# Diffraction of solid edge through aperture

#### FossilLight

Hi,
I am an astronomer working on writing an article about a particular diffraction effect seen when a planet is imaged through a telescope. I wondered if anyone has any theoretical workings or references about the effect that I could add to the article.

When a hard-edged planet is imaged through a telescope the edge of the planetary disc does not finish abruptly but there is a diffraction related ringing effect with a dark ring seen just inside the bright edge. The distance between the edge of the planet and this dark ring is wavelength and aperture related with it being larger for longer wavelengths and smaller apertures. Empirically its angular width seems to be about 60% of the Airy disc diameter for the telescope/wavelength.

The arrangement I guess would be like observing the edge of a bright plane against a dark background through a slit and observing the abruptness of the bright edge as a function of slit width/wavelength. Unfortunately all the literature seems to be about an abrupt edge cutting the light from a distant point source which isn't the same thing.

Can anyone help?

Thanks
FossilLight

#### Woody

This will essentially be the same as the diffraction of a single high contrast point (like a star against the dark background of space).
However, each point on a high contrast boundary line will have its own diffraction pattern.
The sum of all these individual point diffraction patterns will give you a "line diffraction" pattern.

#### FossilLight

This will essentially be the same as the diffraction of a single high contrast point (like a star against the dark background of space).
However, each point on a high contrast boundary line will have its own diffraction pattern.
The sum of all these individual point diffraction patterns will give you a "line diffraction" pattern.
Thanks Woody that makes sense- wonder if you have any references I can quote in my article. Empirical measurements of images seem to indicate the width of the edge from the outer edge of the planet to the middle of the dark arc is about 60% of the diameter of the first dark ring in the Airy disc whereas your theory would suggest it would be the same width as the dark ring.

FossilLight

#### Woody

Sorry No.
I was trying to build a sensible suggestion from the little I know
(rather than giving a definitive authoritative answer).

Have you tried an astronomy forum?

If you do get an answer elsewhere, please post it back for us,
I for one would be interested.

#### FossilLight

Thanks for your kind help in the absence of any other contributions.

Have tried astronomy forums and read all the related posts but nothing about the theory- that’s why I thought I’d try an Optics forum. There must have been some academic treatment of this as the setup is so simple- view of a bright disc or wall through an aperture.

Will post again if I find anything.

Cheers
Martin

#### vidya31

I would like to ask here basic question.
What is diffraction ?

#### Woody

In your initial post you say "imaged through a telescope"
From this I suspect that you are using a camera rather than viewing directly "by eye".

If so perhaps what you are noticing could be an artefact of the camera.
Often the default setting of a digital camera will be to use JPEG compression
(to squeeze more pictures into the cameras memory)
However JPEG compression can give just the sort of problem you describe for very sharp contrast changes.

#### Woody

Diffraction

Hi Vidya,
Diffraction is one of the features of the behaviour of light that leads to the "light wave" description (as opposed to the light ray).

As waves travel past a sharp corner, the do not form a precise sharp shadow
They tend to curl around the corner slightly.
This causes various image artefacts in astronomy, for example the "spikes" around a very bright star.

see: <Wikipedia : Diffraction> for more detail.