Solid state light sources are replacing a tungsten filament based bulbs in Scanning White Light Interferometers. White LEDs generate little heat, feature short switching times, and have long lifetimes. Phosphor-based white LEDs produce a wide spectrum but have two separate peaks which cause interferogram ringing. This makes measuring multi layered structures difficult and may degrade measurement precision even when measuring a single reflecting surface. Most non phosphor white LEDs exhibit a non Gaussian spectrum, but multi-LED based white LEDs can achieve switching times and stability similar to those of single color LEDs. By combining several LEDs and by controlling their input current independently it is possible to create almost an arbitrary spectrum.We designed a new light source by combining a non phosphor white LED (American Opto Plus LED, L-513NPWC-15D) and single color LEDs. This allowed us to fill the spectral gap between the blue and yellow peaks of the non phosphor white LED. By controlling the input current of the LEDs individually a nearly Gaussian shaped spectrum was achieved. This wide continuous spectrum creates short interferograms (FWHM ~1.4 µm) without side peaks. To demonstrate the properties of this source we measured through a 5 µm thick polymer film. The well localized interference created by the source allows measuring both surfaces of thin films simultaneously. We were able to pulse the source at 5.4 MHz.