## 1 Introduction  
Leaf area index (LAI) is an important biophysical variable that indicates the radiation absorption and photosynthetic capacity of a crop canopy [1; 2]. LAI is defined as one half of the total green leaf area per unit of horizontal ground area [3]. It is a unitless measure, although units of m\({}^{2}\)/m\({}^{2}\) are often quoted. The typical LAI values of field crops depend on the species and cultivar, but LAI also varies within species depending on the planting density and the phenological stage of the plant [4; 5; 6]. The determination of LAI, or its temporal course, allows an understanding of ongoing biophysical processes and the prediction of plant growth and, ultimately, crop productivity. Unfortunately, in situ measurement of LAI is time consuming and cannot be operationally applied to large areas. Remote sensing techniques enable crop LAI to be estimated over large areas. In particular, imagining spectroscopy (IS) methods have been developed for agricultural applications [7]. IS divides the optical spectrum into hundreds of contiguous narrow wavebands, allowing a detailed study of vegetation absorption and reflectance characteristics. In the visible wavelengths (400-700 nm), vegetation exhibits strong absorption with reflectance minima in the blue (450 nm) and red (650 nm), and strong reflectance in the near infrared (NIR, 700-1100 nm) spectral region. The sharp increase in vegetation reflectance between red and NIR (690-730 nm) is known as the red edge [8]. Vegetation reflectance in the red edge is strongly related to the chlorophyll content [9]. Additionally, many spectral indices based on this narrow spectral interval have been successful in estimating the LAI of crops [10]. Vegetation indices (VIs), simple functions of reflectance values in two or more spectral bands [11; 12; 13; 14], are designed to amplify the effect of specific vegetation characteristics while minimizing those of the soil background and solar angle [15]. VIs are a common approach to estimate LAI from remote sensing data by establishing a statistical relationship between field-measured LAI and a VI for a specific time and place. A large number of VIs have been developed, such as the normalized difference vegetation index (NDVI, [16]), the soil adjusted vegetation index (SAVI, [17]), the modified soil-adjusted vegetation index (MSAVI, [18]), the simple ratio vegetation index (SR, [19]) and the green atmospherically resistant vegetation index (GARI, [20]). Several new indices have been derived from the classic NDVI, e.g., the blue normalized difference vegetation index (BNDVI, [21]) and the green normalized difference vegetation index (GNDVI, [22]). Further VIs have been derived from SR, e.g., the modified simple ratio index (MSR, [23]). The reflectance signal of a canopy is formed by numerous factors, such as the number of leaves, their biochemical composition, the canopy structure at a specific growth stage, the illumination conditions (the state of the atmosphere and solar angle), and background (soil) reflectance. Hence, the relationship between any single variable, such as LAI, and canopy reflectance is not unique. Specifically, in addition to LAI, a key factor determining the spectral reflectance of a horizontally extensive crop canopy is the leaf tilt angle distribution (LAD) [11; 12; 13; 14]. To our knowledge, only a few studies have examined the impact of LAD on LAI-sensitive narrow-band indices combining empirical measurements and model simulations. The main reason for this is a lack of field measurements of leaf angles. Recently, a photographic LAD method was applied to field crops [11], which provided a robust and low-cost approach for in situ LAD estimation. The leaf angle distribution for a given crop development stage is often considered to be a characteristic of the species or variety [4; 11; 24; 25]. Under this assumption, a small effect of the leaf angle on an LAI-sensitive VI indicates that the index can potentially be used across many species and development stages.