Theory of infrared microspectroscopy for intact fibers.

Infrared microspectroscopy is widely used for the chemical analysis of small samples. In particular, spectral properties of small cylindrical samples are important in forensic analysis, understanding relationships between microstructure and mechanical properties in fibers or fiber composites, and development of cosmetics and drugs for hair. The diameters of the constituent cylinders are typically of the order of the central wavelength of light used to probe the sample. Hence, structure and material spectral response are coupled and recorded spectra are usually distorted to the extent of becoming useless for molecular identification. In this paper, we apply rigorous optical theory to predict the spectral distortions observed in IR microspectroscopic data of fibers. The theory is used, first, to compute the changes that are observed for cylinders of various dimensions under different instrument configurations when compared to the bulk spectrum from the same material. We provide a method to recover intrinsic material spectral response from fibers by correcting for distortion introduced by the cylindrical structure. The theory reported here should enable the routine use of IR microspectroscopy and imaging for the molecular analysis of cylindrical domains in complex materials.

Theory of midinfrared absorption microspectroscopy: I. Homogeneous samples.

Midinfrared (IR) microspectroscopy is widely employed for spatially localized spectral analyses. A comprehensive theoretical model for the technique, however, has not been previously proposed. In this paper, rigorous theory is presented for IR absorption microspectroscopy by using Maxwell's equations to model beam propagation. Focusing effects, material dispersion, and the geometry of the sample are accounted to predict spectral response for homogeneous samples. Predictions are validated experimentally using Fourier transform IR (FT-IR) microspectroscopic examination of a photoresist. The results emphasize that meaningful interpretation of IR microspectroscopic data must involve an understanding of the coupled optical effects associated with the sample, substrate properties, and microscopy configuration. Simulations provide guidance for developing experimental methods and future instrument design by quantifying distortions in the recorded data. Distortions are especially severe for transflection mode and for samples mounted on certain substrates. Last, the model generalizes to rigorously consider the effects of focusing. While spectral analyses range from examining gross spectral features to assessing subtle features using advanced chemometrics, the limitations imposed by these effects in the data acquisition on the information available are less clear. The distorting effects are shown to be larger than noise levels seen in modern spectrometers. Hence, the model provides a framework to quantify spectral distortions that may limit the accuracy of information or present confounding effects in microspectroscopy.

Theory of mid-infrared absorption microspectroscopy: II. Heterogeneous samples.

Fourier transform infrared (FT-IR) spectroscopic imaging combines the specificity of optical microscopy with the spectral selectivity of vibrational spectroscopy. There is increasing recognition that the recorded data may be dependent on the optical configuration and sample morphology in addition to its local material spectral response, but a quantitative framework for predicting such dependence is lacking. Here, a theory is developed to relate recorded data to the spectral and physical properties of heterogeneous samples. The modeling approach combines optical theory through rigorous coupled wave analysis with modeling of sampling geometry and sample structure. The interplay of morphology and dispersion are systematically explored using increasingly sophisticated samples to illustrate the dependence of the detected optical intensity on the spatial sample structure. Predictions of spectral distortions arising from the sample structure are quantified, and experimental validation of the developed theory is performed using a microfabricated standard from a commercial photoresist polymer. The developed framework forms a basis for understanding sample induced distortions in spectroscopic IR microscopy and imaging.

Propagation of spatial coherence in fast pulses.

Diffraction and interferometry with fast pulses are analyzed for the case that the fields are partially correlated in time and in space. This generalizes a previous work [Schoonover, J. Mod. Opt.55, 1541(2008)], where only the temporal correlations of pulsed fields were considered in a Young's interferometer. The meaning of the interferograms is addressed for measurements taken in the near, Fresnel, and far zones of the source. It is shown that single-shot measurements cannot generally be used to infer statistical properties of the source, rather, data averaged over many pulses must be used.

Computationally efficient coherent-mode representations.

The numerical calculation of traditional coherent-mode representations (CMRs) involves an eigenvalue decomposition of the cross-spectral density matrix. An efficient alternative modal representation of a partially coherent field can be realized using an LDL decomposition. Storage requirements are reduced by an amount on the order of the ratio between the coherence length and the source width. The efficiency of calculations requiring a CMR (e.g., numerical evaluation of partially coherent propagation effects) may thus be significantly improved, particularly when low-coherence fields are considered.

The generalized Wolf shift for cyclostationary fields.

Correlation dependent, propagation-induced shifts in the generalized spectra of cyclostationary, random fields are predicted. This result generalizes the Wolf shift for stationary fields and is applicable to periodic trains of fast pulses such as might be generated in comb spectroscopy or other mode-locked pulsed systems. Examples illustrate these shifts for intrinsically stationary fields and the fields generated by a mode-locked laser.

Partially coherent illumination in full-field interferometric synthetic aperture microscopy.

A model is developed for optical coherence tomography and interferometric synthetic aperture microscopy (ISAM) systems employing full-field frequency-scanned illumination with partial spatial coherence. This model is used to derive efficient ISAM inverse scattering algorithms that give diffraction-limited resolution in regions typically regarded as out of focus. Partial spatial coherence of the source is shown to have the advantage of mitigating multiple-scattering effects that can otherwise produce significant artifacts in full-field coherent imaging.

Robust determination of the anisotropic polarizability of nanoparticles using coherent confocal microscopy.

A coherent confocal microscope is proposed as a means to fully characterize the elastic scattering properties of a nanoparticle as a function of wavelength. Using a high numerical aperture lens, two-dimensional scanning, and a simple vector-beam shaper, the rank-2 polarizability tensor is estimated from a single confocal image. A method for computationally efficient data processing is described, and numerical simulations show that this algorithm is robust to noise and uncertainty in the focal plane position. The proposed method is a generalization of techniques that provide an estimate of a limited set of scattering parameters, such as a single orientation angle for rodlike particles. The measurement of the polarizability obviates the need for a priori assumptions about the nanoparticle.

Interferometric Synthetic Aperture Microscopy: Computed Imaging for Scanned Coherent Microscopy.

Three-dimensional image formation in microscopy is greatly enhanced by the use of computed imaging techniques. In particular, Interferometric Synthetic Aperture Microscopy (ISAM) allows the removal of out-of-focus blur in broadband, coherent microscopy. Earlier methods, such as optical coherence tomography (OCT), utilize interferometric ranging, but do not apply computed imaging methods and therefore must scan the focal depth to acquire extended volumetric images. ISAM removes the need to scan the focus by allowing volumetric image reconstruction from data collected at a single focal depth. ISAM signal processing techniques are similar to the Fourier migration methods of seismology and the Fourier reconstruction methods of Synthetic Aperture Radar (SAR). In this article ISAM is described and the close ties between ISAM and SAR are explored. ISAM and a simple strip-map SAR system are placed in a common mathematical framework and compared to OCT and radar respectively. This article is intended to serve as a review of ISAM, and will be especially useful to readers with a background in SAR.

4Pi spectral self-interference microscopy.

Spectral self-interference microscopy (SSM) relies on the balanced collection of light traveling two different paths from the sample to the detector, one direct and the other indirect from a reflecting substrate. The resulting spectral interference effects allow nanometer-scale axial localization of isolated emitters. To produce spectral fringes the difference between the two optical paths must be significant. Consequently, to ensure that both contributions are in focus, a low-numerical-aperture objective lens must be used, giving poor lateral resolution. Here this limitation is overcome using a 4Pi apparatus to produce the requisite two paths to the detector. The resulting instrument generalizes both SSM and 4Pi microscopy and allows a quantification of SSM resolution (rather than localization precision). Specifically, SSM is shown to be subject to the same resolution constraints as 4Pi microscopy.

Spectral self-interference microscopy for low-signal nanoscale axial imaging.

A theoretical and numerical analysis of spectral self-interference microscopy (SSM) is presented with the goal of expanding the realm of SSM applications. In particular, this work is intended to enable SSM imaging in low-signal applications such as single-molecule studies. A comprehensive electromagnetic model for SSM is presented, allowing arbitrary forms of the excitation field, detection optics, and tensor sample response. An evanescently excited SSM system, analogous to total internal reflection microscopy, is proposed and investigated through Monte Carlo simulations. Nanometer-scale axial localization for single-emitter objects is demonstrated, even in low-signal environments. The capabilities of SSM in imaging more general objects are also considered--specifically, imaging arbitrary fluorophore distributions and two-emitter objects. A data-processing method is presented that makes SSM robust to noise and uncertainties in the detected spectral envelope.

Nonparaxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy.

A large-aperture, electromagnetic model for coherent microscopy is presented and the inverse scattering problem is solved. Approximations to the model are developed for near-focus and far-from-focus operations. These approximations result in an image-reconstruction algorithm consistent with interferometric synthetic aperture microscopy (ISAM): this validates ISAM processing of optical-coherence-tomography and optical-coherence-microscopy data in a vectorial setting. Numerical simulations confirm that diffraction-limited resolution can be achieved outside the focal plane and that depth of focus is limited only by measurement noise and/or detector dynamic range. Furthermore, the model presented is suitable for the quantitative study of polarimetric coherent microscopy systems operating within the first Born approximation.

Autocorrelation artifacts in optical coherence tomography and interferometric synthetic aperture microscopy.

Interferometric synthetic aperture microscopy processing of optical coherence tomography data has been shown to allow computational focusing of en face planes that have traditionally been regarded as out of focus. It is shown that this focusing of the image also produces a defocusing effect in autocorrelation artifacts resulting from Fourier-domain data collection. This effect is verified experimentally and through simulation.

Simulation of vector fields with arbitrary second-order correlations.

Temporally-stationary electromagnetic fields with arbitrary second-order coherence functions are simulated using standard statistical tools. In cases where the coherence function takes a commonly-used separable form, a computationally-efficient variation of the approach can be applied. This work provides a generalization of previous spatio-temporal simulators which model only scalar fields and require either restrictions on the coherence function or consider only two points in space. The simulation of a partially-polarized Gaussian Schell-model beam and a partially-radially-polarized beam are demonstrated.