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Journals >Chinese Optics Letters >Volume 15 >Issue 9 >Page 090101 > Article

Chinese Optics Letters
Vol. 15, Issue 9, 090101 (2017)

Boundary evaluation and error correction on pseudo-random spread spectrum photon counting system

Shanshan Shen^1、2, Qian Chen^1、*, Weiji He¹, and Yuqiang Wang³

Author Affiliations

¹Nanjing University of Science and Technology, Jiangsu Key Laboratory of Spectral Imaging & Intelligence Sense, Nanjing 210094, China

²College of Zi Jin of Nanjing University of Science and Technology, Nanjing 210046, China

³The people’s Liberation Army East Sea Fleet 92713 forces

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DOI: 10.3788/COL201715.090101 Cite this Article Set citation alerts

Shanshan Shen, Qian Chen, Weiji He, Yuqiang Wang. Boundary evaluation and error correction on pseudo-random spread spectrum photon counting system[J]. Chinese Optics Letters, 2017, 15(9): 090101 Copy Citation Text

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Abstract

The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying boundary evaluations. Experimental tests prove that range errors caused by the fluctuation of the number of photon counts in the laser echo pulse leads to the range drift of the time point spread function. The function relationship between the range error and the photon counting ratio is determined by using numerical fitting. Range errors due to a different echo energy is calibrated so that the corrected range root mean square error is improved to 1 cm.

{\bar{ε}}_{r}^{2} = 0.25 Q^{- 1} W_{α}^{- 2},

(1)

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{\bar{ε}}_{r}^{2} = \frac{1}{〈 N_{s} 〉} \frac{(σ_{f}^{2} + σ_{T}^{2}) {(2 σ_{f}^{2} + σ_{T}^{2})}^{3}}{σ_{f}^{3} {(3 σ_{f}^{3} + 2 σ_{T}^{2})}^{3 / 2}} + \frac{1}{K} \frac{(σ_{T}^{2}) {(2 σ_{f}^{2} + σ_{T}^{2})}^{3}}{8 σ_{f}^{3} {(3 σ_{f}^{3} + 2 σ_{T}^{2})}^{3 / 2}},

(2)

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G (t) = \exp (- \frac{t^{2}}{2 σ^{2}}) .

(3)

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FWHM = σ \sqrt{8 \lg 2} .

(4)

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a (t) = \sum_{i = 1}^{N} a_{i} G (t - i T_{c}),

(5)

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m_{s} = \frac{P_{R} η}{h υ} \int_{0}^{\infty} \sum_{i = 1}^{N} a_{i} G (t - i T_{c}) d t .

(6)

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y (t) = \frac{P_{R} η}{h υ} a (t - τ_{d}) + \frac{P_{B} η}{h υ} .

(7)

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Ψ (t) = A_{P} a (t - τ_{d}) + B_{P} .

(8)

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c (t) = 1 - \exp [- \int_{0}^{t} Ψ (u) d u] .

(9)

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p (t) = Ψ (t) \exp [- \int_{0}^{t} Ψ (u) d u] .

(10)

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p (t_{1} t_{2} \dots t_{n} | Ψ (t), τ_{d}) = [\prod_{i = 1}^{n} Ψ (t_{i})] \exp [- \sum_{i = 1}^{n} \int_{0}^{t_{i}} Ψ (u) d u] = [\prod_{i = 1}^{n} Ψ (t_{i})] \exp [- \int_{0}^{T} Ψ (u) d u] = [\prod_{i = 1}^{n} Ψ (t_{i})] \exp (- M) .

(11)

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In [p (t_{1} t_{2} \dots t_{n} | Ψ (t), τ_{d})] = In [Ψ (t_{1})] + In [Ψ (t_{2})] + \dots + In [Ψ (t_{n})] + (- M) .

(12)

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- E {\frac{\partial^{2} In [p (t_{1} t_{2} \dots t_{n} | Ψ (t), τ_{d})]}{\partial τ_{d}^{2}}} = - \int_{- \infty}^{\infty} p (t) \times \frac{\partial^{2} In [p (t_{1} t_{2} ... t_{n} | Ψ (t), τ_{d})]}{\partial τ_{d}^{2}} d t = - \int_{0}^{\infty} Ψ (t) \exp [- \int_{0}^{t} Ψ (u) d u] \frac{\partial^{2} In [p (t_{1} t_{2} ... t_{n} | Ψ (t), τ_{d})]}{\partial τ_{d}^{2}} d t .

(13)

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σ_{τ CRLB} = \sqrt{\frac{1}{- E {\partial^{2} In [p (t_{1} t_{2} ... t_{n} | Ψ (t), τ_{d})] / \partial τ_{d}^{2}}}} .

(14)

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R = \frac{R_{\det}}{R_{base}} .

(15)

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References (18)

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Shanshan Shen, Qian Chen, Weiji He, Yuqiang Wang. Boundary evaluation and error correction on pseudo-random spread spectrum photon counting system[J]. Chinese Optics Letters, 2017, 15(9): 090101

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