Pattern recognition with wavelength-multiplexed filters

S. K. Case

doi:10.1364/AO.18.001890

Applied Optics
Vol. 18,
Issue 12,
pp. 1890-1894
(1979)
•https://doi.org/10.1364/AO.18.001890

Pattern recognition with wavelength-multiplexed filters

S. K. Case

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S. K. Case, "Pattern recognition with wavelength-multiplexed filters," Appl. Opt. 18, 1890-1894 (1979)

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Abstract

Wavelength-multiplexed matched spatial filters are used in an incoherent optical pattern recognition system. The system produces color-coded correlation responses which allow the simultaneous recognition of several objects and, in addition, reduces the requirements on filter positioning devices. Analysis of the system, comparison with previous systems, experimental results, and discussions are given.

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Term	Amplitude	Location

U₃₁(x₃,y₃,λ₂)	$\frac{λ_{1} {f_{1}}^{2}}{λ_{2} {f_{2}}^{2}} [0 ((x_{3} - x_{31}) \frac{λ_{1} f_{1}}{λ_{2} f_{2}}, y_{3} \frac{λ_{1} f_{1}}{λ_{2} f_{2}})^{*} 0 ((x_{3} - x_{31}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	$x_{31} = \frac{λ_{2}}{λ_{1}} f_{2} sin θ + x_{o} \frac{λ_{2}}{λ_{1}} \frac{f_{2}}{f_{1}}$
U₃₂(x₃,y₃,λ₂)	$\frac{{f_{1}}^{2}}{{f_{2}}^{2}} [X ((x_{3} - x_{32}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})^{*} 0 ((x_{3} - x_{32}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	x₃₂ = f₂ sinθ
U₃₃(x₃,y₃,λ₁)	$\frac{{f_{1}}^{2}}{{f_{2}}^{2}} [0 ((x_{3} - x_{33}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})^{*} 0 ((x_{3} - x_{33}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	$x_{33} = f_{2} sin θ + x_{o} \frac{f_{2}}{f_{1}}$
U₃₄(x₃,y₃,λ₁)	$\frac{λ_{2} {f_{1}}^{2}}{λ_{1} {f_{2}}^{2}} [X ((x_{3} - x_{34}) \frac{λ_{2} f_{1}}{λ_{1} f_{2}}, y_{3} \frac{λ_{2} f_{1}}{λ_{1} f_{2}})^{*} 0 ((x_{3} - x_{34}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	$x_{34} = \frac{λ_{1}}{λ_{2}} f_{2} sin θ$

Term	Output Wavelength	Amplitude	Centered at x₃ =

U₃₁	λ₂	$\frac{λ_{1}}{λ_{2}} [0 (x \frac{λ_{1}}{λ_{2}}, y \frac{λ_{1}}{λ_{2}})^{*} 0 (x, y)]$	$\frac{1}{2} (1 + \frac{λ_{2}}{λ_{1}}) f sin θ$
U₃₂	λ₂	[X(x,y) * 0(x,y)]	f sinθ
U₃₃	λ₁	[0(x,y) * 0(x,y)]	$\frac{1}{2} (1 + \frac{λ_{1}}{λ_{2}}) f sin θ$
U₃₄	λ₁	$\frac{λ_{2}}{λ_{1}} [X (x \frac{λ_{2}}{λ_{1}}, y \frac{λ_{2}}{λ_{1}})^{*} 0 (x, y)]$	$\frac{λ_{1}}{λ_{2}} f sin θ$

Term	Output Wavelength	Amplitude	Centered at x₃ =

U₃₅	λ₂	$\frac{λ_{1}}{λ_{2}} [0 (x \frac{λ_{1}}{λ_{2}}, y \frac{λ_{1}}{λ_{2}})^{*} X (x, y)]$	$\frac{1}{2} (1 + \frac{λ_{2}}{λ_{1}}) f sin θ$
U₃₆	λ₂	[X(x,y) * X(x,y)]	f sinθ
U₃₇	λ₁	[0(x,y) * X(x,y)]	$\frac{1}{2} (1 + \frac{λ_{1}}{λ_{2}}) f sin θ$
U₃₈	λ₁	$\frac{λ_{2}}{λ_{1}} [X (x \frac{λ_{2}}{λ_{1}}, y \frac{λ_{2}}{λ_{1}})^{*} X (x, y)]$	$\frac{λ_{1}}{λ_{2}} f sin θ$

Term	Amplitude	Location

U₃₁(x₃,y₃,λ₂)	$\frac{λ_{1} {f_{1}}^{2}}{λ_{2} {f_{2}}^{2}} [0 ((x_{3} - x_{31}) \frac{λ_{1} f_{1}}{λ_{2} f_{2}}, y_{3} \frac{λ_{1} f_{1}}{λ_{2} f_{2}})^{*} 0 ((x_{3} - x_{31}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	$x_{31} = \frac{λ_{2}}{λ_{1}} f_{2} sin θ + x_{o} \frac{λ_{2}}{λ_{1}} \frac{f_{2}}{f_{1}}$
U₃₂(x₃,y₃,λ₂)	$\frac{{f_{1}}^{2}}{{f_{2}}^{2}} [X ((x_{3} - x_{32}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})^{*} 0 ((x_{3} - x_{32}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	x₃₂ = f₂ sinθ
U₃₃(x₃,y₃,λ₁)	$\frac{{f_{1}}^{2}}{{f_{2}}^{2}} [0 ((x_{3} - x_{33}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})^{*} 0 ((x_{3} - x_{33}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	$x_{33} = f_{2} sin θ + x_{o} \frac{f_{2}}{f_{1}}$
U₃₄(x₃,y₃,λ₁)	$\frac{λ_{2} {f_{1}}^{2}}{λ_{1} {f_{2}}^{2}} [X ((x_{3} - x_{34}) \frac{λ_{2} f_{1}}{λ_{1} f_{2}}, y_{3} \frac{λ_{2} f_{1}}{λ_{1} f_{2}})^{*} 0 ((x_{3} - x_{34}) \frac{f_{1}}{f_{2}}, y_{3} \frac{f_{1}}{f_{2}})]$	$x_{34} = \frac{λ_{1}}{λ_{2}} f_{2} sin θ$

Term	Output Wavelength	Amplitude	Centered at x₃ =

U₃₁	λ₂	$\frac{λ_{1}}{λ_{2}} [0 (x \frac{λ_{1}}{λ_{2}}, y \frac{λ_{1}}{λ_{2}})^{*} 0 (x, y)]$	$\frac{1}{2} (1 + \frac{λ_{2}}{λ_{1}}) f sin θ$
U₃₂	λ₂	[X(x,y) * 0(x,y)]	f sinθ
U₃₃	λ₁	[0(x,y) * 0(x,y)]	$\frac{1}{2} (1 + \frac{λ_{1}}{λ_{2}}) f sin θ$
U₃₄	λ₁	$\frac{λ_{2}}{λ_{1}} [X (x \frac{λ_{2}}{λ_{1}}, y \frac{λ_{2}}{λ_{1}})^{*} 0 (x, y)]$	$\frac{λ_{1}}{λ_{2}} f sin θ$

Abstract

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Tables (3)

Equations (9)

Applied Optics