Matthieu Dubreuil, Sylvain Rivet, Bernard Le Jeune, and Jack Cariou, "Systematic errors specific to a snapshot Mueller matrix polarimeter," Appl. Opt. 48, 1135-1142 (2009)
Systematic errors specific to a snapshot Mueller matrix polarimeter are studied. Their origins and effects are highlighted, and solutions for correction and stabilization are proposed. The different effects induced by them are evidenced by experimental results acquired with a given setup and theoretical simulations carried out for more general cases. We distinguish the errors linked to some imperfection of elements in the experimental setup from those linked to the sample under study.
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Relationships between Magnitudes of the Peaks—Real Part () and Imaginary Part ()—and Mueller Coefficients () in the Fourier Domain for the Ideal Configuration
Frequency
0
0
0
0
0
0
Table 2
Relationships between Magnitudes of Peaks—Real Part () and Imaginary Part ()—and the Mueller Coefficients () in the Fourier Domain for the True Configuration ()
Frequency
0
0
0
0
0
0
0
0
Table 3
Influence of Phases , , , and on the Mueller Matrix for Vacuum and a Linear Polarizer at a
Mueller Matrix for Vacuum
Mueller Matrix for a Linear Polarizer ()
0
0
0
0
0.01
0
0
0
0
0.01
0
0
0
0
0.01
0
0
0
0
0.01
Phases are expressed in radians. In the ideal case (no phase errors) and for the linear polarizer at , the value of the polarization parameters depolarization index (), diattenuation (D) and retardance (R) are (, , ). When and , these values become , , and .
Table 4
Experimental Mueller Matrix Given by the SMMP for Vacuum and a Linear Partial Polarizer at : Theoretical, without Corrections by , , , and and with Corrections by , , and a
Vacuum
Linear Partial Polarizer at
Theoretical
Without corrections
With corrections
All matrices are normalized by . The experimental setup is composed of two calcite plates () for the coding system () and two calcite plates for the decoding system (). The source is a broadband spectrum source with , and the analysis window of the detection system is sampled with 512 pixels.
Table 5
Simulation of the Influence of the Misalignment Errors , , , and on the Mueller Matrix for Vacuum
Mueller Matrix for Vacuum
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.1
0.1
0.1
0.1
Table 6
Simulation of a Quarter-Wave Plate (, ) at Different Ordersa
(%)
0.055
0.999
89.99
19.99
0.275
0.999
89.94
19.99
0.55
0.998
89.84
19.97
1.1
0.995
89.66
19.93
2.75
0.975
89.55
19.58
5.5
0.917
82.88
18.64
Depolarization index , retardance R, and azimuthal angle α are calculated. The ratio between the evolution with the wavelength of the quarter-wave plate retardance and the evolution with the wavelength of the reference coding plate retardance is given.
Table 7
Experimental Mueller Matrix for the Quartz Wave Plate
Theoretical
Without Correction
With Correction
Tables (7)
Table 1
Relationships between Magnitudes of the Peaks—Real Part () and Imaginary Part ()—and Mueller Coefficients () in the Fourier Domain for the Ideal Configuration
Frequency
0
0
0
0
0
0
Table 2
Relationships between Magnitudes of Peaks—Real Part () and Imaginary Part ()—and the Mueller Coefficients () in the Fourier Domain for the True Configuration ()
Frequency
0
0
0
0
0
0
0
0
Table 3
Influence of Phases , , , and on the Mueller Matrix for Vacuum and a Linear Polarizer at a
Mueller Matrix for Vacuum
Mueller Matrix for a Linear Polarizer ()
0
0
0
0
0.01
0
0
0
0
0.01
0
0
0
0
0.01
0
0
0
0
0.01
Phases are expressed in radians. In the ideal case (no phase errors) and for the linear polarizer at , the value of the polarization parameters depolarization index (), diattenuation (D) and retardance (R) are (, , ). When and , these values become , , and .
Table 4
Experimental Mueller Matrix Given by the SMMP for Vacuum and a Linear Partial Polarizer at : Theoretical, without Corrections by , , , and and with Corrections by , , and a
Vacuum
Linear Partial Polarizer at
Theoretical
Without corrections
With corrections
All matrices are normalized by . The experimental setup is composed of two calcite plates () for the coding system () and two calcite plates for the decoding system (). The source is a broadband spectrum source with , and the analysis window of the detection system is sampled with 512 pixels.
Table 5
Simulation of the Influence of the Misalignment Errors , , , and on the Mueller Matrix for Vacuum
Mueller Matrix for Vacuum
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0
0
0
0
0
0.5
0.5
0.5
0.5
0.5
0.1
0.1
0.1
0.1
Table 6
Simulation of a Quarter-Wave Plate (, ) at Different Ordersa
(%)
0.055
0.999
89.99
19.99
0.275
0.999
89.94
19.99
0.55
0.998
89.84
19.97
1.1
0.995
89.66
19.93
2.75
0.975
89.55
19.58
5.5
0.917
82.88
18.64
Depolarization index , retardance R, and azimuthal angle α are calculated. The ratio between the evolution with the wavelength of the quarter-wave plate retardance and the evolution with the wavelength of the reference coding plate retardance is given.
Table 7
Experimental Mueller Matrix for the Quartz Wave Plate