Should Telescopes Use the Pinhole Camera Technique?

By Joshua N. Winn, Princeton University

Telescopes are build to detect invisible radiation, to go beyond the visible range and explore all these other orders of magnitude. But how should we build and design these telescopes to collect the maximum data possible? Can the pinhole camera mechanism help?

How Do Telescopes Work?

To understand the working mechanism of a telescope, we can begin by making an analogy between a telescope and a bucket for collecting rain. A bucket collects rain no matter what direction it’s coming from, whether it’s falling vertically or coming in at a slant.

For a telescope, we want to point it at something, a star or a galaxy, and only collect the photons coming from a narrow range of directions. We want to make an image, in which each pixel of the image corresponds to a different point on the sky.

Mathematically, an image is a mapping between the direction the photons are coming from, and the position on some surface, whether it’s the pixel in a CCD camera or a cell in your retina. Ideally, we want the number of photons that hits each point on the surface to be proportional to the rate of photons arriving at the Earth from a certain direction in space. But we haven’t said how a telescope performs that mathematical mapping: How does it sort the photons by incoming direction?

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Concept of Pinhole Camera

Conceptually, the simplest way to make an image is with a pinhole camera. Think of a completely dark room except for a small hole in one wall, admitting light. And there’s a screen on the opposite wall. The light that hits a given spot on the screen must have come from the specific direction defined by the line from the hole to that spot. Which means there is a one-to-one correspondence between the X,Y coordinates on the screen, and the direction from which light entered the hole.

At least, there would be a one-to-one correspondence, if diffraction didn’t exist. Photons coming from angles differing by less than about lambda over D radians get blurred together in the image, because of the diffraction of electromagnetic waves.

Finding the Ideal Size of the Hole

Let’s think about how we can achieve the tightest possible focus. Say the distance from the hole to the screen is F, the so-called focal length. And the hole has diameter D. We’ll start with a big hole, and imagine the light from a distant star goes straight through the hole. Ideally, we want the image of the star to be a pinpoint on the screen, but because the hole is so big, the image is a luminous circle of diameter D.

To shrink the circle down into a pinpoint, we should reduce the diameter of the hole. But at some point, D becomes so small, the diffraction limit starts to dominate and the image of the hole stops being a crisp circle and starts fuzzing out. If we keep reducing D beyond that point, the image gets worse, because the diffraction limit goes as lambda over D. The optimal case, the tightest focus, is when the angular diameter of the circular image, D over F, is equal to the diffraction limit, which is roughly lambda over D. Solving for D, we find it’s the square root of lambda times F.

So, we’ve just learned the ideal size for the hole is on the order of the geometric mean of the focal length and the wavelength. If F is, say, a meter, and lambda is a micron, then D should be of order the square root of 10 to the −6, that is, 10 to the −3 meters, which is millimeter.

A Drawback

The optimal hole is so small in a pinhole camera that hardly any light gets through. So, while this can make sharp images over a wide field of view, the images are faint, with a very low signal-to-noise ratio. Even a daylight scene might require an exposure lasting minutes or hours.

That makes pinhole cameras totally useless for optical astronomy, where the light levels are down by so many orders of magnitude. But, variations on the pinhole camera do find use in astronomy.

Adapting the Pinhole Mechanism for Telescopes

Very high-energy photons, X-rays and gamma-rays, punch straight through most materials, so we can’t easily build mirrors or lenses to re-direct their trajectories and focus them. But what we can do is drill a pinhole in a layer of a dense material, like lead, or tungsten, that’s thick enough to block them. And then for the screen we can use germanium crystals, or other materials that produce an optical flash when a high-energy photon hits it.

To mitigate the problem of the small hole, astronomers drill several widely spaced holes. This makes the pattern on the screen confusing, because now it’s the overlap from lots of different pinholes, but if you observe the same scene multiple times, with the camera in different orientations, there are computer algorithms that can disentangle the information and reconstruct the scene. That’s called a multiple-pinhole camera, and there’s another variation called a coded-aperture telescope, which has been used by X-ray astronomers.

In the optical and radio domains, photons don’t pack as much energy, so we can use mirrors to focus them. At optical wavelengths, you could use a lens instead of a mirror, but lenses have a problem. Because they’re made of glass, they act like prisms, even when you don’t want them to—the amount they deflect the light depends at least slightly on its wavelength. That introduces chromatic aberration and hence, what should be a white point in the image turns into a multicolored blob.

Common Questions about the Pinhole Camera Technique

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