Scanning sensor for measuring properties of continuous flat sheet, that is moving in the machine direction, employs an IR radiation source for directing a beam of incident IR radiation that impinges the sheet. The IR source has elongated lamp filament that generates IR radiation and the corresponding spot size formed on the sheet has elongated dimensions with its long axis being aligned with the machine direction. Aligned with the MD maximizes sensor spatial resolution in the cross direction. The sensor can employ a receiver having rectangular geometry with its long axis being aligned also in the MD. Scanning sensor can operate in the reflective, transmissive, or offset transmission mode to monitor characteristics of flat sheets, particularly of paper or plastic products.