The Dutch National Strip Ticket

1. The Dutch National Strip Ticket INTRODUCTION The Dutch National Strip Ticket (Nationale Strippenkaart) is used as payment for tram and bus transportation in the Netherlands. Per 2008 this ticket carries a new hologram (10 x 49 mm), or rather a DOVID (Diffractive Optically Variable Image Device) because it is a 2D-design, which does not display 3D images. As a consequence it actually does not deserve the proper name “hologram”, which it is often given. However, in the following I’ll call it a hologram for simplicity. The hologram contains one or more non-diffractive moiré-generating areas. These features are interesting examples of one-dimensional moiré magnification, and I discuss their optical properties in this slide presentation. During production of the strip ticket the hologram is not registered horizontally and therefore the position of the moiré-generating areas randomly shifts over different tickets. This is shown in the images of different strip tickets in the next few slides.

2. The Dutch National Strip Ticket The moiré-generating areas contain text patterns consisting of the vertically compressed words “OK”, as illustrated below. It is shown that the moiré effect is brought about by overlaying the pattern with a suitable line grating, parallel with the “OK” text lines. Pr Pl The left “OK” pattern has a vertical period Pl = 0.27 mm while the right “OK” pattern has a vertical period Pr = 0.33 mm. As will appear, in this case, the period Pov of the overlay line grating can best be chosen right between Pl and Pr , that is Pov = 0.30 mm.

3. The Dutch National Strip Ticket The period PT of the moiré lines that result from two parallel gratings with unequal grating periods is respectively given by: and for the left and right “OK” patterns respectively. See: Amidror, I., The theory of the moiré phenomenon, Kluwer Acad. Publ., Dordrecht/Boston/London, 2000, p. 20. For the values of the overlay pattern (Pov = 0.30 mm) and the values of the left and right “OK” patterns (Pl = 0.27 mm and Pr = 0.33 mm) one calculates PT= 3 mm for both the left and the right “OK” images. And PT indeed appears to be the size of the observed moiré letter pattern when a line pattern overlay with a period Pp = 0.30 mm is placed over the strip ticket hologram. The observed effect is based on the well known phenomenon of moiré magnification, which in this case is one dimensional and takes place only in the vertical direction. This is why the original “OK” patterns have been compressed vertically. The moiré magnifications of the left and right patterns are Ml = 11 and Mr = 9. The moiré magnification effect is demonstrated in the next slide.

4. The Dutch National Strip Ticket The enlarged left and right “OK” images move in different directions because Pl <Pov < Pr: the left image moves against the overlay movement while the right image moves with the overlay movement. Observe the moiré phenomenon at some distance PT “OK” modulated line pattern with moving screen overlay “OK” modulated line pattern For Pov > Pl the enlarged moiré image is upright, while for Pov < Pr the enlarged moiré image is upside down. Cleverly, the design uses the letters “O“ and “K”, which are independent of this type of image reversal. The next slide demonstrates this image reversal.

5. A moiré magnification demonstration The animations below demonstrate that moiré magnification is upright in case the overlay grating has the lower spatial frequency (Pov > P), while upside down in case the overlay grating has the higher spatial frequency (Pov < P). The overlay grating periods in this example have been adjusted to give about the same magnification in both cases. Observe the screen from a distance for best visibility of the moiré effect. Pov > P Moiré magnification is upright and moves against the overlay grating. Pov < P Moiré magnification is upside down and moves with the overlay grating. End of presentation