4 Spectral shape descriptors

This table is adapted from Montgomerie (2006) and lists all spectral descriptors that are computed by the summary function in pavo.

Color variable	Names used	Formula	Reference
Brightness	Total brightness, total reflectance, spectral intensity	\[B_1=B_T=\int_{\lambda_{min}}^{\lambda_{max}} R_i = \sum_{\lambda_{min}}^{\lambda_{max}} R_i\]	Andersson (1999),Andersson et al. (2002),Örnborg et al. (2002),Andersson, Örnborg, and Andersson (1998),Smiseth et al. (2001),Saks, McGraw, and Horak (2003),Pryke, Lawes, and Andersson (2001),Shawkey et al. (2003)
	Mean brightness	\[B_2=\frac{\sum_{\lambda_{min}}^{\lambda_{max}} R_i}{n_w}=\frac{B_1}{n_w}\]	Delhey et al. (2003),Siefferman and Hill (2005)
	Intensity	\[B_3=R_{max}\]	Andersson (1999),Keyser and Hill (2000),Keyser and Hill (1999)
Saturation	Chroma, reflectance ratio, spectral purity	\[S_1= \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{\sum_{\lambda_{min}}^{\lambda_{max}} R_i} = \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{B_1}\]	Örnborg et al. (2002),Andersson, Örnborg, and Andersson (1998),Smiseth et al. (2001),Siefferman and Hill (2005),Peters et al. (2004),Shawkey et al. (2003)
	Spectral saturation	\[S_2 = \frac{R_{max}}{R_{min}}\]	Andersson (1999)
	Chroma	\[S_3 = \frac{\sum_{\lambda_{R_{max}}-50}^{\lambda_{R_{max}}+50} R_i}{B_1}\]	Shawkey et al. (2003)
	Spectral purity	\[S_4 = \lvert b\text{max}_{neg}\lvert\]	Andersson (1999)
	Chroma	\[S_5=\sqrt{(B_r-B_g)^2+(B_y-B_b)^2}\]	Saks, McGraw, and Horak (2003)
	Constrast, amplitude	\[S_6 = R_{max} - R_{min}\]	Keyser and Hill (2000),Keyser and Hill (1999)
	Spectral saturation	\[S_7 = \frac{\left(\sum_{\lambda_{320}}^{\lambda_{R_{mid}}} R_i - \sum_{\lambda_{R_{mid}}}^{\lambda_{700}} R_i\right)}{B_1}\]	Andersson et al. (2002),Pryke, Lawes, and Andersson (2001)
	Chroma	\[S_8=\frac{R_{max}-R_{min}}{B_2}\]	Andersson et al. (2002),Smiseth et al. (2001)
	Carotenoid chroma	\[S_9=\frac{R_{\lambda_{700}}-R_{\lambda_{450}}}{R_{\lambda_{700}}}\]	Peters et al. (2004)
	Peaky chroma	\[S_{10}=\lvert b\text{max}_{neg} \lvert\frac{R_{max}-R_{min}}{B_2}\]	Örnborg et al. (2002)
Hue	Hue, peak wavelength, spectral location	\[H_1=\lambda_{R_{max}}\]	Andersson (1999),Örnborg et al. (2002),Andersson, Örnborg, and Andersson (1998),Delhey et al. (2003),Smiseth et al. (2001),Keyser and Hill (2000),Siefferman and Hill (2005),Shawkey et al. (2003)
	Hue	\[H_2 = \lambda_{b\text{max}_{neg}}\]	Andersson, Örnborg, and Andersson (1998),Smiseth et al. (2001)
	Hue	\[H_3 = \lambda_{R_{mid}}\]	Andersson et al. (2002),Smiseth et al. (2001),Pryke, Lawes, and Andersson (2001)
	Hue	\[H_4 = \arctan\left(\frac{B_y-B_b}{B_r-B_g}\right)\]	Saks, McGraw, and Horak (2003)
	Hue	\[H_5 = \lambda_{b\text{max}_{pos}}\]	Keyser and Hill (1999)

• \(R_i\): percentage (or proportional) reflectance at the \(i\)th wavelength
• \(\lambda_{max}\), \(\lambda_{min}\): upper and lower (respectively) limits of wavelengths
• \(n_w\): number of wavelength intervals used to calculate \(B_T\)
• \(R_{max}\), \(R_{min}\): maximum and minimum percent reflectances, respectively
• \(\lambda_{R_{max}}\): wavelength at maximum reflectance
• \(b\text{max}_{neg}\), \(b\text{max}_{pos}\): maximum negative and positive slopes of reflectance curve in a region of interest
• \(B_r\), \(B_y\), \(B_g\), \(B_b\): total brightness in red (\(r=625-700\,nm\)), yellow (\(y=550-625\,nm\)), green (\(g=475-550\,nm\)) and blue (\(b=400-475\,nm\)) segments of the spectrum
• \(\lambda_{R_{mid}}\): wavelength at the reflectance midpoint between \(R_{max}\) and \(R_{min}\) (i.e., \(\frac{R_{max}+R_{min}}{2}\))