We introduce an analytical model for Fourier ptychography (FP). The model represents recorded intensity images as linear equations. Here, the sample’s self-correlating components are the unknown variables, while the optical system’s point-spread function’s corresponding components serve as coefficients. This framework facilitates the direct computation of high-resolution complex images from the sample. A standout feature of our model is its ability to verify the uniqueness of the reconstructed image, a critical attribute for numerous quantitative applications. Our linear model offers clear insights into the impact of various experimental factors on accurate reconstruction, such as scanning step, random scanning mode, spatial resolution, and noise. While these factors have been previously acknowledged, their precise roles have remained nebulous. We have also developed an efficient computational method tailored for our model, adept at managing large matrices, thus enhancing the translation of low to high-resolution images. This research elucidates the foundational mathematics behind FP’s efficacy, underscoring its potential for optical measurements and metrology where mathematical uniqueness is paramount.
A type of ptychography-based phase microscope was developed by integrating a spatial light modulator (SLM) into a commercial wide-field light microscope. By displaying a moving pattern on the SLM to change the sample illumination and record the diffraction intensities formed, both the modulus and phase of the transmission function of the sample could be accurately reconstructed with formulas similar to those of common ptychography. Compared with other kinds of phase microscopes, the developed microscope has several advantages, including its simple structure, high immunity to coherent noise, and low requirement for quality optics. In addition, defects in the illumination beam are also removed from the reconstructed image. Further, this microscope’s fast data acquisition ability makes it highly suitable for many applications where highly accurate quantitative phase imaging is important, such as in living cells or other fragile biological samples that cannot sustain continuous imaging over a long period of time.
The image quality in off-axis digital holography (DH) is often degraded by inaccuracies in the reference wave used for reconstruction and the spatial filtering adopted to avoid twin images and zeroth order diffraction. To enhance the image quality in such cases, coherent diffraction imaging is combined with a DH technique to iteratively reconstruct the hologram. By using a small aperture on the sample plane as a spatial constraint and the recorded diffraction pattern as an intensity constraint, a higher spatial resolution than usual is obtained with the proposed method.
A general concept based on harmonic decomposition of pulses has been introduced to model ultra short pulse propagation through homogeneous and inhomogeneous dielectrics. This include propagation through free space, apertures and lens systems. This approach permits us to consider pulses of any arbitrary spatial and temporal characteristics. The pulse characteristics are found to be affected by angular and material dispersion. A computationally efficient method for the proper sampling of spectral phase has been introduced which requires only a minimum number of harmonic fields for the simulation. In the case of free space propagation, pulses maintains their shape but experience temporal and spectral shifts whose magnitudes depends on angular dispersion (diffraction angle). The pulse broadens, becomes asymmetric and chirped in dispersive media because of group velocity dispersion and higher order dispersion in the media. The pulse broadens due to radially varying group delay and group delay dispersion on propagation through focusing elements. The pulse energy at the focus is affected by the interplay of spherical and chromatic aberration by distributing the pulse energy over a large region on the axis.
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