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Review and Comparison of the Main Interferometric Systems |
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1 | (62) |
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Two-Wave Interferometers and Configurations Used in Optical Testing |
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1 | (4) |
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Twyman--Green Interferometer |
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5 | (3) |
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8 | (3) |
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Typical Interferograms in Twyman--Green and Fizeau Interferometers |
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11 | (3) |
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Lateral Shear Interferometers |
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14 | (12) |
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16 | (1) |
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17 | (1) |
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17 | (1) |
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17 | (1) |
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17 | (1) |
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Rimmer--Wyant Method To Evaluate Wavefronts |
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18 | (2) |
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Saunders Method To Evaluate Interferograms |
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20 | (1) |
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Spatial Frequency Response of Lateral Shear Interferometers |
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21 | (2) |
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Regularization Method To Obtain Wavefronts |
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23 | (3) |
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26 | (4) |
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30 | (4) |
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34 | (3) |
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Talbot Interferometry and Moire Deflectometry |
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37 | (2) |
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Common Light Sources Used in Interferometry |
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39 | (2) |
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Aspherical Compensators and Aspheric Wavefronts |
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41 | (1) |
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Imaging of the Pupil on the Observation Plane |
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41 | (10) |
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Imaging the Pupil Back on Itself |
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42 | (1) |
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Imaging the Pupil on the Observing Screen |
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43 | (3) |
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Requirements on the Imaging Lens |
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46 | (5) |
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Multiple-Wavelength Interferometry |
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51 | (12) |
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54 | (9) |
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63 | (32) |
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63 | (3) |
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63 | (3) |
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66 | (2) |
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68 | (7) |
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71 | (1) |
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71 | (1) |
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72 | (1) |
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72 | (1) |
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Symmetry Properties of Fourier Transforms |
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73 | (2) |
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The Convolution of Two Functions |
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75 | (4) |
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78 | (1) |
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The Cross-Correlation of Two Functions |
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79 | (1) |
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80 | (3) |
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Sampling of a Periodical Function |
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83 | (6) |
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Sampling of a Periodical Function with Interval Averaging |
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85 | (4) |
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89 | (6) |
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94 | (1) |
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95 | (32) |
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95 | (1) |
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Histogram and Gray-Scale Transformations |
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96 | (2) |
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Space and Frequency Domain of Interferograms |
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98 | (2) |
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Digital Processing of Images |
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100 | (12) |
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102 | (1) |
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Derivative and Laplacian Operators |
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102 | (1) |
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Spatial Filtering by Convolution Masks |
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103 | (6) |
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109 | (1) |
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Smoothing by Regularizing Filters |
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110 | (2) |
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Some Useful Spatial Filters |
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112 | (4) |
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112 | (2) |
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Hamming and Hanning Window Filters |
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114 | (1) |
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Cosinusoidal and Sinusoidal Window Filters |
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115 | (1) |
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Extrapolation of Fringes Outside of the Pupil |
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116 | (2) |
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Light Detectors Used To Digitize Images |
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118 | (9) |
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Image Detectors and Television Cameras |
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119 | (4) |
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123 | (2) |
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125 | (2) |
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Fringe Contouring and Polynomial Fitting |
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127 | (32) |
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Fringe Detection Using Manual Digitizers |
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127 | (2) |
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Fringe Tracking and Fringe Skeletonizing |
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129 | (6) |
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Spatial Filtering of the Image |
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131 | (1) |
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Identification of Fringe Maxima |
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131 | (2) |
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Assignment of Order Number to Fringes |
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133 | (2) |
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Global Polynomial Interpolation |
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135 | (9) |
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137 | (3) |
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Properties of Zernike Polynomials |
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140 | (1) |
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Least-Squares Fit to Zernike Polynomials |
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141 | (2) |
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Gram-Schmidt Orthogonalization |
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143 | (1) |
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Local Interpolation by Segments |
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144 | (4) |
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Wavefront Representation by an Array of Gaussians |
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148 | (11) |
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150 | (9) |
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Periodic Signal Phase Detection and Algorithm Analysis |
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159 | (100) |
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Least-Squares Phase Detection of a Sinusoidal Signal |
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159 | (6) |
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Quadrature Phase Detection of a Sinusoidal Signal |
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165 | (8) |
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Low-Pass Filtering in Phase Detection |
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168 | (5) |
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Discrete Low-Pass Filtering Functions |
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173 | (6) |
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Examples of Discrete Filtering Functions |
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176 | (1) |
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Wyant's Three-Step Algorithm |
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176 | (1) |
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Four-Steps-in-Cross Algorithm |
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177 | (1) |
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Schwider-Hariharan Five-Step (4 + 1) Algorithm |
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178 | (1) |
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Fourier Description of Synchronous Phase Detection |
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179 | (9) |
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Synchronous Detection Using a Few Sampling Points |
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188 | (13) |
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General Discrete Sampling |
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190 | (4) |
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Equally Spaced and Uniform Sampling |
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194 | (2) |
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Applications of Graphical Vector Representation |
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196 | (2) |
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Graphic Method To Design Phase-Shifting Algorithms |
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198 | (3) |
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Signal Amplitude Measurement |
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201 | (2) |
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Characteristic Polynomial of a Sampling Algorithm |
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203 | (3) |
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General Error Analysis of Synchronous Phase-Detection Algorithms |
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206 | (6) |
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Exact Phase-Error Analysis |
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207 | (3) |
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Phase-Error Approximation in Two Particular Cases |
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210 | (2) |
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Some Sources of Phase Error |
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212 | (27) |
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Phase-Shifter Miscalibration and Nonlinearities |
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214 | (1) |
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Error in the Sampling Reference Functions |
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215 | (1) |
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Error in the Measured Signal |
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216 | (1) |
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Measurement and Compensation of Phase-Shift Errors |
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217 | (3) |
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Linear or Detuning Phase-Shift Error |
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220 | (1) |
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Quadratic Phase-Shift Errors |
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221 | (3) |
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High-Order, Nonlinear, Phase-Shift Errors with a Sinusoidal Signal |
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224 | (2) |
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High-Order, Nonlinear, Phase-Shift Errors with a Distorted Signal |
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226 | (3) |
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Nonuniform Phase-Shifting Errors |
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229 | (2) |
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Phase Detection of a Harmonically Distorted Signal |
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231 | (3) |
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Light-Detector Nonlinearities |
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234 | (1) |
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235 | (4) |
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Shifting Algorithms with Respect to the Phase Origin |
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239 | (8) |
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Shifting the Algorithm by ±π/2 |
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242 | (1) |
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Shifting the Algorithm by ±π/4 |
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243 | (4) |
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Optimization of Phase-Detection Algorithms |
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247 | (2) |
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Influence of Window Function of Sampling Algorithms |
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249 | (3) |
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252 | (7) |
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Appendix. Derivative of the Amplitude of the Fourier Transform of the Reference Sampling Functions |
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253 | (1) |
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254 | (5) |
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Phase-Detection Algorithms |
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259 | (100) |
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General Properties of Synchronous Phase-Detection Algorithms |
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259 | (1) |
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Three-Step Algorithms To Measure the Phase |
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260 | (14) |
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120° Three-Step Algorithm |
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261 | (5) |
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Inverted T Three-Step Algorithm |
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266 | (2) |
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Wyant's Tilted T Three-Step Algorithm |
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268 | (2) |
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Two-Steps-Plus-One Algorithm |
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270 | (4) |
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Four-Step Algorithms To Measure the Phase |
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274 | (7) |
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Four Steps in the Cross Algorithm |
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275 | (3) |
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Algorithm for Four Steps in X |
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278 | (3) |
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281 | (3) |
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Algorithms with Symmetrical N + 1 Phase Steps |
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284 | (20) |
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Symmetrical Four-Step (3 + 1) Algorithm |
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290 | (4) |
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Schwider-Hariharan Five-Step (4 + 1) Algorithm |
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294 | (4) |
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Symmetrical Six-Step (5 + 1) Algorithm |
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298 | (3) |
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Symmetrical Seven-Step (6 + 1) Algorithm |
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301 | (3) |
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Combined Algorithms in Quadrature |
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304 | (17) |
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308 | (7) |
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Schmit and Creath Algorithm |
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315 | (4) |
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Other Detuning-Insensitive Algorithms |
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319 | (2) |
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Detuning-Insensitive Algorithms for Distorted Signals |
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321 | (9) |
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Zhao and Surrel Algorithm |
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322 | (4) |
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326 | (2) |
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Six-Sample, Detuning-Insensitive Algorithm |
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328 | (2) |
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Algorithms Corrected for Nonlinear Phase-Shifting Error |
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330 | (4) |
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Continuous Sampling in a Finite Interval |
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334 | (5) |
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Asynchronous Phase-Detection Algorithms |
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339 | (13) |
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340 | (6) |
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Schwider Asynchronous Algorithm |
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346 | (3) |
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Two Algorithms in Quadrature |
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349 | (1) |
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An Algorithm for Zero Bias and Three Sampling Points |
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349 | (2) |
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Correlation with Two Sinusoidal Signals in Quadrature |
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351 | (1) |
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352 | (7) |
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352 | (3) |
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355 | (1) |
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355 | (4) |
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Phase-Shifting Interferometry |
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359 | (40) |
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Phase-Shifting Basic Principles |
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359 | (1) |
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An Introduction to Phase Shifting |
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360 | (6) |
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Moving Mirror with a Linear Transducer |
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360 | (1) |
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361 | (1) |
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Moving Diffraction Grating |
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362 | (1) |
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363 | (2) |
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Moire in an Interferogram with a Linear Carrier |
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365 | (1) |
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Frequency Changes in the Laser Light Source |
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365 | (1) |
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Simultaneous Phase-Shift Interferometry |
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366 | (1) |
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Phase-Shifting Schemes and Phase Measurement |
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366 | (2) |
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Heterodyne Interferometry |
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368 | (2) |
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370 | (3) |
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Sinusoidal Phase Oscillation Detection |
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373 | (3) |
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Practical Sources of Phase Error |
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376 | (7) |
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Vibration and Air Turbulence |
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376 | (2) |
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Multiple-Beam Interference and Frequency Mixing |
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378 | (3) |
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Spherical Reference Wavefronts |
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381 | (1) |
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382 | (1) |
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Photon Noise Phase Errors |
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382 | (1) |
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Laser Diode Intensity Modulation |
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382 | (1) |
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Selection of the Reference Sphere in Phase-Shifting Interferometry |
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383 | (16) |
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385 | (1) |
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385 | (1) |
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386 | (1) |
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Optimum Tilt and Defocusing in Phase-Shifting Interferometry |
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387 | (2) |
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Temporal Phase-Shifting Techniques |
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389 | (1) |
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Spatial Linear Carrier Demodulation |
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390 | (1) |
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Spatial Circular Carrier Demodulation |
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391 | (1) |
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392 | (7) |
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Spatial Linear and Circular Carrier Analysis |
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399 | (56) |
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Spatial Linear Carrier Analysis |
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399 | (15) |
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Introduction of a Linear Carrier |
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400 | (3) |
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Holographic Interpretation of the Interferogram |
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403 | (4) |
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Fourier Spectrum of the Interferogram and Filtering |
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407 | (4) |
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Pupil Diffraction Effects |
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411 | (3) |
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Space-Domain Phase Demodulation with a Linear Carrier |
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414 | (18) |
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Basic Space-Domain Phase Demodulation Theory |
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414 | (2) |
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Phase Demodulation with an Aspherical Reference |
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416 | (2) |
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Analog and Digital Implementations of Phase Demodulation |
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418 | (1) |
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Spatial Low-Pass Filtering |
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419 | (3) |
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Sinusoidal Window Filter Demodulation |
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422 | (2) |
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Spatial Carrier Phase-Shifting Method |
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424 | (4) |
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Phase-Locked Loop Demodulation |
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428 | (4) |
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Circular Spatial Carrier Analysis |
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432 | (1) |
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Phase Demodulation with a Circular Carrier |
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433 | (7) |
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Phase Demodulation with a Spherical Reference Wavefront |
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433 | (3) |
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Phase Demodulation with a Tilted-Plane Reference Wavefront |
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436 | (4) |
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Fourier Transform Phase Demodulation with a Linear Carrier |
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440 | (7) |
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Sources of Error in the Fourier Transform Method |
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444 | (2) |
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Spatial Carrier Frequency, Spectrum Width, and Interferogram Domain Determination |
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446 | (1) |
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Fourier Transform Phase Demodulation with a Circular Carrier |
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447 | (8) |
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449 | (6) |
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Interferogram Analysis with Moire Methods |
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455 | (20) |
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455 | (1) |
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Moire Formed by Two Interferograms with a Linear Carrier |
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456 | (9) |
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Moire with Interferograms of Spherical Wavefronts |
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458 | (4) |
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Moire with Interferograms of Aspherical Wavefronts |
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462 | (3) |
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Moire Formed by Two Interferograms with a Circular Carrier |
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465 | (5) |
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Moire with Interferograms of Spherical Wavefronts |
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467 | (1) |
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Moire with Interferograms of Aspherical Wavefronts |
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468 | (2) |
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470 | (1) |
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Holographic Interpretation of Moire Patterns |
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470 | (2) |
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472 | (3) |
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473 | (2) |
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Interferogram Analysis without a Carrier |
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475 | (18) |
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475 | (1) |
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Mathematical Model of the Fringes |
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476 | (5) |
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481 | (4) |
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The N-Dimensional Quadrature Transform |
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485 | (5) |
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Using the Fourier Transform To Calculate the Isotropic Hilbert Transform |
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487 | (1) |
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The Fringe Orientation Term |
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488 | (2) |
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490 | (3) |
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491 | (2) |
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493 | (32) |
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The Phase Unwrapping Problem |
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493 | (7) |
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Unwrapping Consistent Phase Maps |
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500 | (4) |
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Unwrapping Full-Field Consistent Phase Maps |
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500 | (2) |
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Unwrapping Consistent Phase Maps within a Simple Connected Region |
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502 | (2) |
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Unwrapping Noisy Phase Maps |
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504 | (7) |
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Unwrapping Using Least-Squares Integration |
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504 | (3) |
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The Regularized Phase Tracking Unwrapper |
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507 | (4) |
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Unwrapping Subsampled Phase Maps |
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511 | (10) |
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513 | (3) |
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Null Fringe Analysis of Subsampled Phase Maps Using a Computer-Stored Compensator |
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516 | (2) |
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Unwrapping of Smooth Continuous Subsampled Phase Maps |
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518 | (2) |
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Unwrapping the Partial Derivative of the Wavefront |
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520 | (1) |
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521 | (4) |
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522 | (3) |
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Wavefront Curvature Sensing |
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525 | (16) |
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Wavefront Determination by Slope Sensing |
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525 | (1) |
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Wavefront Curvature Sensing |
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525 | (12) |
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The Laplacian and Local Average Curvatures |
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526 | (1) |
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Irradiance Transport Equation |
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527 | (2) |
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Laplacian Determination with Irradiance Transport Equation |
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529 | (4) |
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Wavefront Determination with Iterative Fourier Transforms |
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533 | (4) |
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Wavefront Determination with Defocused Images |
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537 | (1) |
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538 | (3) |
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538 | (3) |
| Index |
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541 | |
