Extreme Macro - in a slightly different way


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Stamp photographed with Tamron SP 35-80mm (Model 01A) lens and with same lens plus Plössl 6mm eypies using eyepiece projection.

Magnification ratios are 1:2.5 and 4.5:1 respectively


If you are interested in macro photography, chances are that your experiences have come something like this:

You started out with a standard lens and added some screw-on macro "filters" (actually not "filters" but positive lenses that made the focal length of your standard lens shorter and thus, permitted you to come closer to your subject and view it under a larger viewing angle); next step was to add extension tubes (or bellows) and at some point in time you got the desire for a dedicated macro lens.

Now, what differentiates a "macro lens" from an ordinary lens of the same focal length? Well, optically they differ  in principle ---- not at all. To see that, let us take a look at the "workings" of a photographic lens:


figure 1

Your subject is situated at a distance "s" from the optical centre of your photographic lens with a focal length "f" and forms a picture at the film/sensor plane at distance "b" from the optical centre. No matter whether a wide angle, a telephoto, a normal, a dedicated macro lens there is a simple relation between these parameters that must be obeyed:
1/f = 1/s + 1/b
and the scale of reproduction, "m" (the difference between the actual size of your subject and that of your image) is seen directly from the principle of equidistant triangles as
m = b/s or, using the above relation, m = f/(s-f)
You see that if s equals 2*f then so does b and we have m=1. If s becomes smaller than f then b becomes negative, meaning that no image will be formed. But the smaller s becomes down towards f the larger will b become and so will m. Your image will grow and grow in size and eventually become greater in size than your actual subject - you are in the realm of Extreme Macro, which by definition is m > 1.

But you also see, that the distance b from the lens to the film/sensor plane grows and grows. This is where the extension tubes come into play: They simply permit the lens to be moved sufficiently away from the film/sensor plane to produce a focussed image in accordance with the above, simple relations.

A dedicated macro lens does not differ optically from any other lens in that respect, but mechanically is is so constructed that the lens elements may be moved further away from the camera than is normally the case - it has, so to speak, a variable extension ring built into its focusing mechanism.

Dedicated macro lenses typically provide magnifications of m = 0.5 (conventionally stated as 1:2) or m = 1 (stated as 1:1). Now comes the desire to venture into Extreme Macro. What to do?

The first obvious thing is to add a teleconverter. A teleconverter is a negative lens - i.e. it cannot form a picture by itself but it can bend the rays from your photographic lens and effectively increase the focal length. as shown in the diagram below:


figure 2

The two sets of optics have the same focal length but the front lens (group) in the lower system has a shorter focal length. For example, the upper example could be a sketch of a 100mm lens and the lower on of a 50mm lens with a 2X tele converter ("TC"). If this lower sketch represents a 50mm macro lens, the TC will then double your magnification - without you having to move your lens closer to your subject.

But if you want even more magnification, you are back to using extension tubes, bellows and reversal rings and the larger magnification you want the closer you have to move once again towards your subject until the front element almost touches that (and also excludes most of the ambient light light that may fall on the subject).

Or does it have to be so?

I don't think so. I think/hope that I have found a solution to the problem of increasingly shorter subject-to-lens distances by borrowing an old principle that is very well known in astrophotography for achieving large, effective focal lengths in excess of what can practically be obtained with Barlow lenses (the astronomical telescope's' equivalent of the camera's teleconverter ).

That principle is called EYEPIECE PROJECTION:


figure 3

If you consider the above diagram, showing the principle of eyepiece projection, you will see that it somehow resembles a mix of the two foregoing diagrams. Only, rather than having a combination of a positive (image forming) and a negative (non-image forming) lens, we here have two positive, image forming lenses combined.

Now, this also means that we can apply exactly the same formulae as above for the two lenses, one after the other:

m (small blue object image - intermediate image) = b/s = f/(s-f)
M (Large blue arrow - final image) = B/X = F/(X-F)
And we see that by

a) choosing an eyepiece with a suitable focal length "F", and

b) varying the distance, "X" of the eyepiece from the physical image of the photographic lens,

we can increase the total magnification (substantially as we shall se) without changing the object-to-lens distance (significantly or not at all). At the end of this page, we shall see some numerical examples using actual lenses and eyepieces, but now to



When you get an idea like this and want to try it out, don't rush out and by expensive components; rather try out the idea with such bits and parts that you may have and convince yourself that your idea is not just bright - it is also doable!!! (If not, you may back out in time, richer in experience and not too poor after buying to many, after all, useless parts)
So, I took what I had, and here's what I got so far.

figure 4

The "heart" of my macro-eyepiece set-up. From left to right: Tamron Adaptall-2 M42 Custom Mount for Pentax; Pentax M42 extension tube; Marexar M42 extension tube with inner diameter adapted to fit 1.25" eyepieces; ASTRO Plössl eyepiece: two PK extension tubes to create the desired projection distance, c.f. figure 3 above. The foremost PK tube is fitted with a Pentax M42 to PK adapter (not seen in the photo). A slightly more flexible set-up, using bellows, is shown in Figure 11 below.

figure 5

Eyepiece centred in the coupler made up of the components shown in Figure 1


figure 6

Eyepiece coupler assembled.

Leftmost is the Tamron Adaptall-2 Custom mount that couples to my Tamron SP 35-80 mm f/2.8-38 (Model 01A).

The rightmost Pentax Extension Tube couples to my Pentax DSLR (K200D)


figure 7

Tamron Model 01A, Eyepiece coupler and Pentax K200D assembled.


figure 8

Tulip as photographed near closest macro-focusing distance with Tamron Model 01A alone on Pentax K200D



figure 9.a

figure 9.b

Stamens of same tulip photographed at same distance with Tamron Model 01A + Plössl 9mm + Pentax K200D.

a: Single exposure; b: Stack of 10 images in CombineZM


figure 10

Not too interesting for practical purposes, but the macro-eyepiece-projection set-up retains it's ability to focus at infinity. Here a chimney photographed with the Model 01A lens at 80mm + Plössl 6mm eypiece yielding an effective focal length of 900mm. Inserted is a 100% crop of the chimney taken with the Tamron lens alone at 80mm F.L.

figure 11

In principle the same set-up as in Figure 4 above. Only, here one PK extension tube is replaced by a Pentax M42 bellows for added flexibility. This permits continuous variation of the magnification ratio over a quite large range - and without the need to move camera and tripod. Fine-tuning of focus is permissible (within that range) by means of the lens' focusing mechanism alone. (Ultimately you may have to move the camera a bit).

figure 12

Next Target: Viola Cornuta (I believe) having very small flowers some1˝-2 cm in diameter


figure 13

Ready to shoot. Pentax K200D + Plössl 9mm + Tamron Model 01A. Note the generous working distance.


figure 14

Result(1): Oooh. Was it THAT kind of a violet?!?!

Single exposure with a magnification ratio around 2.25:1


figure 15

Result(2): 4 images stacked in CombineZM. Same set-up and magnification ratios as in Figures 14 and 13 above.

The distance from the centre of the "flower" to the V-shaped slot between the "petals" at right is about 7 mm.

Some numerical examples
As promised in the beginning, here are a few numerical examples based upon the lens and eyepieces actually used in the foregoing examples. First, let us take a look at the
Example 1: Tamron SP 35-80mm CF Macro (Model 01A) lens alone:
I have no information about where the optical centre might be in that lens; (it would be unwise to assume that it is in the physical/mechanical centre of the lens consisting of several elements and groups).

But I can measure the position of my sensor inside the camera and thus, the distance from my subject to the camera. At 80mm focal length and closest focusing distance I find this distance to be close to 268 mm, which is then the sum of s and b in the formulae above.

  • b+s = 268 (as measured)

  • 1/s + 1/(268 - s) = 1/f (from 1/f = 1/s + 1/b)

For a prime lens, the rest of the computation would be easy with a known, fixed focal length and lens groups moving in fixed positions relative to each other. But here we have a zoom-lens where the front focus group moves very much relative to the back master group, and I have no real idea what the focal length is at the 80 mm setting at closest focus.

Here, I have to rely on information from the brochure and my own control measurements:

The brochure tells me that the closest focusing distance is 10.6"  and since 1 inch is 25.4 mm this is 269 mm - check and OK.

The brochure also tells me that the magnification ratio is 1:2.5 and this I can check also - simply by photographing a ruler and see how it covers my sensor, which on my Pentax K200D is 23.5 mm by 15.7mm. And I have convinced myself that this statement is also true to such an extent that I may use that value. This way I have for my particular (zoom) lens:

  • b + s = 268

  • m = b/s = 2.5 - i.e.: b = 2.5*s

Solving for this, I get s= 76.57 and  b= 191.43. Now comes the interesting (in this case) part:

  • 1/f = 1/b + 1/s = 1/76.57 + 1/191.43

This results in f = 54.7 or, shall we say, 55 mm within the uncertainties given!

It is by no means unusual that zooms "creep" in effective F.L. at close range, but it is a fact hidden and a number usually never provided by the manufactures. Anyway, now I have all the numbers and geometric dimensions I need in order to proceed with the design as per Figures 4, 6 and 11 above.

Example 2:Tamron Model 01A + Plössl 9mm:
To begin with, I have a "magnification" of m = 0.4 from the Model 01A itself. Suppose now, that I would like - for a start - to have a magnification around 2.5 for my combined system. Then the eyepiece projection must provide me with a magnification of 2.5/0.4 = 6.25 and that then readily tells me (using the symbols from Figure 3 above):
  • M = 6.25 = 9/(X - 9) which leads to X = 10.44, and further

  • 1/F = 1/9 = 1/10.44 + 1/B leading to B = 65.25

In other words, I have to place my eyepiece such that the optical centre (which to a very good approximation is at the flange where the eyepiece is supported in the telescope's focusing rig) is situated a good one centimetre behind the image formed by the prime lens and use bellows or extension tubes to accomplish a distance of some 6.5 centimetres from the eyepiece centre to the camera sensor.

You may have other eyepieces of different focal lengths and/or different "ambitions", but these simple formulae give one a very good foothold as dimensional guidelines when one starts putting bits and pieces together as I have done here.

Example 3: Exchanging Eyepieces:
Let us now exchange the 9 mm Plössl with a 6mm parfocal eyepiece without changing anything else in the example above to begin with and see, where that takes us. ("Parfocal" for a set of eyepieces means that the optical centres will be in the same position when I exchange one eyepiece with the other).

For the eyepiece I then have B (c.f. Figure 3 above) = 65.25 mm and F = 6 mm from which I can calculate X as

  • 1/X = 1/6 - 1/65.25, which gives me X = 6.64 mm

Now, in the example above, the image formed by the camera lens lies 10.44 mm from the position of the optical centre (which I have not changed) of the eyepiece. Thus, I have to bring the image formed by the lens a further 3.80 mm away from that lens. Using the numbers I found in the first example (unrounded here in order not to involve too many rounding errors), the situation is such that the following condition must be fulfilled:

  • 1/54.69 = 1/s + 1/(76.57 + 3.80) and hence, s = 171.16 mm

And the resulting magnification?

  • m = 54.69/(171.16 - 54.69) = 0.47
  • M = 6/(6.64 - 6) = 9.38

  • M(Total) = m*M = 4.4

Thus, by reducing the focal length of my eyepiece by 33% and nudging my setup about two centimetres closer (from 19 cm to 17 cm as measured from the optical centre of the lens) I have achieved a 176% increase in magnification.

Had I had an eyepiece coupler - of the type frequently used in astrophotography - where the eyepiece may be moved some centimetres forth and back inside the coupler, I wouldn't have had to move my set-up at all. As you see, it takes a movement of just a few centimetres of the lens relatively to the subject but only a couple of millimetres movement of the eyepiece relative to the lens in order to bring the subject into focus once again at this significantly increased magnification.

Example 4: Stretching the Bellows:
As a final example, let us revert to example 2. Leaving the PL 9mm in its coupler we shall extend the bellows shown in Figure 11 (or add more extension tubes) such that the distance from the optical centre of the eyepiece is increased from the 62.25 mm in Example 2 to 100 mm.

Doing exactly the same thing as in example 3, we calculate the re-positioning of the lens relative to the subject in order to bring the subject in focus once again at the sensor plane. The figures now become (ref. the symbols used in Figure 3):

  • 1/X = 1/9 - 1/100 giving, X = 9.89 mm

The shift in X relative to Example 2 is then 10.44 mm - 9.89 mm = 0.55 mm which is also the increase in b required in order to get the image from the lens itself in the right place. Thus:

  • 1/s = 1/54.69 - 1/(76.57 + 0.55), giving s = 188.04 mm

In Example 1 and 2 I had the lens-centre-subject distance at 191.43 mm. In other words: Even though I have extended my bellows by about 3.8 centimetres, I only have to nudge my lens about 3.4 millimetres closer to the subject.

And the resulting magnification this time???

  • m = 54.69/(188.04 - 54.69) = 0.41
  • M = 9/(9.89 - 9) = 10.11

  • M(Total) = m*M = 4.1

figure 16

Quick-and-dirty photograph of same stamp as in the opening image (100% crop from that image inserted for comparison). This time with a 9mm Plössl and the bellows extended some 7 cm from the position seen in Figures 11 and 13. The resulting magnification is around 5 while a very generous working distance is being retained.

Concluding remarks (as for now) 2011-04-03
Most of the above should be seen essentially as a proof-of-concept. Obviously, there is both room an need for improvements.

No doubt the most important one is that of the choice of eyepiece - I do take it for granted that everybody considers a quality photographic lens a self-evident must for any kind of macro photography.

But the eyepiece then? Such comes in many varieties and with hugely different price tags. One should not consider a high price as adequate guarantee that the quality is right for this particular purpose because the trend in astronomical eyepieces are now to a large extent for large apparent field of views (AFOV) which is fine for visual observing but not necessarily needed (or the very best?) for photographic work. Remember, one does not need a lot of glass to capture a small part of the image formed by the photographic lens and then project that part over some relatively large distance as compared to the FL of the eyepiece..

I believe that a good "old-fashioned" quality orthoscopic eyepiece, optimized for planetary photographic work, with an AFOV in the 40-45 degrees range and an F.L. around 10 mm will be fine for this application. I may become wiser, but this is the path I intend to pursue.

Another convenient improvement I have already touched upon, namely the use of a dedicated eyepiece coupler that will allow for sliding the eyepiece forth and back inside the integrated coupler-tube-bellows system. That would ease re-focusing with variations in the extension of the bellows greatly.

And there are....

....well already now, with what I just have, I thinks there are some flowers and insects waiting!

Addendum (2011-05-17)
I haven't got the "ultimate" orthoscopic eyepiece yet, but I managed to find an old, yet brand new (ca. 1980-type in unopened box) eyepiece projection adapter of the sliding eyepiece type, (which unfortunately seems to be quite rare nowadays). Go to page 2 to take a closer(!) look......

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Copyright © 2011 - Steen G. Bruun