LOS WORKSHOPS.

As discussed at the outset of this chapter, our instrument’s tracking volume, and particularly its 120×120 mm X-Y cross-sectional area, makes it unsuitable for use in the majority of AR applications. The tracking volume can be extended in a number of ways, as discussed below.

Additional Sensors

4.6.1.1

The extent of the instrument’s tracking volume can be increased by adding more sensors in an appropriate geometry. Emitters’ 3D positions are calculated by solving an over-defined system of linear equations by least squares; each sensor contributes two equations to the system. Structurally, the calculation scales to more than two sensors and its accuracy should improve (due to a larger number of data points) in cases where three or more sensor sightings of the same emitter are available. In the present geometry, each additional sensor added along the X-axis would increase the tracking volume by about 120 mm in width (and in similar manner for additional sensors added in Y).

We considered the consequences of additional sensors in terms of tracking volume and accuracy. An obvious concern is transitions from sensor pair (A,B) to pair (B,C), i.e., as the target moves laterally in X. We have reason to believe that errors of this form, if non-trivial, should be straightforward to address: First, the transition would not be discontinuous – in the sense that the target will be in view of all three sensors for many pose sample periods. This affords the opportunity to smooth the transition, for example,

by calculating the weighted mean of the emitter positions given by (A,B), (A,B,C) and (B,C), where the weighting shifts according the sensor coordinates from each sensor. Secondly, we can take advantage of the combination of physiological and perceptual phenomena to filter at least the positional pose

components. According to Wallach (1987), human sensitivity to real-virtual displacement is at least an order-of-magnitude smaller in head/body translation compared to head rotation. Secondly, translational velocities and accelerations are miniscule compared to those of rotation (Bussone 2005). Taking these observations into consideration, we hypothesize that filtering position, at the expense of added latency (in position), would be imperceptible; and, by Equation (6), the reduced velocity, on its own, means that the dynamic error due to latency will also be small. Future user studies would enable testing of this

hypothesis and, more generally, yield understanding of per-pose-axis perceptual sensitivity to motion-to- photon latency.

Working Distance

4.6.1.2

Vertical and horizontal FOV increase linearly with distance; sensor spacing and angles could be adjusted to accommodate a larger and wider working volume at a greater distance. The cost, however, is reduced SNR. In the present system, moving from a distance of 800 to 1,200 mm results in a loss of about 6 dB of SNR – about one bit of spatial resolution. The spatial resolution will also be reduced by about 25% at 1,200 mm because the FOV covers a wider distance – amounting to the loss of about another half a bit of resolution. The system would likely still be usable, but at the cost of diminished accuracy

(increased pose uncertainty).

The effects of reduced SNR can be mitigated by improving noise rejection. Specifically, through software configuration changes (a one-line code change to increase TS), we can increase the number of

sensor samples taken per pose sample period. Recalling that our ADCs can digitize at a rate of 1 MHz, each additional sample only costs us only one microsecond. Decimation of the sensor samples by a factor

of four gives the equivalent of 6 dB (one bit) of noise rejection123; the cost to the instrument would be slightly higher latency (due to the additional digitizer sample periods and additional computation). The latency breaks down into an increase in TS by one microsecond per additional sample and an increase in

LTRACK if decimation is implemented in software

124

; if decimation is performed on the raw sensor samples, the software overhead would likely be no greater than one microsecond. Depending on how weak the signal becomes, it may be prudent to increase the gain of the transimpedance amplifiers125 in the sensor’s analog front-end; note that this would not increase noise gain. This change would require modification of the third-party sensor modules (FirstSensor 2013) or building custom sensor modules. This would ensure that one continues to use all of the ADCs’ dynamic range.

Focal Length/Field-of-View

4.6.1.3

Perhaps the simplest and most obvious way to increase tracking volume is to equip the sensors with wider-angle lenses. Again, this would result in a loss of spatial resolution; but, unlike increasing working distance, SNR would remain essentially the same. We estimate126 (but have not verified) that the present instrument, which has some excess spatial resolution (see 4.3.5.1), would see negligible

performance degradation with 35 mm lenses (versus 50 mm) and would most probably still have

acceptable accuracy with 28 mm lenses (though radial distortion correction may become necessary at this focal length). With 28 mm optics, the lateral FOV would be about 228 mm at an 800 mm working distance and about 257 mm at a 900 mm working distance. These sorts of changes, perhaps combined

123 _{Analytically, salient noise sources, such as thermal noise, flicker, and the noise contributions of the amplifiers in}

the analog signal path are almost purely Gaussian and, per our measurements, are substantially more than 1 LSB.

124 _{Decimation could also be implemented within the FPGA fabric, in which case the added latency would be on the}

order of hundreds of nanoseconds.

125 _{A transimpedance amplifier (TIA) converts a current signal into a voltage signal, typically with gain. (See e.g.,}

(Horowitz and Hill 1989)). Such amplifiers are used in the LEPD sensors’ analog front-ends to amplify and buffer the current outputs. For technical reasons, from the amplifier’s standpoint, a TIA has unity (voltage) gain. Thus, increasing the transimpedance gain does not increase (input-referred) noise gain.

126 _{The estimation is based on the increase in linear FOV and the quantization of that increased FOV at the sensor’s}

with additional sensors, would increase the working volume to comfortably accommodate a moderately- active seated person, such as a seated person working at a desk.