Phase-evaluation methods in whole-field optical measurement techniques

Measurement Science and Technology

Volumn 10, Issue 3, 1999, Pages

  Dorrio B V ^a   Fernandez J L ^a  

^a UNIVERSITY OF VIGO   (Spain)

Author keywords

Fringe patterns; Optical measurements; Phase evaluation; Phase shifting

Indexed keywords

ALGORITHMS; FUNCTIONS; LIGHT INTERFERENCE; LIGHT MODULATION; PHASE SHIFT;

FRINGE PATTERNS;

OPTICAL VARIABLES MEASUREMENT;

EID: 0033097246     PISSN: 09570233     EISSN: None     Source Type: Journal    
DOI: 10.1088/0957-0233/10/3/005     Document Type: Review

References (184)

1. Ai Ch and Wyant J C 1987 Effect of piezoelectric transducer non-linearity on phase shift interferometry Appl. Opt. 26 1112-16
2. _1988 Effect of spurious reflection on phase shift interferometry Appl. Opt. 27 3039-45
3. Asundi A 1993 Moire methods using computer-generated gratings Opt. Engng. 31 107-16
4. Asundi A and Chan C S 1994 Phase shifting applied to non-sinusoidal intensity - an error simulation Opt. Lasers Engng. 21 3-30
5. Asundi A and Yung K H 1991a Logical moiré and its applications Exp. Mech. 1 236-42
6. _1991b Phase-shifting and logical moire J. Opt. Soc. Am. A 8 1591-600
7. Barnes T H 1987 Heterodyne Fizeau interferometer for testing flat surfaces Appl. Opt. 26 2804-9
8. Barrientos B, Moore A J, Pérez-López C, Wang L L and Tschudi T 1997 Transient deformation measurement with ESPI using a diffractive optical element for spatial phase-stepping Automatic Processing of Fringe Patterns ed W Jüptner and W Osten (Berlin: Akademie) pp 371-5
9. Boebel D, Packross B and Tiziani H J 1991 Phase shifting in an oblique incidence interferometer Opt. Engng. 30 1910-14
10. Bone D J, Bachor H A and Sandeman J 1986 Fringe-pattern analysis using a 2-D Fourier transform Appl. Opt. 25 1653-60
11. Bönsch G and Böhme H 1989 Phase-determination of Fizeau interferences by phase-shifting interferometry Optik 82 161-4
12. Brophy C P 1990 Effect of intensity error correlation on the computed phase of phase-shifting interferometry J. Opt. Soc. Am. A 7 537-41
13. Brown G M 1993 Fringe analysis for automotive applications Opt. Lasers Engng. 19 203-20
14. Bruning J H, Herriot D R, Gallager J E, Rosenfeld D P, White A D and Brangaccio D J 1974 Digital wavefront measuring interferometer for testing optical surfaces and lenses Appl. Opt. 13 2693-703
15. Carré P 1966 Installation et utilisation du comparateur photoelectrique et interferentiel du Bureau International des Poids et Mesures Metrologia 2 13-23
16. Chang M, Hu Ch-P, Lam P and Wyant J C 1985 High precision deformation measurement by digital phase shifting holographic interferometry Appl. Opt. 24 3780-3
17. Charette P G and Hunter IW 1996 Robust phase-unwrapping method for phase images with high noise Appl. Opt. 35 3506-13
18. Cheng Y Y and Wyant J C 1985 Phase shifter calibration in phase-shifting interferometry Appl. Opt. 24 3049-52
19. Chen J, Ishii Y and Murata K 1988 Heterodyne interferometry with a frequency-modulated laser diode Appl. Opt. 27 124-8
20. Colonna de Lega X and Jacquot P 1996 Deformation measurement with object-induced dynamic phase-shifting Appl. Opt. 35 5115-21
21. Colucci D and Wizinowich P L 1992 Millisecond phase acquisition at video rates Appl Opt. 31 5919-25
22. Creath K 1988 Phase-measurement interferometry techniques Progress in Optics vol 26, ed E Wolf (Amsterdam: Elsevier) pp 349-93
23. _1986 Comparison of phase-measurement algorithms Proc. SPIE 680 19-28
24. _1992 Error sources in phase-measuring interferometry Proc. SPIE 1720 428-35
25. _1993 Temporal phase measurement methods Interferogram Analysis ed D W Robinson and G T Reid (Bristol: Institute of Physics) pp 94-140
26. Creath K, Cheng Y-Y and Wyant J C 1985 Contouring aspheric surfaces using two-wavelength phase-shifting interferometry Opt. Acta 32 1455-64
27. Creath K and Hariharan P 1994 Phase-shifting error in interferometric tests with high-numerical-aperture reference surfaces Appl. Opt. 33 24-5
28. Creath K and Schmit J 1996 N-point spatial phase-measurement techniques for non-destructive testing Opt. Lasers Engng. 24 365-79
29. Dandliker R and Thalmann R 1985 Heterodyne and quasi-heterodyne holographic interferometry Opt. Engng. 24 824-31
30. Davies R N and Bryanston-Cross P J 1996 Application of automatic phase stepping to the measurement of heat transfer Simulation and Experiment in Laser Metrology ed Z Füzessy et al (Berlin: Akademic) pp 295-9
31. Davies DEN and Kingsley S 1974 Method of phase modulating in optical fibers: application to optical-telemetry systems Electron. Lett. 1021-2
32. Deck L L and Groot P J 1998 Punctuated quadrature phase-shifting interferometry Opt. Lett. 23 19-21
33. Dorrío B V, Blanco-García J, Lopez C, Doval A F, Soto R, Fernández J L, Pérez-Amor M 1996 Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile Appl. Opt. 35 61-4
34. Dorrío B V, Doval A F, López C, Soto R, Blanco-García J, Fernandez J L and Perez-Amor M 1995 Fizeau phase-measuring interferometry using the moire effect Appl. Opt. 34 3639-43
35. Dorrío B V, López C, Alén J M, Bugarín J, Fernández J L, Doval A F, Blanco-García J, Pérez-Amor M and Fernandez J L 1998 Multiplicative moire two-beam phase-stepping and Fourier transform methods for the evaluation of multiple-beam Fizeau patterns: a comparison Appl. Opt. 37 1945-52
36. Dorrío B V, López C, Doval A F, Alén J M, Bugarín J, Fernández A, Blanco-García J, Fernández J L and Pérez-Amor M 1997 Measurement range analysis in moire evaluation Fizeau interferometry Appl. Opt. 36 3635-44
37. Ellingsrud S and Rosvold G O 1992 Analysis of data-based TV-holography system used to measure small vibration amplitudes J. Opt. Soc. Am. A 9 237-51
38. Ettl P and Creath K 1996 Comparison of phase-unwrapping algorithms using gradient first failure Appl. Opt. 35 5108-14
39. Facchini M, Alberecht D and Zanetta P 1993 Phase detection algorithm in ESPI fringes with speckle noise reduction by using preliminary time averaging Proc. FASIC Fringe '93 ed W Jüptner and W Osten (Bermen: Akademie) pp 45-50
40. Facchini M and Zanetta P 1995 Derivatives of displacement obtained by direct manipulation of phase-shifted interferograms Appl. Opt. 34 7202-6
41. Farrell C T and Player M A 1992 Phase step measurement and variable step algorithms in phase-shifting interferometry Meas. Sci. Technol. 3 953-8
42. Frantz L M, Sawchuk A A and Ohe W 1979 Optical phase measurement in real time Appl. Opt. 18 3301-6
43. Freischlad K and Koliopoulos Ch L 1990 Fourier description of digital phase-measuring interferometry J. Opt. Soc. Am. A 7 542-51
44. Gao Z, Zhou S and Hu Y 1997 High-speed fringe analysis by using stair-shaped virtual grating demodulation Opt. Lasers Engng. 28411-22
45. Georges M P and Lemaire Ph C 1995 Phase-shifting holographic interferometry that uses bismuth silicon oxide crystals Appl. Opt. 34 7497-506
46. Greivenkamp J E 1984 Generalized data reduction for heterodyne interferometry Opt. Engng. 23 350-2
47. _1987 Sub-Nyquist interferometry Appl. Opt. 26 5245-58
48. Greivenkamp J E and Bruning J H 1992 Phase shifting interferometry Optical Shop Testing ed D Malacara (New York: Wiley) pp 501-98
49. Groot P 1995a Vibration in phase-shifting interferometry J. Opt. Soc. Am. A 12 354-65
50. _1995b Phase-shift calibration errors in interferometers with spherical Fizeau cavities Appl. Opt. 34 2856-63
51. _1995c Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window Appl. Opt. 34 4723-30
52. Groot P and Deck L 1996 Numerical simulations of vibration in phase-shifting interferometry Appl. Opt. 35 2172-8
53. Hariharan P 1987 Digital phase-stepping interferometry: effects of multiple reflected beams Appl. Opt. 26 2506-7
54. _1989a Phase stepping interferometry with laser diodes: effect of changes in laser power with output wavelength Appl. Opt. 28 27-9
55. _1989b Phase stepping interferometry with laser diodes 2: effects of laser wavelength modulation Appl. Opt. 28 1749-50
56. Hariharan P, Oreb B F and Eiju T 1987 Digital phase-stepping interferometry: a simple error-compensating phase calculation algorithm Appl. Opt. 26 2504-5
57. Hibino J M 1997 Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry Appl. Opt. 36 2084-93
58. Hibino K, Oreb B F, Farrant D I and Larkin K G 1995 Phase shifting for nonsinusoidal waveforms with phase-shift errors J. Opt. Soc. Am. A 12 761-8
59. _1997 Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts J. Opt. Soc. Am. A 14 918-30
60. Ho K-P and Kahn JM 1995 Exact probability-density function for phase-measurement interferometry J. Opt. Soc. Am. 12 1984-9
61. Ichioka Y and Inuiya M 1972 Direct phase detecting system Appl. Opt. 11 1507-14
62. Ishii Y 1991 Recent developments in laser-diode interferometry Opt. Lasers Engng. 14 293-309
63. Ishii Y and Onodera R 1995 Laser-diode phase-shifting interferometer insensitive to changes in laser power Proc. SPIE 2544 173-6
64. Jin G, Bao N and Chung P S 1994 Applications of a novel phase-shift method using a computer-controlled polarization mechanism Opt. Engng. 33 2733-7
65. Joenathan C 1994 Phase-measuring interferometry: new methods and error analysis Appl. Opt. 33 4147-55
66. Joenathan C and Khorana B M 1992 Phase measurement by differentiating interferometric fringes J. Mod. Opt. 39 2075-87
67. Johnson G W, Leiner D C and Moore D T 1979 Phase-locked interferometry Opt. Engng. 18 46-52
68. Jozwicki R, Kujawinska M and Salbut M 1992 New contra old wavefront measurement concepts for interferometric optical testing Opt. Engng. 31 422-33
69. Judge T R and Bryanston-Cross P J 1994 A review of phase unwrapping techniques in fringe analysis Opt. Lasers Engng. 21 199-239
70. Kadono H, Ogusu M and Toyooka S 1994 Phase shifting common path interferometer using a liquid-crystal phase modulator Opt. Commun. 110 391-400
71. Kadono H, Takai N and Asakura T 1987 New common-path phase shifting interferometer using a polarization technique Appl. Opt. 26 898-904
72. Kadono H, Toyooka S and Iwasaki Y 1991 Speckle-shearing interferometry using a liquid-crystal cell as a phase modulator J. Opt. Soc. Am. A 8 2001-8
73. Kato J-I, Yamaguchi I and Ping Q 1993 Automatic deformation analysis by a TV speckle interferometer using a laser diode Appl. Opt. 32 77-88
74. Kaufmann G H and Galizzi G E 1997 Evaluation of a method to determine interferometric phase derivatives Opt. Lasers Engng. 27451-65
75. Kaufmann G H and Jacquot P 1990 Phase shifting of whole field speckle photography fringes Appl. Opt. 29 3570-2
76. Kerr D, Mendoza Santoyo F and Tyrer J R 1990 Extraction of phase data from electronic speckle pattern interferometric fringes using a single-phase-step method: a novel approach J. Opt. Soc. Am. 7 820-6
77. Kinnstaetter K, Lohmann A W, Schwider J and Streibl N 1988 Accuracy of phase shifting interferometry Appl. Opt. 27 5082-9
78. Konforti N, Marom E and Wu S T 1988 Phase-only modulation with twisted pneumatic liquid-crystal spatial light modulators Opt. Lett. 3251-3
79. Kong I B and Kim S W 1995 Portable inspection of precision surfaces by phase-shifting interferometry with automatic suppression of phase-shift errors Opt. Engng. 34 1400-4
80. Kothiyal M P and Delisle C 1985 Shearing interferometer for phase-shifting interferometry with polarization phase shifter Appl. Opt. 24 4439-42
81. Kreis T 1986 Digital holographic interference-phase measurement using Fourier-transform method J. Opt. Soc. Am. A 3 847-55
82. _1987 Quantitative evaluation of interference patterns Proc. SPIE 863 68-77
83. _1993 Computer aided evaluation of fringe patterns Opt. Lasers Engng. 19 221-40
84. _1996 Quantitative evaluation of the interference phase Holographic Interferometry (Berlin: Akademic) pp 55-64
85. Kreis T, Geldmacher J and Jüptner W 1993 A comparison of interference phase determination methods with respect to the achievable accuracy Proc. FASIC Fringe '93 ed W Jüptner and W Osten (Bremen: Akademie) pp 51-9
86. Kujawinska M 1993a Spatial phase measurement methods Interferogram Analysis ed D W Robinson and G T Reid (Bristol: Institute of Physics) pp 141-93
87. _1993b The architecture of a multipurpose fringe pattern analysis system Opt. Lasers Engng. 19 261-3
88. Kujawinska M and Wójciak J 1991a Spatial phase-shifting techniques of fringe pattern analysis in photomechanics Proc. SPIE 1554B 503-13
89. _1991b Spatial-carrier phase shifting technique of fringe pattern analysis Proc. SPIE 1508 61-7
90. _1991c High accuracy Fourier transform fringe pattern analysis Opt. Lasers Engng. 14 325-39
91. Kwon O Y 1984 Multichannel phase-shifted interferometer Opt. Lett. 9 59-61
92. Kwon O Y, Shough D M and William R A 1987 Stroboscopic phase-shifting interferometry Opt. Lett. 12 855-7
93. Lai G and Yatagai T 1991 Generalized phase-shifting interferometry J. Opt. Soc. Am. A 8 822-7
94. Larkin K G 1996 Efficient nonlinear algorithm for envelope detection in white light interferometry J. Opt. Soc. Am. A 13 832-4
95. Larkin K G and Oreb B F 1992 Design and assessment of symmetrical phase-shifting algorithms J. Opt. Soc. Am. A 9 1740-8
96. Lesne J L, Le Brun A, Roger D and Dieulesaint E 1987 High bandwidth laser heterodyne interferometer to measure transient mechanical displacements Proc. SPIE 863 13-22
97. Liu J B and Ronney P D 1997 Modified Fourier transform method for interferogram fringe pattern analysis Appl. Opt. 36 6231-41
98. Lowenthal S and Joyeux D 1971 Speckle removal by a slowly moving diffuser associated with a motionless diffuser J. Opt. Soc. Am. 61 847-51
99. Macy W W 1983 Two-dimensional fringe-pattern analysis Appl. Opt. 22 3898-901
100. Malacara D 1990 Updated optical testing bibliography Appl. Opt. 29 1384-7
101. Malacara D, Servin M and Malacara Z 1998 Interferogram Analysis for Optical Testing (New York: Dekker)
102. Malacara D, Servín M, Morales A and Malacara Z 1995 Aspherical wavefront testing with several defocusing steps Proc. SPIE 2576 190-2
103. Malacara-Doblado D, Servin M, Malacara-Hernandez D 1997 Graphical vector description of sampling weights in phase-detecting algorithms Opt. Engng. 36 2086-91
104. Malacara-Hernández D and Malacara-Doblado D 1997 Error analysis of phase detection algorithms Automatic Processing of Fringe Patterns ed W Jüptner and W Osten (Berlin: Akademie) pp 45-51
105. Mallick S 1992 Common-path interferometers Optical Shop Testing ed D Malacara (New York: Wiley) pp 95-122
106. Martini G 1987 Analysis of a single-mode optical fibre piezoceramic phase modulator Opt. Quant. Electron. 19 179-90
107. Massie N A 1980 Real-time digital heterodyne interferometry: a system Appl. Opt. 19 154-60
108. Massie N A and Nelson R D 1978 Beam quality of acousto-optic phase shifters Opt. Lett. 3 46-7
109. Massie N A, Nelson R D and Holly S 1979 High-performance real-time heterodyne interferometry Appl. Opt. 18 1797-803
110. Matthews H J, Hamilton D K and Sheppard J R 1986 Surface profiling by phase-locked interferometry Appl. Opt. 25 2372-4
111. Mercer C R and Beheim G 1991 Fiber optic phase stepping system for interferometry Appl. Opt. 30 729-34
112. Mertz L 1983 Real-time fringe-pattern analysis Appl. Opt. 22 1535-9
113. Morgan C J 1982 Least-squares estimation in phase-measurement interferometry Opt. Lett. 7 368-70
114. Moore A J, Tyrer J R and Mendoza-Santoyo F 1994 Phase extraction from electronic speckle pattern interferometry addition fringes Appl. Opt. 33 7312-20
115. Ng T G 1996 The one-step phase-shifting technique for wave-front interferometry J. Mod. Opt. 43 2129-38
116. Nicolaus R A 1993 Precise method of determining systematic errors in phase-shifting interferometry on Fizeau interferences Appl. Opt. 32 6380-6
117. Nugent K A 1985 Interferogram analysis using an accurate fully automatic algorithm Appl. Opt. 24 3101-5
118. Ohyama N, Kinoshita S, Cornejo-Rodríguez A, Honda T and Tsujiuchi J 1988 Accuracy of phase determination with unequal reference phase shift J. Opt. Soc. Am. A 5 2019-25
119. Onodera R and Ishii Y 1996 Phase-extraction analysis of laser-diode phase-shifting interferometry that is insensitive to changes in laser power J. Opt. Soc. Am. 13 139-46
120. Ovryn B and Haacke E M 1993 Temporal averaging of phase measurements in the presence of spurious phase drift: application to phase-stepped real-time holographic interferometry Appl. Opt. 32 1087-94
121. Owner-Petersen M 1991 Digital speckle pattern shearing interferometry: limitations and prospects Appl. Opt. 30 2730-8
122. Perry K E and McKelvie J 1993 A comparison of phase shifting and Fourier methods in the analysis of discontinuous fringe patterns Opt. Lasers Engng. 19 269-84
123. Pirga M and Kujawinska M 1995 Errors in two-directional spatial-carrier phase shifting method Proc. SPIE 2544 112-21
124. Pirga M and Kujawinska M 1995 Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns Opt. Engng. 34 2459-66
125. Poon C Y, Kujawinska M and Ruiz C 1993 Automated fringe pattern analysis for moire interferometry Exp. Mech. 33 234-41
126. Pryputniewicz R J 1992 Electro-optic holography Proc. SPIE CR46 148-74
127. Ransom P L and Kokal J V 1986 Interferometric analysis by a modified sinusoid fitting technique Appl. Opt. 25 4199-204
128. Rathjen C 1995 Statistical properties of phase-shift algorithms J. Opt. Soc. Am. A 12 1997-2008
129. Reid G T 1986 Automatic fringe pattern analysis: a review Opt. Lasers Engng. 1 37-68
130. Robinson D W 1993 Phase unwrapping methods Interferogram Analysis ed D W Robinson and G T Reid (Bristol: Institute of Physics) pp 194-229
131. Rogala E W and Barrett H H 1997 Phase-shifting interferometry and maximum-likelihood estimation theory Appl. Opt. 36 8871-6
132. Rosenbluth A E and Bobroff N 1990 Optical sources of non-linearity in heterodyne interferometers Prec. Eng. 12 7-11
133. Salbut L and Patorsky K 1990 Polarization phase shifting method for moire interferometry and flatness testing Appl. Opt. 29 1471-3
134. Sasaki O, Okamura T and Nakamura T 1990b Sinusoidal phase modulating Fizeau interferometry Appl. Opt. 29 512-15
135. Sasaki O and Okazaki H 1986a Sinusoidal phase modulating interferometry for surface profile measurement Appl. Opt. 25 3137-40
136. _1986b Analysis of measurement accuracy in sinusoidal phase modulating interferometry Appl. Opt. 25 3152-8
137. Sasaki O, Okazaki H and Sakai M 1987 Sinusoidal phase modulating interferometer using the integrating-bucket method Appl. Opt. 26 1089-93
138. Sasaki O, Takahashi K and Suzuki T 1990a Sinusoidal phase modulating laser interferometer with a feedback control system to eliminate external disturbance Opt. Engng. 29 1511-15
139. Schmit J and Creath K 1995 Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry Appl. Opt. 34 3610-19
140. _1996 Window function influence on phase error in phase-shifting algorithms Appl. Opt. 35 5642-9
141. Schulz G and Elssner K-E 1991 Errors in phase-measurement interferometry with numerical apertures Appl. Opt. 30 4500-6
142. Schwider J 1989 Phase shifting interferometry: reference phase error reduction Appl. Opt. 28 3889-92
143. _1990 Advanced evaluation techniques in interferometry Progress in Optics vol 28, ed E Wolf (Amsterdam: Elsevier) pp 271-359
144. Schwider J, Burow R, Elssner K-E, Grzanna J and Spolaczyk R 1986 Semiconductor wafer and technical flat planeness testing interferometer Appl. Opt. 25 1117-21
145. _1987 Semiconductor wafer and technical flat planeness testing interferometer Measurement 5 98-101
146. Schwider J, Burow R, Elssner K-E, Grzanna J, Spolaczyk R and Merkel K 1983 Digital wave-front measuring interferometry: some systematic error sources Appl. Opt. 22 3421-32
147. Schwider J, Falkenstörfer O, Schreiber H, Zöller A and Sreibl N 1993 New compensating four-phase algorithm for phase-shifting interferometry Opt. Engng. 32 1883-5
148. Servín M, Malacara D, Malacara Z and Vlad V 1994 Sub-Nyquist null aspheric testing using a computer stored compensator Appl. Opt. 33 4103-8
149. Singh H and Sirkis J S 1994 Direct extraction of phase gradients from Fourier-transform and phase-step fringe patterns Appl. Opt. 33 5016-20
150. Sirkis J S, Chen Y-M, Singh H and Cheng A Y 1992 Computerized optical fringe pattern analysis in photomechanics: a review Opt. Engng. 31 304-14
151. Smythe R and Moore R 1984 Instantaneous phase measuring interferometers Opt. Engng. 23 361-4
152. Sotoilov G and Dragostinov T 1997 Phase-stepping interferometry: five-frame algorithm with an arbitrary step Opt. Lasers Engng. 28 61-9
153. Stahl H P 1989 Testing large optics: high-speed phase-measuring interferometry Photonics Spectra. 12 105-12
154. Stetson K A 1990 Theory and applications of electronic holography Proc. SEM Conf. Hologram Interferometry and Speckle Metrology pp 294-300
155. Surrel Y 1993 Phase-stepping: a new self-calibrating algorithm Appl. Opt. 32 3598-600
156. _1996 Design of algorithms for phase measurements by the use of phase stepping Appl. Opt. 35 51-60
157. _1997a Additive noise effect in digital phase detection Appl. Opt. 36 271-6
158. _1997b Design of phase-detection algorithms insensitive to bias modulation Appl. Opt. 36 805-7
159. Suzuki T, Hasegawa J, Sasaki O and Maruyama T 1995 Sinusoidal phase-modulating laser diode interferometer using a self-pumped phase-conjugate mirror Proc. SPIE 2576 299-307
160. Suzuki T, Sasaki O and Maruyama T 1989 Phase locked laser diode interferometry for surface profile measurement Appl. Opt. 28 4407-10
161. Takeda M 1990 Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: an overview Indust. Metrol. 1 79-99
162. _1996 Recent progress in phase unwrapping techniques Proc. SPIE 2782 334-43
163. Takeda M, Ina H and Kobayashi S 1982 Fourier-transform method of fringe-pattern analysis computer-based topography and interferometry J. Opt. Soc. Am. 72 156-60
164. Takeda M and Kitoh M 1992 Spatiotemporal frequency multiplex heterodyne interferometry J. Opt. Soc. Am. A 9 1607-14
165. Takeda M and Mutoh K 1983 Fourier transform profilometry for the automatic measurement of 3-D object shapes Appl. Opt. 22 3977-82
166. Tatsuno K and Tsunoda Y 1987 Diode laser direct modulation heterodyne interferometer Appl. Opt. 26 37-40
167. Toyooka S, Tanahashi T and Tominaga M 1984 Simple heterodyne interferometry using a holographic common-path interferometer Appl. Opt. 23 1460-3
168. Vikhagen E 1990 TV holography: spatial resolution and signal resolution in deformation analysis Appl. Opt. 29 137-44
169. Vikram C S, Witherow W K and Trolinger J D 1993 Algorithm for phase-difference measurement in phase-shifting interferometry Appl. Opt. 32 6250-2
170. Wang J and Grant I 1995 Electronic speckle interferometry, phase-mapping, and nondestructive testing techniques applied to real-time, thermal loading Appl. Opt. 34 3620-7
171. Wang X, Sasaki O, Takebayashi Y, Suzuki T and Maruyama T 1994 Sinusoidal phase-modulating Fizeau interferometer using a self-pumped phase conjugator for surface profile measurements Opt. Engng. 33 2670-4
172. Williams D C, Nassar N S, Banyard J E and Virdee M S 1991 Digital phase-step interferometry: a simplified approach Opt. Lasers Technol. 23 147-50
173. Wingerden J, Frankena H J and Smorenburg C 1991 Linear approximation for measurement error in phase shifting interferometry Appl. Opt. 30 2718-29
174. Wizinowich P L 1990 Phase shifting interferometry in the presence of vibration: a new algorithm and system Appl. Opt. 29 3271-9
175. Womack K H 1984 Interferometric phase measurement using spatial synchronous detection Opt. Engng. 23 391-5
176. Wyant J C 1971 Testing aspherics using two-wavelength holography Appl. Opt. 10 2113-18
177. _1975 Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems Appl. Opt. 14 2622-6
178. _1982 Interferometric optical metrology: basic principles and new systems Laser Focus 5 65-71
179. Wyant J C, Koliopoulos C L, Bhushan B and George O E 1984 An optical profilometer for surface characterization of magnetic media Trans. ASLE 27 101-13
180. Zhao B 1997a A statistical method for fringe intensity-correlated error in phase-shifting measurement: the effect of quantization error on the N-bucket algorithm Meas. Sci. Technol. 8 147-53
181. _1997b Effect of intensity-correlated error due to quantization and noise on phase-shifting method Opt. Lasers Engng. 28 199-211
182. Zhao B and Surrel Y 1995 Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal Opt. Engng. 34 2821-2
183. _1997 Effect of quantization error on the computed phase of phase-shifting measurements Appl. Opt. 36 2070-5
184. Zhang H, Lalor M J and Burton D R 1998 A comparative study of error-compensating phase-shifting algorithms Applied Optics and Optoelectronics 1998 ed K T V Grattan (Bristol: Institute of Physics) pp 33-8