Fourier transform spectrometers (FTSs), based on two-beam interference, benefit from a much higher spectral resolving power than the more commonly used dispersive spectrometers. This is because of the optical path difference (OPD)—which relates to the phase difference—between the two beams. Since the spectral resolution is proportional to the maximum OPD acquired in the interferogram, it can be easily increased in an FTS. However, many of today's FTSs are based on Michelson interferometer architectures and, as such, are sensitive to vibration and misalignment. Additionally, the mechanical scanning required to acquire an interferogram can make the measurements sensitive to temporal error.
To avoid error due to temporal misregistration, interference can be measured across a 2D focal plane array (FPA) or a 1D line array. This allows several points within an interferogram to be measured simultaneously, thereby alleviating temporal error. Unfortunately, due to a reduction in interference contrast, the signal-to-noise ratio decreases as the spectral resolution is increased. This hampers the primary advantage of the FTS. To circumvent this limitation, the concept of spatial heterodyne interferometry (SHI) was introduced, using a Michelson interferometer.1,2 An SHI can be created by replacing the tilted mirrors in a Michelson interferometer with tilted diffraction gratings. This heterodynes (mixes) the 2D interference pattern of the interferometer to a lower spatial frequency. Using this technique, the spectral resolving power of an FTS can be preserved while maintaining high temporal resolution and maximizing the signal-to-noise ratio.
Since the first implementation of the Michelson-based SHI, other SHIs have been introduced, including Sagnac interferometers with diffraction gratings.3 To transition towards SHI instrumentation independent of free-space and/or reflective optics, a recent effort by Velasco et al. focused on creating monolithic fiber-based systems.4 These systems have produced exciting high-spectral-resolution measurements at telecommunications wavelengths (∼1550nm).
In our SHI system design, we used a birefringent polarization interferometer. Although birefringent FTS systems have been known for years,5 efficient spatial heterodyning has not been realizable. The relatively recent advent of efficient polarization gratings (PGs) has changed this. These PGs enable the highly efficient diffraction of light into orthogonally polarized beams using periodically patterned liquid crystals, thereby allowing the same spatial heterodyning that has been enjoyed by the Michelson- and Sagnac-based reflective designs. 6
We used a PG that was created using polymerized liquid crystal with a retardance (phase difference) of a half wave.7 By periodic alignment of the liquid crystal's fast axis (which determines which polarization state will propagate through the retarder fastest), a PG diffracts right and left circularly polarized light into an upward and downward propagating beam, respectively. This occurs with little light leakage (<1%) into components propagating at other angles. The basic optical layout and concept behind our polarization spatial heterodyne interferometer (PSHI) consists of two Nomarski prisms, separated by a half-wave plate8 which refracts horizontal and vertical linearly polarized light into an upward and downward propagating beam, respectively: see Figure 1(a). This configuration enabled the interference that occurs inside the prisms to be localized on a plane outside of them: see Figure 1(b). We inserted a quarter wave plate to convert the linear polarization eigenstates of the Nomarski prisms to circular eigenstates, after which the light was transmitted through a PG. Proper orientation of the PG enabled the light from the prisms to be efficiently diffracted toward the optical axis. This had the effect of decreasing (or heterodyning) the spatial frequency of the Nomarski prisms to lower values—see Figure 1 (c)—such that they can be observed more easily by a detector array or FPA. This ultimately maximized the detected signal-to-noise ratio.
Figure 1. (a) Schematic of a compact polarization-based spatial heterodyne interferometer and interference fringes. Results calculated (b) without and (c) with a polarization grating. NP1 and NP2: Nomarski prisms. HWP: Half wave plate. QWP: Quarter wave plate. PG: Polarization grating.
In summary, we theoretically and experimentally demonstrated the successful calibration of a PSHI for non-imaging spectral measurements.9 Work is currently underway to demonstrate calibrated results10 using PGs to heterodyne a snapshot hyperspectral imaging FTS11 and generally expand the spectral resolution that can be realized in monolithic transmissive birefringent interferometers. This new technique could be useful in a variety of applications, including machine vision, quality control, unmanned air vehicle deployment, and Fraunhofer line discrimination.
Michael Kudenov, Michael Escuti
Department of Electrical and Computer Engineering
North Carolina State University
Michael Kudenov, an assistant professor, is the principal investigator of the optical sensing lab, which focuses on spectral, polarimetric, and interferometric optical sensing systems design, assembly, calibration, and validation.
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