Tag Archives: optics

1/Problem

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Optics basics: Inverse problems at Skulls in the Stars.

Plenty of other techniques exist for measuring the internal structure of objects, using a variety of different types of waves. Magnetic resonance imaging (MRI) subjects a patient to an intense magnetic field, and makes an image by measuring the radio waves emitted when the field is suddenly switched. Ultrasound imaging uses ultrasonic waves to probe the soft tissues of the human body, and is used in mammography.

Each of these techniques is quite different in its range of application, but all require nontrivial mathematical techniques to reconstruct an image from the raw scattered wave data. These mathematical techniques are broadly grouped into a class of problems known as inverse problems, and I thought it would be worth an optics basics post to discuss inverse problems, their common features, and the challenges in solving them.

Somewhere, Under the Rainbow

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Pictured: Rare upside-down rainbow spotted in the UK

Rainbows are formed when sunlight is refracted in a raindrop.

But in a circumzenithal arc, the colours are in reverse order from a rainbow, with violet on the top and red at the bottom.

The arc usually vanishes quickly because the cirrus clouds containing the ice crystals shift their position.

Ice particles in high cirrus clouds occur all year round, but circumzenithal arcs are usually obscured by lower level clouds.

Circumzenithal arcs are so named as they go around the zenith – the point in the sky directly above the observer- rather than the sun.

(Pedantic man notes that rainbows actually refract the light twice)

More on circumzenithal arcs

h/t to Caroline

Shape and the Single Photon

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Shaping Single Photons

When you detect a photon, you can say where, when, and with what frequency it arrived, but before the measurement, these parameters are undefined. The photon’s existence is embodied in a wave function, which gives the probability of measuring the photon at any time, place, and frequency. The wave function for a single photon is usually a “wave packet”–nearly zero everywhere except in a narrow range of space and time. But as long as you don’t detect the photon directly, you can manipulate its wave function into any complicated shape, in theory.

Polarized, Non-politically

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I’ve inadvertently (and advertently) been doing some experimentation with polarized light lately. Liquid Crystal Displays (LCD) typically emit linearly polarized light, and most decent sunglasses act as polarizing filters. This can cause some problems, if you happen to have some gadget whose display is inconveniently set to emit light with horizontal polarization — since reflected light tends to become polarized parallel to the surface from which it reflects, sunglasses are made to filter that light. But it also makes it tough to read any LCD that is oriented to emit that polarization.

There are ways around this, though. I’ve noticed that my iPod screen (unlike my GPS receiver and watch) doesn’t go black at any orientation of my sunglasses, though I do get some shifting rainbows on the screen. Here are two orthogonal orientations of a linear polarizer:

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