Showing papers on "Point spread function published in 2002"

A Wavelet-Based Algorithm for the Spatial Analysis of Poisson Data

Abstract: Wavelets are scalable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero, and thus may be used to simultaneously characterize the shape, location, and strength of astronomical sources. But in addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly nonzero correlation coefficients will be observed only where there are high-order variations in the data; e.g., they will be observed in the vicinity of sources. Source pixels are identified by comparing each correlation coefficient with its probability sampling distribution, which is a function of the (estimated or a priori known) background amplitude. In this paper, we describe the mission-independent, wavelet-based source detection algorithm "WAVDETECT," part of the freely available Chandra Interactive Analysis of Observations (CIAO) software package. Our algorithm uses the Marr, or "Mexican Hat" wavelet function, but may be adapted for use with other wavelet functions. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e., flat-fielded) background maps; (2) the correction for exposure variations within the field of view (due to, e.g., telescope support ribs or the edge of the field); (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds; (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape; and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the robustness of WAVDETECT by applying it to an image from an idealized detector with a spatially invariant Gaussian PSF and an exposure map similar to that of the Einstein IPC; to Pleiades Cluster data collected by the ROSAT PSPC; and to simulated Chandra ACIS-I image of the Lockman Hole region.

Capacitive micromachined ultrasonic transducers: next-generation arrays for acoustic imaging?

Abstract: Piezoelectric materials have dominated the ultrasonic transducer technology. Recently, capacitive micromachined ultrasonic transducers (CMUTs) have emerged as an alternative technology offering advantages such as wide bandwidth, ease of fabricating large arrays, and potential for integration with electronics. The aim of this paper is to demonstrate the viability of CMUTs for ultrasound imaging. We present the first pulse-echo phased array B-scan sector images using a 128-element, one-dimensional (1-D) linear CMUT array. We fabricated 64- and 128-element 1-D CMUT arrays with 100% yield and uniform element response across the arrays. These arrays have been operated in immersion with no failure or degradation in performance over the time. For imaging experiments, we built a resolution test phantom roughly mimicking the attenuation properties of soft tissue. We used a PC-based experimental system, including custom-designed electronic circuits to acquire the complete set of 128/spl times/128 RF A-scans from all transmit-receive element combinations. We obtained the pulse-echo frequency response by analyzing the echo signals from wire targets. These echo signals presented an 80% fractional bandwidth around 3 MHz, including the effect of attenuation in the propagating medium. We reconstructed the B-scan images with a sector angle of 90 degrees and an image depth of 210 mm through offline processing by using RF beamforming and synthetic phased array approaches. The measured 6-dB lateral and axial resolutions at 135 mm depth were 0.0144 radians and 0.3 mm, respectively. The electronic noise floor of the image was more than 50 dB below the maximum mainlobe magnitude. We also performed preliminary investigations on the effects of crosstalk among array elements on the image quality. In the near field, some artifacts were observable extending out from the array to a depth of 2 cm. A tail also was observed in the point spread function (PSF) in the axial direction, indicating the existence of crosstalk. The relative amplitude of this tail with respect to the mainlobe was less than -20 dB.

New paradigm for imaging systems

Abstract: We describe a new paradigm for designing hybrid imaging systems. These imaging systems use optics with a special aspheric surface to code the image so that the point-spread function or the modulation transfer function has specified characteristics. Signal processing then decodes the detected image. The coding can be done so that the depth of focus can be extended. This allows the manufacturing tolerance to be reduced, focus-related aberrations to be controlled, and imaging systems to be constructed with only one optical element plus some signal processing. OCIS codes: 080.3620, 110.0110, 110.2990, 110.0180, 110.4850, 180.0180. 1. Introduction and Background The new paradigm that we describe for the design of imaging systems has been termed wave-front coding. These coded optical systems are arrived at by means of designing the coding optics and the signal processing as an integrated imaging system. The results are imaging systems with previously unobtainable imaging modalities and require a modification of the optics for coding the wave in the aperture stop or an image of the aperture stop. This coding produces an intermediate image formed by the optical portion of the system that gathers the image. Signal processing is then required for decoding the intermediate image to produce a final image. The coding can be designed to make the imaging system invariant to certain parameters or to optimize the imaging system’s sensitivity to those parameters. One example is the use of image coding to preserve misfocus and hence, range or distance information. Another example is the use of different types of codes to make the image invariant to misfocus. These new focusinvariant imaging systems can have more than an order of magnitude increase in the depth of field. Our emphasis in this paper is on the use of the increased depth of focus to design new types of imaging systems. An example of the new imaging systems that can be constructed is a single-element lens that has a small F#, wide field of view, and diffractionlimited imaging. It also can have greatly relaxed assembly tolerances, because of its invariance to focus-related aberrations. Coding of signals for optimally conveying particular information is not new. In radar the transmitted pulses are coded for optimally providing information concerning a target’s range, for example. The appropriate signal processing to extract the range information is designed in conjunction with the transmitted signal. The integrated design of the optical image-gathering portion along with the signal processing normally is not done in the design of imaging systems. There are exceptions such as tomography, coded aperture imaging, and sometimes, interferometric imaging. In 1984 a group that was investigating the limits of resolution pointed out the potential of increasing the performance of imaging systems by jointly designing the optics and the signal processing. 1

Bayesian Image Super-Resolution

Abstract: The extraction of a single high-quality image from a set of low-resolution images is an important problem which arises in fields such as remote sensing, surveillance, medical imaging and the extraction of still images from video. Typical approaches are based on the use of cross-correlation to register the images followed by the inversion of the transformation from the unknown high resolution image to the observed low resolution images, using regularization to resolve the ill-posed nature of the inversion process. In this paper we develop a Bayesian treatment of the super-resolution problem in which the likelihood function for the image registration parameters is based on a marginalization over the unknown high-re solution image. This approach allows us to estimate the unknown point spread function, and is rendered tractable through the introduction of a Gaussian process prior over images. Results indicate a significant improvement over techniques based on MAP (maximum a-posteriori) point optimization of the high resolution image and associated registration parameters.

Image Distortion Correction in EPI: Comparison of Field Mapping With Point Spread Function Mapping

Abstract: Echo-planar imaging (EPI) can provide rapid imaging by acquiring a complete k-space data set in a single acquisition. However, this approach suffers from distortion effects in geometry and intensity, resulting in poor image quality. The distortions, caused primarily by field inhomogeneities, lead to intensity loss and voxel shifts, the latter of which are particularly severe in the phase-encode direction. Two promising approaches to correct the distortion in EPI are field mapping and point spread function (PSF) mapping. The field mapping method measures the field distortions and translates these into voxel shifts, which can be used to assign image intensities to the correct voxel locations. The PSF approach uses acquisitions with additional phase-encoding gradients applied in the x, y, and/or z directions to map the 1D, 2D, or 3D PSF of each voxel. These PSFs encode the spatial information about the distortion and the overall distribution of intensities from a single voxel. The measured image is the convolution of the undistorted density and the PSF. Measuring the PSF allows the distortion in geometry and intensity to be corrected. This work compares the efficacy of these methods with equal time allowed for field mapping and PSF mapping.

Spectral shaping for non-Gaussian source spectra in optical coherence tomography.

Abstract: We present a digital spectral shaping technique to reduce the sidelobes (ringing) of the axial point-spread function in optical coherence tomography for non-Gaussian-shaped source spectra. The spectra of two superluminescent diodes were combined to generate a spectrum with significant modulation. Images of onion cells demonstrate the improved image quality in a turbid biological sample. A quantitative analysis of the accompanying penalty in signal-to-noise ratio is given.

cMiCE: a high resolution animal PET using continuous LSO with a statistics based positioning scheme

Abstract: Objective : Detector designs for small animal scanners are currently dominated by discrete crystal implementations. However, given the small crystal cross-sections required to obtain very high resolution, discrete designs are typically expensive, have low packing fraction, reduced light collection, and are labor intensive to build. To overcome these limitations we have investigated the feasibility of using a continuous miniature crystal element (cMiCE) detector module for high resolution small animal PET applications. Methods : The detector module consists of a single continuous slab of LSO, 25×25 mm 2 in exposed cross-section and 4 mm thick, coupled directly to a PS-PMT (Hamamatsu R5900-00-C12). The large area surfaces of the crystal were polished and painted with TiO 2 and the short surfaces were left unpolished and painted black. Further, a new statistics based positioning (SBP) algorithm has been implemented to address linearity and edge effect artifacts that are inherent with conventional Anger style positioning schemes. To characterize the light response function (LRF) of the detector, data were collected on a coarse grid using a highly collimated coincidence setup. The LRF was then estimated using cubic spline interpolation. Detector performance has been evaluated for both SBP and Anger based decoding using measured data and Monte Carlo simulations. Results : Using the SBP scheme, edge artifacts were successfully handled. Simulation results show that the useful field of view (UFOV) was extended to ∼22×22 mm 2 with an average point spread function of ∼0.5 mm full width of half maximum (FWHM PSF ). For the same detector with Anger decoding the UFOV of the detector was ∼16×16 mm 2 with an average FWHM PSP of ∼0.9 mm. Experimental results yielded similar differences between FOV and resolution performance. FWHM PSF for the SBP and Anger based method was 1.4 and 2.0 mm, uncorrected for source size, with a 1 mm diameter point source, respectively. Conclusion : A continuous detector module with an average FWHM PSF approaching one millimeter has been built and tested. Furthermore, the results demonstrate that our SBP scheme yields improved performance over traditional Anger techniques for our cMiCE detector.

Extended Nijboer-Zernike approach for the computation of optical point-spread functions

Abstract: New Bessel-series representations for the calculation of the diffraction integral are presented yielding the point-spread function of the optical system, as occurs in the Nijboer-Zernike theory of aberrations. In this analysis one can allow an arbitrary aberration and a defocus part. The representations are presented in full detail for the cases of coma and astigmatism. The analysis leads to stably converging results in the case of large aberration or defocus values, while the applicability of the original Nijboer-Zernike theory is limited mainly to wave-front deviations well below the value of one wavelength. Because of its intrinsic speed, the analysis is well suited to supplement or to replace numerical calculations that are currently used in the fields of (scanning) microscopy, lithography, and astronomy. In a companion paper [J. Opt. Soc. Am. A 19, 860 (2002)], physical interpretations and applications in a lithographic context are presented, a convergence analysis is given, and a comparison is made with results obtained by using a numerical package.

Assessment of an extended Nijboer–Zernike approach for the computation of optical point-spread functions

Abstract: We assess the validity of an extended Nijboer–Zernike approach [J. Opt. Soc. Am. A19, 849 (2002)], based on recently found Bessel-series representations of diffraction integrals comprising an arbitrary aberration and a defocus part, for the computation of optical point-spread functions of circular, aberrated optical systems. These new series representations yield a flexible means to compute optical point-spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases of practical interest. Because of the analytical nature of the formulas, there are no discretization effects limiting the accuracy, as opposed to the more commonly used numerical packages based on strictly numerical integration methods. Instead, we have an easily managed criterion, expressed in the number of terms to be included in the Bessel-series representations, guaranteeing the desired accuracy. For this reason, the analytical method can also serve as a calibration tool for the numerically based methods. The analysis is not limited to pointlike objects but can also be used for extended objects under various illumination conditions. The calculation schemes are simple and permit one to trace the relative strength of the various interfering complex-amplitude terms that contribute to the final image intensity function.

Frequency analysis of digital holography with reconstruction by convolution

Abstract: A coherent optical imaging system consisting of recording a digital hologram by a CCD array and numerical reconstruction of the complex wavefield by the convolution method is subjected to a frequency analysis. The point spread function of such a system is a sinc function whose width depends on the aperture defined by the CCD array and parameters of the transfer function used in the reconstruction. A narrow point spread function and thus a sharp reconstructed image can be obtained by the numerical concept of cascaded free-space propagation, which is introduced and demonstrated.

Analytic determination of the pinhole collimator's point-spread function and RMS resolution with penetration

Abstract: Pinhole collimators are widely used to image small organs and animals. The pinhole response function (PRF) of knife-edge pinhole collimators has been estimated previously using geometric constructions without considering penetration and using "roll-off" models that employ an exponential model for the flux. An analytic expression for the PRF on the imaging plane that includes the effect of aperture penetration is derived in this paper by calculating the flux for photons passing through the aperture and those passing through the attenuating material. The PRF is then used to approximate the angular-dependent root-mean-square resolution in the directions parallel and perpendicular to the tilt of the point source. The corresponding aspect ratio is then obtained. The formulas are then compared with experimental data.

Virtual ultrasound sources in high-resolution ultrasound imaging

Abstract: This paper investigates the concept of virtual source elements. It suggests a common framework for increasing the resolution, and penetration depth of several imaging modalities by applying synthetic aperture focusing (SAF). SAF is used either as a post focusing procedure on the beamformed data, or directly on the raw signals from the transducer elements. Both approaches increase the resolution. The paper shows that in one imaging situation, there can co-exist different virtual sources for the same scan line - one in the azimuth plane, and another in the elevation. This property is used in a two stage beamforming procedure for 3D ultrasound imaging. The position of the virtual source, and the created waveform are investigated with simulation, and with pulse-echo measurements. There is good agreement between the estimated wavefront and the theoretically fitted one. Several examples of the use of virtual source elements are considered. Using SAF on data acquired for a conventional linear array imaging improves the penetration depth for the particular imaging situation from 80 to 110 mm. The independent use of virtual source elements in the elevation plane decreases the respective size of the point spread function at 100 mm below the transducer from 7mm to 2 mm.

Image reduction pipeline for the detection of variable sources in highly crowded fields

Abstract: We present a reduction pipeline for CCD (charge-coupled device) images which was built to search for variable sources in highly crowded fields like the M31 bulge and to handle extensive databases due to large time series. We describe all steps of the standard reduction in detail with emphasis on the realisation of per pixel error propagation: Bias correction, treatment of bad pixels, flatfielding, and filtering of cosmic rays. The problems of conservation of PSF (point spread function) and error propagation in our image alignment procedure as well as the detection algorithm for variable sources are discussed: We build difference images via image convolution with a technique called OIS (optimal image subtraction, Alard & Lupton, 1998), proceed with an automatic detection of variable sources in noise dominated images and finally apply a PSF-fitting, relative photometry to the sources found. For the WeCAPP project (Riffeser et al., 2001) we achieve 3� detections for variable sources with an apparent brightness of e.g. m = 24.9 mag at their minimum and a variation ofm = 2.4 mag (or m = 21.9 mag brightness minimum and a variation ofm = 0.6 mag) on a background signal of 18.1 mag/arcsec 2 based on a 500 s exposure with 1.5 arcsec seeing at a 1.2 m telescope. The complete per pixel error propagation allows us to give accurate errors for each measurement.

Tailoring the axial shape of the point spread function using the Toraldo concept.

Abstract: A novel procedure for shaping the axial component of the point spread function of nonparaxial focusing systems by use of phase-only pupil filters is presented The procedure is based on the Toraldo technique for tailoring focused fields The resulting pupil filters consist of a number of concentric annular zones with constant real transmittance The number of zones and their widths can be adapted according to the shape requirements Our method is applied to design filters that produce axial superresolution in confocal scanning systems

A dual path programmable array microscope (PAM): simultaneous acquisition of conjugate and non-conjugate images.

Abstract: A programmable array microscope (PAM) incorporates a spatial light modulator (SLM) placed in the primary image plane of a widefield microscope, where it is used to define patterns of illumination and/or detection. We describe the characteristics of a special type of PAM collecting two images simultaneously. The conjugate image (Ic) is formed by light originating from the object plane and returning along the optical path of the illumination light. The non-conjugate image (Inc) receives light from only those regions of the SLM that are not used for illuminating the sample. The dual-signal PAM provides much more time-efficient excitation than the confocal laser scanning microscope (CLSM) and greater utilization of the available emission light. It has superior noise characteristics in comparison to single-sided instruments. The axial responses of the system under a variety of conditions were measured and the behaviour of the novel Inc image characterized. As in systems in which only Ic images are collected (Nipkow-disc microscopes, and previously characterized PAMs), the axial response to thin fluorescent films showed a sharpening of the axial response as the unit cell of the repetitive patterns decreased in size. The dual-signal PAM can be adapted to a wide range of data analysis and collection strategies. We investigated systematically the effects of patterns and unit cell dimensions on the axial response. Sufficiently sparse patterns lead to an Ic image formed by the superposition of the many parallel beams, each of which is equivalent to the single scanning spot of a CLSM. The sectioning capabilities of the system, as given by its axial responses, were similar for a given scan pattern and for processed pseudorandom sequence (PRS) scans with the same size of the unit cell. For the PRS scans, optical sectioning was achieved by a subtraction of an Inc image or, alternatively, a scaled widefield image from the Ic image. Based on the comparative noise levels of the two methods, the non-conjugate subtraction was significantly superior. A point spread function for Ic and Inc was simulated and properties of the optical transfer functions (OTFs) were compared. Simulations of the OTF in non-conjugate imaging did not suffer from the missing cone problem, enabling a high quality deconvolution of the non-conjugate side alone. We also investigated the properties of images obtained by subjecting the Ic and Inc data to a combined maximum likelihood deconvolution.

Theoretical analysis for three-dimensional integral imaging systems with double devices.

Abstract: By adoption of double-device systems, integral imaging can be enhanced in image depth, viewing angle, or image size. Theoretical analyses are done for the double-image-plane integral imaging systems. Both ray optics analysis and wave optics analysis confirm that the double-device integral imaging systems can pick up and display images at two separate image planes. The analysis results are also valuable in the understanding of the conventional integral imaging systems for image positions off the central depth plane.

Measurement of the three-dimensional microscope point spread function using a Shack–Hartmann wavefront sensor

Abstract: Summary We present a technique to measure the wavefront in the exit pupil of a microscope to determine the microscope’s three-dimensional point spread function (PSF) experimentally. The wavefront yields the microscope PSF through a Fourier transform that models propagation of light from the exit pupil to the image plane. A Shack–Hartmann wavefront sensor is used to measure the wavefront shape by recording lateral displacements of a grid of focused spots created by a lenslet array. The displacement of each spot is related to the local wavefront slope. Thus, with appropriate sampling across the exit pupil, the entire wavefront can be reconstructed. This technique does not require the use of a sub-resolution object to obtain the three-dimensional microscope PSF. Consequently, larger, brighter fluorescent objects may be imaged, thereby reducing the requirements for detector sensitivity and leading to a three-fold increase in the axial range over which the PSF is measured. The Shack–Hartmann technique results in a description of the PSF as a continuous function whose sampling is not dependent on the size of the CCD pixels. The Shack–Hartmann sensor is not limited by the numerical aperture of the objective and can easily be calibrated to measure the PSF at any wavelength.

Ultrasound Imaging and Its Modeling

Abstract: Modern medical ultrasound scanners are used to image nearly all soft tissue structures in the body. The anatomy can be studied from gray-scale B-mode images, where the reflectivity and scattering strength of the tissues are displayed. The imaging is performed in real time with 20 to 100 images per second. The technique is widely used, since it does not use ionizing radiation and is safe and painless for the patient. This chapter gives a short introduction to modern ultrasound imaging using array transducers. It includes a description of the different imaging methods, the beam-forming strategies used, and the resulting fields and their modeling.

Axial tomographic confocal fluorescence microscopy.

Abstract: By physical rotation of the sample, axial tomography enables the acquisition of otherwise inaccessible spatial information from an object. In combination with confocal microscopy, the method can fundamentally improve the effective three-dimensional (3D) resolution. In this report we present a novel method for high resolution reconstruction of confocal axial tomographic data. The method automatically determines the relative angles of rotation, aligns the data from different rotational views and reconstructs a single high resolution 3D dataset. The reconstruction makes use of a known point spread function and is based on an unconstrained maximum likelihood deconvolution performed simultaneously from multiple (in our case three) angular views. It was applied to simulated as well as to experimental confocal datasets. The gain in resolution was quantified and the effect of choice of overrelaxation factors on the speed of convergence was investigated. A clearly improved 3D resolution was obtained by axial tomography together with reconstruction as compared with reconstruction of confocal data from only a single angular view.

Estimating image blur in the wavelet domain

Abstract: In this paper, a wavelet based method is proposed to estimate the blur in an image using information contained in the image itself. We look at the sharpness of the sharpest edges in the blurred image, which contain information about the blurring. Specifically, a smoothness measure, the Lipschitz exponent, is computed for these sharpest edges. Its value is related to the variance of a gaussian point spread function. This value is only dependent on the blur in the image and not on the image contents. This allows us to estimate the variance of the blur directly from the image itself. With minor modifications, the method can be extended to other types of blur that are described by one parameter (airy disks, out-of-focus blur, …).

3-D Imaging

Abstract: In this chapter we discuss various imaging techniques that can retrieve the depth coordinate which is lost by the projection of the object onto an image plane. These techniques fall into two categories. They can either retrieve only the depth of a surface in 3-D space or allow for a full reconstruction of volumetric objects. Often depth imaging and volumetric imaging are both called 3-D imaging. This causes a lot of confusion.

Monte Carlo simulations of pinhole imaging accelerated by kernel-based forced detection

Abstract: Pinhole collimation can provide both higher sensitivity and resolution than parallel hole collimation when used to image small objects. When objects are placed close to the pinhole, small pinhole diameters combined with high-magnification pinhole geometries yield ultra high resolution images. With Monte Carlo (MC) calculations it is possible to simulate accurately a wide range of features of pinhole imaging. The aim of the present work is to accelerate MC simulations of pinhole SPECT projections. To achieve speed-up, forced detection (FD), a commonly used acceleration technique, is replaced by a kernel-based forced detection (KFD) step. In KFD, instead of tracing individual photons from the source or last scatter position to the detector, a position dependent kernel (point spread function (PSF)) is projected on the detector. The PSFs for channel and knife edge pinhole apertures model the penetration effects through the aperture material. For simulations, the PSFs are pre-calculated and stored in tables. The speed-up and accuracy achieved by using KFD were validated by means of digital phantoms. MC simulations with FD and with KFD converge to almost identical images. However, KFD converges to an equal image noise level one to four orders of magnitude faster than FD, depending on the number of photons simulated. A simulator accelerated by KFD could serve as a practical tool to improve iterative image reconstruction.

Restoring SPOT images using PSF-derived deconvolution filters

Abstract: This work presents the theoretical and practical aspects of the procedure to derive a Point Spread Function (PSF) of a SPOT image. The PSF of an image can be approximated by the use of linear step structures that are recorded in the image. Deconvolution filters are enhancement filters derived specifically for each image from its PSF, so that they can to restore the original signal for its use in cartographic remote sensing applied to cadastral proposes or urban areas.

Deconvolution with a spatially-variant PSF

Abstract: Application of deconvolution algorithms to astronomical images is often limited by variations in PSF structure over the domain of the images. One major difficulty is that Fourier methods can no longer be used for fast convolutions over the enitre images. However, if the PSF is modeled as a sum of orthogonal functions that are individually constant in form over the images, but whose relative amplitudes encode the PSF spatial variability, then separation of variables again allows global image operations to be used. This approach is readily adapted to the Lucy-Richardson deconvolution algorithm. Use of the Karhunen-Loeve transform allows for a particularly compact orthogonal expansion of the PSF. These techniques are demonstrated on the deconvolution of Gemini/Hokupa'a adaptive optics images of the galactic center.

Analysis of tubular structures in three-dimensional confocal images.

Abstract: Knowledge about the relationship between morphology and the function of neurons is an important instrument in understanding the role that neurons play in information processing in the brain. In paricular, the diameter and length of segments in dendritic arborization are considered to be crucial morphological features. Consequently, accurate detection of morphological features such as centre line position and diameter is a prerequisite to establish this relationship. Accurate detection of neuron morphology from confocal microscope images is hampered by the low signal to noise ratio of the images and the properties of the microscope point spread function (PSF). The size and the anisotropy of the PSF causes feature detection to be biased and orientation dependent. We deal with these problems by utilizing Gaussian image derivatives for feature detection. Gaussian kernels provide for image derivative estimates with low noise sensitivity. Features of interest such as centre line positions and diameter in a tubular neuronal segment of a dendritic tree can be detected by calculating and subsequently utilizing Gaussian image derivatives. For diameter measurement the microscope PSF is incorporated into the derivative calculation. Results on real and simulated confocal images reveal that centre line position and diameter can be estimated accurately and are bias free even under realistic imaging conditions.

Measurement of the presampled two-dimensional modulation transfer function of digital imaging systems.

Abstract: The purpose of this work was to develop methods to measure the presampled two-dimensional modulation transfer function (2D MTF) of digital imaging systems A custom x-ray "point source" phantom was created by machining 256 holes with diameter 0107 mm through a 05-mm-thick copper plate The phantom was imaged several times, resulting in many images of individual x-ray "spots" The center of each spot (with respect to the pixel matrix) was determined to subpixel accuracy by fitting each spot to a 2D Gaussian function The subpixel spot center locations were used to create a 5 x oversampled system point spread function (PSF), which characterizes the optical and electrical properties of the system and is independent of the pixel sampling of the original image The modulus of the Fourier transform of the PSF was calculated Next, the Fourier function was normalized to the zero frequency value Finally, the Fourier transform function was divided by the first-order Bessel function that defined the frequency content of the holes, resulting in the presampled 2D MTF The presampled 2D MTF of a 01 mm pixel pitch computed radiography system and 02 mm pixel pitch flat panel digital imaging system that utilized a cesium iodide scintillator was measured Comparison of the axial components of the 2D MTF to one-dimensional MTF measurements acquired using an edge device method demonstrated that the two methods produced consistent results

New class of axially apodizing filters for confocal scanning microscopy

Abstract: A new class of axially apodizing continuously transmitting filters is analytically determined and numerically implemented. The longitudinal and lateral properties of the associated point-spread function are displayed both for a single filtered lens and for a combination with a laterally superresolving mask in a confocal configuration. Interesting imaging properties relative to the increase in axial contrast and transverse resolving power for dephasing ring-free pupil filters of moderate losses in luminosity are predicted.