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Imaging problems Depth of field in imaging But not ideal! Maps (and blurs) a very narrow angle range from one object point Dq r/L to one image point. Depth of field in imaging Sometimes a nice effect, sometimes a problem Increasing depth of field by closing lens aperture (f-stop) Pinhole camera: simplest imaging system to make How does it work? But not ideal! Maps (and blurs) a very narrow angle range from one object point Dq r/L to one image point. What is the limit to the resolution? 20 minute exposure taken with a pinhole camera Solar eclipse viewing Holes in the leaf canopy create images of the eclipse on the ground. Abberations Latin aberrare "go astray" Chromatic Aberration Problem: n = n(l), so f = f(l) Chromatic Aberration Chromatic Aberration Correction: Use a lens pair, with the strongest lens (smallest f) of low dispersion coupled with a weaker one (long f) of high dispersion calculated to match the focal lengths for two chosen wavelengths. Cemented doublets (“achromats”) of this type are a mainstay of lens design. Spherical aberration in lenses, mirrors Problem: Even for light rays parallel to the optical axis, at large distances (h) from the axis, small angle approximation breaks down: f = f(h) Spherical aberration Expensive correction: Use aspherical lenses or mirrors for fixed imaging/object distances…new optics for each distance. Used if need more light. Spherical aberration Cheapher correction : Choose best spherical lens radii If you want to best focus a laser beam with a planoconvex lens, which way should you face the flat side: _______ the laser a) toward b) away) Spherical aberration Correction : Choose best spherical lens radii You get a different curve for each do, di pair (new position factor) Spherical aberration Cheapest, most flexible correction: Restrict h: Aperture or “field stop”. f # f D Effect on light-gathering ability or “speed” of optical system: Spherical aberration and Hubble They paid a lot for a primary hyperbolic mirror Spherical aberration and Hubble hyperbolic design e= 1.00115 Problem: e = 1.00660. Test optics: assembled wrong Spherical aberration and Hubble Test optics were assembled incorrectly. Corrective optics installed 3 yrs later Corrected with two more mirrors “Pincushion” “Barrel”