The recent development of a dense pattern, multiple pass optical cell based on cylindrical mirrors makes possible a differential spectroscopic method that removes (nearly) all common mode features including laser noise, laser distortion, and unwanted optical interference fringes (etalons). The cylindrical mirror cell is similar to other astigmatic cells in that the beam enters through a hole drilled in the center of one mirror. Key differences, however, include the property that for most re-entrant beam trajectories have N passes (where N/2 is odd) through the cell, the N/2 spot is always located at the center of the far mirror. In the differential cell approach, a pellicle beamsplitter located just behind a hole in the far mirror transmits a portion of the beam and reflects the remainder to continue the second set of N/2 passes before exiting through the entrance hole. The two beams - one exiting at the far mirror after N/2 passes, the other exiting at the entrance mirror following N passes - are the reference and sample beams, respectively, applied to a noise canceler circuit. Proof-of-principle experiments reported here using near-infrared measurements of methane absorbance show the differential method does work. The optical system used, however, introduced excessive astigmatism in the beam reflected from the pellicle beam splitter because of the displace of the pellicle from the cell mirror surface. That astigmatism made it difficult to align the return beam for the complete set of N/2 passes and to focus the exit beam onto the photodiode detector. Design improvements are discussed.