What is missing from a picture of brightness?

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.

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.

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.

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.

When light is split into components, which number is observed?

Film in the preceding example integrates intensity during an exposure. Switch to individual photons meeting a polarizer and the observation is a pass or a rejection. Resolve the input polarization in a basis set by the filter; the squared magnitude along the transmission direction gives a probability. When the calculation yields a number between zero and one, say whether it describes a frequency over repeated trials or a single reading. A continuous arrow in a diagram does not make the detector report half a photon.

Is this an exposure or a reconstruction from many measurements?

Berry shows both molecular graphics constrained by crystallography and time-lapse microscopy. In Raskar’s around-the-corner example the camera receives multiply reflected light; a hidden object emerges from several acquisitions and their arrival times. Jepsen uses a scattering maze to explain why recording a field after scattering can guide light back to a focus. Cover the finished image and name what the detector supplied and what a reconstruction or reference record added. Holographic refocusing and time-of-flight reconstruction have different experimental conditions.