Construction, calibration, and testing of a four-detector photopolarimeter

Abstract

A computer-controlled four-detector photopolarimeter (FDP) has been constructed using four windowless planar-diffused Si photodiodes, operational amplifiers, an analog-to-digital (A/D) converter, and a personal computer with peripherals. A nonplanar light path is selected with incidence angles at the first three detectors of ∼65° and with rotations of ∼45° between the successive planes of incidence. The last detector, which is coated for minimum reflectance, intercepts the beam at a small angle and the residual light it reflects is dumped. A 1-mW He–Ne laser beam (λ=632.8 nm) passes through the polarizing optics of an ellipsometer to provide the polarization states needed for calibration and testing. With an optimum set of calibration states, the instrument matrix A is determined. The FDP is subsequently tested and found to correctly measure the normalized Stokes parameters of a large number of states with an average absolute error of ∼0.01, which is attributed to imperfections in the calibration optics. This first prototype instrument has a precision of ∼0.2%.

Mueller polarimetric imaging for surgical and diagnostic applications: a review

“…There have been several calibration methods developed with various drawbacks such as assumptions or requirement for prior knowledge. For example, Fourier modulation based methods assume that the angular increment of rotating elements is perfect, or that the linear retarders used in the PSG and PSA do not have any diattenuation, or that linear polarizers show no retardance [186,187]. These assumptions can simplify the calibration procedurese.…”

“…It is noted that the matrix norm employed to characterize the backward stability and serve as the Figure of merit to optimise the M PSG and M PSA in Eq. (10) could be the 1-norm, the 2-norm (Euclidean norm) or the 1-norm (sup-norm) [170,183]. Nevertheless, the 2-norm is more frequently used since it is simply the square root of the largest eigenvalue of MM*, where * stands for the conjugate matrix.…”

“…Fourier analysis here serves as an alternative method to the general method based on matrix inverse or pseudoinverse in Equation (36) and (37) to solve Equation (35). The primary advantages of this dual-rotated-retarder configuration are fewer moving parts, reduced instrumentation cost, and that the calibration can be done without the need for reference samples the following assumptions: 1) both the linear retarders used in the PSG and PSA exhibit no diattenuation and depolarization; 2) the increment of rotation of both the linear retarders is highly reproducible [169,170]. The disadvantages are the long image acquisition time resulting from the mechanical components and that the signal is usually oversampled.…”

“…In polarimetry, the matrix A can be replaced by the PSA and PSG instrumental matrices M PSA and M PSG determined by the state vectors selected. The determinant was first introduced as the parameter to assess the backward stability for polarimetry in [170]. The absolute value of the determinant corresponds to the volume enclosed by the end points of the PSA or PSG state vectors in the Poincare sphere.…”

General analysis and optimization of the four-detector photopolarimeter

“…3 If the surface of D 3 is optically isotropic and planar (coated or uncoated) and is tilted by a small angle (<100), the reflectance of that surface, r 3 , stays independent of the polarization of incident light. This follows from the stationary property of reflection near normal incidence, which is discussed elsewhere.…”