CCD Size & Resolution: Trade-Off Explained

[Paffin]

Hello guys,
thanks in advance for the help.
I have come across a theoretical problem which I hope you will be able to help me solving.

It is all base on resolution (Rayleigh criterion) and Nyquist sampling theorem connected to camera capabilities.
So, resolution (Rayleigh criterion) is roughly calculated as 0.61 λ /NA (of the objective, to simplify)
The theorem of nyquist say that to sample correctly a wave you should acquire at minimum twice the maximum frequency in order to sample correctly.

Now, if a camera has pixel size of 3.75 um (side of the square pixel)
If we acquire an image with a 60x Obj with 1.4 NA for λ=480nm we get roughly 0,22 um max resolution.
Now we magnify this to 60x and we get 13.2 um, this should be the distance between imaging point on the camera optical plane.

So, our pixel size is below 2x this length and therefore we are able “to sample” this correctly without any loss.
Am I correct until here?

My question is, seems that the smaller the pixels, the better is the sampling however, is common knowledge that larger CCDs have a far better performance in terms of brightness.
My question is, what is the trade-off between the sampling ability and the sensitivity? What is the link I am missing?

Thanks for the help,
Paffin

 

[Drakkith]

My question is, what is the trade-off between the sampling ability and the sensitivity? What is the link I am missing?

Bigger pixels gather more light and can thus image fainter objects or use shorter exposure times, but they have less maximum resolution than smaller pixels since fine details may be lost on the larger pixels.

 

[phyzguy]

The point is that you don't gain anything by having pixels smaller than the Nyquist criterion. This is called being "oversampled". It's not true that the smaller the pixel size, the better the sampling. In your case, the pixel size should be 6.5 microns, so with the smaller pixels you are losing light sensitivity as Drakkith pointed out, with no corresponding gain in resolution.

 

[Andy Resnick]

Now, if a camera has pixel size of 3.75 um (side of the square pixel)
If we acquire an image with a 60x Obj with 1.4 NA for λ=480nm we get roughly 0,22 um max resolution.

No, that means a point object will be imaged as a blob approximately 0.22 microns in diameter. Not only point objects, any object smaller than 0.22 microns in diameter will be imaged indistinguishably from a point object- you cannot tell me if the object is 0.22 microns, 0.20 microns, or 0.1 microns in diameter. The Rayleigh criterion does tell you (in the diffraction limit) how far apart 2 point objects must be to be imaged as 2 distinct blobs.

Now we magnify this to 60x and we get 13.2 um, this should be the distance between imaging point on the camera optical plane.

No, this is the size of the airy disc at the sensor.

So, our pixel size is below 2x this length and therefore we are able “to sample” this correctly without any loss.
Am I correct until here?

Sort of- because the Airy disc is 3X the size of a pixel (monochrome camera!), your imaging system is camera-limited. You could use a camera with smaller pixels. Alternatively, if so inclined, you can also locate the center of an Airy disc at sub-pixel resolution.

Even so, it's true that larger pixels give better signal-to-noise ratios, especially in low-light applications.