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Computational Test bench and Flow Chart for Wavefront Sensors Úrsula V. Abecassis1,2, Davies W. de Lima Monteiro3, Luciana P. Salles3, Rafaela Stanigher3, Euller Borges3 1 Department of Electronics and Telecommunications, Instituto Federal do Amazonas – IFAM, Brazil. 2 Graduate Program in Electrical Engineering PPGEE- Federal University of Minas Gerais - Av. Antônio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil. 3 Department of Electrical Engineering Federal University of Minas Gerais – Av. Antônio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil. ABSTRACT The wavefront reconstruction diagram has come to supply the need in literature of an ampler vision over the many methods and optronic devices used for the reconstruction of wavefronts and to show the existing interactions between those. A computational platform has been developed using the diagram’s orientation for the taking of decision over the best technique and the photo sensible and electronic structures to be implemented. This work will be directed to an ophthalmological application in the development of an instrument of help for the diagnosis of optical aberrations of the human eye. KEY WORDS: Computational test bench, Flow Chart, wavefront sensors and ophthalmology. INTRODUCTION Adaptive Optics is a multidisciplinary topic with a growing number of applications, from ophthalmology to astronomy, each with their respective requirements. There are, to date, many methods, algorithms, components and devices that can be combined in a vast variety of ways for a wavefront-sensor design in Adaptive Optics. There is also an increasing number of didactic books, scientific papers and websites that assist one through the meanders of wavefront sensing, control and actuation. Nevertheless, they often tackle a specific subject or are organized in a sequential structure of general topics, short of displaying in a straightforward fashion how elements can be chosen to work together. Most groups indeed have the knowledge to make suitable decisions, but for a newcomer, the realm of available options is often fuzzy, from device to system level. In this context, we have envisioned a chart that will be useful to aid the visualization of possible choices and how they relate to each other. We will focus on wavefront sensing and propose a method to display the available options, from wavefront generation to error analysis, aiming to assist in decision making and in organizing a Test bench for simulation and optimization of a device or sensing system. This is based on a flow chart branching downwards and laterally, linking together only structurally feasible options. This detector sub-block of an Adaptive Optics system alone features such numerous pathways that we limit ourselves to detail just a few of the possible tracks to Optical Modelling and Design III, edited by Frank Wyrowski, John T. Sheridan, Jani Tervo, Youri Meuret, Proc. of SPIE Vol. 9131, 91312A · © 2014 SPIE CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2051643 Proc. of SPIE Vol. 9131 91312A-1 illustrate how one can couple simulation codes and tools to design a system and preview its performance. The chart is flexible enough to accommodate new developments on devices and codes. As the chart is communally extended to actuation and control, and its branches are cooperatively populated with simulation models, a more complete mapping of possible systems will result. We will present simulation results that include the effect of several components, including the sampling plane, photodetectors and electronic circuitry on wavefront reconstruction. 2. FLOW CHART FOR WAVEFRONT SENSORS The flow chart is a tool that allows a broad and organized overview of the existing techniques and structures in the setting of adaptive optics, which composes the wavefront sensors. Noting that in the complexity of this scenario the organization of the flow chart is a didactic form for presentation. The flow chart for wavefront sensors methodology will be described in general by a block diagram. Each block of the diagram represents a section in the wavefront sensing process, which is in [1]. Figure 2.1 shows the steps in a simplified manner. At the first section, are declared and initialized all functions and global variables, which could be used in the calculations process of the wavefront sensor. The use and choice of the parameters of this section depends on the technology involved in the process. At the second section, happens the generation, detection and visualisation of the wavefront. The visualisation of the input wavefront is fundamental in this step, because is with those datas that the sensor will be able to describe the wavefront that will be reconstructed and treated. The input wavefront may have aberrations from atmospheric disturbances, aberrations of the human eye, or other specific application . Depending on the method chosen, modal [2] or zonal [3] with there are several characteristics techniques for detecting of wavefronts. At sampling plan, the input wavefront can be sampled, for exemple, through Castro lenses [4], optical aperture with Liquid Crystal Display (LCD) [5], or a microlens array [6], which has the function of providing information on the local inclination of the wavefront input. In other words, it is at this stage that will be sampled parts of the wave front entrance in the shape of light spots, regarding the same to the next step. The 4th section, receives through the sampling plan, points of light that can be projected on cameras like Charge-Coupled Devices (CCD) or Complementary Metal-Oxide-Semiconductor (CMOS) [7], or even in the surface of the optical position sensitive detectors (PSDs) [8]. With treatment of light spots captured by the focal plane, is possible to obtain local information from the aberrated wavefront and estimate its topology. The 5th section refers to the reconstruction of the aberrated wavefront through the information from the local deviations of the light spots from the sampling process and from the sensor and processes the data (sections 3 and 4). With this information and knowing the Proc. of SPIE Vol. 9131 91312A-2 distance between the sampling plans and detection, is determined the best representation in terms of Zernike polynomials describing the wavefront measurement. In this step, you can choose how the wavefront will be reconstructed. The wavefront can be reconstructed without or with the use of electronic modules. These modules consist of electronic circuits that actually shape the system in practice. Electronics modules of 5th section refers to optoelectronic models, electronic circuits and conversion of electronic signals. In the last stage of the diagram, 6th section, is calculated the Root Mean Square (RMS) reconstruction error, between the output wavefront (reconstructed), and the input wavefront (original). The reconstruction error will measure the accuracy of the reconstructed wavefront relative to the original one. With those numbers will be possible to analyze and find solutions to minimize noise from the sensor itself or electronic modules involved. i 1- Inicial Parameters 4- Sensor and Data processing 2-Wavefront 3- Sampling Plan 1 5- Wavefront reconstruction 6- Calculation of the Reconstruction error I Figure 2.1 - Block diagram of the wavefront sensor flow chart in a simplified manner. 3. Computational Test bench The flow chart shows an overview of the organizational structure of wavefront sensor. This computational test bench is a software developed to simulate one of the many ways that one could elect to reconstruct wavefronts. This Test bench models a wavefront sensor enabling design it and optimize it to suit various applications. Seeking to evaluate different structures and techniques that make up a wavefront sensor without the necessity of fabricate it, that is, select and analyze structures attached to the sensor or aggregates electronics modules. This tool also help in analyzing the efficiency of a new structure of a wavefront sensor. Proc. of SPIE Vol. 9131 91312A-3 The computational test bench was designed, adapting a code in C language, originally developed in Delft - Netherlands by Gleb Vdovin and Davies W. de Lima Monteiro [9] and modified by Luciana P. Salles [10] and Otávio G. Oliveira [11]. The initial structure of the computational Test bench was constructed using the Hartmann-Shack technique of wavefront sensor. Arrows in the Flow Chart in [1]. indicate the path followed on the test bench. The computational test bench structures will be explained below. Among the parameters that can boot the platform are: the wavelength of operation, the number of terms of Zernike polynomials, the number of microlenses in the microlens array, variables used to initialize the electronic modules when the algorithm requests them. In the phase of generating and detecting the wavefront, the input wavefront (aberrated wavefront) is constructed from prior knowledge of the amplitude of the Zernike coefficients [12] as specific statistics per application, in the case of this work are for ophthalmological applications [13]. The usage of Hartmann-Shack was done due to the fact that it presents a compact configuration that is robust to vibrations, because their components are generally secured together, has low cost, has a quick wavefront reconstruction since it uses relatively simple mathematical models to find the coefficients that describe the topology of a wavefront with modal method [9-11]. Finally, there is the calculus of the reconstruction error (RMS) between the output wavefront ( , ) and the input wavefront ( , ) that is given by: = ∑ ( ( , )− −1 ( , )) ,(3.1) where is the total number of grid points used to coordinates in which, the wavefront ( , ) values are calculated for each point ( , ) function is described. ( , ) and using equations (3.3) and (3.2) respectively. ( , )=∑ ( , )(3.2) ( , )=∑ ( , )(3.3) 4) METHODOLOGY AND SIMULATION RESULTS 4.1 Methodology The conventional aberrations such as defocus, astigmatism, coma and spherical aberration, correlate with a subset of Zernike polynomials, and some of these are of interest for analysis. The unit of measurement of wavefronts used in this work is the micrometer (µm). Wavefronts used in this work are obtained through statistical models of ocular aberrations based on [13]. Where it registered the normal ranges and mean values of the Zernike coefficients for average pupil diameter of 5.7 mm. 109 people participated in the experiment were normal and measures the aberrations of the right and left eyes. These distributions of aberrations were described in 20 Zernike terms, and the terms piston and x and y inclinations were not considered. Proc. of SPIE Vol. 9131 91312A-4 To evaluate the results of simulations of the reconstruction error RMS platform will be chosen three paths of the flow chart, serving as an initial validation for the same. The established pathways can be seen in [1], through the paths indicated by the two arrows of colors pink and red, except for three exceptions in the way indicated by the red arrow, the intensity profile of the spot and the type of position-sensitive detectors (quad-cell)[8]. At first, simulation was used for the spot intensity profile of the circular type and the quad-cell with circular perimeter geometry and sensitivity homogeneous. The parameters and devices used for the simulation results were the same for analyze the effects of the reconstruction error in each selected path on the test bench. The other path is the same path followed by the pink arrow, with the difference of using the response quad-cell without linearization, approaching the data with a sigmoidal function with a known Boltzmann function. The computational test bench has 6 stages: Parameter initial wavefront, sampling plan, sensor and treatment of sensor data, reconstruction of the wavefront and calculation of the reconstruction error. Following will be presented how the test bench was organized for the simulations. All the parameters and values of the test bench simulations were adjusted by observing the ophtalmology requirements, it is mentioned as an example the wavelength of operation and maximum power of the laser incident on the eyeball is approximately 1.78 mW. 1) All the parameters and values of the test bench simulations were adjusted by observing the ophthalmic requirements. 2) The input wavefronts used in this work were the average values of the Zernike coefficients, recorded by Porter [13]. The numbers of the terms of Zernike polynomials used for reconstruction of the wavefront is 20 terms. 3) In the sampling plan were used microlenses static and contiguous. The array of microlenses was the regular square type and a circular sinc2 intensity profile. The simulations were performed with 16, 36, 64 and 100 microlenses. 4) In this step we used the optical sensor position sensitive (PSD) of type quad-cell (QC) with circular perimeter geometry and sensitivity homogeneous. 5) The wavefronts were reconstructed considering with and without electronics modules. Emphasizing that the devices used in electronics module are DIMOS technology models and this system does not include the influence of noise. 6) Evaluating and comparing the reconstruction error (RMS) in the three selected paths in the platform will be adopted the following procedure: a) The first path (arrow pink without linearization) will go through a stage of sampling with reconstruction without electronics modules and step over the position of the optical sensor type QC considering sigmoidal function approximation. b) The second path (pink arrow) traverses the stage of sampling with reconstruction without electronics modules and step over the position of the optical sensor type QC considering a linear function approximation of its response. c) The third path (red arrow with the three exceptions discussed above) traverses the sampling reconstruction with electronic modules and optical position sensor type QC considering a linear function approximation of its response. Proc. of SPIE Vol. 9131 91312A-5 4.2 Simulation Results Analyzing Figure 4.1, the RMS reconstruction error using the electronic modules is much higher compared to reconstructions without them. This proves that there really is a significant difference in physically implementing electronic in a wavefront sensor simulation. One can extract important information about parameters optimization and the behavior of various types of electronic structures without necessarily installing them in an optical or electronic device. Besides, one can also test and verify new structures in order to improve the performance of a specific wavefront, e.g. with human eye’s aberrations. The amplitudes of the average values of the Zernike coefficients of the wavefront vary from 0.0009 μm to 0.2181 μm, being considered low in amplitude compared with the error that suppliers use to ensure good optical structures, which is λ/10 = 0.0634 μm for red laser. For the reconstruction of this wavefront were despised the terms tilt and defocus. The term tilt was discarded because it is not an actual aberration; and the term defocus usually has way too high of an amplitude, and can be optically corrected to prioritize the resolution of other terms. These smaller amplitudes of the Zernike coefficients of the wavefront impact in the quad-cell response. The response of quad-cell depends on the intensity profile and the size of the spot. When a spot type sinc2 travels over the surface of a circular homogeneous quad-cell, the response of quad-cell is a nonlinear behavior. This response of the quad-cell can be approximated by a sigmoidal function [10]. Another approach used in this work is called the linear approximation. This approach is made in a certain range around the center of the quad-cell response curve, aiming also to approximate the response of the QC in relation to the position of the spot on the sensor. With these considerations, when the wavefront aberration is constituted by large amplitudes the spot focus will be at the ends of the QC, and therefore sigmoid approximation will result in a smaller error. However, when the amplitudes are smaller, the spot focus will be closer to the center of the QC, where linear approximation is privileged. That can be observed in Figure 4.1. Another important aspect to be analyzed in Figure 4.1 is that the greater the number of microlenses, the largest the reconstruction error. Simply by the fact that the greater the number of sampling points, the more trustworthy will be the reconstruction. Proc. of SPIE Vol. 9131 91312A-6 á )rter's Coefficientt without tilt and ciefocus for Z =20 V 0 0` `-0 ó- °°- °- óiaqwnN sua\oniW 4o 0 SMANI °N°o`e pazAI2waoN Wa'tla013.2, o aberrations using 20 Zernike terms. t Figure 4.1 - Waveefront for the average vaalues of the ocular Show wing the RMSS error for th he three routes followed d through thee platform and the number of micro olenses used d in the recon nstruction sim mulation. Following, will be shown in Figure 4.2 4 the wavvefront reco onstructed w with and wiithout electronic modulees through paths p stated earlier in Figgure 4.1. Ob bserving Figu ure 4.2, theere may seeem that there is not much m difference between the reference wavefrront and reconstructed one. But in n any waveffront reconsstruction pro ocess, theree is the intro oduction of error, e which h means therre exists what we call a residue bettween the reference and the reconsstructed wavvefronts. That can be seeen in Figuree 4.3 which shows s the reesidual figures. An nalyzing the residuals in Figure 4.3, we w note thatt in the reco onstruction w without electronic modu ules, their amplitudes a a lower when are w compaared to the ones in thee figure witth the recon nstruction with w electron nic modules, confirming again that the t reconstrruction errorr with the use u of electtronics increeases. This kind k of analysis providees more cleearly this tyype of inform mation when compared to the analyysis that can n be done through the reesults from Figure F 4.2. The results presented by the wavefro ont reconstrruction confiirms that th he computing test bench is "workin ng". Getting reconstructted wavefronts so closee to the refeerence wave efront motivvates the en nhancementt this platfo orm for the specific purrpose of evaluating diffferent techn niques and sttructures thaat are part of the contextt of wavefront sensing. Proc. of SPIE Vol. 9131 91312A-7 Slpnoldal Response Robroneo oa loon AIM u,+ ANC 41 0 Linear. Response Linoar. Rosponso wnh Ebctromcs o wo PM en eaw Figure 4.2-Mean values of Porter ocular aberrations reconstructed with 100 microlenses showing the wavefronts: a) reference b) without electronics modules using QC sigmoidal response c) without electronics modules using QC response linearized and d) with electronics modules using QC with linearized response. Uneer. Residual without Electronics Linear. Residual with Electronics 4 MO Figure 4.3 - Residual wavefront between the reference WF and WF reconstructed using QC with linearized response. a) Without electronics module and b) with the electronic module. CONCLUSION The proposed work focuses studies in the area of adaptive optics, more precisely in the wavefront sensor. Here was shown a flow chart and a computational tool which have great applicability in adaptive optics, concentrating on ophthalmologic application , and presented preliminary results in order to explain the whole scenario of a computational test bench that aims to evaluate different techniques and structures of a wavefront sensor. Proc. of SPIE Vol. 9131 91312A-8 Wavefronts were reconstructed using only the program written in C language, and the digital simulation platform (Spice) which allows analysis of the electronic circuit behavior close to real implementation of the circuitry. Modifications were made to improve the performance of the platform. Among which is worth mentioning the automation of the wavefront reconstruction steps. In addition to the modifications made during this step, investigation and improvement of the computational platform must continue, now considering what was exposed in the simulation results. Acknowledgments This work was supported by CAPES National Agency, the national agency for funding the National Council for Scientific Research (CNPq) and the funding agencies of the State Foundation for Research Support of the State of Amazonas (FAPEAM) and Minas Gerais (FAPEMIG) and the Graduate program in Electrical Engineering (PPGEE). References [1] http://www.cpdee.ufmg.br/~optma/ (accessed in 14/12/2013) [2] R. Cubalchini, “Modal wavefront estimation from phase derivative measurements.” J Opt Soc Am, v.69, p. 972-977, 1979. [3] W. H. Southwell, “Wavefront estimation from wavefront slope measurements.”J Opt Soc Am, v.79, p. 998-1006, 1980. [4] L. A. Carvalho, et al., “Quantitative comparison of different-shaped w. sensors and preliminary results for defocus aberrations on a mechanical eye”, Arq Bras Oftalmol, 69(2), p.239-47, 2006. [5] M. F. Guasti, et al., “LCD pixel shape and far-field diffraction patterns”, Elsevier, Optik 116, p.265– 269, 2005. [6] O. G. de Oliveira and D. W. de Lima Monteiro, “Optimization of the hartmann-shack microlens array”. Optics and Lasers in Engineering, 49(4):521– 525, 2011. [7] J. Vaillant, "Wavefront sensor architectures fully embedded in an image sensor," Applied Optics, vol. 46, pp. 7110-7116, 2007. [8] L. P. Salles, O. G. Oliveira, D. W. de Lima Monteiro, “Wavefront Sensor Using Double-efficiency Quad cells for the Measurement of High-order Ocular Aberrations”, 2009. [9] D. W. de Lima Monteiro, “CMOS-based Integrated Wavefront sensor” PhD Thesis, Delft University of Tecnology, Delft, 2002. [10] L. P. Salles, "Sensor óptico de frentes de onda com quadricélula de dupla eficiência quântica em tecnologia CMOS padrão" Doctorate Thesis, Belo Horizonte, 2010. [11] O. G. Oliveira, “Optimized microlens-array geometry for Hartmann-Shack Wavefront Sensor: design, fabrication and test.” Doctorate Thesis, Belo Horizonte, 2012. [12] R. J. Noll, “Zernike polynomials and atmospheric turbulence,”J. Opt. Soc. Am. 66, 207–211 (1976). [13] J. Porter, et al. “Monochromatic aberrations of the human eye in a large population”. Journal of the Optical Society of America, v. 18, n. 8, p. 1793-1803, 2001. Proc. of SPIE Vol. 9131 91312A-9