Microscopy Primer by Frithjof A. S. Sterrenburg

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Geometric Optics
Physical Optics
Special Microscopy Techniques

Key: italics: text for experimenters  blue: keywords   red: beware!


The laws by which fine detail is made visible in an optical instrument are called physical optics. The reason why physical optics are quite different from geometric optics is that light consists of waves (not “straight arrows” as geometric optics treats them) and are affected by the object. Ray tracings are fine to show where the image lies, but they do not yield information on the properties of the image. We’ll assume that the quality of the objective is perfect so that performance will not be impaired by serious aberrations.

Image formation
The theory of image formation was formulated by Ernst Abbe in the late 19th century.  Abbe treated the object as a fine grating and although that is not an exact description of say, plant sections, it is a very good approximation of the regular structure of diatoms.

When light passes through a grating it is scattered (diffracted) so that it becomes a fan - or rather, a cone, Fig. 36. A narrow parallel bundle of light that enters the object is therefore split into an undeviated (straight through) bundle and deviated bundles on both sides. The undeviated light contains no information about the object, it’s simply the background illumination. The deviated light contains the object’s information. The image is formed behind the lens, where the deviated and undeviated light interact (interfere).

A reasonable image can already beobtained when the two deviated bundles closest to the undeviated light (the first-order maxima) are passed through the objective to interfere with the undeviated light. If the higher-order maxima are not included in image formation, the image is not perfect but it can be seen that a grating is involved and the fineness of the grating can be determined. That is to say: there is just sufficient resolution.
The degree of diffraction, i.e. the angle between the two first-order maxima, depends on two factors:

Diffraction can be demonstrated beautifully with a slide of the diatom  Pleurosigma angulatum. Focus normally with the 100x oil immersion objective, then close the condenser iris as far as it will go. Check the aperture with a centering telescope (the unaided eye won’t do here because the image is small). A star-shaped diffraction pattern is seen, each of the six points of the star is a spectrum with violet inside (less markedly diffracted) and red outside (markedly diffracted). These are the first-order maxima and this is exactly what the theory predicts!

Because diffraction by finer detail increases the angle between the first-order maxima, it’s now evident why high resolving power requires a wide “angle of admittance” of the objective, i.e. a high NA.

Another advantage of the immersion objective can now also be explained (Fig. 37): as the angle of the diffracted image-forming rays coming out of the object increases, there comes a point where by Snell’s law the angle of these rays becomes 90ş or more when they pass from the top of the cover-glass into the air. That is to say, they do not leave the cover-glass but are reflected backwards so that the diffracted rays representing the fine image detail do not enter the objective at all. By using an immersion lens, this total reflection is avoided and for fine gratings information-carrying rays also enter the objective.

The advantages of an oil immersion objective are, therefore, three-fold:

Water immersions do not completely solve these problems but nevertheless reduce them very considerably.

The condenser’s contribution
So far we assumed that the specimen is illuminated by a narrow beam of parallel light. From Abbe’s theory it followed that an image results when the two first-order maxima can interfere with the undeviated light. Actually, only one first-order maximum is already sufficient: because it is representative for the grating, it carries just enough information to create an image when it alone interferes with the undeviated light. (If you happen to be a radio ham: it’s the equivalent of single sideband).

That means that if the light is made to strike the specimen obliquely (Fig. 38), both one first-order maximum and the undeviated light can be caught by the objective - the angle of admittance of the objective appears to be doubled. If you illuminate obliquely from all sides instead of from one side only, you get a cone of light at an angle equal to the angle of admittance of the objective. And that is exactly what the condenser supplies.

We’ve seen earlier that in order to fill an immersion objective completely with light, the condenser must also be oiled to the slide. This is very bothersome, increases glare and may so reduce contrast that you can’t benefit from the improvement in resolution. The condenser iris is (almost) never fully opened anyway with objectives of any NA because this would reduce contrast. Only the most recent apochromats permit full illumination of their aperture and even so, they still show somewhat better contrast when the condenser is slightly stopped down.

The resolution with brightfield microscopy can be calculated reasonably well with the formula
                 d  =   1.22  *   l  /  NAobj + NAcond

where: d= resolution in µm;  l = wavelength of the light used (0.5 µm for white light as average value);    NAobj  =  NA of the objective;    NAcond = NA of the condenser. The latter is the effective NA, that is the portion of the full NA actually in use as controlled by the condenser iris!

From this formula, you can easily calculate that the gain in resolution by immersion of the condenser (NAcond raised from 0.95 to 1.2) is only marginal. Likewise, reducing the size of the condenser iris to about 80% of the full aperture of an objective only slightly reduces resolution while greatly improving contrast. The formula shows that for light of 0.5 µm wavelength, NAobj = 1.3 and  NAcond  = 0.95 (“dry”) the maximum resolution the microscope can give equals about 0.26 µm. This is the limit you can reach in routine practice.

What magnification?
Whereas we’ve worried a lot about ensuring high NA, we’ve not yet once mentioned magnification. The reason is that whilst ensuring high resolution is absolutely crucial, magnification says nothing about the information content of the image. In his theory, Abbe also treated magnification, but here he tripped up wonderfully because he made wildly optimistic assumptions of the performance of the human eye, as later research has shown. So don’t believe older books!

Magnification is a matter of convenience and ensuring that none of the information in the image is lost. Here is how to decide on magnification, and for an example I consider a specimen that contains detail with a fineness of 0.3 µm :

Visual observation:
At a comfortable reading distance of 25 cm (which is what we approximate in microscopy), people with very sharp eyes can resolve 0.3 mm, others reach 0.5 mm. Magnification of 1000x is OK for some, 1500x is better for others.

Document films as used in professional photomicrography can have a resolving power of 100 lines per mm, i.e. 10 µm. Let’s be very conservative, assume less perfect film and make it  60 µm. Then the minimum effective magnification on the film for 0.3 µm detail would be at least 200x. Because camera systems mostly reduce power 2x, this would require at least 400x from the microscope. For contact prints, the rules for visual observation apply, so print at least at 1000x to 1500x for our example, or simply more if you think it makes for more convenient viewing - e.g. at a larger distance than 25 cm.

Consumer-type digital cameras with 4 Megapixels and more are able to handle the information in a microscope image. A 3x optical zoom is necessary to avoid vignetting. It may be necessary to disable the autofocus function and set the camera at infinity. Save the images in non-compressed format (bmp) and only convert to compressed format (e.g. jpeg) after all image processing has been finished.

Prints in journals:
If your pictures are going to be published, they will be printed using a fine screen. This will slightly impair image quality so for the fine structure in our example I would suggest at least 1500x and better 2000x. For a “close-up” of a relevant portion of  the image you might even use 2500x here. For a poor-quality journal the printer’s screen will be coarser and you may have to use higher magnification.

- Video monitor, computers
This “coarse screen” situation also arises if you show microscopic images on a video- or computer monitor. A normal TV has only 625 lines for the entire height of the screen, a normal computer monitor has 600 or 768 for the entire height and 800 or 1000 for the entire width. This means that you can never hope to show the detail in a hard copy photograph at the same picture size on screen, you need a much larger scale and scrolling of the picture may be unavoidable. Digital is not always better!

When scanning hard copy photomicrographs, and certainly when scanning negatives, you will have to remember what you do: many of my negatives on document film indeed contain detail near 50 lines per mm, which requires a scan with at least 1250 dpi. Because of the “landscape” screen format of most computers you’d better rotate pictures for optimum viewing.

Conventional wisdom (Abbe) had it that horrible things happened when magnification was greater than about 1000x the NA of the objective, but these are fables. When looking through a microscope at very high magnification (say 2000x) you’ll notice the residual imperfections in the lenses - and the preparation! - more, the field of view becomes smaller and the image becomes darker. So the image will not be really crisp, that’s all. But if you have a superb photomicrograph on negative or CDROM, you can blow it up to spectacular poster size for a presentation to let people enjoy it!

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September 2002
© Frithjof A. S. Sterrenburg

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