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We report on photometric observations of sunspots carried out with the Cartesian Full Disk Telescope (CFDT) at the San Fernando Observatory (SFO). The pixel size is 5.1 arc-sec and the wavelength for the data discussed here is 6723~\AA. Fluctuations in total solar irradiance due to sunspots are often modeled using a constant value of alpha, which we are calling the bolometric contrast of a sunspot. We have defined $\alpha_{eff}$ as $DEF/(2 \times PSI)$, where $DEF$ is the sunspot's photometric deficit relative to the quiet photosphere, and $PSI$ is the digitally determined Photometric Sunspot Index (Willson et al. , 1981). For 40 sunspot groups, we find that $\alpha_{eff} = (0.276 \pm 0.051) + (3.22 \pm 0.34) 10^{-5} A_s$, where $A_s$ is the corrected area of the sunspot in micro-hemispheres. The coefficient of determination is $r^2 = 0.1936$, which is significant at the $p = 0.005$ level. We also find that $\alpha_{eff}$ is highly correlated with the ratio of umbral to total spot area ($A_u/A_s$). For 86 sunspot-days we find $\alpha_{eff} = (0.219 \pm 0.018) + (0.643 \pm 0.028) (A_u/A_s)$ with the linear coefficient of determination $r^2 = 0.859$. This suggests that an improved PSI can be constructed from knowledge of a sunspot's umbral to total area ratio. The use of such an improved PSI or, better still, actual photometry should reduce the statistical noise in comparisons with spacecraft measurements of the total solar irradiance. This work has been partially supported by grants from NSF and NASA.
