B I O G R A P H YChristopher Hammond(pictured) obtained hisMA at Cambridge Uni-versity, and his PhD inmetallurgy from LeedsUniversity. His researchinterests lie in the rela-tionships between the structure and prop-erties of metallic alloys in general, and tita-nium alloys in particular. His main areas ofexpertise are in polarised light microscopy,the interpretation of electron and X-ray dif-fraction patterns and crystallography. He isthe author of The Basics of Crystallographyand Diffraction (Oxford University Press,2001) and the Honorary Keeper of the coll-ection of 20th C microscopes in Oxford, UK.

Dr Julian Heath is the Editor of Microscopyand Analysis.

A B S T R A C TWe present a new set of symmetrical ray dia-grams of the optical pathways in trans-mitted, reflected and epifluorescence lightmicroscopes equipped with infinity-corrected optics. It is intended that the sym-metry and simplicity of these diagrams willaid both novice and experienced micro-scope users in their understanding of theprinciples of Köhler illumination and ofimage formation in the light microscopeand will explain the reasons why the correctset-up and alignment of the microscope is so very important for the production of optimal images.

A C K N O W L E D G E M E N T SWe are deeply indebted to Dr Peter Evennett for his valuable input into this project, and we would like to take thisopportunity to acknowledge his major con-tribution to light microscopy over the years.

K E Y W O R D S light microscopy, transmitted, reflected, flu-orescence light microscopes, optical path-ways, infinity-corrected optics, ray diagrams

A U T H O R D E TA I L SDr C. Hammond, Institute for Materials Research, University of Leeds, Leeds LS2 9JT, UKTel: +44 (0)113 343 2382 Email: c.hammond@leeds.ac.ukEmail(JPH): ma.teched@btinternet.com

Microscopy and Analysis 20(5):5-8 (UK), 2006

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I N T R O D U C T I O N The light microscope consists of an illumina-tion system before the specimen (object) andan imaging system after it. The optical compo-nents of the microscope comprise a sophisti-cated train of aberration-minimised multi-element lenses, prisms and beamsplitters thatare integrated with a light source and a set ofdiaphragms. Together, these elements providethe high-quality images that modern micro-scopists demand. However, neither the out-ward appearance of a microscope (Figure 1a)nor the to-scale optical schematics supplied bythe manufacturer (Figure 1b) are particularlyhelpful in providing useful information to theuser as to how the light microscope actuallyworks.

In geometrical optics, the pathways of lightthrough optical systems are demonstrated byray diagrams. Indeed, ray tracing is used in thedesign of the train of optical elementsbetween the light source and the detector. Raydiagrams are also essential in the teaching ofoptics and microscopy. They can provide aclear demonstration of the mechanism ofimage formation and, importantly for users oflight microscopes, they allow an understand-ing of the positions of the two sets of conju-gate (aperture and field) planes and the func-tions of the diaphragms associated with themwhich is essential if a student or user is toobtain images of optimum resolution, qualityand contrast.

But ray diagrams are not popular with stu-dents. (The late Professor Barer used to saythat one such diagram was enough! [1]) It iscertainly true that ray diagrams can appearvery confusing to both novices and even expe-rienced users and attempts to simplify theminto separate diagrams showing the ‘image-

Symmetrical Ray Diagrams of the OpticalPathways in Light MicroscopesChris Hammond, Institute for Materials Research, University of Leeds, UK and Julian Heath, Cambridge, UK

forming rays’ and the ‘illuminating rays’, orthe ‘orthoscopic’ and ‘conoscopic’ ray dia-grams in books on polarised-light microscopy[2], can only make things worse. A studentmay be forgiven for thinking that light pathssuddenly and mysteriously change simply byremoving the eyepiece or flipping in aBertrand lens.

Furthermore, when the light microscope isrepresented by a ray diagram, it is difficultusing ray paths to show an image magnifica-tion of say 1003 because, obviously, the imagewould have to be drawn 1003 larger than theobject and the imaging part of the ray dia-gram would need to be hugely expanded.

An elegant solution to all these problems isto draw the light paths corresponding to avery low (3-43) magnification and also showthe illuminating and imaging systems as sym-metrically related either side of the objectplane. Such a ray diagram was produced in1998 for the case of a light microscope withfinite (i.e. 160 mm) tube length-correctedobjectives [3]. Today, most new microscopesare designed with infinity-corrected opticalsystems, so a new set of ray diagrams is nowcalled for.

In this article we now present a set of sym-metrical ray diagrams of the optical paths intransmitted, reflected and epifluorescencelight microscopes equipped with infinity-corrected objectives. The diagrams show theimportant similarities and differences in theoptical trains of the three standard types ofmicroscope.

SYMMETRICAL RAY DIAGRAM FORTRANSMI TTED LIGHT MICROSCOPEFigure 2 shows a symmetrical ray diagram of atransmitted-light microscope with infinity-

Figure 1: (a) A standard upright light microscope with transmitted- and reflected-light illumination systems. (b) Schematic of the optical pathways.Images courtesy of Carl Zeiss UK.

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corrected optics.The first thing to observe inFigure 2 is the mirror symmetry of the illumi-nating and imaging optical components (rep-resented by simple lenses) each side of theobject plane: the condenser lens correspondsto the objective lens; the auxiliary lens corre-sponds to the tube lens; and the lamp collectorlens corresponds to the eyepiece lens. The sym-metry extends from the lamp filament (wavyred line) to its image which constitutes the exitpupil (aka Ramsden disc or eyepoint). It is atthis point, where all the pencils of parallel raysconverge, that the lens of the eye or camera is(or should be) placed. If not, then the mostconvergent pencils of rays will be cut off andthe image will be vignetted.

We will now follow the ray paths from justthree points on the filament: one in the centreof the filament, on the optical axis (the redrays) and two either side (the green and bluerays). First consider the rays emitted from thegreen point on the filament. Of course, therays spread out in all directions, but we havejust drawn three – two that just pass the outerlimits of the field diaphragm and one that isparallel to the optical axis. As we follow thesethree rays through the microscope we see thatthe action of the lamp collector and auxiliarylenses is to recombine or focus these rays toform an image of the green point on the fila-ment in front of the condenser. Hence, for allrays, an image (point by point) of the filamentoccurs and it is in the plane of this image of thefilament that the illuminating aperturediaphragm is placed under the conditions ofKöhler illumination.

The filament and its image are said to occurin conjugate planes (i.e. what is in focus in oneplane is in focus in the other). Again, tracingthe paths of these rays through the condenserlens and objective lens, we see that they arefocused in the back focal plane of the objec-tive lens, and, after passing the tube lens andeyepiece lens these rays are focused at a planecalled the exit pupil. In short, the exit pupil isan image of the filament. (In practice it is usu-ally demagnified and is best observed using a103 or 203 magnifier.) The filament itself andthe three planes in which it is in focus arecalled the aperture set of conjugate planes,marked A1-4 in Figure 2.

Now let us look at the pattern of light rays atthe illuminated field diaphragm. Notice thatthe light from the GRB points on the filament(the green, red and blue rays) is focused at dif-ferent points in this plane – the laterallyinclined rays are focused at its margins

Figure 2: Symmetrical ray diagram of a transmitted light microscope with infinity-corrected optics, showing the object in a reflection plane of symmetrywith respect to the optical components of the illuminating and imagingsystems and the field set of conjugate planes (F1, F2, F3, F4), and at acentre of symmetry with respect to the aperture set (A1, A2, A3, A4) ofconjugate planes. Three sets of rays (green, red and blue) arising from three separate points(G, R, B) in the filament illuminate the whole area of the object as a seriesof parallel pencils of light and are focused in the aperture set ofconjugate planes. The pupil of the eye is situated at or near the exit pupiland the lens of the eye produces the final image on the retina (or at theplane of the film or CCD detector in a camera, as shown in Figure 4).

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whereas the rays parallel to the optical axis arefocused in the centre. This means that the illu-minated field diaphragm is uniformly illumi-nated with light. It doesn’t matter whether ornot the green, red or blue rays are of equalintensity (i.e. that the light emanating fromeach region of the filament is of uniformintensity); if one set of rays is absent it justmeans that the uniform illumination will beweaker. This is the basis of Köhler illuminationand we can see (following the rays through asbefore) that the same principle applies at theobject itself, at the primary image and at theretina of the eye (or the film or CCD detector).These four planes – at the illuminated fielddiaphragm, object, primary image andretina/detector – are called the field set of con-jugate planes, marked F1-4 on Figure 2.

Now, having begun to understand the lightpaths, we can proceed to understand the func-tions of the illuminated field and illuminatingaperture diaphragms – for convenience wewill just call them the field and aperturediaphragms.

If we decrease the size of the fielddiaphragm then the rays will illuminate asmaller area of the object, i.e. this diaphragmadjusts the illuminated field. If we decreasethe size of the aperture diaphragm then asmaller area of the filament contributes to theillumination at the object and the angles ofincidence of the rays at the condenser will besmaller. However, the illuminated fieldremains the same. It is very important to con-vince yourself of this fact because the settingof the aperture diaphragm is of vital impor-tance in obtaining the optimum conditions forresolution and contrast. The sine of the half-angle of the cone of light illuminating theobject (multiplied by the refractive index ofthe immersion oil in the case of an oil-immer-sion objective lens) is called the numerical

Figure 4: Modification of the imaging pathways shown in Figures 2 and 5 for the case when using a film or CCD camera.The detector is placed to coincide either with the plane of the eye retina or the primary image plane, e.g. in adedicated side-mounted imaging extension on the microscope.

Figure 3: Extension to the ray diagram in Figure 2 showing an additional lamp collector relay lens which provides an imageof the filament in the plane of the illuminating aperture diaphragm. This arrangement is an option for theillumination systems of transmitted-light microscopes but is required for reflected-light microscopes.

aperture (NA) of the condenser. In Figure 2 thecondenser and objective lenses are preciselymatched – they have identical focal lengthsand numerical apertures and the object isplaced exactly one focal length from each lens.Notice the symmetry once again: light diverg-ing from points in the front focal plane of thecondenser are projected as parallel pencilsthrough the objective then focused again inthe back focal plane of the objective lens.

Correspondingly, the light diverging frompoints in the object are projected by the objec-tive lens as parallel pencils to infinity! Thefunction of the tube lens is to focus these par-allel pencils at the primary (or intermediate)image plane. The magnification M of the pri-mary image is thus determined by the ratioftl / fo and not by the magnification of theobjective lens alone. So when you see infinity-corrected objective lenses marked 103, thisvalue assumes a certain focal length tube lensto go with them.

A particular benefit of using an infinity-corrected objective and a tube lens is that thelight passing between them consists of para-llel pencils so any optical accessory, such asretardation plates, fluorescence filters, beam-splitters, etc., can be placed in this region with-out upsetting the optical aberration-correcting properties of the objective lens.

In practice, the focal lengths and numericalapertures of the condenser and objectivelenses are never precisely matched as in Figure2. In order to match the focal lengths wewould need a different condenser lens foreach objective. This is achieved automaticallyin the reflected-light microscope, as describedbelow, but for transmitted light we use thesame condenser (perhaps with a flip-top lens:in for high powers and out for low powers) fora whole range of objectives.

The optical design of condensers is therefore

something of a compromise. One ‘ideal’arrangement, which was used in the days of‘brass and glass’, was to use as a condenser anidentical objective lens ‘in reverse’. However,this also suffered the defect that, except forvery low powers, the front focal plane of theobjective/condenser lens was inaccessible.

A further reason why, in practice, the NAs ofthe condenser and objective lenses are rarelymatched as shown in Figure 2 is because thisdoes not provide the optimum conditions forresolution and contrast. As the NA of the con-denser is decreased (by decreasing the size ofthe condenser aperture diaphragm) resolutiondecreases but contrast increases. The optimumsetting (dependent on the specimen) is whenthe NA of the condenser is between 2/3 and4/5 of that of the objective. Decreasing it stillfurther not only results in loss of resolutionbut, worse, the introduction of false detail.

The explanation of all these effects belongsof course to the domain of physical ratherthan geometrical optics.

SYMMETRICAL RAY DIAGRAM FORR E F L E C T E D L I G H T A N D E P I -F L U O R E S C E N C E M I C R O S C O P E SFigure 5 is a symmetrical ray diagram of areflected-light or epifluorescence microscopeequipped with infinity-corrected optics.

For reflected light, the ray diagram in Figure2 may be considered to be folded twice over:first folded over in the plane of the object (sothat the illuminating and imaging opticalcomponents coincide), and second in a planeat 45o to the optical axis in the parallel-lightregion between the objective lens and thetube lens.

The geometrical result is shown in Figure 5.The plane of the 45o folding corresponds tothe position of a semitransparent beamsplitterreflector which admits light from the illumi-

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nating system at 90o to the major optical axis.Now we see that the condenser lens andobjective lens are precisely matched: the samelens functions as both a condenser and objec-tive lens. But there is one thing missing: theaperture diaphragm in the front focal planeof the condenser lens (now coincident withthe back focal plane of the objective lens). Anilluminating aperture diaphragm cannot beplaced here because it would restrict theimaging aperture to that of the condenser.Instead, the illuminating system must projectan image of the illuminating aperturediaphragm and filament into the back focalplane of the objective lens. In this way, as withtransmitted light, the aperture of the objec-tive lens can be adjusted independently of theaperture of the illumination system. The onlyconjugate plane upstream is at the filamentitself. However, since this is inside a lamp it isusually inaccessible (and the aperturediaphragm would get rather hot, unless thesource was an array of cool LEDs). The illumi-nating system therefore incorporates a fur-ther lens upstream, generally called a relaylens, which projects an image of the filamentinto this position. Such a relay lens is shown inthe illuminating system in Figure 5 and in theoptional extension to the transmitted lightray diagram (Figure 3).

The equal distances (twice the focal length)between the relay lens, filament and imagecorrespond to the special case of a magnifica-tion of the filament of unity.

Figure 5 explains a commonly-heard query:“Why are the positions of the field and aper-ture diaphragms reversed in reflected light?”The answer is: “Because the aperturediaphragm has leapfrogged one conjugateplane upstream.” Figure 5, and more clearly inFigure 3, show that the field diaphragm couldin fact leapfrog to a position just in front ofthe filament (i.e. the focal length of the relaylens). Which position is chosen is a matter ofindividual microscope design (indeed, some-times both are used) but the geometrical prin-ciples of all the designs are simple and thesame.

Figure 4 shows that the final image may berecorded on film or CCD detector either at aplane corresponding to the retina (cf. Figures2 and 5) or at the primary image plane. Thelatter configuration is often used in side-mounted dedicated camera extensions. (C-mount camera adapters usually incorporate alens system which reduces the size of the pri-mary image by a factor of 0.25 - 0.75.)

C O N C L U S I O NWe have produced a set of symmetrical ray

diagrams of the optical pathways in transmit-ted, reflected and fluorescence light micro-scopes equipped with infinity-correctedoptics. We hope that the symmetry and sim-plicity of these diagrams will aid both noviceand experienced microscope users in theirunderstanding of the principles of Köhler illu-mination and of image formation in the lightmicroscope and will explain the reasons whythe correct set-up and alignment of the micro-scope is so very important for the productionof optimal images [see 4-6 for further info].

R E F E R E N C E S 1. Barer, R. Teaching Microscopy to Medical Students. In:

Teaching Microscopy (1st Edn). pp78-92, MicroscopePublications, Chicago, IL, 1977.

2. Hallimond, A. F. The Polarizing Microscope. 3rd Edn. VickersInstruments, York, UK, 1996.

3. Hammond, C. A symmetrical representation of the geo-metrical optics of the light microscope. Journal ofMicroscopy 192(1):63-68, 1998.

4. Murphy, D. B. Fundamentals of Light Microscopy andElectronic Imaging, John Wiley and Sons Inc, NY, 2001.

5. Heath, J. P. Dictionary of Microscopy, John Wiley and SonsLtd, Chichester, UK, 2005.

6. Molecular Expressions Microscopy Primer website:http://micro.magnet.fsu.edu/primer/index.html

©2006 John Wiley & Sons, Ltd

Figure 5: Symmetrical ray diagram of reflected-light andepifluorescence microscopes with infinity-correctedoptics, showing the object in a reflection plane ofsymmetry with respect to the optical components of theilluminating and imaging systems and the field set ofconjugate planes (F1, F2, F3, F4), and at a centre ofsymmetry with respect to the aperture set (A1, A2, A3,A4) of conjugate planes. Three sets of rays (green, red and blue) arising from threeseparate points (G, R, B) in the filament illuminate thewhole area of the object as a series of parallel pencils oflight and are focused in the aperture set of conjugateplanes. The pupil of the eye is situated at or near the exitpupil and the lens of the eye produces the final image onthe retina (or at the plane of a film or CCD detector in acamera, as shown in Figure 4).