Page 99 - Fundamentals of Light Microscopy and Electronic Imaging

82 DIFFRACTION AND INTERFERENCE IN IMAGE FORMATION

Let us first consider the image of an object such as a diffraction grating with lines
spaced just a few micrometers or less apart. Light that passes through the grating (we
might imagine any microscope specimen) and does not interact with it is called direct
light and forms a small central spot (the 0th-order diffraction spot) in the middle of the
diffraction pattern. Light that becomes diffracted (diffracted waves) forms a pattern of
widely separated 1st-, 2nd-, 3rd-, etc.-order spots flanking the 0th-order spot. The dif-
fraction patterns of periodic objects such as diatoms or striated muscle can be observed
by closing the condenser diaphragm down to a minimum and inspecting the diffraction
plane with a Bertrand lens. It is understood that the light contained in the diffraction pat-
tern goes on to form the image of the grating through interference in the real intermedi-
ate image plane in the eyepieces of the microscope. Looking at the image through the
eyepieces, we do not see the diffraction pattern, but the inverse transform that is derived
from it. Thus, we say that the object image is the inverse transform of the diffraction pat-
tern in the back aperture. The reciprocal nature of the space relationships of the two
images is described as follows: Fine periodic features separated by short distances in the
object and image are seen as widely separated diffraction spots in the diffraction image;
coarse features separated by relatively long distances in the object and real intermediate
image take the form of closely separated diffraction spots close to the central 0th-order
spot in the diffraction pattern.
Joseph Gall demonstrated this relationship by placing a transparent image (photo-
graphic negative) of a periodic polymer at the back aperture and by providing illumina-
tion from a pinhole placed at the lamp’s field stop. There was no specimen on the stage
of the microscope. Looking in the eyepieces, the diffraction pattern (the inverse trans-
form) of the polymer is observed. Used this way, the microscope functions as an optical
diffractometer (Gall, 1967). Thus, images located in the diffraction plane and in the
image plane are inverse transforms of one another, and the two images exhibit space
relationships that are related as the reciprocal of the space relations in the other image.
The exercise at the end of this chapter reinforces these points. We will revisit this con-
cept throughout the book, particularly in the chapters on phase contrast microscopy and
in the section on fast Fourier transforms in Chapter 15.

PRESERVATION OF COHERENCE: AN ESSENTIAL REQUIREMENT
FOR IMAGE FORMATION

Our discussion of the role of diffraction and interference in image formation would not
be complete without considering the requirement for coherent light in the microscope.
Object illumination with rays that are partially coherent is required for all forms of inter-
ference light microscopy (phase contrast, polarization, differential interference contrast)
discussed in the following chapters.
Nearly all “incoherent” light sources, even incandescent filament lamps, are par-
tially coherent—that is, the waves (wave bundle) comprising each minute ray emanat-
ing from a point on the filament vibrate in phase with each other. In reality, the degree
of coherence within a given ray is only partial, since the photons vibrate slightly out of
phase with each other. The distance over which the waves exhibit strong coherence is
also limited—just a few dozen wavelengths or so—so that if you examined the ampli-
tude of the ray along its length, you would see it alternate between high-amplitude
states, where the waves vibrate coherently, and low-amplitude states, where waves are
transiently out of phase with each other. In contrast, laser beams can be coherent over