Digital Stereo Macro Photography
Page 1: BASICS

All modern cameras can focus close-up, but macrophotography demands more magnification than close-up photography.

If a 24mm vertical object is too tall to fit in the camera viewfinder, you are taking a macro photograph.

Separating macrophotography from close-up photography by a magnification value may seem arbitrary, but at least 8 factors become important in 3D macrophotography, which are often neglected in close-up photography:

1. Converging the camera axis (toe-in) as magnification rises. Otherwise the horizontal angle of view becomes lower, which is not always desirable on modern letterbox shaped screens.
2. Using a smaller digital sensor to help overcome low depth of field. (Increased 35mm conversion factor: C.)
3. Focus stacking to further increase the depth of field.
4. Camera shake is magnified and camera macro stands or tripods become important
5. Light loss at small f numbers causes problems and flash becomes more useful; both for bright light and stopping movement.
6. The lens gets very close to the object (reduced working distance) which frightens live insects and leaves little space to get the lights in.
7. The stereo base drops so that two lenses will not fit side by side. No problem for single camera macro stereo but involves a mirror box for two camera macrophotography.
8. In close-up 3D photography, a maximum distance, m, of twice the nearest (2n) works fine. But in the macro range it becomes necessary to drop the thickness to get m less than 2n, or Maximum Acceptable Deviation (MAD) is exceeded on a small computer screen.

The role of mathematics becomes more significant in macro photography, but many people just play around until the image on the camera live screen or view-finder looks right and ignore the maths.

The definition of macro photography in the digital age has changed from reproduction ratio in the camera (of more than 1:1), to the total magnification on the final image.

According to Wikipedia, (2011), digital macro photography means a total magnification of at least life size on a 150x100mm print (6x4 inch, which is the common post-card size).

Defining macro photography as life size on a postcard is much less demanding than the old 35mm film requirement. You can get away with a reproduction ratio, in a 35mm sensor size digital camera, of only 1/4 the old standard.

35mm frame magnification to reach 100mm print height = 100/24 = 4.2

Reproduction ratio [1/4]
  * Frame magnification [4.2]"
     =  Total magnification of [1.05]

Digital macro photography definition

Macro photography on this web site means:
total magnification on a postcard of more than 4.2

This is equivalent to the old film-based definition.

It can be simplified to:

If you photograph an old 35mm slide and it gets too big to fit on your camera screen, you are moving from close-up photography to macro photography.

or, the same thing:

If a 24mm vertical object is too tall to fit in the camera viewfinder, you are taking a macro photograph.

Reproduction ratio

Reproduction ratio is magnification in the camera.

A common definition in the days of 35mm film cameras said macro photography required a magnification on the film of more than life size (>1).  Many dedicated macro lenses have the reproduction ratio marked on the rotating distance scale. So once you wound the focus ring out to more than a magnification of 1 (1:1), you were performing macro photography.

Frame magnification

Frame magnification is magnification from the sensor up to the final print (or computer, or projection screen). Frame magnification in film days was done in an enlarger.

Frame magnification from a 35mm film frame (36x24mm)
to a 150x100mm print (6x4inch or postcard size) is:
150/36 = 4.2

Total magnification

[Total magnification] equals
[reproduction ratio] times
[frame magnification] -----(1)

If the reproduction ratio in the camera was 1:1, which was the old film limit for macro photography, total magnification on a postcard was 4.2. That is where my definition of macro photography; being more than 4.2 magnification on a postcard; comes from.

Rearranging to find the desired reproduction ratio:
[reproduction ratio] =
[total magnification] /
[frame magnification] -----(2)

Small sensor correction, C.

In general, if the conversion factor from digital camera to 35mm full frame sensor is C:

Required frame magnification =  
C*[35mm frame magnification] ----(3)

So, with a small digital sensor, there is less magnification in the camera and more magnification of the frame to reach the same final magnification on the print.

C for a 4/3 digital format (Panasonic, Olympus) is 2.

C for a Canon Kiss camera is 1.6

[Reproduction ratio required to fill the small sensor]
=
[35mm reproduction ratio] / C

With your chosen camera and viewing system, the frame magnification may become a constant which only has to be computed once.

Cropping

However, if you crop the image to a smaller size, frame magnification has to increase to once again to fill the viewing screen or print. Cropping is equivalent to sophisticated digital zoom. When modern cameras with large pixel numbers are used, cropping, combined with increased frame magnification, is a valid method to obtain higher magnification. In fact it is a desirable method, since it improves the depth of field.

Computer frame magnification

I no longer bother with prints and see digital photographs on a computer, or projected.

Computer monitors come in all sizes, but my favourite is 295mm high. So macro photography on my 295mm screen means a total magnification of:
295/24 = 12.3 times, or more.

You can easily work out the magnification required for macro photography on your own monitor.

Small digital camera sensors

Digital camera sensors can be less than full 35mm size (24 x 36mm). If the sensor is half the size of a full 35mm frame (as it is for the common 4/3 digital format favoured by Olympus and Panasonic) then you need only half the 35mm camera magnification to fill the sensor. But frame magnification from the half size sensor to postcard size has to be twice as much. [4.2 x 2 = 8.4]

The 35mm camera equivalent is always quoted when you buy a digital camera. For the 4/3 format, C = 2. That means a 50mm focal length lens on a 4/3 format camera is equvalent to a 50 x C = 50 x 2 = 100mm lens on a 35mm camera.

Required reproduction ratio in the camera to get 4.2 magnification on a postcard from a 4/3 digital camera sensor is (equation (2) and (3)):
4.2 / 8.4 =  0.5

So, when I use an old macro lens from 35mm film days on my Olympus camera, I set the magnification to 0.5 (1:2) to move from close up to macro photography.

Advantage of a small sensor

The advantage of a small digital sensor in macro photography is

1. increased depth of field, which improves as the reproduction ratio falls.
2. Bigger working distance, from lens to object. (The smaller sensor makes the lens behave as a telephoto lens).

The disadvantage of a small sensor is more noise.

However, the biggest problem faced in macro photography is a small depth of field, followed by a small working distance making it difficult to get the lighting in place and frightening insects. The increased noise is a small price to pay for reducing these problems.

BUT focus stacking is a far better way to increase depth of field and reduce diffraction blur, at the price of much greatercomplexity, and a rise in noise. So if you prefer a big sensor for high magnification, low noise stereo, you had better learn focus stacking. And if you want to understand all this, you had better keep reading on!

Supplementary lens ("diopter")

Extra magnification comes from using a smaller focal length. A cheap way to drop the focal length (F) is to add a magnifying glass in front of the macro lens. Such lenses are sold as supplementary lenses, sometimes called "diopters" on the internet but that seems a funny name to me

It is better to use an achromatic lens (no colour aberration, achieved by using at least two different glasses in assembly).  Achromatic lenses are easy to obtain now that film cameras are obsolete. Get hold of an old but high quality achromat from a discarded camera.

Currently I am experimenting with a Mamiya medium format lens screwed off the main lens, so the diaphragm is no longer in the system. The focal length of this combination of achromatic surplus glass and macro lens has to be measured. See the next column for how I do this.

Computing the focal length of a macro lens plus a supplementary lens

Various formulae are available for  computing the effective focal length of a combination of lenses, and need various corrections.

I favour measuring the focal length under the conditions of macro photography, by-passing complex corrections. I do this by measuring the magnification power of the lens combination.

1. Set your macro lens focus on infinity
2. Add on the supplementary lens.
3. Mount the macro lens + supplement on a long extension tube of measured length.
   (E)
   and fasten to the camera.
4. Focus on and photograph a ruler engraved in millimeters.
5. View the ruler image on your computer.
6. Measure the height of the image frame
   (H)
7. Measure the length of a section of the ruler on the image,
   (A)
   and divide by the number of millimeters in that section,
   (a)

Total magnification onto the computer screen is:

M2 = A / a

Frame magnification, M1, in 35mm terms is:

M1 = H / 24

Reproduction ratio in the camera in 35mm equivalents is:

R = M2 / M1

= 24 A / H a

The focal length of your lens combination in 35mm equivalents, F, is:

F = E / R

F = H a E / 24 A

Magnification and stereo base

The simple pin-hole camera formula for stereo base, with infinity in the picture:

B = n P / F

can be simplified, once the magnification is known,

M = F / n

to:

B = P / M

B = Stereo base
P = Parallax desired (usually 1.2 for stereoscopes)
M = Magnification
n = Distance to nearest object.
E = length of Extension tubes.

For a reproduction ratio of 1:1, B = 1.2mm.

But infinity is not included with a close-up photograph

Oh dear, I thought the above formula was improbably simple!

Including infinity in close-up stereo photography is too much of an eye-strain. Usually the maximum distance (m) is less than twice the closest distance (n) for a satisfactory macroscopic 3D picture, which the general population can view.

B = P / (Mn - Mm)(a)

B = stereo base

Mn = Magnification at nearest distance (n) where:

Mn = ( F + E ) / n (b)

Mm = Magnification at maximum distance (m) where:

Mm = ( F + E ) / m(c)

Combining equations a, b, c:

B = P / ( ( F + E ) * ( 1 / m - 1 / n ) )

B = P mn / (m-n)   ( 1/F - ( m+n ) / 2mn )

The Bercovitz formula comes into its own in macroscopic 3D. The simple "pin-hole" formulae do not allow for lenses which focus close by moving away from the sensor. Pin-hole formulae work pretty well for objects further away, where the focus movement is rather small compared with the lens focal length.

The formula requires you to measure the distance from the lens first nodal point to the nearest object (n) and to the furthest object (m). That might be pretty easy.

But where is the first nodal point, especially if the lens is focusing internally?

Pin hole formula for stereo base gives same answer as Bercovitz

Modification of the pin-hole formula to include magnification matches the Bercovitz formula.

R = 1:r + E / F

R is magnification in the camera, or Reproduction Ratio.
1:r is magnification marked on the macro lens
E is length of extension tubes
F is lens focal length
n is the distance from the first nodal point of the lens to the object.

n = F ( 1 + 1 / R)

The magnification formula means the step in the Bercovitz formula where the extension is computed can be left out, because extension is being measured directly and the sometimes difficult to measure nearest distance (n) is being computed instead. The formula which does that is given later.

How do you measure R (reproduction ratio) in a simple way?

1. Set up the camera with extension tubes and supplementary lenses you intend to use.
2. Aim at a mm ruler running vertically in the frame
3. Measure the frame height in the viewfinder (or on the camera screen using LiveView).
4. Working in 35mm  equivalents, where the frame measures 36 x 24mm:

(35mm equivalent Reproduction Ratio) = (measured height) / 24

The viewfinder height may be slightly smaller than the true frame height. Try not to get obsessive about that!

There are a couple of corrections to apply to this.

True reproduction ratio

The true magnification is needed if you are using a macro lens with 35mm reproduction ratios marked on it.

True reproduction ratio = (35mm equivalent) / C

C = 35mm conversion factor. (2 for 4.3 format digital cameras, ...etc)

Cropping factor

1. You do not want to fill the frame if you aim to convert to 16:9 aspect ratio by cutting a slice off top or bottom of the picture.
2. If focus stacking is to be used, there is a loss of picture around the edges, or deformity at the edges (especially with CombineZ) but Zerene stacker also needs a safety margin, which is cut off later.

That means the 35mm equivalent frame actually used is less than 24mm. So in calculating the in camera magnification (reproduction ratio) you have to allow for a smaller frame size. Say, 20mm, but experience with your rig teaches you how much needs to be cut off to get the correct final magnification factor.

Starting with the object size

Trial and error by screwing the extension tubes is a pain (it is a lot easier with bellows).

So, measure how tall your subject is. I use a plastic dial micrometer.

Add on the additional frame height required for the cropping factor.

R = object height + cropping margin

Then you can compute the extension tube length to fit your subject without a lot of messing about by trial and error.

E = R F / C

E = length of extension tubes required
R = object height + cropping margin
F = focal length of lens
C = 35mm conversion factor

Magnification with extension tubes

Higher levels of magnification require winding the lens out until it focuses close, but only dedicated macro lenses will get you up to 1:1 magnification in 35mm equivalent terms.

More magnification requires supplementary lenses (diopters) in front of the lens or, my favourite method, extension tubes.

E = the length of the extension tubes between the camera and the lens,

e = extra extension gained by winding the lens focus out beyond the infinity position.

F = focal length of the lens

R = reproduction ratio (magnification in the camera)

R = ( E + e ) / F -----(4)

More extension and/or a smaller focal length increases the magnification.

The first decision is how much magnification you want in the camera (R).

Now arrange the required lens focal length (F) and the extension (E) to reach this magnification, using equation (4).

OR just mess about changing the extension tubes and winding the lens focus ring until magnification looks right on the camera view-finder. This non mathematical method is easier with a bellows than with extension tubes.

Example

The extra magnification from winding out the lens is not always so easy to measure.

Some macro lenses wind the lens out both in front of the focus ring and behind it. My favourite lens:
Nikon 55mm Micro-NIKKOR
does just that, to reach a maximum reproduction ratio of 1:2 (half size, which as we have seen is macro size on a 4/3 digital camera). The posterior lens elements actually move backwards, (to keep the field perfectly flat), making the extension a bit of a guess, because the nodal points of the lens are moving as it focuses. But the lens reproduction ratio (r) is given on the lens focus ring (1:2 = 1/2 size) and so the total reproduction ratio (R) can be computed:

R = 1:r + E / 55

Focusing with extension tubes

Focusing a camera in the close-up range is simply done by turning the focusing ring, or using auto-focus, just the same as ordinary photography.

Focusing in the macro range is not done that way.

An extension tube set has several lengths, which can be coupled together for various magnifications, or you can combine two sets of tubes for even more magnification.

Alternatively, use a macro bellows system, which usually includes a focusing stage.

At high magnification, the lens focus ring (or a variable bellows extension) no longer works as a useful focusing system. Winding out the lens or increasing the extension increases the magnification, but makes only slight difference to the focus.

Focusing stage

Focusing at high magnification is done by moving the whole system:
camera + extension tubes + lens,
backwards and forwards until focus is achieved. This is best done using a screw manipulator mounted on a tripod.

This works well in the studio, or on the forest floor, but is not so easy for insect photography in the field.

Hand held focusing

There is a limit to how much focusing you can do hand-held, but experts manage it, especially when using flash (which fires so fast it overcomes camera-shake).

It is even possible to arrange focus stacking hand-held:

1. Put the camera on motor drive (rapid sequence images).

2. Get the focus right.

3. Start the camera and gently move forwards and back to vary the focus. This works better if your elbows are supported on a bolster.

4. Subsequently choose the best focus. Or choose several different foci and perform focus stacking on the images.

5. For stereo, this must be done a second time, after shifting the camera side-ways; which works on a fungus, but not often on live insects or flowers blowing in the wind.

6. For macro stereo, at high magnification, it is better to use a mechanical rig. This works fine on plants, but frequently means you can only work with dead or frozen insects.

Parallel optical axis:
Stereo window setting causes image loss

With parallel cameras, the diagram shows that at 1:1 reproduction ratio (magnification of 1 in the camera), the image width which has to be cut off to make the final stereo window is the same as the stereo base.

As magnification increases further, the final image width drops even more.

1:1 reproduction ratio occurs when the distance, n, from the first nodal point on the lens to the nearest object is equal to the distance from the second nodal point to the sensor. (F+E).

When the stereo image is set up during post processing, n usually becomes the distance to the stereo window.

For a full width stereo image you need to toe in the cameras and correct for keystone distortion during post-processing.

In close-up photography, a square picture is acceptable, a portrait format is useful for orchids and mushrooms, but a thin vertical image is not always so good.

The only way to get a macro, stereo image to fit a letterbox shaped computer screen is to toe in the cameras.