OPHIR BeamSquared, User Manual

Page: 83 / 112

Astigmatism and Asymmetry 6.1.4
The Astigmatism and Asymmetry values are not covered in the ISO procedure, but are provided as ancillary
values that may be of use depending on the laser and individual concerns.
The Astigmatism result provides a figure of merit that indicates the presence and severity of on-axis
astigmatism. The equation that defines this value was created by Ophir-Spiricon and may or may not agree
with other conventions in use. The results from this equation provide the following information:

Results near 0 indicate a lack of significant astigmatism.
 Results from 0 to 1 indicate increasing degrees of astigmatism, but the two waist locations are
contained within the other’s Rayleigh range.

Results from 1 to 2 indicate higher degrees of astigmatism. The waist locations no longer fall within the
other’s Rayleigh range, but the two Rayleigh ranges overlap.
 Results greater than 2 indicate significantly large amounts of astigmatism, where the Rayleigh ranges
no longer have any region of overlap.
Equation 13 – Astigmatism
𝐴𝑠𝑡 =
|𝑍
01𝑋
− 𝑍
01𝑌
|
(𝑍
𝑅1𝑋
+ 𝑍
𝑅1𝑌
) 2
⁄
The circularity of the beam is depicted with the Asymmetry result. This value compares the two waist widths
and therefore only has significance if there is little or no Astigmatism. Asymmetry values approaching 1
indicate that the beam appears circular in the waist region. Values greater than 1 indicate Ellipticity or
asymmetric behavior.
Equation 14 – Asymmetry
𝐴𝑠𝑦 = 𝑡ℎ𝑒_𝑔𝑟𝑒𝑎𝑡𝑒𝑟_𝑜𝑓 {
𝑊
01𝑋
𝑊
01𝑌
} 𝑜𝑟 {
𝑊
01𝑌
𝑊
01𝑋
}
Focal Length Calculation 6.1.5
The focal length of a lens is a function of the wavelength of interest. In order to obtain accurate results, the
focal length of the lens must be corrected for the wavelength in use. Lenses of similar design can vary in focal
length due to the substrate and wavelength of interest.
When choosing a lens, the wavelength-adjusted focal length must be computed using Equation 15 and the
calibration data supplied with the lens. The Automated BeamSquared version loads lens information and
calculates the new focal length automatically according to the laser wavelength entered by the user.
Equation 15 – Focal Length at a new λ
𝑓
𝜆
=
𝑓
𝑐𝑎𝑙
(𝑛
𝑐𝑎𝑙
− 1)
(𝑛
𝜆
− 1)
Where:
𝑓
𝑐𝑎𝑙
The calibration focal length of the lens
𝑛
𝑐𝑎𝑙
The index of refraction of the lens substrate at the calibration wavelength
𝑛
𝜆
The index of refraction of the lens substrate at the new wavelength, λ