Experimental comparison of a liquid-crystal point-diffraction interferometer (LCPDI) and a commercial phase-shifting interferometer and methods to improve LCPDI accuracy
Mark J. Guardalben, Lutao Ning, Nieraj Jain, Devon J. Battaglia, and Kenneth L. Marshall
Mark J. Guardalben, Lutao Ning, Nieraj Jain, Devon J. Battaglia, and Kenneth L. Marshall, "Experimental comparison of a liquid-crystal point-diffraction interferometer (LCPDI) and a commercial phase-shifting interferometer and methods to improve LCPDI accuracy," Appl. Opt. 41, 1353-1365 (2002)
We compare the phase measurements of a fused-silica witness sample made with a liquid-crystal point-diffraction interferometer (LCPDI) with measurements made with a Zygo Mark IV xp phase-shifting interferometer and find close agreement. Two phase-shift-error sources in the LCPDI that contribute to measurement discrepancies are frame-to-frame intensity changes caused by the dichroism of the dye and alignment distortions of the host liquid crystal. An empirical model of the phase-shift error caused by the host alignment distortions is presented and used to investigate the performance of two different phase-detection algorithms. It is suggested that by proper choice of LCPDI fabrication parameters and phase-acquisition methods, the device’s accuracy can be significantly improved.
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Relative Comparison of Different Unwrapping Algorithms with Intentionally Noisy Data (Low-Contrast Fringes)
Comparison Parameter
Centered Linear, Path Dependent
Box Mask and Linear, Path Dependent
Tile Unwrap
Tile Unwrap and Box Mask
p–v (2π rad)
9.07
3.23
2.77
2.670
rms (2π rad)
0.45
0.13
0.10
0.094
Computation time relative to linear unwrap starting at edge of array
1:1
3:1
5:2
4:1
Note: Among the algorithms tested the tile unwrapping algorithms showed the least number of unwrapping errors. The tile unwrapping algorithm with a tile size of 10 × 10 pixels was used for the experimental results reported. p–v, peak to valley.
Table 2
Several Focus and Voltage Conditions Investigated for the LCPDI in Empty-Cavity Measurements
Focus
Voltage (rms at 2 kHz)
Close to best focus (1 to 2 fringes)
Low-voltage regime (0–1.21 V)
Intermediate focus position (3 to 4 fringes)
High-voltage regime (3.8–7 V)
Far from best focus (8 to 9 fringes)
Off center (lateral movement of the LCPDI)
On center (no lateral movement)
Note: Conditions giving least residual phase error: intermediate focus with low-voltage regime.
Comparison of Residual Errors (2π rad) Obtained with Five-and Six-Frame Algorithms with both Experimental and Simulated Interference Images
Errors
Experiment
Simulation
Five Frames
Six Frames
Five Frames
Six Frames
p–v
0.1450
0.2780
0.1000
0.1330
rms
0.0167
0.0220
0.0164
0.0220
H = 0.84; A = 0.37; B = 0.06; C = 0.016; D = E = 0.002; F = G = 1; M = 0.
Note: Simulated images were obtained with the indicated values of constants A–
M corresponding to the phase perturbation shown in Fig.
8.
Table 6
Comparison of Residual Errors (2π rad) Obtained with Five-and Six-Frame Algorithms and only Linear and Quadratic Phase-Shift-Error Termsa
Errors
Spatially Nonuniform
Spatially Uniform
Five Frames
Six Frames
Five Frames
Six Frames
p–v
0.0944
0.1053
0.0176
0.0022
rms
0.0154
0.0178
0.0061
0.0008
ε1 = 0.38, ε2 = -0.14
Phase-shift-error coefficients are given in the table.
Tables (6)
Table 1
Relative Comparison of Different Unwrapping Algorithms with Intentionally Noisy Data (Low-Contrast Fringes)
Comparison Parameter
Centered Linear, Path Dependent
Box Mask and Linear, Path Dependent
Tile Unwrap
Tile Unwrap and Box Mask
p–v (2π rad)
9.07
3.23
2.77
2.670
rms (2π rad)
0.45
0.13
0.10
0.094
Computation time relative to linear unwrap starting at edge of array
1:1
3:1
5:2
4:1
Note: Among the algorithms tested the tile unwrapping algorithms showed the least number of unwrapping errors. The tile unwrapping algorithm with a tile size of 10 × 10 pixels was used for the experimental results reported. p–v, peak to valley.
Table 2
Several Focus and Voltage Conditions Investigated for the LCPDI in Empty-Cavity Measurements
Focus
Voltage (rms at 2 kHz)
Close to best focus (1 to 2 fringes)
Low-voltage regime (0–1.21 V)
Intermediate focus position (3 to 4 fringes)
High-voltage regime (3.8–7 V)
Far from best focus (8 to 9 fringes)
Off center (lateral movement of the LCPDI)
On center (no lateral movement)
Note: Conditions giving least residual phase error: intermediate focus with low-voltage regime.