Theory of laser beam apodization with a graded random phase window

Journal Article · Fri Jul 01 00:00:00 EDT 1988 · Appl. Opt.; (United States)

DOI:https://doi.org/10.1364/AO.27.002708· OSTI ID:7231794

Haas, R A

Analysis indicates that graded random phase modulation can be used to apodize a laser beam. In the case of an obscuration or hard edge, it can prevent the formation of Fresnel diffraction ripples. For example, suppose laser radiation of wavelength ..sigma.. interacts with a central obscuration of halfwidth a followed immediately by a window. If the exit surface of the window is randomly modulated with a Gaussian amplitude transverse correlation length l and a mean square amplitude approx.(t/sup 2/) (r) that decreases smoothly from a peak height at the obstacle of approx...sigma../sup 2/ with a transverse scale length L / a >> l, then the Fresnel diffraction ripples normally produced by the obscuration are eliminated. Following the apodizer the laser beam consists of two components. One is widely scattered with mean intensity I-bar/sub s/. The other is essentially unscattered and apodized with mean intensity I-bar/sub a/. The scattered light has an angular divergence proportional to ..sigma../l. The apodizer intensity transmission is T/sub a/ = exp(-..cap alpha../sup 2/ approx.(t/sup 2/)= (r)), where ..cap alpha.. = 2..pi..(n - 1)/..sigma.. and n is the window refractive index. Tayloring approx.(t/sup 2/) (r) can produce desired apodization profiles for hard edges and obscurations. Interference between the scattered and unscattered radiation produces intensity fluctuations on the laser beam that have the characteristics of laser speckle. The magnitude of these fluctuations is greatest near the apodizer and at the edge of the apodized beam. The local intensity probability density of the fluctuations is approximately the modified Rician density.

• Research Organization: University of California-Davis, Department of Applied Science, Livermore, California 94550
• OSTI ID: 7231794
• Journal Information: Appl. Opt.; (United States), Journal Name: Appl. Opt.; (United States) Vol. 27:13; ISSN APOPA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300 -- Engineering-- Lasers-- (-1989)
657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APERTURES
ATTENUATION
BEAM OPTICS
COHERENT SCATTERING
DIFFRACTION
ELECTROMAGNETIC RADIATION
FLUCTUATIONS
LASER RADIATION
MODULATION
OPENINGS
RADIATIONS
SCATTERING
VARIATIONS
WINDOWS