Nathan Hagen

Review of snapshot spectral imaging technologies

Abstract. Within the field of spectral imaging, the vast majority of instruments used are scanning devices. Recently, several snapshot spectral imaging systems have become commercially available, providing new functionality for users and opening up the field to a wide array of new applications. A comprehensive survey of the available snapshot technologies is provided, and an attempt has been made to show how the new capabilities of snapshot approaches can be fully utilized.

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

A snapshot Image Mapping Spectrometer (IMS) with high sampling density is developed for hyperspectral microscopy, measuring a datacube of dimensions 285 × 285 × 60 (x, y, λ). The spatial resolution is ~0.45 µm with a FOV of 100 × 100 µm2. The measured spectrum is from 450 nm to 650 nm and is sampled by 60 spectral channels with average sampling interval ~3.3 nm. The channel’s spectral resolution is ~8nm. The spectral imaging results demonstrate the potential of the IMS for real-time cellular fluorescence imaging.

Multiscale lens design

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.

Fourier transform channeled spectropolarimetry in the MWIR

A complete Fourier Transform Spectropolarimeter in the MWIR is demonstrated. The channeled spectral technique, originally developed by K. Oka, is implemented with the use of two Yttrium Vanadate (YVO(4)) crystal retarders. A basic mathematical model for the system is presented, showing that all the Stokes parameters are directly present in the interferogram. Theoretical results are compared with real data from the system, an improved model is provided to simulate the effects of absorption within the crystal, and a modified calibration technique is introduced to account for this absorption. Lastly, effects due to interferometer instabilities on the reconstructions, including nonuniform sampling and interferograms translations, are investigated and techniques are employed to mitigate them.

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

Abstract. 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.

Snapshot imaging Mueller matrix polarimeter using polarization gratings

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 systems performance in the presence of noise.

Snapshot Mueller matrix spectropolarimeter

We present a new snapshot technique for performing spectrally resolved Mueller matrix polarimetry. The basic approach is an extension of the channeled spectropolarimetry technique, employing frequency-domain interferometry to encode polarization information into modulation of the spectrum.

Analysis of computed tomographic imaging spectrometers. I. Spatial and spectral resolution

Computed tomographic imaging spectrometers measure the spectrally resolved image of an object scene in an entirely different manner from traditional whisk-broom or push-broom systems, and thus their noise behavior and data artifacts are unfamiliar. We review computed tomographic imaging spectrometry (CTIS) measurement systems and analyze their performance, with the aim of providing a vocabulary for discussing resolution in CTIS instruments, by illustrating the artifacts present in their reconstructed data and contributing a rule-of-thumb measure of their spectral resolution. We also show how the data reconstruction speed can be improved, at no cost in reconstruction quality, by ignoring redundant projections within the measured raw images.

Quantitative sectioning and noise analysis for structured illumination microscopy.

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.

Gaussian profile estimation in one dimension

We present several new results on the classic problem of estimating Gaussian profile parameters from a set of noisy data, showing that an exact solution of the maximum likelihood equations exists for additive Gaussian-distributed noise. Using the exact solution makes it possible to obtain analytic formulas for the variances of the estimated parameters. Finally, we show that the classic formulation of the problem is actually biased, but that the bias can be eliminated by a straightforward algorithm.