ‘dry’ lens found on most microscopes, and that will give a resolution roughly equal to the wavelength of light. Why ‘dry’? Because if our sample is sitting in something with a higher refractive index than air, we should in principle be able to get better resolution, since the wavelength of light becomes shorter the higher the refractive index.
The snag is that we must keep the refractive index constant the same all the way to the objective, or the highest-angle rays will be bent away and won’t reach the lens. So if our specimen is in a permanent mounting medium of refractive index (n) ~ 1.5, we put immersion oil of the same index between the coverslip and the lens. The NA is now conventionally given as the sine of the acceptance angle multiplied by n, and an oil immersion objective can get up to an NA of 1.4. This will now give us a resolution of about half the wavelength of light, which is pretty impressive when you think about it.
With living samples in water (n = 1.3) we have to use a water immersion objective, and the resolution boost will be a bit less.
Aberrations
So far it all seems easy – we just make a lens which is very wide compared to its working distance. Unfortunately lenses are not perfect, and two imperfections are particularly problematic. Spherical aberration is an inherent property of a simple lens – the lens is more powerful at the edge that in the centre, so the image will not be sharp.
Chromatic aberration is an inherent property of glass – it has different refractive indices at different wavelengths. That is why a prism splits white light into a spectrum. This means that we cannot get all colours in focus at the same time. We can overcome this by using just one colour, and this works well, for example, when looking at living cells under phase contrast. But in the wider picture, we would be throwing out one of the great advantages of light microscopy – the ability to show different structures or substances in different colours.
Correction collar to adjust for coverslip thickness.
Unfortunately, both these aberrations get worse with increasing NA, and they do so very much more rapidly than the resolution increases. Without correcting these aberrations we cannot hope to make a usable high-NA lens. Fortunately we can correct them, but it requires multiple optical elements, which is why high-NA objectives are expensive. However, spherical aberration can only be corrected for one precise set of optical conditions and, for example, using the wrong thickness of coverslip, or using an oil-immersion lens on a sample in water, will spoil the correction. It becomes so tricky that very high NA objectives often have a correction collar to adjust for different coverslip thicknesses (in a dry lens) or temperature and salinity (in a water lens).
Chromatic correction come in various grades, from achromat (basic correction) through fluorite (better) to apochromat (best). Best correction is not always best for your experiment, though, since apochromats contain a lot of glass and will therefore absorb more light than fluorites. Some apochromats also do not transmit UV very well, which can be a problem in fluorescence. Also, lenses are only corrected for a particular range of wavelengths – usually blue to red. Their performance can be very bad outside this range, and with the increasing use in microscopy of violet and UV at the short end and far-red and near IR at the long end, this can be a problem. Apochromats with different correction ranges have become available to meet this need.
Finally, the objective is only one of several optical elements in a microscope, and manufacturers design all of these to work together. Swapping objectives between different brands of microscope is therefore not a good idea.
Further reading: Optical Imaging Techniques in Cell Biology, by Guy Cox. 2nd edition. CRC Press, 2012. 316 pages
