An endoscope objective has a circular clear aperture of area in air ( ) and collects…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

What an Instrument Can See, Ch Radiance, etendue and a throughput budget that is spent

Problem

An endoscope objective has a circular clear aperture of area A=4.0 mm2A = 4.0\ \mathrm{mm}^2 in air (n=1n=1) and collects light out to a half-angle of θ=45∘\theta = 45^\circ from the axis. ((a)) Compute the exact wide-angle etendue Ξ=πn2Asin⁡2θ\Xi = \pi n^2 A \sin^2\theta. ((b)) Compute the paraxial approximation Ξpar=πn2Aθ2\Xi_{\mathrm{par}} = \pi n^2 A \theta^2, with θ\theta in radians. ((c)) By what percentage does the paraxial formula overestimate the exact etendue at this angle?

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