Laser speckle contrast imaging (LSCI) is a method to visualize and quantify tissue perfusion and blood flow. A common flaw in LSCI variants is their sensitivity to the optical setup parameters and that they operate well only on statistics of undistorted laser speckle patterns. The signal saturation of the sensors makes the contrast calculation misleading; hence the illumination level must be well controlled. We describe the theoretical explanation for the saturation-caused degradation. We introduce a linear extrapolation method to eliminate the overexposure induced error up to an extent of 60-70% saturated pixel count. This, depending on the contrast value and use case, enables to use 3-8 times higher external illumination level with no deterioration of the contrast calculation and thus the measured blood flow index. Our method enables a higher signal-to-noise ratio in darker areas by allowing the use of higher illumination, utilizing a larger portion of the dynamic range of the sensors, and making the illumination level setting less cumbersome.