Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems

Abstract

Most homodyne interferometers have a quadrature detector system that includes two polarizing beam splitters that cause nonlinearity of the order of a few nanometers by phase mixing. Detectors should have the same gains to reduce nonlinearity under the assumption that there is no loss in optical components. However, optical components exhibit some loss. We show that nonlinearity can be reduced to an order of 0.01 nm when the detector gains are adjusted by simulation to include the optical characteristics. The compensated nonlinearity is 18 times smaller than that when the four detector gains are set to be equal.

Impact of the Imperfect Polarizing-Beam Splitter and Quarter-Wave Plate and Non-Ideal Laser Beam on the Accuracy of Nano-Displacement Laser Encoder

“…We use arctangent method for calculation of the phase difference caused by displacement and non-linearity from polarizing-beam splitter [6]: For non-ideal case we have: [14]. The retardation error of quarter wave plates is supposed 0.05 rad.…”

“…Nonlinearity in laser interferometers has been modeled by several methods such as Jones matrix analysis, neural networks, and adaptive algorithms [10]- [13]. The nonlinear errors can arise with imperfection of optical components such as polarizing-beam splitters (PBSs), quarter-wave plates (QWPs), and laser source [14]- [16]. We have investigated, modelled, and simulated the periodic nonlinear error of the laser encoder by considering non-ideal PBS and QWP [17].…”

“…Q and 0 Q are the Jones matrix of quarter-wave plates with fast axis at 45˚ and 0˚, respectively, and Ε is the electric field of laser beam with s-and ppolarizations [6], [14]:…”

Optical Interference Signal Processing in Precision Dimension Measurement

“…In order to obtain the orthogonal signals, 4-channel signal receiving systems are designed in the optical systems. Fig.4 shows a typical 4-channel signal receiving systems (Keem et al, 2004). …”

“…(Song et al, 2000) uses phasemodulated grating to compensate for nonorthogonal errors. (Keem et al, 2004) uses Jones matrix calculation to investigate the remaining error of a homodyne interferometer with a quadrature detector system. (Cheng et al, 2009) uses the normalized waveforms to eliminate DC offsets and amplitude variation.…”