Looking Down from Space

Aperture is Everything!

In optics, the aperture is the opening through which light is collected to form an image. In the optical case, the size of the aperture is the diameter of the objective lens (cameras, binoculars etc.) or the diameter of the primary mirror (reflecting telescopes).

In the case of radar dishes, (also radio telescopes and satellite dishes) the aperture is defined by the dimensions of the radiation collecting surface.
Whether it's images for astronomy, earth surveillance, or the FBI, one of the most important aspects of image creation and image analysis, is the amount of clearly defined detail contained in an image.

Image analysts and photographers refer to this as image resolution or simply resolution

Consider the two images below.

The image above has high resolution.

The image above has low resolution.

It is common misconception that poor resolution can be overcome by higher magnification. Unfortunately, that is not the case.

There are ONLY two ways to increase the resolution of an image; one is to increase the aperture of the imaging device, such as a camera lens or telescope mirror, the other is to increase the frequency of the imaging radiation.

It is quite easy to calculate the limiting angular resolution of any imaging device, whether it's a radio telescope, Doppler radar, a digital camera, or a small backyard telescope.

The angular resolution (in radians) of a circular aperture is given by

where is the wavelength of the imaging radiation and D is the diameter of the circular aperture. The graph below shows the effect if increasing D (the diameter of a radar dish) from 50 metres to 240 metres. For purposes of illustration, angular resolution has been translated to linear resolution using an assumed (arbitrary) distance of 800 km.

Transparency Master 		Recall that angles measured in radians are dimensionless. In your calculations you must have both the aperture and the wavelength expressed in the same units.

In the example to the left, the limiting angular resolution was computed with both the aperture D and the wavelength in units of centimetres.

To fully understand these concepts work through this

Student Assignment

Illustrations showing how increasing aperture
improves image resolution

This series of illustrations shows the effect of increasing-aperture. For these examples a series of "off-the-shelf" small telescopes was chosen, each with a different aperture. In these illustrations we imagine we are looking at two laser reflectors on the dark surface of the Moon*, each placed about 5 kilometres apart. We also will assume a perfectly still, clear, non-scattering, and non-absorbing atmosphere).

[*This example uses a distance to the Moon of 357 157 km, its perigee distance on August 25 2001]
35mm aperture

Transparency Master		 The smallest aperture in this series is 35mm, about the size used in small light-weight binoculars. The limiting linear resolution of red light (wavelength 656 nm) at the Moon's perigee distance is about 6.7 km. But our lunar reflectors are only about 5 km apart! Therefore, they cannot be resolved into distinct points of light, even when magnified (as shown the right-most image).
50mm aperture

Transparency Master		 Increasing the aperture of our telescope to 50mm improves the telescope's angular resolution. Smaller angles can be resolved and hence smaller linear distances on the Moon can be also be resolved. For our 50 mm aperture telescope the resolving limit is about 4.7 km on the lunar surface. The laser reflectors are at the resolution limit and can just be seen as two distinct, but slightly fuzzy points.
80mm aperture

Transparency Master		 When the telescope aperture increases to 80 mm the linear resolution on the Moon's surface has improved to about 2.9 km. The laser reflects are now seen as clear unique points of light. Furthermore the images are much brighter, not only because the aperture "collects" more light, but also because the light is concentrated into a smaller point-like image.
200mm aperture

Transparency Master		 With an aperture of 200 mm the results of improved image resolution are clearer, brighter, and more distinct images of the laser reflectors on the lunar surface.
As these illustration show, the key to producing high resolution images is having as large an aperture as possible. It is RADARSAT's ability to synthetically produce large apertures (for microwave radiation) that is responsible for its amazing ability to produce very detailed images of the Earth's surface.

© 2001 Canadian Space Agency
Produced by YES I Can! Science Team