Twenty years (1987-2007) of data were provided by Greg Henry of Tennessee State University.  The data were obtained from the 0.4-m Vanderbilt/Tennessee State Automated Photometric Telescope on Mount Hopkins, AZ.  Magnitudes of II Pegasi were recorded through
blue and visual (B and V, respectively) filters.  Two filters were used in order to take advantage of limb darkening, which is the effect of the edge of the stellar disk looking darker than the center, if the image could be resolved.  This is a result of seeing hotter, deeper layers, which will appear brighter, when looking at the center of the star.  Limb darkening is more drastic in some filters than others.  This effect, along with a relationship between the spot intensity and the photosphere intensity, will help better locate the spot in Light-Curve Inversion.  The latitude is better determined by the use of several filters (Harmon & Crews 2000).

The magnitude values of the star were converted into intensities via I = 100^(m_max-m)/5, where I is the ratio of the maximum to a specific intensity of the star at a specific period in time, m is a magnitude of the star, and m_max is the smallest magnitude over the period of study.  The smallest magnitude corresponds to the maximum brightness.  This relation normalizes the intensities, which are plotted against the rotation phase of II Pegasi in a light curve.  The rotation phase relates to the period of rotation of the star.  An arbitrary point in time is taken as a reference time.  The decimal part of the number of rotations that the
star has made since the reference time is the phase.  The length of days necessary to complete a light curve varies from data set to data set.  This is due to the necessity to obtain a reasonably complete coverage in rotational phase from 0 to 1.  In some cases it takes weeks to obtain the complete light curve as there is typically one data point per day of observation.

After the light curve is obtained, the next step in this process is to reconstruct the stellar surface via Light-curve Inversion.  One of the benefits of Light-curve Inversion is that it makes no a priori assumptions regarding the number, shape, size, and location of spots.  The surface of the star is divided into a set of patches in order to recreate the surface from the light curve.  

First, the surface is divided into latitude bands, which are designated by i. Band i = 1 is defined to be the band at the north pole, which is the pole that is visible from Earth.  The latitude bands are broken into patches; there are M_i patches in each band (see the image to the left; source:  Harmon & Roettenbacher 2006).  Patches within a latitude band are labeled by j, with j ranging from 1 to M_i; j = 1 is the patch next to the prime meridian, a line that connects the pole to the intersection of the equator and the star’s approaching limb at the time of the first observation, in increasing value in the direction of rotation. Each of these patches has approximately the same area, which is achieved by M_i being approximately proportional (the approximation being due to the number of patches being required to be an integer) to the cosine of the latitude of the patch.

The intensity, I_k, of the whole star is due to the radiation that is received at Earth from the hemisphere that is facing Earth at the time at which the intensity was measured, t_k, k = 1, 2, ..., P, where P is the total number of points in the light curve.  A patch’s contribution to the total intensity seen at Earth is the specific intensity it emits in the direction of Earth times the solid angle subtended by the patch, if no radiation is absorbed along the line of sight.  The solid angle is defined as Ω_k;ij =A_k;ij/d², where A_k;ij is the area of the patch (i, j) at time t_k projected onto the sky and d is the distance from Earth to the star.  

Patches on the back side of the star contribute nothing to the sum, so their contributions are set to zero.  The goal is not to find  I_k, but to find calculated specific intensities that match the actual specific intensity distribution as nearly as possible.  Only relative intensities are sought,
so the light curve intensities are normalized with a maximum value of 1.

The values calculated by the algorithm compose a surface that produces a reconstructed light curve that is similar to the original light curve.  The original and reconstructed light curves differ by the estimate of the noise (for more details see Harmon & Crews 2000).