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  • Vol. 8, Iss. 1 — Feb. 4, 2013
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Measurement of object structure from size-encoded images generated by optically-implemented Gabor filters

Heidy Sierra, Jing-Yi Zheng, Bryan Rabin, and Nada N. Boustany  »View Author Affiliations


Optics Express, Vol. 20, Issue 27, pp. 28698-28706 (2012)
http://dx.doi.org/10.1364/OE.20.028698


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Abstract

We use optical Fourier processing based on two dimensional (2D) Gabor filters to obtain size-encoded images which depict with 20nm sensitivity to size while preserving a 0.36μm spatial resolution, the spatial distribution of structural features within transparent objects. The size of the object feature measured at each pixel in the encoded image is determined by the optimal Gabor filter period, Smax, that maximizes the scattering signal from that location in the object. We show that Smax (in μm) depends linearly on feature size (also in μm) over a size range from 0.11μm to 2μm. This linear response remains largely unchanged when the refractive index ratio is varied and can be predicted from numerical simulations of Gabor-filtered light scattering. Pixel histograms of the size-encoded images of isolated spheres and diatoms were used to generate highly resolved size distributions (“size spectra”) exhibiting sharp peaks characterizing the known major structural features within the studied objects. Dynamic signal associated with changes in selected feature sizes within living cells is also demonstrated. Taken together, our data suggest that a label-free, direct and objective measurement of sample structure is enabled by the size-encoded images and associated pixel histograms generated from a calibrated optical processing microscope based on Gabor filtering.

© 2012 OSA

1. Introduction

2. Methods

2.1 Optical setup

The optical setup for Gabor filtering was previously described with the use of a digital micro-mirror device (DMD) as a Fourier filter [10

10. J.-Y. Zheng, R. M. Pasternack, and N. N. Boustany, “Optical scatter imaging with a digital micromirror device,” Opt. Express 17(22), 20401–20414 (2009). [CrossRef] [PubMed]

]. In the present study, the set up was modified by replacing the DMD with a reflective liquid crystal device (LCD, Holoeye Photonics, LC-R-2500). The laser illumination is at λ = 641.6nm and the sample is imaged with a 63X oil-immersion objective with numerical aperture (NA) = 1.4. The magnification at the image was 0.23 µm/CCD pixel. As described previously, the method consists of acquiring filtered dark-field images on the CCD (512 pixels x 512 pixels, Roper Scientific, Cascade 512B) while spatial filters corresponding to two-dimensional (2D) Gabor filters are displayed in Fourier space on the LCD. The signal in the dark-field images, which are collected after the transmitted light (or zeroth order of diffraction) is blocked, depends on the intensity of the light scattered by the object. In the present setup, CCD image acquisition is synchronized with the LCD display using a home-made graphical user interface programmed in Java.

In Fourier space, each Gabor filter consists of a center-shifted 2D Gaussian function located at spatial frequency f = (u, v) [11

11. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2(7), 1160–1169 (1985). [CrossRef] [PubMed]

]. In our studies, we set the standard deviation of the Gaussian to σf = 1/πS in the frequency domain, where S=1/u2+v2is the Gabor filter period in object space. This corresponds to setting the Gaussian envelope of the filter in the space domain to σs = S/2, which defines the spatial extent of the filter in object space. The location (u, v) may be described in terms of the polar and azimuthal scattering angles (θ, φ) with 1/S = sinθ/λ, and φ = arctan(v/u).

Calibration of the Fourier plane was achieved as in [9

9. R. M. Pasternack, Z. Qian, J.-Y. Zheng, D. N. Metaxas, and N. N. Boustany, “Highly sensitive size discrimination of sub-micron objects using optical Fourier processing based on two-dimensional Gabor filters,” Opt. Express 17(14), 12001–12012 (2009). [CrossRef] [PubMed]

], using the known positions of the diffraction orders of a grid of lines with 10 µm spacing. The calibration resulted in ∆f = 0.007 cycles/μm per LCD pixel. In the present studies we investigated sample structures along a fixed azimuth angle, φ = 0° or φ = 90°, and by varying the frequency location of the filters between fmin = 0.203 cycles/µm and fmax = 2.69 cycles/µm (356 filters). These high and low frequency limits correspond to Gabor period values of 0.37µm and 4.93µm, respectively. The frequency extent of the 0th order of diffraction corresponds to 0.196 cycles/μm and frequencies below 0.203 cycles/μm were not considered in our analysis. We note that centering Gabor filters on frequencies exceeding f = NA/λ = 2.18 cyc/μm results in displaying approximately 50% of the Gaussian on the LCD but still allows for significant signal collection. The 2D Gabor filters were implemented on the LCD as gray-scale 8-bit images with 1024x768 pixels. The filters were normalized by setting the Gaussian’s maximum amplitude to 255 on the 8-bit grayscale. Filtered dark field images were collected sequentially as the LCD cycled through the 356 Gabor filter bank (Fig. 1(a)
Fig. 1 (a) The object scattering pattern (colormap) is sequentially filtered by a set of Gabor filters (2D gray Gaussians) in Fourier space. (b) A dark-field image stack of the object is collected in which each filtered image corresponds to the application of a different Gabor filter in Fourier space. (c) and (d) The first analysis consisted of segmenting filtered sphere images and analyzing the signal from each whole sphere segment as a function of Gabor filter period. Data in (d) show the measured (red line) and simulated (blue line) signal for a 0.86µm diameter sphere segment, and Smax(segment), the Gabor period at which the maximum signal occurs. (e) and (f), the second analysis consisted of finding Smax, the optimum Gabor period resulting in maximum signal, at each pixel within the filtered image stack. A profile of Smax, is shown in (f) for a line of pixels taken across the center of a 0.11µm sphere within the Smax-encoded image shown in (e).
-1(b)) at each azimuth angle, φ. The current maximum rate of image collection is around 7 filtered frames per second. For each collected filtered image, a background image consisting of imaging mounting or immersion medium was also collected and subtracted from the sample’s image prior to further data processing.

2.2 Sample preparation

Poly(meyhyl-methacrylate) (PMMA, n = 1.49) spheres (Bangs Laboratories) or polystyrene (n = 1.59) spheres (Polysciences) were immersed in a water-based acrylamide gel (n~1.33) or suspended in immersion oil (Cargille Type B, n = 1.515). The acrylamide gel suspension was prepared by combining acrylamide premix (BioRad Laboratories), the sphere stock solution diluted to 10%, 1% ammonium persulfate (BioRad Laboratories) in deionized water, and 1% tetramethylelthylenediamine (TMED, BioRad Laboratories) in deionized water with the following proportions (V:V:V:V) 16 parts acrylamide gel: 3 parts spheres: 2 parts ammonium persulfate: 2 parts TMED. The diameter of the spheres were (in µm) 0.11, 0.41 0.71, 0.73, 1.08, 1.8 for the PMMA spheres, and 2.98µm for polystyrene. The mean sphere size is measured and provided by the manufacturer. The standard deviation of the sphere size distribution within a given batch is typically 5-10% for the PMMA spheres and 0.139μm (4.5%) for the 2.98μm polystyrene spheres.

The diatom sample was obtained from the “8-From Test Plate” diatom slide purchased from Klaus D. Kemp (Somerset, England). BAEC cells were obtained from Lonza-Clonetics. The cells were cultured and mounted for imaging as previously described [3

3. N. N. Boustany, R. Drezek, and N. V. Thakor, “Calcium-Induced Alterations in Mitochondrial Morphology Quantified in Situ with Optical Scatter Imaging,” Biophys. J. 83(3), 1691–1700 (2002). [CrossRef] [PubMed]

].

3. Results and discussion

3.1 On the linear relationship between Smax and the size of isolated objects

In our first analysis, we considered the image total signal (sum of intensity values) from each single sphere by individually segmenting the spheres in each filtered image within the collected image stack, and calculating the signal (sum of intensity values) in the segment containing the whole area of the sphere (Fig. 1(c) and 1(d)). We used 10 pixels × 10 pixels segments for spheres with diameter 0.11, 0.41, 0.71 or 0.73 µm; 15 pixels × 15 pixels segment for spheres with diameter 1.08 or 1.8µm and 20 pixels × 20 pixels segment for the 2.98µm spheres. The segments sizes were varied so as to include the whole area of each sphere. The total intensity signal per sphere segment measured in the image was plotted as a function of Gabor filter period for each of the 356 Gabor filters applied on the LCD at orientation φ = 0 (Fig. 1(d) red line). The Gabor filter period corresponding to the segment’s maximum intensity response, (Smax(segment)) was then plotted against sphere diameter for the different immersion conditions (Fig. 2
Fig. 2 Gabor filter period Smax(segment) giving maximum signal plotted against sphere diameter. The signal was measured within image segments encompassing a whole sphere. Experimental data for spheres suspended in an aqueous gel (filled black circles) or immersion oil (filled red circles) are shown along with theoretical predictions based on Mie theory (connected open black and red circles for suspensions in gel and oil respectively). The solid red and black lines are linear fits to the experimental data and have a slope of 2.23. Experimental data are mean +/− standard deviation for measurements from 10 isolated sphere segments. Simulated data from a cube with its side oriented perpendicular to the incident field are also shown (connected green open squares).
, black and red filled circles). A linear fit to the data yielded a slope of 2.23 for spheres immersed in either water-based gel or immersion oil. Thus, the optimum Gabor filter period appears to approximate twice the sphere size. The linear relationship between Smax(segment) and sphere diameter was conserved over a diameter range from 0.1 µm to 2µm.

To find out if this linear relationship between Smax(segment) and sphere diameter could be predicted from scatter theory, we used Mie theory to generate the 2D scattering intensity as a function of (θ, φ) for each sphere size. We used the open-source code MieTab (Prof. August Miller, New Mexico State University) to simulate the intensity scattering patterns of transparent spheres with diameters ranging from 0.08µm to 3.5µm and index of refraction n1 = 1.48. Two immersion mediums n0 = 1.33 (water) or n0 = 1.515 (oil) were assumed. We also assumed the use of an objective with NA = 1.4, and unpolarized illumination with wavelength λ = 0.638µm. This NA and wavelength correspond to a maximum frequency fmax = 2.19 cycles/µm which limits the scattering angle to 67° for spheres suspended in oil and 90° for spheres suspended in water. The scattering angles (θ, φ) were converted to frequency position (u,v) in Fourier space with 1/u2+v2 = sinθ/λ, and φ = arctan(v/u) and a scattering functionO(u,v) was obtained. The filtered scattered response Ri was taken as the product of O(u,v) with each Gabor filterGi(u,v) with period Si for i = 1:N; N is the number of filters:

Ri=|uvO(u,v)Gi(u,v)|
(1)

The simulated Gabor filters were centered on the same 356 frequencies as those used experimentally. The simulated response Ri at each filter period (Fig. 1(d) blue line) corresponds to the predicted total filtered intensity which would be measured experimentally within a sphere segment as a function of Gabor filter period. Thus, to compare the simulation results with the experimental data, the Gabor period corresponding to the maximum of {Ri = 1:N} was taken as the predicted Smax(segment) (e.g. filter period that corresponds to the maximum of the blue simulated curve, Fig. 1(d)).

As found experimentally, the simulations showed a linear relationship between Smax(segment) and sphere diameter (Fig. 2, connected open red and black circles). A comparison by calculating the root mean squared (rms) error shows an agreement of 93% between simulated and experimental data values. A linear fit to the simulated data resulted in a slope of 2.23 as found in the experiment. This linearity is conserved for sphere diameters ranging between 0.1 and 3.5µm for simulated data. As expected, the lower limit of this range is set by the numerical aperture of the system. For spheres with diameter below 0.1µm, the scattering intensity patterns collected within the angular range of the setup become similar and the response to varying Gabor filter periods become indistinguishable. The upper diameter limit in the experimental data was reached at 2µm and agrees with the frequency extent of the blocked zeroth order which was 0.196 cycles/μm (corresponding to a period of 5.1μm). The zeroth order block was not accounted for in the simulations which did not result in an upper limit on the simulated linear range. To evaluate the effect of object shape we also performed simulations for a cube with one side oriented perpendicular to the incident field and whose scattering function was numerically calculated using a finite- difference time-domain (FDTD) simulation (Rsoft Design Group, Ossining, NY). The cube width was varied from 0.11µm to 3.5µm. The cube’s index of refraction was n1 = 1.48 and the immersion medium’s index was n0 = 1.515 (oil). We found that even in this case the linear relationship with slope of 2.23 is preserved between Smax and cube size (Fig. 2 connected green open squares).

3.2 Spatial distribution of Smax across the imaged sample

The experimental results from isolated spheres and simulations strongly suggest that the Gabor filter responses are selectively sensitive to object size and do not vary significantly with refractive index changes or object shape. Nonetheless most biological samples in which we propose to apply this method, do not consist of single isolated particles and cannot be arbitrarily segmented for signal analysis. Thus, to investigate the ability of our method to provide size distribution across the sample’s spatial extent, we analyzed the Gabor filter responses on a pixel-by-pixel basis at imaging resolution. In this case, the Gabor filter period, Smax, yielding maximum signal was found at each pixel within the stack of filtered images. A two-dimensional map encoding the spatial distribution of Smax values across the sample is then generated (Fig. 1(e)). The size maps for the spheres with diameter 0.71µm and 0.73µm show that the pixel histograms of the Smax maps are clearly distinguishable even for these sphere samples whose diameters differ by only 20nm (Fig. 3
Fig. 3 (a): Size-encoded images of two samples of PMMA spheres with 0.71µm and 0.73µm diameter suspended in gel. At each pixel, the color scale encodes Smax, the Gabor filter period giving maximum signal. For clarity only a limited field of view ~36µm × 36µm (156pixels × 156pixels) is shown. (b): Pixel histograms of the size-encoded images of the two sphere samples.
). The full-width-at-half-maximum (FWHM) of the main peak in each of the two distributions reflects the error in our measurement of Smax associated with each mean sphere diameter, and is 17.7nm and 19.7nm for 0.71µm and 0.73µm, respectively.

The main peaks of the two histograms occur at Smax value which are within 6% of the value of [2.23 × (diameter)], and are therefore in very good agreement with the linear relationship measured in Fig. 2. As can be seen in Fig. 3, there can be a significant number of pixels that may fall outside the main peak. According to the manufacturer, the standard deviation of the bead size distributions in these samples is typically 5-10% of the mean size. Thus, most of the measured Smax values are well within the expected sphere size distribution. Pixels with very large Smax values outside the expected standard deviation may be the result of sample inhomogeneities where some spheres formed small clumps of varying widths and shapes that were not well dissociated during sample preparation.

Since the Gabor filters’ Gaussian envelope’s standard deviation, σs, depends on the filter period S, the filters are scaled versions of each other. Thus the relationship between an object’s size and best-matching filter period is the same as that between a scaled version of the object and another “scaled” filter’s period. One would expect that this should also preserve the resolution of our Smax encoded images, since small details in the object will respond strongly to high frequency filters which will have a large Gaussian standard deviation in Fourier space (and a small standard deviation in image space). To determine the resolution of our Smax encoded maps, we measured the point spread function obtained from an Smax map of the 0.11µm spheres (Fig. 1(e)). We found that the FWHM of the signal profile across the center of the sphere’s encoded image was approximately 1.5 pixels (half of 3 pixels wide) and corresponds to an image resolution of 0.345μm. While we have kept σs = S/2 in our experiments, decreasing σs could result in greater spatial resolution albeit at the expense of sensitivity to size. The ratio σs/S may be varied . However the filters remain confined in both object and Fourier space due to their Gaussian envelope, and in this way achieve maximal combined space-frequency resolution as noted previously [11

11. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2(7), 1160–1169 (1985). [CrossRef] [PubMed]

]. Thus, the product (σs × σf)2 = 1/4π2 is minimized, where σs and σf are the standard deviations of the Gabor filter’s Gaussian envelopes in the object space and frequency space, respectively.

The size maps and associated pixel histograms obtained from the sphere samples suggest that the morphology of an object may be depicted by mapping out the sizes of its sub-structures, and that differences on the order of 20nm between structures can be detected. The pixel histogram of the size-encoded maps therefore directly provides a highly resolved “size spectrum” of the object. To investigate how this technique will apply to more heterogeneous sample, we collected data from diatoms using the same bank of Gabor filter periods as those used for the spheres. In this case, we collected data at orientations φ = 0° and φ = 90°. Size maps of the diatom were obtained as described above by processing the data separately at each of the two orientations. Figure 4
Fig. 4 Size-encoded images of pleurosigma angulatum diatom and associated pixel histograms shown for Gabor filter orientations at φ = 0 (left panels) and φ = 90° (right panels). The colorscale in the images encodes Smax, the Gabor filter period resulting in maximum signal at each pixel. The inset in the top right panels depicts the expected arrangement of the holes in the diatom’s frustule. For clarity, histograms show only the pixels values below 0.7µm.
shows results for a Pleurosigma Angulatum diatom.

One of the main characteristics of this diatom species is an array of hexagonally arranged holes. The holes themselves are ~0.4µm in diameter while the center-to-center spacing between the holes is 0.65µm (Fig. 4(a) inset, and [12

12. D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, New York) (2001).

]). The spacing between two vertically oriented lines of holes is 0.56µm and the distance between two hole edges is ~0.25μm. When the Gabor filters are oriented horizontally (φ = 0), the pixel histogram shows a large peak at 0.56 µm with a FWHM of 0.020µm that is in good agreement with the expected 0.56 µm spacing between the vertical lines of holes. However, it is not currently possible to assess whether our filters are sensing the period of the lines or the space between two hole edges which would also result in an Smax value of 0.56 (0.25*2.23, based on the relationship between object size and Gabor period in Fig. 2). We observed additional structures including significant peaks at Smax = 0.40µm and 0.50μm at φ = 0, and Smax = 0.47µm and 0.50μm at φ = 90°. These peaks could reflect on the slight variations between hole or line spacing across different regions of the frustule. The peak at 0.4 (φ = 0) corresponds largely to structures within the horizontal midline of the frustule. The map at φ = 90° also contained a dominant peak at 1.57µm (dark red regions in the image not included in the histogram shown), which was absent at φ = 0. This peak corresponds to pixels located at the boundaries of the frustule and the horizontal pattern along the internal structure of the diatom. Based on the sphere data, we would expect the diameter of an isolated single hole to be best matched by a Gabor period of 0.4 × 2.23 = 0.89µm. Peaks at this value are absent in the histograms indicating that periodic features and potentially spacing between features, rather than single isolated features, are the main contributors to the angular scattering pattern in samples with regularly spaced structures. Still, this also implies that the data obtained from the size maps presented here will require careful interpretation. While the Gabor filtering methodology provides high sensitivity to variations in sample texture, it does not rely on the actual visualization of the sample. In this context, the advantage of the method lies in the ability to detect changes on the order of tens of nanometers in the dimension of the measured features. This sensitivity to object size is borne out by the quality factor of the main peaks which are on the order of 20nm in width in the diatom’s size histograms.

One of the drawbacks of the method presented here is the requirement to collect a large number of filtered images in order to achieve high sensitivity to changes in object size, or high resolution “size spectra”. For biological samples such as living cells, which consist of many structures with a broad distribution of sizes [13

13. J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. 30(18), 2442–2444 (2005). [CrossRef] [PubMed]

], it could be justifiable to collect a limited number of filtered images in selected size ranges of interest. This would be advantageous for time-lapse studies with the goal of tracking dynamic changes. We used this approach to measure intracellular dynamics in Bovine Aortic Endothelial cells (BAEC) in culture. The parameters for the Gabor filters in this experiment consisted of 13 filter periods (in µm) S = [0.30, 0.32, 0.35, 0.39, 0.43, 0.49, 0.56, 0.66, 0.79, 0.99, 1.18, 1.35, 1.62] repeated at orientations φ = 0° to φ = 330° in 30° increments. The whole set of filtered images was collected for 69 time points with 10 sec. between each set. Each set of filtered images took approximately 1.5min. to be collected. The signal was summed at all orientations before obtaining Smax, the Gabor filter period giving maximum signal, at each pixel. Size maps encoding the spatial distribution of Smax across the sample were obtained at different time points for single cells. A representative cell which migrated during imaging is shown in Fig. 5
Fig. 5 (a) Size-encoded images of an endothelial cell at different time-points during migration on a glass coverslip under normal growth conditions. At each pixel, the colorscale encodes the Gabor filter period Smax which maximizes the filtered image signal. Only 13 selected Gabor filter periods were used. (b) Average pixel value within the cell region plotted as a function of time.
. The images showed a period of decreased subcellular feature size between 45min and 80min. The onset of this fluctuation was relatively sudden and was synchronized with the migration of the cell on the substrate. The data suggest that the size maps obtained with the Gabor filtering method are able to capture cellular structural dynamics and provide time-varying morphological phenotypes that could ultimately be utilized to study dynamic cellular function.

4. Conclusion

Acknowledgments

This work was supported by the National Science Foundation grant DBI-0852857 to NNB. We thank Robert M. Pasternack for his contributions to the optical setup.

References and links

1.

M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, and B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys. 8(30), 3486–3495 (2006). [CrossRef] [PubMed]

2.

H. Fang, M. Ollero, E. Virkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 9(2), 267–276 (2003). [CrossRef]

3.

N. N. Boustany, R. Drezek, and N. V. Thakor, “Calcium-Induced Alterations in Mitochondrial Morphology Quantified in Situ with Optical Scatter Imaging,” Biophys. J. 83(3), 1691–1700 (2002). [CrossRef] [PubMed]

4.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A. 104(44), 17255–17260 (2007). [CrossRef] [PubMed]

5.

C. S. Mulvey, A. L. Curtis, S. K. Singh, and I. J. Bigio, “Elastic scattering spectroscopy as a diagnostic tool for apoptosis in cell cultures,” IEEE J. Sel. Top. Quantum Electron. 13(6), 1663–1670 (2007). [CrossRef]

6.

W. J. Cottrell, J. D. Wilson, and T. H. Foster, “Microscope enabling multimodality imaging, angle-resolved scattering, and scattering spectroscopy,” Opt. Lett. 32(16), 2348–2350 (2007). [CrossRef] [PubMed]

7.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res. 69(3), 1199–1204 (2009). [CrossRef] [PubMed]

8.

H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A. 105(51), 20118–20123 (2008). [CrossRef] [PubMed]

9.

R. M. Pasternack, Z. Qian, J.-Y. Zheng, D. N. Metaxas, and N. N. Boustany, “Highly sensitive size discrimination of sub-micron objects using optical Fourier processing based on two-dimensional Gabor filters,” Opt. Express 17(14), 12001–12012 (2009). [CrossRef] [PubMed]

10.

J.-Y. Zheng, R. M. Pasternack, and N. N. Boustany, “Optical scatter imaging with a digital micromirror device,” Opt. Express 17(22), 20401–20414 (2009). [CrossRef] [PubMed]

11.

J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2(7), 1160–1169 (1985). [CrossRef] [PubMed]

12.

D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging (Wiley, New York) (2001).

13.

J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett. 30(18), 2442–2444 (2005). [CrossRef] [PubMed]

OCIS Codes
(070.4790) Fourier optics and signal processing : Spectrum analysis
(170.1420) Medical optics and biotechnology : Biology
(170.1530) Medical optics and biotechnology : Cell analysis
(290.5820) Scattering : Scattering measurements
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Image Processing

History
Original Manuscript: October 9, 2012
Manuscript Accepted: November 12, 2012
Published: December 10, 2012

Virtual Issues
Vol. 8, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Heidy Sierra, Jing-Yi Zheng, Bryan Rabin, and Nada N. Boustany, "Measurement of object structure from size-encoded images generated by optically-implemented Gabor filters," Opt. Express 20, 28698-28706 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-27-28698


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References

  1. M. A. van Dijk, A. L. Tchebotareva, M. Orrit, M. Lippitz, S. Berciaud, D. Lasne, L. Cognet, and B. Lounis, “Absorption and scattering microscopy of single metal nanoparticles,” Phys. Chem. Chem. Phys.8(30), 3486–3495 (2006). [CrossRef] [PubMed]
  2. H. Fang, M. Ollero, E. Virkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, “Noninvasive sizing of subcellular organelles with light scattering spectroscopy,” IEEE J. Sel. Top. Quantum Electron.9(2), 267–276 (2003). [CrossRef]
  3. N. N. Boustany, R. Drezek, and N. V. Thakor, “Calcium-Induced Alterations in Mitochondrial Morphology Quantified in Situ with Optical Scatter Imaging,” Biophys. J.83(3), 1691–1700 (2002). [CrossRef] [PubMed]
  4. I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci. U.S.A.104(44), 17255–17260 (2007). [CrossRef] [PubMed]
  5. C. S. Mulvey, A. L. Curtis, S. K. Singh, and I. J. Bigio, “Elastic scattering spectroscopy as a diagnostic tool for apoptosis in cell cultures,” IEEE J. Sel. Top. Quantum Electron.13(6), 1663–1670 (2007). [CrossRef]
  6. W. J. Cottrell, J. D. Wilson, and T. H. Foster, “Microscope enabling multimodality imaging, angle-resolved scattering, and scattering spectroscopy,” Opt. Lett.32(16), 2348–2350 (2007). [CrossRef] [PubMed]
  7. K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69(3), 1199–1204 (2009). [CrossRef] [PubMed]
  8. H. Subramanian, P. Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells,” Proc. Natl. Acad. Sci. U.S.A.105(51), 20118–20123 (2008). [CrossRef] [PubMed]
  9. R. M. Pasternack, Z. Qian, J.-Y. Zheng, D. N. Metaxas, and N. N. Boustany, “Highly sensitive size discrimination of sub-micron objects using optical Fourier processing based on two-dimensional Gabor filters,” Opt. Express17(14), 12001–12012 (2009). [CrossRef] [PubMed]
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