## Rationale## Efficiency maximized with parabolic reflector and secondary lens.Adjunct page to this related article. There are two issues to consider when building a lens-based projector for free-space optical communications
The angle of the beam projected by a lens is proportional to the diameter of the light source ( A smaller light source ( Lens-to-source distance is closely related to the focal length of the lens. If the purpose of the lens is to project a
The efficiency of the projection system is the proportion of light energy produced by the source actually projected in the beam. Efficiency can be expressed numerically as the angle subtended by the projection lens divided by the dispersion angle of the source (x100 to put it in percentage terms). So, for example, if the dispersion angle of the source is 360 degrees and the angle subtended by the projection lens is 36 degrees, the efficiency of the system is (36/360) x 100 = 10%. Larger diameter lenses at a given distance subtend larger angles, therefore are more efficient.
The efficiency with which a lens projects light from a dispersed source is related to it's f-number. The f-number (also called f/N) is the ratio of a lens's focal length ( A "too-small" lens (f-number > f/N
Substituting 100° (the dispersion angle for the LED used in this project) for θ The usual way to achieve very low f-numbers without excessive lens thickness and weight is with some form of Fresnel lens. This projector takes a hybrid approach. It uses a concentrating "lens" (it looks like a parabolic reflector to me; parabolic reflectors are another way to achieve very short focal lengths) to "pre-narrow" the dispersion angle of the stock LED. This lens (Ledil CA10324_Rocket-SS), narrows the dispersion angle to 8 degrees (according to its datasheet). The decrease in dispersion angle from 100° to 8° comes with an increase in the apparent diameter of the source - from about 2mm to 25mm. Plugging this value (8°) into the above equation [2] produces an f/N
For optimal efficiency the secondary lens is positioned at the distance where the outer rays produced by the calculated "just-right" f/N
As a practical matter it is not necessary to determine the position of the virtual source, it's only necessary to equip the system with a secondary lens of sufficiently low f-number, as discussed above, and position it the correct distance from the primary lens. The distance the secondary should be spaced from the primary is calculated as follows: Substituting the diameter of the primary lens used in the project (25mm) and the calculated maximum secondary f/N (7.1), the primary to secondary distance (D) calculates to 178mm. By default then, the virtual point source is 108mm behind the primary lens [286 - 178 = 108]. With the secondary lens properly spaced, the projected spot (onto a sheet of white paper a few meters away) should appear fully filled in and uniformly illuminated. A "focused" image should not appear. A higher intensity area may appear in the center of the spot. This is caused by light coming directly from the LED (not reflected by the primary lens). See: Adjusting the Pointing Scope.
The apparent diameter of the light source (as viewed by a distance observer) has been increased from 25mm (the diameter of the primary lens) to 70mm (the diameter of the secondary lens). Intensity of the projected light beam increases by a factor of (70/25)
Since the dispersion angle (8°) of the "pre-narrowed" source is completely subtended (and then some) by the secondary lens, numerically at least, the system could be thought of as being "100% efficient". It is not, of course. In the real world, transmission losses, losses caused by misalignment, and spurious light emitted from the source (beyond the half-power point), prevent that.
If the narrowest beam width with the highest efficiency is desired, select a light source with the smallest possible radiating surface, then select the longest available focal length lens or combination of lenses having an f-number equal to or less than the f/N ## Related Article## Sewer Pipe LED Projector |