Fraunhofer diffraction pattern

Figure 13. Fraunhofer diffraction pattern of a single slit illuminate with coherent monochromatic light the intensity distribution is shown for two...

Figure 1.7. Fraunhofer diffraction pattern for circular aperture or opaque disk (from Weiner, 1984).

G. I. Zahalak and S. P. Sutera, Fraunhofer diffraction pattern of an oriented mono-disperse system of prolate ellipsoids, J. Colloid Inter. Sci., 82,423 (1981). 

D < 500 pm, Fraunhofer Diffraction Pattern Analysis (FDPA) can be employed in measuring particle size distributions (4,5). For the particles in the intermediate range, 0.7 pm < D < 10 pm, Mie theory of scattering holds and Turbidity Spectra (TS) can furnish information about particle sizes (6). 

Airy formula, intensity distribution of the Fraunhofer diffraction pattern, 148... 

The laser diffraction meter consists of a parallel monochromatic light beam, 7 mm in diameter, from a 5-mW helium-neon laser, transmitted across the spray. Light diffracted by droplets and particles produces a Fraunhofer diffraction pattern. Light from the diffraction pattern is collected by 31 semicircular photosensitive rings, and the hght energies... 

Chapter 1 is concerned with the fundamental principles of image formation by a lens. These principles were first formulated by Ernst Abbe in 1873 and are basic to the chapters that follow. According to the Abbe theory, the image of an illuminated object is the result of a twofold diffraction process. First, the Fraunhofer diffraction pattern of the object is formed in the back focal plane of the lens. Second, the light waves travel... 

These ideas can be illustrated by considering the coherence of a circular source of diameter a. The correlation / i2 is equal to the normalized intensity of the Fraunhofer diffraction pattern from a circular aperture of diameter a (see Figure 1.7b). From this it follows that hy2 becomes zero when... 

Figure 8. Three typical Fraunhofer diffraction patterns. In polydisperse systems, the interpretation of the relationship between these patterns and the size distribution can be difficult and requires sensitive photomultipliers. The transmitted beam is blocked out, and the detectors are arranged outward from the center. In some cases a single detector has a movable mask to measure diffracted light intensity as a function of position. Subtle differences in size distribution (i.e., log-normal vs bimodal, etc.) cannot be distinguished, and generally some assumption must be input to the data reduction programs.

In the following summary of contrast enhancement techniques, it is assumed that specimens are being observed in transmission, that they are not self-luminous, and that the light source is not imaged onto the specimen by the microscope condenser. All these assumptions describe typical conditions for LCP microscopy. Figures 5 and 6 show ray diagrams for a normally incident and obliquely incident beam of parallel rays, respectively. In both cases, the objective back focal plane contains the Fraunhofer diffraction pattern of the specimen. 

Figure 13.29 (a) A single space mask pattern and (b) its corresponding Fraunhofer diffraction pattern. These are Fourier transform pairs. (Reprinted with permission from Taylor Francis Group LLC. )... 

If a long narrow slit is illuminated by monochromatic light the intensity pattern observed far from the slit (the Fraunhofer diffraction pattern) is given by the expression ... 

Another widely used particle size analyser is based on the forward scattering of laser light through a dilute (< 1 % by volume) suspension of crystals retained in a small ( 10mL) agitated cell. The resulting Fraunhofer diffraction pattern is detected and translated, by means of the instrument software, into a particle size distribution (BS ISO 13320, 2000). 

The total effect of the dS wavelets can be integrated across dE to get an expression for the far field or Fraunhofer diffraction pattern. The initial exponential term in (1.4) refers the wave to an origin at t = 0, but we are only... 

When a parallel light beam passes a limiting aperture with diameter a, a Fraunhofer diffraction pattern is produced in the plane of the focusing lens L2 (Fig. 4.9). The intensity distribution 7(0) as a function of the angle 0 with the optical axis of the system is given by the well-known formula [4.3]... 

Although it does not influence the spectral resolution, the much larger diffraction by the entrance slit imposes a limitation on the transmitted intensity at small slit widths. This can be seen as follows when illuminated with parallel light, the entrance slit with width b produces a Fraunhofer diffraction pattern analogous to (4.6) with a replaced by b. The central diffraction maximum extends between the angles 30 = X/b (Fig. 4.11) and can completely pass the limiting aperture a only if 230 is smaller than the acceptance angle a/ f of the spectrometer. This imposes a lower limit to the useful width of the entrance slit. 

FIGURE 3.2 A Fraunhofer diffraction pattern under two different contrast levels. The circle drawn around the right hand pattern has a radius 1.5 times that of the geometrical shadow of the object. The area between the shadow and the circle represents the area from which the light to form the pattern is obtained. (The patterns were calculated using the Fresnel Diffraction Explorer, which may be obtained from Danger Research http //daugerresearch.com/)... 

Fraunhofer diffraction patterns are named after Joseph Fraunhofer, a German physicist (1787—1826) who invented the diffraction grating. It can be shown that the Fraunhofer diffraction pattern of a fineparticle is the same as the two-dimensional Fourier Transform. (One-dimension Fourier Transforms were discussed in the chapter on shape.) It is difficult to explain in simple terms what is meant by the Fourier Transform in two and three-dimensional space but computer programs are readily available to calculate the two-dimensional Fourier Transform. In Figure 7.2 the calculated two-dimensional Fourier Transforms of the four shapes shown are given along... 

X-Ray Fiber slit, a Fraunhofer diffraction pattern will be observed through... 

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