*3.4. Spectral Mathematical Transformation*

Before estimation model of surface parameters based on spectral reflectance is established, it is often necessary to perform nonlinear mathematical transformation for original spectral reflectance (R). The commonly used non-linear mathematical transformations include: root mean square transform ( <sup>√</sup> R), reciprocal transform (1/R), logarithmic transformation (lgR), and logarithm reciprocal transformation (1/lgR). The main purpose is that linear relationship between spectral reflectance and surface parameters is transformed into a nonlinear relationship, a relatively simple linear regression analysis is performed to obtain approximately nonlinear results, and various forms of estimation models are established to improve the recognition accuracy. In addition, non-linear transformation can enhance spectral difference to some extent; it is convenient to distinguish the influence on spectrum caused by the difference of surface parameters. Spectral reflectance R and its four kinds of spectral transformation curves are shown in Figure 2.

**Figure 2.** Spectral reflectance of soil and its four mathematical transformation forms: (**a**) R; (**b**) √ R; (**c**) 1/R; (**d**) lgR; and (**e**) 1/lgR.
