In previous work, the information obtained from existing small (8x8) ASP arrays was sufficient to localize the three-dimensional position of a single point source with high precision [28]. The information in each ASP was converted to a vector representing the intensity and incident angle observed by a given pixel (composed of 8 sensors with responses of the form in Eq. 3.1). Simple triangulation of these vectors was sufficient to determine a three-dimensional location for the source. However, multiple sources, such as those in Fig. 3.3, generate responses that cannot be well described with a single angle. In addition, the periodic nature of an ASP’s response leads to ambiguity that is difficult to resolve when multiple sources are present. Additional information is needed to find the position of multiple sources. The key to localizing multiple sources is to rely on diversity in angle-sensitive pixels, in particular, by varying α and β in adjacent pixels. If adjacent ASPs have distinct angular sensitivities, their responses will be less correlated, recovering
Figure 3.4: 32x32 array of angle sensitive pixels (8192 individual sensors) manufac- tured in 130nm standard CMOS process. Approximate dimensions: 700 microns wide, 1200 microns long.
more information about the available incident light, aiding in the localization of multiple sources. For the manufacturing process used here, four ASP designs, two with small vertical inter-grating spacing and two with large vertical inter-grating spacing, provided good performance. Based on simulation, the ASPs with small inter-grating spacing are predicted to have a low periodicity response (small β) to incident angle; large inter-grating spacing results in an ASP with a high periodicity response to incident angle (large β).
3.4
Results
We manufactured a 32x32 array of ASPs using all four designs in an IBM ana- log/mixed mode 130nm CMOS process. Figure 3.4 shows a photo of the entire array. All measurements were taken with bare dies as received from the foundry. We did not perform any post-processing or modification on the dies. To confirm angle sensitivity, we fixed packaged dies to a freely rotating mount facing a col-
limated beam of light generated by a green LED (center wavelength 532nm and spectral width 25nm). As the chip rotated, we measured the response of each of the four ASP designs to changes in incident angle. The observed responses are very similar to the predicted ASP responses. Two measured responses from particular ASPs, one low periodicity (small inter-grating spacing) and one high periodicity (large inter-grating spacing), are shown in Fig. 3.5(a) and 3.5(b).
These directly measured responses contain both intensity as well as incident angle information. To extract the structure-dependent response of the two different ASPs, we subtracted complementary sensory outputs (those with identical β but with α’s different by π) to obtain the curves of Fig. 3.5(c) and 3.5(d). If we normalize by the sum of the same pair of outputs, Eq. 3.1 predicts the result to have a sinusoidal response of the form
I = Iom cos(βθ + α) (3.2)
Figures 3.5(e) and 3.5(f)demonstrate the periodic response to incident angle for two phases (α=0, π/2) and two periodicities (β = 12, 20). The measured incident angle dependent curves closely follow the sinusoidal model of Eq. 3.2.
Localization was performed using the difference-and-normalize approach used to generate Eq. 3.2. As overall intensity information is normalized, all of our re- sults rely exclusively on the measured angular information. Suppressing intensity information provides better insensitivity to measurement artifacts such as fixed pattern noise. Furthermore, the fact that ignoring intensity information does not degrade our ability to localize sources indicates that there is far more useful infor- mation in local angular information than in intensity.
For multiple source localization, we placed two fluorescent clumps (irregularly shaped, approximately 100 microns in size, and composed of Invitrogen Fluo- Spheres with 510nm emission peak) at a height of approximately 1.5mm above
2.5 2 1.5 1 0.5 0 -40 -20 0 20 40 R esponse (V)
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(a) 2.5 2 1.5 1 0.5 0 -40 -20 0 20 40 R esponse (V)
Incident angle, degrees
(b) 1.5 1 0.5 -0.5 -1 0 -40 -20 0 20 40 Dif fer enc e (V)
Incident angle, degrees -1.5 (c) 1.5 1 0.5 -0.5 -1 0 -40 -20 0 20 40 Dif fer encee (V)
Incident angle, degrees -1.5 (d) 1.5 1 0.5 -0.5 -1 0 -40 -20 0 20 40 Norma liz ed Dif fer ence (V)
Incident angle, degrees -1.5 (e) 1.5 1 0.5 -0.5 -1 0 -40 -20 0 20 40 Norma liz ed Dif fer ence (V)
Incident angle, degrees -1.5
(f)
Figure 3.5: Representative ASP outputs: (a) and (b), response to incident angle for the four different offsets α in one orientation for two ASPs with different βs; (c) and (d), difference between responses of complementary offsets (pairs where α’s are different by π); (e) and (f), difference between responses of complementary offsets normalized by their respective sums. These two normalized outputs are sinusoidal in nature and exhibit a phase shift of π/2.
(a) (b)
(c) (d)
(e) (f)
Figure 3.6: Example array outputs for different source configurations. (a) and (b), one fluorescent source for two sensors with different β values; (c) and (d), different fluorescent source at another location for same types of sensor; (e) and (f), both sources simultaneously illuminated. Responses in (e) suggest either single distant source or relatively uniform illumination. Responses in (f) suggest a single nearby source. Considering both (e) and (f) together suggests that the source arrangement is more complex (multiple sources).
(a) (b) (c)
Figure 3.7: Estimated position of a single source based on correlations between predicted and observed sensor outputs: (a) estimate using only low periodicity ASPs, (b) estimate using only high periodicity ASPs, (c) estimate using both types of ASP.
(a) (b) (c)
Figure 3.8: Estimated position of two sources based on correlations between pre- dicted and observed sensor outputs: a) estimate using only low periodicity ASPs, b) estimate using only high periodicity ASPs, c) estimate using both types of ASP. the array. Figures 3.6(a)–3.6(d) show the fluorescence responses recorded for one orientation of two different ASP types with different β values when the two clumps were stimulated individually. The periodic nature is clearly apparent. Stimulating both clumps simultaneously and measuring from the same ASP types, we observe the responses in Figs. 3.6(e) and 3.6(f).
To determine the fluorescent source arrangement in three dimensions, we pre- dicted the response of each sensor to a source at each location (using Eq. 3.2)
and correlated these predicted responses to the actual response to estimate the likelihood of a source at each location. First, this technique was used to attempt identification of a single source. Using only the responses of a single ASP type with low β, we observe a high likelihood for sources in two locations (Fig. 3.7(a)). If we use only the response of a single ASP type with high β, we observe many possible sources (Fig. 3.7(b)). When we use the predictions both sensor types provide, we find the more precise position of a single source (Fig. 3.7(c)).
We observe similar results in the presence of two sources. Figures 3.8(a) and 3.8(b) illustrate ambiguous source location estimates when using only a single ASP type. However, the combination of both low β and high β ASPs permits not only determination of the presence of two sources but also localization of their position (Fig. 3.8(c)).