Assessment of deformation of human red blood cells in flow cytometry: measurement and simulation of bimodal forward scatter distributions.

Light scattering by single cells is widely applied for flow cytometric differentiation of cells. However, even for human red blood cells (RBCs), which can be modeled as homogeneous dielectric particles, the potential of light scattering is not yet fully exploited. We developed a dedicated flow cytometer to simultaneously observe the forward scattering cross section (FSC) of RBCs for orthogonal laser beams with incident wave vectors k → 1 and k → 2 . At a wavelength λ = 632.8 nm , bimodal distributions are observed in two-dimensional dot plots of FSC( k → 1 ) vs. FSC( k → 2 ), which result from the RBCs' random orientation around the direction of flow, as well as from the distributions of their size and their optical properties. Typically, signals of 7.5 × 10 4 RBCs were analyzed. We actively oriented the cells in the cytometer to prove that orientation is the main cause of bimodality. In addition, we studied the wavelength dependence of FSC( k → 1 ) using λ = 413.1 nm , 457.9 nm , 488 nm and 632.8 nm, covering both weak and strong light absorption by the RBCs. Simulations of the light scattering by single RBCs were performed using the discrete dipole approximation (DDA) for a range of sizes, orientations and optical properties to obtain FSC distributions from RBC ensembles. Using the axisymmetric biconcave equilibrium shape of native RBCs, the experimentally observed distributions cannot be reproduced. If, however, an elongated shape model is employed that accounts for the stretching of the cell by hydrodynamic forces in the cytometer, the features of the strongly bimodal measured frequency distributions are reproduced by the simulation. Elongation ratios significantly greater than 1 in the range of 1.5 to 2.5 yield the best agreement between experiments and simulated data.

Determining the refractive index of human hemoglobin solutions by Kramers-Kronig relations with an improved absorption model.

The real part of the refractive index of aqueous solutions of human hemoglobin is computed from their absorption spectra in the wavelength range 250-1100 nm using the Kramers-Kronig (KK) relations, and the corresponding uncertainty analysis is provided. The strong ultraviolet (UV) and infrared absorbance of the water outside this spectral range were taken into account in a previous study employing KK relations. We improve these results by including the concentration dependence of the water absorbance as well as by modeling the deep UV absorbance of hemoglobin's peptide backbone. The two free parameters of the model for the deep UV absorbance are fixed by a global fit.

Improved grating reconstruction by determination of line roughness in extreme ultraviolet scatterometry.

The accurate determination of critical dimensions and roughness is necessary to ensure the quality of photoresist masks that are crucial for the operational reliability of electronic components. Scatterometry provides a fast indirect optical nondestructive method for the determination of profile parameters that are obtained from scattered light intensities using inverse methods. We illustrate the effect of line roughness on the reconstruction of grating parameters employing a maximum likelihood scheme. Neglecting line roughness introduces a strong bias in the parameter estimations. Therefore, such roughness has to be included in the mathematical model of the measurement in order to obtain accurate reconstruction results. In addition, the method allows to determine line roughness from scatterometry. The approach is demonstrated for simulated scattering intensities as well as for experimental data of extreme ultraviolet light scatterometry measurements. The results obtained from the experimental data are in agreement with independent atomic force microscopy measurements.

A maximum likelihood approach to the inverse problem of scatterometry.

Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 - 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.