Publications by authors named "Nathan Hagen"

35 Publications

Minimizing scattering-induced phase errors in differential interference contrast microscopy.

J Biomed Opt 2020 12;25(12)

Utsunomiya University, Department of Optical Engineering, Tochigi, Japan.

Significance: Differential interference contrast (DIC) microscopes allow noninvasive in vivo observation of transparent microstructures in tissue without the use of fluorescent dyes or genetic modification. We show how to modify a DIC microscope to measure the sample phase distribution accurately and in real-time even deep inside sample tissue.

Aim: Our aim is to improve the DIC microscope's phase measurement to remove the phase bias that occurs in the presence of strong scattering.

Approach: A quarter-wave plate was added in front of the polarization camera, allowing a modified phase calculation to incorporate all four polarization orientation angles (0 deg, 45 deg, 90 deg, and 135 deg) captured simultaneously by the polarization camera, followed by deconvolution.

Results: We confirm that the proposed method reduces phase measurement error in the presence of scattering and demonstrate the method using in vivo imaging of a beating heart inside a medaka egg and the whole-body blood circulation in a young medaka fish.

Conclusions: Modifying a polarization-camera DIC microscope with a quarter-wave plate allows users to image deep inside samples without phase bias due to scattering effects.
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http://dx.doi.org/10.1117/1.JBO.25.12.123703DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7734411PMC
December 2020

Dynamic calibration for enhancing the stability of a channeled spectropolarimeter.

Appl Opt 2020 Oct;59(30):9424-9433

Channeled spectropolarimeters are optical instruments that measure the spectral dependence of the polarization of light without any mechanically moving parts. An important factor in achieving stable and accurate measurements is the calibration process, especially in dynamic environments where temperature fluctuations or other factors affect the retardance of the components in the polarimeter. In previous research, a self-calibration algorithm that accounts for these variations was developed, without any additional reference measurements. In this paper, we identify an ambiguity in the self-calibration phase, which limits the allowed temperature changes to surprisingly small ranges. We show how to adaptively estimate and correct for the phase ambiguity using a polynomial curve-fitting algorithm, extending the temperature range to virtually all practical scenarios. Lastly, we demonstrate the ability of the modified self-calibration algorithm to provide stable reconstruction of the Stokes vector for a temperature range >40, using an experimental channeled spectropolarimeter.
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http://dx.doi.org/10.1364/AO.409054DOI Listing
October 2020

Compensating for nonlinear dispersion in channeled spectropolarimetry.

Appl Opt 2020 Jun;59(16):5032-5040

All common waveplate materials exhibit nonlinear dispersion of retardance, producing an unwanted chirp in the interference fringes that channeled spectropolarimeters use for heterodyning polarization data. After showing how to quantify this nonlinearity, we survey the common waveplate materials and find that MgF has significantly lower nonlinearity than any other available material. We also quantify the degree of crosstalk caused by dispersion nonlinearity and show that, unlike in linear dispersion, the degree of crosstalk depends on the sequence of how the phase calibration is implemented. Regardless of how the calibrated phases have been obtained, shifting each channel to baseband prior to windowing minimizes crosstalk error.
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http://dx.doi.org/10.1364/AO.388473DOI Listing
June 2020

Single shot 3D profilometry by polarization pattern projection.

Appl Opt 2020 Feb;59(6):1654-1659

We demonstrate a uniaxial 3D profilometry system illuminating the sample with a linear polarization pattern and measuring a polarization camera. The linear polarization pattern is generated by a spatial light modulator and a quarter-wave plate in the optical system. The system can measure four different fringe patterns with a phase difference of 90 deg simultaneously in the polarization camera. Therefore, we can measure three-dimensional shapes in a single shot. We present the measurement principles of the system and show the results of a real-time 3D profilometry experiment.
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http://dx.doi.org/10.1364/AO.382690DOI Listing
February 2020

Alignment precision of polarization components.

Appl Opt 2019 Dec;58(36):9750-9756

Recent research publications in the polarization literature have discussed methods of correcting for azimuthal alignment errors of optical elements in postprocessing. However, we show that high angular precision is not difficult to achieve during system alignment, so that postprocessing correction should be unnecessary. We estimate the alignment precision achievable for linear polarizers and waveplates in polarization systems. This shows that using an optical signal model for alignment allows a precision limited by the quality of the optics and detectors rather than the quality of the mechanics, rendering millidegree alignment precision possible with ordinary rotational mounts.
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http://dx.doi.org/10.1364/AO.58.009750DOI Listing
December 2019

Angularly selective microstructured surface for tuning seasonal sunlight interaction.

Opt Express 2019 Dec;27(25):36426-36437

In the temperate latitudes, high-reflectivity exterior surfaces save energy spent on ventilation and cooling during summer, but cost energy on heating in winter. Angularly selective surfaces that adjust their reflectivities by sun position allow beneficial effects in both seasons - high reflectivity in summer and high absorption in winter. Here we show how a planar microstructured surface can produce such an angularly selective behavior and estimate its energy efficiency under direct solar irradiance at 35° N. Results show that such an ideal angularly selective surface has the potential to improve efficiency by up to 43.2% compared to a conventional concrete surface. Numerical results for an aluminum one-dimensional periodic structure indicate that it achieves a 25.7% improvement of efficiency. Finally, we validate the designed structure by measuring the reflectivity of the fabricated surface at a series of angles.
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http://dx.doi.org/10.1364/OE.27.036426DOI Listing
December 2019

Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters.

Appl Opt 2019 Jul;58(21):5644-5649

We present a new real-time Stokes parameter measurement technique using three polarized beam splitters without mechanical motion or electrical tuning. This system can analyze the polarization state of light at 30 kHz, limited only by the speed of the detector analog to digital converters. The optical system is also compact (52×30×25  mm) because it consists only of small volume optical devices. We show that the system can measure arbitrary polarization states with an accuracy of better than 0.006 in the normalized Stokes parameters. We also demonstrate the ability to measure fast dynamic polarization states by analyzing the state produced by a fast rotating quarter-wave plate and the time-dependent stress induced in a PMMA block by hitting the block with a hammer.
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http://dx.doi.org/10.1364/AO.58.005644DOI Listing
July 2019

Quantitative discrimination of biological tissues by micro-elastographic measurement using an epi-illumination Mueller matrix microscope.

Biomed Opt Express 2019 Aug 9;10(8):3847-3859. Epub 2019 Jul 9.

Graduate School of Engineering, Utsunomiya University, Utsunomiya, Tochigi, 321-8585, Japan.

We propose a method for estimating the stiffness of bio-specimens by measuring their linear retardance properties under applied stress. For this purpose, we employ an epi-illumination Mueller matrix microscope and show the procedures for its calibration. We provide experimental results demonstrating how to apply Mueller matrix data to elastography, using chicken liver and chicken heart as biological samples. Finally, we show how the histograms of linear retardance images can be used to distinguish between specimens and quantify the discrimination accuracy.
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http://dx.doi.org/10.1364/BOE.10.003847DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6701520PMC
August 2019

Erratum: Video-rate quantitative phase analysis by a DIC microscope using a polarization camera: errata.

Biomed Opt Express 2019 06 23;10(6):2967-2968. Epub 2019 May 23.

Department of Optical Engineering, Utsunomiya University, 7-1-2 Yoto, Utsunomiya, Tochigi, Japan.

[This corrects the article on p. 1273 in vol. 10, PMID: 30891345.].
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http://dx.doi.org/10.1364/BOE.10.002967DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6583344PMC
June 2019

Video-rate quantitative phase analysis by a DIC microscope using a polarization camera.

Biomed Opt Express 2019 Mar 19;10(3):1273-1281. Epub 2019 Feb 19.

Department of Optical Engineering, Utsunomiya University, 7-1-2 Yoto, Utsunomiya, Tochigi, Japan.

This paper describes how to take advantage of the replacement of an intensity camera with a polarization camera in a standard differential interference contrast (DIC) microscope. Using a polarization camera enables snapshot quantitative phase analysis so that real-time imaging of living transparent tissues become possible. Using our method, we quantify the phase measurement accuracy using a phantom consisting of glass beads embedded in lacquer. In order to demonstrate these advantages, we image the pumping heart and blood flow in a living egg.
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http://dx.doi.org/10.1364/BOE.10.001273DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6420286PMC
March 2019

Robust full Stokes imaging polarimeter with dynamic calibration.

Opt Lett 2019 Feb;44(4):891-894

We present a full Stokes imaging polarimeter using a rotating retarder in combination with a polarization camera-a detector array on which a pixelated polarizer array is attached. By itself, a polarization camera cannot capture the full Stokes parameters, but we add a rotating retarder in front and show how it can be used to provide full Stokes images. In addition, we demonstrate the advantage that it can be recalibrated dynamically while taking measurements, allowing accurate measurements even in environments where the retardance in changing.
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http://dx.doi.org/10.1364/OL.44.000891DOI Listing
February 2019

Stokes polarimeter performance: general noise model and analysis: erratum.

Appl Opt 2018 08;57(24):6998

We correct two errors in Appl. Opt.57, 4283 (2018)APOPAI0003-693510.1364/AO.57.004283.
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http://dx.doi.org/10.1364/AO.57.006998DOI Listing
August 2018

Statistics of normalized Stokes polarization parameters.

Authors:
Nathan Hagen

Appl Opt 2018 Jul;57(19):5356-5363

The normalized Stokes parameters are formed from the ratio of the polarization components to the intensity component of light. Such ratio distributions are known to have an undefined mean and variance, and yet researchers in the polarization community work with these normalized parameters all the time. We show that while in theory the normalized parameters have a pathological probability density, in practice they are quite well-behaved. We provide expressions for their approximate densities and confirm the results with laboratory measurements.
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http://dx.doi.org/10.1364/AO.57.005356DOI Listing
July 2018

Stokes polarimeter performance: general noise model and analysis.

Appl Opt 2018 May;57(15):4283-4296

We calculate the photometric Stokes parameter covariance matrices and SNRs estimated by polarimeters exposed to general noise distributions, such as mixed Poisson-Gaussian (PG) noise. The measurement model includes the effects of optical losses and detector quantum efficiency, enabling quantitative comparison of instruments that have different photometric efficiencies. We demonstrate this capability by comparing the performance of many common polarimeter configurations, including diattenuator-based systems, such as Azzam's four-detector polarimeter [Opt. Lett.10, 309 (1985)OPLEDP0146-959210.1364/OL.10.000309] and Kudenov's stacked photovoltaic polarimeter [Opt. Express24, 14737 (2016)OPEXFF1094-408710.1364/OE.24.014737]. Working with the full covariance matrix under mixed PG noise, we also show that instruments optimized under assumptions of Gaussian noise simultaneously exhibit optimal behavior under Poisson noise.
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http://dx.doi.org/10.1364/AO.57.004283DOI Listing
May 2018

Hyperspectral optical tomography of intrinsic signals in the rat cortex.

Neurophotonics 2015 Oct 12;2(4):045003. Epub 2015 Nov 12.

University of California, Irvine, Beckman Laser Institute and Medical Clinic, Laser Microbeam and Medical Program, 1002 Health Sciences Road, Irvine, California 92612, United States; University of California, Irvine, Department of Biomedical Engineering, 5200 Engineering Hall, Irvine, California 92697, United States.

We introduce a tomographic approach for three-dimensional imaging of evoked hemodynamic activity, using broadband illumination and diffuse optical tomography (DOT) image reconstruction. Changes in diffuse reflectance in the rat somatosensory cortex due to stimulation of a single whisker were imaged at a frame rate of 5 Hz using a hyperspectral image mapping spectrometer. In each frame, images in 38 wavelength bands from 484 to 652 nm were acquired simultaneously. For data analysis, we developed a hyperspectral DOT algorithm that used the Rytov approximation to quantify changes in tissue concentration of oxyhemoglobin ([Formula: see text]) and deoxyhemoglobin (ctHb) in three dimensions. Using this algorithm, the maximum changes in [Formula: see text] and ctHb were found to occur at [Formula: see text] and [Formula: see text] beneath the surface of the cortex, respectively. Rytov tomographic reconstructions revealed maximal spatially localized increases and decreases in [Formula: see text] and ctHb of [Formula: see text] and [Formula: see text], respectively, with these maximum changes occurring at [Formula: see text] poststimulus. The localized optical signals from the Rytov approximation were greater than those from modified Beer-Lambert, likely due in part to the inability of planar reflectance to account for partial volume effects.
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http://dx.doi.org/10.1117/1.NPh.2.4.045003DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4718192PMC
October 2015

Quantitative sectioning and noise analysis for structured illumination microscopy: erratum.

Opt Express 2015 Oct;23(21):27633-4

We correct an error in the original manuscript, where an unrecognized assumption was made about the relationship between the out-of-focus light and the in-focus light. We summarize the condition under which the assumption may still hold, and mention alternative methods researchers can use to obtain accurate quantitative sectioning.
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http://dx.doi.org/10.1364/OE.23.027633DOI Listing
October 2015

Wide-field compact catadioptric telescope spanning 0.7-14 μm wavelengths.

Appl Opt 2013 Jun;52(18):4334-42

Department of Electrical and Computer Engineering and Fitzpatrick Institute for Photonics, Duke University, Durham, North Carolina 27708, USA.

We present a wide-field compact f-1.2, f-1.6 effective illumination catadioptric telescope that spans the wavelengths 0.7-14.0 μm. Such a telescope replaces several telescopes designed for different infrared bands, while having a track length shorter than most single-band telescopes. Incorporated with a suitable multiband focal plane array, many wavelength bands may be imaged simultaneously in the same instrument. We have constructed and tested prototypes of the telescopes and found the performance is near the predicted values.
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http://dx.doi.org/10.1364/AO.52.004334DOI Listing
June 2013

Image mapping spectrometry: calibration and characterization.

Opt Eng 2012 Nov;51(11)

Rice University Department of Bioengineering 6100 Main Street Houston, Texas 77005.

Image mapping spectrometry (IMS) is a hyperspectral imaging technique that simultaneously captures spatial and spectral information about an object in real-time. We present a new calibration procedure for the IMS as well as the first detailed evaluation of system performance. We correlate optical components and device calibration to performance metrics such as light throughput, scattered light, distortion, spectral image coregistration, and spatial/spectral resolution. Spectral sensitivity and motion artifacts are also evaluated with a dynamic biological experiment. The presented methodology of evaluation is useful in assessment of a variety of hyperspectral and multi-spectral modalities. Results are important to any potential users/developers of an IMS instrument and to anyone who may wish to compare the IMS to other imaging spectrometers.
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http://dx.doi.org/10.1117/1.OE.51.11.111711DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3433068PMC
November 2012

Snapshot advantage: a review of the light collection improvement for parallel high-dimensional measurement systems.

Opt Eng 2012 Jun;51(11)

Rice University, Bioengineering Department, 6500 Main Street, Houston, Texas 77005.

The snapshot advantage is a large increase in light collection efficiency available to high-dimensional measurement systems that avoid filtering and scanning. After discussing this advantage in the context of imaging spectrometry, where the greatest effort towards developing snapshot systems has been made, we describe the types of measurements where it is applicable. We then generalize it to the larger context of high-dimensional measurements, where the advantage increases geometrically with measurement dimensionality.
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http://dx.doi.org/10.1117/1.OE.51.11.111702DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3393130PMC
June 2012

Snapshot imaging Mueller matrix polarimeter using polarization gratings.

Opt Lett 2012 Apr;37(8):1367-9

College of Optical Science, The University of Arizona, 1630 E. University Boulevard, Tucson, Arizona 85721, USA.

A snapshot imaging Mueller matrix polarimeter (SIMMP) is theoretically described and empirically demonstrated through simulation. Spatial polarization fringes are localized onto a sample by incorporating polarization gratings (PGs) into a polarization generator module. These fringes modulate the Mueller matrix (MM) components of the sample, which are subsequently isolated with PGs in an analyzer module. The MM components are amplitude modulated onto spatial carrier frequencies which, due to the PGs, maintain high visibility in spectrally broadband illumination. An interference model of the SIMMP is provided, followed by methods of reconstruction and calibration. Lastly, a numerical simulation is used to demonstrate the system's performance in the presence of noise.
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http://dx.doi.org/10.1364/OL.37.001367DOI Listing
April 2012

Foveated endoscopic lens.

J Biomed Opt 2012 Feb;17(2):021104

Rice University, Department of Bioengineering, Houston, Texas 77005, USA.

We present a foveated miniature endoscopic lens implemented by amplifying the optical distortion of the lens. The resulting system provides a high-resolution region in the central field of view and low resolution in the outer fields, such that a standard imaging fiber bundle can provide both the high resolution needed to determine tissue health and the wide field of view needed to determine the location within the inspected organ. Our proof of concept device achieves 7 ≈ 8 μm resolution in the fovea and an overall field of view of 4.6 mm. Example images and videos show the foveated lens' capabilities.
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http://dx.doi.org/10.1117/1.JBO.17.2.021104DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3380820PMC
February 2012

Compound prism design principles, III: linear-in-wavenumber and optical coherence tomography prisms.

Appl Opt 2011 Sep;50(25):5023-5030

Department of Bioengineering, Rice University, Houston Texas 77005, USA.

We extend the work of the first two papers in this series [Appl. Opt. 50, 4998-5011 (2011), Appl. Opt. 50, 5012-5022 (2011)] to design compound prisms for linear-in-wavenumber dispersion, especially for application in spectral domain optical coherence tomography (OCT). These dispersive prism designs are believed to be the first to meet the requirements of high resolution OCT systems in direct-view geometry, where they can be used to shrink system size, to improve light throughput, to reduce stray light, and to reduce errors resulting from interpolating between wavelength- and wavenumber-sampled domains. We show prism designs that can be used for thermal sources or for wideband superluminescent diodes centered around wavelengths 850, 900, 1300, and 1375 nm.
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http://dx.doi.org/10.1364/AO.50.005023DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3302657PMC
September 2011

Compound prism design principles, II: triplet and Janssen prisms.

Appl Opt 2011 Sep;50(25):5012-5022

Department of Bioengineering, Rice University, Houston Texas 77005, USA.

Continuing the work of the first paper in this series [Appl. Opt. 50, 4998-5011 (2011)], we extend our design methods to compound prisms composed of three independent elements. The increased degrees of freedom of these asymmetric prisms allow designers to achieve greatly improved dispersion linearity. They also, however, require a more careful tailoring of the merit function to achieve design targets, and so we present several new operands for manipulating the compound prisms' design algorithm. We show that with asymmetric triplet prisms, one can linearize the angular dispersion such that the spectral sampling rate varies by no more than 4% across the entire visible spectral range. Doing this, however, requires large prisms and causes beam compression. By adding a beam compression penalty to the merit function, we show that one can compromise between dispersion linearity and beam compression in order to produce practical systems. For prisms that do not deviate the beam, we show that Janssen prisms provide a form that maintains the degrees of freedom of the triplet and that are capable of up to 32° of dispersion across the visible spectral range. Finally, in order to showcase some of the design flexibility of three-element prisms, we also show how to design for higher-order spectral dispersion to create a two-dimensional spectrum.
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http://dx.doi.org/10.1364/AO.50.005012DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3302658PMC
September 2011

Compound prism design principles, I.

Appl Opt 2011 Sep;50(25):4998-5011

Department of Bioengineering, Rice University, Houston, Texas 77005, USA.

Prisms have been needlessly neglected as components used in modern optical design. In optical throughput, stray light, flexibility, and in their ability to be used in direct-view geometry, they excel over gratings. Here we show that even their well-known weak dispersion relative to gratings has been overrated by designing doublet and double Amici direct-vision compound prisms that have 14° and 23° of dispersion across the visible spectrum, equivalent to 800 and 1300 lines/mm gratings. By taking advantage of the multiple degrees of freedom available in a compound prism design, we also show prisms whose angular dispersion shows improved linearity in wavelength. In order to achieve these designs, we exploit the well-behaved nature of prism design space to write customized algorithms that optimize directly in the nonlinear design space. Using these algorithms, we showcase a number of prism designs that illustrate a performance and flexibility that goes beyond what has often been considered possible with prisms.
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http://dx.doi.org/10.1364/AO.50.004998DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3302667PMC
September 2011

Quantitative sectioning and noise analysis for structured illumination microscopy.

Opt Express 2012 Jan;20(1):403-13

Department of Bioengineering, Rice University, Houston, Texas 77005, USA.

Structured illumination (SI) has long been regarded as a nonquantitative technique for obtaining sectioned microscopic images. Its lack of quantitative results has restricted the use of SI sectioning to qualitative imaging experiments, and has also limited researchers' ability to compare SI against competing sectioning methods such as confocal microscopy. We show how to modify the standard SI sectioning algorithm to make the technique quantitative, and provide formulas for calculating the noise in the sectioned images. The results indicate that, for an illumination source providing the same spatially-integrated photon flux at the object plane, and for the same effective slice thicknesses, SI sectioning can provide higher SNR images than confocal microscopy for an equivalent setup when the modulation contrast exceeds about 0.09.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3336372PMC
http://dx.doi.org/10.1364/OE.20.000403DOI Listing
January 2012

Depth-resolved image mapping spectrometer (IMS) with structured illumination.

Opt Express 2011 Aug;19(18):17439-52

Department of Bioengineering, Rice University, Houston, Texas 77005, USA.

We present a depth-resolved Image Mapping Spectrometer (IMS) which is capable of acquiring 4D (x, y, z, λ) datacubes. Optical sectioning is implemented by structured illumination. The device's spectral imaging performance is demonstrated in a multispectral microsphere and mouse kidney tissue fluorescence imaging experiment. We also compare quantitatively the depth-resolved IMS with a hyperspectral confocal microscope (HCM) in a standard fluorescent bead imaging experiment. The comparison results show that despite the use of a light source with four orders of magnitude lower intensity in the IMS than that in the HCM, the image signal-to-noise ratio acquired by the IMS is 2.6 times higher than that achieved by the equivalent confocal approach.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3190403PMC
http://dx.doi.org/10.1364/OE.19.017439DOI Listing
August 2011

Analytic-domain lens design with proximate ray tracing.

J Opt Soc Am A Opt Image Sci Vis 2010 Aug;27(8):1791-802

Department of Physics, Duke University, Durham, North Carolina 27708, USA.

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.
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http://dx.doi.org/10.1364/JOSAA.27.001791DOI Listing
August 2010

Snapshot Image Mapping Spectrometer (IMS) with high sampling density for hyperspectral microscopy.

Opt Express 2010 Jul;18(14):14330-44

Department of Bioengineering, Rice University, Houston, TX, 77005, USA.

A snapshot Image Mapping Spectrometer (IMS) with high sampling density is developed for hyperspectral microscopy, measuring a datacube of dimensions 285 x 285 x 60 (x, y, lambda). The spatial resolution is approximately 0.45 microm with a FOV of 100 x 100 microm(2). The measured spectrum is from 450 nm to 650 nm and is sampled by 60 spectral channels with average sampling interval approximately 3.3 nm. The channel's spectral resolution is approximately 8nm. The spectral imaging results demonstrate the potential of the IMS for real-time cellular fluorescence imaging.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2909105PMC
http://dx.doi.org/10.1364/OE.18.014330DOI Listing
July 2010

Multiscale lens design.

Opt Express 2009 Jun;17(13):10659-74

Department of Electrical and Computer Engineering, Fitzpatrick Institute for Photonics, Duke University, Durham, NC 27708, USA.

While lenses of aperture less than 1000lambda frequently form images with pixel counts approaching the space-bandwidth limit, only heroic designs approach the theoretical information capacity at larger scales. We propose to use the field processing capabilities of small-scale secondary lens arrays to correct aberrations due to larger scale objective lenses, with an ultimate goal of achieving diffraction-limited imaging for apertures greater than 10,000lambda .We present an example optical design using an 8 mm entrance pupil capable of resolving 20 megapixels.
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http://dx.doi.org/10.1364/oe.17.010659DOI Listing
June 2009

Gaussian profile estimation in two dimensions.

Appl Opt 2008 Dec;47(36):6842-51

Fitzpatrick Institute for Photonics, Duke University, Durham, North Carolina 27708, USA.

We extend recent results for estimating the parameters of a one-dimensional Gaussian profile to two-dimensional profiles, deriving the exact covariance matrix of the estimated parameters. While the exact form is easy to compute, we provide a set of close approximations that allow the covariance to take on a simple analytic form. This not only provides new insight into the behavior of the estimation parameters, but also lays a foundation for clarifying previously published work. We also show how to calculate the parameter variances for the case of truncated sampling, where the profile lies near the edge of the array detector. Finally, we calculate expressions for the bias in the classical formulation of the problem and provide an approach for its removal. This allows us to show how the bias affects the problem of choosing an optimal pixel size for minimizing parameter variances.
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http://dx.doi.org/10.1364/ao.47.006842DOI Listing
December 2008