Laser beam shaping in far-field zone by means of liquid crystal modulator (LCM) and semipassive bimorph deformable
mirror (SBDM) both placed in near-field is discussed. Phase delay of LCM and SBDM is calculated by means of
Gerchberg-Saxton (GS) algorithm. The analysis of GS algorithm accuracy, convergence and stability is conducted; the
influence of laser radiation characteristics, optical scheme parameters and initial phase estimation on algorithm
performance is considered. Hybrid combination of Hill-climbing and GS algorithm is proposed for beam-shaping quality
improvement. However, GS algorithm is known to fail in the case of multimode beam formation. To broaden the GS
algorithm application area, we suggest the modification of the algorithm that makes possible not only single-mode beam
shaping but also multimode one. The phase delay of LCM or SBDM is calculated as the sum of each mode phase
multiplied by its relative intensity. Several practical examples of singlemode and multimode beam transformations are
shown.
Optical interferometry, especially the lateral Shearing interferometer, has long played a
role in wavefront sensing. Phase-Shifting Interferometry and also Self-Referencing
Interferometry have significant advantages over the Shack-Hartmann wavefront sensor.
Phase difference between two interfering beams is determined by measuring the intensity
while the phase difference between the two interfering beams is changed in a known
manner three times. The phase difference can then be determined in the presence of
aberration. Adaptive wavelets will be applied to Phase-Shifting Interferometry in order
to address both noise and coherence and increase the depth of fringes. Phase is
determined by means of wavelet ridge extraction which will increase the depth of
interference fringes and improve resolution.
This paper describes the use of closed-loop adaptive optical system to improve the focusing of femtosecond laser beam.
Our adaptive system corrects for the low-order aberrations of laser. But even if the aberrations of the laser beam are
compensated the focal spot obtained with parabolic mirror is still far from ideal one. And the reason is the aberrations of
the parabolic mirror and its poor adjustment.
Comparison of phase-conjugate and multi-dither algorithms to correct for the parabolic mirror aberrations is presented.
The principle of proper adjustment of the parabolic mirror based on M2 minimization is shown.
We present human eye wavefront generator (HEWG) introduced inside aberrometer for dynamic reproduction of human
eye aberrations. It's main element is bimorph deformable mirror and a telescope. Deformable mirror generates human
eye aberrations in real time. We have recorded aberrations time traces for plurality of subjects using aberrometer and
reproduced them with the help of the generator at 10Hz frequency, that is inherit to human eye aberrations dynamics.
Experimental results indicate that HEWG can reproduce dynamics of human eye aberrations with residual error less than
λ/10 microns. Such a model can be useful for testing, for example, customized contact lenses or wavefront guided
aberrometers.
We discuss possible ways to enlarge the size of high-resolution area (isoplanatic patch) in fundus imagers equipped
with adaptive optics. We first developed customized human eye models of several subjects. Then we considered
immersion and multiconjugate methods of isoplanatic patch widening. Using immersion method we obtained about twotimes
enlargement of isoplanatic patch size for the developed eye models. For optimal configuration of a multiconjugate
system with two correctors and five reference sources isoplanatic patch area increased two times if compared with the
case of conventional correction. We consider immersion method to be more preferable due to its relative simplicity and
low-cost.
In this paper we investigate anisoplanatism effect in human eye. We measured off-axis aberrations of eyes of several
subjects and also performed measurements of corneal and internal optics aberrations. Using the results of the
experiments we estimated anisoplanatism effect in human eye and developed human eye models reproducing on-axis and
off-axis eye aberrations and their distribution between optical elements of the eye.
In this paper we estimate isoplanatic patch size of human eye using experimental results of human eye aberrations
measurements. For examined subjects it was found to be in the range 1.1° to 2.5°. The size of isoplanatic patch for
Gulistrand-Navarro model was calculated, it was found to be close to values obtained experimentally. We also measured
contribution of corneal surface and internal optics into total aberrations of the eye. We modified Gullstrand-Navarro eye
model to reproduce on-axis and off-axis performance of the eyes of each measured subject. The distribution of aberrations
between optical elements of the eye was taken into account when modeling. We also investigated isoplanatic patch size
widening methods such as average phase correction using 2 beacons and immersion method based on compensation of
external corneal surface refraction with immersion liquid. Immersion method was found to be the most appropriate for
isoplanatic patch widening as it allows us to increase isoplanatic patch size almost twice without loss of image quality at the
center of the image.
We present a novel algorithm of bimorph mirror grid determination. Its usability is demonstrated on practical examples of defining electrode grid to form a vortex beam. We briefly describe the developed finite element bimorph mirror model, designed to evaluate an arbitrary electrode response function.
In this paper we implement technique of intracavity bimorph flexible mirror control that allows to manipulate laser beam parameters (increase power, decrease divergence) and to form a given intensity profile at any distance including a far-field formation. Intracavity mirror surface profile is controlled by number of voltages calculated by means of genetic algorithm combined with hill-climbing one. Then the traditional Fox-Li approach is applied. It is numerically shown the possibility of successful formation of super Gaussian beam shape in near field, ring-like beam in far-field, possibility of significant power increase of TEM00 mode and far-field peak intensity enlargement.
In both scientific and industrial laser beam applications is essential for users to know what could be expected from the
laser beam. That is why analysis of the laser beam parameters is very important during laser use in various industrial and
scientific applications. To describe the beam one can use a beam quality factor M2 that characterizes the degree of
imperfection of a laser beam.
There are many methods of beam quality determination. The most common way is to use a device based on techniques
described in the International Standard ISO11146 "Test methods for laser beam parameters: Beam widths, divergence
angle and beam propagation factor". For example we can use M2-sensor that we design and produce in our Lab.
The measurement of the beam quality factor according to ISO11146 is not a simple procedure and might take a long
time. And for some applications fast beam quality determination is needed. Moreover sometimes it is not necessary to
know the exact value of M2, only estimation of M2 is just needed. And for the beam quality estimation we suggest to use
Shack-Hartmann wavefront sensor. With this sensor we can easily and fast measure the wavefront of the beam and then
according to the wavefront calculate M2.
The comparison of two sensors is presented. Advantages and disadvantages are pointed out.
The main disadvantage of contemporary bimorph flexible mirrors is that they used to have rather large aperture. At
the same time semipassive bimorph flexible mirror is one of the most widely used devices in various adaptive systems. We
present a novel approach of multilayer bimorph (multimorph) mirrors and a numerical model to simulate them, based on a
variation approach of the finite elements method in order to reduce the size (diameter) of these wavefront correctors. The
multilayer bimorph mirror consists of a substrate and a number of piezoceramic layers. The electrode grid of each layer is
determined separately to reproduce low order aberrations. We also present our results in reproduction of the wavefront
phase dislocations (vortices) with the help of tiny bimorph mirror.
In this work we present results of the given intensity distribution formation in the far-field by means of extracavity and
intracavity techniques. In both cases we consider formation by means of flexible mirror composed of semipassive
bimorph element. As extracavity technique we apply iterative Gerchberg-Saxton algorithm and as intracavity one we
consider genetic algorithm of mirror voltage control.
The problem of correct measurement of human eye aberrations is very important with the rising widespread of a surgical procedure for reducing refractive error in the eye, so called, LASIK (laser-assisted in situ keratomileusis). In this paper we show capabilities to measure aberrations by means of the aberrometer built in our lab together with Active Optics Ltd. We discuss the calibration of the aberrometer and show invalidity to use for the ophthalmic calibration purposes the analytical equation based on thin lens formula. We show that proper analytical equation suitable for calibration should have dependence on the square of the distance increment and we illustrate this both by experiment and by Zemax Ray tracing modeling. Also the error caused by inhomogeneous intensity distribution of the beam imaged onto the aberrometer's Shack-Hartmann sensor is discussed.
In this paper we consider anisoplanatism effect as a fundamental limitation on the size of high resolution area
(isoplanatic patch) of retinal images obtained using fundus cameras equipped with adaptive optics. Isoplanatic patch
size was estimated using experimental results for on-axis and off-axis eye aberrations measured by Shack-Hartmann
technique. Isoplanatic patch size varied among examined subjects in the range from 1.5o to 2.5o which is in good
agreement with results obtained using ray-tracing technique1. We estimated isoplanatic patch size for Gullstrand eye
model and found it to be close to the values obtained from experimental results for subjects with good vision. We also
discuss the possibilities of Gullstrand eye model modifications for modeling anisoplanatism effect for each particular
subject. We also estimated the efficiency of multibeacon correction method and found out that this method allows us to
almost twice increase the area with high resolution.
We demonstrate how closed-loop adaptive optical system can be used to obtain a good focused beam. The optimal correction of the high-power beam aberrations can be found by use of genetic and hill-climbing algorithms. A bimorph mirror is used as a wavefront corrector and CCD camera at the focal plane of the lens is a sensor. This adaptive system can correct for the low-order slow changing aberrations without any measurements of the wavefront.
Formation of the given laser beam intensity and phase is an important practical and scientific problem. Semipassive bimorph flexible mirror is one of the most widely used devices for this purpose. We present a novel approach of multilayer bimorph (multimorph) mirrors and a numerical model to simulate them, based on a variation approach of the finite elements method. The multilayer bimorph mirror consists of a substrate and a number of piezoceramic layers. The electrode grid of each layer is determined separately to reproduce low order aberrations.
In this presentation a model of human eye based on bimorph flexible mirror is introduced. We demonstrate experimental data of reproducing low- and high-order aberrations typical for human eye with RMS error about 5%. The presented temporal spectra of measured human eye aberrations have the main power within the range of 10 Hz. We discuss the possibility to reproduce it with our eye model. We show invalidity for the ophthalmic calibration purposes to use analytical equation based on thin lens formula. We show that proper analytical equation suitable for calibration should have dependence on the square of the distance increment and we illustrate this both by experiment and by Zemax Ray tracing modeling.
In this presentation we report our results of investigation of anisoplanatism effect in human eye. We measured aberrations of human eye depending on the location of beacon source on the retina and determined the value of the isoplanatic patch. We show that the size of isoplanatic patch depends on the direction of compensation and determine an optimal direction for every patient. To enhance quality of retina image correction we introduce lamellar eye model where aberrations of human eye are considered to be induced in two thin phase screens corresponding to cornea and crystal lens locations. For that model we found the optimal corrector location which differs from the one for the one-layer eye model.
In this presentation a dynamic model of human eye based on bimorph flexible mirror is introduced. We demonstrate experimental data of reproducing low- and high-order aberrations typical for human eye with RMS error about 5% and discuss possibility to reproduce their time-tracings.
All extended optical systems with aberrations suffer from anisoplanatism effect. In this presentation we investigate anisoplanatism in human eye. For that purpose we use a reference source (beacon) obtained by focusing of a dim laser beam on the retina and consider increasing the retina resolution within anisoplanatic angle by means of ideal wavefront corrector and a real bimorph flexible one. The numerical simulations of isoplanatic patch size of human retina were made for different beacon positions and based on the aberrations measured by means of custom wavefront-guided aberrometer. We found out that in particular human eye the existence of optimal correction directions is possible. As the behavior of Zernike coefficients varies from subject to subject the existence of optimal correction angle is a feature of a particular eye. We also estimated the contribution of low-order and high-order aberrations in anisoplanatism effect for the subjects we measured. We found out that aberrations with strongly variable amplitude across the visual field have effect on the isoplanatic patch size most. In this paper we illustrated the isoplanatic patch enlargement with variation of beacon position by presenting two-dimensional retina and test object images. Also anisoplanatism in two-layer human eye model has been discussed. As the main part of the eye's aberrations is induced by the surfaces of the cornea and the crystal lens, our model consists of two thin phase screens that correspond to the cornea and the lens. Then we used such two-layer model to minimize residual mean-square error of correction by means of just one applied corrector.
In this paper a new algorithm of bimorph deformable mirror the best-suited electrodes shape and position determination is suggested. This algorithm is based on solving an inverse problem of defining the best electrodes position from the required phase distribution formation. The first part of the algorithm is an approximate determination of mirror electrodes position, which is based on linear dependence of electrical field in piezoceramics from laplasian of corresponding mirror deformation. Exact locating of the electrodes is the second part of the algorithm and is performed during iterative procedure. During the procedure relative root mean square deviation of computed mirror profile from the demanded one is minimized. To calculate mirror deformation on every iteration step we use a specially developed finite element model of the bimorph mirror. By using the developed algorithm, we demonstrate possibility to increase quality of reproducing various phase profiles, for example those, corresponding to human eye aberrations and even to form vortex beam.
In this paper we implement a new technique of intracavity bimorph flexible mirror control, that allows to manipulate laser beam parameters (increase power, decrease divergence) and to form a given intensity profile at any distance including a far-field. Intracavity mirror surface profile is controlled by number of voltages calculated by means of genetic algorithm combined with hill-climbing one. Then the traditional Fox-Li approach is applied. We have numerically shown the possibility of successful formation of super Gaussian beam in near field, ring-like beam in far-field, and the possibility of significant power increase of TEM00 mode and far-field peak intensity enlargement.
We discuss the new type of the closed loop adaptive optical system with bimorph corrector and M2 meter. The study of some multi-dither algorithms to be used in the system is presented. Multi-dither approach is applied to 40-TW TiS fs laser in JAERI, Japan, to improve the focusability of laser beam. We demonstrate that it is possible to obtain 75% of input power in first diffraction maximum with use both phase conjugate and multi-dither adaptive optical systems.
The areas of adaptive optics application have increasingly expanded beyond astronomy over past ten years. One of the most striking examples is visual science. Fundus camera equipped with adaptive optics has been extensively investigated over past few years and employed with great success in obtaining fine images of the human retina in real time. But even if the aberrations of the human eye are corrected with adaptive optics the quality of retinal images is still degraded by anisoplanatism effect. We can obtain high-resolution image only if decorellation of the phase that is incident from the beacon on the retina and the point being imaged is small. The wavefront compensation is effective only within a finite area - the isoplanatic patch. On the basis of Zernike decompositions of the aberrated wavefront for different retinal angles we have been able to calculate the residual mean-square error for the corrected wavefront. We estimated the isoplanatic angle in human eye as the angular distance between the two sources where the mean-square error is equal to 1 square rad . Computer simulations illustrating the degrading effects of anisoplanatism on retinal imaging performance of adaptive optics system are presented. In the paper we discuss the limitations of isoplanatic patch enlargement by examining an ideal adaptive corrector that provides compensation of all Zernike modes. We simulated the blur of the retinal image induced by the eye's aberrations and the compensation of these aberrations by the corrector thus illustrating the performance of anisoplanatism-limited adaptive optics systems.
The problem of correct eye aberrations measurement is very important with the rising widespread of a surgical procedure for reducing refractive error in the eye, so called, LASIK (laser-assisted in situ keratomileusis). The double-pass technique commonly used for measuring aberrations of a human eye involves some uncertainties. One of them is loosing the information about odd human eye aberrations. We report about investigations of the applicability limit of the double-pass measurements depending upon the aberrations status introduced by human eye and actual size of the entrance pupil. We evaluate the double-pass effects for various aberrations and different pupil diameters. It is shown that for small pupils the double-pass effects are negligible. The testing and alignment of aberrometer was performed using the schematic eye, developed in our lab. We also introduced a model of human eye based on bimorph flexible mirror. We perform calculations to demonstrate that our schematic eye is capable of reproducing spatial-temporal statistics of aberrations of living eye with normal vision or even myopic or hypermetropic or with high aberrations ones.
The intracavity way of intensity distribution formation is discussed. The examples of a such formation by means of bimorph flexible corrector are shown. The whole structure of adaptive system for the intracavity given intensity formation is considered.
Nowadays it is very important to know such beam parameters as beam diameter, divergence angle, beam propagation factor M2. It is very useful for many laser applications as well during experimentation. Thus we made an appropriate device, which consists of hardware and software. It allows one to measure the main parameters of a laser beam. The algorithm of measurements is based on double and multiple beam diameter measurements. The beam diameter is defined as a second moment of the intensity distribution function of the beam at some cross-section. The measurements and calculations are made according to the International Standard 1501 1 146 'Test methods for laser beam parameters: Beam widths, divergence angle and beam propagation factor". The software includes options for evaluation of short-term and long-term power (or intensity) instability. It is also possible to do Gaussian or Flat-top fit to the beam intensity that is used to evaluate how close the beam is to TEM00 mode or to the uniform beam.
The knowledge of such beam parameters as beam diameter, divergence angle, beam propagation factor M2 is very useful for many laser applications. Thus it is necessary to know these parameters of a laser beam while doing some laser experiments or for characterization a laser beam of industrial lasers. We developed and constructed a low-cost M2 -sensor allowing to measure the main parameters of a laser beam. The algorithm of the measurements is based on double and multiple beam diameter measurements. Beam diameter is defined as the second moment of the intensity distribution function of the beam at some cross-section. The software of M2 -sensor includes options for evaluation of short-term and long-term laser power stability. It is also possible to do Gaussian and flat-top fit to the beam intensity that is used to evaluate how close the beam is to TEM00 mode or to uniform beam.
When an adaptive optical system is applied for laser beam control it is very important to know the beam parameters such as beam width, divergence angle, beam quality factor M2, etc., before and after correction. That is why the sensor making such estimations should be included in any laser adaptive optical system. This paper describes the sensor design, possibilities, the principle of measurements, and its place in the whole adaptive optical system.
When adaptive optical system is applied for laser beam control it is very important to know the beam parameters such as beam width, divergence angle, beam quality factor M2 etc. before and after correction. That is why the sensor making such estimations should be included in any laser adaptive optical system. This paper describes the sensor design, possibilities, the principals of measurements and its place in the whole adaptive optical system.
Formation of the given intensity distributions of fundamental mode by means of intracavity controlled mirror is discussed. Such mirror is a water-cooled bimorph flexible one having four controlling electrodes. Analysis has confirmed the possibility to form doughnut-like and super- gaussian intensity distributions at the output of the stable resonators of industrial CW CO2 lasers. Results of experimental formation of the super-gaussian fundamental modes of the 4th and 6th orders by means of the intracavity flexible mirror are presented. The increase of power up to 12% and the enlarging of the peak value of the far-field intensity in 1.6 times in the comparison with the traditional gaussian TEM00 mode of the same resonator are observed.
Diffraction analysis of the formation of low losses, large beam width and high far-field intensity peak value of the given super-gaussian fundamental modes by means of intracavity controlled mirror is presented. Such mirror is a water-cooled bimorph flexible one having four controlling electrodes. Analysis has confirmed the possibility to form various intensity distribution inside laser cavity and at the output of the stable resonators of industrial CW CO2 and YAG:Nd3+ lasers. Distortions of the given intensity distributions caused by thermal deformations of the resonator mirrors is taken into account. It is shown the possibility to compensate partially for such distortions with the help of the intracavity controlled mirror. Experimental formation of the super-gaussian fundamental modes of the 4th and 6th orders of the industrial CW CO2-laser with stable resonator by means of the intracavity flexible mirror is shown. The increase of power of the formed fundamental modes up to 10% and the enlarging of the peak intensity in the far-field zone in 1.6 times in the comparison with the traditional gaussian TEM00 mode of the same resonator are observed.
The diffraction analyses of formation of the given fundamental mode intensity distribution in near-field zone by intracavity adaptive mirrors are discussed. Such mirror was a bimorph flexible one with three concentric rings of controlled electrodes. The calculations were carried out for industrial CW CO2 laser.
Kestrel Corporation has designed and is now building a dual- band infrared Fourier transform ultraspectral imager for aircraft deployment. Designed for installation in a Cessna 206, this instrument will have a 15 degree FOV, with an IFOV of 1.0 mrad. The target spectral resolution is better than 1.5 cm-1 over 2000 to 3000 cm-1 and 0.4 cm-1 over 850 to 1250 cm(superscript -1$. using 512 spectral channels. The device will use a variety of spectral enhancement techniques to achieve this unprecedented spectral resolution. Computer simulations of the optical systems demonstrates sub-wavenumber resolutions and signal to noise ratios of over 900.
The results of reproduction the given phase profile by active bimorph mirror for obtaining super-Gaussian output radiation of CW CO2 laser are reported. The RMS of such approximation - about 1.3%.
The investigation of the possibility to influence the output beam parameters of single-mode lasers by methods of intracavity adaptive optics was carried out. Intracavity adaptive mirrors can compensate static and dynamic aberrations of the resonator optical elements. At the same time such mirrors can allow the spatial configuration of cavity to form with the higher filling of laser medium and lower diffraction losses of the fundamental mode.
A reduction of the divergence of a laser beam by a factor of 2 - 2.5 was achieved in a multimode regime of laser generation using an intracavity controlled mirror. It was shown that various radiation mode structures may be formed at the laser output and in the far-field zone. The correspondence between the shape of deformed flexible mirror and configuration of generated mode has been detected.
A reduction of the divergence of a laser beam by a factor of 2 - 2.5 was achieved in a multimode regime of laser generation using an intracavity controlled mirror. It is shown that various radiation mode structures may be formed at the laser output and in the far-field zone. The correspondence between the shape of a deformed flexible mirror and the configuration of a generated mode has been detected.
In this work an intracavity adaptive system for controlling the radiation of a CW YAG:Nd3+ laser is proposed. Two types of correctors were worked out: a tilt corrector and a bimorph flexible mirror (BFM) .The system permits to reduce by three times laser beam divergence, to decrease by ten times the power instability and to form various output intensity distributions.
Parameters of a laser beam depend on different intracavity distortions. In the majority of cases these distortions act as pure phase ones: fluctuations of refractive index of active medium, thermal mirror deformations etc. This distorts the spatial distribution of the radiation intensity and increase the beam divergence. Placing an electronically controlled mirror into cavity one can reduce such undesirebale effects, influence the geometry of the generated modes and suppress the output power fluctuations.
In this work we used two types of adaptive mirrors: a tilt corrector and a BFM. Our first task was to stabilize output power of the CWYAG.'Nd3+laser both 1,064? and second harmonic (0,53?) radiation. For this purpose COAT feedback with simple tilt corrector was used. The main results were -10 times reduction instability of 1,064? radiation and 15 times - 0,53? radiation. The YAG:Nd3+ laser was employed as an example to show the possible correction of the lower aberrations of a thermal lens by the 17 electrode BFM1. Under the laser pump current variation from 10 to 34 A the fivefold compensation for the thermal lens astigmatism and other aberrations was obtained. For enlarging the laser beam on BFM we proposed a resonator shown on Fig. 1. As expanding lens we used the end of the active
element (AE) with meniscus. Our BFM differed from the one used in Ref. 1 because it had the form of a concave mirror even without any applied voltage to the electrodes. On the Fig. 2 we show the possibility to reduce the laser beam divergence choosing the voltage on BFM electrodes. Output laser beam profile in the multymode regime of generation is shown by curve 1. Curve 2 on Fig. 2 demonstrates the possibility of threefold reduction of laser beam divergence by the intracavity BFM. Also the experimental results of intracavity formation of radiation spatial structure were obtained. Intracavity phase correction made it possible to influence the output near-field and far-field radiation intensity distribution.
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