The depth of focus (DOF) defines the axial range of high lateral resolution in the image space for object position. Optical devices with a traditional lens system typically have a limited DOF. However, there are applications such as in ophthalmology, which require a large DOF in comparison to a traditional optical system, this is commonly known as extended DOF (EDOF). In this paper we explore Programmable Diffractive Optical Elements (PDOEs), with EDOF, as an alternative solution to visual impairments, especially presbyopia. These DOEs were written onto a reflective liquid cystal on silicon (LCoS) spatial light modulator (SLM). Several designs of the elements are analyzed: the Forward Logarithmic Axicon (FLAX), the Axilens (AXL), the Light sword Optical Element (LSOE), the Peacock Eye Optical Element (PE) and Double Peacock Eye Optical Element (DPE). These elements focus an incident plane wave into a segment of the optical axis. The performances of the PDOEs are compared with those of multifocal lenses. In all cases, we obtained the point spread function and the image of an extended object. The results are presented and discussed.
Novel thermovision imaging systems having high efficiency require very sophisticated optical components. This paper describes the diffractive optical elements which are designed for the wavelengths between 8 and 14 μm for the application in the FLIR cameras. In the current paper the authors present phase only diffractive elements manufactured in the etched gallium arsenide. Due to the simplicity of the manufacturing process only binary phase elements were designed and manufactured. Such solution exhibits huge chromatic aberration. Moreover, the performance of such elements is rather poor, which is caused by two factors. The first one is the limited diffraction efficiency (c.a. 40%) of binary phase structures. The second problem lies in the Fresnel losses coming from the reflection from the two surfaces (around 50%). Performance of this structures is limited and the imaging contrast is poor. However, such structures can be used for relatively cheap practical testing of the new ideas. For example this solution is sufficient for point spread function (PSF) measurements. Different diffractive elements were compared. The first one was the equivalent of the lens designed on the basis of the paraxial approximation. For the second designing process, the non-paraxial approach was used. It was due to the fact that f/# was equal to 1. For the non-paraxial designing the focal spot is smaller and better focused. Moreover, binary phase structures suffer from huge chromatic aberrations. Finally, it is presented that non-paraxially designed optical element imaging with extended depth of focus (light-sword) can suppress chromatic aberration and therefore it creates the image not only in the image plane.
This work is dedicated to the evaluation of the chromatic properties of high order kinoforms. Typical kinoform (of the first order) is a phase only structure having the phase retardation varying in the range 0-2π. Such structures are very commonly used in many practical applications for different ranges of electromagnetic radiation like ultraviolet, visible, infrared, terahertz and millimeter waves. Besides those benefits such structures have one crucial disadvantage - they suffer from big chromatic aberration. This limits their practical application only to the narrowband work, where main wavelength must be well defined (Δλ/λ<<1). This paper presents other type of diffractive structures called high order kinoforms (HOK). They exhibit phase retardation of n2π, where n is an integer number much bigger than 1. Due to this fact they are relatively thin and therefore can be manufactured using laser lithography in thick photoresist (deeply etched). On the other hand they are thick enough to suppress chromatic aberrations. In comparison to the well-known Fresnel lens, the high order kinoform structure has precisely controlled phase retardation between different zones. In the case of the Fresnel lens (known from XVIII/XIX century), phase retardations between different zones are random (designing process is based on the geometrical optics). In the case of the high order kinoform working as the spherical lens - taking into account the real size of the detector - it can be shown that the most of the energy being focused in the focal spot will be registered by the detector for different wavelengths. The paper presents simple theoretical considerations, numerical modeling and their experimental evaluation.
The "peacock eye" phase diffractive element focuses an incident plane wave into a segment of the optical axis although
it introduces certain amount of aberration. This paper evaluates the extended depth of focus imaging performance of the
peacock eye phase diffractive element and explores some potential applications in ophthalmic optics. Two designs of the
element are analyzed: a single peacock eye, which produces one focal segment along the axis, and a double peacock eye,
which is a spatially multiplexed element, that produces two focal segments with partial overlapping along the axis. The
performances of the peacock eye-based elements are compared with the performance of a multifocal lens in the image
space through numerical simulations as well as optical experiments. In all the cases considered, we obtain the point
spread function and the image of an extended object. The results are presented and discussed.
The aged human eye is commonly affected by presbyopia, and therefore, it gradually loses its capability to form images of objects placed at different distances. Extended depth of focus (EDOF) imaging elements can overcome this inability, despite the introduction of a certain amount of aberration. This paper evaluates the EDOF imaging performance of the so-called peacock eye phase diffractive element, which focuses an incident plane wave into a segment of the optical axis and explores the element's potential use for ophthalmic presbyopia compensation optics. Two designs of the element are analyzed: the single peacock eye, which produces one focal segment along the axis, and the double peacock eye, which is a spatially multiplexed element that produces two focal segments with partial overlapping along the axis. The performances of the peacock eye elements are compared with those of multifocal lenses through numerical simulations as well as optical experiments in the image space. The results demonstrate that the peacock eye elements form sharper images along the focal segment than the multifocal lenses and, therefore, are more suitable for presbyopia compensation. The extreme points of the depth of field in the object space, which represent the remote and the near object points, have been experimentally obtained for both the single and the double peacock eye optical elements. The double peacock eye element has better imaging quality for relatively short and intermediate distances than the single peacock eye, whereas the latter seems better for far distance vision.
The elements for manipulating THz beams can be designed both on the basis of the microwave and on the optical
technology. Similarly to typical optical components, refractive lenses and diffractive structures can be used in the THz
range. For many practical applications the passive THz systems require sophisticated optical elements with a large
numerical aperture (NA). The expected resolution of the optical setup is close to the diffractive limit. Therefore the
aperture diameter of such optical elements is mostly in the range between 100 and 250 mm or even more and their focal
length is often equal to the diameter. A standard refractive high NA spherical lens for the THz range exhibits high signal
attenuation due to significant thickness. For typical converging lenses their attenuation is higher near the optical axis
(low geometrical aberrations) than in the peripheral regions (high geometrical aberrations). This additionally boosts
overall geometrical aberrations of the lens. Here we propose a sophisticated Fresnel-type structure. It should be thin
enough to provide low attenuation and thick enough (high order kinoform) to avoid chromatic aberration. Due to special
design process the spherical aberration of the structure can be significantly decreased. Computer modeling and
experimental results are presented.
A very simple scheme of holographic projection is presented with some experimental results showing good quality
image projection without any imaging lens. This technique can be regarded as an alternative to classic projection
methods. It is based on the reconstruction real images from three phase iterated Fourier holograms. The illumination is
performed with three laser beams of primary colors. A divergent wavefront geometry is used to achieve an increased
throw angle of the projection, compared to plane wave illumination. Light fibers are used as light guidance in order to
keep the setup as simple as possible and to provide point-like sources of high quality divergent wave-fronts at optimized
position against the light modulator. Absorbing spectral filters are implemented to multiplex three holograms on a single
phase-only spatial light modulator. Hence color mixing occurs without any time-division methods, which cause rainbow
effects and color flicker. The zero diffractive order with divergent illumination is practically invisible and speckle field is
effectively suppressed with phase optimization and time averaging techniques. The main advantages of the proposed
concept are: a very simple and highly miniaturizable configuration; lack of lens; a single LCoS (Liquid Crystal on
Silicon) modulator; a strong resistance to imperfections and obstructions of the spatial light modulator like dead pixels,
dust, mud, fingerprints etc.; simple calculations based on Fast Fourier Transform (FFT) easily processed in real time
mode with GPU (Graphic Programming).
A method of a digital holography based on the use of a self-imaging of the phase element is presented and assessed in
terms of image quality and resolution. The experimental results of digital hologram acquisition and reconstructions are
given for a standard USAF test pattern. The self imaging effect is used in the reference beam of the Mach-Zehnder
interferometer in order to project a structured phase modulated beam directly onto the photosensitive matrix of a digital
camera. The main advantage of this method is a simple optical setup and the possibility of performing phase-shifting
with a single camera exposure. The numerical reconstruction takes advantage of the Talbot effect and does not involve
any approximation or interpolation techniques. In order to evaluate the applicative potential of the method, in this work
the image quality is checked for various parameters of the optical setup, especially the period of the self-imaging
structure and imaging distances.
There is a continuous demand for the computer generated holograms to give an almost perfect reconstruction with a
reasonable cost of manufacturing. One method of improving the image quality is to illuminate a Fourier hologram with a
quasi-random, but well known, light field phase distribution. It can be achieved with a lithographically produced phase
mask. Up to date, the implementation of the lithographic technique is relatively complex and time and money
consuming, which is why we have decided to use two Spatial Light Modulators (SLM). For the correctly adjusted light
polarization a SLM acts as a pure phase modulator with 256 adjustable phase levels between 0 and 2π. The two
modulators give us an opportunity to use the whole surface of the device and to reduce the size of the experimental
system. The optical system with one SLM can also be used but it requires dividing the active surface into halves (one for
the Fourier hologram and the second for the quasi-random diffuser), which implies a more complicated optical setup. A
larger surface allows to display three Fourier holograms, each for one primary colour: red, green and blue. This allows to
reconstruct almost noiseless colourful dynamic images. In this work we present the results of numerical simulations of
image reconstructions with the use of two SLM displays.
A study of imaging in an isoplanatic optical setup with a spatially incoherent illumination is presented. In such optical
setups a light intensity distribution in an image plane can be calculated by a convolution of an input field with a Point
Spread Function (PSF). Additionally a numerical simulation of incoherent monochromatic illumination is done by an
integration of intensity images obtained with different random initial phase distributions (equivalent to a long exposure
with a rotating diffuser in an optical setup). When an optical system is non space-invariant the point source image
changes in various regions of the image plane and imaging simulation becomes complicated. Method with a simple
convolution with PSF distribution cannot be applied because there is no one well defined PSF for the whole optical
setup. This second method needs a bigger computational effort but can provide imaging modelling for both isoplanatic
and non space invariant situations. In this contribution we compare the two mentioned methods in terms of imaging
quality and its agreement with theoretical expectations. We give some statistical analysis of a contrast and noise level of
the obtained pictures. We discuss the advantages and limitations of both modelling techniques for typical greyscale test
A method of color projection of 2D images utilizing red, green and blue laser sources and Fourier holograms addressed
on a single phase modulator has been reported. High quality rich-colored images were achieved, although the main
difficulty in reaching the TV-quality is the presence of a 0th diffractive order. It is inevitably created due to a limited fill
factor and phase modulation nonlinearity of the used Spatial Light Modulator (SLM) device. However, in certain
conFigureurations the light energy contributing to the spurious diffractive order can be focused in a single point in space
and absorbed with an amplitude filter. In this work we present the experimental results of a color projection with the
non-diffracted peak shifted outside the viewing range in both transverse directions and along the optical axis.
This work presents the observation, measurement and utilization of phase modulation in-time flickering, on a high-end
Liquid Crystal on Silicon (LCoS) Spatial Light Modulator (SLM). The flicker due to binary driving electronics is a
negative effect. However, this drawback can be minimized by appropriate adjustment of phase modulation depth, which
results in a time-synchronization of peak efficiencies for selected wavelengths. In this paper optimal parameters for three
wavelengths of primary RGB colors are investigated. The result is optimal performance of the SLM for full-color
The experimental demonstration of a blind deconvolution method on an imaging system with a Light Sword optical
element (LSOE) used instead of a lens. Try-and-error deconvolution of known Point Spread Functions (PSF) from an
input image captured on a single CCD camera is done. By establishing the optimal PSF providing the optimal contrast of
optotypes seen in a frame, one can know the defocus parameter and hence the object distance. Therefore with a single
exposure on a standard CCD camera we gain information on the depth of a 3-D scene. Exemplary results for a simple
scene containing three optotypes at three distances from the imaging element are presented.
The paper presents a proposal of multiorder varifocal moiré zone plates, which change their focal length because
of the lateral displacement of their two components with transmittances described by a cubic profile. The newly
introduced element turns out to be an intermediate solution of the hitherto existing elements, which are the
refractive Alvarez lens and its diffractive counterpart. Some of the expected properties of multiorder varifocal
moiré zone plates are discussed, as well as reasons, because of which this newly introduced set of elements can
be of interest in practical applications.
A diffractive optical element with self-imaging capabilities is used to make a phase-shifting digital holography optical system simpler and cheaper. Sequential phase-shifting requires multiple exposures, and parallel phase-shifting demands a more complicated optical system. As opposed to typical phase-shifting methods, using the self-imaging diffractive optical element requires only one exposure on a low-cost CMOS matrix, and due to the small number of needed elements, the optical system is very compact. Instead of the approximation and interpolation methods, the properties of the self-imaging effect are utilized in the recording process and in the numerical reconstruction process.
The possibility of encoding multiple asymmetric symbols into a single thin binary Fourier hologram would have a practical application in the design of simple translucent holographic head-up displays. A Fourier hologram displays the encoded images at the infinity so this enables an observation without a time-consuming eye accommodation. Presenting a set of the most crucial signs for a driver in this way is desired, especially by older people with various eyesight disabilities. In this paper a method of holographic design is presented that assumes a combination of a spatial segmentation and carrier frequencies. It allows to achieve multiple reconstructed images selectable by the angle of the incident laser beam. In order to encode several binary symbols into a single Fourier hologram, the chessboard shaped segmentation function is used. An optimized sequence of phase encoding steps and a final direct phase binarization enables recording of asymmetric symbols into a binary hologram. The theoretical analysis is presented, verified numerically and confirmed in the optical experiment. We suggest and describe a practical and highly useful application of such holograms in an inexpensive HUD device for the use of the automotive industry. We present two alternative propositions of car viewing setups.
This paper presents numerical analysis of imaging quality of a refractive light sword optical element (LSOE). For comparison other optical imaging elements with extended focal depth, such as the bifocal lens, the trifocal lens, the forward axicon and the backward axicon, were also checked. The parameters of all elements were assumed according to the human eye parameters in order to check possibilities of presbyopia compensation. Obtained results allow to state that the LSOE is a promising solution for compensation of insufficient human eye accommodation.
The digital reconstruction of an optically recorded hologram has become a fast developing method and has found a vast practical application in many branches of science and industry. An especially invented diffractive optical element with self imaging properties is placed in the reference beam. In the recording process this element forms its self-image in the hologram plane. Self-imaging properties of the diffractive optical element provide the possibility of recording a digital hologram by means of the phase-shifting without any additional imaging components. The innovation of the proposed method lies in using a self-imaging diffractive optical element which enables a significant simplification of a spatial phase shifting optical setup used to record the digital hologram with only a small decrease of the quality of the reconstructed image.
The numerical iterative method of design of multi-plane Fresnel holograms is presented. It assumes encoding several flat grayscale images into a single thin phase-only element. Each image is placed at a variable distance and the number of images is not limited, thus many interesting applications can be considered. The paper presents the application of such holograms to reconstruct a colorful two-dimensional image with the use of a single spatial light modulator and three laser beams, i.e. red, green and blue. The given solution helps reduce the total cost of a potential holographic projection device since a single light modulator is used instead of three and no refractive volume optics is necessary to form the final image. The reconstructed three component RGB images overlap to form the color image on the screen. Sub-images are reconstructed simultaneously therefore no time-domain sequential switching is required, which is known to cause the obstructing rainbow effect. The proposed holographic projection method allows to obtain a fine image even when several pixels of the light modulator are damaged. The description of the method is given, followed by the results of numerical simulations.
The paper presents experiments with a refractive light sword optical element (LSOE). A refractive version of the LSOE was prepared in photoresist by gray scale photolithography. Then we examined chromatic aberrations of the produced element and compared them with those corresponding to a lens. For this purpose we performed two experiments, the first one where white light illumination was used and the latter one by the help of monochromatic illumination with three different wavelengths. The obtained results lead to the conclusion that the refractive LSOE does not exhibit significant chromatic aberrations and can be successfully used for imaging with extended depth of focus in polychromatic illumination.
This paper presents design of the linear binary phase diffractive axicon with radially varying diffraction efficiency. The designed element was manufactured using the method based on the application of the High Energy Beam Sensitive (HEBS) glasses. The parameters of the produced axicon were measured showing close resemblance to the Bessel beam. The obtained results lead to the conclusion that the linear diffractive axicon with radially varying diffraction efficiency represents an asymptotic version of the Bessel beam and can be successfully used as a single element for producing focal segments of constant width and constant axial intensity.
We present an experimental confirmation of optical properties of multiplane holograms designed with our novel iterative method. The method allows encoding many input intensity distributions into a single phase-only hologram. The object planes can be placed at variable distances, and their content is fully customizable. The reconstructed three-dimensional (3D) scenes exhibit high contrast and low noise level in all designed image planes. The results of numerical simulations are compared with those of a reconstruction in an optical setup. Holograms for optical reconstructions were manufactured using two methods: photographic and electron beam lithography (EBL). Experimental results achieved with both methods are compared. We present our research on a new class of iterative holograms, containing up to eleven object planes, designed in close distance to each other. The elements exhibit unusual light focusing possibilities and extraordinary imaging properties, thus introducing a number of possible practical applications, which are discussed.
The communicate presents a new interpretation of the Talbot effect for periodical objects limited by finite apertures.
According to the proposed approach, a self-image of a real, finite object is a superposition of deformed images of an
elementary cell. The singular elementary cell image is equivalent to that formed in a proper optical system. The theoretical
description makes possible to define a structure of self-images. Particularly, the approach enables a determination of
apertures' dimensions which lead to self-images of a reasonable quality in a desired region of an image plane. The theory is
illustrated and verified by numerical simulations.
We present an achromatization procedure for multiple images obtained with the Talbot illuminator. It consists on joining in
one optical arrangement an achromatic Fresnel diffraction setup and the kinoform Talbot illuminator. In this way the multiple
images produced by the Talbot illuminator are obtained using totally incoherent light, both spatially as well as temporally.
We present the experimental results which confirm the correctness of the proposed approach.
The paper presents abilities of the Light Sword Optical Element (LSOE) for imaging with extended depth of
focus. The LSOE belongs to the class of optical elements focusing incident light into a segment of the optical axis.
The elements of this kind can be used as correctors of some defects of human eye accommodation, especially in a
case of presbyopia. The paper illustrates imaging properties of the LSOE. In particular, the point spread functions
of the LSOE are analysed numerically. Imaging properties of the LSOE are compared with properties of optical
elements being potentially useful for presbyopia correction as axicons, bifocal lens and trifocal lens. The
experimental results illustrating usefulness of the LSOE in a case of presbyopia are given.
Compared with conventional optical systems, diffractive optical elements are more suitable to transform laser diode beams because they can form more complex wavefronts and better fulfill requirements of miniaturization. However, high numerical aperture needed to collimate the fast axis of edge-emitting laser diodes demands extremely high spatial frequency elements when single DOE is used. That involves complicated design methods based on rigorous diffraction theory and fabricating technology with sub-wavelength resolution and nanometer accuracy. To overcome these difficulties we propose a transmission DOE consisting of elliptical and cylindrical zone plates fabricated onto opposite sides of a substrate. The main advantage of such a solution lies in fact that each of the zone plates has smaller spatial frequency and can be made even as 8-phase-level element with theoretically 95% diffraction efficiency using available microlithographic technology. In result, monolithic
collimating system that allows to compensate astigmatism and to convert an elliptical laser diode light beam to circular one can be achieved with NA higher than 0.5 and efficiency over 80%.
We present simulations of averaged intensity of light behind apodized phase masks. Two types of apodization profile were assumed: Gaussian and tanh. In reality, because of limitations of electron-beam exposure system used for phase mask fabrication, we simulated phase masks with eight values of step height. For comparison, the averaged intensity distributions behind ideal phase masks with variable intensity were also calculated. Simulations and description of
intensity distribution perturbations due to phase jumps in real apodized phase masks were performed.
A novel iterative method of generating three-plane, phase-only computer-generated holograms is presented. It is based on the iterative Fresnel ping-pong two-plane algorithm. A modification is introduced to extend the method for three planes, i.e., two object planes and a hologram itself. The described method enables the design of low-noise and high-efficiency phase-only holograms using a numerical Fresnel propagation algorithm. The source method is described, followed by the modified algorithm. Numerical simulation results and algorithm parameters are discussed, followed by a discussion of the method limitations.
We present a class of diffractive elements that can be used in medical applications. We describe their physical properties, in particular the point spread functions and modulation transfer functions. Our analyses consist of the detailed numerical simulations. The obtained results correspond to the different setup parameters and confirm usefulness of such structures in medical aspect, especially in presbyopia treatment.
The work presents the encryption process in the optical arrangement with the Talbot array illuminator (TAIL). The object to be encrypted is multiplicated, forming a periodical structure. Then the obtained periodical structure is placed in an optical set-up with a TAIL. The encryption is based on the Fresnel diffraction behind the TAIL. The encrypted image has a form resembling an elementary cell of the amplitude sampling filter. The decryption is based on the Talbot effect.
We present the abilities of diffractive elements for imaging with extended depth of focus. The elements of interest belong to the class of diffractive structures focusing incident light into a segment of the optical axis. We describe the imaging properties of the two following elements of this kind: the annular axicon and the light sword optical element (LSOE). In particular, the point spread functions and the modulation transfer functions of axicons and LSOEs are analyzed experimentally and numerically in detail. The obtained results correspond to different defocusing parameters. The performed experiments confirm the usefulness of axicons and LSOEs for imaging with extended depth of focus.
Moire patterns in the form of equilateral hyperbolic zone plates have been studied. They are created by a mutual rotation of basic grids which turn out to be zone plates described by conic curves and include as a special case hyperbolic and elliptical zone plates. The obtained moire zone plates change their focal length in function of the rotation's angle between the superposed grids that generated them and therefore they can be of interest in three-point method used for determination of small displacements of great engineering structures. Simulations as well as experimental results are presented.
In the present communicate the experimental results are shown, which deal with the interference pattern created by superposition of multiple Bessel beams. They confirm our earlier results obtained analytically as well as by simulations. The interfering Bessel beams were obtained in a standard way, i.e., a field produced by a set of concentric annular apertures of narrow width illuminated by a plane wave was transformed by a lens into a set of Bessel beams.
The apodization of diffractive optical elements can be realized by a local change of their diffraction efficiency. In the case of lithographic elements with step-like structure of the period, the variable diffraction efficiency can be achieved by a gradual transformation of the 2m step kinoform into its conjugate counterpart across the apodization region. In the present contribution we show experimental results confirming this idea, which until now was verified only by simulations. The apodized quaternary grating with locally varying diffraction efficiency was obtained on a SLM device as a programmable diffractive optical element by changing gradually the period's profile. Knowledge of the phase heights of the SLM's pixels is required for successful implementation of the apodization function. It was determined from Fresnel images of the binary phase gratings with different phase step height programmed on the SLM. The Fresnel images become then binary and their visibility depends on the phase height of the grating in a known way, what makes possible to calibrate the SLM.
The paper describes the optical properties of the selected diffractive elements being promising for imaging with extended depth of focus. According to the results of our previous investigations, diffractive versions of the axicon and the light sword optical element were chosen for an analysis. Particularly we have examined the point spread functions of the above elements. The investigated optical properties of the selected diffractive structures were compared with the analogous properties of the conventional Fresnel lens. The results of the numerical simulations were verified experimentally in the optical set-up.
Design of equilateral hyperbolic zone plate moire pattern formed by a mutual rotation of two basic grids is studied in detail. The advantages of this zone plate moire pattern are analysed in comparison with solutions for other moire zone plates. Two most important advantages are: a constant aperture of the element during the mutual rotation of basic grids and a lack of aberrations due to their undesired displacements. The applicability of considered moire pattern for the three point alignment technique is mentioned.
In the communicate an optical characteristics of the phase sampling filter, a recently designed new diffractive structure is presented. The phase sampling filter is a kinoform version of the known earlier amplitude sampling filter, which in turn is a periodic array of transparent openings placed in an opaque screen and forms multiple images of a single object in the near diffraction zone. It can be shown that the sampling filter, both in an amplitude and in a phase version, is equivalent to a microlenses array. There are discussed quantities relevant for the evaluation of the image quality, such
as the impulse response function, the optical transfer functions, and the resolution.
In this work we theoretically calculate the self-image field amplitude of a finite periodic object. It is compared with the field of the image of an unitary cell of the same object formed by a lens. The results are verified by simulations of the two processes.
A novel and efficient method for Bessel beams generation is proposed. It relies on using a toroidal zone plate as an element forming the ring focus and subsequent Fourier transforming of the ring focus into the Bessel beam. The proposed solution, thanks to focusing of all illuminating wave into the ring focus allows to achieve greater efficiency than earlier solutions. Moreover it enables to generate higher order Bessel beams by adding a linear angular phase term to the transmittance of the zone plate. The proposed method is confirmed by numerical simulations.
The contribution presents the analytic design of diffractive optical elements focusing light into output curves. The approach is accurate within the scope of the Fresnel diffraction theory and the stationary phase method. The method includes arbitrary focal lines (2D and 3D) parametrized by differentiable functions and different types of holograms (Fourier, Fresnel). The detailed analysis illustrating principles of designing is given for conical diffractive elements.
Conventional diffractive optical elements with symmetry of revolution like spherical zone plate or axicons are modified by an addition of linear phase change n(theta) along the angular coordinate, where n is a natural number. In consequence of such manipulation the zone borders convert from circles into spirals and the elements modified in this way exhibit a dark dip in the center of the intensity distributions of their diffraction fields, in some cases (e.g. for n equals 1) smaller than the position of the first minimum of the respective distribution of the conventional case. The new family of elements is illustrated by examples of a spiral zone plate as well as spiral linear and logarithmic axicons, and their possible applications in alignment techniques are discussed.
The Light Sword Optical Element (LSOE) is a diffractive structure focusing light into a fragment of the optical axis. An interesting property of the LSOE is its ability for imaging with extended depth of field. Optical Transfer Function (OTF) and Point Spread Function (PSF) are usually applied for description of imaging arrangements. During our investigations several binary phase LSOE structures were fabricated. The structures differ each other with their modulation factor and apertures. A typical main focal length was equal to 74 mm in a case of coherent He-Ne laser illumination of LSOEs. Aperture diameter belonged to the range [2.8 mm, 5.5 mm], the modulation factor varied from 10% to 40% of the main focal length. Each structure was analyzed in the optical system as well as by computer simulation. PSFs of LSOE structures were measured in the optical system and were calculated numerically. Modulated Transfer Functions (MTFs) were calculated on the base of calculated and measured PSFs. Theoretical and experimental results were compared and discussed. Moreover, the experimental and numerical analysis of the Siemens star imaging was performed.
A general, nonparaxial differential equation is derived describing the refracting surface of revolution, which is able to focus light into a segment of the optical axis that has an arbitrary length, position, and longitudinal intensity distribution. The approach is based on the energy conservation principle in the geometric-approximation and ray-tracing equations. Also presented are numerical solutions for uniform-intensity axicons because the equation has only analytic solutions in the limiting cases of a stigmatic lens and classical axicon.
In this contribution, new computer-generated diffractive optical elements are proposed that are able to concentrate an incident beam into line segments of various lengths, arbitrary inclination in respect to the optical axis, as well as any distribution of the longitudinal intensity. The approach is based on the energy conservation principle taken in the scope of the geometrical optics approximation and equations of the paraxial ray tracing. Hyperbolic zone plate, linear zone plate, conical zone plate, as well as elements focusing light into the segment of the optical axis are shown to be limiting cases of the proposed elements.
The generalization of the circular zone plate with ring focus onto elements focusing light into an ellipse is proposed. The transmittance of obtained zone plate is given in explicit form basing on scaling property of Fourier transform.
Derived in the comunicate formula allows to find equation of basic grid for desired moire pattern and kind of displacement. As an illustration few examples of potentially practical application are given.