Calculate Rayleigh Range, Far-field Divergence Angle, and Spot Size at the Moon
What is the process to illuminate the moon with earth-based sources using initial waist sizes of 0.5 mm and 0.5 m, and how can we find the Rayleigh range, far field divergence angle, and spot size at the moon for each initial beam waist when using different sources?
Calculation Process
Formula Used
The formula to find the Rayleigh range is given as: Rayleigh range (Z_R) = (π * w_0^2) / λ, where w_0 represents the initial beam waist, and λ is the wavelength of the source.
Specific Calculations
Initial beam waist = 0.5 mm = 0.5 x 10^-3 m
Rayleigh range ≈ 1.24 x 10^3 m
Far-field divergence angle ≈ 0.40 degrees
Spot size at the moon ≈ 1.31 x 10^6 m
Initial beam waist = 0.5 m
Rayleigh range ≈ 7.85 x 10^6 m
Far-field divergence angle ≈ 6.37 x 10^-5 degrees
Spot size at the moon ≈ 1.63 x 10^4 m
Initial beam waist = 0.5 m
Rayleigh range ≈ 3.37 x 10^7 m
Far-field divergence angle ≈ 9.39 x 10^-8 degrees
Spot size at the moon ≈ 1.39 x 10^4 m