fPitch: a new pattern for lenticular pitch measurement
The traditional pitch measurement pattern
The traditional pitch measurement pattern is an array of bands stacked vertically. Each band is a grid with a different pitch value. The pitch values of the bands form an arithmetic sequence with a pre-specified increment.
An example of a traditional pitch pattern view is shown in Figure 1. Physically, this pattern was 300mm wide and 200mm high and was printed with a printing density of 720 pixels per inch. There are 20 bands with pitch values between 39.5lpi and 40.5lpi. The view shown in Fig. 1 is created by putting a lens with a pitch of exactly 40.00lpi on the printed pattern.
The pitch is determined by visual inspection of the view. One usually selects the pitch value of the band with the longest black interval (preferably, the whole band should be black). If there are two bands with longest and approximately equal black intervals (as in Fig. 1), one usually will estimate the pitch as the mean of the two corresponding bands' pitch values. In this case, this estimate will yield 40.00lpi, which happens to be the exact value.
Figure 1: Pitch measurement pattern view
The main problem with this measurement method is the fact that the view depends on the viewing angle. For example, The same pattern from a different viewing angle looks as shown in Fig. 2:
Figure 2: The pitch measurement pattern of Fig. 1 from another viewing angle
Judging from this view, one may be tempted to estimate the lpi value as 39.974lpi, which is wrong. Experts will prefer the view of Fig. 1 over the view of Fig. 2 because it has a mirror symmetry relative to the chosen lpi value line (which is between the two longest bands). The view of Fig. 2 is clearly asymmetric in this respect, and should not be used for pitch measurement.
The symmetry criterion is relatively easy to apply in this example, in which the measured pitch is located in the pattern center. It is far more difficult if the measured pitch lies near the pattern edges, either the top or the bottom. In such cases, the traditional pattern can lead to an error.
The fPitch pattern
It is hard to avoid the impression that the views shown in Figures 1 and 2 are discrete samples of a certain continuous pattern. This continuous pattern can be revealed by stacking a large number of bands with very small height and with no gaps between them. Such a pattern was introduced and analyzed in the Lenticular Imaging book. The continuous pattern offers better accuracy and reduces the chances of error from using skewed views. We call this continuous pattern 'fPitch'.
A symmetric view of an fPitch pattern is shown in Figure 3. In this view, there is no need for guessing; it can be seen clearly that the pitch value is 40.00lpi.
Figure 3: Symmetrical view of an fPitch pattern
In Figure 4 below a skew view of the fPitch pattern is displayed. The asymmetry is clearly noticeable, indicating that this view must not be used for pitch measurement.
Figure 4: Skew view of an fPitch pattern
fPitch pattern center mode
fPitch pattern has two modes: edge and center.
The shape behind the fPitch pattern is a cross. Figure 3 displays only the right half of this cross. In certain applications, it might be useful to show the whole cross. A pattern showing the whole cross is said to be in center mode.
A view of an fPitch pattern in the center mode is shown in Figure 5. A white hairline was drawn at the center to help in the alignment of the viewing angle for achieving a symmetrical view.
The view in Figure 3 is of a pattern in an edge mode.
Figure 5: Symmetrical view of a centered fPitch pattern
The center node pattern points to a pitch value of 40.00lpi, exactly as the edge pattern.
With a centered pattern, one can measure the pitch values both on the left and the right edges. When the view is perfectly symmetric, as in Figure 5, the edge values are identical (in this example 40.00lpi).
A skew view of this pattern is shown in Figure 6. In this view, the edge pitch values are slightly different, but their average is the correct pitch value, namely 40.00lpi. Therefore, with a centered pattern, the precise pitch value can be determined also from skew views.
Figure 6: Asymmetrical view of a centered fPitch pattern
fPitch pattern in real life
The views shown in figures 3 through 6 are computer-generated. A photo of a real fPitch pattern view is shown in Figure 7.
Figure 7: A real-life photo of an fPitch pattern view
The views shown in figures 1 through 6 are computer-generated. Among other things, they represent an ideal lens. This means, among other things, that there are no pitch variations or grid distortions. Real lenses have both to a certain degree. Such defects cause distortions in the fPitch view and make the measurement ambiguous. Lens defects affect also band patterns views, but the distortion geometry is displayed much more accurately by the fPitch pattern.
A view of a pattern with a heavily distorted (real) lens is shown in Figure 8: