Self-mixing interferometry (SMI) represents a simple, robust, and self-aligned technique for metrology applications. Still, its applicability on diffuse targets is limited to distances up to few meters. We present an enhanced approach based on the detection of the frequency-modulated (FM) self-mixing signal. The FM signal detection is achieved using an acetylene edge filter that maps laser frequency variations into intensity variations as the laser wavelength is tuned to the edge of the steep absorption profile. An experimental comparison between the enhanced and the conventional SMI approach is presented. The new approach yields to about two orders of magnitude larger signal-to-noise ratio and extends the applicability of SMI into new fields allowing longer detection ranges and lower backscattering signals.