Investigation of Intensity Distribution in Image plane for Different Focus Errors in Optical System Illuminated by Coherent light Operating with an Annular Aperture

For simulating the laws of intensity distribution in image plane, the theory of Fresnel diffraction had been used based on Talbot effect of grating. Under the approximation condition of Fresnel diffraction, the space distribution of complex amplitude in the diffraction field in image plane had been expressed for transitivity function in object plane. The calculation results had shown three parts. The first one was that the width in the flat-top range of maximum intensity was increasing and the border was very clear when the scratch number was increasing. The Talbot effect was more and more obvious as the scratch number of the grating was larger and larger. The second one was that the central positions of the maximum intensity in image plane were in x=· kd on image plane, where k was integral number and d was grating constant. The Talbot effect will be loss with the distance between grating plane and image plane larger and larger. The third one was very important. When the distance between the grating plane and image plane was half-odd multiple of Talbot distance, the central positions of the maximum intensity in image plane were in x=· (2k+1)d on image plane. The positions were the centers of two neighbor-hood positions of maximum intensity in image plane when the distance between the grating plane and image plane was integral number times of Talbot distance. The important phenomenon was found. The phenomenon was the maximum light intensity appeared in the same time in x=· kd and x=· (2k+1)d on image plane.

Propagation characteristics of flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture

The time-averaged electric energy density near the focus of a lens or mirror system with annular aperture is calculated. The distribution shows greater difference from the paraxial approximation than for the full circular aperture. The vector distribution of the polarisation after focusing greatly affects the field near the focus. In particular, a mirror with annular aperture which deflects a plane-polarised wave through a small angle gives a distribution in the focal plane which exhibits bright rings around a dark centre. The field distribution of an annular system is found to consist of just two modes of free space.

Expressions are obtained for the three-dimensional irradiance distribution of aberration-free diffraction patterns by semitransparent and phase, annular and annulus apertures. The irradiance distributions in the geometrical focal plane and along the optical axis have been given for several cases of annular and annulus apertures. The results are discussed and illustrated graphically.

Process windows have become narrower as nano-processing technology has advanced. The semiconductor industry, faced with this situation, has had to impose extremely severe tool controls. Above all, with the advent of 90-nm device production, demand has arisen for strict levels of control that exceed the machine specifications of ArF exposure systems. Consequently, high-accuracy focus control and focus monitoring techniques for production wafers will be necessary in order for this to be achieved for practical use. Focus monitoring techniques that measure pattern placement errors and resist features using special reticle and mark have recently been proposed. Unfortunately, these techniques have several disadvantages. They are unable to identify the direction of a focus error, and there are limits on the illumination conditions. Furthermore, they require the use of a reticle that is more expensive than normal and they suffer from a low level of measurement accuracy. To solve these problems, the authors examined methods of focus control and focus error measurement for production wafers that utilize the lens aberration of the exposure tool system. The authors call this method FMLA (focus monitoring using lens aberration). In general, astigmatism causes a difference in the optimum focal point between the horizontal and vertical patterns in the same image plane. If a focus error occurs, regardless of the reason, a critical dimension (CD) difference arises between the sparse horizontal and vertical lines. In addition, this CD difference decreases or increases monotonously with the defocus value. That is to say, it is possible to estimate the focus errors to measure the vertical and horizontal line CD formed by exposure tool with astigmatism. In this paper, the authors examined the FMLA technique using astigmatism. First, focus monitoring accuracy was investigated. Using normal scholar type simulation, FMLA was able to detect a 32.3-nm focus error when 10-mλ astigmatism was present. Furthermore, we verified that it was possible to experimentally detect a 20-nm focus error for gate layer of 90-nm logic devices. In tilt error evaluation, the estimated tilt error value was separated by 0.3-ppm from the input value into exposure tool parameters. Finally, when FMLA was applied to gate layer of 90-nm logic devices, inter lot distribution was decreased from 6.8-nm to 2.8-nm, and it was proved that FMLA using astigmatism was an effective method in device manufacturing.

The paper presents the results of a study showing the possibility of reducing the size of speckles to increase the sensitivity and accuracy of the measuring system based at the use of methods of speckle photography and speckle interferometry. The theoretical and experimental results the average size of speckles formed in the double-exposure specklegram depends on the aperture diaphragms of the optical system – circular aperture, annular aperture, square aperture and frame aperture – are presented. The experimental results forming of the diffraction halo and the Young’s fringes for a circular, annular, square and frame apertures are presented.

A commonly used estimate for the resolution limit imposed by spherical aberration in electron microscopes is the radius of the circle of least confusion rℓc. The radius of least confusion is calculated for a point object and a single energy, and is referred to object space. There are a number of reasons for questioning the usefulness of the radius of least confusion as a measure of resolution. If the intensity were uniformly distributed over the circle of confusion at different depths in the image it would be natural to assume that best resolution occurs in the plane in which the circle of confusion is smallest. However, the intensity is not uniform. Furthermore the effect of a distribution of electron energies and a non-zero object size (required for a non-zero current) should be included in calculating resolution, especially in emission microscopy, where the chromatic aberration can be very large, and low emission current density can limit the smallness of details which can be viewed or recorded. In an earlier work Storbeck, and recently my colleagues and I using a different approach, have taken these effects into account in resolution studies based on the intensity distribution in the image.In emission microscopy the aberrations introduced by the accelerating field as well as those due to the objective lens must be considered. In our calculations the spherical aberration coefficients due to the field and the lens are referred to virtual specimen space (the image space of the accelerated electrons) at unit magnification, where they are combined, as are the chromatic aberration coefficients. The object for the microscope is a small disc centered on the axis. The emission current density is uniform, with a cosine angular distribution, and an emission energy distribution chosen to fit the particular application. The intensity distribution in the image plane is calculated first for monoenergetic beams, as a function of the axial position of the plane. The distribution curves in Fig. 1 exhibit the effects of spherical aberration and object size as the defocus changes. The shapes of the curves are due to the behavior of the image disc as a function of the emission angle αe. Between the plane of least confusion and the paraxial plane, as αe increases from 0° the image disc at first moves away from the axis in the azimuth of emission (retrograde direction). After reaching a maximum displacement, which depends on the distance from the paraxial plane, the image disc moves back to the axis and into the opposite azimuth as αe continues to increase. The intensity on the axis is highest when the retrograde displacement is equal to the image disc radius, Fig. 1c. This intensity distribution turns out to be more favorable for resolution than does the distribution in the plane of least confusion, Fig. If, even though the beam spreads over a larger area. The smaller the object radius and spherical aberration coefficient are, the closer the high-intensity plane is to the paraxial plane. For a monoenergetic beam the high-intensity plane for the smallest object which can provide the required current in the image is the optimum image plane for geometrical resolution. For a beam with a range of energies the total intensity distribution is obtained from the weighted sum of single-energy distributions calculated for a series of values in the energy range and for a given position of the image plane, Fig. 2. A good approximation to the plane providing best resolution for the beam as a whole is the high-intensity plane for the average energy.

Information encoding by spectral anomalies of spatially coherent light diffracted by an annular aperture

Propagation characteristics of flattened Gaussian beams through an annular apertured optical system remain unknown. Here we derive the approximate analytical expressions of flattened Gaussian beams passing through a paraxial optical system with an annular aperture based on the Collins integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions. Meanwhile, the corresponding closed-forms for the unapertured or circular apertured or circular black screen cases are also given. Some numerical examples are given to illustrate the propagation properties of flattened Gaussian beams through an optical system with an annular aperture. the numerical examples would be useful for some engineering applications.

The annular aperture diffracted energy distribution in the image plane for an extended incoherent source has been calculated and tabulated for source sizes up to five times the size of the Airy disk and for annular aperture ratios up to 0.5. It is shown that for a scanning instrument an increase in the instantaneous field of view from one to two times the Rayleigh limit degrades the effective resolution by a factor significantly less than two.

Wavefront coding can extend the depth of field of traditional optical system by inserting a phase mask into the pupil plane. In this paper, the point spread function (PSF) of wavefront coding system with annular aperture are analyzed. Stationary phase method and fast Fourier transform (FFT) method are used to compute the diffraction integral respectively. The OTF invariance is analyzed for the annular aperture with cubic phase mask under different obscuration ratio. With these analysis results, a wavefront coding system using Maksutov-Cassegrain configuration is designed finally. It is an F/8.21 catadioptric system with annular aperture, and its focal length is 821mm. The strength of the cubic phase mask is optimized with user-defined operand in Zemax. The Wiener filtering algorithm is used to restore the images and the numerical simulation proves the validity of the design.

A new quantitative measurement of strain distributions is performed by optical spatial filtering in an optical differentiation system. In this method, the strain distribution can be converted to the light intensity distributions in the image plane, and three strain components can be obtained by a microphotometric method from only a single specimen without time-consuming numerical calculations, such as in Moiré or photoelastic photoelastic methods. An experimental example is performed in order to show the practical usefulness of the present method, and some considerations on deterioration in the fidelity of the system performance are also given.

The aim in this paper is to analyse, for the examples chosen, the influence of particular aberrations of the point-object hologram on the light intensity distribution in the plane which is assumed to be the image plane. The numerical method used for calculating the light intensity at any image point is that presented in an earlier paper. The calculations have been carried out for three cases of holographic imaging. The recording and reconstruction geometry has been chosen so that it was possible to examine the influence of the particular aberration on the image quality. The calculated energy distribution in the aberration spots is consistent with those resulting from using third-order aberration theory as well as from ‘ray-tracing’ calculations.

A new form of laser beam, called anomalous vortex beam (AVB), has been proposed recently. Here we study the propagation characteristics of the AVB passing through a paraxial ABCD optical system with an annular aperture. The approximate analytical expressions are derived based on the Collins integral formula. Some numerical examples are given to illustrate the intensity distribution of the AVB through a paraxial ABCD optical system with an annular aperture. It is shown that the field distribution depends on the topological charge \(m\), the waist \(w_{0}\), and the width of annular aperture.

This research has been carried out to determine the distribution of the intensity in the image of object with a Sharp-Edge using coherent illumination. In this research, a special formulas have been derived called the Edge spreads Function (ESF) .This formula is very useful for theoretical and practical studies since it is applicable to system with any kind and amount of aberrations that are present in the optical systems by using pupil function technique. Also optimum balance values for each kind of aberration were determined, these values have been used in programs prepared specially for calculating (ESF) using quick basic programming language with Simpson method for numerical integrals in order to calculate the intensity of different quantities of aberrations such as focus error and spherical aberration (first, Third, fifth – orders) . As well as the effect of Apodization upon the image of sharp Edge object resulting from an optical system operating with a small circular aperture. The main aim of this research is testing the Optical Systems which use Coherent light and make decision of this Systems validity range. we found that using the exit pupil technique is useful to calculate the complex intensity also the analysis capability when using coherent light is better than the incoherent light and the relation between the focus error and the quantity of aberration.