Dynamics of Thin-Film Thermal Detectors in Infrared Imaging Systems. 1: Basic Equations and Fourier Analysis

U. Martens; F. Kneubühl

doi:10.1364/AO.13.001455

Applied Optics
Vol. 13,
Issue 6,
pp. 1455-1459
(1974)
•https://doi.org/10.1364/AO.13.001455

Dynamics of Thin-Film Thermal Detectors in Infrared Imaging Systems. 1: Basic Equations and Fourier Analysis

U. Martens and F. Kneubühl

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U. Martens and F. Kneubühl, "Dynamics of Thin-Film Thermal Detectors in Infrared Imaging Systems. 1: Basic Equations and Fourier Analysis," Appl. Opt. 13, 1455-1459 (1974)

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Abstract

The complete Fourier analysis in space and time is performed for a three-dimensional model of thin-film thermal-imaging systems. The model includes heat losses by thermal radiation and by heat conduction within the film as well as into the adjacent medium. Dirac δ functions are used for the description of the specific heat and the thermal conductivity. The exact solutions of the basic heat equation are applied for a comparison of different types of the Panicon, a passive thermal imaging device. The relevant temperature response is illustrated in the Fourier space. The inclusion of the adjacent medium implies an occasional maximum of the response function in k space.

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		Panicon	Membrane Panicon m = xenon	Membrane Panicon m = vacuum
T	K	300	300	300
8σT³	W cm⁻² K⁻¹	1.22 × 10⁻³	1.22 × 10⁻³	1.22 × 10⁻³
b	cm	0.5 × 10⁻³	1.0 × 10⁻³	1.0 × 10⁻³
α	1	0.4	0.4	0.4
∊/α	1	1	1	1
λ_f	W cm⁻¹ K⁻¹	1.0 × 10⁻³	1.5 × 10⁻³	1.5 × 10⁻³
λ_m	W cm⁻¹ K⁻¹	2 × 10⁻³	5.3 × 10⁻⁵	0
ρ_fc_f	W see cm⁻³ K⁻¹	1.2	1.2	1.2
ρ_mc_m	W sec cm⁻³ K⁻¹	1.5	1.0 × 10⁻³	0
A	W cm⁻² K⁻¹	1.22 × 10⁻³	1.22 × 10⁻³	1.22 × 10⁻³
B	W K⁻¹	2.5 × 10⁻⁶	3.8 × 10⁻⁶	3.8 × 10⁻⁶
C	W sec cm⁻² K⁻¹	1.5 × 10⁻³	3 × 10⁻³	3 × 10⁻³
D	W cm⁻¹ K⁻¹	5 × 10⁻³	2.7 × 10⁻⁴	0
a_m	cm² sec⁻¹	1.3 × 10⁻³	5.3 × 10⁻²	—
w₀	cm	4.1	0.22	0
ω₀	sec⁻¹	0.8	0.4	0.4
k₀	cm⁻¹	22	18	18

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Applied Optics