Theory of Thermal Imaging Using Infrared to Visible Image Up-Conversion

K. F. Hulme; J. Warner

doi:10.1364/AO.11.002956

Applied Optics
Vol. 11,
Issue 12,
pp. 2956-2964
(1972)
•https://doi.org/10.1364/AO.11.002956

Theory of Thermal Imaging Using Infrared to Visible Image Up-Conversion

K. F. Hulme and J. Warner

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K. F. Hulme and J. Warner, "Theory of Thermal Imaging Using Infrared to Visible Image Up-Conversion," Appl. Opt. 11, 2956-2964 (1972)

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Abstract

A novel method of thermal imaging based on the up-conversion of infrared radiation in nonlinear optical crystals is analyzed. An equation is derived giving the temperature resolution in terms of the pump laser energy E_p. For a proustite–ruby system based on the 8–13-μ band, a temperature resolution of better than 1 °C is predicted when the number of resolvable spots is 100 × 100 and E_p = 10 J. Numerical results are also provided for eighteen possible systems having different combinations of pump laser (neodymium or ruby), infrared band (3–5 μ or 8–13 μ), nonlinear crystal (Ag₃AsS₃, AgGas₂, ZnGeP₂, or LiNbO₃), and imaging photocathode [S-1,S-20, GaAs/(Cs,O), or In(As,P)/(Cs,O)].

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Factor	Value	Comment
k	1	This low value is justified on the grounds that, when looking at an over-all image, the observer integrates over several picture elements to discern a shape.
η_c	2.2 × 10⁻⁷	W⁻¹ cm² cm⁻²; type 1 matching (see Ref. 2).
η_D	2 × 10⁻²	Assumes a filter transmission factor of 20% and a photocathode quantum efficiency of 10%.
η_i	2.703	See Refs. 4 and 5.
A	1.026 × 10⁻⁴	rad² (cm⁻¹)⁻¹; calculated from Eq. (A2) using refractive index data given in Ref. 5.
N_{ν_i}	5.808 × 10⁻⁶	W cm⁻² sr⁻¹ (cm⁻¹)⁻¹; room temperature blackbody spectral radiance at 1250 cm⁻¹.
dN_{ν_i}/dT	1.164 × 10⁻⁷	W cm⁻² sr⁻¹ (cm⁻¹)⁻¹ K⁻¹.
ν_i′	1250	cm⁻¹; tangentially phase-matched at center of field of view.
ν_i′ − ν_i″	225	cm⁻¹; set by a half-cone angle of 1 rad into the proustite crystal.
θ_m	29	degrees; type 1 tangential matching for ν_i = 1250 cm⁻¹.
ϕ_p	94	mrad.
k_s	2.84 × 10⁵	cm⁻¹ extraordinary ray	All calculated from refractive index data given by Ref. 5
k_p	2.68 × 10⁶	cm⁻¹ ordinary ray
k_i	1.70 × 10⁴	cm⁻¹ ordinary ray
dk_i/dν_i	17.4	cm⁻¹ (cm⁻¹)⁻¹
dΔk/dν_i	5.7	cm⁻¹ (cm⁻¹)⁻¹

Factor	Value	Comment
k	1	This low value is justified on the grounds that, when looking at an over-all image, the observer integrates over several picture elements to discern a shape.
η_c	2.2 × 10⁻⁷	W⁻¹ cm² cm⁻²; type 1 matching (see Ref. 2).
η_D	2 × 10⁻²	Assumes a filter transmission factor of 20% and a photocathode quantum efficiency of 10%.
η_i	2.703	See Refs. 4 and 5.
A	1.026 × 10⁻⁴	rad² (cm⁻¹)⁻¹; calculated from Eq. (A2) using refractive index data given in Ref. 5.
N_{ν_i}	5.808 × 10⁻⁶	W cm⁻² sr⁻¹ (cm⁻¹)⁻¹; room temperature blackbody spectral radiance at 1250 cm⁻¹.
dN_{ν_i}/dT	1.164 × 10⁻⁷	W cm⁻² sr⁻¹ (cm⁻¹)⁻¹ K⁻¹.
ν_i′	1250	cm⁻¹; tangentially phase-matched at center of field of view.
ν_i′ − ν_i″	225	cm⁻¹; set by a half-cone angle of 1 rad into the proustite crystal.
θ_m	29	degrees; type 1 tangential matching for ν_i = 1250 cm⁻¹.
ϕ_p	94	mrad.
k_s	2.84 × 10⁵	cm⁻¹ extraordinary ray	All calculated from refractive index data given by Ref. 5
k_p	2.68 × 10⁶	cm⁻¹ ordinary ray
k_i	1.70 × 10⁴	cm⁻¹ ordinary ray
dk_i/dν_i	17.4	cm⁻¹ (cm⁻¹)⁻¹
dΔk/dν_i	5.7	cm⁻¹ (cm⁻¹)⁻¹

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Applied Optics