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The alternative form of the Fisher information matrix of Poisson distributed observations The Icth element of the Fisher score vector of Poisson distributed observations follows from (3.47):

Two useful techniques that have been proposed and demonstrated for analyzing large departure surfaces or aliased interferograms are sub-Nyquist interferometry and two-wavelength PSI 14131 Aliasing Before describing either of these extended range techniques, it is useful to discuss aliasing in more detail Aliasing is the property of a sampled imaging system which causes high-frequency content in the input to be lost or obscured and displayed at lower spatial frequencies, that is, at frequencies less than the Nyquist frequency This property can be graphically demonstrated in Figure 1443 where two different spatial frequency inputs are sampled For illustration, ini nitely small pixels are assumed and the dots represent sampled values at the pixels In Figure 1443(a), the fringe frequency is two-third the Nyquist frequency, or the sampling rate is three pixels per fringe or cycle The sampled output is clearly at the same frequency as the input.

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When the SNR is large, the following approximation can be used:

The Info Palette window offers you context-sensitive Quick Help as you work. It s great for beginners, but you ll eventually find it a nuisance because it takes up screen space. To open the Info Palette window, choose Help Info Palette or press Ctrl+5. As you use commands, a brief explanation appears. Figure 3-13 shows the screen that appears when you start the ARC command. Figure 3-13: The Info Palette window displays Help for the command you re using.

The fringe frequency in Figure 1443(b) is four-third the Nyquist frequency, with only three pixels for every two fringes There are insuf cient pixels to resolve this frequency, but the recorded samples are exactly the same as for the lower frequency measured in (a) Since the detected outputs in (a) and (b) are identical, the displayed output in (b) occurs at a frequency of 2fN =3 instead of 4fN =3 The effect of aliasing on the displayed fringe pattern is to replace fringes of spatial frequency greater than the Nyquist frequency with lower frequency fringes and corrupts the normal interpretation of the fringe pattern More importantly for PSI, aliasing is an indication that the wavefront phase is changing at a rate greater than p per pixel Under this condition, the phase unwrapping operation described so far in Section 14.

1.5 1 Amplitude 0.5 0 0.5 1 1.5 (a) 1 0.5 0 20 40 60 80 Time (t ) 100 120 140 160

12 must fail as this process restricts the wavefront change to p per pixel This failure is predicted by the Whittaker Shannon sampling theorem which states that if a scene is bandlimited to within the Nyquist frequency of the sensor, the scene can be recovered without error from the sampled image The default PSI phase unwrapping operation is based upon the assumption that this bandlimited requirement is met It is important to note that this theorem does not state anything about the possibility of image recovery when this condition is not met If the input scene or fringe pattern is not bandlimited to the Nyquist frequency, some additional information or a priori knowledge about the wavefront or surface under test is required to properly recover and unwrap the phase..

14. Choose View Visual Styles Conceptual. You can now visualize the drawing better. 15. Save your drawing. It should look like Figure 23-22. If you look carefully, you ll see that the edge of the cheese wedge goes slightly through the plate.

Listing 23-4 (continued)

Figure 5.12 shows an example of the effects of sampling on spectral leakage, or two-tone characteristics, when the discrete Fourier transform is used for 100 samples. The minor signal has a frequency corresponding to the 16th bin, and the major signal has its frequency varied between the 10th and 11th bins.

Routers These are intelligent devices that guide data packets between LANs and networks. Just like hubs or switches have ports to connect individual hosts, routers have ports to connect individual LAN segments, as shown in Figure 28-3. Based on the packet s destination IP address, routers move data packets between LAN segments by figuring out the optimal path that a packet must take through the maze of various LANs.

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