Page 91 - Fundamentals of Light Microscopy and Electronic Imaging

74 DIFFRACTION AND INTERFERENCE IN IMAGE FORMATION

Wavefronts

(a) (b)

Figure 5-10
Huygens’ wavelets are used to describe the propagation of (a) planar and (b) spherical
wavefronts.

wavefront serves as the source of spherical secondary wavelets, such that the wavefront
at some later time is defined by the envelope covering these wavelets. Further, if wave
propagation occurs in an isotropic medium, the secondary wavelets have the same fre-
quency and velocity as the original reference wavefront. The geometrical construction
of Huygens’ wavelets is a useful device for predicting the locations of wavefronts as
modified by both refraction and diffraction; however, Huygens’theory does not account
for many wave-optical phenomena of diffraction, which require the application of newer
approaches in physical optics.
When applied to the diffraction grating, we can use the construction of Huygens’
wavelets to determine the location of the diffraction spots and the diffraction angle. Take
a moment to study the construction for a diffraction grating with spacing d in Figure
5-11, which emphasizes the concept that the diffraction spots occur at angles where the
optical path lengths of constituent waves are an integral number of wavelengths . At
locations between the diffraction spots, waves vary by a fraction of a wavelength and
destructively interfere. Although Huygens’ wavelet construction accounts for the loca-
tions of diffraction spots, it does not account for all aspects of the diffraction process.
For example, the sum of all of the energy present in the luminous regions of the diffrac-
tion pattern is known to equal the energy incident on the grating. This is inconsistent
with ray particle models and predictions from the geometrical construction of wavelets
that photons are distributed uniformly on the diffraction screen, being annihilated where
there is destructive interference. We enter here a murky area where the wave and parti-
cle natures of light are difficult to reconcile.