Techniques that involve the analysis of polarized light (polarimetry) have been used in target detection, remote sensing, astronomy, microscopy, and biomedical diagnostics.1 Biomedical applications of polarimetry include the study of optical properties of tissues, turbid suspensions, ophthalmology, and imaging of skin abnormalities, including melanoma.2–4 The combination of polarimetry and imaging enhances contrast and reveals information about the structure and orientation of the sample.
A Mueller matrix polarimeter (MMP) measures the optical properties of a sample by analyzing the polarization of light that is transmitted through or reflected/scattered from the sample. The measured properties are represented by a 16-element real matrix. A typical MMP, shown in Figure 1, incorporates a polarization state generator (PSG) that generates the incident polarization states and a polarization state analyzer (PSA) that analyzes the polarization of the light departing from the sample. In contrast, a Stokes polarimeter (SP) measures only the polarization state of light, which is represented by a four-component Stokes vector.
Figure 1. This schematic diagram shows a transmission-mode MMP with PSG and PSA.
A special class of polarimeters that use nematic liquid crystal (LC) technology, offer good pointing stability, a large clear aperture, and low power consumption.3 Although basic LC optical devices are available from several vendors in the US, there are no commercially available, ready-to-use PSG or PSA modules. To fill this gap in the market, we have developed a universal polarization generator/analyzer (PGA) module (Figure 2A) that can function as either a PSG or a PSA in a MMP. A single PGA can also be used as a Stokes polarimeter (SP) for remote sensing or light source/component testing. The PGA consists of two large-aperture (>3cm) optically contacted LC variable retarders in a temperature-controlled housing, and is driven by our μLC422 USB controller (Figure 2B).
Figure 2. Pictured are the liquid crystal PGA (A) and the μLC422 controller (B).
To test the PGA performance in a SP configuration, we analyzed two series of polarized input states, represented on a Poincaré sphere in Figure 3. The linear states (A) were generated by a polarizer rotated from -90° to 90° in 10° intervals. In case (B), an additional wave plate oriented at 45° was placed after the polarizer. The SP was calibrated at 633nm using the procedure developed by Azzam et al.5 The Stokes vector was calculated from N intensity measurements (for N = 100 and N = 4), corresponding to different voltages applied the LC elements. Due to massive data processing and storage associated with pixel-to-pixel operation, imaging applications require as few measurements as possible. In response to this requirement, we designed a new 4-point (N = 4) algorithm, based on numerical optimization of the LC voltage settings.6
Figure 3. The trajectories on the Poincar sphere representing the measured polarization states generated by a rotated polarizer (A) and a rotated polarizer, followed by a waveplate at 45°(B).
An example data set, obtained with the 4-point data reduction algorithm for 19 elliptically polarized states is shown in Figure 4 The measured quantities were normalized Stokes parameters (S1/S0, S2/S0 and S3/S0), degree of polarization (DOP), and ellipticity of the polarization ellipse. The experimental values deviated from the theoretical ones by less than ≤ 1% for most of the data points. We learned that the 4-point algorithm did not produce more deviation than the 100-point algorithm. Also, there were no noticeable differences between the error magnitudes for the data obtained for the linear versus non-linear states. The main sources of error were noise caused by the electronics and systematic errors caused by imperfect calibration and alignment of the optical components.
Figure 4. This polarization data (elliptical states) was obtained with a 4-point data-reduction algorithm.
Figure 5 shows the histograms of the measured parameters for an arbitrarily chosen polarization state generated with a polarizer set at 47.8° and followed by a retarder (R = 0.2471 wave) at 45°. The distribution widths (approximated as full width/half maximum) of S1/S0 and S2/S0 are less than 0.01. For S3/S0 and the DOP this number is less than 0.005. The measured average DOP is 0.9990.
Figure 5. Shown is the distribution (100 measurements, bin size 0.001) of the normalized Stokes parameters and degree of polarization for [1,-0.0188,0.189,-0.981]T state.
We demonstrated that our new integrated PGA module could be used in imaging polarimetry. Using the 4-point data reduction algorithm, the PGA measured the Stokes parameters with an accuracy better than 1%. The significance of this result is that the optimized 4-point data reduction can be used with low-light-level imaging applications that require long integration times. Currently, we are developing a new imaging MMP that incorporates two PGA modules.