# Diffraction limit (Rayleigh criterion) and circular image on the screen

In the angular resolution, we explain the diffraction limit (Rayleigh criterion) by showing a circular image on screen. I wonder is there an inbuilt assumption that light source is a point source.? I guess what I am not able to understand is why we always try to understand diffraction limit by a circular image on screen? This is how I explain circular image to myself. Please let me know if this is correct. I think there is an inbuilt assumption that source is a point source. Diffraction limit is for any optical instrument including our eye and I am thinking when we look at an object, every point from that object will create a circular image and when you join the images from all these points, you see the image of the object. is that correct way to look at it.?

• the usual assumption is a plane wave to hit the screen, in practice it means a point source but very far away so the spherical waves are essentially plane waves. Dec 27, 2018 at 15:24

## 2 Answers

Re. "I wonder is there an inbuilt assumption that light source is a point source.?"

Answer: There almost certainly is an assumption that the image is an image of a single point. There also may be an assumption that the light source is narrow band--a single frequency. There would be no assumption that the light source is a 'point source'--unless the light source is itself the object to be imaged. I assume there is a point object illuminated by a separate light source.

Re. "when we look at an object, every point from that object will create a circular image and when you join the images from all these points, you see the image of the object. is that correct way to look at it.?"

Answer: That is the correct way to look at it. But better to say 'sum the images' instead of 'join the images'. Your 'circular image' is the 'point spread function' (a Bessel function or Mexican hat function in the far field if the light is a single frequency)--the image of a single point.

In general, since this imaging process is linear the object can be decomposed into its constituent points. And then the image of each point can be obtained. Then all of the point images can be summed together to obtain the image of the object. This is the Green's function or impulse response approach.

• Assuming the OP meant the point imaged = point light source, your answer sounds contradictory. I assume you imagine the imaged point to be illuminated by a point source. Dec 28, 2018 at 3:59
• Yes, I made that assumption. Why does it sound contradictory? Dec 28, 2018 at 15:21
• @ Tom B now I see the problem. I edited my answer. Dec 28, 2018 at 16:51

Yes. Though you should probably say "cylindrically symmetric" instead of circular.

As hyportnex's comment says, a distant point source is (in the limit) equivalent to a plane wave arriving on the imaging device. A distant source (as you suggest) can be broken down into a mosaic of point sources.

When each distant point source is imaged it results in a cylindrically symmetric reproduction with a width characteristic of the diffraction limit of the imaging device.