This table is adapted from @Montgomerie2006 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 | \[B_1=B_T=\int_{\lambda_{min}}^{\lambda_{max}} R_i = \sum_{\lambda_{min}}^{\lambda_{max}} R_i\] | @Andersson1999,@Andersson2002,@Ornborg2002,@Andersson1998,@Smiseth2001,@Saks2003,@Pryke2001,@Shawkey2003
| Mean brightness | \[B_2=\frac{\sum_{\lambda_{min}}^{\lambda_{max}} R_i}{n_w}=\frac{B_1}{n_w}\] | @Delhey2003,@Siefferman2005
| Intensity | \[B_3=R_{max}\] | @Andersson1999,@Keyser2000,@Keyser1999
Saturation | Chroma, reflectance ratio, spectral purity | \[S_1= \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{\sum_{\lambda_{min}}^{\lambda_{max}} R_i} = \frac{\sum_{\lambda_a}^{\lambda_b} R_i}{B_1}\] | @Ornborg2002,@Andersson1998,@Smiseth2001,@Siefferman2005,@Peters2004,@Shawkey2003
| Spectral saturation | \[S_2 = \frac{R_{max}}{R_{min}}\] | @Andersson1999
| Chroma | \[S_3 = \frac{\sum_{\lambda_{R_{max}}-50}^{\lambda_{R_{max}}+50} R_i}{B_1}\] | @Shawkey2003
| Spectral purity | \[S_4 = \lvert b\text{max}_{neg}\lvert\] | @Andersson1999
| Chroma | \[S_5=\sqrt{(B_r-B_g)^2+(B_y-B_b)^2}\] | @Saks2003
| Constrast, amplitude | \[S_6 = R_{max} - R_{min}\] | @Keyser2000,@Keyser1999
| Spectral saturation | \[S_7 = \frac{\left(\sum_{\lambda_{320}}^{\lambda_{R_{mid}}} R_i - \sum_{\lambda_{R_{mid}}}^{\lambda_{700}} R_i\right)}{B_1}\] | @Andersson2002,@Pryke2001
| Chroma | \[S_8=\frac{R_{max}-R_{min}}{B_2}\] | @Andersson2002,@Smiseth2001
| Carotenoid chroma | \[S_9=\frac{R_{\lambda_{700}}-R_{\lambda_{450}}}{R_{\lambda_{700}}}\] | @Peters2004
| Peaky chroma | \[S_{10}=\lvert b\text{max}_{neg} \lvert\frac{R_{max}-R_{min}}{B_2}\] | @Ornborg2002
Hue | Hue, peak wavelength, spectral location | \[H_1=\lambda_{R_{max}}\] | @Andersson1999,@Ornborg2002,@Andersson1998,@Delhey2003,@Smiseth2001,@Keyser2000,@Siefferman2005,@Shawkey2003
| Hue | \[H_2 = \lambda_{b\text{max}_{neg}}\] | @Andersson1998,@Smiseth2001
| Hue | \[H_3 = \lambda_{R_{mid}}\] | @Andersson2002,@Smiseth2001,@Pryke2001
| Hue | \[H_4 = \arctan\left(\frac{B_y-B_b}{B_r-B_g}\right)\] | @Saks2003
| Hue | \[H_5 = \lambda_{b\text{max}_{pos}}\] | @Keyser1999

- \(R_i\): 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., \(\frac{R_{max}+R_{min}}{2}\))

# References