Phase shift method

The phase shift method ( English Phase Shifting ) is a measuring method in the optics ( interferometry , fringe projection ) and electronics is used to control the phase position of a modulated signal to be determined by pointwise intensity measurements.

principle

The phase position of the signal is shifted at least twice by a known value (spatially or temporally), while the intensity is measured at one point. The phase position can be calculated from three or more measured values.

example

Example for phase shifting with four steps and phase angle.

{\ displaystyle \ pi / 2}

In an ideal arrangement, the measured intensity values for the phase position satisfy the following formula: ${\ displaystyle p_ {i}}$ ${\ displaystyle i}$

{\ displaystyle p_ {i} = O + A \ cdot \ sin (\ varphi + i \ Delta \ varphi)}

This includes the intensity offset , the amplitude of the signal, the phase value sought and the phase shift for each level. ${\ displaystyle O}$ ${\ displaystyle A}$ ${\ displaystyle \ varphi}$ ${\ displaystyle \ Delta \ varphi}$

For a phase shift method with four stages and the calculation formula for the phase is: ${\ displaystyle \ Delta \ varphi = \ pi / 2}$

{\ displaystyle \ cot \ varphi = {\ frac {p_ {3} -p_ {1}} {p_ {2} -p_ {0}}}}

Uniqueness

When using one wavelength, the phase measurement is only unambiguous within one period . Heterodyne phase shifting (see also heterodyne receiver ), which works with several wavelengths, is suitable for absolute phase measurement . The uniqueness area then corresponds to the wavelength of the beat . Unwrapping processes are used so that the uniqueness is possible across period boundaries . Due to the limitation of arctane, phase jumps up to π or λ / 2 can be detected.

Technical implementation

The implementation takes place in the different application areas with different techniques. Basically, the measurement can take place integrating during the shifting ( phase shifting ) or at rest with a constant phase shifting ( phase stepping ). The evaluation differs only insignificantly.

Interferometry

In interferometry , the phase shift is generated by shifting the reference wave with respect to the object wave . This creates an overlay which can be measured by the different intensity values. The course of this can be represented as an oscillation.

Fringe projection

With fringe projection , either the slide in the projector or an element in the imaging beam path is shifted or, in programmable systems such as DMD projectors (Digital Micromirror Device), a correspondingly shifted image is projected.

use

Phase shifting methods are used in white light interferometry to create height maps for material surfaces. These can be used for quality assurance, for example of weld seams.

literature

P. Carré: Installation et utilization du comparateur photoélectrique et interférentiel du bureau international des poids et mesures. Metrologica 2 (1), pp. 13-23, 1966
K. Creath: Comparison of phase-measurement algorithms. Surface characterization and testing 680, pp. 19-28, 1986
G. Wiora: Optical 3D measurement technology: Precise shape measurement with an extended strip projection method. Dissertation, chap. 4.3, p. 67ff, Heidelberg University Library, 2001 ( online )