OPHIR BeamSquared, User Manual

Page: 82 / 112

Using this convention, a positive result means that the waist is located before the reference datum; a negative
result means that it is after the reference datum.
In Manual mode, the reference datum is the lens principle plane. The modified equation applies to
Automatic mode only.
Waist Location Relative to Laser Aperture 6.1.2.3.2
The alternate method applies when the Z
laser
value is non-zero. In this case, the entered value should
represent the beam path distance from the reference datum to the laser aperture. For the BeamSquared, the
reference datum is the red BeamSquared case at the input aperture. The displayed Waist Location results are
now relative to the laser aperture.
Equation 10 – Waist Location when Z
laser
> 0
𝑍
𝐿
= 𝑍
𝑙𝑎𝑠𝑒𝑟
− 𝑍
01∗
Using this convention, a positive result means that the waist is located in front of the laser aperture, a
negative result means that it is behind the aperture, i.e. not accessible.
For convenience, all results are positive when the waist is in front of the BeamSquared or in front of the laser
and negative when not accessible, either after the BeamSquared or behind the laser aperture. In this
computation, no adjustment is made to correct for the small difference between the H1 and H2 principal
planes.
Rayleigh Range 6.1.3
The Rayleigh range is the distance from the waist where a beam of a circular diameter increases to twice the
area at the waist, or where the diameter increases by √2. This is also the distance where the wavefront radius
of curvature reaches its minimum value. This latter definition is most appropriate considering non-circular
beams and beams with astigmatism. The Rayleigh range value is computed for each axial beam orientation
and is used to describe a region where a laser is generally regarded as being collimated. The separate X and Y
results convey the region where the beam is likely collimated, especially where they coincide.
The Rayleigh range, Z
R
, for both the artificial and real laser is computed, respectively, by:
Equation 11 – Rayleigh Range – Artificial
𝑍
𝑅2
=
𝑊
02
𝛩
2
Equation 12 – Rayleigh Range – Real
𝑍
𝑅1
=
𝑊
01
𝛩
1