高斯光束的matlab仿真.docx
高斯光束的matlab仿真教学内容
高斯光束的m a t l a b仿真题目：根据高斯光束数学模型，模拟仿真高斯光束在谐振腔中某一位置处的归一化强度分布并给出其二维、三维强度分布仿真图；用Matlab读取实际激光光斑照片中所记录的强度数据（读取照片中光斑的一个直径所记录的强度数据即可，Matlab读取照片数据命令为imread）,用该数据画出图片中激光光斑的强度二维分布图，与之前数学模型仿真图对比。
（如同时考虑高斯光束光斑有效截面半径和等相位面特点，仿真高斯光束光强、光斑有效截面半径以及等相位面同时随传播距离z的变化并给出整体仿真图可酌情加分。
）原始光斑如图1所示，用imread命令读入matlab后直接用imshow命令读取即可，CCD采集的高斯光束光强分布图1 CCD采集的高斯光束强度分布读入的数据是一个224 X 244的矩阵，矩阵中的数值代表光强分布。
用读入的数据取中间一行（122行）画出强度分布如图2所示。
50100150200020406080100120140160180实验测量高斯曲线图2 实验测量高斯曲线用理论上的高斯曲线公式画出理论高斯曲线如图3所示。
-40-30-20-1001020304000.20.40.60.81理论高斯曲线图3 理论高斯曲线M 文件如下：A=imread('D:\documents\作业\激光原理与应用\高斯.bmp');A1=A(:,122);x1=1:1:224;x2=-100:1:100;a2=exp(-x2.^2/10);figureimshow(A);axis offtitle('\fontsize{12}CCD 采集的高斯光束光强分布');figureplot(x2,a2,'linewidth',1,'color','b');axis([-40 40 0 1.2])title('\fontsize{12}实验测量高斯曲线')figureplot(x1,A1,'linewidth',1,'color','r')title('\fontsize{12}理论高斯曲线')axis([50 200 0 180])画三维强度分布。
基于matlab高斯光束经透射型体光栅后的光束传输特性分析(附源程序)
目录1 基本原理 (1)1.1耦合波理论 (1)1.2高斯光波的基本理论 (9)2 建立模型描述 (10)3仿真结果及分析 (10)3.1角度选择性的模拟 (10)3.2波长选择性的模拟 (13)3.3单色发散光束经透射型布拉格体光栅的特性 (15)3.4多色平面波经透射型布拉格体光栅的特性 (17)4 调试过程及结论 (18)5 心得体会 (20)6 思考题 (20)7 参考文献 (20)8 附录 (21)高斯光束经透射型体光栅后的光束传输特性分析1 基本原理1.1耦合波理论耦合波理论分析方法基于厚全息光栅产生的布拉格衍射光。
当入射波被削弱且产生强衍射效率时，耦合波理论分析方法适用耦合波理论分析方法适用于透射光栅。
1.1.1耦合波理论研究的假设条件及模型耦合波理论研究的假设条件：(1) 单色波入射体布拉格光栅；(2) 入射波以布拉格角度或近布拉格角度入射；(3)入射波垂直偏振与入射平面；(4)在体光栅中只有两个光波：入射光波 R 和衍射光波 S；(5)仅有入射光波 R 和衍射光波 S 遵守布拉格条件，其余的衍射能级违背布拉格条件，可被忽略；(6)其余的衍射能级仅对入射光波 R 和衍射光波 S 的能量交换有微小影响；(7)将耦合波理论限定于厚布拉格光栅中；图1为用于耦合波理论分析的布拉格光栅模型。
z 轴垂直于介质平面，x 轴在介质平面内，平行于介质边界，y 轴垂直于纸面。
边界面垂直于入射面，与介质边界成Φ角。
光栅矢量K垂直于边界平面，其大小为2/=Λ，Λ为光栅周期，θ为入射角。
Kπ图1布拉格光栅模型R —入射波，S —信号波，Φ—光栅的倾斜角，0θ—再现光满足布拉格条件时的入射角（与z 轴所夹的角），K —光栅矢量的大学，d —光栅的厚度，r θ和s θ—再现光波和衍射光波与z 轴所夹的角度，Λ—光栅周期。
光波在光栅中的传播由标量波动方程描述：220E k E ∇+= （1）公式（2）中(),E xz 是y 方向的电磁波的复振幅，假设为与y 无关，其角频率为ω。
(完整word版)MATLAB环境下的正弦信号及高斯白噪声仿真程序说明
MATLAB 环境下的正弦信号及高斯白噪声仿真程序说明一、信号的产生及时域观察1、设定正选信号的频率为10HZ ，抽样频率为100HZ ；2、设定N(0,0.25)高斯白噪声，及噪声功率为0.25W ；3、最后将噪声叠加到正弦信号上，观察其三者时域波形。
二、信号频谱及白噪声功率谱的求解与观察1、对原正弦信号直接进行FFT ，得出其频谱；2、求白噪声的自相关函数，随机序列自相关函数的无偏估计公式为：1^01()()()N m xx n r m x n x n m N m --==+-∑ 01m N ≤≤- ^^()()xx xx r m r m =- 01m N <<-对所求自相关函数进行FFT 变换，求的白噪声的功率谱函数。
源程序：1.产生正弦信号fs=100;fc=10;x=(0:1/fs:2);n=201;y1=sin(2*pi*fc*x); %原正弦信号，频率为10a=0;b=0.5; %均值为a ，方差为b^2subplot(2,2,1);plot(x,y1,'r');title('y=sin(20pi*x)');ylabel('y');xlabel('x/20pi');grid;2.产生高斯白噪声y2=a+b*randn(1,n); %高斯白噪声subplot(2,2,2);plot(x,y2,'r');title('N(0，0.25)的高斯白噪声');ylabel('y');xlabel('x/20pi');grid;3.复合信号y=y1+y2; %加入噪声之后的信号subplot(2,2,3);plot(x,y,'r');title('混合信号');ylabel('y');xlabel('x/20pi');grid;4.复合信号功率谱密度%求复合信号的自相关函数m=50;i=-0.49:1/fs:0.49;for j=1:mR(j)=sum(y(1:n-j-1).*y(j:199),2)/(n-j);%无偏自相关函数的估计Rx(49+j)=R(j);Rx(51-j)=R(j);endFy2=fft(Rx); %傅里叶变换得出复合信号功率谱函数Fy21=fftshift(Fy2); %功率谱校正f=(0:98)*fs/99-fs/2;subplot(2,2,4);plot(f,abs(Fy21),'r');axis([-50 50 -0.5 1]);title('复合信号功率谱函数图');ylabel('F(Rx)');xlabel('w');grid;。
matlab 椭圆高斯光束
matlab 椭圆高斯光束椭圆高斯光束是一种特殊的光束，具有椭圆形状和高斯分布特征。
它在许多领域中都有重要的应用，如光学通信、激光加工和显微镜成像等。
本文将介绍椭圆高斯光束的基本概念、特性以及其在不同领域中的应用。
椭圆高斯光束是一种具有椭圆形状的光束。
它的横向和纵向的光强分布分别由椭圆和高斯函数决定。
椭圆高斯光束的强度分布在横向和纵向上都呈现出高斯分布的特点，中心光强最大，向两侧逐渐减小。
椭圆高斯光束的横向和纵向的光强分布形状由其参数决定，包括椭圆的长轴和短轴长度、高斯函数的束腰半径等。
椭圆高斯光束在光学通信中有着重要的应用。
光纤通信是一种基于光传输的通信技术，而椭圆高斯光束可以在光纤中传输更多的信息量。
传统的圆形高斯光束在光纤中容易发生模式间干涉，导致信号失真。
而椭圆高斯光束的椭圆形状可以减小模式间干涉的影响，提高传输效率和质量。
椭圆高斯光束在激光加工领域也有广泛应用。
激光加工是一种利用激光束对材料进行切割、焊接、打孔等加工过程的技术。
椭圆高斯光束可以根据不同材料和加工要求进行调节，使激光加工过程更加精确和高效。
椭圆高斯光束的横向和纵向的光强分布形状可以控制加工的切割线形和焊接接头的形状，提高加工质量和效率。
在显微镜成像领域，椭圆高斯光束也有重要的应用。
显微镜是一种观察微观物体的仪器，而椭圆高斯光束可以提供更高的分辨率和对比度。
椭圆高斯光束的椭圆形状可以使得显微镜在不同方向上的分辨率更加均匀，提高显微镜成像的效果。
同时，椭圆高斯光束的高斯分布特征可以提供更好的对比度，使得显微镜观察到的图像更清晰和细节更丰富。
除了上述应用领域，椭圆高斯光束在其他领域中也有着广泛的应用。
例如，在光学测量中，椭圆高斯光束可以用于测量物体的形状和尺寸；在光学成像中，椭圆高斯光束可以用于改善图像的分辨率和对比度；在光学传感中，椭圆高斯光束可以用于检测物体的表面形态和材料特性等。
椭圆高斯光束作为一种特殊的光束，在光学领域中有着重要的应用。
MATLAB 高斯光束传播轨迹的模拟
B1：xx光束传播轨迹的模拟设计任务：作图表示xx光束的传播轨迹（1）基模高斯光束在自由空间的传播轨迹；（2）基模高斯光束经单透镜变换前后的传播轨迹；（3）基模高斯光束经调焦望远镜变换前后的传播轨迹。
function vargout = B1(vargin)% B1 M-file forB1.fig%B1, by itself, creates a new B1 or raises the existing%singleton*.%%H = B1 returns the handle to a new B1 or the handle to%the existing singleton*.%%B1('CALLBACK',hObject,eventData,handles,...) calls the local%function named CALLBACK inB1.M with the given input arguments.%%B1('Property','Value',...) creates a new B1 or raises the%existing singleton*.Starting from the left, property value pairs are%applied to the GUI before B1_OpeningFunction gets called.An%unrecognized property name or invalid value makes property applicationGUIDE, GUIDATA, GUIHANDLES% Copyright 2002-2003 The MathWorks, Inc.% Edit the above text to modify the response to help B1% Last Modified by GUIDE v2.5 21-Oct-2010 17:52:32% Begin initialization code - DO NOT EDIT gui_Singleton = 1;gui_State = struct('gui_Name',mfilename, ... 'gui_Singleton',gui_Singleton, ...'gui_Callback',[]);if nargin && ischar(vargin{1})gui_State.gui_Callback = str2func(vargin{1}); endif nargout});else});end% End initialization code - DO NOT EDIT% --- Executes just before B1 is made visible. % hObjecthandle to figure% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA)handles.output = hObject;% Update handles structureguidata(hObject, handles);% UIWAIT makes B1 wait for user response (see UIRESUME)% uiwait(handles.figure1);% vargoutcell array for returning output args (see VARGOUT);% hObjecthandle to figure% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA) vargout{1} = handles.output;% --- Executes on button press in pushbutton1.function pushbutton1_Callback(hObject, eventdata, handles)% hObjecthandle to pushbutton1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA) handles.W0=str2double(get(handles.editW0,'string'));handles.B=str2double(get(handles.editB,'string'));guidata(hObject,handles);Z=-100:100;W=(handles.W0*10^4)*(sqrt(1+handles.B^2*(Z*10^6).^2./(pi^2*(handles.W0*10^4)^4)));plot(Z,W,'b',Z,-W,'b');% --- Executes on button press in pushbutton2.function pushbutton2_Callback(hObject, eventdata, handles)% hObjecthandle to pushbutton2 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA)handles.W0=str2double(get(handles.editW0,'string'));handles.B=str2double(get(handles.editB,'string'))/1000;handles.Z=str2double(get(handles.editZ,'string'))*1000;handles.f=str2double(get(handles.editf,'string'))*10;L=(handles.Z-handles.f)*handles.f^2/((handles.Z-handles.f)^2+pi^2*handles.W0^4/handles.B^2)+handles.f;T1=-handles.Z:1:handles.Z;Y1=handles.W0*sqrt(1+T1.^2*handles.B^2/(pi^2*handles.W0^4));T2=handles.Z:1:(handles.Z+2*L);W1=(handles.W0*handles.f/sqrt((handles.f-handles.Z)^2+pi^2*handles.W0^4/handles.B^2));Y2=W1*sqrt(1+(T2-handles.Z-L).^2/(pi^2*W1^4/handles.B^2));plot(T1,Y1,'b',T1,-Y1,'b',T2,Y2,'r',T2,-Y2,'r');% --- Executes on button press in pushbutton3.function pushbutton3_Callback(hObject, eventdata, handles)% hObjecthandle to pushbutton3 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)handles.W0=str2double(get(handles.editW0,'string'));handles.B=str2double(get(handles.editB,'string'))/1000;handles.f1=str2double(get(handles.editf1,'string'))*10;handles.Z=str2double(get(handles.editZ,'string'))*1000;handles.f2=str2double(get(handles.editf2,'string'))*10;L=(handles.Z-handles.f1)*handles.f1^2/((handles.Z-handles.f1)^2+pi^2*handles.W0^4/handles.B^2)+handles.f1;T1=-handles.Z:1:handles.Z;Y1=handles.W0*sqrt(1+T1.^2*handles.B^2/(pi^2*handles.W0^4));T2=handles.Z:1:(handles.Z+L+handles.f2);W1=(handles.W0*handles.f1./sqrt((handles.f1-handles.Z)^2+pi^2*handles.W0^4./handles.B^2));Y2=W1*sqrt(1+(T2-handles.Z-L).^2./(pi^2*W1^4/handles.B^2));W2=W1*sqrt(1+handles.f2^2/(pi^2*W1^4/handles.B^2));T3=(handles.Z+L+handles.f2):1:3*(handles.Z+L+handles.f2);Y3=W2;plot(T1,Y1,'b',T1,-Y1,'b',T2,Y2,'r',T2,-Y2,'r',T3,Y3,'g',T3,-Y3,'g');grid on;function editW0_Callback(hObject, eventdata, handles)% hObjecthandle to editW0 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editW0 as text%str2double(get(hObject,'String')) returns contents of editW0 as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editW0 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); endfunction editB_Callback(hObject, eventdata, handles)% hObjecthandle to editB (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editB as text%str2double(get(hObject,'String')) returns contents of editB as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editB (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));endfunction editZ_Callback(hObject, eventdata, handles)% hObjecthandle to editZ (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editZ as text%str2double(get(hObject,'String')) returns contents of editZ as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editZ (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); endfunction editf_Callback(hObject, eventdata, handles)% hObjecthandle to editf (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editf as text%str2double(get(hObject,'String')) returns contents of editf as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editf (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); endfunction editf1_Callback(hObject, eventdata, handles)% hObjecthandle to editf1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editf1 as text%str2double(get(hObject,'String')) returns contents of editf1 as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editf1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); endfunction editf2_Callback(hObject, eventdata, handles)% hObjecthandle to editf2 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editf2 as text%str2double(get(hObject,'String')) returns contents of editf2 as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editf2 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); end% --- Executes on mouse press over axes background.% hObjecthandle to axes1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% --- Executes on button press in pushbutton4.function pushbutton4_Callback(hObject, eventdata, handles)close(gcf)% hObjecthandle to pushbutton4 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% --- Executes on key press over pushbutton4 with no controls selected. % hObjecthandle to pushbutton4 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)。
高斯光束方孔衍射计算机仿真实验
目录摘要 (I)Abstract (II)1 绪论 (1)2 高斯光束的特性 (2)2.1 基模高斯光束 (2)2.2 基模高斯光束在空间的传输规律 (3)2.3 高斯光束的参数 (4)2.4 方孔衍射的实验装置 (5)2.5 方孔衍射场及其光强分布 (5)2.6 方孔衍射的特征 (6)3 特殊的高斯的光束方孔衍射 (8)3.1 高斯光束通过后宽孔径条件下的传播特性 (8)3.2 高斯光束通过单缝衍射后的光强分布 (8)3.3 高斯光束通过方孔衍射后的光强分布 (9)4 高斯光束方孔衍射计算机仿真实验 (11)4.1 方孔衍射实验的设计与MATLAB模拟仿真 (11)4.2 方孔衍射的实验 (11)4.2.1 参数的设定 (11)4.2.2 程序的编写和调试 (12)4.3 实验模拟结果分析 (12)5 高斯光束的质量因子 (14)5.1 基模高斯光束的质量因子 (14)5.2 非傍轴标量的高斯光束的质量因子 (15)6 结束语 (19)致谢 (20)参考文献 (21)附录 (22)摘要激光的应用已经遍及科技，经济，军事和社会发展的许多领域，40余年来激光科学技术以其强大的生命力谱写了一部经典的科学交叉的创造发明史，他生动的体现了人的知识和技术创新活动是如何推动社会的发展从而造福人类的物质与精神生活的。
展望未来，激光在科学发展与技术应用两方面都还有巨大的机遇，挑战和创新的空间。
作为激光应用技术中的重要部分光的衍射特性一直是人们研究与探讨的对象，而本文所要讨论的就是衍射中最常见的一种高斯光束的矩孔衍射的效应问题。
我们将对高斯光束的特性与孔径衍射原理的理论作分析与研究，再设计实验参数与程序通过在MATLAB的模拟与仿真中多次的改变参数的数值来分析孔径的大小与光波的波长对孔径衍射后的场强分布及衍射的图案的影响。
最后结合理论与实际掌握高斯光束的方孔衍射效应遵循的基本原理完成本次的设计。
关键词：激光；高斯光束；方孔衍射；MA TLAB仿真AbstractThe application of the laser has already spread over science and technology, economy, many realms of the military and social development, more than 40 year the laser science technique wrote a science of classic to cross by its strong vitality table of the creation invention history, his vivid body now the person's knowledge and technique creative activity is how push a society of the development brings benefit to mankind thus of material and spiritual life of.Prospect future, the laser develops to apply both side with technique to all still have huge opportunity in science, challenging with the creative space.Be the important part light in the laser application technique to shoot characteristic to has been object of people research and study, but this text wants to discuss of be the effect problem that the rectangular aperture diffraction shoots medium most familiar Gauss light beam shoot.We will shoot the theories of the principle to make the analysis and research to the characteristic and bore path of the Gauss light beam, designing again the experiment parameter and procedure to pass after the MATLAB of imitate with imitate really win many numbers of change parameters shoot to the bore path to analytical size of the bore path and the wave-length of the light wave of the field is strong to distribute and the rectangular aperture diffraction shoot of the influence of the pattern .Combine theories finally with controls the rectangular aperture diffractionof the Gauss light beam to shoot physically the effect follow of basic principle completion is time originally of design.Keywords:laser；Gauss light beam；Diffraction in Rectangular Aperture；matlab to imitate1 绪论自从世界上第一台激光器问世至今，激光已涉足于许多科学学科和技术领域，并分化出不少重要的分支学科和交叉学科，激光技术、纤维光学和集成光学，也打开了光计算机的信息传输、存储和处理的时代的大门。
高斯光束及其传播特性的仿真
高斯光束的基本性质
稳态传输的电磁场满足亥姆霍兹方程： (4.1) 容易证明，平面波和球面波都是式 (4.1) 的特解。高斯 光束则不同，它不是式(4.1)的精确解，而是缓变振幅近似 （SVA）下的一个特解。在柱坐标系中设 (4.3) E (r , z ) A(r , z ) exp(ikz) 因此可得到形如
2
(4.15)
( z ) tan1
z 1 z tan 2 ZR w0
(4.16) (4.17)
将式(4.14)带入式(4.3)可将E(r,z)表示为
2 A0 w0 r2 r E (r , z ) exp 2 exp i k z ( z ) w( z ) w ( z) 2 R( z )
X2 (n1 / n2 )Y1 A2 2 X 1 AB ( X 12 Y12 ) B 2
2 1 2 1
( X Y ) BD X1 ( AD BC) AC X2 A2 2 X 1 AB ( X12 Y12 ) B 2
(4.46)
实际工作中最感兴趣的是X1=X2=0，即研究入射与出射高 斯光束束腰间的变换问.28)
用复参数q可将式(4.14)简洁地表示为
ikr 2 iZ R A(r , q ) A0 exp q 2q
(4.29)
这样高斯光束可由复参数q确定。当q已知时，R(z)、 w(z)可按下式求出：
1 1 Re R q
物像比例公式：
wi
(4.61)
(s
fw0 f) Z
2
0
高斯光束的matlab仿真
题目：根据高斯光束数学模型，模拟仿真高斯光束在谐振腔中某一位置处的归一化强度分布并给出其二维、三维强度分布仿真图；用Matlab读取实际激光光斑照片中所记录的强度数据（读取照片中光斑的一个直径所记录的强度数据即可，Matlab读取照片数据命令为imread）,用该数据画出图片中激光光斑的强度二维分布图，与之前数学模型仿真图对比。
（如同时考虑高斯光束光斑有效截面半径和等相位面特点，仿真高斯光束光强、光斑有效截面半径以及等相位面同时随传播距离z的变化并给出整体仿真图可酌情加分。
）原始光斑如图1所示，用imread命令读入matlab后直接用imshow命令读取即可，CCD采集的高斯光束光强分布图1 CCD采集的高斯光束强度分布读入的数据是一个224 X 244的矩阵，矩阵中的数值代表光强分布。
用读入的数据取中间一行（122行）画出强度分布如图2所示。
图2 实验测量高斯曲线用理论上的高斯曲线公式画出理论高斯曲线如图3所示。
图3 理论高斯曲线50100150200020406080100120140160180实验测量高斯曲线-40-30-20-1001020304000.20.40.60.81理论高斯曲线M文件如下：A=imread('D:\documents\作业\激光原理与应用\高斯.bmp');A1=A(:,122);x1=1:1:224;x2=-100:1:100;a2=exp(-x2.^2/10);figureimshow(A);axis offtitle('\fontsize{12}CCD采集的高斯光束光强分布');figureplot(x2,a2,'linewidth',1,'color','b');axis([-40 40 0 1.2])title('\fontsize{12}实验测量高斯曲线')figureplot(x1,A1,'linewidth',1,'color','r')title('\fontsize{12}理论高斯曲线')axis([50 200 0 180])画三维强度分布。
反常高斯漩涡光束matlab实现
反常高斯漩涡光束matlab实现
反常高斯漩涡光束是一种具有特殊相位和振幅分布的光束，它在光学领域有着广泛的应用。
在Matlab中，可以通过以下步骤实现反常高斯漩涡光束的模拟：
1. 定义反常高斯漩涡光束的参数，包括振幅、波长、漩涡阶数、高斯因子等。
2. 构造反常高斯漩涡光束的振幅分布，可以使用公式：
U(r,theta) = A * exp(-(r/w)^2) * exp(-i * l * theta) * exp(-(r/w)^2)^(2p+1)
其中，r和theta分别表示极坐标系下的径向和角向坐标，A为振幅，w为高斯因子，l为漩涡阶数，p为反常高斯漩涡光束的指数。
3. 根据振幅分布和波长计算相位分布，可以使用公式：
phi(r,theta) = k * r^2 / (2 * f) + l * theta
其中，k为波数，f为焦距。
4. 将振幅分布和相位分布组合起来，得到反常高斯漩涡光束的复振幅分布。
5. 可以使用Matlab的图形绘制函数，如surf、mesh等，将光束的复振幅分布可视化。
需要注意的是，反常高斯漩涡光束的实现过程比较复杂，需要对Matlab的数学计算和图形绘制函数有一定的掌握。
同时，需要根据具体应用场景和实验条件调整光束的参数，以达到最佳的实验效果。
高斯光谱 matlab
高斯光谱 matlab
在Matlab中，可以使用以下函数生成高斯函数的光谱：
```matlab
function y = gaussian_spectrum(x, sigma, mean, amplitude)
y = amplitude * exp(-((x-mean).^2)/(2*sigma^2));
end
```
该函数根据输入的参数生成一个高斯函数的光谱。
其中，参数`x`表示自变量的取值，`sigma`表示高斯函数的标准差，
`mean`表示高斯函数的均值，`amplitude`表示高斯函数的振幅。
下面是一个使用该函数生成高斯光谱的示例：
```matlab
% 定义自变量的取值范围
x = -10:0.1:10;
% 生成高斯光谱
sigma = 1; % 标准差
mean = 0; % 均值
amplitude = 1; % 振幅
y = gaussian_spectrum(x, sigma, mean, amplitude);
% 绘制高斯光谱
plot(x, y);
xlabel('x');
ylabel('Spectrum');
title('Gaussian Spectrum');
```
运行这段代码将会得到一个绘制了高斯光谱的图形。
可以通过调整`sigma`、`mean`和`amplitude`的值来控制高斯光谱的形状和大小。
高斯过程的matlab程序实现
高斯过程的matlab程序实现高斯过程作为一种强大的建模工具，广泛应用于各种领域，如机器学习、统计学、信号处理等。
Matlab作为一种功能强大的编程语言和计算软件，在高斯过程的实现方面提供了很好的支持。
本文将介绍高斯过程的基本理论和Matlab程序实现，以帮助读者了解和应用这一工具。
一、高斯过程基本理论高斯过程（Gaussian Process，简称GP）是一种用于处理连续随机变量的方法，它是一组无限个随机变量的集合，任意一组随机变量的联合分布都是高斯分布，且每个随机变量是对其他随机变量的线性组合。
也就是说，高斯过程可以看作是高斯分布的一个推广，它不再是单个随机变量的分布，而是一组随机变量的联合概率分布。
高斯过程的定义如下：设X是定义在D上的高斯过程，当对于任意的n个点$x_1,x_2,...,x_n$，其联合分布$(X(x_1),X(x_2),...,X(x_n))$服从高斯分布，且其均值向量为0，协方差矩阵为$K(x_i,x_j)$ ，即：$$\begin{bmatrix}X(x_1)\\X(x_2)\\\vdots\\X(x_n)\end{bmatrix} \sim\mathbb{N}\left(\begin{bmatrix}0\\0\\\vdots\\0\end{bmatrix}, \begin{bmatrix}K(x_1,x_1) &K(x_1,x_2) & \cdots & K(x_1,x_n)\\ K(x_2,x_1) &K(x_2,x_2) & \cdots & K(x_2,x_n)\\ \vdots & \vdots & \ddots & \vdots\\ K(x_n,x_1) & K(x_n,x_2) &\cdots & K(x_n,x_n)\end{bmatrix}\right)$$其中，协方差函数$K(x_i,x_j)$的选择是高斯过程的核心，直接影响着高斯过程的性质和应用效果。
高斯光束的matlab仿真设计
题目：根据高斯光束数学模型，模拟仿真高斯光束在谐振腔中某一位置处的归一化强度分布并给出其二维、三维强度分布仿真图；用Matlab读取实际激光光斑照片中所记录的强度数据（读取照片中光斑的一个直径所记录的强度数据即可，Matlab读取照片数据命令为imread）,用该数据画出图片中激光光斑的强度二维分布图，与之前数学模型仿真图对比。
（如同时考虑高斯光束光斑有效截面半径和等相位面特点，仿真高斯光束光强、光斑有效截面半径以及等相位面同时随传播距离z的变化并给出整体仿真图可酌情加分。
）原始光斑如图1所示，用imread命令读入matlab后直接用imshow命令读取即可，CCD采集的高斯光束光强分布图1 CCD采集的高斯光束强度分布读入的数据是一个224 X 244的矩阵，矩阵中的数值代表光强分布。
用读入的数据取中间一行（122行）画出强度分布如图2所示。
50100150200020406080100120140160180实验测量高斯曲线图2 实验测量高斯曲线用理论上的高斯曲线公式画出理论高斯曲线如图3所示。
-40-30-20-1001020304000.20.40.60.81理论高斯曲线图3 理论高斯曲线M文件如下：A=imread('D:\documents\作业\激光原理与应用\高斯.bmp');A1=A(:,122);x1=1:1:224;x2=-100:1:100;a2=exp(-x2.^2/10);figureimshow(A);axis offtitle('\fontsize{12}CCD采集的高斯光束光强分布');figureplot(x2,a2,'linewidth',1,'color','b');axis([-40 40 0 1.2])title('\fontsize{12}实验测量高斯曲线')figureplot(x1,A1,'linewidth',1,'color','r')title('\fontsize{12}理论高斯曲线')axis([50 200 0 180])画三维强度分布。
MATLAB高斯光束传播轨迹的模拟
B1：xx 光束传播轨迹的模拟设计任务：作图表示xx 光束的传播轨迹( 1)基模高斯光束在自由空间的传播轨迹；( 2)基模高斯光束经单透镜变换前后的传播轨迹；( 3)基模高斯光束经调焦望远镜变换前后的传播轨迹。
function vargout = B1(vargin)% B1 M-file forB1.fig%B1, by itself, creates a new B1 or raises the existing%singleton*.%%H = B1 returns the handle to a new B1 or the handle to%the existing singleton*.%%B1('CALLBACK',hObject,eventData,handles,...) calls the local%function named CALLBACK inB1.M with the given input arguments.%%B1('Property','Value',...) creates a new B1 or raises the%existing singleton*.Starting from the left, property value pairs are%applied to the GUI before B1_OpeningFunction gets called.An%unrecognized property name or invalid value makes property applicationGUIDE, GUIDATA, GUIHANDLES% Copyright 2002-2003 The MathWorks, Inc.% Edit the above text to modify the response to help B1% Last Modified by GUIDE v2.5 21-Oct-2010 17:52:32% Begin initialization code - DO NOT EDIT gui_Singleton = 1;gui_State = struct('gui_Name',mfilename, ... 'gui_Singleton',gui_Singleton, ...'gui_Callback',[]);if nargin && ischar(vargin{1})gui_State.gui_Callback = str2func(vargin{1}); endif nargout});else});end% End initialization code - DO NOT EDIT% --- Executes just before B1 is made visible.% hObjecthandle to figure% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA)handles.output = hObject;% Update handles structure guidata(hObject, handles);% UIWAIT makes B1 wait for user response (see UIRESUME)% uiwait(handles.figure1);% vargoutcell array for returning output args (see VARGOUT);% hObjecthandle to figure% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA) vargout{1} = handles.output;% --- Executes on button press in pushbutton1.function pushbutton1_Callback(hObject, eventdata, handles)% hObjecthandle to pushbutton1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA)handles.W0=str2double(get(handles.editW0,'string'));handles.B=str2double(get(handles.editB,'string')); guidata(hObject,handles);Z=-100:100;W=(ha ndles.W0*10八4)*(sqrt(1+ha ndles.B^2*(Z*10八6)八2./(p22*(ha ndles.W0*10八4)八4)));plot(Z,W,'b',Z,-W,'b');% --- Executes on button press in pushbutton2.function pushbutton2_Callback(hObject, eventdata, handles)% hObjecthandle to pushbutton2 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA)handles.W0=str2double(get(handles.editW0,'string'));handles.B=str2double(get(handles.editB,'string'))/1000;handles.Z=str2double(get(handles.editZ,'string'))*1000;handles.f=str2double(get(handles.editf,'string'))*10;L=(ha ndles.Z-ha ndles.f)*ha ndles"2/((ha ndles.Z-han dles.f)A2+pi A2*ha ndles.WOM/ha ndles.B^2)+ha ndles.f;T1=-handles.Z:1:handles.Z;Y1=handles.W0*sqrt(1+T1.A2*handles.BA2/(piA2*handles.W0A4)); T2=handles.Z:1:(handles.Z+2*L);W1=(handles.W0*handles.f/sqrt((handles.f-han dles.Z)A2+pi A2*ha ndles.WOM/ha ndles.BT)); Y2二W1*sqrt(1+(T2-ha ndles.Z-L).A2/(pi A2*W1A4/ha ndles.BA2));plot(T1,Y1,'b',T1,-Y1,'b',T2,Y2,'r',T2,-Y2,'r');% --- Executes on button press in pushbutton3.function pushbutton3_Callback(hObject, eventdata, handles)% hObjecthandle to pushbutton3 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB % handlesstructure with handles and user data (see GUIDATA)handles.W0=str2double(get(handles.editW0,'string'));handles.B=str2double(get(handles.editB,'string'))/1000;handles.f1=str2double(get(handles.editf1,'string'))*10;handles.Z=str2double(get(handles.editZ,'string'))*1000;handles.f2=str2double(get(handles.editf2,'string'))*10;L=(handles.Z-handles.f1)*handles.f1A2/((handles.Z-handles.f1)A2+piA2*handles.W0A4/handles.BA2)+handles.f1;T1=-handles.Z:1:handles.Z;Y1=handles.W0*sqrt(1+T1.A2*handles.BA2/(piA2*handles.W0A4));T2=handles.Z:1:(handles.Z+L+handles.f2);W1=(handles.W0*handles.f1./sqrt((handles.f1-handles.Z)A2+piA2*handles.W0A4./ha ndles.BT)); Y2二W1*sqrt(1+(T2-ha ndles.Z-L)八2./(pi A2*W1A4/ha ndles.BT));W2=W1*sqrt(1+ha ndles.f2A2/(piA2*W1A4/ha ndles.BA2));T3=(handles.Z+L+handles.f2):1:3*(handles.Z+L+handles.f2);Y3=W2;plot(T1,Y1,'b',T1,-Y1,'b',T2,Y2,'r',T2,-Y2,'r',T3,Y3,'g',T3,-Y3,'g');grid on;function editW0_Callback(hObject, eventdata, handles)% hObjecthandle to editW0 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editW0 as text%str2double(get(hObject,'String')) returns contents of editW0 as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editW0 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); endfunction editB_Callback(hObject, eventdata, handles)% hObjecthandle to editB (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editB as text%str2double(get(hObject,'String')) returns contents of editB as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editB (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));endfunction editZ_Callback(hObject, eventdata, handles)% hObjecthandle to editZ (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editZ as text%str2double(get(hObject,'String')) returns contents of editZ as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editZ (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispcset(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); end function editf_Callback(hObject, eventdata, handles)% hObjecthandle to editf (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editf as text%str2double(get(hObject,'String')) returns contents of editf as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editf (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');else set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); end function editf1_Callback(hObject, eventdata, handles)% hObjecthandle to editf1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editf1 as text %str2double(get(hObject,'String')) returns contents of editf1 as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editf1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white'); elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); end function editf2_Callback(hObject, eventdata, handles)% hObjecthandle to editf2 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% Hints:get(hObject,'String') returns contents of editf2 astext %str2double(get(hObject,'String')) returns contents of editf2 as a double % --- Executes during object creation, after setting all properties.% hObjecthandle to editf2 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% Hint:edit controls usually have a white background on Windows.%See ISPC and COMPUTER.if ispc set(hObject,'BackgroundColor','white');elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor')); end% --- Executes on mouse press over axes background.% hObjecthandle to axes1 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% --- Executes on button press in pushbutton4.function pushbutton4_Callback(hObject, eventdata, handles)close(gcf)% hObjecthandle to pushbutton4 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)% --- Executes on key press over pushbutton4 with no controls selected. % hObjecthandle to pushbutton4 (see GCBO)% eventdatareserved - to be defined in a future version of MATLAB% handlesstructure with handles and user data (see GUIDATA)11 /。
拉盖尔高斯光束 厄米高斯光束MATLAB仿真
激光原理by贾而穑 130212114厄米高斯光束MATLAB仿真其中主程序文件：plotHermiteGaussianBeams.m子程序文件：HermitePoly.m程序如下：plotHermiteGaussianBeams.m%-------------------------------------------------------------------------% % auther：Erse Jia% Student ID 130212114%-------------------------------------------------------------------------% %% Hermite Gaussian Beams%% SET PARAMETERS% Physical parameterslambda = 500; % nmk = 2*pi/lambda;% The two parameters for the gaussian beam (and derived quantities)z0 = 1;A0 = 1;W0 = sqrt(lambda*z0/pi);W = @(z) W0*sqrt(1+(z/z0)^2);R = @(z) z*(1+(z/z0)^2);Zeta = @(z) atan(z/z0);% The coefficients for the Hermite-Gaussian (HG) beam of order (l,m)A = [ 1 0 0 0;1 1 0 0;0 0 0 0;0 0 .2 0];% Display Parametersres = 800;z = 1e-9;x = linspace(-2*W(z),2*W(z),res);y = linspace(-2*W(z),2*W(z),res);[X Y] = meshgrid(x,y);X = X(:);Y = Y(:);%% RUN THE SIMULATION% Preallocate MemoryU = zeros(length(X),1);Utemp = zeros(length(X),1);Utemp2 = zeros(length(X),1);% Calculate Values that are independent of HG Polynomial orderlpf = exp(-1i*k*z - 1i*k*(X.^2 + Y.^2)/(2*R(z))); %lateral phase factoru = sqrt(2)*X/W(z);v = sqrt(2)*Y/W(z);for l = 1:size(A,1)%if there are any terms of this order, calculate the x-HG (so you don't %need to repeat for each value of mif sum(A(l,:) ~= 0) ~= 0Utemp2 = (W0/W(z))*polyval(HermitePoly(l-1),u).*exp(-u.^2/2);elsecontinue;endfor m = 1:size(A,2)if A(l,m) ~= 0Utemp = Utemp2.*(polyval(HermitePoly(m-1),v)).*exp(-v.^2/2);Utemp = A(l,m)*Utemp.*lpf*exp(1i*(l+m+1)*Zeta(z));U = U + Utemp;endendend%% DRAW PLOTSfigure;U = reshape(U,res,res);imagesc(x,y,abs(U).^2);axis square;set(1,'color','w');title('Hermite-Gaussian Beam of Order');xlabel('x (nm)');ylabel('y (nm)');HermitePoly.m%-------------------------------------------------------------------------% % HermitePoly.m by Erse Jia% Student ID 130212114% Given nonnegative integer n, compute the% Hermite polynomial H_n. Return the result as a vector whose mth% element is the coefficient of x^(n+1-m).% polyval(HermitePoly(n),x) evaluates H_n(x).%-------------------------------------------------------------------------%function hk = HermitePoly(n)if n==0hk = 1;elseif n==1hk = [2 0];elsehkm2 = zeros(1,n+1);hkm2(n+1) = 1;hkm1 = zeros(1,n+1);hkm1(n) = 2;for k=2:nhk = zeros(1,n+1);for e=n-k+1:2:nhk(e) = 2*(hkm1(e+1) - (k-1)*hkm2(e));endhk(n+1) = -2*(k-1)*hkm2(n+1);if k<nhkm2 = hkm1;hkm1 = hk;endendend结果：拉盖尔高斯光束MATLAB仿真主程序文件：DrawtheLaguerreGaussbeam.m子程序文件：LG.mDrawtheLaguerreGaussbeam.m%-------------------------------------------------------------------------% % auther：Erse Jia% Student ID 130212114%-------------------------------------------------------------------------% clear all;close all; clcparams = [0 0 1];% Use function handleu0 = @(rho, phi)LG(params, rho, phi);R = @(x, y)(x<0)-(x>=0);u = @(rho, phi)R(rho.*cos(phi), rho.*sin(phi)).*u0(rho, phi);[X, Y] = meshgrid(linspace(-5, 5, 200));Rho = sqrt(X.^2 + Y.^2);Phi = atan(Y./X);figure(1)set(1,'color','w');Z = u(Rho, Phi);surf(X, Y, -Z)shading interpset(gca,'box','on');grid off;xlabel('x position');ylabel('y position');zlabel('z');colorbar;LG.mfunction y = LG( params, rho, phi )m = abs(params(1));p = params(2);w = params(3);if w==0msgbox('params(0) can not be equal to 0');endt = rho./w;y = sqrt(2*factorial(p)/pi/factorial(m+p))/w.* (sqrt(2).*t).^m ....* L([p m], 2*t.^2).* exp(-t.^2 + 1i*m*phi);function y = L(params, x)fact = @(x)arrayfun(@factorial, x);n = params(1); % pk = params(2); % mm = 0:n;a = factorial(n+k)*ones(1,length(m));b = fact(n-m);c = fact(k+m);d = fact(m);e = (-1).^m;y = zeros(size(x));for s = 1:n+1y = y + a(s) ./ b(s) ./ c(s) ./ d(s) .* e(s) .* x.^m(s); endendend结果：。
高斯光束传播及其MATLAB仿真
目录一、高斯光束 (1)1简介： (1)2. 命名 (1)二、高斯定律的传播 (2)1.振幅分布特性 (2)2.等相位面特性 (2)3.高斯光束的瑞利长度 (3)4.高斯光束的远场发散角 (4)三、用MATLAB仿真高斯光束的优势 (4)四、提出高斯光束的问题 (4)五、问题的求解 (5)六、问题的MATLAB程序 (7)1、程序如下： (7)2.最终运行 (10)七、结束语 (17)八、参考文献 (17)九、成绩评定 (18)一、高斯光束1简介：通常情形，激光谐振腔发出的基模辐射场，其横截面的振幅分布遵守高斯函数，故称高斯光束。
2.命名关于光斑大小的查询，其实问的就是光斑的束腰直径或束腰半径。
束腰，是指高斯光绝对平行传输的地方。
半径，是指在高斯光的横截面考察，以最大振幅处为原点，振幅下降到原点处的0.36788倍，也就是1/e倍的地方，由于高斯光关于原点对称，所以1/e的地方形成一个圆，该圆的半径，就是光斑在此横截面的半径；如果取束腰处的横截面来考察，此时的半径，即是束腰半径。
沿着光斑前进，各处的半径的包络线是一个双曲面，该双曲面有渐近线。
高斯光束的传输特性，是在远处沿传播方向成特定角度扩散，该角度即是光束的远场发散角，也就是一对渐近线的夹角，它与波长成正比，与其束腰半径成反比，故而，束腰半径越小，光斑发散越快；束腰半径越大，光斑发散越慢。
我们用感光片可以看到，在近距离时，准直器发出的光在一定范围内近似成平行光，距离稍远，光斑逐渐发散，亮点变弱变大；可是从光纤出来的光，很快就发散；这是因为，准直器的光斑直径大约有400微米，而光纤的光斑直径不到10微米。
同时，对于准直器最大工作距离的定义，往往可理解为该准直器输出光斑的共焦参数，该参数与光斑束腰半径平方成正比，与波长成反比，计算式是：3.1415926*束腰半径*束腰半径/波长。
所以要做成长工作距离（意味着在更长的传输距离里高斯光束仍近似成平行光）的准直器，必然要把光斑做大，透镜相应要加长加粗。