Low-mass stars ( M \lesssim 0.4 M _ { \odot } ) are thought to comprise the bulk of the stellar mass of galaxies but they constitute only of order a percent of the bolometric luminosity of an old stellar population .
Directly estimating the number of low-mass stars from integrated flux measurements of old stellar systems is therefore possible but very challenging given the numerous variables that can affect the light at the percent level .
Here we present a new population synthesis model created specifically for the purpose of measuring the low-mass initial mass function ( IMF ) down to \sim 0.1 M _ { \odot } for metal-rich stellar populations with ages in the range 3 - 13.5 Gyr .
Our fiducial model is based on the synthesis of three separate isochrones and a combination of optical and near-IR empirical stellar libraries in order to produce integrated light spectra over the wavelength interval 0.35 \mu m < \lambda < 2.4 \mu m at a resolving power of R \approx 2000 .
New synthetic stellar atmospheres and spectra have been computed in order to model the spectral variations due to changes in individual elemental abundances including C , N , Na , Mg , Si , Ca , Ti , Fe , and generic \alpha elements .
We demonstrate the power of combining blue spectral features with surface gravity-sensitive near-IR features in order to simultaneously constrain the low-mass IMF , stellar population age , metallicity , and abundance pattern from integrated light measurements .
Finally , we show that the shape of the low-mass IMF can also be directly constrained by employing a suite of surface gravity-sensitive spectral features , each of which is most sensitive to a particular mass interval .