Measuring Laser Beam
Divergence
Background:
The
National Institute of Standards and Technology, (NIST), has endorsed a
laser beam divergence measurement technique that involves measuring the
beam diameter at the ideal focal point of an imaging lens. A number of
diameter measurement techniques can be used for focal plane divergence
measurements including variable apertures, scanning pinholes, knife
edges, and CCD arrays. U.S. Laser has adopted the CCD method for
diameter measurements, in conjunction with the focal plane technique.
The
ideal focal point of a lens is defined as the point in space where the
focus would be if the beam entering the lens was perfectly collimated.
This point is also known in optics as the paraxial back focal point.
This point is located exactly at a distance F_{b}
from the vertex of the lens. Since all laser beams diverge, the actual
focus is located farther from the lens than the ideal focal length (see
Figures 1 and 2 for an illustration). For this application we are
concerned only with the ideal focus and not with the actual focus. Once
the beam diameter at the ideal focus is known, the beam divergence may
be calculated using a simple formula.
Selection
of an Imaging Lens:
The
CCD imaging lens will have a back focal length of (F_{b})
millimeters, as measured from the vertex of the output surface. The CCD
detector surface will be located exactly at the lens back focal length
for the laser wavelength, regardless of whether there is actually a
waist (focus) at that point. It is important that two conditions are
met by the lens:
1.
The working fnumber, defined as the lens focal length divided by the
beam diameter at the lens should be least 10, and preferably over 20.
If the fnumber is less than 10, aberration corrected optics must be
used.
2.
The lens should be selected such that the beam image on the CCD is as
large as possible without overfilling. Overfilling the CCD array will
result in false diameter readings. Underfilling the CCD will result in
a loss of image resolution. A good rule of thumb is to have the CCD
approximately ½ to ⅔ filled.
Setup and Procedure:
A schematic of the setup for divergence measurement
is shown below in Figure 1. The procedure for measuring the divergence
is as follows:
1. Set up the laser (or fiber), a lens of focal
length F, and the CCD camera as shown in Figure 1.
2. Make sure the lens is oriented correctly
(fronttoback) to minimize aberrations. The steepest curvature should
face away from the CCD camera.
3. Place the CCD camera so that the pickup is
exactly F_{b} millimeters from the center of the
last surface of the imaging lens.
4. With the beam profiler, measure the beam
diameter at this point in both the horizontal and vertical directions.
Denote them as D_{x} and D_{y}.
For these measurements use the diameters inside which 86.5% of the
total power falls.
5. The divergences in the horizontal (x) and
vertical (y) directions can be calculated using the formula:
where D_{x,y} is either D_{x}
or D_{y}, depending on which axis is being
measured, and F is the effective focal length of the lens at the laser
wavelength.
6. For elliptical beams, the average divergence
(average of x and y) can be calculated using the formula:
References:
1.
Laser FarField Beam Profile Measurements by the Focal Plane Technique, National
Bureau of Standards, March 1978.
2. Simple
Beam Propagation Measurements on Ion Lasers, SPIE Vol. 1414
Laser Beam Diagnostics, 1991.
3.
Standard for the Measurement of Beam Widths, Beam Divergence, and
Propagation Factors, Proposal for a Working Draft, ISO/TC 172/SC 9/WG
1, April 29, 1992.
Figure 1. Setup for
measuring divergence with lens and a CCD camera. The lens is placed a
distance F_{b} from the lens vertex. With
a collimated input beam, the true focus falls directly on the CCD array.
Figure 2. Same setup as Figure
1, except with an uncollimated (diverging) input beam. In
this case, the true focus falls somewhere behind the CCD array.
