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Modified range equation for exact modeling and design optimization of active laser remote sensing systems

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Abstract

An exact modeling for laser target illumination and electro-optic detection parameters used in most common laser remote sensing systems, such as laser microphones, LiDARs, laser range finders, laser spot tracking, laser designation, stand-off laser spectroscopy (Raman, LIBS, LIF,…), laser imaging of remote targets and all laser transceiver system having a laser source and an electro-optical detection measure in one assembly. The model makes possible to embed most basic parameters in one equation to ease the design of the main system components from engineering point of view, instead of the currently used general models. The resulting equation corrects calculations for short standoff target detection parameters.

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Abbreviations

\(\alpha\) :

Linear absorption coefficient of atmosphere for the laser wavelength (m−1)

\(\alpha_{Q}\) :

Linear absorption coefficient of atmosphere for the peak target emission wavelength (m−1)

\(\beta\) :

Optical magnification (dimensionless)

\(\lambda\) :

Laser wavelength (m)

\(\delta\) :

Laser beam divergence (Rad)

\(\varepsilon\) :

Optical system transitivity (dimensionless)

\(\eta\) :

Responsivity of the electro-optic detector (A W−1)

θ:

Inclination of target surface with respect to the axe of the falling laser radiation (deg)

\(\varphi\) :

Diameter of the optical collector (m)

\(\Omega_{S}\) :

Solid angle in front of the laser source (Rad)

\(\Omega_{T}\) :

Solid angle in front of the target (Rad)

\(A_{D }\) :

Surface area of electro-optical detector (m2)

\(A_{I }\) :

Surface area of laser spot in the image plane (m2)

\(A_{R }\) :

Surface area of the receiver collector (m2)

\(A_{T}\) :

Surface area of the target laser spot (m2)

\(B\) :

Feedback loop

\(C\) :

Radius of the circle of confusion (m)

\(d\) :

Distance to target (m)

\(d_{L}\) :

Theoretical distance at which the applicability limit of standard range equation ends (m)

\(F\) :

Optical collector focal length (m)

\(\Delta F\) :

Optical collector focal depth (m)

\(f\) :

f-number of the optical collector

\(G\) :

Amplifier gain (dimensionless)

\(G_{n}\) :

Gain of the n-th amplifier (dimensionless)

\(h_{D }\) :

Radius of target laser spot image on the detector (m)

\(h_{T}\) :

Radius of the laser spot image on the target (m)

\(I_{R }\) :

Intensity of the diffuse laser radiation from the target at the receiver aperture

\(I_{S }\) :

Intensity of the laser source radiation (W m−2)

\(I_{T }\) :

Intensity of the diffuse laser radiation from target vicinity (W m−2)

\(J\) :

Electro-optic detector photo-current (A)

\(K\) :

Scattering coefficient of the Lambertiant target (dimensionless)

\(l\) :

Target laser spot image distance from optical collector (m)

\(M\) :

Ratio between \(A_{T}\) and \(A_{D}\) (dimensionless)

\(N\) :

Noise factor (dimensionless)

\(N_{n}\) :

Noise factor of the n-th amplifier (dimensionless)

\(P_{D}\) :

Received laser power at the electro-optical detector window (W)

\(P_{S }\) :

Laser source beam optical power (W)

\(Q\) :

Quantum efficiency of the laser-matter interaction (dimensionless

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Acknowledgements

The authors are very grateful to the committee of Physics Department of the Faculty of Science at Cairo University for their support and helpful suggestions.

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, Cairo University, Giza, Egypt

    H. S. Ayoub

  2. OptoElectronics Department, Military Technical College, Cairo, Egypt

    A. M. Mokhtar

  3. Engineering Physics Department, Laser Photonics Research Center, Military Technical College, Cairo, Egypt

    Ashraf F. El-Sherif

  4. Department of Basic Science, ELGazeera High Institute for Engineering and Technology, Cairo, Egypt

    Y. H. Elbashar

  5. Egypt Nanotechnology Center (EGNC), Cairo University, Giza, Egypt

    Y. H. Elbashar

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  1. H. S. Ayoub
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  2. A. M. Mokhtar
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  3. Ashraf F. El-Sherif
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  4. Y. H. Elbashar
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Correspondence to Y. H. Elbashar.

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Ayoub, H.S., Mokhtar, A.M., El-Sherif, A.F. et al. Modified range equation for exact modeling and design optimization of active laser remote sensing systems. Opt Quant Electron 53, 110 (2021). https://doi.org/10.1007/s11082-021-02759-5

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