Principles of Modern Radar - Volume 2 1891121537

6.6 Image Metrics 241The contrast ratio quantifies the shadow depth achievable relative to a terrain of agiven mean radar reflectivity. Equivalently, it determines how bright a no-return area willappear in the image. The ultimate contrast achieved within a SAR image can be limitedby the hardware (e.g., antenna dimensions and array configuration, electronic noise floor,and quantization noise), the processing chain, the collection geometry, or the terrain itself.Many of these can be controlled to some extent by the system designer. By studying thecontrast ratio, it is possible to balance system parameters to achieve a design that meetsthe specified requirement.Carrara et al. [4] describe the distributed target contrast ratio (DTCR) to quantifythe ability to visually distinguish between two adjacent types of terrain, one having highbackscatter and the other having low. The DTCR is defined asDTCR = σ 0,high + σ n,totalσ 0,low + σ n,total= σ 0,high + σ n,add + σ n,multσ 0,low + σ n,add + σ n,mult= σ 0,high + σ n + MNR ¯σ 0σ 0,low + σ n + MNR ¯σ 0(6.28)where the quantities used in this equation are given in Table 6-3. The total noise σ n,totalis decomposed into σ n,add and σ n,mult , which are the additive and multiplicative noise,respectively. The third line of equation (6.28) comes from [4] where common usageassumes that the most significant multiplicative noise sources can be combined into a singlemultiplicative noise ratio (MNR) value that is proportional to the average scene backscatter.Special applications might consider additional sources of multiplicative noise, such asvolume scattering due to rain. In this case, the multiplicative noise cannot be simplifiedand written as σ n,mult = MNR ¯σ 0 . The following sections describe the constituent sourcesof additive and multiplicative noise relevant to SAR.A typical radar application for the DTCR might compare the (low) backscatter from asmooth asphalt road to the (high) backscatter from surrounding vegetated terrain. We willpursue the limiting case for which the low backscatter regions of interest are shadows orno-return areas, so σ 0,low is zero by definition. For notational simplicity the high backscatterregion will be denoted simply as σ 0 . This leads to the quantity sought; the terrain to shadowcontrast ratio, or more simply, the contrast ratio (CR) of the image,CR = σ 0 + σ n + MNR ¯σ 0σ n + MNR ¯σ 0(6.29)TABLE 6-3σ 0,highσ 0,lowσ n,totalσ n,addσ n,mult¯σ 0MNRQuantities Contributing to DTCRBackscatter coefficient for brighter image regionBackscatter coefficient for darker image regionEquivalent backscatter coefficient of total noiseEquivalent backscatter coefficient of additive noiseEquivalent backscatter coefficient of multiplicative noiseAverage backscatter coefficient for the terrainMultiplicative noise ratio