Target intensity correction method based on incidence angle and distance for a pulsed Lidar system

Baoling Qi; Baoling Qi; Guohui Yang; Yu Zhang; Chunhui Wang

doi:10.1364/AO.505690

Applied Optics
Vol. 63,
Issue 10,
pp. A86-A97
(2024)
•https://doi.org/10.1364/AO.505690

Target intensity correction method based on incidence angle and distance for a pulsed Lidar system

Baoling Qi, Guohui Yang, Yu Zhang, and Chunhui Wang

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Baoling Qi, Guohui Yang, Yu Zhang, and Chunhui Wang, "Target intensity correction method based on incidence angle and distance for a pulsed Lidar system," Appl. Opt. 63, A86-A97 (2024)

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- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: September 14, 2023
- Revised Manuscript: January 23, 2024
- Manuscript Accepted: February 8, 2024
- Published: March 6, 2024
Virtual Issues
Applied Optics Radiography, Applied Optics, and Data Science 2023 (2024)

Abstract

Pulsed light detecting and ranging (Lidar) is capable of acquiring comprehensive target information within a single pulse, including distance and intensity data. Intensity data reflects the target’s backscattered intensity and is commonly regarded as a crucial observational parameter associated with target reflectivity information. Multiple studies have indicated the potential of intensity data in various applications within pulsed Lidar contexts. However, the intensity data is influenced by the incident angle and distance; hence it cannot directly manifest target characteristics. Consequently, a prerequisite for its usage is the implementation of intensity calibration. This paper presents a target intensity correction method based on an improved tail model, designed for preprocessing intensity data. First, the pulse echo signal equation is derived by incorporating the improved tail model with the detected target. On this foundation, a target echo intensity correction model is established to correct the intensities at various incident angles to those at the normal direction. Lastly, the derived approach is validated through simulation analysis, and practical experiments are conducted on a constructed pulsed Lidar system. These experiments meticulously investigate the influences of incident angle and distance, two prominent factors, on echo intensity. In the context of incident angle correction experiments, the mean absolute errors (MAEs) in calibrated values for diverse targets all remain within 0.04 V. Prior to correction, the maximum MAE for the cystosepiment is 0.505 V; after the correction it is reduced to merely 0.02 V, indicating a 96% reduction in error. Furthermore, all discrepancies exhibit an error standard deviation (ESD) of 0.03 V or less, showcasing favorable stability. For distance correction, under normal incidence conditions, a diverse set of targets is measured at different distances to achieve corrected MAE and ESD within 0.05 V. Consequently, the proposed method effectively achieves intensity correction concerning incident angles and distances. To achieve this, a reflectivity lookup table for the relevant targets was established. Combining this with the corrected intensity information enabled target identification in the three-dimensional imaging of pulsed Lidar.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Fig. 1. Schematic diagram of pulsed Lidar system.

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Fig. 2. Schematic diagram of target detection principle.

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Fig. 3. Schematic diagram of the correction model principle.

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Fig. 4. Echo pulses of the same target at different distances and angles.

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Fig. 5. Echo pulse intensities of the same target at different distances and angles. (a) Different distances and (b) different angles.

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Fig. 6. Experiment system and environment. (a) Experiment system and (b) experiment environment.

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Fig. 7. Echo signals at different angles of incidence.(a) 50% standard reflectance plate. (b) Ferrous plate.

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Fig. 8. Echo signals at different distance. (a) 50% standard reflectance plate. (b) Ferrous plate.

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Fig. 9. Before and after correction echo pulse intensity at different incident angles. (a) Reflectivity plate. (b) Cardboard. (c) Cystosepiment. (d) Clothes.

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Fig. 10. Before and after correction echo pulse intensity at different distances.(a) Reflectivity plate. (b) Cardboard. (c) Cystosepiment. (d) Clothes.

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Fig. 11. Target imaging scene diagram.

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Fig. 12. Three-dimensional distance and intensity images after intensity calibration.(a) Distance image. (b) Intensity image.

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Tables (4)

Table 1. Specifications of the Lidar System

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Table 2. MAE and ESD of Intensity before and after Incident Angle Correction for Different Targets

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Table 3. MAE and ESD of Intensity before and after Distance Correction for Different Targets

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Table 4. Reflectivity of Different Targets with Intensity Calibration

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Equations (23)

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P_{t} (t) = P_{0} (\frac{t - t_{d}}{τ}) \exp (- {(\frac{t - t_{d}}{τ})}^{2}) ∙ H_{e} (t - t_{d}),

H_{e} (x) = \frac{1}{2} (1 + \tanh \frac{x}{e}),

P_{r} = \frac{P_{t}}{Ω_{t} R_{t}^{2}} ∙ \frac{σ_{s}}{4 π R_{r}^{2}} ∙ \frac{π D^{2}}{4} η_{a t m} η_{s y s},

g (x, y) = \frac{2 P_{t}}{π w^{2}} \exp (- 2 \frac{(x^{2} + y^{2})}{w^{2}}),

w = w_{0} \sqrt{1 + {(\frac{λ z}{π w_{0}^{2}})}^{2}},

w_{0} = \frac{2 λ}{π φ},

d σ = 4 π f_{r} (ϕ) \cos^{2} ϕ d A,

d P_{r} (t) = g (x, y) P_{t} (t - t_{d}) f_{r} (ϕ) \cos^{2} ϕ \frac{π D^{2}}{4 R_{r}^{2}} η_{a t m} η_{s y s} d S .

P_{r} (t) = \frac{π D^{2}}{4 R_{r}^{2}} η_{a t m} η_{s y s} \iint g (x, y) P_{t} (t - t_{d}) f_{r} (ϕ) \cos ϕ d S .

\begin{aligned} P_{r} (t) & = \frac{P_{0} D^{2}}{2 w^{2} R_{r}^{2}} η_{a t m} η_{s y s} \iint e^{- 2 (\frac{x^{2} + y^{2}}{w^{2}})} (\frac{t - \frac{2 R}{c} - \frac{2 x \tan ϕ}{c}}{τ}) \\ \times e^{- \frac{{(t - \frac{2 R}{c} - \frac{2 x \tan ϕ}{c})}^{2}}{τ^{2}}} f_{r} (ϕ) \cos ϕ d x d y . \end{aligned}

\begin{aligned} P_{r} (t) & = \frac{P_{0} D^{2} f_{r} (ϕ) \cos ϕ η_{a t m} η_{s y s}}{2 w^{2} R_{r}^{2}} \int_{- \infty}^{+ \infty} e^{- 2 \frac{y^{2}}{w^{2}}} d y \int_{- \infty}^{+ \infty} \\ - (\frac{2 R - c t + 2 x \tan ϕ}{c τ}) e^{- (\frac{{(2 R - c t + 2 x \tan ϕ)}^{2}}{c^{2} τ^{2}} + \frac{2 x^{2}}{w^{2}})} d x . \end{aligned}

\int_{- \infty}^{+ \infty} e^{- 2 \frac{y^{2}}{w^{2}}} d y = w \sqrt{\frac{π}{2}} e r f (\infty) = w \sqrt{\frac{π}{2}} .

\begin{aligned} P_{r} (t) & = \frac{\sqrt{π} P_{0} D^{2} f_{r} (ϕ) \cos ϕ η_{a t m} η_{s y s}}{2 \sqrt{2} w R_{r}^{2}} \int_{- \infty}^{+ \infty} - (\frac{2 R - c t + 2 x \tan ϕ}{c τ}) e^{- (\frac{{(2 R - c t + 2 x \tan ϕ)}^{2}}{c^{2} τ^{2}} + \frac{2 x^{2}}{w^{2}})} d x \\ = - C_{c} \int_{- \infty}^{+ \infty} (\frac{k_{c}}{c τ} + \frac{2 \tan ϕ}{c τ} x) e^{- (a_{c} x^{2} + b_{c} x + c_{c})} d x, \end{aligned}

\begin{aligned} P_{r} (t) = \frac{π P_{0} D^{2} f_{r} (ϕ) \cos ϕ η_{a t m} η_{s y s}}{4 w^{2} R_{r}^{2} (1 - \frac{w^{2} \tan^{3} ϕ}{c^{2} τ^{2} + 2 w^{2} \tan^{2} ϕ})} (\frac{t - \frac{2 R}{c}}{\sqrt{τ^{2} + \frac{2 w^{2} \tan^{2} ϕ}{c^{2}}}}) e^{- {(\frac{t - \frac{2 R}{c}}{\sqrt{τ^{2} + \frac{2 w^{2} \tan^{2} ϕ}{c^{2}}}})}^{2}} . \end{aligned}

I F_{i} = \frac{1}{\sum_{j = 1, j \neq i}^{N_{w} + 1} F_{i, j}},

t_{s} = \frac{\sum_{i = 1}^{N_{w} + 1} I F_{i} ∙ t_{i}}{\sum_{i = 1}^{N_{w} + 1} I F_{i}}, P_{s} = \frac{\sum_{i = 1}^{N_{w} + 1} I F_{i} ∙ P_{i}}{\sum_{i = 1}^{N_{w} + 1} I F_{i}},

Δ t_{T o F} = t_{se} - t_{sr},

R = \frac{1}{2} c ∙ Δ t_{T o F},

I_{c}^{'} = I_{t} ∙ \frac{\cos ϕ_{0}}{\cos ϕ} ∙ ε ∙ \frac{R_{r}^{2}}{R_{0}^{2}},

I_{t} = I_{0} * f_{r} (ϕ),

f_{r} (ϕ) = k_{d} \cos ϕ + \frac{(1 - k_{d})}{\cos^{5} ϕ} \exp (- {(\frac{\tan ϕ}{m})}^{2}),

I_{c} = \frac{I_{c}^{'}}{f_{r} (ϕ)} .

ρ = \frac{I_{c}}{I_{0}} ρ_{0},

Parameter	Value
Laser wavelength	1064 nm
Pulse width	4 ns
Angle of divergence	2 mrad
Model of APD	PDB430C
APD response frequency band	250 MHz
Spectral response frequency band	600 to 1150 nm
Size of APD photosensitive surface	3 mm
Receiving system optical aperture	50 mm
Oscilloscope sampling rate	5 GSa/s
Oscilloscope bandwidth	1 GHz

	MAE/V		ESD/V
Target Object	Before Correction	After Correction	Before Correction	After Correction
Reflectivity plate	0.172	0.035	0.119	0.023
Cardboard	0.359	0.02	0.242	0.014
Cystosepiment	0.505	0.02	0.354	0.023
Clothes	0.26	0.024	0.184	0.027

	MAE/V		ESD/V
Target Object	Before Correction	After Correction	Before Correction	After Correction
Reflectivity plate	0.937	0.025	0.475	0.024
Cardboard	1.043	0.045	0.533	0.045
Cystosepiment	1.435	0.039	0.734	0.044
Clothes	1.094	0.028	0.572	0.028

Target Object	Before Correction
Reflectivity plate	0.47-0.52
Cardboard	0.30-0.35
Cystosepiment	0.69-0.73
Clothes	0.15-0.22

Parameter	Value
Laser wavelength	1064 nm
Pulse width	4 ns
Angle of divergence	2 mrad
Model of APD	PDB430C
APD response frequency band	250 MHz
Spectral response frequency band	600 to 1150 nm
Size of APD photosensitive surface	3 mm
Receiving system optical aperture	50 mm
Oscilloscope sampling rate	5 GSa/s
Oscilloscope bandwidth	1 GHz

Abstract

Data availability

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Figures (12)

Tables (4)

Equations (23)

Applied Optics