## Computational signal-to-noise ratio analysis for optical quadrature microscopy

Optics Express, Vol. 17, Issue 4, pp. 2400-2422 (2009)

http://dx.doi.org/10.1364/OE.17.002400

Acrobat PDF (758 KB)

### Abstract

Optical quadrature microscopy (OQM) was invented in 1997 to reconstruct a full-field image of quantitative phase, and has been used to count the number of cells in live mouse embryos. Here we present a thorough SNR analysis that incorporates noise terms for fluctuations in the laser, aberrations within the individual paths of the Mach-Zehnder interferometer, and imperfections within the beamsplitters and CCD cameras to create a model for the resultant phase measurements. The current RMS error of the OQM phase images has been calculated to be 0.08 radians from substituting images from the instrumentation into the model.

© 2009 Optical Society of America

## 1. Introduction

5. D. O. Hogenboom and C.A. DiMarzio, “Quadrature detection of a Doppler signal,” Appl. Opt. **37**, 2569–2572 (1998). [CrossRef]

6. Y. Glina, G. A. Tsihrintzis, C. M. Warner, D. O. Hogenboom, and C. A. DiMarzio, “On the use of the optical quadrature method in tomographic microscopy,” Proc. SPIE, **3605**, 101–106 (1999). [CrossRef]

10. A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. **175**, 329–336 (2000). [CrossRef]

12. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic Phase Microscopy,” Nat. Methods **4**, 717–719 (2007). [CrossRef] [PubMed]

13. D. S. Marx and D. Psaltis, “Polarization quadrature measurement of subwavelength diffracting structures,” Appl. Opt. **36**, 6434–6440 (1997). [CrossRef]

16. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. **24**, 291–293 (1999). [CrossRef]

17. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. **29, **2503–2505 (2004). [CrossRef]

18. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. **30**, 1165–1167 (2005). [CrossRef] [PubMed]

19. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. **31**, 775–777 (2006). [CrossRef] [PubMed]

20. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. **22**, 1268–1270 (1997). [CrossRef] [PubMed]

24. D. Paganin and K. A. Nugent, “Noninterferometric Phase imaging with partially coherent light,” Phys. Rev. Lett. **80**, 2586–2589 (1998). [CrossRef]

26. C. Preza, “Rotational-diversity phase estimation from differential interference contrast microscopy images,” J. Opt. Soc. Am. A **17**, 415–424 (2000). [CrossRef]

*in vitro*fertilization (IVF) [32–33

32. J. A. Newmark, W. C. Warger II, C. C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the Number of Cells in Preimplantation Embryos by Using Non-invasive Optical Quadrature Microscopy in Conjunction with Differential Interference Contrast Microscopy,” Microsc. Microanal. **13**, 118–127 (2007). [CrossRef] [PubMed]

34. W. C. Warger II and C. A. DiMarzio, “Modeling of optical quadrature microscopy for imaging mouse embryos,” Proc. SPIE **6861**, 68610T (2008). [CrossRef]

## 2. Quadrature detection

*S*and

*P*polarization states of the laser beam act as the two unknown signal paths in Fig. 1. Polarizing the reference and signal paths at 45 degrees provides equal amounts of

*S*and

*P*polarization. The reference path then transmits through a quarter-wave plate to create circular polarization, where one polarization state has a 90-degree phase shift with respect to the other. The 45-degree polarized signal and circularly polarized reference beams mix within a non-polarizing recombining beamsplitter, and a polarizing beamsplitter separates the two polarization states of the mixed signal into the I and Q channels that are acquired with two CCD cameras. In practice, both outputs of the recombining beamsplitter are separated into two separate I and Q channels in a balanced detection configuration to remove the DC components that result from the additive combination of the fields in the beamsplitters and the square law detection required for optical frequencies.

## 3. Optical layout for OQM

*x*⃗ and

*y*⃗ basis vectors of the system. The 45-degree linearly polarized light enters the optical path of the Nikon Eclipse TE2000U microscope by reflecting from a narrow bandstop dichroic splitter centered at 633 nm with a 30-nm bandstop defined by the full width at half maximum. The dichroic splitter reflects the 633 nm light from the laser and transmits the white light from the halogen light source of the microscope for brightfield and differential interference contrast (DIC) microscopy [36

36. W. C. Warger II, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. **12**, 044006 (2007). [CrossRef] [PubMed]

*x*⃗ and

*y*⃗ basis vectors of the system can be positioned before the recombining beamsplitter to ensure the signal path is polarized at 45 degrees before mixing with the reference path.

*x*⃗ and

*y*⃗ basis vectors of the system, and a quarter-wave plate oriented at 45 degrees to the axis of the polarizer to produce circularly polarized light. A lens matches the wavefront of the beam in the reference path to the wavefront of the beam in the signal path, and the 45-degree linearly polarized signal path mixes with the circularly polarized reference path at the 50/50 non-polarizing recombining beamsplitter. A balanced detection configuration has been implemented such that both outputs of the recombining beamsplitter are acquired instead of just one. The two mixed beams that are output from the recombining beamsplitter travel through polarizing beamsplitters to separate the quadrature components, and four synchronized 8-bit CCD cameras (XC-75, Sony Electronics Inc., Park Ridge, New Jersey) acquire images of the sample from each output of the two polarizing beamsplitters with a framegrabber (Matrox Genesis LC, Dorval, Canada) that has the ability to buffer four simultaneous video channels.

## 4. Ideal electric field analysis

*E*⃗

_{ref}) and signal (

*E*⃗

_{sig}) paths. The 50/50 non-polarizing beamsplitter splits the irradiance of the incident laser light, which is proportional to the intensity or the square of the electric field, thereby providing 1/√2 of the incident field in each path. Each path passes through a linear polarizer oriented at 45 degrees to the basis set to ensure 45-degree polarized light in each path:

*E*/1√2 and

_{R}*E*/1√2 are the amplitudes of the fields from the laser that pass through the linear polarizers,

_{S}*ϕ*is the phase of the laser output,

*j*is √-1,

*ω*is the angular frequency,

*t*is time, and

*x*⃗ and

*y*⃗ are the basis vectors of the system, which are projections of the field in the

*S*and

*P*directions with respect to the polarizing beamsplitters. The reference path travels through a quarter-wave plate with axes oriented at 45 degrees relative to the laser’s polarization axis thereby producing circular polarization:

*α*):

*λ*is the wavelength of the laser,

*n*

_{0}is the refractive index of the immersion medium, and

*n*and

_{s}*h*are the refractive index and thickness of the sample, respectively.

*x*⃗ component and transmitting the

*y*⃗ component, where the

*x*⃗ and

*y*⃗ components are defined as the

*S*and

*P*polarization states with respect to the polarizing beamsplitters. Four CCD cameras, numbered 0 to 3 and spatially registered with an affine transform [37

37. C. L. Tsai, W. C. Warger II, G. S. Laevsky, and C. A. DiMarzio, “Alignment with sub-pixel accuracy for images of multi-modality microscopes using automatic calibration,” J. Microsc., **232**, 164–176 (2008). [CrossRef]

*E*and

_{S}*E*are real, the complex conjugates of the magnitudes can be removed and Eqs. (11) – (14) reduce to:

_{R}*via*the summation:

*k*defines the signal captured at a specific CCD camera. The subtraction of the pure signal (

*S*), reference (

_{k}*R*), and dark detector voltage (

_{k}*D*) from the individual signals in Eqs. (11) – (14) removes the aberrations in each path and leads to the reconstruction:

_{k}*D*simplifies the notation for the subtraction of the dark detector current from

_{k}*M*,

_{k}*R*, and

_{k}*S*. The images for

_{k}*D*are subtracted from each image because a value proportional to

_{k}*D*exists in every image acquired with a CCD camera. Images are acquired for

_{k}*S*,

_{k}*R*, and

_{k}*D*by blocking the signal and reference arms individually and simultaneously. Additional noise results from imperfections in the beamsplitters, such as a 50/50 beamsplitter not splitting the irradiance of the light into equal halves. Thus, the division by the square root of the pure reference images normalizes the camera signals and leads to the current reconstruction that has been used for OQM:

_{k}## 5. SNR analyses for phase reconstructions

### 5.1. Mathematical description of balanced mixing

*x*⃗ and

*y*⃗ basis vectors of the system, and the reference path is circularly polarized by the quarter-wave plate oriented at 45 degrees to the laser polarization:

*E*and Ϛ are the amplitude and phase of the laser fluctuations that pass through the linear polarizers, respectively, and × denotes a multiplication. The signal path transmits through the sample that induces a change in magnitude (A) and phase (

_{N}*α*):

_{r}and X

_{s}are the amplitudes and

*χ*and

_{r}*χ*are the phases of the aberrations in the reference and signal paths, respectively. The two paths mix at the recombining beamsplitter and each output travels through a polarizing beamsplitter that separates the quadrature components. Imperfections within the beamsplitters and coherent noise in the CCD cameras provide fixed pattern noise in each path with a magnitude

_{s}*E*

^{R}

_{Ck}and

*E*

^{S}

_{Ck}in Eqs. (27) and (28), where the superscript

*R*and

*S*designate the reference and signal paths, respectively. Four CCD cameras convert a general irradiance

*I*into a current:

_{k}*η*is the quantum efficiency of the silicon chip (electrons/photon),

_{k}*q*is the charge of an electron (1.6 × 10

^{-19}c),

*h*is Planck’s constant (6.6 × 10

^{-34}Wsec

^{2}),

*ν*is the frequency of the laser (sec

^{-1}),

*A*is the area of a pixel (m

_{pixel}^{2}),

*I*is the irradiance of the beam (Wm

_{k}^{-2}), and

*i*is the dark current noise. It is important to note that the dark current noise fluctuates randomly from image to image so we have included a different dark current noise term for every image acquired during the reconstruction. The images captured for the mix of the signal and reference paths (

_{D,k}*M*) and containing all of the various noise terms can then be expressed:

_{k}*i*is the dark current in the mix images and we have assumed the magnitude of each term is real. Balanced mixing of Eq. (30)

_{M,k}*via*the summation in Eq. (19) provides the reconstructed current of the mixed signal:

*S*) and noise (

*N*) terms provides:

_{S}*E*

_{B}

*e*

^{j(ωt + β)}and dark current in the CCD cameras

*i*, the reconstruction in Eq. (19) for the blank image with the sample moved out of the field of view provides the signal (

_{BM, k}*B*) and noise (

*N*) terms:

_{B}_{S}and Γ

_{R}). In the following subsection, we subtract images of the individual DC terms to reduce the noise within the resultant image.

### 5.2. Mathematical description of balanced mixing and DC term subtraction

*i*) by blocking both paths, where

_{D,k}*i*and

_{S,k}*i*are the dark current terms for the images of the signal and reference images, respectively. Subtracting

_{R,k}*i*from Eqs. (30), (53), and (54) and substituting into the reconstruction in Eq. (20) provides:

_{D,k}*S*) and noise (

*N*) terms:

_{S}*B*) and noise (

*N*) terms:

_{B}*i*and

_{BR,k}*i*are the dark current terms for the signal and reference images with the sample moved out of the field of view, respectively. Following the same procedure described in the previous subsection provides the reconstructed magnitude and phase induced by the sample:

_{BS,k}### 5.3. Mathematical description of balanced mixing, DC term subtraction, and normalization of camera signals

*i*from Eqs. (30), (53), and (54) into the reconstruction in Eq. (21) provides:

_{D,k}*S*) and noise (

*N*) terms:

_{S}*B*) and noise (

*N*) terms:

_{B}## 6. Modeling of the phase reconstructions

*χ*-

_{s}*χ*) corresponds to the wavefront mismatch between the reference and signal paths when the sample is not within the field of view. Using the same approximations described in Section 5.3, the reconstruction in Eq. (21) for the image of the blank provides the expression:

_{r}*B*in Eq. (49), and the images acquired with the signal path blocked provided the images for

_{Sk}*R*in Eq. (50). Seven sets of images with the same field of view and containing random numbers between 0 and 2 were created for each camera to model the dark current noise terms

_{k}*i*,

_{M,k}*i*,

_{BM,k}*i*,

_{S,k}*i*,

_{BS,k}*i*,

_{R,k}*i*, and

_{BR,k}*i*. The images for

_{D,k}*B*,

_{Sk}*R*, and the dark current noise were then substituted into Eqs. (44)–(48), (52), (61)–(63), (65), (73)–(75), and (77) to create the images shown in Fig. 4 that model Ψ, Φ, Γ

_{k}_{S}, Γ

_{R}, I

_{S,M}, I

_{B,M}, I

_{M}, I

_{S}, I

_{B}, I

_{BM}, I

_{S,Norm}, I

_{B,Norm}, and I

_{BM,Norm}.

*h*), the refractive index of the bead (

*n*), and the refractive index of the immersion oil (

_{s}*n*

_{0}) were set to 99.12 μm, 1.489, and 1.5124, respectively. An image of the ideal phase for the bead (

*α*) was created with the bead centered on the same pixel in the field of view as the experimental image. Fig. 5(a), 5(d), and 5(g) show the resultant wrapped phase from the reconstructions in Eqs. (43), (60), and (72), and Fig. 5(b), 5(e), and 5(h) show the wrapped experimental results from the reconstructions in Eqs. (19), (20), and (21) that were also divided by a blank image created from the same reconstructions with the sample moved out of the field of view, respectively. Fig. 5(c), 5(f), and 5(i) show plots of the unwrapped phase values through the center of both the model and experimental phase reconstructions to show the accuracy of the phase measurement of a 99 μm PMMA bead immersed in oil, and the correlation of the noise inherent in each phase reconstruction.

### 6.1. Inherent noise in the phase reconstructions

*versus*the constant phase values between -4π and 4π. The error bars show the standard deviation of the phase error across the field of view. The maximum RMS error across the 8π measurements was 0.31 radians, 0.14 radians, and 0.08 radians for the reconstructions in Eqs. (43), (60), and (72) that divide the sample image by the blank image, respectively, and 0.20 radians, 0.10 radians, and 0.05 radians for the reconstructions in Eqs. (51), (64), and (76) that assume a constant wavefront mismatch across the field of view and do not divide by a blank image, respectively. The periodicity of the error can be explained by the strong contribution of multiplicative noise in the reconstructions from the fixed pattern noise. DC term subtraction and camera normalization reduces the amplitude of the periodicity, but the fixed pattern noise must be reduced in the experimental system for the noise to approach a constant value over the range -4π to 4π. It is important to note that the amplitude of the periodic error is 0.06 radians for the current OQM reconstruction, which is less than 0.3% of the maximum phase that we are measuring from 100 μm diameter mouse embryos [33

33. W. C. Warger II, J. A. Newmark, C. M. Warner, and C. A. DiMarzio, “Phase subtraction cell counting method for live mouse embryos beyond the eight-cell stage,” J. Biomed. Opt. **13**, 034005 (2008). [CrossRef] [PubMed]

## 7. Conclusion

39. K. Creath, “Phase-Measurement Interferometry Techniques,” Progress in Optics **26**, E. Wolf (Elsevier Science Publishers, 1988), 349–393. [CrossRef]

^{P}-norm algorithm to unwrap our phase images [40] because it seems to provide the most repeatable and accurate results for circular objects, such as PMMA beads and mouse embryos [33

33. W. C. Warger II, J. A. Newmark, C. M. Warner, and C. A. DiMarzio, “Phase subtraction cell counting method for live mouse embryos beyond the eight-cell stage,” J. Biomed. Opt. **13**, 034005 (2008). [CrossRef] [PubMed]

33. W. C. Warger II, J. A. Newmark, C. M. Warner, and C. A. DiMarzio, “Phase subtraction cell counting method for live mouse embryos beyond the eight-cell stage,” J. Biomed. Opt. **13**, 034005 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | C. DiMarzio, “Optical quadrature interferometry utilizing polarization to obtain in-phase and quadrature information,” U.S. Patent No. 5,883,717, Mar. 16, 1999. |

2. | C. DiMarzio, “Optical quadrature interferometer,” U.S. Patent No. 6,020,963, Feb. 1, 2000. |

3. | D. O. Hogenboom, C. A. DiMarzio, T. J. Gaudette, A. J. Devaney, and S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. |

4. | V. N. Bringi and V. Chandrasekar, |

5. | D. O. Hogenboom and C.A. DiMarzio, “Quadrature detection of a Doppler signal,” Appl. Opt. |

6. | Y. Glina, G. A. Tsihrintzis, C. M. Warner, D. O. Hogenboom, and C. A. DiMarzio, “On the use of the optical quadrature method in tomographic microscopy,” Proc. SPIE, |

7. | J. J. Stott, R. E. Bennett, C. M. Warner, and C. A. DiMarzio, “Three-dimensional imaging with a quadrature tomographic microscope,” Proc. SPIE, |

8. | D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, “Quantitative Phase Measurements Using a Quadrature Tomographic Microscope,” Proc. SPIE, |

9. | C. M. Warner, J. A. Newmark, M. Comiskey, S. R. De Fazio, D. M. O’Malley, M. Rajadhyaksha, D. J. Townsend, S. McKnight, B. Roysam, P. J. Dwyer, and C. A. DiMarzio, “Genetics and imaging to assess oocyte and preimplantation embryo health,” Reprod. Fertil. Dev. |

10. | A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. |

11. | F. Charriére, A. Marian, F. Montfort, J. Kuehn, and T. Colomb, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. |

12. | W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic Phase Microscopy,” Nat. Methods |

13. | D. S. Marx and D. Psaltis, “Polarization quadrature measurement of subwavelength diffracting structures,” Appl. Opt. |

14. | Z. Yaqoob, J. Wu, X. Cui, X. Heng, and C. Yang, “Harmonically-related diffraction gratings-based interferometer for quadrature phase measurements,” Opt. Express |

15. | A. Lebedeff, “Polarization interferometer and its applications,” Rev. Opt., Theor. Instrum. |

16. | E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. |

17. | G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. |

18. | T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. |

19. | G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. |

20. | I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. |

21. | A. Dubois, L. Vabre, and A. C. Boccara, “Sinusoidally phase modulated interference microscope for highspeed high-resolution topographic imagery,” Opt. Lett. |

22. | H. Iwai, C. Fang-Yen, G. Popescu, A. Wax, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Quantitative phase imaging using actively stabilized phase-shifting low-coherence interferometry,” Opt. Lett. |

23. | T. Yamauchi, H. Iwai, M. Miwa, and Y. Yamashita, “Low-coherent quantitative phase microscope for nanometer-scale measurement of living cells morphology,” Opt. Express |

24. | D. Paganin and K. A. Nugent, “Noninterferometric Phase imaging with partially coherent light,” Phys. Rev. Lett. |

25. | A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. |

26. | C. Preza, “Rotational-diversity phase estimation from differential interference contrast microscopy images,” J. Opt. Soc. Am. A |

27. | M. R. Arnison, C. J. Cogswell, N. I. Smith, P. W. Fekete, and K. G. Larkin, “Using the Hilbert transform for 3D visualization of differential interference contrast microscope images,” J. Microsc. |

28. | M. R. Arnison, K. G. Larkin, C. J. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. |

29. | B. Heise, A. Sonnleitner, and E. P. Klement, “DIC image reconstruction on large cell scans,” Microsc. Res. Tech. |

30. | H. Ishiwata, M. Itoh, and T. Yatagai, “A new method of three dimensional measurement by differential interference contrast microscope,” Opt. Commun. |

31. | M. Shribak and S. Inoue, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. |

32. | J. A. Newmark, W. C. Warger II, C. C. Chang, G. E. Herrera, D. H. Brooks, C. A. DiMarzio, and C. M. Warner, “Determination of the Number of Cells in Preimplantation Embryos by Using Non-invasive Optical Quadrature Microscopy in Conjunction with Differential Interference Contrast Microscopy,” Microsc. Microanal. |

33. | W. C. Warger II, J. A. Newmark, C. M. Warner, and C. A. DiMarzio, “Phase subtraction cell counting method for live mouse embryos beyond the eight-cell stage,” J. Biomed. Opt. |

34. | W. C. Warger II and C. A. DiMarzio, “Modeling of optical quadrature microscopy for imaging mouse embryos,” Proc. SPIE |

35. | L. W. Couch II, |

36. | W. C. Warger II, G. S. Laevsky, D. J. Townsend, M. Rajadhyaksha, and C. A. DiMarzio, “Multimodal optical microscope for detecting viability of mouse embryos in vitro,” J. Biomed. Opt. |

37. | C. L. Tsai, W. C. Warger II, G. S. Laevsky, and C. A. DiMarzio, “Alignment with sub-pixel accuracy for images of multi-modality microscopes using automatic calibration,” J. Microsc., |

38. | M. Born and E. Wolf, |

39. | K. Creath, “Phase-Measurement Interferometry Techniques,” Progress in Optics |

40. | D. C. Ghiglia and M. D. Pritt, |

41. | S. Braganza and M. Lesser, “An efficient implementation of a phase unwrapping kernel on reconfigurable hardware,” Proc. Application-Specific Systems, Architectures, and Processors (IEEE, 2008) 138–143. |

**OCIS Codes**

(030.4280) Coherence and statistical optics : Noise in imaging systems

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(180.3170) Microscopy : Interference microscopy

**ToC Category:**

Microscopy

**History**

Original Manuscript: October 17, 2008

Revised Manuscript: December 28, 2008

Manuscript Accepted: January 8, 2009

Published: February 5, 2009

**Virtual Issues**

Vol. 4, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

William C. Warger II and Charles A. DiMarzio, "Computational signal-to-noise ratio analysis for optical quadrature microscopy," Opt. Express **17**, 2400-2422 (2009)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-4-2400

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### References

- C. DiMarzio, "Optical quadrature interferometry utilizing polarization to obtain in-phase and quadrature information," U.S. Patent No. 5,883,717, Mar. 16, 1999.
- C. DiMarzio, "Optical quadrature interferometer," U.S. Patent No. 6,020,963, Feb. 1, 2000.
- D. O. Hogenboom, C. A. DiMarzio, T. J. Gaudette, A. J. Devaney, and S. C. Lindberg, "Three-dimensional images generated by quadrature interferometry," Opt. Lett. 23, 783-785 (1998). [CrossRef]
- V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar: Principles and Applications (Cambridge University Press, 2001), pp. 37-38.
- D. O. Hogenboom and C. A. DiMarzio, "Quadrature detection of a Doppler signal," Appl. Opt. 37, 2569-2572 (1998). [CrossRef]
- Y. Glina, G. A. Tsihrintzis, C. M. Warner, D. O. Hogenboom, and C. A. DiMarzio, "On the use of the optical quadrature method in tomographic microscopy," Proc. SPIE 3605, 101-106 (1999). [CrossRef]
- J. J. Stott, R. E. Bennett, C. M. Warner, and C. A. DiMarzio, "Three-dimensional imaging with a quadrature tomographic microscope," Proc. SPIE 4261, 24-32 (2001). [CrossRef]
- D. J. Townsend, K. D. Quarles, A. L. Thomas, W. S. Rockward, C. M. Warner, J. A. Newmark, and C. A. DiMarzio, "Quantitative Phase Measurements Using a Quadrature Tomographic Microscope," Proc. SPIE 4964, 59-65 (2003). [CrossRef]
- C. M. Warner, J. A. Newmark, M. Comiskey, S. R. De Fazio, D. M. O’Malley, M. Rajadhyaksha, D. J. Townsend, S. McKnight, B. Roysam, P. J. Dwyer, and C. A. DiMarzio, "Genetics and imaging to assess oocyte and preimplantation embryo health," Reprod. Fertil. Dev. 16, 729-741 (2004). [CrossRef]
- A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000). [CrossRef]
- F. Charrière, A. Marian, F. Montfort, J. Kuehn, and T. Colomb, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006). [CrossRef] [PubMed]
- W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, "Tomographic Phase Microscopy," Nat. Methods 4, 717-719 (2007). [CrossRef] [PubMed]
- D. S. Marx and D. Psaltis, "Polarization quadrature measurement of subwavelength diffracting structures," Appl. Opt. 36, 6434-6440 (1997). [CrossRef]
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