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Coded apertures for efficient pyroelectric motion tracking

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Abstract

Coded apertures may be designed to modulate the visibility between source and measurement spaces such that the position of a source among N resolution cells may be discriminated using logarithm of N measurements. We use coded apertures as reference structures in a pyroelectric motion tracking system. This sensor system is capable of detecting source motion in one of the 15 cells uniformly distributed over a 1.6m×1.6m domain using 4 pyroelectric detectors.

©2003 Optical Society of America

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Figures (10)

Fig. 1.
Fig. 1. Schematic representation of the system model
Fig. 2.
Fig. 2. Visibility map for each of the four points in the measurement space. The colored area has a visibility 1 and the other regions have a visibility 0
Fig. 3.
Fig. 3. The angular response pattern of the detector f(θ) used in this work as a function of θ
Fig. 4.
Fig. 4. The plot of response pattern of the detector f(θ) as a function of θ for a mask with a single square hole of size 2mm×2mm is shown in (a) and for a mask with two holes of sizes 2mm×2mm separated by 4mm is shown in (c). The corresponding sensor responses when a source moves at an angular velocity of 8 degrees per second at a distance 40cm is shown in (b) and (d)
Fig. 5.
Fig. 5. The response of the four detectors shown in a single plot. The source is a hot object moving at a velocity 32cm/s at a distance of 1m from the sensor. The source moves through cells with signature vectors [0 0 1 0], [1 0 1 1], [1 1 0 1] and [1 0 0 1]
Fig. 6.
Fig. 6. The event signal of the four detectors derived from the detector signals shown in Fig. 5
Fig. 7.
Fig. 7. Plot showing the state vectors at different time instances as the source moves through cells with signature vectors [0 0 1 0], [1 0 1 1], [1 1 0 1] and [1 0 0 1]
Fig. 8.
Fig. 8. Plot showing the source position at the time instants 2.6, 4, 5.3 and 6.7 seconds. The source is a robot carrying a hot object moving at a velocity of 32cm/s.
Fig. 9.
Fig. 9. Plot showing the source position at the time instants 2.6, 3.8, 5 seconds as the source moves through cells with signature vectors [1 0 0 0], [0 1 1 1] and [1 0 0 1]. The source is a robot carrying a hot object.
Fig. 10.
Fig. 10. Plot showing the source position at the time instants 1.8, 2.6 and 3.4 seconds as a human walks through cells with signature vectors [0 0 0 1], [1 1 0 0] and [1 0 1 0].

Tables (1)

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Table 1. The map showing signature vectors of different cells

Equations (7)

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η = log ( N ) m
s i ( t ) = v ( r i , r ) s ( r , t ) d r i { 1 , 2 , , N } .
m i ( t ) = h ( t t ) s i ( t ) d t i { 1 , 2 , , m } ,
m ˜ i ( t ) = f { m i ( t ) } .
s j = 1 if M = χ j .
h ( θ , t ) = f ( θ ) g ( t ) .
S ˜ = S ˜ o ( 1 e t τ e ) e t τ t
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