tokens: magnification, which depends on the microlensing model and blending. Our method conserves the variability and noise in the original light curves, as well as information on the quality of individual measurements. Let be the flux of the source and the unmagnified flux from possible blended stars and/or the lens itself. The flux of the baseline object () is magnified during a microlensing event by a factorwhere A ( t ) is the model magnification and is the blending parameter. If there is no blending ( f s = 1), then A ′( t ) = A ( t ); if the blending is very strong (), the observed magnification . To inject a microlensing event into the database light curve, we needed to transform the observed flux and its uncertainty to . The naive transformation is incorrect because it preserves the original photon noise during the magnified part of the event. To illustrate this, let us consider a constant I = 19.5 star with a typical rms light-curve scatter of 0.1 mag (left panel of Figure 9 ). The transformation A ′( t ) = 100 would shift the mean magnitude to I ′ = 14.5, but it would preserve the original scatter, whereas the observed scatter of constant stars of that magnitude is much smaller (Figure 9 ). Figure 9. The rms light-curve scatter as a function of the mean magnitude of a star in the I band in the OGLE-IV field BLG521.12. Left panel: real data. Right panel: constant stars injected on top of real light curves (, where 0 ≤ Δ m ≤ 0.75 is drawn from a uniform distribution). The orange line is the best-fit model from Skowron et al. ( 2016 ). Assuming that every observed fluctuation in brightness of the initial light curve from its mean brightness ( F i − F 0 ) is due to the observational noise, the following transformation ensures that the photon noise is properly scaled:where F 0 and are the mean flux in the baseline and the magnified mean flux, respectively (the corresponding magnitudes are m 0 and ). The ratio can be calculated by assuming the photometric noise model of Skowron et al. ( 2016 ):In this simple model, the observed scatter is the sum of the Poisson noise contributions from the object and background (parameterized by m B ). To verify the proposed model, we injected “constant” stars on top of real light curves from the database (which correspond to the transformation ). The right panel of Figure 9 shows the rms scatter of simulated light curves, which is consistent with that of real data. Our simple model underpredicts the scatter of the brightest stars ( I ≲ 15), likely because the accuracy of their photometry is limited by the accuracy of modeling the PSF and thus the quality of image subtractions, not by the photon noise. This effect does not influence our detection efficiency simulations, because the vast majority of events are fainter than I = 15. Similarly, we used the noise model of Skowron et al. ( 2016 ) to transform the uncertainties:When the predicted uncertainties were equal to or below 0.003 mag, we assumed mag, as in the
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