## Microscopic particle discrimination using spatially-resolved Fourier-holographic light scattering angular spectroscopy

Optics Express, Vol. 14, Issue 23, pp. 11088-11102 (2006)

http://dx.doi.org/10.1364/OE.14.011088

Acrobat PDF (4140 KB)

### Abstract

We utilize Fourier-holographic light scattering angular spectroscopy to record the spatially resolved complex angular scattering spectra of samples over wide fields of view in a single or few image captures. Without resolving individual scatterers, we are able to generate spatially-resolved particle size maps for samples composed of spherical scatterers, by comparing generated spectra with Mie-theory predictions. We present a theoretical discussion of the fundamental principles of our technique and, in addition to the sphere samples, apply it experimentally to a biological sample which comprises red blood cells. Our method could possibly represent an efficient alternative to the time-consuming and laborious conventional procedure in light microscopy of image tiling and inspection, for the characterization of microscopic morphology over wide fields of view.

© 2006 Optical Society of America

## 1. Introduction

2. S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. **30**, 3305–3307 (2005). [CrossRef]

3. S. A. Alexandrov, T. R. Hillman, T. Gutzler, M. B. Same, and D. D. Sampson, “Particle sizing with spatiallyresolved Fourier-holographic light scattering angular spectroscopy,” in *BiOS 2006:Multimodal Biomedical Imaging*,
F. S. AzarD. N. Metaxas
, eds., Proc. SPIE6081, 608104 (2006). [CrossRef]

2. S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. **30**, 3305–3307 (2005). [CrossRef]

3. S. A. Alexandrov, T. R. Hillman, T. Gutzler, M. B. Same, and D. D. Sampson, “Particle sizing with spatiallyresolved Fourier-holographic light scattering angular spectroscopy,” in *BiOS 2006:Multimodal Biomedical Imaging*,
F. S. AzarD. N. Metaxas
, eds., Proc. SPIE6081, 608104 (2006). [CrossRef]

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

6. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. **38**, 6994–7001 (1999). [CrossRef]

7. 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] [PubMed]

8. P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a non-invasive contrast imaging technique allowing quantitative visualisation of living cells with subwavelength axial accuracy,” Opt. Lett. **30**, 468–470 (2005). [CrossRef] [PubMed]

9. M. Gustafsson and M. Sebesta, “Refractometry of microscopic objects with digital holography,” Appl. Opt. **43**, 4796–4801 (2004). [CrossRef] [PubMed]

10. M. Sebesta and M Gustafsson, “Object characterization with refractometric digital Fourier holography,” Opt. Lett. **30**, 471–473 (2005). [CrossRef] [PubMed]

11. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express **13**, 4492–4506 (2005). [CrossRef] [PubMed]

12. V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express **14**, 5168–5177 (2006). [CrossRef] [PubMed]

13. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. **97**, 168102 (2006). [CrossRef] [PubMed]

14. J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. **7**, 378–387 (2002). [CrossRef] [PubMed]

19. A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, “Bacteria size determination by elastic light scattering,” IEEE J. Sel. Top. Quantum Electron. **9**, 277–287 (2003). [CrossRef]

20. W. P. Van De Merwe, J. Czégé,M. E Milham, and B. V. Bronk, “Rapid optically based measurements of diameter and length for spherical or rod-shaped bacteria *in vivo*,” Appl. Opt. **43**, 5295–5302 (2004). [CrossRef] [PubMed]

22. J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidativestress-induced mitochondrial swelling,” Biophys. J. **88**, 2929–2939 (2005). [CrossRef] [PubMed]

23. J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. **30**, 2442–2444 (2005). [CrossRef] [PubMed]

24. Y. L. Kim, Y. Liu, R. K Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. **9**, 243–256 (2003). [CrossRef]

28. A. Wax, C. Yang, R. R. Dasari, and M. S. Feld, “Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy,” Opt. Lett. **26**, 322–324 (2001). [CrossRef]

## 2. Methodology

*ξ*,

*η*) and recording (

*x*,

*y*) planes, and the coordinate systems used to describe them. The complex representations of the Fourier transform of the scattered wave and the plane reference wave in the recording plane may be denoted

*U*(

_{S}*x*,

*y*)=

*U*

_{0S}(

*x*,

*y*)exp[-

*jφ*(

_{S}*x*,

*y*)] and

*U*(

_{R}*x*,

*y*)=

*U*

_{0R}exp[-

*jφ*

*(*

_{R}*x*,

*y*)], respectively, where

*U*

_{0S}(

*x*,

*y*) is a real (positive) spatially-varying amplitude, and

*U*

_{0R}is a constant amplitude (assumed real and positive, without loss of generality). The term

*φ*(

_{S}*x*,

*y*) is the phase of the Fourier transform of the sample wave,

*φ*(

_{R}*x*,

*y*)=

*k*sin

*θ*(

_{r}*x*cos

*ϕ*+

_{r}*y*sin

*ϕ*) is the phase of the reference wave, linear with respect to spatial position,

_{r}*k*=2

*π*/λ represents optical wavenumber, and λ is the wavelength of the source. The angle

*θ*is the incident angle of the reference wave (relative to the

_{r}*z*-axis, which is normal to the Fourier plane) and

*ϕ*is the azimuthal angle, i.e., the angle between the reference plane of incidence and the

_{r}*x*coordinate axis.

^{-1}denotes the inverse Fourier-transform operator, defined by the equation:

*ν*,

_{x}*ν*) represent the coordinates in the transform space. In Eq. (2),

_{y}*u*is the inverse Fourier transform of

_{S}*U*, and

_{S}*δ*represents the Dirac delta function. The first term on the right-hand side of the equation, Γ

_{u}(

*ν*,

_{x}*ν*)=

_{y}*u*(

_{S}*ν*,

_{x}*ν*)⊗

_{y}*u**

_{S}(-

*ν*, -

_{x}*ν*), is a zero-order autocorrelation and the second term is a high-intensity zero-order spot, located at the origin. The third and fourth terms are first-order twin images of the sample field and its (spatially inverted) complex conjugate, each translated in opposite directions due to the influence of the exponential carrier factors. If the first-order images are sufficiently spatially separated from the zero-order images, the squared magnitude of the entire transformed distribution yields reconstructed twin images of the scattered power from the sample. Otherwise, the first two terms can be removed by recording the sample and reference intensities separately, and subtracting both from Eq. (1).

_{y}*u*(

_{S}*ν*,

_{x}*ν*) is a scaled version of the scattered field distribution in the object plane. We denote the latter distribution by

_{y}*V*(

_{O}*ξ*,

*η*) (utilizing the input plane coordinate system), such that:

*M*is a constant (with dimensions of squared length) dependent on the optical elements of the setup and proportional to the illumination wavelength.

*K*, the Fourier transform of

_{g}*k*, may be represented:

_{g}*I*(

*x*,

*y*) is divided by the quadratic correction factor, we obtain (noting that the inverse of

*K*is equal to its complex conjugate):

_{g}*K*are taken to be (-

_{g}*x*/

*M*,-

*y*/

*M*) as in Eq. (7). It is clear from Eq. (9) that, after the recorded hologram is multiplied by the quadratic defocus correction factor, only one of the twin reconstructed images will be focused; the other will be doubly defocused.

**k**

_{R}and

**k**

*, respectively, onto the recording plane. For an axial sample wave, this difference, the fringe vector*

_{S}**k**

*=*

_{F}**k**

*-*

_{R}**k**

*, is depicted along with*

_{S}**k**

_{R}and

**k**

*in Fig. 1. The wavevectors both have magnitude*

_{S}*k*and

**k**

*has magnitude*

_{F}*k*=2

_{F}*k*sin(

*θ*/2). The fringe vector is oriented at angle

_{r}*θ*/2 to the recording plane, thus, its projection onto the plane has magnitude

_{r}*k*cos(

_{F}*θ*/2). The spatial period of the fringe pattern is therefore:

_{r}2. S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. **30**, 3305–3307 (2005). [CrossRef]

3. S. A. Alexandrov, T. R. Hillman, T. Gutzler, M. B. Same, and D. D. Sampson, “Particle sizing with spatiallyresolved Fourier-holographic light scattering angular spectroscopy,” in *BiOS 2006:Multimodal Biomedical Imaging*,
F. S. AzarD. N. Metaxas
, eds., Proc. SPIE6081, 608104 (2006). [CrossRef]

*a priori*sample regions of interest. In the second technique, we select such sample regions from the reconstructed object plane field distribution (where all detected scattering angles are utilized to form the reconstruction). The field within each region is Fourier-transformed to obtain a map of the scattering angle distribution. The principal advantage of this technique is the fact that it allows direct access to these two-dimensional maps. The distribution of the scattered power in each may be used to determine sample properties within the selected region.

*λ*=632.8nm and a FWHM angular resolution of Δ

*θ*=1.0°, this yields a sample spatial resolution δ

*d*=32

*µ*m. Despite the fact that this value is clearly too large to directly resolve sample microstructure, it does not represent an impediment in our approach.

## 3. Experimental setup and procedure

*f*

_{1}=15mm) and illuminated by a plane wave. Its optical Fourier spectrum is imaged onto the recording plane via the lenses L2 and L3 (of focal lengths

*f*

_{2}=15cm and

*f*

_{3}=26cm, respectively). For this setup, the scaling constant

*M*=

*λ*

*f*

_{1}

*f*

_{3}/

*f*

_{2}. Recording is performed using a charge-coupled device (CCD) matrix sensor (12 bit, 1392×1040 pixels, pixel length Δ

*r*=4.65

*µ*m). The reference wave is expanded using the telescopic system T and is directed offaxis onto the CCD matrix at angle

*θ*of approximately 2.3°.

_{r}*θ*≅49°, the angular deviation

_{i}*θ*range is about 17° (in air), centered on the axis. If the sample background medium is water (

_{d}*n*

_{med}=1.33), the scattering angles

*θ*which can be detected range from 139° to 152°. A rectangular field stop is placed in a plane conjugate to the sample, in order to restrict the field of view to a 1mm×2mm area, thus enabling clear identification of the first-order twin images.

_{s}*ξ*,

*η*,

*x*, and

*y*axes, depicted in Fig. 1, are aligned with the horizontal and vertical axes of the CCD recording area, respectively, and the azimuthal angle

*ϕ*

_{i}≅35°. For our system parameters, curves in the recording plane corresponding to constant scattering angle

*θ*(but varying azimuthal angle) are displayed in the left panel of Fig. 3. The curves are well approximated by straight lines perpendicular to the illumination-wave plane of incidence (in the paraxial approximation), i.e., oriented at angle

_{s}*ϕ*to the

_{i}*y*-axis. (The angular error associated with this straight-line approximation is less than 0.2° over virtually the entire recording plane.) The distance between two such lines corresponding to a scattering angle difference of

*θ*

*s*_{,diff}is approximately

*x̃*

_{diff}=(

*Mn*

_{med}/

*λ*)

*θ*

_{s}_{,diff}.

*ξ*,

_{s}*η*) in the sample plane is a circle centered at the point (

_{s}*x*,

_{s}*y*)=(

_{s}*f*

_{3}/

*f*

_{2})(

*ξ*,

_{s}*η*) of diameter (

_{s}*f*

_{3}/

*f*

_{2})

*D*, where

_{L}*D*is the diameter of the objective lens. Consider the sample area for which the CCD recording area lies entirely within this region. If the CCD recording area was circular with diameter

_{L}*D*, then this area would also be a circle with diameter

_{R}*D*=

_{S}*D*-(

_{L}*f*

_{2}/

*f*

_{3})

*D*(if

_{R}*D*>(

_{L}*f*

_{2}/

*f*

_{3})

*D*, and zero otherwise). Of course, for our setup, the recording area is rectangular, with dimensions 4.8×6.5 mm. The corresponding sample areas for a range of different objective lens diameters are shown in the right panel of Fig. 3. For our case, the objective lens diameter

_{R}*D*≅ 6mm, so that its NA was 0.2.

_{L}*d*be the diameter of the sample (or an alternative representative length). Then to ensure that the twin reconstructed images are spatially separated from the zero-order terms, it is necessary that [30, p. 309]:

_{s}*H*>2(D

_{f}*r*/√2), where the factor √2 arises due to the effective pixel size in a diagonal direction, and the factor 2 arises from Nyquist’s theorem, i.e., by Eq. (10):

*θ*<5.5°. Our choice of

_{r}*θ*=2.3° clearly violates the lower limit, so there will be some overlap between the zero-order terms and the twin images. As explained above, however, this can be overcome by digitally subtracting the recorded reference and sample waves from the hologram. Equation (13) demonstrates that, for a given CCD sensor size and wavelength, if

_{r}*d*is increased, then

_{s}*M*must undergo a corresponding increase to satisfy the inequality. That is, there is a trade-off between measured scattering angle range and sample size.

*θ*detectable by our system, from about 139° to 152° as described above. The choice of microsphere suspensions was natural since their angular scattering pattern follows a distinctive modulation (ripple) pattern described by Mie theory, with an (angular) period which (for the most part) decreases with increasing sphere diameter. Our samples comprised polysterene spheres suspended in distilled water. The microspheres were diluted to a volume concentration of 0.1% and a droplet was deposited into a 10×20 mm well on a microscope slide. To demonstrate the application of our approach to biological samples, we utilized a smear of erythrocytes, or red blood cells (RBCs). The RBCs were diluted with a droplet of NaCl solution (9%) and evenly smeared over a microscope slide. A coverslip was placed over the sample, and sealed at the edges. The normal RBC shape is a discocyte, an axially-symmetric disc indented on the axis [31

_{s}31. A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. **52**, 13–18 (2005). [CrossRef] [PubMed]

31. A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. **52**, 13–18 (2005). [CrossRef] [PubMed]

**30**, 3305–3307 (2005). [CrossRef]

## 4. Results

*m*=

*n*

_{sph}/

*n*

_{med}=1.59/1.33=1.20, for a range of particle sizes. The ripple patterns are readily apparent, as well as the dependence of their angular periods on sphere size. It is this parameter of the curves that we utilize to determine sphere size in our samples. To assign a value to the apparent angular period in each case, a high-pass filter was applied to the curve in order to fit it accurately to a sinusoidal curve. The angular period was originally estimated from the average fringe spacing over the angle range 120°-170°, and the (4th-order Butterworth) filter cutoff frequency was equal to 0.75 times the estimated fringe frequency. The filtered curves are shown in red. They were fitted (in a minimum least-squares sense) to sinusoidal curves, and the frequencies recorded. By this process, it may be shown that the ripple angular frequency is almost linearly dependent on the Mie size parameter

*α*=

*πdn*

_{med}/

*λ*, where

*d*is the sphere diameter. Such an approximation is valid (at least) over the refractive index ratio range

*m*=1.1-1.25, yielding a maximum error in detected diameter of less than 1

*µ*m (for sphere sizes ranging from 1 to 20

*µ*m) and a mean error of about 0.2

*µ*m. A more direct Mie inversion procedure may be used for particle size/refractive index values outside these ranges. Thus, particle size can be recovered from the measured ripple angular frequency, to a degree of accuracy which should be sufficient for many applications. The minimum particle size measurable by our system can be estimated by determining the sphere diameter for which one full ripple cycle is visible over the angular range used. As is clear from Fig. 4, this minimum size is about 2

*µ*m, assuming

*m*is within the given range. In general, the particle-size sensitivity of our approach is limited by angular range and refractive index to the same extent as alternative angular-scattering-spectroscopy techniques [14

14. J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. **7**, 378–387 (2002). [CrossRef] [PubMed]

*µ*m [20

20. W. P. Van De Merwe, J. Czégé,M. E Milham, and B. V. Bronk, “Rapid optically based measurements of diameter and length for spherical or rod-shaped bacteria *in vivo*,” Appl. Opt. **43**, 5295–5302 (2004). [CrossRef] [PubMed]

22. J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidativestress-induced mitochondrial swelling,” Biophys. J. **88**, 2929–2939 (2005). [CrossRef] [PubMed]

32. J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, “Evaluation of spherical particle sizes with an asymmetric illumination microscope,” IEEE J. Sel. Top. Quantum Electron. **9**, 301–306 (2003). [CrossRef]

*µ*m spheres in water. The apparent brightness of the scattering regions of the sample (right-hand side) is clearly dependent on the recording plane strip-mask position (shown on the left-hand side) and, thus, on scattering angle.

*µ*m and 9.9

*µ*m (with standard deviations 0.9

*µ*m and 0.5

*µ*m), respectively. The systematic error of 10–15% is due possibly to errors in the system scaling constant

*M*(due to the large tolerances of the optical components used), leading to a smaller range of scattering angles being imaged onto the CCD detector than predicted theoretically. The relatively large variation in the values measured in the former case is due to the difficulty in precisely detecting the period of low-frequency fringes using a detector encompassing a limited angular range. In both cases, the scatterers on the far left of the reconstruction take on a ‘streaked’ appearance. This is due to vignetting at the boundary of the sample region; the scatterers are reconstructed using a reduced range of spatial frequencies, so they exhibit a resolution loss (and apparent broadening) in one direction.

*µ*m spheres. The two particle sizes are clearly distinguishable by their distinct hues used in the latter representation. Six different regions, three of each particle size, are highlighted as before. The detected sphere sizes are consistent with those measured in the previous two figures.

*ϕ*≅140°.) Thus, the angle of the lines of constant scattering angle has been likewise varied. Clear ripple structure is apparent in the recorded power spectra (and highly visible peaks along the yellow dotted line in their inverse Fourier transforms), corresponding to a uniform spatial frequency. Since red blood cells are not spherical, it is not strictly appropriate to utilize Mie theory to determine their sizes. Nonetheless, for the purpose of comparison with the previous results, the same Mie inversion procedure was applied to the sample, and a false-color map of particle size generated, as before. (The fact that the relative refractive index

_{i}*m*between the blood cells and their background was outside the range specified earlier in this section was ignored for the purpose of this simple analysis.) For this sample, despite the fact that a majority (65%) of detected particle sizes were within 1

*µ*m of themean value (ignoring spurious outliers), there was much more variation in the detected blood cell sizes than in the sphere sizes of the earlier experiments. This is probably accounted for by the natural variation in the size and orientation of the particles, as well as the general inaccuracies inherent in applying aMie-theory inversion procedure to a distribution of non-spherical particles. However, the mean detected size of about 6

*µ*m correlates well with typical red-blood-cell sizes reported in the literature [31

31. A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. **52**, 13–18 (2005). [CrossRef] [PubMed]

## 5. Discussion and Conclusion

*θ*=1.3° (in air), and Δ

*d*=25

*µ*m. Utilizing the full mask length to reconstruct the sample, the angular/spatial resolutions in the direction of varying azimuthal angle are given by 8.9° (rectangular length)/6

*µ*m (main lobe length). In principle, an image can be formed from a single exposure, in common with conventional microscopy, however, since we do not require spatial resolutions high enough to measure microparticle sizes directly, our system optical requirements are very modest. We can utilize a low-magnification, low-numerical-aperture objective, which allows us to form images over long working distances and millimeter-scale fields of view. This ability to form millimeter-scale images that provide the angular distribution of the scattered light in each local area is unique to our method.

21. N. N. Boustany, S. C. Kuo, and N. V. Thakor, “Optical scatter imaging: subcellular morphometry *in situ* with Fourier filtering,” Opt. Lett. **26**, 1063–1065 (2001). [CrossRef]

33. M. T. Valentine, A. K. Popp, D. A. Weitz, and P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. **26**, 890–892 (2001). [CrossRef]

*m*=1.1-1.25. If we were able to improve our processing procedure to consider other parameters such as peak position or relative magnitude, our approach could have even greater discriminatory powers. Curiously, even for samples composed of identical particles (as in Figs. 6, 7), the peaks in the one-dimensional scattering spectra were not aligned over the five images. This observation is partially accounted for by the variation in the size of the particles used (the manufacturerspecified standard deviation was 0.14 and 0.21

*µ*m, respectively, for the 5.4 and 11.4

*µ*m sphere sizes; diameter variations of about 0.3 and 0.2

*µ*m, respectively, would be sufficient to account for complete contrast reversal of the Mie ripples). Also, any variation in the particle shape from sphericity could account for these anomalies.

13. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. **97**, 168102 (2006). [CrossRef] [PubMed]

## Acknowledgments

## References and links

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2. | S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. |

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

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7. | 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. |

8. | P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a non-invasive contrast imaging technique allowing quantitative visualisation of living cells with subwavelength axial accuracy,” Opt. Lett. |

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19. | A. Katz, A. Alimova, M. Xu, E. Rudolph, M. K. Shah, H. E. Savage, R. B. Rosen, S. A. McCormick, and R. R. Alfano, “Bacteria size determination by elastic light scattering,” IEEE J. Sel. Top. Quantum Electron. |

20. | W. P. Van De Merwe, J. Czégé,M. E Milham, and B. V. Bronk, “Rapid optically based measurements of diameter and length for spherical or rod-shaped bacteria |

21. | N. N. Boustany, S. C. Kuo, and N. V. Thakor, “Optical scatter imaging: subcellular morphometry |

22. | J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidativestress-induced mitochondrial swelling,” Biophys. J. |

23. | J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. |

24. | Y. L. Kim, Y. Liu, R. K Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. |

25. | Y. Liu, Y. L. Kim, and V. Backman, “Development of a bioengineered tissue model and its application in the investigation of the depth selectivity of polarization gating,” Appl. Opt. |

26. | M. Bartlett, G. Huang, L. Larcom, and H. Jiang, “Measurement of particle size distribution in mammalian cells |

27. | Y. Liu, Y. L. Kim, X. Li, and V. Backman, “Investigation of depth selectivity of polarization gating for tissue characterization,” Opt. Express |

28. | A. Wax, C. Yang, R. R. Dasari, and M. S. Feld, “Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy,” Opt. Lett. |

29. | R. N. Graf and A. Wax, “Nuclear morphology measurements using Fourier domain low coherence interferometry,” Opt. Express |

30. | J. Goodman, |

31. | A. Karlsson, J. He, J. Swartling, and S. Andersson-Engels, “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. |

32. | J. C. Ramella-Roman, P. R. Bargo, S. A. Prahl, and S. L. Jacques, “Evaluation of spherical particle sizes with an asymmetric illumination microscope,” IEEE J. Sel. Top. Quantum Electron. |

33. | M. T. Valentine, A. K. Popp, D. A. Weitz, and P. D. Kaplan, “Microscope-based static light-scattering instrument,” Opt. Lett. |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(090.0090) Holography : Holography

(100.2000) Image processing : Digital image processing

(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation

(170.1650) Medical optics and biotechnology : Coherence imaging

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

**ToC Category:**

Fourier Optics and Optical Signal Processing

**History**

Original Manuscript: September 12, 2006

Revised Manuscript: October 30, 2006

Manuscript Accepted: October 31, 2006

Published: November 13, 2006

**Virtual Issues**

Vol. 1, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

Timothy R. Hillman, Sergey A. Alexandrov, Thomas Gutzler, and David D. Sampson, "Microscopic particle discrimination using spatially-resolved Fourier-holographic light scattering angular spectroscopy," Opt. Express **14**, 11088-11102 (2006)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-23-11088

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### References

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