For a given wavelength $\lambda$, is there a limit on the size of the sensor pixel, regardless of the optical equipment attached to the sensor or the nature of the censor?
[Physics] What’s the size of the smallest possible pixel size that can be physically detected using an electronic device
electronicsoptics
Related Solutions
It's easy to check if your calculations are right from this (rather crude) drawing:
There you see that the size of an object is related to the size of the image according to $$h_o=h_i\frac{D}{f}$$ where $h_o$ and $h_i$ are the sizes of the object and image. $f$ is not a focal distance, but the distance from the pinhole to the sensor or film.
So, if you have a 10cm object at 10m from the camera, and you want that to be 0.5mm (50px width), you need to place the sensor 0.5mm*10m/10cm=5cm behind the pinhole. If you do that, the angle your camera will see is $\tan(\alpha)=h_\mathrm{CCD}/(2f)$. The field of view is defined as twice this angle ($\mathrm{FOV}=2\alpha$). With the above numbers, the vertical FOV is 4.1º and the horizontal FOV is 5.5º.
Both equations are in fact structurally similar with Abbe limit given by $d= \dfrac{\lambda}{2\mathrm{NA}}$
And Rayleigh limit given by $d =1.22 \dfrac{\lambda} {2\mathrm{NA}}= 0.61\dfrac{\lambda} {\mathrm{NA}}$
where lambda is the wavelength and $\mathrm{NA}$ the numerical aperture of the light collecting lens.
The factor 1.22 comes from the definition of Bessel function of 1st kind,the fact that 1st minima of the diffraction pattern appears at 1.22 units from the central zero.
Rayleigh criterion is thus a modification of the Abbe Resolution limit. The Rayleigh criterion states that in order for 2 closely placed PSF to be resolved, the central maxima of one should lie exactly at the first minima of the second one. Since the Airy pattern is defined by the Bessel function, the minimum separation between the 2 patterns should be $1.22 \lambda/ 2\mathrm{NA}$ instead of just $\lambda/2\mathrm{NA}$ considering that the first minima will be at 1.22 times the unit from the central maxima.
Best Answer
For visible photons, I believe this is really a quantum mechanical question. The absorption of light into a detector is a quantum phenomena. It some way, it is the coupling of the frequency of light with a dipole in the atomic media. That dipole moves with the frequency of the light and this coupling can cause absorption and photoelectrons to be formed as the excited electron decays.
From this viewpoint, they limit of absorption is based upon the coupling efficiency as a function of the confinement of the optical field.
This is not restricted to quantum mechanics. One such classical dipole is your TV antenna. It is much less than $\lambda$ in size, yet it absorbs RF photons. Patch and coiled antennas have a lateral dimension even smaller than a wavelength.
Metamaterials have been made from split ring resonators which form capacitive and inductive features much smaller than $\lambda$.