The point-spread function (PSF) plays a fundamental role in deciding the resolution of an optical microscope. One way to find the experimental PSF is to image sub-resolution nanobead. However, the PSF can also be approximated numerically by knowing the optical arrangement of the imaging system. In this paper, we estimate the experimental three-dimensional PSF of a widefield microscope by taking several z-stacks of an arbitrary target, followed by application of our 2D PSF estimation scheme to each z slice. Here we use a standard resolution test target as the arbitrary target whose geometrical-optics predicted image can be easily constructed.
Zernike polynomials are orthogonal polynomials that form a complete basis set and can be easily used to describe aberrations present in an optical system. Zernike modes find applications in various fields like adaptive optics (AO), optical imaging, ophthalmology, free space optical (FSO) communication, etc. Since the modes are orthogonal, they can express any arbitrary wavefront as their linear combinations. The orthogonality of the modes enables the calculation of the expansion coefficients and suggests the independent behaviour of the Zernike mode. In this work, we numerically estimate the wavefront, defined as Zernike modes, using various state of the art phase retrieval methods. We use the Zonal wavefront sensor (ZWFS) and Transport of Intensity Equation (TIE) for phase reconstruction and then calculate the orthogonality between reconstructed Zernike modes. It is found that the reconstructed Zernike modes are not perfectly orthogonal, which is mainly due to the discrete representation of the Zernike modes. We further investigate how the change in the number of zones in a ZWFS affects orthogonality. We also simulate TIE to retrieve the phase and compare the orthogonality results with ZWFS. This study will be helpful in applications where a wavefront described using Zernike mode needs to be reconstructed, and improvement in the orthogonality is required, which is achieved by increasing the number of zones in the ZWFS and representing Zernike modes in a more continuous form.
The wavefront measurement accuracy of a grating array based zonal wavefront sensor (GAWS) can be affected by the non-uniform focal spot array and unwanted orders in the detector plane. The non-uniform focal spot array is the outcome of the non-uniform nature of the incident illumination beam’s intensity profile. This paper describes a method that dynamically modulates the laser beam’s intensity using computer generated holography, making the focal spot array uniform and eliminating unwanted spots in a detector plane, thereby enhancing the accuracy of the wavefront measurement. Here, we present proof-of-principle simulation results that demonstrate the working of the proposed improvements in GAWS.
If a zonal wavefront sensor such as the Shack-Hartmann wavefront sensor is used to measure the surface profile, the sensing scheme apart from the test wavefront requires a reference wavefront. In order to switch between the two there is a need to replace the test surface by a reference surface such as a mirror. This often introduces inaccuracies in the measurement. In this paper, we introduce an experimental arrangement comprising wave plates and polarizing beam splitters where both the reference and the test wavefronts can be simultaneously present or one can easily switch from reference wavefront to test wavefront.
Grating array based zonal wavefront sensor (GAZWFS), using an array of gratings implemented with a liquid crystal spatial light modulator (LCSLM) to display the gratings, offers a flexible measurement approach. But the wavefront with a large slope may not accurately be sensed by the sensor like any Shack- Hartmann type sensor. In this paper, we propose a zone wise scanning method to improve the dynamic range of GAZWFS by blocking and unblocking the individual gratings. The estimation of the wavefront and expansion of the dynamic range of GAZWFS by the zone wise scanning method is demonstrated by numerical simulation and a proof-of-principle experimental implementation.
Spot diagrams are the intersection coordinate points in the image plane of the incoming rays from a point object. When the point object is imagined to be at infinity, the spot diagram can be considered as a representation of the point spread function (PSF) of the imaging lens. The performance of an imaging system for various applications can be analyzed with the help of the spot diagrams. In this paper, we will present our work using exact ray tracing that can be employed to compute the spot diagrams of both scalar and vector beams such as radially polarized beam, azimuthally polarized beam, etc.
One important parameter in the case of translation of an optically trapped particle is the maximum achievable speed of translation in optical trapping. While the parameter is expected to have a dependence on the particle diameter and the viscosity of the medium, there will also be dependence on the laser power and step size of the moving trap. In this paper, we will experimentally investigate the maximum translation speed of a given trapped particle in a certain medium achievable in a holographic optical trap. We will implement the holographic trap using a liquid crystal spatial light modulator with a computer interface and use latex beads in water for trapping.
A modal wavefront sensor is known for its quick detection, flexibility and simplicity in the measurement of the various aberration modes (in the form of an orthogonal basis set such as the Zernike modes) present in the wavefront of an incident beam. But the output of these type of sensor suffers from inter-modal crosstalk that may arise due to the coexistence of a large number of aberration modes in the incident beam. This leads to degradation of the quality of the sensor output, resulting in inaccuracy in the measurement of aberration modes. Booth et al. provided an optimized expression of the sensor output that reduced the inter-modal cross-talk and improved the linear response of the sensor to a great extent. However, the issue of cross-talk still persists and the sensor for a particular mode is still vulnerable to the presence of other modes. In the present work, we present an analytical study of the influence of inter-modal cross-talk on the output of a holographic modal wavefront sensor for various aberration modes. Theoretical, simulation and experimental results are presented for better visualization of the cross-talk effect.
Cross-talk between different modes has always been an intrinsic issue of a modal wavefront sensor. Efforts have been put to reduce the effect of these inter-modal cross-talk either by varying the detector aperture or by changing the mode of intensity measurement at the detector. Since the modal wavefront sensor considers the incident wavefront as a linear combination of some orthogonal basis set, say the Zernike polynomials, the presence of cross-talk between the different modes of these basis set greatly affects the sensor output. As a result the measure of the modal content of the various orthogonal modes in the incident wavefront are affected, leading to inaccuracy in measurements. In this work we present a new method of measurement of the orthogonal modes present in an incident wavefront. The proposed method can be considered as a modified version of the modal wavefront sensing technique proposed by Neil et al, having advantages in terms of cross-talk reduction between modes and linearity enhancement, in the process of measurement of various orthogonal modes present in the incident wavefront. In this paper we also present some of our simulation results in support of our proposed sensing technique.
The incorporation of polarization control on the illumination beam in a laser scanning confocal microscope allows extraction of the orientational information of submicroscopic features of a sample being studied. In this paper, we present the implementation of an optical arrangement that generates homogeneous as well as non-homogeneous user define polarization profiles over the cross-sectional area of a laser beam. A confocal system is built with this optical arrangement to obtain images of the same target with different polarized illumination beams such that there is considerable reduction in the time gap between two consecutive illuminations of each location of the sample.
A polarized light scanning optical microscopy is an important imaging technique popular for its ability to determine the information on molecular orientation of the sample being studied. The determination of the molecular orientation directly depends on the electric field orientation around the focus of a lens, which is used to focus the light to illuminate the sample. In this paper, we present the effect on the electric field orientation at the focal plane of the lens due to the presence of a few primary optical aberration present in the light beam.
The high resolution applications of a laser scanning imaging system very much demand the accurate positioning of the illumination beam. The galvanometer scanner based beam scanning imaging systems, on the other hand, suffer from both short term and long term beam instability issues. Fortunately Computer generated holography based beam scanning offers extremely accurate beam steering, which can be very useful for imaging in high-resolution applications in confocal microscopy. The holographic beam scanning can be achieved by writing a sequence of holograms onto a spatial light modulator and utilizing one of the diffracted orders as the illumination beam. This paper highlights relative advantages of such a holographic beam scanning based confocal system and presents some of preliminary experimental results.
The estimation of the Point Spread Function (PSF) of an imaging system is important for various post acquisition processes. The PSF can be estimated by knowing the optical arrangement of the imaging system or can be obtained by using a point object. Both the techniques have their own limitations. In this paper we propose a new PSF estimation technique based on a target that can be reconfigured programmably. We will show that a target with different illumination areas can be imaged to establish a relation between the image plane and the object plane via a PSF. The relation thus allows one to estimate the PSF of the imaging system.
Reduced wavefront estimation time in a Shack-Hartmann type wavefront sensor plays an important role in any high speed application of the sensor. Exploiting computer generated holography technique, one can generate an array of binary diffraction grating pattern to produce an array of focal spots, similar to that in a Shack Hartmann wavefront sensor (SHWS). The transmittance functions of each of such a grating pattern can be configured to produce a one dimensional (1D) array of focal spots of a desired order. In this paper, we show that the formation of 1D array, further facilitates in the process of single indexed wavefront estimation in its true sense that considerably reduces the wavefront estimation time.
Wavefront estimation from measured slope value is an integral part in Shack Hartmann type zonal wavefront sensors that are widely used to analyze the optical aberrations in numerous application areas. Using a specific estimation algorithm, these measured slopes are converted into wavefront phase values. Hence, accuracy in wavefront estimation lies in proper interpretation of these measured slope values using an appropriate estimation algorithm. One of the important sources of error in a basic wavefront estimation process is the algorithm discretization error that primarily depends on the estimation scheme adopted. Basically, this type of error is a result of the finite sampling of the slope geometry. Algorithm discretization error plays an important role and is needed to be considered while choosing a particular estimation geometry as it determines how well the estimation process reconstructs a phase profile. In this paper, we investigate the algorithm discretization error in a recently proposed improved zonal phase-gradient algorithm18 which is a modified form of the popular Southwell geometry. The error is calculated theoretically to ascertain the causes of error and also find ways to reduce it. Both the estimation algorithms are modeled using Taylor series expansion to show the order of discretization error and eventually make a comparison of the improved geometry with the standard Southwell geometry.
In confocal microscopy the polarization of the illumination beam plays an important role in determining the orientation of the fluorescent molecules being illuminated. The efficiency of the excitation depends on the angle between the excitation electric field and the direction of the molecular dipole. In order to determine the orientation of the fluorescent molecules in the focal plane the molecules are to be excited using two mutually orthogonal electric fields. In this paper we show how a computer generated holography technique can be implemented using a ferroelectric liquid crystal spatial light modulator to conveniently obtain two images of the same target once with an X polarized illumination beam and another with a Y polarized illumination beam.
Liquid Crystal Spatial Light Modulators (LCSLM) are of great importance in various scientific applications such as adaptive optics, optical microscopy, optical trapping etc., due to their capability to dynamically reconfigure the amplitude, phase and polarization profiles of the incoming beam. Here LCSLMs are basically used to display computer generated holograms which give rise to diffraction orders. Recently we have observed that the fluctuations in both the diffracted and undiffracted beam, which may cause great disturbances in the applications, have a close relationship with the power on-off instants of the LCSLM. Thus there exists some link between the heat dissipation from the LCSLM panel and the beam fluctuations. In this paper we provide a detailed investigation on the cause and nature of the beam fluctuations in the LCSLM.
The Shack Hartmann wavefront sensor (SHWS), named after Johannes Franz Hartmann and Roland Shack, is one of the most well-known and popularly used optical wavefront sensor that finds numerous applications in various optical technologies. SHWS samples the incident wavefront by means of a lenslet array to produce an array of regular 2D array of focal spots on the detector plane of a digital camera, in the case of an unaberrated plane wavefront. If the incident wavefront is aberrated or deviates from a plane wavefront, the respective focal spots get shifted from its reference positions corresponding to the regular grid. If the incident wavefront aberration increases or has a very large curvature, the focal spot of one lenslet may enter the detector sub-aperture of the nearby lenslet. Thus, the SHWS has a limited dynamic range that is restricted to aberrations which do not allow the sub-images to be displaced out from their own detector sub-array. It makes the SHWS sensitive to cross-talk when higher order aberrations are present thereby unavoidably a ecting the wavefront estimation process. The array of tiny lenses of the SHWS can be replaced by an array of gratings followed by a focusing lens, generating an array of focal spots which is similar to that as in the case of a SHWS. In this paper, the spatial frequency of such a grating array based zonal wavefront sensor is configured to produce lesser number of rows of focal spots. The reduction in the number of focal spot rows reduces the amount of cross talk in the vertical direction. In this paper we present preliminary experimental results to demonstrate the above stated reduction in crosstalk.
An azimuthally polarized beam when passes through a helical phase mask, gives rise to a circularly symmetric focal spot which appears very similar to the focal spot of normal linearly polarized beam with a plane wavefront. However it is noticed that common monochromatic aberrations have different degree of influence on the two types of beams, that is the azimuthally polarized beam with a helical phase mask and linearly polarized beam with a plane wavefront. In this paper we present a detailed investigation on the effect of primary aberrations on the two types of vector beams.
Wavefront sensing and reconstruction finds numerous applications in the field of optical technology. Zonal estimation from the wavefront difference or slope data is an important wavefront reconstruction approach. In this reconstruction method, the wavefront is estimated at specific grid points directly from the wavefront differences by using the least-square method. One of the important sources of error in wavefront estimation process is the detector or CCD centroiding error which may propagate in a basic wavefront estimation process, thereby degrading the performance of the wavefront sensor. Hence, quantification of this error is important as this may be considered as one of the selection parameter of a particular estimation geometry. In the present work, we compute the wavefront difference based (WFDB) error propagation coefficient due to this centroiding error for an improved zonal phase-gradient model which is formally applicable for a Shack-Hartmann (S-H) type sensor and show that the improved model offers a substantial reduction of error propagation. The theoretical error propagation coefficient is shown to have a strong correlation with the experimentally obtained RMS errors for the same model.
Radially polarized beams have cylindrically symmetric polarization profile. When focused tightly such beam gives rise to a strong axially polarized electric field component at the focus. Owing to this unique property, radially polarized beams have found applications in a number of important areas. There has been published research work on the properties of the radially polarized beam in the presence of primary monochromatic aberrations. However optical system involving such beam may also contain second order aberrations. Unfortunately there has not been any such study in the available literature. In this work we will employ vectorial diffraction theory to investigate the effect of the focal field components due to the presence of second order aberrations.
We propose a scanning optical microscope, for samples introducing spatially varying aberrations to the illumination
beam. It is implemented with a microscope that has binary hologram based beam scanning mechanism where
illumination beam phase profile is varied from pixel to pixel. Unlike a conventional scanning microscope, the scanning is
achieved by the beam diffracted from a binary hologram written on the display panel of a liquid crystal spatial light
modulator. The aberration correction is achieved without a separate wavefront sensor. For correcting the aberration in the
illumination beam the signal is maximized by changing the shape of the binary hologram in terms of chosen Zernike
mode coefficients.
High speed wavefront sensing is important in real time profile analysis, analysis of fluid dynamics, ophthalmology and so on. Conventional Shack-Hartmann wavefront sensor uses an array of tiny lenses and a digital camera to record the focal spot array. Thus the frame rate of the sensor depends on the camera. In this paper we present a zonal wavefront sensor where the array of lenses is replaced by an array of gratings followed by a focusing lens. The gratings can be configured to generate just one array of focal spots. This reduction in row of the focal spot array leads to increase in the frame rate of the proposed wavefront sensor.
The maximum lateral resolution achievable with a confocal microscope is twice that of a wide field microscope.
However, the spatial frequency content in the confocal image near the cutoff has very poor signal and is hardly of
any practical use. Barring in the fluorescence mode, no technique can provide significant resolution enhancement
simultaneously both in the reflection and fluorescence mode of the confocal microscope. This paper describes a
technique based on aperture engineering that can significantly enhance the high spatial frequency content in the
image of a confocal microscope, in principle, working either in the reflection or the fluorescence mode. Results
obtained from numerical simulations and experimental implementation are presented.
Zonal wavefront sensors of the Shack-Hartmann type have dynamic range and spatial resolution which are
determined by the micro lens diameter and focal length. Increase in the spatial resolution requires reduction in
the aperture size of each micro lens which effects the dynamic range. This paper presents a zonal wavefront sensing
scheme based on an array of gratings that can provide programmable control over both the spatial resolution
and the dynamic range. In the proposed scheme the outline of the photodetector array can be independent of
the outline of the incident beam whose wavefront is to be measured. In this paper the scheme is implemented
using a twisted nematic liquid crystal spatial light modulator.
In this work, we describe the design and implementation of a laser scanning confocal microscope with active beam forming
optics. We demonstrate dynamic control over intensity and polarization properties of the beam using the technique of
programmable diffractive optics. This technique is used facilitate active aberration correction in the beam and to generate
radially polarized pupil function in order to get an on-axis axially polarized point spread function. We also develop the
high numerical aperture theory to calculate the focal point spread function for a radially polarized pupil function. We
describe the design and implementation of a simple vector beam formation unit consisting of a polarizing beam splitter
and two right angled prisms in conjunction with a ferro-electric spatial light modulator. We also describe the design and
implementation of a beam scanning system comprising of a novel off-axis scanner mirror that maintains registration of the
conjugate pupil planes in the system.
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