Checklist of the Collembola: Simulating structural colours of scales in Entomobryomorpha (Collembola)
http://www.collembola.org/publicat/colour.htm
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Last updated on
2023.08.11
by Frans Janssens
Frans Janssens,
Department of Biology, University of Antwerp, Antwerp, B-2020, Belgium
Abstract.
Simulating structural colours of thin transparant body scales
in Entomobryomorpha (Collembola) based on a simplified application of optical
thinfilm theory.
Introduction
Note : the text is still in an embryological state...
To be completed.
Principle
Colour system used = RGB.
Lightsource = white daylight (RGB values = 255,255,255).
Primary scale colours red, green and blue.
To get a max red scale : Rmax + Gmin + Bmin = 255,0,0
To get a max green scale : Rmin + Gmax + Bmin = 0,255,0
To get a max blue scale : Rmin + Gmin + Bmax = 0,0,255
These values correspond with the primary RGB colours.
Primary blue scale
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Primary green scale
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Primary red scale
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Secondary scale colours cyan, magenta and yellow.
Secondary colours are formed by combining two primary colours.
Secondary yellow(=red+green) scale
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Secondary magenta(=red+blue) scale
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Secondary cyan(=green+blue) scale
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Simplified model of iridisation
The model of the iridisation is based on thinfilm theory.
1st simplification : white sunlight only contains the primary colours red + green + blue (RGB).
In this simplified model only the behaviour of those 3 monochrome primary colours
are taken into account.
2nd simplification : incident lightwaves are always orthogonal at the scale surface.
Iridisation is then caused by interference of 2 refelected light waves:
1. reflected wave at the upper surface of the scale with 180 degrees phase shift.
2. reflected wave at the lower surface of the scale without phase shift.
The thickness of the scale determines the length of the path of the second
reflected wave.
The two reflected waves are superimposed in the composed reflected wave
which is the wave that determines the structural colour of the scale.
The thickness of the scale determines the level of destruction or construction
of the 2 waves in the composed reflected wave.
If the scale thickness is an even multitude of 1/4 of the incident wavelength
then the out of phase reflected waves compensate eachother.
Light intensity then is minimised (destructed).
If the scale thickness is an odd multitude of 1/4 of the incident wavelength
then the in phase reflected waves amplify eachother.
Light intensity then is maximised (constructed).
3rd simplicification : the intensity of the light wave changes in
lineair fashion from minimum to maximum level.
Then the lightintensity of the reflected composed wave behaves like a saw-tooth
function of the number of 1/4 wavelength multitudes.
4th simplification : the impact on the structural scale colour of
the scale roughness (surface structures
such as cilia, spinulae, ribs, or inter(ciliary)connections),
has not been taken into account.
5th simplification : loss of intensity (luminance) of the
transitive and reflective light is not taken into account.
The simulated visual colour of the scale then is the hypothetical
structural colour always with maximum luminance.
Quantified model
Red light wavelength = 700 nm.
Green light wavelength = 550 nm.
Blue light wavelength = 400 nm.
Scale thickness as a function of multiples of 1/4 of the wave length (0-10):
Red : 0, 175, 350, 525, 700, 875, 1050, 1225, 1400, 1575, 1750
Green : 0, 137.5, 275, 412.5, 550, 687.5, 825, 962.5, 1100, 1237.5, 1375
Blue : 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000
The structural colour of the scale
(= the colour of the reflected composed wave)
is a function of the thickness of the scale.
Constructive scale thicknesses:
Red : 175, 525, 875, 1225, 1575
Green : 137.5, 412.5, 687.5, 962.5, 1237.5
Blue : 100, 300, 500, 700, 900
Destructive scale thicknesses:
Red : 350, 700, 1050, 1400, 1750
Green : 275, 550, 825, 1100, 1375
Blue : 200, 400, 600, 800, 1000
Proof of concept: Tomocerus vulgaris : scale thickness = 450 nm
Tomocerus vulgaris
Scale thickness = 450 nm
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Red = 450/175 = 2.57 -> even multiple = destruction -> red = 0 + 0.57 = 0.57 or 57%
Green = 450/137.5 = 3.27 -> odd multiple = construction -> green = 1 - 0.27 = 0.73 or 73%
Blue = 450/100 = 4.50 -> even multiple = destruction -> blue = 0 + 0.50 = 0.50 or 50%
To determine the colour of the reflected composed wave
it is required to take into account the (complementary) subtractive
colour system CMY(K=0) (used for reflected light)
iso the additive RGB colour system (used for lightsources).
Cyan = 57%
Magenta = 73%
Yellow = 50%
This CMY combination = purple.
The colour matches with the body colour of T. vulgaris when observed
in daylight.
This result is considered as proof of concept for the simplified
iridisation model.
To display the simulated colour on a computer screen the CMY values have
to be converted to RGB values : RGB = 255*(1-CMY).
To be completed.
Simulated intrinsic structural colours of scales
Examples of scales between 50 nm and 1200 nm thickness.
The background of the scales is transparant.
Hence reflected waves from the background are not taken into account.
Scale thickness = 50 nm
Scale thickness = 50 nm
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Scale thickness = 100 nm
Scale thickness = 100 nm
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Scale thickness = 200 nm
Scale thickness = 200 nm
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Scale thickness = 300 nm
Scale thickness = 300 nm
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Scale thickness = 400 nm
Scale thickness = 400 nm
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Scale thickness = 500 nm
Scale thickness = 500 nm
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Scale thickness = 600 nm
Scale thickness = 600 nm
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Scale thickness = 700 nm
Scale thickness = 700 nm
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Scale thickness = 800 nm
Scale thickness = 800 nm
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Scale thickness = 900 nm
Scale thickness = 900 nm
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Scale thickness = 1000 nm
Scale thickness = 1000 nm
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Scale thickness = 1100 nm
Scale thickness = 1100 nm
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Scale thickness = 1200 nm
Scale thickness = 1200 nm
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To be completed.
Case studies
Lepidocyrtus cyaneus or lanuginosus : scale thickness = 130 nm
Scale thickness = 130 nm
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Heteromurus nitidus : scale thickness = 224 nm
Scale thickness = 224 nm
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Heteromurus major : scale thickness = 265 nm
Scale thickness = 265 nm
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Cyphoderus albinus : scale thickness = 300 nm
Scale thickness = 300 nm
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Tomocerus vulgaris : scale thickness = 450 nm
Scale thickness = 450 nm
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Impact of longitudinal ribs on scale colour
In Tomoceridae, the scales have longitudinal ribs.
The colours of two interferences are considered separately:
1. these produced inbetween the ribs (at scale thickness)
2. these produced through the ribs (at scale thickness + rib height)
The 2 RGB values are add together to simulate the resulting composed light.
Tomocerus vulgaris : scale thickness including longitudinal ribs = 750 nm
Scale with ribs thickness = 750 nm
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Tomocerus vulgaris : scale thickness 450 nm with longitudinal ribs of height 300 nm
Scale thickness = 450 + ribs of 300 nm
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Pogonognathellus longicornis : scale thickness = 700 nm
Scale thickness = 700 nm
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Pogonognathellus longicornis : scale thickness including longitudinal ribs = 1400 nm
Scale with ribs thickness = 1400 nm
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Pogonognathellus longicornis : scale thickness 700 nm with longitudinal ribs of height 700 nm
Scale thickness = 700 + ribs of 700 nm
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Single scale layer
What is the effect of the cuticular/epidermal layer?
Assume 1 layer of scales at altitude d (= distance between the
top face of the scale and the cuticula).
The incident wave is reflected
1. at the top surface of the scale with 180 phase shift,
2. at the lower surface of the scale without phase shift,
3. at the cuticular surface with 180 phase shift.
The 3 reflected waves are superimposed in the composed reflected wave
which is the wave that determines the structural visual colourof the scale.
Interference of those 3 reflected waves:
the thickness of the scale determines
the length of the path of the reflected refracted wave through the scale.
the altitude of the scale determines
the length of the path of the at the cuticula reflected wave.
Both the thickness of the scale and the altitude of the scale
determine the level of destruction or construction of the respective
refelected waves in the composed reflected wave.
If the scale thickness is an even multitude of 1/4 of the incident wavelength
then the in phase reflected wave at the lower surface of the scale
will be destructive in respect to the at the top surface reflected wave.
Light intensity then is minimised.
If the scale thickness is an odd multitude of 1/4 of the incident wavelength
then the in phase reflected wave at the lower surface of the scale
will be constructive in respect to the at the top surface reflected wave.
Light intensity then is maximised.
If the scale altitude is an even multitude of 1/4 of the incident wavelength
then the out of phase reflected wave at the cuticular surface
will be constructive in respect to the at the top surface reflected wave.
Light intensity then is maximised.
If the scale altitude is an odd multitude of 1/4 of the incident wavelength
then the out of phase reflected wave at the cuticular surface
will be destructive in respect to the at the top surface reflected wave.
Light intensity then is minimised.
The superposition of the 3 reflected waves eventually determines the final
structural colour of the scale.
Note: the impact on the structural scale colour of the epicuticular
ultrastructure (cuticular roughness) has not been taken into account.
Scale altitude = 500 nm; scale thickness = 450 nm
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Scale altitude = 675 nm; scale thickness = 450 nm
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It is clear that the altitude of the scale has an impact on the structural
colour of the scale.
A difference of altitude of about
1/4 of the wavelength of the incident light
(for monochrome red light = 175 nm; green = 137.5 nm; blue = 100 nm)
has a distinct change in structural colour of the scale.
Impact of intrinsic body colour
The colour of the epidermis will affect the at the cuticula reflected light.
Intrinsic body colour examples :
White, as in cave Pseudosinella : RGB=255,255,255
Yellow, as in Tomocerus minor
or Heteromurus nitidus : RGB=255,255,0
Blue, as in Lepidocyrtus (Lanocyrtus) cyaneus : RGB=0,0,255
Black, as in Lepidocyrtus paradoxus : RGB=0,0,0
In summary,
a white skin will reflect all light,
a yellow skin will reflect only red and green light,
a blue skin will reflect only blue light, and
a black skin will reflect no light.
Due to the selective reflection and absorption
of the light that passes through the scale,
the body colour has an impact on the structural
colour of the scale.
Examples of scales with identical thickness (450 nm) and altitude (500 nm),
and only the body colour is different :
Scale altitude = 500 nm; scale thickness = 450 nm
Body colour = white
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Scale altitude = 500 nm; scale thickness = 450 nm
Body colour = yellow
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Scale altitude = 500 nm; scale thickness = 450 nm
Body colour = blue
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Scale altitude = 500 nm; scale thickness = 450 nm
Body colour = black
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Case study : Lepidocyrtus paradoxus
Lepidocyrtus paradoxus
Scale altitude = 280 nm; scale thickness = 230 nm
Body colour = black
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Lepidocyrtus paradoxus from Belgium
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Case study : Heteromurus nitidus
Heteromurus nitidus
Scale altitude = 250 nm; scale thickness = 224 nm
Body colour = yellow
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Note the distinct impact of the scale altitude and body colour
when compared to the intrinsic more bluish structural colour of the scale.
Acknowledgements
We would like to thank Marie-Louise Huskens for using her image(s)
as illustrations in this paper.
References
To be completed.
