One can use the flux tube to do radiometric calculations for a pinhole camera in which a small hole in one screen projects light onto a second screen.
At the Earth's surface the sunlight at normal incidence is about 1 kilowatt/meter2. We can use this value to calculate the light flux passing through the pinhole. If the pinhole radius is ro then the flux is calculated as follows.
Since the rays of the Sun diverge by an angle θS which is the Sun's angular radius, the approximate radius of the flux tube at distance d is rd = ro + d·θS.
Knowing the radius of the flux tube we can calculate its area at distance d from the pinhole.
Equating the product E·A = Φ at each end of the flux tube we get the irratiance, E, at distance d.
One sees that as d goes to 0 cm the quantities approach the values at the pinhole. As the distance increases the inverse square law takes over. If one wishes to use a pinhole camera for an eclipse one needs to enclose the image in a box for better contrast and have a side opening of some sort to view the projected image. One can get a sharper image by using a small pinhole but the point of diminishing returns occurs when diffraction takes over. Increasing the distance of the second screen creates a larger but dimmer image.