41. The result is that if the gap is very narrow only diffraction patterns with bright centers can occur. 42. The mapping from a crystal structure to its image or diffraction pattern has been relatively well understood and documented. 43. The Fraunhofer diffraction pattern is shown in the image together with a plot of the intensity vs . angle. 44. Only by considering the full dynamical model through multislice calculations can the diffraction patterns generated by PED be simulated. 45. Goodman uses this method to derive expressions for the diffraction pattern obtained with sinusoidal amplitude and phase modulation gratings. 46. An example of what a diffraction pattern obtained in this way may look like is shown in figure 2. 47. James Gregory discovered the diffraction grating by passing sunlight through a bird feather and observing the diffraction pattern produced. 48. These sheets then stack with very little long range order resulting in Bragg diffraction patterns with very broad peaks. 49. By analyzing the diffraction pattern using software, scientists can make a map of the electron density in the crystal. 50. Then a diffraction pattern is created by using the power spectrum function in Digital Micrograph software ( middle ).