How does the diffraction pattern known as the Airy disk get generated by shining light through a pinhole? Or more generally, what causes diffraction of light? Diffraction of light occurs because of its transverse wave nature. We have already said that when light hits an object, it is diffracted. This phenomenon is best understood by an examination of Huygens' Principle. In 1678, the Dutch pysicist Christiaan Huygens wrote a treatise on the wave theory of light in which he presented a theory now known as Huygens' Principle. It states that every point on a wave front can be thought of as a new point source for waves generated in the direction the wave is traveling or being propagated. OR-- the wavefront of a propagating wave of light at any instant conforms to the envelope of spherical wavelets emanating from every point on the wavefront at the prior instant (with the understanding that the wavelets have the same speed as the overall wave). Fresnel later elaborated on Huygens' Principle by stating that the amplitude of the wave at any given point equals the superposition of the amplitudes of all the secondary wavelets at that point (with the understanding that the wavelets have the same frequency as the original wave). These are termed Huygens’ wavelets. The formation of the Airy disk can best be described by looking at how imaging of a luminous point occurs in a lens system such as is found in the compound microscope. The following diagram shows what happens.

If a luminous point at A is projected through the
front
lens of an objective O_{1}, and assuming that the light is
monochromatic,
light coming from point A will define wave surfaces as spheres (e.g., S_{o})
with their centers at A. Assuming the objective to be a perfect
lens,
the light going through it will also produce wave surfaces as spheres
as
well (e.g., S_{i}).
The centers of these spheres are at point A'_{0}
which is a geometrical image of A.

The
diagram on the right shows vibrations going to a point A'_{1}
from
M and M_{0}. The amplitudes are opposite each other when they
reach
the plane (indicated by line P and extending out from the page) where
our
diffraction image is generated. We would now have a dark area at
point A'_{1} because the luminous amplitudes cancel each other
out and add up to zero. The same situation would happen if A'_{1}
were on the other side at the same distance from A'_{0}.
And in fact if one considered the whole plane of line P as shown by the
square in perspective, the image would be a dark ring with a radius A'_{1}-A'_{0}
with A'_{0} at the center as shown by the circle.
If
the vibrations coming from points M and M_{0} were imaged at a
point A'_{2} on line P twice as from point A'_{0}
as A'_{1}, the amplitudes of the vibrations would once again be
additive and one would then see a bright ring in the plane of line
P.
It also follows that the intensities of the vibrations at all the
points
on the plane of line P results from vibrations from all the points on
wave
surface S_{i}, not just those from points M and M_{0}.

If all this information is taken together, then the
image
seen in the plane of line P would be a very bright central circular
disk
surrounded by alternately bright and dark rings whose intensity
decreases
rapidly as distance increases: the **Airy disk. **It can
also be seen that the distances between the bright and dark rings will
change with changes in the wavelength of light.

It must be remembered that any object observed in
the
microscope is subject to the phenomena described here and this has
important
consequences for the generation of enlarged images in the microscope
and
is why the concept of **numerical
aperture** is so important in microscopy.

*Diagrams redrawn from Francon, M. 1961. *Progress
in Microscopy. *Pergamon Press: London (also Row, Peterson
and
Co.: Elmsford, NY).