Compact fiber-coupled three degree-of-freedom displacement interferometry for nanopositioning stage calibration

Abstract

Heterodyne displacement interferometry is a widely accepted methodology capable of measuring displacements with sub-nanometer resolution in many applications. We present a compact heterodyne system capable of simultaneously measuring Z-displacement along with changes in pitch and yaw using a single measurement beam incident on a plane mirror target. The interferometer's measurement detector utilizes differential wavefront sensing to decouple and measure these three degrees of freedom. Reliable rotational measurements typically require calibration; however, two analytical models are discussed which predict the readout of rotational scaling factors.

Dynamic Doppler Frequency Shift Errors: Measurement, Characterization, and Compensation

“…Thus, it can measure the spectrum in every local section, whose period is the width of the window, localizing the signal with varied frequency throughout a larger time period. The STFT is (17) where the w(t) is the window function, τ is the hop size, which determines the speed of the window moving along the time axis, and F( f, τ ) is the spectrum of the signal in every short period; the frequency which is corresponding to the maximum value of F( f, τ ) is the primary frequency of the signal in this local section. There are a variety of window functions available, commonly Hanning, Hamming, cosine, and Gaussian that can be applied to establish the bin size over which the STFT is computed [30].…”

“…2 is for the reference signal, while the bottom path is for measurement signals; it could be one channel from single-element photodiode, or four channels from our quadrant photodiode, based on our custom interferometer topology [15]- [17]. Fig.…”

Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology

“…where φ represents detected phase of quadrant A, B, C, or D, L pitch and L yaw represent a calibrated equivalent length in pitch and yaw measurements that is primarily dependent on beam diameter, detector size, alignment errors, and beam wavefront. A detailed description for this three DOF interferometer 26 and a model which effectively predicts the equivalent lengths (L pitch and L yaw ) with high accuracy 27 are shown in our previous work.…”

Positioning control effectiveness of optical knife edge displacement sensor-embedded monolithic precision stage

“…Displacement sensing technology in precision positioning systems is the key to fast and robust positioning control and high resolution measurement relied on by high-tech manufacturing and metrology operations [9][10][11][12][13]. Non-contact sensors such as capacitive sensors (CS) and optical sensors (laser interferometer and laser encoder) are traditionally used in high precision stage applications due to their ability to perform dynamic motion characterization and fast and high resolution measurement [1,2].…”

“…However, majority of their sensing systems are based on CS [2,4,5], position sensitive detectors [9,10,13], laser encoders [6,7] or laser interferometers [11]. Recently, with progress of microelectromechanical system (MEMS) technology, many MEMS motion stages have been introduced, but the total displacement is limited to a few tens of µm even though those are promising for high bandwidth and high resolution [23,24].…”