From: PO2::"frithjof@PI.NET" "F.A.S. Sterrenburg" 24-OCT-1995 17:32:52.83 To: Multiple recipients of list DIATOM-L CC: Subj: MOUNTING MEDIA Gene Stoermer is quite right: universities assume a microscope is as simple as a coffee-grinder: plug in and go. The general student's insight into (and love of) microscopy is therefore not stimulated. Earlier this year, I have stealthily checked 6 microscopes at that time in active use in a renowned institute - none of these had even halfway correct illumination, with ground glasses masking the fact that the lamp filament was out of whack, for instance... Some personal background: my interest in diatoms is the direct result of my interest in microscope optics. I was so lucky as to have a father who was a highly competent microscopist (he still is, at the age of 96) and was not afraid to explain to a youngster what "refractive index times the sine of half the angle of admittance" (this is the numerical aperture...) means. As a result, I became interested in resolving diatoms. Because of this interest, I took courses in geometric and physical optics while at the university. Unfortunately my book on microscopy with simple chapters on the laws of optics is in Dutch, one of my papers in that field is "Enhancing the visibility of diatoms", Microscopy 33, July-December 1978. No reprints left, sorry! Resolving power and contrast have been admirably treated by people like Francon or Osterberg. The problem is that these treatises are fiercely mathematical. Because I am not too sure E-mail takes differential equations and calculus anyway, I will try to do without formulae. I will limit myself to brightfield (resolving power is somewhat different with PC). Let's go back to Abbe and his diffraction gratings - which is what many diatoms are par excellence (Gyros and Pleuros!). When light passes such a grating, some of it goes straight through (called the zero order maximum), the rest is diffracted as separate bundles (called first, second etc. order maxima). The finer the structure, the more these bundles diverge. For formal resolution of the grating the two first order maxima must pass through the objective. Hence the importance of a large angle of admittance (=high NA) of the objective. The general formula for the potential resolving power was given in the 19th century by Nelson. It says: resolving power= wavelength of the light/NA of objective PLUS effective NA of condenser. Note that this formula contains the effective NA of the condenser and this is weighted as much as the NA of the objective. Which means: you need a full cone of admitted light if you need to see fine detail. Note also that the refractive index of the mountant is not a parameter. When the diatoms are mounted on the lower surface of the cover (as they must be), the bundles caused by diffraction by the diatom "grating" DO NOT PASS THROUGH THE MOUNTANT. The mountant therefore has no effect on their divergence, nor does it affect the NA of the objective - i.e. it has no effect on resolution. It is possible for the best optics to show nothing, however, because OUR EYE NEEDS A MINIMUM LEVEL OF CONTRAST. While resolving power is in the optics, visibility is in our eyes. In other words: the lenses MAY resolve something, only without some minimum contrast we can't see they do so. To see contrast, our eye requires amplitude differences. It's an AM radio. Diatoms do not cause marked amplitude differences, they cause phase shifts. What we need is an FM radio. Without trickery, maximum resolution and maximum contrast are mutually exclusive - stopping down the iris improves contrast but destroys resolution. Only when differences in phase become very large does our eye interpret them as amplitude differences. What a mountant with an RI greatly different from that of the diatom frustule does is: increase the phase shifts caused by the object, thus ensuring that the detail which is hopefully resolved actually can be seen by us AM radios. Simple practical tests to prove the above are the following, and I assure you you'll have fun carrying them out: 1) if RI would affect resolution, a very low RI would considerably reduce it. Pleurosigma angulatum (which can just be resolved with a 40x NA 0.65 objective) should therefore become unresolvable when mounted in air - which has the lowest RI possible, = 1.0. In fact, a dry mount is the best way of seeing P. angulatum resolved with a 40x Na 0.65 objective! Just because it's the most contrasty. Contrast depends on the difference in RI, not its absolute value. 2) Make a slide of Amphipleura pellucida in Canada balsam. You won't see anything regardless of your optics. Using the same optics, switch in DIC - oil immersion, of course. The striae are immediately VISIBLE (your lenses did resolve them too when you looked at them without DIC!!). Vary the contrast and see the striae disappear. You can also use polarized light, by the way, see Plate 51, 1bis in Germain's flora. Under these conditions, A. pellucida can be resolved with any student's microscope. To summarize: resolution does not equate visibility. The former requires capture of first order diffraction maxima by the objective, the latter asks for amplitude differences. Physically these are unrelated. It's possible to resolve structure without seeing it, but the converse is not true. I have received many questions about a good and non-mathematical primer in geometric and physical optics but the best one in English I've ever seen (Teach yourself microscopy, W.G. Hartley, London 1962) seems not to have been reprinted. It's all explainable in down-to-earth terms and you can easily test everything yourself. With some support in production and distribution, a simple primer would perhaps stimulate the aspiring professional to love the instrument as much as several redoubtable microscopists in the Quekett club do, for instance. From: PO2::"frithjof@PI.NET" "F.A.S. Sterrenburg" 25-OCT-1995 08:32:47.88 To: Multiple recipients of list DIATOM-L CC: Subj: resolution/contrast Some additions to my previous comments on this subject that began with the coffee-grinder analogy. Reading Stoermer's E-mail I thought "hey, this is fun " and started writing off the cuff. However, I now find that a more formal supplementary treatment is necessary. Previous statements remain unaltered! First of all, I most decidedly do not 'confound' resolution and contrast, on the contrary. Nor do they confound me... I am likewise amazed that confusion still exists around the subject and fully agree with Stoermer that it deserves an explanation understandable to non-physicists. This I propose to do at least partially, with some practical tests you can do for yourself. I urge readers to carry them out. I regret not having mastered sending drawings via E-mail yet, but it seems the issue requires a printed and illustrated treatment anyway. First of all, it is physically (literally) impossible to confuse resolution and contrast, for several reasons. I will treat the general case of any object - or collection thereof - seen against a background. I will then show that this is not limited to microscopy but is also valid for astronomy or naked-eye observation. 1) There is a fundamental semantic difference between resolution and contrast. Let's define resolution as the optical imaging of closely adjacent details in such a manner that the individual images of these details are indeed presented separately to our eyes. Likewise we'll define contrast: it is the difference in amplitude between the light from the background and the light passing through the object. The semantic difference is that one cannot speak of "the resolution of a detail" any more than (to quote from Zen) one can speak of the clapping of ONE hand. For resolution to be a meaningful term you need at least two details. One cannot, therefore, formally resolve "a diatom" - one can only resolve its texture of closely adjacent areolae. It is possible, however, to speak of the contrast between ONE detail and its background. 2) The second fundamental difference is physical, as indicated: resolution is a matter of angular separation, contrast one of amplitudes. If you wish to phrase this in terms of wave physics: resolution requires a certain minimum separation between the two diffraction discs your optics generate out of two details (areolae, "dots"), while contrast is a matter of the height of the diffraction discs if you plot their intensity graphically. 3) The third fundamental difference is physiological. In the end, it's our eye that detects the image. For two details to be observed, their images must fall on the retina far enough apart to generate separate neurological stimuli. For contrast to be perceived, the amplitude of the background light must differ from that of the light transmitted through the object by a certain amount so that sensory discrimination becomes possible for us. Strict separation between resolution and contrast is helpful and it can be illustrated by examples unrelated to microscopy. 1) Look at the stars, at a dark night. Whether you can resolve closely adjacent stars depends on your visual acuity (the ophthalmologists' visus). This visual acuity is not altered in any way when the sun rises, but the stars drown in the background light. No contrast = no image. 2) The resolving power of a TV set is totally fixed: vertically by the number of lines (somewhere over 500 in the USA if I'm not mistaken, over 600 in Europe). Horizontally it is fixed by the pixel size of the screen. Look at a TV screen with a magnifier. Now turn the contrast control fully counterclockwise - there's nothing left to resolve. To return to Stoermer's original notes. The pitch black shadows are not the results of phase-contrast or DIC. What I referred to is examination of a heavily silicified diatom in a high RI mountant, in completely ordinary brightfield without any contrast enhancement. Try Triceratium favus in naphrax, for instance. Now an optical test to show that mountant RI affects contrast, not resolution. Take a piece of copper wire (electricity) and hold it against a bright background. You see a maximum amplitude difference. A glass rod held up against the background gives a smaller amplitude difference, but you can see it (difference in RI between glass and air). Now dip the glass rod into immersion oil and hold it up against the light. It vanishes: contrast is zero because the RI's are equal. Because ONE glass rod does not produce an image on our retina, two glass rods separated by whatever distance will not do so either. Resolution is irrelevant here because there are no images to be separated. We should remember that the physics of resolution were elucidated a century ago. Abbe's work has not been refuted, neither has that of other 19th century physicists like Rayleigh or Airy. In other words: we have a corpus of scientific data here that has stood the test of time. Since then, refinements have been added: Abbe did not take complete account of the physiology of perception and this was updated by Hartridge in the Fifties. Also, one has to consider the degree of coherence of the light, there are slight differences between self-luminous and non self-luminous details etc. But basically, Nelson's formula defines resolving power of the microscope. Contrast led to a flurry of studies when contrast enhancement became possible, late Fourties, early Fifties. A venerable but superb book: Bennett, Osterberg, Jupnik and Richards: "Phase microscopy", Wiley, New York 1951. What is clear, then, is that our discussions cannot touch upon anything really new. For physicists, this issue is well-explored terrain. Now here comes an argument: if mountant refractive index would determine resolution, the literature should contain innumerable references to a formula that shows the relation between RI and resolving power. I herewith offer the sum of $ 100.- (one hundred US dollars) for the first reader who sends me a formula expressing resolving power as a function of mountant RI, in the form of a Xerox of the publication, of course. Date of receipt VIA SNAIL MAIL, not E-mail, (to ensure authenticity) will be decisive in the granting of this award.