Page 101 - Fundamentals of Light Microscopy and Electronic Imaging

84 DIFFRACTION AND INTERFERENCE IN IMAGE FORMATION

For a given ray incident at an object, it is now possible to see that a coherence rela-
tionship exists between the diffracted and undiffracted (0th-order) beams. This coher-
ence relationship is maintained between the object and the image plane, where waves
recombine and interfere. At that site, the myriad coherent wave partners add incoher-
ently with other waves to produce the final image. This important concept underlies
many forms of light microscopy.

Exercise: Diffraction by Microscope Specimens

• Determine the periodicity of unknown diffraction gratings using the dif-
fraction equation, mλ d sin . Measure the distances in centimeters
between the 1st- and 0th-order spots on a projection screen and the distance
between one of the spots and the grating to calculate sin and the grating
spacing, d. It is easiest to perform this measurement using a narrow, mono-
chromatic beam such as that provided by a laser pointer.
• Review Koehler illumination and check the focus of the illuminator of your
microscope. Focus on a piece of diffraction grating mounted on a glass
microscope slide with a 40 dry objective, and calculate the spacing using
the eyepiece reticule and calibration factor determined in the exercise for
Chapter 1. For accuracy, measure the number of eyepiece units covering 10
or more spacings on the stage micrometer, repeat the procedure 10 times,
and determine the mean value. How well do the two numbers agree?
• Examine and compare the diffraction patterns of various other specimens
on the projection screen and estimate their periods (suggestions: micro-
scopic barbules on a bird feather, grooves on a semitransparent CD disk). If
the CD is completely opaque, treat it as a reflection grating, tilting the CD
at a 45° angle to form a right triangle between the 0th-order spot, the CD,
–
and the light source using the equation for a 90° reflection: d 2λ/sin .
Use the laser pointer as a light source.
• Focus the grating in monochromatic green light using a 10 objective with
your microscope, stop down (maximally constrict) the condenser aperture
diaphragm, and look to see if you can still resolve the grating in normal
viewing mode. Examine the diffraction pattern of the grating with an eye-
piece telescope under conditions where the image is not resolved, barely
resolved, and fully resolved. Do you agree with Abbe’s conclusion that a
minimum of two adjacent diffraction orders is required for resolution?
• Using the same condenser position, remove the green filter and examine the
grating in red and blue light. For each color filter, examine the pattern of
diffraction spots with the eyepiece telescope and note the corresponding
changes in the spacing between the 1st-order diffraction spots. Do your
observations agree with the relationship between spatial resolution and
wavelength?