Early de-oxygenation (initial dip) is an indicator of the primal cortical activity source in functional neuro-imaging. In this study, initial dip's existence and its estimation in relation to the differential pathlength factor (DPF) and data drift were investigated in detail. An efficient algorithm for estimation of drift in fNIRS data is proposed. The results favor the shifting of the fNIRS signal to a transformed coordinate system to infer correct information. Additionally, in this study, the effect of the DPF on initial dip was comprehensively analyzed. Four different cases of initial dip existence were treated, and the resultant characteristics of the hemodynamic response function (HRF) for DPF variation corresponding to particular near-infrared (NIR) wavelengths were summarized. A unique neuro-activation model and its iterative optimization solution that can estimate drift in fNIRS data and determine the best possible fit of HRF with free parameters were developed and herein proposed. The results were verified on simulated data sets. The algorithm is applied to free available datasets in addition to six healthy subjects those were experimented using fNIRS and observations and analysis regarding shape of HRF were summarized as well. A comparison with standard GLM is also discussed and effects of activity strength parameters have also been analyzed.