Image Processing Reference
In-Depth Information
In actual imaging systems, the signal component at and over the Nyquist frequency is
removed or reduced by using an optical low-pass filter (OLPF) to avoid impacts caused
by false signals, as indicated in Figure 6.6a. The difference between Figure 6.6c and
d is the sampling phase. While the amplitude at the Nyquist frequency is retained in
Figure 6.6c, it is zero in Figure 6.6d. This result is due to the difference between the
sampling phases, as explained in Figure 6.2. The sampling phases in Figure 6.6c and d
correspond to those of Figure 6.2b and c, respectively.
Figure 6.7a and b show real pictures of a CZP chart taken by image sensors. In the CZP
chart, the resolutions at the right and left edges of the line passing through the center mean
600 television (TV) lines,* while the top and bottom edges correspond to 450 TV lines.
Figure 6.7a shows an emphasized picture of a CZP chart taken with a CCD with a 4.1 μm
pitch square pixel with 955(H) × 550(V) numbers without an OLPF. Figure 6.7a shows many
false signals of concentric circles, especially the strong signal observed at the Nyquist fre-
quency of 550 TV lines in both the picture and the measured signal amplitude. Figure 6.7b
is a picture taken with the OLPF set just in front of the sensor to suppress the false sig-
nal. The false signal is suppressed to an unobservable level in the picture and the ampli-
tude shows almost zero at the Nyquist frequency. Comparing the amplitude graphs of
Figure 6.7a and b, it can be seen in Figure 6.7b that the false signal at the Nyquist frequency
is removed completely and the amplitude decreases with the frequency, especially at areas
higher than the Nyquist frequency by the effect of OLPF.
An OLPF is a low-pass filter of spatial frequency, as its name indicates. 1,2 The most com-
monly used base material for OLPFs is crystalline quartz. Using birefringence of the crys-
tal, the incident light beam is split into two parts, an ordinary ray and an extraordinary
ray, as shown in Figure 6.8. While the ordinary ray propagates to the pixel directly under-
neath, the extraordinary ray is one-pixel pitch shifted through the crystal and, accord-
ingly, reaches the pixel next to the pixel that the ordinary beam arrives at, as shown.
600 TV lines
Without OLPF
With OLPF
450
TV lines
600
400
200
0
200
400
600
600
400
200
0
200
400
600
Nyquist frequency
Nyquist frequency (550 TV-line)
(a)
(b)
FIGURE 6.7
Examples of pictures of a CZP chart taken at 4.1 μm pitch with a 955(H) × 550(V) pixel CCD: (a) without OLPF;
(b) with OLPF.
* In a TV line expression system, a pair of black and white lines is counted as two lines.
The thickness of the OLPF is chosen so that the shift distance through the crystal equals one-pixel pitch.
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