Sigma LBA-500PC Effective Area and Effective Diameter, Far-Field Divergence Angle computations

Where:

F= The Top Hat Factor (area under the curve)

6.20Effective Area and Effective Diameter

All of the pixels that are above the clip level are included in the Effective Area and Diameter results. If an aperture is present then the analysis is confined to just the pixels inside the aperture. The sum of the areas of all the pixels above the clip level is the Effective Area. The Effective Diameter is the diameter of a circle that will just contain the Effective Area as shown below:

		ed = 2 ⋅	ea
			π
Where:
ed	=	Effective diameter
ea	=	Effective area

6.21 Far-Field Divergence Angle computations

The LBA-PC can calculate Far Field Full-Angle beam divergence in two orthogonal axes. Two methods are provided, the Focal Length and the Far-Field. The Focal Length method requires the use of a focusing optic, while the Far-Fieldmethod requires that all measurements be performed in the far-field of your laser beam. Each method is discussed below. In each discussion you can assume results are duplicated for each axis.

6.21.1The Focal Length Method

This method is based upon the beam width of a focused beam’s spot size and the focal length of the focusing optic. Divergence results will be computed in the X and Y aligned axes of the beam if Elliptical results are disabled, or for Major and Minor axes beam orientations if Elliptical results are enabled.

The Focal Length divergence method provides a means for finding the far-field beam divergence at any point in the beam propagation path. As shown below, the calculation performed by the LBA is quite simple, however the optical setup must be done with great care. The user to suit his particular application must provide the optic. The focusing optic must be large enough to accommodate the input beam, without introducing diffraction effects. You can use either refracting or reflecting focusing optics, but in either case, you must place your camera’s detector at the exact focal length of the optical element. The Divergence result is based upon the focused spot size as described in the equation below:

 W		f	
divergence = tan−1			
	f
			

Where:
Wf =	The width of the focused spot at distance f from the optic.
Operator’s Manual	141	LBA-PC

Doc. No. 10654-001, Rev 4.10