KEYWORDS: Image restoration, Signal to noise ratio, Point spread functions, Simulation of CCA and DLA aggregates, Microscopy, 3D image processing, Image processing, Computer simulations, Focus stacking, Imaging systems
Effectiveness of extended depth of field microscopy (EDFM) implementation with wavefront encoding methods is reduced by depth-induced spherical aberration (SA) due to reliance of this approach on a defined point spread function (PSF). Evaluation of the engineered PSF’s robustness to SA, when a specific phase mask design is used, is presented in terms of the final restored image quality. Synthetic intermediate images were generated using selected generalized cubic and cubic phase mask designs. Experimental intermediate images were acquired using the same phase mask designs projected from a liquid crystal spatial light modulator. Intermediate images were restored using the penalized space-invariant expectation maximization and the regularized linear least squares algorithms. In the presence of depth-induced SA, systems characterized by radially symmetric PSFs, coupled with model-based computational methods, achieve microscope imaging performance with fewer deviations in structural fidelity (e.g., artifacts) in simulation and experiment and 50% more accurate positioning of 1-μm beads at 10-μm depth in simulation than those with radially asymmetric PSFs. Despite a drop in the signal-to-noise ratio after processing, EDFM is shown to achieve the conventional resolution limit when a model-based reconstruction algorithm with appropriate regularization is used. These trends are also found in images of fixed fluorescently labeled brine shrimp, not adjacent to the coverslip, and fluorescently labeled mitochondria in live cells.
A novel 3D patterned illumination system using an incoherent light source has potential benefits for structured illumination microscopy (SIM) such as lowered intensity requirements and tunable modulating frequency. The illumination system, based on a coherent source, a set of parallel slits and a beam-splitting Fresnel biprism, generates localized interference fringes with a continuously-tunable range of lateral and axial spatial frequency combinations that are not easily accessible using other existing methods of generating structured illumination. Here we present adaptation of this system to a wide-field fluorescence microscope that tests its suitability for SIM imaging. Numerical simulations and experimental data are used to compare theoretical and practical system properties. Results demonstrate that theoretically predicted illumination properties can be used to select system design parameters and accurately produce specific illumination properties at the microscope sample plane. As part of an imaging system, this illumination approach may improve the applicability of super-resolution SIM to a greater variety of samples.
We demonstrate 3D microscope imaging using computational optical sectioning microscopy (COSM) with an engineered point-spread function (PSF) robust to depth-induced spherical aberration (SA). Earlier we demonstrated that wavefront encoding (WFE) using a squared cubic (SQUBIC) phase mask reduces the PSF depth-variance in the presence of SA and that space-invariant (SI) restoration of simulated images using a single WFE-PSF does not lead to artifacts as in the conventional case. In this study, we show experimental verification of our WFE COSM approach. The WFE system used is a commercial microscope with a modified side port imaging path, where a spatial light modulator projects the SQUBIC phase mask on the back focal plane of the imaging lens. High resolution images of a test sample with 6 μm in diameter microspheres embedded in UV-cured optical cement (RI = 1.47) were captured using both the engineered and the conventional imaging paths of the system. The acquired images were restored using a regularized SI expectation maximization algorithm based on Tikhonov-Miller regularization with a roughness penalty. A comparative study quantified in terms of the correlation coefficients between the XZ medial sections of the restored images, from experimental data, shows an 11% reduction in depth sensitivity in the SQUBIC system compared to the conventional system.
KEYWORDS: Digital image correlation, Data modeling, Microscopy, Error analysis, Point spread functions, Data acquisition, Statistical modeling, Phase measurement, Image acquisition, 3D modeling
Knowledge of prior sample information, such as a refractive index (RI) map, can be used to improve image formation models enabling more accurate three-dimensional (3D) restoration in fluorescence microscopy. RI is an indicator of cell composition and structure that allows a more comprehensive representation of the 3D structure of a specimen than fluorescence alone. Due to the integral nature of sample phase, the challenge to compute the RI map is to decouple RI and thickness. Our work investigates the feasibility of determining RI of a specimen from differential interference contrast (DIC) microscopy data acquired by using different wavelengths in illumination. This spectral diversity in the data is exploited to determine sample thickness and RI. Results from simulated and experimental data of polystyrene bead samples are presented to analyze this approach. Phase images were estimated from the DIC data using an alternating minimization algorithm. This study shows that the maximum estimated phase delay is accurate within approximately 7 percent error relative to the 2D phase model. The sensitivity of this integrated approach allows RI to be computed within approximately 0.4 percent error relative to values from the literature.
Wavefront coding techniques are currently used to engineer unique point spread functions (PSFs) that enhance existing microscope modalities or create new ones. Previous work in this field demonstrated that simulated intensity PSFs encoded with a generalized cubic phase mask (GCPM) are invariant to spherical aberration or misfocus; dependent on parameter selection. Additional work demonstrated that simulated PSFs encoded with a squared cubic phase mask (SQUBIC) produce a depth invariant focal spot for application in confocal scanning microscopy. Implementation of PSF engineering theory with a liquid crystal on silicon (LCoS) spatial light modulator (SLM) enables validation of WFC phase mask designs and parameters by manipulating optical wavefront properties with a programmable diffractive element. To validate and investigate parameters of the GCPM and SQUBIC WFC masks, we implemented PSF engineering in an upright microscope modified with a dual camera port and a LCoS SLM. We present measured WFC PSFs and compare them to simulated PSFs through analysis of their effect on the microscope imaging system properties. Experimentally acquired PSFs show the same intensity distribution as simulation for the GCPM phase mask, the SQUBIC-mask and the well-known and characterized cubic-phase mask (CPM), first applied to high NA microscopy by Arnison et al.10, for extending depth of field. These measurements provide experimental validation of new WFC masks and demonstrate the use of the LCoS SLM as a WFC design tool. Although efficiency improvements are needed, this application of LCoS technology renders the microscope capable of switching among multiple WFC modes.
KEYWORDS: Point spread functions, Simulation of CCA and DLA aggregates, Imaging systems, Expectation maximization algorithms, Wavefronts, Computer simulations, Monochromatic aberrations, Microscopy, Image processing, Objectives
Imaging thick biological samples introduces spherical aberration (SA) due to refractive index (RI) mismatch between specimen and imaging lens immersion medium. SA increases with the increase of either depth or RI mismatch. Therefore, it is difficult to find a static compensator for SA1. Different wavefront coding methods2,3 have been studied to find an optimal way of static wavefront correction to reduce depth-induced SA. Inspired by a recent design of a radially symmetric squared cubic (SQUBIC) phase mask that was tested for scanning confocal microscopy1 we have modified the pupil using the SQUBIC mask to engineer the point spread function (PSF) of a wide field fluorescence microscope. In this study, simulated images of a thick test object were generated using a wavefront encoded engineered PSF (WFEPSF) and were restored using space-invariant (SI) and depth-variant (DV) expectation maximization (EM) algorithms implemented in the COSMOS software4. Quantitative comparisons between restorations obtained with both the conventional and WFE PSFs are presented. Simulations show that, in the presence of SA, the use of the SIEM algorithm and a single SQUBIC encoded WFE-PSF can yield adequate image restoration. In addition, in the presence of a large amount of SA, it is possible to get adequate results using the DVEM with fewer DV-PSFs than would typically be required for processing images acquired with a clear circular aperture (CCA) PSF. This result implies that modification of a widefield system with the SQUBIC mask renders the system less sensitive to depth-induced SA and suitable for imaging samples at larger optical depths.
Point-spread function engineering (PSF), achieved by placing a phase mask at the pupil plane of the imaging lens to encode the wavefront emerging from an imaging system, can be employed to reduce the impact of spherical aberration (SA) in 3D microscopy. In a previous study, the effect of SA on a confocal scanning microscope using a squared cubic phase mask (SQUBIC) was investigated using computer simulations. Here the effect of the SQUBIC design parameter on the insensitivity of the engineered PSF to SA is investigated using a metric based on the second-order moment of the axial variability of the PSF. We show that it is possible to find the optimum SQUBIC for the insensitization to SA.
This paper describes the development of a new instrument for calibrating satellite imaging sensors - the Polarization
Hyperspectral Image Projector (PHIP). The PHIP instrument is capable of producing realistic standards-based satellite
imagery, simultaneously projecting spectral, spatial and polarization scenes. The feasibility study outlined here
demonstrates that liquid crystal devices are capable of producing arbitrary polarization states. Boulder Nonlinear
Systems is currently developing a complete spectral/spatial/polarization instrument to be delivered to NASA in 2013.
A phase shifting differential interference contrast (DIC) microscope, which provides quantitative phase information and
is capable of imaging at video rates, has been constructed. Using a combination of phase shifting and bi-directional
shear, the microscope captures a series of eight images which are then integrated in Fourier space. In the resultant image
the intensity profile linearly maps to the phase differential across the object. The necessary operations are performed by
various liquid crystal devices (LCDs) which can operate at high speeds. A set of four liquid crystal prisms shear the
beam in both the x and y directions. A liquid crystal bias cell delays the phase between the e- and o-beams providing
phase-shifted images. The liquid crystal devices are then synchronized with a CCD camera in order to provide real-time
image acquisition. Previous implementation of this microscope utilized Nomarski prisms, a rotation stage and a
manually operated Sénarmont compensator to perform the necessary operations and was only capable of fixed sample
imaging. In the present work, a series of images were taken using both the new LCD prism based microscope and the
previously implemented Sénarmont compensator based system. A comparison between these images shows that the new
system achieves equal and in some cases superior results to that of the old system with the added benefit of real-time imaging.
An extension of Nomarski differential interference contrast microscopy enables isotropic linear phase imaging through the combination of phase shifting, two directions of shear, and Fourier space integration using a modified spiral phase transform. We apply this method to simulated and experimentally acquired images of partially absorptive test objects. A direct comparison of the computationally determined phase to the true object phase demonstrates the capabilities of the method. Simulation results predict and confirm results obtained from experimentally acquired images.
Quantitative structured-illumination phase microscopy (QSIP) uses a conventional bright field microscope to
quantitatively measure the optical path length profiles of homogenous phase-only objects. The illumination in QSIP is
structured with a predetermined pattern by placing an amplitude mask in the field diaphragm of the microscope. From
the image of the amplitude mask, a numerical algorithm implementing a closed form analytical solution calculates the
object's optical path length profile. In this paper, we investigate the accuracy of the numerical algorithm used and show
that it can be made arbitrarily accurate by using numerical optimization. We then analyze the effect of the system's
numerical aperture (NA), and show that QSIP can be used with a wide range of NAs for objects with small phase
gradients, and can be used with relatively lower NAs for objects with large phase gradients.
Phase-shifting differential interference contrast (DIC) provides images in which the intensity of DIC is transformed into
values linearly proportional to differential phase delay. Linear regression analysis of the Fourier space, spiral phase,
integration technique shows these values can be integrated and calibrated to provide accurate phase measurements of
objects embedded in optically transparent media regardless of symmetry or absorption properties. This approach has the
potential to overcome the limitations of profilometery, which cannot access embedded objects, and extend the
capabilities of the traditional DIC microscope, which images embedded phase objects, but does not provide quantitative
information.
In this paper, we report on the status of our current algorithms and extensions for improved algorithms for extracting phase from images acquired with differential-interference-contrast (DIC) microscopy. Our algorithms are based on two different approaches for the computation of a specimen's phase function or optical path length (OPL) distribution from DIC images. The first approach uses an iterative phase-estimation method that minimize the I-divergence discrepancy measure using the conjugate-gradient technique to estimate the OPL from multiple DIC images acquired at different specimen rotations. The method is based on the assumption that the specimen does not absorb light. The second approach is a non-iterative method that is based on a geometric-optics model and the phase-shifting technique that allows separation of the amplitude and phase gradient information from DIC images thereby allowing computation of the desired phase from its gradient. We show results from both methods and discuss the tradeoff between complexity (with respect to data-acquisitiona and computation) and accuracy. Our long term goal is to develop a new and improved method based on a combination of our two approaches.
Experimental verification of our previously proposed linear phase imaging technique for differential inference contrast microscopy (DIC) microscopy is presented. This technique first applies phase-shifting methods to DIC to acquire linear phase gradient images in two orthogonal directions. A special Fourier integration algorithm is then applied to the combined phase gradient images to create a single linear phase image in which intensity is proportional to phase. This overcomes the limitations of traditional DIC, which cannot accurately measure the phase (i.e. refractive index or thickness) of embedded 3D phase objects. The linear phase imaging technique is implemented using a standard DIC microscope altered to allow controlled phase shifting, a low noise CCD camera, and post-processing in Matlab. The results presented confirm the linear proportionality of intensity to phase in these images.
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