Characterization of an optical-fiber reflectometer for in situ measurement applications

D. Hernandez; G. Olalde; E. Milcent; A. Beck

doi:10.1364/AO.34.007952

Applied Optics
Vol. 34,
Issue 34,
pp. 7952-7958
(1995)
•https://doi.org/10.1364/AO.34.007952

Characterization of an optical-fiber reflectometer for in situ measurement applications

D. Hernandez, G. Olalde, E. Milcent, and A. Beck

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D. Hernandez, G. Olalde, E. Milcent, and A. Beck, "Characterization of an optical-fiber reflectometer for in situ measurement applications," Appl. Opt. 34, 7952-7958 (1995)

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Abstract

We present studies of apparatus based on optical-fiber probes for measuring the reflectivity of opaque materials. The probes are designed for in situ applications at high temperatures and in situations for which access is difficult. First, we present a method in which the hemispherical reflectivity and the angular distribution of the reflected flux are obtained from bidirectional measurements. Second, we describe a method to measure the reflectivity in only the normal direction; this method is available only for diffuse materials. Both methods of use of the device were validated through the use of commercial diffuse standards and specific materials with particular surface microstructures.

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Variable or Symbol	Definition
λ	Wavelength
ɛ	Emissivity
ρ	Reflectivity
θ _o	Optical-fiber aperture angle
θ _i	Incident angle
θ _r	Reflection angle
Ω _i	Solid angle of illumination
Ω _r	Solid angle of observation
Φ ^I	Incident flux
Φ ^E	Emitted flux
Φ ^R	Reflected flux
Φ ^E ⁺ ^R	Emitted and reflected flux
NA	Numerical aperture
OF	Optical fiber
I	Detected signal value
a	Radius of the OF core
r	Radius of the OF
L _i	Intensity of the illumination flux from the OF in the incident direction θ _i
L _r	Intensity of the reflected flux from the sample in the observed direction θ _r from the incident direction θ _i
T	Temperature
S _F	Surface area of the OF core
S _I	Surface area illuminated by the OF
S _O	Surface area observed by the OF
S _A	Active surface area at the intersection of S _I and S _O on the sample surface and observed by the OF
R	Radius of the illuminated or the observed surface from the normal direction and at distance d
e	Half-interaxis between the two parallel OF’s of the normal probe
d	Distance between the observation face of the OF and the sample surface
d _M	Observation distance that corresponds to the maximum signal of a normal probe
k	Proportionality factor
t	Time

Parametera Reflectivity	Spectralon Reference Samples			Experimental Samples

	Number 98	Number 75	Number 50	Polished Gold	Oriented Surface
ρ″(0.0) (sr⁻¹)	0.390	0.305	0.202	3.532	0.028
ρ″(0.10) (sr⁻¹)	0.388	0.299	0.190	2.000	0.028
ρ″(0.20) (sr⁻¹)	0.378	0.294	0.186	0.876	0.042
ρ″(0.30) (sr⁻¹)	0.363	0.285	0.180	0.141	0.039
ρ″(0.40) (sr⁻¹)	0.342	0.272	0.720	0.056	0.042
ρ″(0.50) (sr⁻¹)	0.313	0.253	0.160	0.035	0.039
ρ″(0.60) (sr⁻¹)	0.275	0.227	0.144	0.022	0.032
ρ′^∩(0)	0.980	0.780	0.496	0.906	0.108
${ρ_{st}^{'}}^{\cap} (0)$ b	0.980	0.760	0.500

Variable or Symbol	Definition
λ	Wavelength
ɛ	Emissivity
ρ	Reflectivity
θ _o	Optical-fiber aperture angle
θ _i	Incident angle
θ _r	Reflection angle
Ω _i	Solid angle of illumination
Ω _r	Solid angle of observation
Φ ^I	Incident flux
Φ ^E	Emitted flux
Φ ^R	Reflected flux
Φ ^E ⁺ ^R	Emitted and reflected flux
NA	Numerical aperture
OF	Optical fiber
I	Detected signal value
a	Radius of the OF core
r	Radius of the OF
L _i	Intensity of the illumination flux from the OF in the incident direction θ _i
L _r	Intensity of the reflected flux from the sample in the observed direction θ _r from the incident direction θ _i
T	Temperature
S _F	Surface area of the OF core
S _I	Surface area illuminated by the OF
S _O	Surface area observed by the OF
S _A	Active surface area at the intersection of S _I and S _O on the sample surface and observed by the OF
R	Radius of the illuminated or the observed surface from the normal direction and at distance d
e	Half-interaxis between the two parallel OF’s of the normal probe
d	Distance between the observation face of the OF and the sample surface
d _M	Observation distance that corresponds to the maximum signal of a normal probe
k	Proportionality factor
t	Time

Parametera Reflectivity	Spectralon Reference Samples			Experimental Samples

	Number 98	Number 75	Number 50	Polished Gold	Oriented Surface
ρ″(0.0) (sr⁻¹)	0.390	0.305	0.202	3.532	0.028
ρ″(0.10) (sr⁻¹)	0.388	0.299	0.190	2.000	0.028
ρ″(0.20) (sr⁻¹)	0.378	0.294	0.186	0.876	0.042
ρ″(0.30) (sr⁻¹)	0.363	0.285	0.180	0.141	0.039
ρ″(0.40) (sr⁻¹)	0.342	0.272	0.720	0.056	0.042
ρ″(0.50) (sr⁻¹)	0.313	0.253	0.160	0.035	0.039
ρ″(0.60) (sr⁻¹)	0.275	0.227	0.144	0.022	0.032
ρ′^∩(0)	0.980	0.780	0.496	0.906	0.108
${ρ_{st}^{'}}^{\cap} (0)$ b	0.980	0.760	0.500

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Applied Optics