The Pinhole Camera

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 r_o then the flux is calculated as follows.


Since the rays of the Sun diverge by an angle θ_S which is the Sun's angular radius, the approximate radius of the flux tube at distance d is r_d = r_o + d·θ_S.



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.