Photometry Transformation from RGB Bayer Filter System to Johnson-Cousins BVR Filter System

The RGB Bayer filter system consists of a mosaic of R, G, and B filters on the grid of the photo sensors which typical commercial DSLR (Digital Single Lens Reflex) cameras and CCD cameras are equipped with. Lot of unique astronomical data obtained using an RGB Bayer filter system are available, including transient objects, e.g. supernovae, variable stars, and solar system bodies. The utilization of such data in scientific research requires that reliable photometric transformation methods are available between the systems. In this work, we develop a series of equations to convert the observed magnitudes in the RGB Bayer filter system ($R_B$, $G_B$, and $B_B$) into the Johnson-Cousins BVR filter system ($B_J$, $V_J$, and $R_C$). The new transformation equations derive the calculated magnitudes in the Johnson-Cousins filters ($B_{Jcal}$, $V_{Jcal}$, and $R_{Ccal}$) as functions of RGB magnitudes and colors. The mean differences between the transformed magnitudes and original magnitudes, i.e. the residuals, are $\Delta(B_J-B_{Jcal})$ = 0.064 mag, $\Delta(V_J-V_{Jcal})$ = 0.041 mag, and $\Delta(R_C-R_{Ccal})$ = 0.039 mag. The calculated Johnson-Cousins magnitudes from the transformation equations show a good linear correlation with the observed Johnson-Cousins magnitudes.