Optics Application Examples

Application 1: Emitter-Detector Applications

Determine Goal of Design

Although lenses are often used in imaging applications, in many cases the goal of the simple lens is the projection of light from one point to another. To be useful, emitters, detectors, lasers, and fiber optics usually require a lens for some form of light structuring. Figure A shows a typical example of how a plano-convex lens can be used to limit a detector's field of view. Considered in reverse, the figure might represent an emitting setup. This arrangement is particularly beneficial when using an LED or other broad field source. Such sources commonly appear in light-gate applications and require precise aiming toward the detector.

Figure A

Determine Light Transmission

Knowing where the light will go is only the first step in designing a light-projecting system; it is just as important to know how much light is transmitted. The Numerical Aperture (NA) and F-number (F/#) of the lens measure the amount of light a lens can collect.

f/# = f ÷ D

NA = 1 ÷ (2*f/#)

NA = sin (θ ÷ 2)

Where f is the focal length of the lens, D is the diameter of the lens and ? is the acceptance angle of the lens.

As f/# decreases, Theta (the acceptance angle) increases and the lens becomes capable of gathering more light. Matching a source's emitted cone of light with the accepting cone of a lens avoids underfilling and overfilling the lens, thus creating a more efficient system.

Determine Throughput

When using a lens as a tool to convey light from an emitter to a detector, it is important to consider what is known as throughput (TP), a quantitative measurement of transmitted light energy. Because emitters and detectors are areas and not points, lens diameter affects throughput even when the f/# remains constant. Referring again to Figure A, here are the calculations to determine the throughput of a lens:

Example

As an example, consider the task of collimated light emitted from a 1/4" diameter light guide (#40-639). The NA for the light guide is 0.55. The F/# can be calculated using equation 1.2:

0.55 = 1÷ (2*f/#)

F/# = 0.9

Due to physical constraints, we want as small a diameter as possible; still, we want the largest throughput possible. Looking at our TECHSPEC™ plano-convex lens matrix, we see a selectionof f/1 lenses (meaning the f/# equals 1). For this example we will consider lenses with diameters of 6, 12 and 25mm. An F/1 lens will have a focal length equal to the diameter of the lens (Refer to Equation 1.1). Using equation 1.4 calculate the TP for each of the three lens choices.

The results demonstrate that the 12mm diameter lens yields the best compromise between small diameter and large throughput.

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