A Reflective Pin Hole Telescope

(supervisor: Tony Cook)

Nature of project: experimental, data analysis

Available to full-time physicists or joint students.

Project description and methodology

Telescopes are usually thought of as having a big collector lens or mirror to gather electromagnetic radiation (in a specific broad waveband), and focus it onto a collector or camera. Another possible telescope design (intended for bright objects) is a Pin Hole telescope. Here we effectively have a relatively small solid angle aperture, the angular diameter of which (at the far end) defines the telescope resolution. Effectively it's like a Pin Hole camera, except that we use an optically flat mirror and place an opaque cardboard, or plastic, mask over this with a small hole cut into it - making a reflective pin hole. By pointing the non-covered part of the mirror at the Sun, an image of the solardisk can be projected onto a piece of paper on a wall. You can achieve slightly better than naked eye resolution of the Sun this way, and it has even been shown to work with the Moon. Although the resolution cannot compare with what can be achieved with a telescope looking at these large solid angle objects, imagine having a mirror in space, just a few cm across and projecing an image over hundreds or thousands of km to a collection of telescopes. The pin hole could be used to form an aperture of milliarc sec or smaller angles, and possibly be used to image the surfaces of stars or even exoplanets.

The aim of this project is simply to find a relationship between image resolution and a combination of hole aperture size and distance to the screen. A rough estimate of image resolution that can be obtained is:

resolution(radians)= 2arcTan(0.5d/D)

where d is the hole diameter (m) and D is the distance to the screen (m)

However this is affected by diffraction on the hole edge, and you would expect this to have more of an effect for small aperture holes versus larger ones at greater values of D.

Build a Pin Hole telescope using initially a single pipe with an effective angular aperture of < 0.05 degrees (10 resolution elements across the solar disk), and use multiple sidereal (Earth's rotation) passages of the Sun across it to form a crude image of the Sun - but which would demonstrate the principle.

The project would attempt to find out the following: (a) What is the polar diagram of the instrument like? (b) To what extent does diffraction affect the angular resolving capability as the pipe aperture (diameter) is reduced? (c) Would using several holes at intervals be better at reducing internal reflections, instead of using a contiguous pipe?

A successful project will develop beyond the above in one/some of the following directions:
1) Use an artifical Sun (LED torch with mutiple bulbs), a small mirror a distance away, and a screen. Capture the image and measure the sharpness at different distance between the screen and the mirror. Use a brightness profile through the image to study sharpness of edges as a way to quantify sharpness.

2) Now try varying the size (d) of the aperture placed over the mirror and quantify sharpness at different distances (D).

3) How can you improve the visibility of the image - how much light shielding is needed (cardboard around the region where the image forms on the screen)?

4) Try this on the real Sun - over what distance in tens of metres can you project the image. Find an optimal distance and aperture.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

Additional scope or challenge if taken as a Year-4 project: Place the mirror on a platform which can be turned in azimuth and altitude - program this so as to keep the image of the Sun at a fixed spot on the screen.

Initial literature for students:

  1. https://science.nasa.gov/science-news/science-at-nasa/balloon/mixe2/ (accessed 2016 Sep 20)
  2. E. Renner (2012) Pinhole Photography: From Historic Technique to Digital Application.
  3. H. Bradt (2004) Astronomy Methods: A Physical Approach to Astronomical Observations, p106-108.
  4. Leitner, J. (2007) Formation flying system design for a planet-finding telescope-occulter system, SPIE, Proceedings Volume 6687, UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts III; 66871D (2007); doi: 10.1117/12.731626

Novelty, degree of difficulty and amount of assistance required

Average level - you just need a sunny day, and a mirror placed outside, shining an image of the disk either onto the wall of a building (in shade) or through a window into the Physics Lab. As an alternative you could use an artifical Sun in the Lab e.g. an LED torch on the other side of the room.

Project milestones and deliverables (including timescale)

milestoneto be completed by
Decide what equipment/parts you will needChristmas
Find the resolution that you can achieve, using the LED torch, for different values of d and Dend of February
Experiment using the real Sun - see how resolution is affected as the reflection angle changesmid-March
What are the trade-offs between hole size vs distance in terms of image brightness + how can you improve the shielding of the image from stray light?Easter

Students taking this project will have to submit a full risk assessment form