Diffraction Pattern & Intermediate Image of Periodic Structures

Gain valuable information about diffraction patterns of periodic structure and intermediate images of periodic structures in microscopy. The foundational knowledge article explains the relationship between line spacing in a periodic grid and the separation of the diffraction pattern image in the back focal plane of a microscope objective. It also highlights the effects of white and monochromatic light on diffraction patterns and how they can be used to transform diffraction patterns into sharp images.

Key Learnings:

• There is a reciprocal relationship between line spacings in a periodic grid and the separation of the diffraction pattern image in the back focal plane.
  
• Spatial filters can be used to manipulate diffraction patterns in the back focal plane of the objective and therefore affect the specimen’s image in the intermediate image plane.
  
• The appearance of the intermediate image depends on the diffraction orders which contribute to the image formation.
  

The image seen at the objective’s back focal plane of a microscope is the diffraction pattern of the specimen (line grating or grid). Here, the condenser aperture diaphragm represents the light source. The different images of the condenser aperture diaphragm are the maxima of the diffraction pattern caused by the periodic spacings in the specimen. With white light, we see images of the condenser aperture diaphragm in the various spectral colors superimposed in each diffraction maximum. When the sample is illuminated with monochromatic light (by activating the appropriate button of your instrumentation), the diffraction maxima are transformed into periodically repeating sharp images of the condenser aperture diaphragm of the chosen color. As the wavelength of the monochromatic light is increased (towards yellow and red colors), the images of the condenser aperture diaphragm opening become further apart, in proportion to the increased wavelength of light. The opposite occurs when wavelengths are decreased into the green and blue regions of the visible light spectrum: the condenser aperture diaphragm images move closer together.

The picture in the tutorial displays the diffraction pattern in the back focal plane of the microscope objective. On the bottom left, you see the actual line grating (object). On the bottom right is the intermediate image (image). To operate the tutorial, use the Choose a Grid pull-down menu to select between Line Grating, Orthogonal Dots and Hexagonal Grating.

• After selecting Line Grating, choose between Polychromatic and Monochromatic Light. When activating the Monochromatic check box, set the slider to the desired wavelength.
• After selecting Orthogonal Dots or Hexagonal Grating, choose between Polychromatic and Monochromatic Light. Polychromatic Light offers you several options of spatial filters. Monochromatic Light also offers you to choose between the same spatial filter options and wavelengths.

The Spatial Filters pull-down menu, which is activated when you select the Hexagonal Grating or Orthogonal Dots, allows you to place spatial filters (e.g. Right Diagonal) to eliminate different diffraction maxima from the diffraction patterns in the back focal plane of the objective. Select between vertical, horizontal, and diagonal spatial filters. When the filters are inserted into the back focal plane, the corresponding Image pattern that appears to the right of the Object is changed accordingly.

For example, if you select the Orthogonal Dots along with the Right Diagonal spatial filter, the resulting microscope image appears as a series of parallel lines at a 45-degree-angle . Other spatial filters produce similar effects, depending on their orientation.

The purpose of this tutorial is to explore the reciprocal relationship between line spacings in a periodic grid, simulating a diffracting object, and the separation of the diffraction pattern image in the back focal plane of the objective. When the line grating has larger periodic spacings, multiple images of the condenser aperture diaphragm appear in the objective’s back focal plane. When white light is used to illuminate the line grating, the images of the condenser aperture diaphragm produce higher order diffraction maxima with a blue fringe closer to the zero order (central) maximum and with a green-yellow-red spectrum further out towards the edge of the back focal plane (objective aperture). When monochromatic light is used to illuminate the line grating, the images of the condenser aperture diaphragm produce clear higher order diffraction maxima in the chosen color.