Theory Of Tracking Accuracy Of Laser Systems

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Abstract
Optical rangefinders, lidars, and laser tracking systems offer new options for a variety of applications. When a laser system operates in a tracking regime, it must continuously estimate target angle coordinates. This purpose may be achieved by means of a quadrant detector (QD) incorporated in the optical receiver. In this paper, performance of the QD-based laser tracker is evaluated theoretically. Angle measurement span, angle estimation bias, and angle estimation variance are analyzed with the emphasis on the quantitative evaluation of the estimation bias and variance. It is shown that the estimation error contains both systematic error (signal-independent bias) and signal-dependent bias. The systematic error is caused by the signal processing circuitry of the receiver; this error is rather large (up to 1 1.5% of the measurement span), but may be easily cancelled by means of a permanent look-up correction table stored in a ROM (read-only memory). Signal-dependent bias cannot be cancelled with the same technique since it depends on the a priori unknown signal intensity. Fortunately, signal-dependent bias decreases when the SNR (signal-to-noise ratio) increases, at a rate proportional to s/SNR; however, it increases rapidly when the light spot approaches the end of the measurement span. Estimation variance is also evaluated. It is found to decrease when the SNR increases, at a rate roughly proportional to SNR. Estimation variance remains approximately constant as the light spot moves over the measurement span. Thus, the main consequence of the deviation of the light spot from the QD center is the increase of the estimation bias, rather than a change of the estimation variance.
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