sub-pixel coordinates. We quantify the strength of correlation by calculating Spearman’s $\rho$ coefficient [@Press1987]. We model the pixel phase effect as a function of the $x$ and $y$ coordinates, and find that linear and quadratic fits do not correct the observed correlation. We model the pixel phase effect using a cubic function of the $x$ and $y$ coordinates [@Knutson2008; @Heinze2015]: $$\label{eq:pixelphase}
    f(x,y) = P_0 + P_1x + P_2y + P_3 xy + P_4 x^2 + P_5 y^2 + P_6x^3 + P_7 y^3 + P_8x^2y + P_9 xy^2$$ where $f(x,y)$ represents the measured flux, $P_i$ are the fitted coefficients, and $x$ and $y$ are the sub-pixel coordinates. [We correct the light curves of the target and reference stars using Equation \[eq:pixelphase\], and find that the fitted coefficients $P_i$ are similar for the target and reference stars.]{} We find that this correction decreases the correlation between the flux and pixel position for each observation (Figure \[fig:2M0045\_pixelphase\] for ). We present the final corrected light curves in the top panels of Figure \[fig:2M0045\_full\_lc\], \[fig:2M0501\_full\_lc\] and \[fig:2M1425\_full\_lc\]. [We additionally show how the $x$ and $y$ pixel positions vary during each observation in Figures \[fig:xypos\_2M0045\], \[fig:xypos\_2M0501\] and \[fig:xypos\_2M1425\]. The variation in pixel position does not 