# Feather diffraction

##### Many bird feathers diffract light.  The diffraction pattern relates to the microscopic structure.

A feather plus a bright light source (laser pen or LED) demonstrate grating diffraction of light.

Feather diffraction can also break up sunlight into spectral colors.  Students can observe wide and narrow diffraction patterns from a single feather, because the fine combs making up the structure have more than one periodicity.  Different birds of course display different diffraction patterns.  Use the diffraction pattern to analyze the spacing in the comb, and compare with a microscope view of the feather. (See below a typical feather micrograph).

###### How to observe feather diffraction

The key to observing diffraction is a well-collimated light source.  One of the best is dappled sunlight coming through tall trees.  You could be walking outdoors with your students and pick up a feather from the ground, hold it up at arms length so dappled light comes through it, and observe beautiful rainbow colors from several orders of diffraction.  Students will be impressed!

For more quantitative work, a laser pointer is ideal.  In a darkened room, hold it 30 cm or so from a feather.  Point it at a relatively translucent part of the feather, and observe diffraction on a wall or the ceiling.

Or place any small, bright light source such as a single-LED illuminator behind the feather, and look through the feather at the light source.  Your students will see many orders of diffraction.  Each diffraction spot will be an entire image of the light source.  White or colored LEDs work — white LED lamp diffraction breaks the emission up into the  component colors of the LED.

###### There are several gratings in feathers

This figure shows the structure of a feather.  The main vertical support structure is the ‘shaft’.  The ‘barbs’ emanating in a V-pattern from the shaft are visible to the naked eye, but are still closely spaced enough to diffract light.  The ‘barbules’ are much finer structures attached to the barbs.  The barbules are not resolvable by the naked eye, so it is interesting to study their microscopic arrangement by diffraction .

###### Typical diffraction patterns

Each orientation of barbules  produces its own diffraction pattern.  For example, barbules that are vertically oriented produce two strong first order diffraction spots to the left and right of the principle maximum spot.  2nd and higher order spots are possible, but are weaker because the barbule array is not perfectly periodic.

In addition there is another full set of barbules at roughly right angles — approximately horizontal barbules.  These will produce a similar pattern consisting of the principle maximum, two strong first order spots, and possibly some weaker higher order spots.  This pattern will be in a vertical row of spots because this grating is horizontal.

The horizontal and vertical barbule gratings produce patterns that just add together, one on top of the other.  The next figure shows the diffraction spots from barbules on the left and right sides of the feather in the SEM picture above:

A third overlapping diffraction pattern comes from the areas between barbs where barbules actually cross each other.  This pattern fills in diagonal locations between the vertical and horizontal rows of spots.  An example of a feather pattern showing multiple orders from horizontal and vertical gratings as well as a few off-axis diagonal spots from crossed gratings is shown next:

###### Students can calculate the barbule separation

Students can:

1.   Set up a laser pointer and feather-holder in front of a wall in a stable configuration.
2.   Measure the distance, x,  from the principle maximum to a first-order diffracted spot.
3.   Measure the distance, L, from the feather to the wall.  The diffraction angle is θ = tan-1 (x/L) ≈ x/L
4.   Calculate the barbule separation d from the formula, d sin θ =  λ, where λ is the wavelength of the light.  The wavelength of a typical red laser pointer is λ = 650 nm.  Again, sin θ ≈ x/L is a good approximation.
Barb separation
1.   Carefully examine of the principle maximum from a good feather.  You will see a row of fine maxima at an angle in between the two rows of barbule diffraction spots
2.   Get a new x’, a new θ’, and find a new d’, the separation between barbs.
3.   Estimate directly the barb separation using a magnifying glass and a small ruler that has millimeter markings.  Compare this with the measure you got from diffraction.
###### Discussion

Tabulate results from different feather types in front of the class, and open discussion of the different results.  Is there an aerodynamic or structural reason why feathers have such a highly ordered configuration?  Do other animals, such as moths, produce diffraction spots?  Why do barbules cross?

###### Materials

Chicken and pheasant plumage make excellent gratings.  Clearest results come from light-colored, almost transparent little feathers.  For breaking up sunlight, heavier feathers such as pigeon feathers are excellent, and they are available on the ground everywhere during many seasons of the year.

Fine chemise cloth produces beautiful, geometric spots, depending on the weave.  Fine wire mesh (for sieves) is also effective.  Adjacent fibers in woven cloth are not identical, but are either ‘over-under-over’ or ‘under-over-under’ fibers.  If the incoming light beam impinges on them at right angles to the cloth, there is little difference and the diffraction pattern is simpler.  If the incoming beam impinges at an angle, additional intermediate spots appear.  Hence diffraction