The measurement routine started with measurements of multiangular spectra of the tree in the goniometer. We used the LAGOS (Laboratory goniometer system) goniometer [3,4], which is a large goniometer (radius of 2 m) capable of measuring in all view angles over the hemisphere, excluding zenith angles larger than ∼76° (Fig. 1). To illuminate the trees, we used a 1000 W brightness stabilized tungsten halogen lamp that generated a conical light beam (opening angle of approx. 22°) using a Köhler illuminator with aspherical reflector and a condenser. The lamp was pointing at the tree from 1.75 m distance at zenith angle of 40°, and it illuminated the tree completely (Fig. 1). We used an ASD FieldSpec 3 non-imaging spectrometer (serial number 16006), which measured in the wavelength range of 350–2500 nm, and outputted spectra at 1 nm intervals. All measurements were performed in digital numbers (DN) and converted into physical quantities in post-processing. The spectrometer's detector unit, i.e., a bare fiber-optic bundle with nominal field-of-view (FOV) of 25°, was pointing at the center of the goniometer from 1.94 m distance (Fig. 1). The spectrometer has three separate detectors: visible-near-infrared (VNIR, 350–1000 nm), shortwave-infrared 1 (SWIR1, 1001–1800 nm), and shortwave-infrared 2 (SWIR2, 1800–2500 nm), which have slightly different FOVs, because they view the target through separate optical fibers in the bundle.

Side-view of the LAGOS goniometer and the measurement setup with the light source and spectrometer. View zenith angles (θ) are denoted with green marks on the goniometer's arc. The tree was always exactly in the center of the goniometer, and the vertical mid-point of the tree crown was at the base level, i.e., the light beam and sensor's field-of-view were pointing exactly to the center of the tree crown. Symbol h indicates the height of the frame that holds the black background canvas and that was adjusted depending on tree height.

The measurements were performed in eight view azimuth angles (φ), and in seven view zenith angles (θ) per azimuth (Fig. 2). The view azimuth angles included the principal (φ = 0°) and cross-plane (φ = 90°), and in addition, six azimuth angles at 15°, 45°, 75°, 115°, 135°, and 165°. The principal and cross-plane were included because they are interesting for interpretation of remote sensing data, and the latter six view azimuth angles were important to obtain a systematic sampling over the hemisphere. The view zenith angles were −76.2°, −48.6°, −21.2°, ±0°, +21.2°, +48.6°, and +76.2°. They correspond to the nodes of Gauss-Legendre integration so that cosθ are the Gauss-Legendre weights. The only exception was the principal plane, in which two view zenith angles behind the lamp (θ = [+48.6°, +76.2°]) could not be measured because the lamp obstructed the FOV. In total, there were thus 47 different view angles (Fig. 2). Because the measurement in nadir (φ = 0°, θ = 0°) was performed separately for each azimuth angle, there were seven repetitions of nadir measurement, which resulted in total of 54 measurements per tree. The integration time was 2.18 s for each individual spectrum, and 10 individual spectra were averaged into one measurement. Before and after the measurements of a tree, a white reference was measured in nadir. The white reference was a calibrated Zenith Lite® panel with dimensions of 20 × 20 cm and nominal reflectance of 95%. It was placed in the center of the goniometer, using a tripod. Three white reference measurements were taken both before and after the tree measurements. All white reference measurements per tree were averaged into one value in the data processing.

Top-view of the goniometer showing the angle notation used in the data collection. There were eight view azimuth angles (φ), and seven view zenith angles (θ) per azimuth, except in the principal plane (φ = 0°), where view zenith angles behind the lamp could not be measured.

We placed a spectrally black (Sunbrella® Solid VV M100) acrylic canvas attached to a wooden frame (1.3 m × 1.5 m) below the tree (or white reference), so that the fraction of illumination beam that was not intercepted by the tree (or white reference) was captured by the canvas (Fig. 1). This ensured a well-controlled and predictable background signal (stray light), which could be later removed in the data processing. The canvas had directional-hemispherical reflectance factor (DHRF) of 0.013–0.02 (measured with an integrating sphere). The height of the wooden frame, and thus the canvas, could be adjusted (Fig. 1). We used four pre-defined heights: 0.6 m, 0.65 m, 0.69 m, and 0.74 m. The height of the canvas was selected based on the tree height so that the pot of the tree was below the canvas, while the entire tree crown was above the canvas and fully illuminated by the light beam (Fig. 1). This setup ensured that the signal recorded by the spectrometer was composed of the signal from the tree, and additionally stray light, which mainly originated from the canvas. The amount of stray light depended on the directional scattering characteristics of the canvas, and on the illuminated area seen by the spectrometer (Fig. 1). The stray light was measured once for each view angle and for each frame height. The stray light was ratioed to the white reference measured in nadir view. We call this ratio as ‘stray light fraction’. An estimate of stray light for each tree could then be calculated based on the white reference measurement and stray light fraction.

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