A dry microscope objective images a specimen in air at a vacuum wavelength of
PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Interference and diffraction
What an Instrument Can See, Ch Pupils: the aperture of a linear system
Problem
A dry microscope objective images a specimen in air at a vacuum wavelength of 550nm. Refer everything to the specimen side, where the marginal ray makes a half angle θ with the axis in air, and take the tolerated geometrical blur diameter there to be c=2.0μm.
((a)) At NA=0.25 and at NA=0.90, compute the quarter-wave depth of focus λ0/(2n(1−cosθ)) and the geometrical range c/tanθ, and say which one sets how far the focus can move in each case.
((b)) Find the numerical aperture at which the two ranges are equal, and give that common range.
((c)) Show that, at small angles, the ratio of the two ranges is about λ0/(cθ), and use it to explain why, at this fixed c, the wave floor wins at low numerical aperture and the blur circle at high numerical aperture.