I wrote: > Nevertheless, I have a feeling that it may not be possible to improve > on a simple pinhole.
Let me reconsider that. Consider an aperture a distance L from a surface, so that the image of the sun through an infinitesimal pinhole would have the diameter D = L*(0.5 degree). With a circular pinhole of diameter d<D, the brightness in the center of the image compared to that on an unobstructed surface is (d/D)^2. At the edge of the image, the brightness drops to zero over the distance d. With an annular slit of inner diameter D and thickness d, the brightness in the exact center of the image is zero. The brightness rises rapidly moving away from the center to very nearly (d*D) / ((pi/4)*D^2) at a distance of d, and increases more slowly to about (pi/2) times that value after that. (Mathematics available on request, at least in principle.) Considering only the initial rise over the distance D, the change in brightness with the annular slit is (4/pi)*(D/d) greater than with the circular pinhole. This factor is by design greater than one and can be made much greater. As an example, if you can work with a brightness 1/10 that of unobstructed sunlight, then a circular pinhole allows you to increase the accuracy by a factor of 3, but an annular aperture allows you can gain a factor of ten. If you can work with dimmer light, the improvement is even more dramatic. I don't know if it really works this way. Maybe all that bright light around blinds you so you can't see the small dark spot. On the other hand, your visual acuity may be increased by the fact that your pupil contracts. Experiments are needed. This analysis does suggest to me that significant gains might be obtainable for some geometries, e.g., noon marks, where the angle of the incoming light is always about the same, and it gives some guidance in choosing aperture dimensions. (Wouldn't it be great if we can come up with a useful sundial feature that the ancients didn't know about?) Cheers, Art
