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Standard instrumentation for the assessment of the respiration rate is largely used in medicine. Spirometers, textile-based capacitive sensors or photopletismography are all contact devices used for such aim; the main drawback in their use is the necessity to have a direct contact between the instrument and the patient, which in some cases can limit the use of such devices. In this paper, we present an optical, fully no-contact measurement method for monitoring of the respiration rate, based on the assessment of chest wall movements (velocity and displacement) by a laser Doppler vibrometer (LDVi). The proposed method is operated at a distance of 1.5 m, on different point of the patient thoracic and abdominal area. The measurement procedure was already demonstrated to precisely perform for what concern the monitoring of the cardiac activity. In this paper, we have monitored 33 patients with a reference instrument (spirometer) and with the proposed non-contact method. Statistical analysis (Bland-Altman) of the respiration rate measured with both instruments is reported. We also report a study on the optimal position on the thoracic area based on quality of the signal measured on the same population of subject. Results demonstrate the possibility to continuously monitor the respiration rate with a mean difference respect to the spirometer data of 13 m ( relative error: 0.35%).