## The advantages of parametric design

I work primarily in OpenSCAD when making designs for 3D printing (and 2D designs for lasercutting). This means that instead of a WYSIWYG interface based primarily on using the mouse, my designs are all scripted in a programming language that looks a lot like C. This might seem a bit more difficult at first (and it is certainly less than ideal for some situations) but it makes for a pretty simple way to generate repetitive structural elements in basic flow control, i.e. for loops. Even more important, it means that I can substantially change a design by modifying the variable values passed to a function (called modules in OpenSCAD). For the sake of an example, take Lieberkühn reflectors for macrophotography. Lieberkühn reflectors are a classic illumination technique that have mostly fallen out of style in favour of more modern illumination such as LED or fibre-based lighting, but remains quite elegant and offers a few unique advantages. I have been working with these in conjunction with a few different lenses, and mostly with the help of a macro bellows. The bellows makes for variable working distances as well as magnifications, so the focus of one Lieberkühn will be the most effective only within a narrow range of macro-bellows lengths. Parametric designs such as the ones I create and work with in OpenSCAD allow me to change attributes such as the nominal working distance without starting each design from scratch. For example:

35mm Lieberkühn focus

30mm Lieberkühn focus

25mm Lieberkühn focus

20mm Lieberkühn focus

This approach has proven highly useful for me in terms of both creating highly customisable design and iterating to get fit just right. I’ll post results of my latest exploration of Lieberkühn reflectors soon after I receive the latest realisation in Shapeways bronzed steel.

## Teaser photomicrography

Here’s something you may not know about the old manual Canon auto bellows and macro lens: the threaded adapter that connects a 20mm f3.5 (or 35mm f2.8) macro lens to the bellows employs the same threading standard as the typical microscope objective, known as the Royal Microscopical Society standard, 20.32 mm diameter with a pitch of 0.706 mm per turn, dates back to 1896 when it replaced an earlier standard.

The impact of this design choice for macrophotographers is that one can use any standard microscope objective, adding a great deal of options for imaging with the auto bellows and potentially pushing the capabilities of bellows macro into photomicrography. This can result in some very short working distances, and the sterics of the objective and subject mean there won’t generally be a lot of room for illumination sources. I designed this simple 3D printed microphotography objective hood for use with bright transverse illumination such as from a fiber optic illuminator. You may be familiar with the type of lens flare that can arise from this illumination setup-typically a haze effect that decreases the overall contrast of the image while increasing the brightness, particular toward the middle of the image.

I took the images below through a 10X NA = 0.25 objective (on the right, with lens hood).

My camera battery is charging, no spare, and I don’t have a worthwhile illumination source handy to shoot proper test shots (these were illuminated with a handheld torch). Nonetheless, I couldn’t resist taking these half-portraits, and I’ll post them here as a teaser. I will use these gorgeous metallic bees for Lieberkühn tests as well. For now, enjoy these Osmia aglaia photos while my camera charges.

## Quantitative comparisons of macrophotography with and without Lieberkühn reflectors

In order to quantitatively examine the effect of the the 3D printed Lieberkühn reflectors I described previously, I came up with two image quality metrics relevant to their use, both measured on the “dark side” of the image subject. The metrics we will look at today are average intensity and, as a measure of contrast, the standard deviation of pixel values on a line trace.

I’ll be using the Megachile photo from the previous post for these analyses.

The first line trace begins at right eye and extends back behind the wing:

If we plot these values together, we see that the photo taken with the Lieberkühn (values in black) is brighter and brings out a lot more detail, while the photo taken without is relatively flat and dark. We see similar results for second and third traces, taken across the tegula and along the wing.

If we compare the average values:

octave3.2:25> mean(RE523(:,2)) %with Lieberkühn, right eye trace
ans = 102.00
octave3.2:26> mean(RE524(:,2))%w/o Lieberkühn, right eye trace
ans = 54.093
octave3.2:28> mean(AT523(:,2))%with Lieberkühn, trace across tegula
ans = 81.553
octave3.2:27> mean(AT524(:,2))%w/o Lieberkühn, trace across tegula
ans = 51.288
octave3.2:29> mean(W523(:,2))%with Lieberkühn, across the wing
ans = 103.85
octave3.2:30> mean(W524(:,2))%w/o Lieberkühn, across the wing
ans = 53.045

We see that taken together, the averages of the plots from the photo taken with the Lieberkühn are about 80% brighter than those without.

mean(Lieberkühn)/mean(no Lieberkühn) = 1.8142

octave3.2:56> std(RE523(:,2)))%with Lieberkühn, right eye trace
ans = 20.316
octave3.2:55> std(RE524(:,2))%w/o Lieberkühn, right eye trace
ans = 7.3926

octave3.2:54> std(AT523(:,2))%with Lieberkühn, trace across tegula
ans = 17.737
octave3.2:53> std(AT524(:,2))%w/o Lieberkühn, trace across tegula
ans = 13.227

octave3.2:52> std(W523(:,2))%with Lieberkühn, across the wing
ans = 12.746
octave3.2:51> std(W524(:,2))%w/o Lieberkühn, across the wing
ans = 8.2902

Using standard deviation as a metric for image detail, we get an increase of about 75% in standard deviation over the dark photo by using the reflector.

octave3.2:30> (20.316+17.737+12.746)/(7.3926+13.227+8.2902)
ans = 1.7572

The averages, standard deviation etc. may seem a bit redundant at this point; you don’t need to plot a pixel-value profile to see that the image with the reflector is much brighter and more detailed than the photo taken without.

## First tests of 3D printed Lieberkühn reflectors

Here I will report my initial tests of my Lieberkühn reflector designs, “hot” off the 3D printers at Shapeways.

I am testing a squeeze-to-attach Lieberkühn that roughly fits a Canon f/3.5 20mm focal length macro lens (above), and a 58mm threaded version (below), tested with a Canon 35mm f/2.8 manual tilt shift lens. I used a Canon auto macro bellows and a Nikon D5100 with an adapter for all test images.
I haven’t added any reflective material to them yet, so they are essentially “Lieberkühn diffusers” for these tests. I used a domestic desk lamp with a 750 lumen halogen bulb to illuminate the specimens, for slightly off-axis trans illumination.

These are the legs on a cicada molt from last year’s 17-year brood. The photo was taken with the 35mm Canon tilt-shift lens at about the shortest macro-bellows distance possible.

And here is a shot of the same view with the reflector attached. I used a 1/13 second exposures at ISO 1600 and f/5.6 for both shots.

The large claws up front with (below) and without (above) the reflector. Again this was taken at f/5.6, an ISO 0f 1600, and 1/13 second exposure time. I increased the bellows distance slightly for this shot, increasing the magnification.

Although the fill light is definitely better in the shots with the reflector, in some cases a photographer may prefer the image without using it, e.g. to bring out the small details with shadow. The cicada molt is partially transparent, giving a nice effect to the light transmitted through the subject.

I took the two photos of a leaf-cutter bee (Megachile genus, female) below with the same setup. The difference in lighting with and without the reflector is pretty drastic.

I made the next two pairs of photos using the 20mm macro lens and the squeeze Lieberkühn reflector. The photos contain some apparent lens flare resulting from the off-axis light source, manifesting as a slight general brightening (and resulting loss of contrast) in the middle of each image. I am not sure if the aberration is reduced with the addition of the reflector or if it just looks that way due to the rest of the image being brighter. Looks like a job for some quantitative comparisons, for the next post.

The position of the lamp and bellows stand were maintained for each pair of images. The bellows was set at the same distance but displaced between exposures to make room to attach the reflectors without disturbing the subjects, so the comparison images may be focused ever-so-slightly at different depths.

The lighting was definitely improved by the use of reflectors for these (mostly opaque) subjects. The images above were intended as a qualitative investigation, I will be looking into the performance and useability of the designs further.

As a final note, compare the print of the 58mm threaded reflector with the render from the STL file. The consistency is inhomogenous, with some bulges introduced during manufacture that were not part of the design file. Can’t say that I’m impressed with the print quality.

## Designing 3D printable Lieberkühn Reflectors for macro- and micro-photography

Designing a Lieberkühn Reflectors for macro- and micro-photography

A Lieberkühn Reflector gets its name from one Johann Nathaniel Lieberkühn, who invented the speculum that bears his name which you may recognize from reflective headband decorations for doctor costumes. The name is generally changed from “speculum” to “reflector” when referring to optical reflectors used in photography and microscopy, perhaps because the term has drifted from its original Latin root meaning “mirror” to refer to probing instruments for dilating orifices.

Lieberkühn reflectors were a way to bathe an opaque specimen in fill light. Lieberkühn reflectors and their use have unfortunately fallen by the wayside with the advent of modern conveniences like LEDs and fiber optic illumination. The above example from the collection of the Royal Microscopical Society displays a Lieberkühn on a simple microscope. In use, the reflector would be pointed towards the specimen, and fed light by a second mirror like the one on the rightmost microscope. Both of the microscopes pictured were on display at the Museum of the History of Science in Oxford

The working part of the Lieberkühn reflector is a parabolic mirror, which doesn’t add the spherical aberrations of hyper- or hypo-bolic configurations. As an added benefit, mirrors don’t tend to add chromatic dispersion or other aberrations associated with refraction (though they can effect polarisation). A parabola can be described as a a particular slice through a cone , but for the purposes of my first prototype, the functional description in cartesian coordinates will do.

$y = alpha x^2$
Where $alpha$ depends on the focal length of the parabola.
$alpha = 1 /4 f$

To get a functional, 3-dimensional mirror, I describe the parabola in terms of the focal length and a given radius as a 2D trace and spin it with rotate_extrude() in OpenSCAD. Leaving an aperture in the middle leaves room for light to reach the objective. The reflector shown below has a 4mm central aperture for the objective, 16mm focal length and 32mm diameter.

I have sent a few prototypes (matched to particular lenses or objectives) to Shapeways for prototyping. After some characterisation these will appear on theBilder shoppe.