How To Evaluate Laser Beam Quality? (Part 2)

3. StrehlRate

Streller ratio is defined as the ratio of the far-field peak light intensity on the actual beam axis to the peak light intensity on the ideal beam axis with the same power and uniform phase. Its expression is:

SR≈exp (-(2πδΥ λ)2) (5)

Where, Δ- wave aberration of the laser beam,λ- laser wavelength. Streller's ratio factor reflects the peak light intensity on the far-field axis, which depends on the wavefront error and can reflect the influence of wavefront distortion on the beam quality.

Streelby SR plays an important role in evaluating the adaptive optical correction effect of high-energy laser weapon systems. The high-energy laser weapon system mainly consists of two subsystems: high-energy laser and beam directional device.

When the high-energy laser weapon system has an adaptive optical correction, only the beam quality of the outgoing beam from the laser, the beam quality of the outgoing beam of the beam director, and the beam quality of the high-energy laser to the target surface are not enough to reflect the improvement of the beam quality of the adaptive system in the energy space transport of the high energy laser, and the beam quality of the beam before and after the adaptive correction should be evaluated.

n=SRS 'n (6)

The above formula can reflect the correction effect of the wavefront distortion by the adaptive optical system. In the closed-loop operating condition, the adaptive optical system also has the problem of jitter, which will seriously affect the quality of the beam.

Based on the analysis of the main factors affecting beam quality, the method of zero feedback compensation and wavefront distortion compensation is of great practical significance for beam quality control. However, the Strehl ratio only reflects the peak light intensity on the far-field optical axis, and can not give the light intensity distribution concerned by energy application.

4. M-factor

The M2 factor of laser beam quality is recognized by the international optical community and recommended by the International Organization for Standardization (ISO). The M2 factor overcomes the limitation of common beam quality evaluation methods, and it is of great significance to use the M2 factor as an evaluation standard for quality control and auxiliary design of laser systems.

The M2 factor evaluation method is often used for the laser beam with continuous intensity distribution in the beam section generated by low-power lasers. Because the second moment of the beam is used to define the beam width, the measuring instrument is required to be high.

In the brightness formula, the laser beam waist diameter is used to represent the luminance area of the light source ΔS{{0}}λd2o, the laser beam far field divergence Angle is used to represent the solid Angle of the light source ΔΨ=14πθ2f, and the d0θf product is expressed by the M2 factor, then the laser beam brightness formula can be expressed: B= pδs ·ΔΨ=P(M2)2·λ2(21) The characteristics of the laser beam can be expressed by several parameters, such as power, wavelength, and beam quality. The beam quality M2 factor is an essential parameter to characterize the high brightness and good spatial coherence of the laser beam.

The distribution of the light field in the spatial and frequency domains is used to represent the beam quality M2 factor, that is, M2= 4πσs-σSv, it can be known that the M2 factor can reflect the characteristics of the intensity distribution and phase distribution of the light field]. Compared with other evaluation methods, the M2 factor can better reflect the essence of beam quality, has strong universality, and integrally reflect the spatial distribution of light intensity.

The M2 factor is not suitable for evaluating the beam quality of a high-energy laser. The resonant cavity of high energy laser is generally unstable, and the output laser beam is irregular, so there will be no "optical waist". Moreover, for a high-energy laser beam with discrete energy distribution, the spot radius calculated by the definition of the second moment is far from the actual. The resulting M2 factor error is large.

The M2 factor requires that the intensity distribution of the beam cross-section cannot have a steep edge, for example, for a "super-Gaussian beam" the M2 factor is not applicable.