Information in a light beam relative to the width of the beam?

[Zelebg]

In the process of trying to understand holography I encountered a detail that I kind of knew before, but just now I realized I have no idea how it works, how is it even possible. I’m talking about a simple pinhole camera where supposedly no matter how tiny a hole is a beam of light would still contain all the information to construct a picture of the whole visual field.

1. Am I mistaken in some way that a lense is actually necessary to obtain full information from the scene?
2. Where is the limit, just how narrow a light beam can still contain all the information from the scene?
3. What defines the resolution or amount of information in a light beam relative to beam width?
4. If apparent from these questions, where exactly is my confusion, what did I miss or forget?

 

[.Scott]

Certainly every piece of a hologram contains a full view of the subject as seen from that piece. But the resolution will be limited to the diameter of the aperture (pin hole). The information that passes through the aperture is like an Fourier Transform with the "DC" information at the center and all other spatial information contained in areas beyond the center - the further from center, the higher the spatial frequency. So with a small pin hole, you will get a blurry image because it is missing the "edge" information. If you make the pin hole small enough, you will ultimately end up with a single blur that represents only the average illumination.

 

[Zelebg]

Certainly every piece of a hologram contains a full view of the subject as seen from that piece. But the resolution will be limited to the diameter of the aperture (pin hole). The information that passes through the aperture is like an Fourier Transform with the "DC" information at the center and all other spatial information contained in areas beyond the center - the further from center, the higher the spatial frequency. So with a small pin hole, you will get a blurry image because it is missing the "edge" information. If you make the pin hole small enough, you will ultimately end up with a single blur that represents only the average illumination.

I guess my problem there is that I understand photography in the context where resolution is proportional to the number of photons hitting the detector, so less photons less information, but instead of missing pixels in high resolution image, we get low resolution image blurred over high resolution number of pixels.

Another thing, how about we put a lense in there and focus light at the pinhole - where is the limit now at how sharply we can focus the beam and narrow the pinhole while preserving resolution or the same amount of information?

 

[.Scott]

... or just increase the exposure time. (but this won't work).

The number of photons is not the problem. A small enough portion of the hologram will simply not have enough information.

In normal photography, the f-stop is never reduced to a pin hole. If it was, problems with diffraction would become acute and they could not be resolved by increasing the photon count with a time exposure or intense light. At a certain point, your image is the diffraction pattern and the actual image takes a back seat.

 

[hutchphd]

I’m talking about a simple pinhole camera where supposedly no matter how tiny a hole is a beam of light would still contain all the information to construct a picture of the whole visual field.

What do you mean by a "beam" of light? I'm not certain I understand your concept here...

 

[PeterDonis]

supposedly no matter how tiny a hole is a beam of light would still contain all the information to construct a picture of the whole visual field

This "supposedly" is not true as you state it. It's only true if the hole is much larger than the wavelength of the light. This is not an issue in a practical sense since even a pinhole a tenth of a millimeter wide (which is about as small as you can see with the naked eye) is still a thousand times larger than the wavelength of visible light. But "no matter how tiny" is still not correct; there are limits.

 

[Zelebg]

What do you mean by a "beam" of light? I'm not certain I understand your concept here...

From the responses I realize my problem is not in the relation between information and the width of a beam of light, but between information/resolution and the surface area of some holographic media.

A small enough portion of the hologram will simply not have enough information.

It confuses me why is lack of information evenly distributed to still contain the whole picture in low resolution, instead of to manifest as missing parts of the picture. However, now I realize holographic “picture” is not directly relevant to photons, but interference, although I still can not say that resolves this mystery for me.