Why do we use solar filters instead of simply reducing aperture of the telescope?

Question

Everywhere I read that to view the Sun in the telescope, one has to use a solar filter. The filter must be handled carefully to avoid any holes in it and even mustn't be stretched so as to avoid reducing its reflectivity in some spots. Otherwise it becomes dangerous due to possibility of overexposing/burning observer's retina.

But, if all we need is to reduce illuminance, and covering part of the telescope's aperture won't obscure the image (since the aperture is far from being in focus), why not simply reduce the aperture to a very small hole? Photo cameras do this all the time, why wouldn't this work for telescopes? Or does a solar filter block IR/UV light, in addition to reducing visible illuminance?

Answer 1

Suppose we want to make the Sun appear only as bright as the full Moon does in a 5-inch telescope. A difference of 14 magnitudes is a factor of 400 000; we can either add a filter transmitting 2.5 millionths of the light (including UV and IR), or reduce the aperture diameter by a factor of 630. We can achieve that by covering the 5-inch aperture with either a large #14 welding shade, a similarly dark solar filter, or a mask with a 0.2 mm pinhole.

However, angular resolution is inversely related to aperture. For a wavelength of 500 nm and an aperture of 0.2 mm, the Rayleigh criterion gives 1.2 * (500 nm / 0.2 mm) = 0.003 radian = 10 arcminutes, about 1/3 the angular diameter of the Sun. Even large sunspots would be blurred beyond recognition. A 1.0 mm hole would give 2 arcmin resolution but make the Sun too bright for direct viewing.

Answer 2

You would have to make the aperture so small diffraction would wreck the view. Also, resolution of a telescope is proportional to aperture, so the telescope with reduced aperture would also have reduced resolving power.

As indicated in the comments, you should NEVER look at the sun with your naked eye or any optical device without proper solar filtering, e.g. Baader solar foil for a telescope.

Answer 3

If you try (do not do this!) stopping down a digital camera and aiming it at the sun, you will almost certainly discover that, for anything larger than a pinhole, the sun will be imaged in a small enough spot to damage the pixels involved. Further, unless the pinhole stop is placed prior to all intermediate images (which depends heavily on the lens design), it's likely the sunlight could damage other optical surfaces. Ditto for DoNotLookAtTheSun thru a tiny pinhole.

It is possible in theory to design a telescope stop which is not a small hole but rather a strategic radially adjusted pattern to limit the total light transmitted without losing the high-frequency phase information necessary to produce a clean image, but that's not worth the pain and effort. It is much easier to use a uniform filter and avoid introducing any spatial frequency (diffraction) losses.