## 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.