A Continuous Field Image: Hubble Deep Field & Exoplanets

[vinven7]

The Hubble deep field image was constructed by collecting photons from a specific region of space over a continuous duration of time; in this case ten days. As the number of collected photons increase, higher the resolution of the image.

If this duration increases, how much more resolution do you get to see? Specifically what if we had a continuous field of view of a certain galaxy - is there some distance for which you could see things in very high definition? Would we be able to see features on exoplanets ? This is of course a function of distance from us, but I am curious to know what kind of information we have about this.

 

[Drakkith]

As the number of collected photons increase, higher the resolution of the image.

The resolution does not depend on the number of photons. Instead, the 'quality' of the image increases as you gather more light. A short exposure is very 'grainy' and has a low signal-to-noise ratio compared to a long exposure.

If this duration increases, how much more resolution do you get to see?

None.

Resolution is a function of the size of the optical system, specifically the diameter of the aperture, and the size of the pixels on the sensor. Smaller pixels give higher resolution, as long as your optical system can bring the size of the airy disk down to approximately the same size as the pixels or smaller.

 

[sophiecentaur]

The resolution does not depend on the number of photons.

That statement could be over-simplified. Basic signalling theory tells us that the limit to resolution depends, not only on the (spatial) bandwidth but on signal to noise ratio. The basic Raleigh criterion is only a rule of thumb. The shape of the dip between two peaks can be refined and refined without limit by integration over a long time. Shannon tells us that the apparent limits, due to pixel size (spatial sampling rate) and aperture can always be exceeded by reducing the bandwidth of the system enough.
This is 'only' an extension of what every good amateur Astrophotographer can get by stacking dozens of images from a light polluted urban environment; a bit more sophisticated than that, though.

 

[Drakkith]

That statement could be over-simplified.

I suppose. I wasn't thinking of some of the advanced techniques that can be used to make up for limitations in pixel size and other factors.

 

[sophiecentaur]

limitations in pixel size

That's only a form of sub-sampling which, for non periodic data, can run a coach and horses through what we think of as gospel - ie, The Nyqyuist Criterion. Rules of thumb need to be treated on a case by case basis.

 

[Drakkith]

Ah, well, there you have it then.