Table 4.

Selected intensity correction and calibration methods (A, B, C, D denote empirical coefficients, ref denotes a reference).

Reference	Scanner	Level	Targets	Parameters	Theoretical Model	Empirical Model
Luzum et al. [94]	(ALS) Optech ALTM 1233	1	n/a	range (R)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}$	n/a
Coren & Sterzai [68]	(ALS) Optech ALTM3033	1	homogenous surface (asphalt road)	range (R)angle of incidence (α) atm. attenuation coeff. (a)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{1}{\cos \text{α}}$	$I_c=I\times e^{-AR}$
Starek et al. [73]	(ALS) Optech ALTM 1233	1	n/a	range (R)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}$	n/a
Hofle & Pfeifer [70]	(ALS) Optech ALTM 3100	1	homogenous surface (asphalt road)	range (R)angle of incidence (α) atm. attenuation coeff. (a) transmitted energy (ET)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{1}{\cos \text{α}}\times {10}^{-2aR}\times \frac{E_{Tref}}{E_{Tj}}$	$I_c= I_{1000}\times f\left(R\right)$ $f\left(R\right)=A{R}^2+BR+\left(1-{1000}^{2}A -1000 B\right)$
Jutzi and Gross [71]	(ALS) RIEGL LMS—Q560	1	homogenous surface (roof planes)	range (R)angle of incidence (α) atm. attenuation coeff. (a)	n/a	$I_c=I\times R^A\times e^{2BR}\times co{s}^C\left(\text{α}\right)\times e^D$
Korpela et al. [27]	(ALS) Optech ALTM3100Leica ALS50	1	homogenous surface	range (R) automatic gain control (Gc)	n/a	$I_{c= }I\times \frac{{R_i}^A}{{R_{ref}}^A}+\text{I}\times \text{B}\times \left(\text{C}-\text{Gc}\right)$
Vain et al. [95]	(ALS) Leica ALS50-II	1	brightness calibration targets (tarps)	automatic gain control (Gc)	n/a	$I_c=A+B\times I+C\times I\times \text{Gc }$
Habib et al. [96]	(ALS) Leica ALS50	1	n/a	range (R) angle of incidence (α)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{1}{\cos \text{α}}$	n/a
Yan et al. [58]	(ALS) Leica ALS50	1	n/a	range (R) angle of incidence (α) atm. attenuation coeff. (a)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{1}{\cos \text{α}}\times e^{-2aR}$	n/a
Ding et al. [69]	(ALS) Leica ALS50-I	1	overlapping scan areas	range (R) angle of incidence (α) atm. attenuation coeff. (a)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{1}{\cos \text{α}}\times {10}^{-2aR}$	$I_{c*}=I_c\times R^A\times {10}^{-2BR}\times co{s}^C\left(\alpha \right)\times e^D$ and Phong model
Ahokas et al. [77]	(ALS) Optech ALTM 3100	3	brightness calibration targets (tarps)	range (R) atm. attenuation coeff. (a) transmitted energy (ET) reflectance (ρ)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{E_{Tref}}{E_{Tj}}$	$\text{ρ}=A\times I_c+B$
Kaasalainen et al. [61]	(ALS) Optech ALTM 3100 Topeye MK Leica ALS50	3	sand and gravel	range (R) angle of incidence (α) total atmosphere transmittance (T) pulse energy (ET)	method described by Vain et al. (2009)	$\text{ρ}=\frac{I_c}{I_{ref}}$ where: Iref is reference Intensity measured at the same range of targets
Vain et al. [65]	(ALS) Above scanners + Optech ALTM 2033	3	natural & commercial targets, brightness calibration targets (tarps)	range (R)angle of incidence (α) total atmosphere transmittance (T) pulse energy (ET)	$I_c=I\times \frac{{R_i}^2}{{R_{ref}}^2}\times \frac{1}{\cos \text{α}}\times \frac{1}{T^2}\times \frac{E_{Tref}}{E_{Tj}}$	$\text{ρ}=I_c\times \frac{{\text{ρ}}_{ref}}{I_{c.ref}}$
Briese et al. [97]	(ALS) RIEGL VQ820-G LMS-Q680i VQ-580	3	asphalt road, stone pavement	range (R) angle of incidence (α) detected power (Pr) empirical calibration constant (Ccal) reflectance (ρ)	$\text{ρ}=C_{cal}\times \frac{{R_i}^2}{\cos \text{α}}$	$C_{cal}={\text{ρ}}_{ref}\times \frac{\cos {\text{α}}_{ref}}{{R_{ref}}^2}$
Errington et al. [98]	(TLS) 3DLS-K2	1	overlapping scan areas	range (R) angle of incidence (α) pseudo-reflectance (ρ)	n/a	The separation model proposed by Pfeifer et al. (2008)
Fang et al. [21]	(TLS) Z + F Imager5006i	1	White paper targets	range (R) angle of incidence (α) near-distance effect (n(R))	n/a	$I=n\left(R\right)\times \frac{A\times (1-B+B\cos \text{α})}{R^2}$
Pfeifer et al. [63,64]	(TLS) Riegl LMS-Z420i & Optech ILRIS 3D	3	brightness calibration targets (Spectralon )	range (R) angle of incidence (α) reflectance (ρ)	n/a	(1) $I=g_1\left(R\right)·g_2\left(\text{ρ}\cos \left(\alpha \right)\right)$ (2) $I=g_3\left(\text{ρ}\cos \left(\alpha \right), g_4\left(R\right)\right)$ where: g1: linear, g2: xA, g3: cubic polynomial, g4: vector valued
Kaasalainen et al. [59,60]	(TLS) FARO LS HE80	3	brightness calibration targets (Spectralon)	range (R) reflectance (ρ)	n/a	$\text{ρ}={10}^{\frac{\frac{I}{I_{ref}}-A}{B}}$ where: Iref is 99% Spectralon ® reference Intensity measured at the same range of targets
Kaasalainen et al. [59]	(TLS) Leica HDS6000	3	brightness calibration targets (Spectralon) gravel	range (R)	n/a	$\text{ρ}=\frac{I}{I_{ref}}$ where: Iref is 99% Spectralon ® reference Intensity measured at the same range of targets