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Chapter 13:
Double-Passage Problems: Laser Radar Systems
Overview: In this chapter we investigate the double-pass problem that arises in laser radar applications. Namely, the double-passage of an optical wave through the atmosphere to a target and back through exactly the same atmospheric turbulence, but in the opposite direction, can lead to an enhancement in the mean irradiance near the optical axis of the return (echo) beam known as enhanced backscatter (EBS), also called the backscatter amplification effect (BSAE). Because the spatial coherence of the echo beam and the irradiance fluctuations can also be affected by the double-passage phenomenon, it is important to understand these effects in the design of a laser radar system. We begin by modeling the backscattered wave in free space from a smooth target of finite size. This involves the introduction of two sets of Gaussian beam parameters as discussed in Chap. 10. In the presence of atmospheric turbulence we can identify two types of double-passage propagation paths—one called the folded path and the other called the reciprocal path. Each type of path requires separate mathematical treatment with effects from both types of path contributing to the notion of EBS or BSAE. Mathematical models for the mutual coherence function associated with a finite smooth reflector (target) in bistatic and monostatic systems are developed first under the assumption of weak irradiance fluctuations. These models include the mean irradiance, which identifies the spot size of the echo wave, and the BSAE. We follow this with a treatment of the scintillation index and the spatial coherence properties for the same smooth targets. The BSAE associated with a small unresolved target, also known as a "€œpoint target,"€ is developed under both weak and strong irradiance fluctuations. This is followed by a similar treatment of the scintillation index. Last, we develop models for the limiting case of a fully diffuse (Lambertian) surface that also includes both weak and strong scattering of the optical wave. We distinguish between the cases of a "€œslow detector"€ and a "€œfast detector"€ in comparison with the temporal fluctuations associated with the rough surface.
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