Abstract
Charged-couple devices (CCD) and complementary metal oxide semiconductor (CMOS) image sensors, in conjunction with the second moment radius analysis method, are effective tools for determining the radius of a laser beam. However, the second moment method heavily weights sensor noise, which must be dealt with using a thresholding algorithm and a software aperture. While these noise reduction methods lower the random error due to noise, they simultaneously generate systematic error by truncating the Gaussian beam’s edges. A scale factor that is invariant to beam ellipticity and corrects for the truncation of the Gaussian beam due to thresholding and the software aperture has been derived. In particular, simulations showed an order of magnitude reduction in measured beam radius error when using the scale factor—irrespective of beam ellipticity—and further testing with real beam data demonstrated that radii corrected by the scale factor are independent of the noise reduction parameters. Thus, through use of the scale factor, the accuracy of beam radius measurements made with a CCD or CMOS sensor and the second moment are significantly improved.
Highlights
Charged-couple devices (CCD) and complementary metal oxide semiconductor (CMOS) image sensors have become standard beam radius measurement tools due to their ability to return a two-dimensional (2-D) beam intensity profile
An image sensor (CCD or CMOS) in conjunction with the second moment radius analysis method can accurately measure the radius of a laser beam; the second moment method heavily weights noise and noise reduction techniques such as thresholding and a software aperture must be used before calculating the second moment beam radius
Simulated laser beams tested the effectiveness of the scale factor and its elliptical invariance by comparing the measured beam radii—corrected and uncorrected—to the generated beams’ actual radii
Summary
Charged-couple devices (CCD) and complementary metal oxide semiconductor (CMOS) image sensors have become standard beam radius measurement tools due to their ability to return a two-dimensional (2-D) beam intensity profile. The thresholding algorithm is applied to the image sensor data before using a software aperture or calculating the second moment.[13] Thresholding entails first sampling an unilluminated portion of the sensor (e.g., the four corners) to determine the mean μ and standard deviation σn of the background noise. The software aperture can be applied to exclude extraneous noise from the second moment calculation yet retain valid beam data. Fig. 1), and a balance must be struck between eliminating extraneous noise and removing valid data.[15] Theoretical work and simulations have shown that the optimal software aperture size varies with both the value n used in thresholding[14] and the radius of the beam.[11] n is predetermined, the beam radius is generally not known before measurement, and. WðzÞ is the radius of the beam when the intensity is 1∕e2
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