Optics II:, Exams of Optics

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Optics II:

practical photographic lenses

CS 178, Spring 2010

Marc Levoy

Computer Science Department

Stanford University

Outline ! why study lenses? ! thin lenses

• graphical constructions, algebraic formulae ! thick lenses
• (^) lenses and perspective transformations ! depth of field ! aberrations & distortion ! vignetting, glare, and other lens artifacts ! diffraction and lens quality ! special lenses
• telephoto, zoom

Dispersion ! index of refraction varies with wavelength

• higher dispersion means more variation
• amount of variation depends on material
• index is typically higher for blue than red
• so blue light bends more

(wikipedia)

Chromatic aberration ! dispersion causes focal length to vary with wavelength

• for convex lens, blue focal length is shorter ! correct using achromatic doublet
• strong positive lens + weak negative lens = weak positive compound lens
• (^) by adjusting dispersions, can correct at two wavelengths

(wikipedia)

red and blue have the same focal length

Examples ! other possible causes

• demosiacing algorithm
• per-pixel microlenses
• lens flare

(wikipedia) (toothwalker.org)

lateral (^) longitudinal

• correctable in software - not

Software correction of lateral chromatic aberration ! Panasonic GF1 corrects for chromatic aberration in the camera (or in Adobe Camera Raw)

• need focal length of lens, and focus setting Q. Why don’t humans see chromatic aberration?

Examples Canon 135mm f/2.8 soft focus lens sharp (^) soft focus

(Canon)

Hubble telescope before correction after correction

Focus shift ! Canon 50mm f/1.2 L

(wikipedia)

(diglloyd.com)

focused at f/1.

Focus shift ! Canon 50mm f/1.2 L ! narrowing the aperture pushed the focus deeper

(wikipedia)

shot at f/1.

(diglloyd.com)

Coma ! magnification varies with ray height (distance from optical axis)

(ryokosha.com)

(Hecht)

Astigmatism ! tangential and sagittal rays focus at different depths ! my full eyeglass prescription

• right: -0.75 -1.00 axis 135, left: -1.00 -0.75 axis 180 focus of tangential rays focus of sagittal rays

(Pluta)

In class I declared my prescription incorrectly written on this slide. I was wrong; it is correctly written. The diagram I made on the whiteboard (see next slide) of a rotated bi- cylindrical lens (t wo perpendicular cylindrical lenses, of different curvatures, the whole affair made using a single piece of glass and rotated around the optical axis to a particular angle) was for my right eye, where the long axis of the second correction (-1.00 diopters) is at 135º. The correction for my left eye has different curvatures, and the long axis of the second correction (-0.75 diopters) is at 180º.

Field curvature ! spherical lenses focus a curved surface in object space onto a curved surface in image space ! so a plane in object space cannot be everywhere in focus when imaged by a planar sensor

(Hecht)

Distortion ! change in magnification with image position (a) pincushion (b) barrel ! closing down the aperture does not improve this

(Smith) (Kingslake)

pincushion distortion