​✅作者简介热爱科研的Matlab仿真开发者擅长毕业设计辅导、数学建模、数据处理、程序设计科研仿真。完整代码获取 定制创新 论文复现点击Matlab科研工作室 关注我领取海量matlab电子书和数学建模资料个人信条做科研博学之、审问之、慎思之、明辨之、笃行之是为博学慎思明辨笃行。 内容介绍一、引言在光学领域准确模拟高斯光束的传播对于众多应用至关重要如激光加工、光学成像和光通信等。菲涅尔光谱和角光谱方法为高斯光束传播模拟提供了有效的途径而基于角谱传播算法的自聚焦自适应相位屏ASPSAP技术进一步提升了模拟的精度和效率。本文将深入探讨如何利用菲涅尔光谱和角光谱 ASPSAP 来模拟聚焦高斯光束的传播。二、理论基础一高斯光束基础高斯光束是一种在激光光学中广泛应用的光束形式其电场分布在横截面上呈高斯函数形式。对于沿 z 轴传播的基模高斯光束在 z0 平面束腰平面的电场分布为四ASPSAP 技术自聚焦自适应相位屏ASPSAP是一种基于角谱传播算法的技术用于模拟光波在复杂介质或具有聚焦特性的系统中的传播。它通过引入自适应相位屏来模拟介质或光学元件对光波的相位调制。在聚焦高斯光束传播模拟中ASPSAP 可以有效地处理透镜等聚焦元件对光束的作用。通过迭代更新相位屏的相位分布使其能够准确模拟光束在聚焦过程中的波前变化从而提高模拟的精度和效率。⛳️ 运行结果 部分代码function [K, dK] K_dK_ising_PK( lambda, data )% Objective function for minimum probability flow model fitting for Ising% models with additional terms (K-pairwise maximum entropy models)% Original author (version for Ising models): Jascha Sohl-Dickstein (2012)% Web: http://redwood.berkeley.edu/wiki/Jascha_Sohl-Dickstein% Modified by Marcel Nonnenmacher to support extended Ising models% Inputs:% lambda [ J(:),L(:) ]: Concatentation of extended IsingV(K) parameters% data.x: d-by-n matrix, columns are binary data vectors% data.counts sum(data.x,1);% data.mask: d-by-n boolean matrix, gives which of the bit-flipped% data vectors are already present in the raw data.% Outputs:% K: K(lambda), the evaluated objective function of MPF% dK: gradient, first n^2 elements correspond to J, rest to L% Precomputations%------------------------------------------------------------[d, n] size( data.x );J reshape(lambda(1:d^2), d, d);L lambda(end-d:end);% assumes size(L) [d1,1], i.e. also a feature for K 0!!!% Compute objective function%------------------------------------------------------------diagJ diag(J);dxn 2*data.x-1; % in n-th row flips n-th entries of each x% Kfull is a [d, n] matrix containing the contribution to the% objective function from flipping each bit in the rowsk data.counts(ones(d,1),:) 1; % activity counts (1 for indexing)Kfull exp(dxn .* (J*data.x) ...(1/2) * ( -diagJ(:,ones(1,n)) L(k) - L(k-dxn) ) );if isfield(data, doubleMask) % correction if samples differ by one bitKfull Kfull .* data.doubleMask;endK sum(Kfull(:));% Compute derivatives dK/dJ of the standard Ising parameters%------------------------------------------------------------dJ (Kfull.*dxn) * data.x - (1/2)*diag( sum(Kfull, 2) );dJ (dJ dJ)/2;% Compute derivatives dJ/dL of the activity count extension%------------------------------------------------------------indCount logical(full(sparse(1:n,data.counts1,1,n,d1)));indCountMinu1 zeros(n, d1);indCountMinu1(:,2:end) indCount(:,1:end-1); % CouldindCountPlus1 zeros(n, d1); % be madeindCountPlus1(:,1:end-1) indCount(:,2:end); % fasterdL (1/2) * ( sum( Kfull, 1) * indCount ...- sum( data.x .* Kfull, 1) * indCountPlus1 ...- sum( (1-data.x) .* Kfull, 1) * indCountMinu1 );% Assemble output%------------------------------------------------------------K K / n;dK [dJ(:); dL(:)];dK dK / n; 参考文献[1]周胜国,沈学举.扩束准直光学系统中光学元件失调对高斯光束传输变换的影响分析[J].应用光学, 2008, 29(2):5.DOI:10.3969/j.issn.1002-2082.2008.02.020.更多免费数学建模和仿真教程关注领取