HackerWhat is missing from a picture of brightness?
Follow rotating hands, short tones and holographic exposures to separate three questions: what is in a wave, what the observation window permits, and what the instrument actually records.
Questions in this reading · 2
Stop the hand you want to measure
Imagine several spinning hands tracing an outline. You want to measure one hand but can only observe the tip of the whole chain. The Fourier series demonstration rotates the observer’s frame at the target rate, then averages over a complete period. The target stands still while other integer rotations cancel. You measure a component relative to that frame, without ever identifying “its” stroke in a single image.
Passages and timestamps · 1
So taking the average of this modified function is a clever way to kill all the terms other than c2.Replace the full period with a very short recording. Cancellation may not have time to happen. Two close tones can both match the brief signal; a short pulse helps locate arrival time but cannot also have arbitrarily narrow frequency content. The observation window was a condition on the earlier claim that the other hands cancel.
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The shorter it lasts in time, the less certain you can be about what its exact frequency is.Film records brightness. How can phase leave a trace?
Photograph two beams separately. They have the same frequency and brightness but their crests arrive at different times. Film integrates intensity during exposure; that measurement alone does not tell you the phase. Holography adds a coherent reference. Alignment then changes whether the waves reinforce or cancel, so relative phase affects the exposure pattern. The film still records light and dark; it has not acquired a clock fast enough to follow the optical field.
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When the first beam is in sync with that reference wave, the two will constructively interfere, producing a wave that has twice the amplitude, so the film gets exposed a lot at that point.Refraction also adds waves, but the observable is different. Radiation from driven charges in glass combines with the incoming wave and shifts the crests of the resultant field. Successive layers accumulate that shift, making the crests travel more slowly. The first experiment encodes relative phase in a record; the second changes propagation phase by superposition. Their measurements and apparatus are not interchangeable.
Passages and timestamps · 1
a wave that's simply traveling slower, oscillating up and down with the same frequencyTry it on your own example
Given only an exposure, what else must you know to discuss phase? Given a brief recording, could extra decimal places substitute for a longer observation?