Misaligned Optical Systems Research Articles

Improvement of misalignment tolerance in free-space optical interconnects

In this paper, the use of micro lenses with non-uniform transmittance apertures as an alternative to those with uniform transmittance apertures in optical communication systems is proposed. In particular, we consider the use of micro lenses with tapered Gaussian transmittance profiles to improve the misalignment tolerance in optical interconnects. We study the effects of utilizing Gaussian transmittance profiles on the propagation of light beams and the signal to crosstalk ratio of misaligned optical systems. Moreover, we consider the use of uniform transmittance profiles in optical systems for the sake of comparison. To this end, the crosstalk optical noise is modeled at the plane of the detectors array considering the two scenarios of uniform and Gaussian apertures. This was possible after finding the optical field for both scenarios at the of the detectors array. Numerical results clearly demonstrate the significant improvement in decreasing the crosstalk and increasing the signal to crosstalk ratio in the considered optical systems upon utilizing the Gaussian profiles.

2D calculation of parasitic fields in misaligned multipole electron-optical systems

The effects of geometrical imperfections in electron-optical components are usually evaluated in 3D simulations. These calculations inherently take a long time, require a large amount of memory, and do not directly produce the necessary axial field functions. We present a 2D perturbation method to calculate parasitic fields in misaligned multipole systems. Our method is based on finding an equivalent potential perturbation, similarly to Sturrock’s method, but does not rely on the potential being differentiable. The method is directly applicable to both electrostatic and non-saturated magnetic problems. It does not require any 3D data and it is fully compatible with existing finite element method codes such as EOD. The proposed method produces axial field functions with an accuracy of units to a few tens of percents, depending on the number of unperturbed multipole field components used and the geometry. The results can then be used, for instance, to determine the parasitic imaging aberrations of the misaligned optical system using standard methods, in order to evaluate the effect of mechanical design tolerances.

Alignment algorithm of nonsymmetric off-axis reflective astronomical telescopes based on the modified third-order nodal aberration theory.

For pupil-offset off-axis reflective astronomical telescopes with designed tilts and decenters, owing to the absence of symmetry, axial and lateral misalignments exhibit strong coupling. The astigmatic and coma aberration fields of the misaligned optical systems are not only effected by lateral misalignments but also closely related to axial misalignments. However, the traditional misalignment algorithm based on nodal aberration theory (NAT) usually ignore the effect of axial misalignments on the aberration fields of optical systems when constructing calculation models. As a result, the presence of axial misalignments in pupil-offset off-axis telescopes with designed tilts and decenters will invalidate the traditional NAT-based lateral misalignment algorithm, which makes it difficult to be applied to actual computer-aided alignment experiments. In order to solve this issue, on the framework of modified NAT, third-order astigmatic, third-order coma, and third-order spherical net aberration fields of pupil-offset off-axis systems with designed tilts and decenters induced by axial and lateral misalignments are separated from the total aberration fields, and their inherent relations are analytically expressed. On this basis, in order to construct a solution model that can simultaneously and quantitatively calculate the axial and lateral misalignments, a method is proposed to fit the partial derivative coefficient matrix of misalignments according to field dependence of the net aberrations induced by misalignments. The simulation and actual alignment experiments were performed on a real wide-field off-axis three-mirror telescope using the constructed solution model, which proved the feasibility of the proposed method. Simulation experiments show that for different misalignment conditions generated randomly, both axial and lateral misalignments have achieved convergent solution results. In the actual alignment experiment, the average RMS wavefront errors of the nine field of views is corrected from 1.9 λ to 0.12 λ (λ = 632.8nm) through 3-5 iterations.

失调拼接式光学系统波前及像场统计特性研究

失调拼接式光学系统波前及像场统计特性研究

Numerical Calculation of Misaligned Optical System under Interference Vibration

For the purpose of providing a method to estimate the effect of vibration on ultrasonic combustion engine in laser diagnosis, numerical simulation and experimental technology in this report for misalignment of basic optical system under interference vibration are studied. To provide a method to estimate the effect of vibration on the optical performance of a combustion diagnostic optical system, a numerical calculation method for the misaligned optical system under interference vibration was proposed. With the ANSYS finite element analysis software, the physical model of misaligned optical system under interference vibration was developed and the transient dynamic analysis was inspired by vibration displacement got by sensors .Then dynamic response of the mirror was obtained by transient dynamic analysis. On the basis of the matrix optics, geometrical optics theory and the mechanic vibration theory, the vibration misalignment matrix of mirror was analyzed, and the vibration misalignment model was also built. Meanwhile, the method of simulating calculation of misaligned optical system under interference vibration was inferred. Furthermore, an experiment was carried out to validate the method. The results show that the high precision of the simulation and the relative error of simulation calculation and experimental data can reach at 4.1% and 0.8% in the horizontal and vertical direction. The calculation proves to be highly precise. This research can be used in improving the stability and capability for avoiding vibration of laser diagnostics integrated system in intricacy environment. The numerical method can be used in laser diagnostics application.

Propagation of the finite Olver beams through an apertured misaligned ABCD optical system

In this paper, an analytical propagation expression of Finite Olver Beams passing through a misaligned ABCD optical system is derived using the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions. Some numerical results are presented in the work for reason to illustrate the effect of misalignement on the distribution characteristics of the Finite Olver Beams passing through the misaligned optical system with a rectangular aperture.

Novel theory for propagation of tilted Gaussian beam through aligned optical system

A novel theory for tilted beam propagation is established in this paper. By setting the propagation direction of the tilted beam as the new optical axis, we establish a virtual optical system that is aligned with the new optical axis. Within the first order approximation of the tilt and off-axis, the propagation of the tilted beam is studied in the virtual system instead of the actual system. To achieve more accurate optical field distributions of tilted Gaussian beams, a complete diffraction integral for a misaligned optical system is derived by using the matrix theory with angular momentums. The theory demonstrates that a tilted TEM00 Gaussian beam passing through an aligned optical element transforms into a decentered Gaussian beam along the propagation direction. The deviations between the peak intensity axis of the decentered Gaussian beam and the new optical axis have linear relationships with the misalignments in the virtual system. ZEMAX simulation of a tilted beam through a thick lens exposed to air shows that the errors between the simulation results and theoretical calculations of the position deviations are less than 2‰ when the misalignments εx, εy, εx', εy' are in the range of [−0.5, 0.5] mm and [−0.5, 0.5]°.

Property study of beam generated by Gaussian mirror through the misaligned optical system with aperture

Based on the diffraction theory, the diffraction properties of the beam generated by Gaussian mirror through the misaligned optical system with aperture are studied in detail. Two methods are used for solving the light field of the beam generated by Gaussian mirror through the misaligned optical system. Two analytical expressions derived by two different methods are consistent approximately when the diffraction aperture is very small. The numerical examples show that the diffraction beam will deviate obviously from the beam center when the misalignment line deviation and angle deviation are too large. M2-factor of the beam generated by Gaussian mirror is given by the numerical calculations. Therefore, the results can provide the references for studying the optical properties of the beam generated by Gaussian mirror.

Characteristic study of anomalous vortex beam through a paraxial optical system

Characteristics of an anomalous vortex beam (AVB) through the paraxial optical systems are studied. The analytical formulas for the AVBs through the aligned and misaligned optical systems are derived by using the Collins integral equation. As the numerical examples, the intensity distributions for the AVBs in the free space and the convergent optical system are given. It is shown that the far fields for AVBs will be determined by the main parameters, such as width of beam waist w0, n, m (n is the order of the AVB, m is the topological charge). Furthermore, the analytical formula of M2 factor of AVB is derived by using the second-order moments associated with the intensity distributions. The study results can provide references for the application of AVBs.

Changes in the polarization and coherence of a stochastic electromagnetic vortex beam propagating through a misaligned optical system with aperture

An analytical expression for the elements of the cross-spectral density matrix of a stochastic electromagnetic vortex beam passing through a misaligned optical system with aperture is derived. Some analyses are illustrated by numerical examples relating to changes in the spectral degree of polarization and the spectral degree of coherence for a stochastic electromagnetic vortex beam passing through such an optical system. It was found that the topological charge, the radius of the aperture and the displacement have different influences on the changes in the spectral degree of polarization and the spectral degree of coherence.

Propagation Characteristics of Airy-Gaussian Beams Passing through a Misaligned Optical System with Finite Aperture

Propagation characteristics of finite Airy-Gaussian beams through an apertured misaligned first-order ABCD optical system are studied. In this work, the generalized Huygens-Fresnel diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions are used. The propagation of Airy-Gaussian beam passing through: an unapertured misaligned optical system, an apertured aligned ABCD optical system and an unapertured aligned ABCD optical system are derived here as particular cases of the main finding. Some numerical simulations are performed in the paper.

Propagation of Airy beam passing through the misaligned optical system with hard aperture

By expanding the hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression for the two-dimensional Airy beam passing through an apertured and misaligned paraxial ABCD optical system has been derived. Based on the derived formula, the propagation properties of Airy beam through the misaligned optical system with hard aperture are illustrated numerically. From the numerical results we find that the center of the output beam is deviated from the optical axis and the position of the output beam is affected by the misaligned parameters, and can be controlled by adjusting them. Our results provide an effective and fast way for studying the paraxial propagation of Airy beam through apertured and misaligned paraxial ABCD optical systems.

Design and optimization of the sine condition test for measuring misaligned optical systems

By taking a new look at an old concept, we have shown in our previous work how the Abbe sine condition can be used to measure linearly field-dependent aberrations in order to verify the alignment of optical systems. In this paper, we expand on this method and discuss the design choices involved in implementing the sine condition test (SCTest). Specifically, we discuss the two illumination options for the test: point source with a grating or flat-panel display, and we discuss the tradeoffs of the two approaches. Additionally, experimental results are shown using a flat-panel display to measure linearly field-dependent aberrations. Last, we elaborate on how to implement the SCTest on more complex optical systems, such as a three-mirror anastigmat and a double Gauss imaging lens system.

Propagation of elegant Laguerre Gaussian beam through a misaligned optical system

The analytical formula of elegant Laguerre Gaussian beam (ELGB) through the misaligned optical system is derived by using the diffraction integral equation. Based on the formula, the propagation properties of ELGB are studied in detail, the numerical examples are given to confirm the correctness of our calculated results. It is shown that the parameters (La, θa,φ,z,m) will influence the intensity distributions and beam shapes of ELGB, these results are useful in the application of laser beams.

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

The approximate analytical formula for flattened Gaussian beams through a misaligned optical system with a misaligned annular aperture was derived by the extended Huygens–Fresnel principle. Some numerical simulations are illustrated to the effects on the propagation of flattened Gaussian beams by the misaligned annular aperture. To compare the difference between annular apertured system and circular apertured system, the circular apertured system is also studied. The results show that angle misalignments and lateral displacements of aperture create asymmetrical average intensity distribution at receiving plane z=500. The effects on intensity distribution by angle misalignments of annular aperture were small. In annular aperture case, the smooth of intensity distribution was worse with escalating obscure ratio ɛ in near-field; the side-lobes increased and the central lobe decreased with escalating obscure ratio ɛ in far-field. At receiving plane z=500: for circular aperture, the side-lobes decreased, even to be neglected, with the increasing of truncation parameter δ; for annular aperture, the side-lobes increased with the increasing of truncation parameter δ. In addition, it is found that the aligned thin lens can fix asymmetry of intensity distribution which was caused by the misaligned annular aperture.

Focal shift and focal switch of phase-lock partially coherent flat-topped array beams passing through an aligned and misaligned lens system with aperture

The focal shift and focal switch of phase-lock partially coherent flat-topped (PCFT) array beams passing through a lens system with aperture is studied in detail. It is shown that there is a focal shift for mention beam propagating through aligned optical system and the amount of the focal shift depend on optical system and beam characteristics. In addition, a new phenomenon called focal switch occurs for misaligned optical system, i.e. the focal shift experiences a sudden transition as the aligned optical system turns to misalign one. It is shown that, the necessary conditions for the focal switch to take place are also investigated.

Propagation of Modified Bessel-Gaussian Beams in a Misaligned Optical System

The formalism of generalized diffraction integral for paraxial misaligned optical systems is used to investigate the propagation of the Modified Bessel-Gaussian (MBG) beam through a misaligned thin lens. The properties of the propagation of MBG beam traveling through this misaligned ABCD optical system are discussed. A special case of misaligned circular thin lens is illustrated analytically and numerically. The shape of the MBG beam at the exit of the misaligned optical system is unchanged; however the center of the beam is shifted from the propagation axis in correlated manner with the design parameters of the optical system.

Propagation of Coherent Gaussian Schell-Model Beam Array in a Misaligned Optical System

Based on a generalized Collins formula, the analytical formula for the propagation property of coherent Gaussian Schell-model (GSM) beam array through a misaligned optical system is derived. As numerical examples, the propagation of a coherent GSM beam array in a typical misaligned optical system with a thin lens is evaluated. The influence of different misalignment parameters is calculated and the normalized-intensity distribution is graphically illustrated.

振动干扰下光路失调的数值计算

For the purpose of providing a method to estimate the effect of vibration on the optical performance of a burning diagnosis optical system,a numerical calculation method for the misaligned optical system under interference vibration was proposed.Based on the finite element analysis software ANSYS,the physical model of misaligned optical system under interference vibration was developed and the transient dynamic analysis was inspired by a reflector displacement in the vibration response.Then,the dynamic response of the reflector was obtained by transient dynamic analysis.On the basis of the matrix optics,geometrical optics theory and the mechanic vibration theory,the vibration misalignment matrix of planar reflector was analyzed,and the vibration misalignment model was also built.Meanwhile,the method of simulating calculation of misaligned optical system under interference vibration was inferred.Furthermore,an experiment was carried out to validate the method.The results show the the relative error of simulating calculation and experimental data can reach 4.1% and 0.8% in the horizontal and vertical directions,respectively.

Focal shift and focal switch of partially coherent flat-topped beams passing through an alignment and misalignment lens system with aperture

The focal shift and focal switch of partially coherent flat-topped (PCFT) beams passing through a lens system with an aperture are studied in detail. We have shown that a focal shift is also present for beams propagating through an aligned optical system and the amount of the focal shift depends not only on the radius aperture of the focusing system, but also on the spatial coherence and order of the flat-topped beam of the incident partially coherent light. A new phenomenon called ‘focal switch’ occurs for misaligned optical systems, i.e. the focal shift experiences a sudden transition as the aligned optical system becomes misaligned, and the influence of the spatial coherence, order of flat-topped beam and aperture size reduction, on the focal switch is investigated in detail. Finally, the necessary conditions for the focal switch to take place are investigated.