Image Processing Reference
In-Depth Information
Nyquist frequency input distribution
(two-pixel cycle)
Ordinary ray
Extraordinary ray
OLPF
(crystal)
OLPF thickness is adjusted so
that separation distance equals
pixel pitch
Distributionof f N component at
sensor surface becomes flat.
Pixel
DISAPPEAR
Image sensor
FIGURE 6.8
Principle operation of an optical low-pass filter.
Because one cycle of the Nyquist frequency input is a two-pixel pitch, it has the spatial
frequency shown by the black and white bars in Figure 6.8. Each intensity of the bars is
divided in half: one half is underneath the pixel and the other adjoins the pixel. (The OLPF
thickness is adjusted so that the separation distance equals the pixel pitch.) Therefore,
each pixel receives a light intensity of half a black bar and half a white bar of the Nyquist
frequency component of input, shown at the top of the figure. This means that the inten-
sity of this frequency component is distributed equally to each pixel, or no amplitude. As
the component of the Nyquist frequency vanishes through the OLPF in this way, the false
signal is greatly reduced, as shown in Figure 6.7b.
As can be understood from the mechanism, the frequency whose amplitude is deleted
perfectly is only one point, the effect remains around the target frequency to reduce the
signal amplitude, as shown in the bottom graph in Figure 6.7b. Thus, the OLPF deletes
the Nyquist frequency component, which causes a false signal and reduces the amplitude
around it and the higher-frequency component of it.
The case of a smaller pixel pitch is discussed. Figure 6.9 shows pictures of a CZP
chart taken by an image sensor at 1.8 μm pitch and 3096(H) × 2328(V) pixels without an
OLPF. Since the resolution of the CZP with a full angle of view is only 600 TV lines, it
was taken with an adjusted angle of view so that the resolution at the horizontal edge
of the CZP is 2350 TV lines, as shown in Figure 6.9a; an expanded picture is shown in
Figure 6.9b. Despite no OLPF, the false signal due to aliasing at the Nyquist frequency is
only slightly observed in the especially emphasized image. While it is observed in the
amplitude distribution, the level is quite light compared with that of the 4.1 μm pixel in
Figure 6.7. Thus, it seems that the Nyquist frequency has moved to a higher-frequency
region where the MTF of the lens is not high, resulting from the achievement of higher-
resolution sensors based on the progress of pixel shrinkage technology. Since the level
of the false signal is light, it tends to be processed using a digital signal processor (DSP)
without an OLPF. Although it depends on the application, two OLPFs are necessary for
vertical and transversal directions or more than two for diagonal directions. Because
one OLPF works for only one direction, it is necessary for the number of OLPF plates
to be in accordance with the number of directions. Additionally, as the thickness of an
OLPF is in the order of hundreds of micrometers, it is effective in achieving thinner
imaging systems, thereby avoiding OLPF usage, since the trend is to reduce the size of
the system.
 
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