Upscaling image resolution of compact imaging systems using wavefront coding and a property of the point-spread function

We propose an image-resolution upscaling method for compact imaging systems. The image resolution is calculated using the resolving power of the optics and the pixel size of a digital image sensor. The resolution limit of the compact imaging system comes from its size and the number of allowed lenses. To upscale the image resolution but maintain the small size, we apply wavefront coding and image restoration. Conventional image restoration could not enhance the image resolution of the sensor. Here, we use the upscaled image of a wavefront-coded optical system and apply an image-restoration algorithm using a more precisely calculated point-spread function (PSF) as the deconvolution filter. An example of a wavefront-coded optical system with a 5-megapixel image sensor is given. The final image had a resolution equivalent to that of a 10-megapixel image using only four plastic lenses. Moreover, image degradation caused by hand motion could also be reduced using the proposed method.     

On the Limitations of the Confocal Scanning Optical Microscope as a Profilometer

Abstract

We present a numerical study of the performance of a one-dimensional Confocal Scanning Optical Microscope (CSOM) when used as a profiler of highly reflecting surfaces. The study is conducted by means of a computer simulation that describes the interaction between the incident beam and the sample in a fairly rigorous manner. The degradation of the depth discrimination as a function of the local surface slope is illustrated with examples, and a criterion for the maximum allowable slope is proposed. We also show that the instrument has difficulties in profiling surfaces that have steps or sharp edges and it is argued that, in general, problems are encountered when the surface profile cannot be considered locally flat in the scale of the Point Spread Function (PSF) of the optical system. This implies that the lateral resolution of the instrument is far worse as a profilometer than when used as an imaging system, and that the unresolved features introduce spurious details on the estimated profile.     

Non-contact technique for testing antique optical instruments based on wavefront sensing

A non-contact method for analysing the image quality of old and delicate optical instruments is proposed. The technique is based on the use of a Shack–Hartmann wavefront sensor to obtain the Zernike coefficients of the wavefront at a certain plane, the application of our own software for the calculation of the point spread function (PSF) and a later convolution with the Gaussian image of the object to simulatethe image seen through the instrument. We have applied this technique to a terrestrial telescope from the beginning of the twentieth century. In order to test the quality of the method, the simulated PSFs and images are compared with the real ones. The main advantage of this method lies in the fact that the tested instruments do not suffer any harm due to dismantling or excessive manipulation required to transport it to outdoor observation areas.     

Microscopic time-resolved two-dimensional imaging with a femtosecond amplifying optical Kerr gate

We demonstrate microscopic time-resolved two-dimensional (2D) imaging that is based on a femtosecond amplifying optical Kerr gate (fs-amp OKG). The contribution of the optical nonlinear effects to the transverse imaging performance and the limit of the transverse resolving power are investigated. The optical Kerr effect in the excited state with amplification, used in the fs-amp OKG, does not deteriorate the quality of the time-resolved image at transverse resolutions up to at least 5.5 microm. We obtain a femtosecond-time-resolved 2D image of a microscopic object with a transverse resolution of 1.7 microm.     

Compensating for nonstationary blurring by further blurring and deconvolution

In many imaging systems, the point spread function (PSF) is nonstationary. Usually, a computation‐intensive iterative algorithm is used to deblur the nonstationary PSF. This article presents a new idea of using a noniterative method to compensate for the spatially variant PSF. This method first further blurs the image with a nonstationary kernel so that the resultant image has a stationary PSF, then deblurs the resultant image using an efficient decovolution technique. The proposed method is illustrated and implemented by single photon emission computed tomography applications. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 221–226, 2009     

用点扩展函数确定卫星反射后的脉冲强度

卫星激光测距系统是一个非相干成象光学系统。卫星形状效应是由于卫得上不同位置的反射器对光子反射的时间不同而引起的脉冲强度重新分布的现象。非相干成象系统在等晕区内是空间不变性的光强线性系统。成象光学系统中象强度等于输入物强度与光瞳点扩展函数的卷积。用卫星的点扩展函数描述卫星形状效应,能非常简便地计算出被卫星反射后的脉冲强度分布。讨论了激光测距卫星的点扩展函数的求解方法和表达形式,并分别推导和计算了Lageos卫星和自行设计卫星的点扩展函数以及点扩展函数作用后的脉冲强度分布。     

4Pi microscopy deconvolution with a variable point-spread function

To remove the axial sidelobes from 4Pi images, deconvolution forms an integral part of 4Pi microscopy. As a result of its high axial resolution, the 4Pi point spread function (PSF) is particularly susceptible to imperfect optical conditions within the sample. This is typically observed as a shift in the position of the maxima under the PSF envelope. A significantly varying phase shift renders deconvolution procedures based on a spatially invariant PSF essentially useless. We present a technique for computing the forward transformation in the case of a varying phase at a computational expense of the same order of magnitude as that of the shift invariant case, a method for the estimation of PSF phase from an acquired image, and a deconvolution procedure built on these techniques.     

Characterization of the Advanced Satellite for Cosmology and Astrophysics x-ray telescope: preflight calibration and ray tracing

The x-ray properties of multinested thin-foil mirror x-ray telescopes (XRT's) on board ASCA, the Advanced Satellite for Cosmology and Astrophysics, were fully evaluated with an x-ray pencil beam.Scanning over the telescope aperture of 35 cm in diameter with an x-ray pencil beam, we found the effective area of a set of XRT's to be 325, 200, and 113 cm(2) at energies of 1.5, 4.5, and 8.0 keV, respectively. We derive the point-spread functions (PSF's) of the XRT's by measuring the image profile at the focal plane with an x-ray CCD. The PSF is found to exhibit a sharp core concentrated within 30 arcsec and a broad wing extended to 3 arcmin in half-power diameter. We also evaluate the contribution of stray light, which is caused by the single reflection of x rays by primary or secondary mirrors and by the backside reflection of the mirrors. To obtain the characteristics of the XRT in the energy region of 0.5-10.0 keV, incorporated with the measurements at discrete energies, we develop a ray-tracing method with the telescope design parameter, the PSF, and optical constants. In particular, we obtain the optical constants around the gold-atom M shell (Au-M) absorption-edge energies by measuring the reflectivity of our mirror sample, with monochromatized x-rays in the energy range of 2.0-3.5 keV from synchrotron radiation. Taking into account the PSF's and optical constants, we find that our ray-tracing program can reproduce all these XRT performances.     

Gradient-index human lens as a quadratic phase transformer

The correspondence between the linear integral transform and the ray-transfer matrix of a first-order optical system is used to evaluate the transmittance function of gradient-index (GRIN) human lens regarded as a quadratic phase transformer. The size of the GRIN crystalline lens has been considered for redefining the effective transmittance function by the pupil function. The role that the GRIN nature of the human lens plays in the retinal image quality using the point spread function (PSF) is commented on. The simulation results show that the effective radius of the output face of the lens decreases with increasing thickness and that it is higher for flat end surfaces than for curved end faces. On the other hand, the simulation results also show, for small pupil sizes, that the GRIN nature of the human lens is a retinal image degradation source producing the spread of the PSF and that the curved end surfaces of the lens constitute a retinal image quality improve factor contributing to the narrowing of the PSF.     

Influence of the optical feedback on the large signal modulation characteristics of the external cavity semiconductor laser

After taking into account the multiple reflections of light in external cavity, the influence of the optical feedback on the large signal modulation characteristics of the external cavity semiconductor laser (ECSL) has been theoretically investigated. The numerical simulations show that, with the increase of the modulation index, the peak photon number of the ECSL tends to higher level on the whole. When the optical feedback is strong or weak, the peak photon number of the ECSL shows single period. However, the peak photon number exhibits bifurcation or chaos for different modulation index when the optical feedback is intermediate.     

Analysis of depth profiling data obtained by confocal Raman microspectroscopy

The nominal depth resolution achieved in confocal Raman microscopy is on the order of a few micrometers. Often, however, the depth resolution is decreased by light refraction at the sample surface. The problem can be avoided with the use of an immersion objective and index matching oils. Through this intervention the instrument point-spread function (PSF) can be assumed to be independent of the depth of focus in the sample, and spatially invariant depth profiles can be acquired. In this work the instrument PSF was determined by measuring a depth profile of a thick uniform sample and calculating the first derivative of the depth profile curve. The first-derivative method was also used to determine sample thickness. Convolution with the PSF makes it possible to simulate the behavior of the instrument with different sample functions. It is also possible to use the instrument PSF to deconvolve depth-profiling data. Deconvolution reduces the blurring effect of the instrument and increases the depth resolution. Deconvolution can also be used in analysis of the sample surface position and in layer structure analysis. In this paper we show how the convolution integral can be used with the immersion sampling technique to determine the PSF and how the sample thickness can be determined.     

Trajectories in parallel optics

In our previous work we showed the ability to improve the optical system's matrix condition by optical design, thereby improving its robustness to noise. It was shown that by using singular value decomposition, a target point-spread function (PSF) matrix can be defined for an auxiliary optical system, which works parallel to the original system to achieve such an improvement. In this paper, after briefly introducing the all optics implementation of the auxiliary system, we show a method to decompose the target PSF matrix. This is done through a series of shifted responses of auxiliary optics (named trajectories), where a complicated hardware filter is replaced by postprocessing. This process manipulates the pixel confined PSF response of simple auxiliary optics, which in turn creates an auxiliary system with the required PSF matrix. This method is simulated on two space variant systems and reduces their system condition number from 18,598 to 197 and from 87,640 to 5.75, respectively. We perform a study of the latter result and show significant improvement in image restoration performance, in comparison to a system without auxiliary optics and to other previously suggested hybrid solutions. Image restoration results show that in a range of low signal-to-noise ratio values, the trajectories method gives a significant advantage over alternative approaches. A third space invariant study case is explored only briefly, and we present a significant improvement in the matrix condition number from 1.9160e+013 to 34,526.     

Experimental and simulated angular profiles of fluorescence and diffuse reflectance emission from turbid media

Given the wavelength dependence of sample optical properties and the selective sampling of surface emission angles by noncontact imaging systems, differences in angular profiles due to excitation angle and optical properties can distort relative emission intensities acquired at different wavelengths. To investigate this potentiality, angular profiles of diffuse reflectance and fluorescence emission from turbid media were evaluated experimentally and by Monte Carlo simulation for a range of incident excitation angles and sample optical properties. For emission collected within the limits of a semi-infinite excitation region, normalized angular emission profiles are symmetric, roughly Lambertian, and only weakly dependent on sample optical properties for fluorescence at all excitation angles and for diffuse reflectance at small excitation angles relative to the surface normal. Fluorescence and diffuse reflectance within the emission plane orthogonal to the oblique component of the excitation also possess this symmetric form. Diffuse reflectance within the incidence plane is biased away from the excitation source for large excitation angles. The degree of bias depends on the scattering anisotropy and albedo of the sample and results from the correlation between photon directions upon entrance and emission. Given the strong dependence of the diffuse reflectance angular emission profile shape on incident excitation angle and sample optical properties, excitation and collection geometry has the potential to induce distortions within diffuse reflectance spectra unrelated to tissue characteristics.     

Theoretical considerations on imaging of micron size electron beam with optical transition radiation

Optical transition radiation (OTR) has been widely used to image electron beam profile. In this paper, we systematically investigated the issues related to imaging of electron beam with OTR. It is found that the point-spread function (PSF) largely depends on the acceptance angle of the lens and is only very weakly dependent on beam energy and the distance from the OTR target to the lens. This excludes the potential obstacles to imaging of high-energy electron beam for which, the photons are emitted in a relatively small cone and the far field condition is hard to fulfill. The image of a whole beam is found by convoluting the real beam distribution with the PSF. It is shown that for micron size beam, the image formed with OTR largely deviates from the real beam distribution. And the real beam distribution could be restored from deconvoluting the image with the PSF. The effectiveness of the restoration is demonstrated, which opens up the possibility of measuring micron size beam profile with OTR.     

Angular motion point spread function model considering aberrations and defocus effects

When motion blur is considered, the optics point spread function (PSF) is conventionally assumed to be fixed, and therefore cascading of the motion optical transfer function (OTF) with the optics OTF is allowed. However, in angular motion conditions, the image is distorted by space-variant effects of wavefront aberrations, defocus, and motion blur. The proposed model considers these effects and formulates a combined space-variant PSF obtained from the angle-dependent optics PSF and the motion PSF that acts as a weighting function. Results of comparison of the new angular-motion-dependent PSF and the traditional PSF show significant differences. To simplify the proposed model, an efficient approximation is suggested and evaluated.     

Improvement of transcutaneous fluorescent images with a depth-dependent point-spread function

The point-spread function (PSF) for transcutaneous fluorescent imaging was obtained as an analytical solution in a closed form. It is applicable to cases in which the optical property of the image-blurring turbid medium is considered to be fairly homogeneous. We proposed a technique to improve a transcutaneous image by using depth-dependent PSF. Contrast of the fluorescent image was improved for depths of 1-15 mm in a scattering medium (micro(s)' = 1/mm). The visible depth was more than doubled with this technique. An experiment with a rat demonstrated considerable improvement of a transcutaneous image of the cerebral vein at a specified depth. The spread image of the heart was reduced to the correct size by use of the PSF with the actual depth of the heart.     

Depth Transfer by an Imaging System

In many applications such as three-dimensional (3-D) data acquisition, the scanning of 3-D objects or 3-D display, it is necessary to understand how an imaging system can be used to obtain information on the structure of an object in the direction perpendicular to the image plane, i.e. depth information. In certain cases the formation of a 3-D image can be described by a theory based on optical transfer functions (OTF): the image intensity distribution is given by the 3-D convolution of the object and a 3-D point spread function (PSF); equivalently, in 3-D Fourier space the image spectrum is the product of the object spectrum and a 3-D OTF. This paper investigates the 3-D PSFs and OTFs that are associated with different pupil functions of the imaging system.     

Three-dimensional remote sensing by optical scanning holography

A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.     

Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating

Comparative studies have been made on the holographic plane grating and the ruled varied-line-spacing (VLS) plane grating designed for two kinds of objective Monk-Gillieson type high-resolution grazing incidence monochromator, I and II. The ray-traced performance of monochromator types I and II on a synchrotron radiation beam line was evaluated in terms of resolving power and spectral purity by the introduction of new concepts of effective Gaussian line and purity profiles. The resolving power defined on the basis of the effective Gaussian profile is consistent with the spectral purity of the beam emerging from the exit slit and is more realistic as compared with those defined in the conventional manner, especially when spectral images have asymmetric profiles. It is concluded that holographic plane gratings recorded with a spherical and an aspheric wave front are capable of providing high resolution with high spectral purity and are fully interchangeable with the corresponding ruled VLS plane gratings. This interchangeability provides more flexibility for users in choosing a proper grating for a high-resolution grazing incidence monochromator of the Monk-Gillieson type.     

Beam shape effects on grating spectrometer resolution

The collimated optical beam in a grating spectrometer may be circular or elliptical in cross section, so that different parts of the beam illuminate different numbers of grooves on the grating. Here we estimate the consequent loss in spectral resolution relative to that obtained with a beam that illuminates a fixed number of grooves. The effect reduces the intrinsic resolving power of the spectrometer by ~15%, exclusive of other contributions such as finite entrance-slit width.