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Focal Length
Focal Length

All lenses, regardless of their shape, share certain common characteristics. The most important is focal length. It is critical to understand just how focal length is measured and how the lens focus point is affected through various factors.

Focal Length

As illustrated in Figure 1, three different values describe lens focal length. The most common is the effective focal length (EFL), which determines the lens magnification power and is the measure most commonly used describing a lens focal length in specification tables.

The EFL is calculated by formulae and relates to a non-physical “principal plane” in or near the lens. The non-physical plane position varies with the lens design and cannot be located from visual inspection. The back focal length (BFL) and working distance (WD) relate the focal point to physical points on the lens surface which are easily observed.

Only when presented with an object at infinity -- which corresponds to a perfectly collimated input -- will a lens form a spot at an image distance corresponding to its EFL. For any other object distance, the image forms further from the lens than the focal length. Ideally, image distance is related to object distance by the formula:

EFL FormulaEFL Formula

where o is the distance from the object to the first principal point of the lens, i is the distance from the second principal point to the image, and f is the lens focal length. The geometry of this situation is shown on Figure 2. When dealing with lasers, the object is generally considered to be the beam waist. Laser manufacturers provide data on the beam waist location relative to the laser so the image distance can be readily calculated.

This relationship is important because in many laser beam delivery systems -- “flying optics” systems -- the lens system moves relative to the laser’s beam waist during operation. As a result, the focal spot position will also shift.

There are several real-world effects which influence focal position for a lens, especially in high-power laser systems. Laser power absorption during operation causes the lens to heat up. The temperature change leads to a change in index of refraction, the optic’s thermal expansion, and stress induced changes in index of refraction (photoelastic effects). The result is thermal lensing which causes an operational change in focal length.

Thermal Stress: Starting clockwise at the top left: The progression of a thermally stressed lens. Object and Image Distance: Relationship of object and image distance
Thermal Stress: Starting clockwise at the top left: The progression of a thermally stressed lens. Object and Image Distance: Relationship of object and image distance
   
 
           
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