Machine vibration measurement using non contacting probes are taken:

Non-contacting probes, typically eddy-current proximity probes, are fundamental to monitoring critical rotating machinery. They are mounted on a stationary part of the machine, such as the bearing housing, and measure the instantaneous gap to the rotating shaft. Therefore, the measurement captured is the displacement of the shaft relative to the probe's fixed mounting point. This method is essential for machines with fluid-film bearings, where significant shaft motion can occur within the bearing clearance. The primary output of the transducer is a voltage proportional to this relative displacement, typically expressed in mils or micrometers (peak-to-peak).

A. Absolute casing velocity: This measurement is taken with seismic transducers, such as velocity pickups or accelerometers (with their signal integrated), mounted directly on the machine casing.
B. Absolute casing displacement: This is measured using specialized low-frequency seismic transducers or by double-integrating the signal from an accelerometer mounted on the casing.
C. Relative shaft velocity: While a velocity signal can be electronically derived by differentiating the displacement signal, the non-contacting probe is fundamentally a displacement transducer; it does not directly measure velocity.

1. API Standard 670, 5th Edition, "Machinery Protection Systems," November 2014.

Section 7.2.1: "A noncontacting eddy-current proximity probe system... shall be used for measuring radial shaft vibration."

Section 7.2.2: "The measurement of radial shaft vibration shall be relative to the machine bearing housing."

Section 7.2.4.1: "The vibration monitor shall be scaled to read in terms of peak-to-peak displacement."

2. Bently Nevada (Baker Hughes) Application Note, "How the Proximity Probe and Proximitor® Sensor Work," Document 173312 Rev. C.

Page 1, Introduction: "The Bently Nevada proximity probe is a non-contacting transducer that measures the distance between its tip and a target surface... When used to observe a machine shaft, it is called a vibration or position measurement." This confirms its function as a relative displacement sensor.

3. Scheffer, C., & Girdhar, P. (2004). Practical Machinery Vibration Analysis and Predictive Maintenance. Newnes.

Chapter 3, Section 3.2.3, "Proximity Probes": "Proximity probes are non-contacting transducers that measure displacement... They measure the relative displacement between the probe tip and the shaft." (p. 54).