Geometric information within 1D streams of electrons/photons

Question

How is light—or actually any frequency in the EM spectrum—self-encoding and self-modulating 3D info in its 1D self, so that it “knows,” once it strikes a surface, to discharge all the data perfectly as a 2D image?? It’s not like FM or AM circuitry is being employed here... light is self-modulating to encode 3D scenery data perfectly without external interference to self-induce a modulation.

Answer 1

Time is the dimension you are missing!

At the end of the day the video signal amplitude at any given moment represents brightness (and colour) at one point, but that point scans across quickly and down the screen slowly.

Both the phosphors decay time and the eyes flicker fusion frequency combine to give the impression of a complete image.

The geometry is encoded in the sync pulses (Negative going pulses that drop below the normal black level) that are detected to reset the scan circuits to the start of a line or top of the screen.

Answer 2

light is self-modulating to encode 3D scenery data perfectly without external interference to self-induce a modulation.

The only case I can think of where that is true is in a hologram, where coherent light is split into 2 beams that interfere with each other (so technically not 'external' interference). Different path lengths to and from the 3D object 'modulate' the phases of the beams relative to each other, creating varying brightness when they interfere at the recording surface. this encodes the 3D image as a combination of Fresnal 'zone plates', which reproduce the image when illuminated by a point source.

In most optical imaging systems non-coherent light is focused by some external component which selectively bends, reflects or occludes the beams to produce an image on the 2D surface. This could be a lens, concave mirror, or pinhole. The focusing device uses the spatial directions of the beams to resolve the image. Without this 'external interference' no image is produced because the light is a mixture of photons with random frequencies and phases coming from all different directions.

A 1D image can be obtained by measuring the time taken for a pulse to reach the object and reflect back from it. This was how early RADAR worked, with only distance to the aircraft being shown. To get a 2D or 3D image the antenna must produce a narrow beam and be rotated to sweep across the sky. The other spatial dimensions are again encoded in the direction of the beam.

Answer 3

photons go through the tiny hole and then splay back into an inverted 2D image

The answer is more readily found when the photons are treated as waves rather than particles. In a real-life scene there are waves (photons) coming from every angle, and those can be treated as mathematically independent, so lets focus (no pun intended) on a wave coming straight on the axis of your pinhole camera. That electromagnetic wave, having come from a far-away point source (say, a star), is essentially a spherical wavefront, but because the hole is so small it can be treated as "flat" or having uniform field strength, and the strength of the wave is uniform across the hole. (You can see this by putting a ring on a soccer ball -- a small ring allows you to see an approximately "flat" surface within the ring, but with a larger ring the curvature of the ball becomes obvious.)

Since the field strength at the focus (the back of the camera) is the 2d Fourier transform of the field at the hole (essentially uniformly flat), the light resolves to a point in the 2d-plane (that is, its a Dirac impulse function in two dimensions). Thus, the light from the star resolves to a single (spatial) impulse, which is a point of light, on the back of the camera.

This math can be applied independently, to every star in the sky, but accounting for the angle of arrival, so the image is created with little dots of light spread out across the back of the camera. As you get further off center, the approximation of "flat" and "uniform" (on the hole) becomes less and less true, so the edge of the image is fuzzy.

With a larger opening, the approximation of "flat" also begins to fail. Using a lens is actually compensating for a specific curvature of the field, so source that are too-far and too-near don't quite fit the equation, giving the lens a "depth of field". Shrink the aperture (make the useful hole in the lens smaller), and depth of field increases. A 3d camera takes advantage of this by effectively measuring the curvature of the field.

Answer 4

My question is applicable to the EM spectrum in general, but more specifically in the case of visible light, we can clearly see a continuous wave refracting into its discrete photons that transform to geometrically reflect what has been modulated when it hits the surface. Radio waves are manually induced modulation (encoding) and visible light waves are self-induced.

Other people have explained image formation abstractly, but I can give you a good example of how a 1D (transverse) wave can be modulated to form a 2D image.

Imagine a LIDAR/SONAR/RADAR scanner composed of a transmitter sending out a beam of radiation (light, sound, whatever) and a receiver (could be a lens, microphone, etc) pointed in the same direction. As the transmitter rotates, it will scan a line of energy across the surroundings. As the scanner passes over an object, it will reflect signal back in proportion to its reflectivity. This modulates the return signal with information about each point's reflectivity. The receiver will then detect this modulated signal, and color in a pixel in proportion to how much signal it receives. Gradually you can built up first a 1D line of pixels and then a 2D image.

This is imaging using raster scanning (1 point at a time), but if you just get two receivers side by side, you can map out two adjacent pixels for each location you point at. Get 4 pixels and you can map out 4 at once. Get 10 million and you can map out an entire 10 megapixel image in one shot. Each receiver is detecting a single 1D signal, and each signal is modulated by the reflectivity of whatever it is pointed at.

Now if you want to know why each receiver can detect a different point in the scene without them all seeing the same point (or maybe the sum of all points at once), you need to understand diffraction and Fourier optics (which other answers have addressed). But conceptually, it should be clear that if you have N receivers each pointed in a slightly different direction, you should be able to receive N modulated signals in parallel.

EDIT

Thanks for the answer... how do you apply such logic to the image created by a pin-hole camera?

The pinhole camera is the 2D array example above (lots of parallel receivers), each pointed through the pinhole. Since the area around the pinhole completely blocks signal, each receiver can only receive signal from one spot through the pinhole. That the modulation from that spot is what it records.

You can actually draw this pretty easy. Imagine a 2x2 pixel sensor behind a pinhole. Draw a line with a ruler from each pixel on the sensor through the pinhole. You'll see that each strikes a different point in the surrounding scene.